Post on 24-Mar-2020
Research ArticleCartesian Mesh Linearized Euler Equations Solver forAeroacoustic Problems around Full Aircraft
Yuma Fukushima1 Daisuke Sasaki2 and Kazuhiro Nakahashi3
1 Institute of Fluid Science Tohoku University Sendai 980-8577 Japan2Department of Aeronautics Kanazawa Institute of Technology Nonoichi 921-8501 Japan3Japan Aerospace Exploration Agency Chofu 182-8522 Japan
Correspondence should be addressed to Yuma Fukushima fukushimaedgeifstohokuacjp
Received 30 January 2015 Accepted 26 March 2015
Academic Editor Mohamed Gad-el-Hak
Copyright copy 2015 Yuma Fukushima et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
The linearized Euler equations (LEEs) solver for aeroacoustic problems has been developed on block-structured Cartesian meshto address complex geometry Taking advantage of the benefits of Cartesian mesh we employ high-order schemes for spatialderivatives and for time integration On the other hand the difficulty of accommodating curved wall boundaries is addressedby the immersed boundary method The resulting LEEs solver is robust to complex geometry and numerically efficient in aparallel environmentThe accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensionaltest cases Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed The results showgood agreement with analytical computational and experimental results Finally noise propagation around fuselage-wing-nacelleconfigurations is computed as a practical example The results show that the sound pressure level below the over-the-wing nacelle(OWN) configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of theOWN configuration
1 Introduction
To satisfy the severe requirements of environmentally fri-endly aircraft the applications of significant technologicaladvances to conventional aircraft are needed Presentlysome of the most urgent targets are noise emission andfuel consumption Green aviation which seeks to meet thedemands of the noise regulations of the next generationhas been proposed and intensively studied worldwide [1ndash9]The continual reduction of noise has been steadily advancedfor about 40 years mainly due to improvements in engineperformance [4] Examples of these advances are an increaseof the bypass ratio the use of geared fan machinery andthe improvement of liners and vanes However airport noiseregulations are becoming increasingly stringent Aircraftof the next generation must meet these regulations withsufficient margin for future tougher limits
The noise generated from aircraft is classified into twomain groups airframenoise and engine noise Airframenoiseis mainly turbulent noise generated from high-lift devices
and landing gears Engine noise is the sum of fan andjet noises During takeoff fan and jet noises are dominantbecause the engine is at full throttle On the other handthe airframe and fan noises are dominant during landingUnder both conditions fan noise is one of the dominantfactors of community noise generated fromaircraft To realizea dramatic reduction of engine noise shielding the fannoise from the engine nacelle by the fuselage or wings isone of the reasonable approaches that have been applied[10ndash12] Various unique aircrafts have been proposed andevaluated from this point of view using computational andexperimental approaches To design such unconventionalaircraft it is imperative that noise propagation be reliablyanalyzed to estimate the shielding effect accurately
A common computational approach used to analyzenoise propagation is based on the linearized Euler equations(LEEs) which is one of the accurate methods available forcapturing the propagation of sound [13] LEEs can addressnoise propagation from known noncompact sound sourcesin a nonuniform mean flow field The method can also
Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2015 Article ID 706915 18 pageshttpdxdoiorg1011552015706915
2 International Journal of Aerospace Engineering
address scattering diffraction and reflection by objects LEEsare often solved on body-fitted structured and unstruc-tured meshes [14ndash17] From a practical point of view thesemeshes have some drawbacks in the computation of realisticcomplex geometries Body-fitted structured mesh is fit tothe object and is able to adapt to detailed componentsprecisely however the computational cost of mesh gener-ation around an entire aircraft or more complex geometryis quite high Unstructured mesh is applicable to complexgeometry however it generally achieves low-order accuracyin space In addition high-order unstructuredmethods incurconsiderable computational cost Due to these reasons asimple Cartesian mesh is the focus of the present researchGeneration of Cartesian mesh is based on the simple divisionof the computational domain and thus it can easily accom-modate complex geometries Furthermore a high-orderscheme is easily employed by the extension of stencils Rapidcomputation is achieved owing to the simple computationalstructure of the Cartesian mesh However the main problemassociated with Cartesian mesh is numerical error causedby the staircase wall boundary In this research a block-structured Cartesian mesh method denoted as the building-cube method (BCM) [18ndash22] and the immersed boundarymethod (IBM) are applied to solve the abovementionedproblemUsing the BCM an appropriatemesh resolution canbe locally assigned over the entire computational domainIBM helps to maintain a practical minimum mesh size andto achieve highly accurate wall boundary conditions
The purpose of this research is to develop the LEEs solverto compute noise propagation around complex geometryeasily and robustly To achieve this purpose the BCM isemployed in conjunction with IBM First a one-dimensionalwave propagation problem is evaluated Second acousticscattering around a sphere is computed Third noise prop-agation from the JT15D nacelle is computed and comparedwith results obtained from other sources At last noisepropagation around fuselage-wing-nacelle configurations iscomputed and the noise shielding effect of the over-the-wing nacelle (OWN) configuration is estimated as a realisticcomputation around complex geometry
2 Computational Method
21 Linearized Euler Equations In the Euler equations thephysical quantities 119876 are divided into a mean flow fieldvector 119876
0and fluctuation vector 119876
1015840 By linearization of theEuler equations around 119876
0= 119876 minus 119876
1015840 the time evolutionequations of 119876
1015840 are obtained in (1) These are the LEEs Inthe LEEs the sound source term 119878 is added to incorporatea realistic sound source For computation of the LEEs Sand the mean flow field vector 119876
0are introduced The time
evolution of 1198761015840 is then computed The governing equations
are nondimensionalized by the mean flow density 1205880 speed
of sound c and reference length D
1205971198761015840
120597119905+ 11986010
1205971198761015840
120597119909+ 11986020
1205971198761015840
120597119910+ 11986030
1205971198761015840
120597119911+ 1198601015840
1
1205971198760
120597119909
+ 1198601015840
2
1205971198760
120597119910+ 1198601015840
3
1205971198760
120597119911= 119878
1198761015840
=
[[[[[[[[[
[
1205881015840
1199061015840
1
1199061015840
2
1199061015840
3
1199011015840
]]]]]]]]]
]
1198760
=
[[[[[[[[
[
1205880
11990610
11990620
11990630
1199010
]]]]]]]]
]
1198601198950
=
[[[[[[[[[[[[[[
[
1199061198950
1205751119895
1205880
1205752119895
1205880
1205753119895
1205880
0
0 1199061198950
0 01205751119895
1205880
0 0 1199061198950
01205752119895
1205880
0 0 0 1199061198950
1205753119895
1205880
0 1205741205751119895
1199010
1205741205752119895
1199010
1205741205753119895
1199010
1199061198950
]]]]]]]]]]]]]]
]
1198601015840
119895=
[[[[[[[[[[[[[[[
[
1199061015840
1198951205751119895
1205881015840
1205752119895
1205881015840
1205753119895
1205881015840
0
0 1199061015840
1198950 0 minus120575
1119895
1205881015840
12058820
0 0 1199061015840
1198950 minus120575
2119895
1205881015840
12058820
0 0 0 1199061015840
119895minus1205753119895
1205881015840
12058820
0 1205741205751119895
1199011015840
1205741205752119895
1199011015840
1205741205753119895
1199011015840
1199061015840
119895
]]]]]]]]]]]]]]]
]
(1)
Here 120574 = 14 is the specific heat ratio 120575119894119895is the Kronecker
delta In the computations with mean flow field 1205971198760120597119909
1205971198760120597119910 and 120597119876
0120597119911 are neglected to avoid the instability
waves caused by the shear mean flow field The effect ofneglecting the terms about the gradient of themean flow fieldis discussed in [23]
22 Computational Mesh of the BCM The computationalmesh of BCM is generated by the following procedures intwo dimensions [24] The computational domain is dividedinto an aggregation of square areas (cubic areas in threedimensions) where each area is denoted as a ldquocuberdquo as shownin Figure 1(a) Each cube is then divided by an equispacedCartesianmesh as shown in Figure 1(b) Cells located outsidethe wall boundary are defined as fluid cells On the otherhand cells located inside the wall boundary are defined aswall cells In this method all cubes have the same number ofcells so that the computational effort required for all cubes isessentially equivalent in parallel computation and excellentparallel efficiency is achieved Each cube has three overlapcells as shown by the hatched cells in Figure 1(b) for data
International Journal of Aerospace Engineering 3
Cube
(a) Computational domain and cube boundary (b) Computational cells in a cube (15 times 15 cells 3 overlap cells)
Figure 1 Computational mesh of the building-cube method (BCM) in two dimensions
exchange When a cube is locally refined the cube selectedfor refinement is divided into four cubes (eight cubes in threedimensions) and each cube is subdivided by prescribed cellsAfter the refinement the size of the cube is smoothed so thatthe sizes of adjacent cubes are restricted to the same doubleor half that size The sizes of adjacent cubes are checked forall cubes If the size of an adjacent cube is larger than doublethe size of a focusing cube the adjacent cube is divided intofour cubes (eight cubes in three dimensions) and each cubeis subdivided by prescribed cells
23 Computational Algorithm of the LEEs Solver Figure 2shows the computational algorithm of the LEEs solverAt the beginning mesh information object shape initialconditions and the mean flow field are given The meanflow field is computed by the compressible Euler solver inthis research The details of the compressible Euler solverare provided in [25] The computational scheme of inviscidflux is changed from that of the reference to the simple low-dissipative advection upstream splitting (SLAU) [26] scheme
The spatial derivative of the LEEs solver is computedby the dispersion relation preserving (DRP) scheme [27]Through the use of the overlap cells a fourth-order DRPscheme using seven-point stencils can be implemented overthe entire area of the computational domain Time integra-tion is computed by a six-stage fourth-order Runge-Kuttascheme [28] In the time integral six subiterations constituteone time step In addition artificial selective damping [27] ofthe seven-point stencils is applied at each iteration to elim-inate the nonphysical oscillation The above computationsincluding boundary treatments are parallelized for all cubesusing Open Multi-Processing (OpenMP)
24 Wall Boundary For computation by Cartesian mesh itis important to apply mesh to wall boundaries realistically
because real surfaces have curvature Therefore variousIBMs have been proposed for diverse implementations Inthe present solver an IBM that employs a ghost cell (GC)approach using an image point (IP) [29] is applied Wallcells adjacent to fluid cells are defined as GCs The IP isdefined from the GC in the direction normal to the closestwall boundary as shown in Figure 3(a) In this processsurface stereo lithography (STL) data is used to determinethe intersection point of the normal vector with the wallboundary The physical quantities of the IP are interpolatedby the inverse distance weighting method of (2) using 3 times 3 times
3 = 27 stencils as illustrated in Figure 3(b)
119876IP =
27
sum
119894=1
119908 (119894) times 119876119904
(119894) times mask (119894)
119908 (119894) =ℎ (119894)minus2
sum27
119895=1ℎ (119895)minus2
(2)
Here 119876IP is the physical quantities of the IP 119876119904isthe physical
quantities of stencils 119908 is the weight function based on thedistance ℎ between the IP and stencils and mask is a valuethat reflects whether the stencil is a fluid cell or wall cell Fluidcells have mask = 1 and wall cells have mask = 0
The physical quantities of a GC are computed by thefollowing equations so that the slip condition is satisfied usingthe physical quantities of the IP
VGC = VIP minus (1 + (119889IP119889GC
)) times (VIP sdot n)n
119901GC = 119901IP
120588GC = 120588IP
(3)
Here 119889IP is the distance from the IP to the wall surface 119889GCis the distance from the GC to the wall surface n is the unit
4 International Journal of Aerospace Engineering
Input mesh initial condition and mean flow field
Data exchange at cube boundary
Compute spatial derivative and input
Damping in buffer zone
Output data
Para
llel f
or cu
bes
Subi
tera
tion
Upd
ate t
ime s
tep
Update of Q998400sub(n)
Q998400sub(n)
Fluctuation vector Q998400(n+1)
Fluctuation vector Q998400(n)
120655Q998400120655x 120655Q
998400120655y 120655Q
998400120655z 120655Q0120655x 120655Q0120655y 120655Q0120655z S
Figure 2 Computational algorithm of the linearized Euler equations (LEEs) solver
Fluid cell
Ghost cell
Wall cell
Wall boundary
Image point
(a) Definition of GC and IP
Fluid cell
Ghost cell
Qs(1)
Qs(2)
Qs(3)
Qs(4)
Qs(5)
Qs(6)
Qs(7)
Qs(8)
Qs(9)
QIP
mask(1) = 1
mask(6) = 0
h(1)
(b) Interpolation to IP
Figure 3 The immersed boundary method (IBM) using an image point (IP) based on a ghost cell (GC)
normal vector of the wall surface and VIP 119901IP and 120588IP arethe velocity vector pressure and density at the IP and VGC119901GC and 120588GC are those at the GC respectively In this study119889GC + 119889IP = 175Δ119909 to avoid the instability caused by thewall boundary condition The spatial derivative at the fluidcell adjacent to the GC is conducted using the second-ordercentral difference based on the physical quantities of the GC
25 Cube Boundary At the boundaries between cubes withdifferent sizes the three overlap cells are hanging nodesTherefore data exchange with interpolation is needed In
the solver Lagrange interpolation [30] is employed for dataexchange at the boundary as given by
119876119900
(119909119900 119910119900 119911119900)
= sum
119895119896119897
119876119904
(119909119895 119910119896 119911119897) times 119908119895
(119909119900) times 119908119896
(119910119900) times 119908119897(119911119900)
119908119895
(119909119900) = prod
119894 =119895
(119909119900
minus 119909119894)
(119909119895
minus 119909119894)
International Journal of Aerospace Engineering 5
119908119896
(119910119900) = prod
119894 =119896
(119910119900
minus 119910119894)
(119910119896
minus 119910119894)
119908119897(119911119900) = prod
119894 =119897
(119911119900
minus 119911119894)
(119911119897
minus 119911119894)
(4)
Here 119876119900represents the physical quantities of an overlap
cell 119876119904represents the physical quantities of stencils 119908
119895 119908119896
and 119908119897are computed weight functions based on the distance
between an overlap cell and stencils and 119909119900 119910119900 and 119911
119900are the
coordinates of an overlap cellFigure 4(a) illustrates the stencils used for data exchange
from smaller to larger cubes in two dimensions In this figureblack points are the fluid cells of a larger cube The shadedfluid cells of the larger cube are the overlap cells The whitecircles are stencils of the smaller cube and are used for theinterpolation Interpolation to three overlap cells per one rowis needed The stencils of the overlap cell that is closest to theboundary are 2 times 2 times 2 = 8 points and those of the other twocells are 4 times 4 times 4 = 64 points so that the location of stencils issymmetrical For interpolation from larger to smaller cubesas shown in Figure 4(b) stencils of 3 times 3 times 3 = 27 points areused for four rows in three dimensions which achieves third-order accuracy
26 Outer Boundary In LEEs computation outgoing wavesshould be damped so that the inner sound field is notdisturbed by reflected waves To this end the buffer zoneboundary condition [31] is implemented in the presentsolver To damp the outgoing waves gradually the magnitudeof the damping coefficients varies as a quadratic functionof the coordinates toward the outer boundary Equations(5) provide the damping equation in the buffer zone Thefluctuation vector is damped in each direction individually
1198761015840(119899)119909
= (1 minus 120590 (119909)) times 1198761015840(119899)
1198761015840(119899)119910
= (1 minus 120590 (119910)) times 1198761015840(119899)
1198761015840(119899)119911
= (1 minus 120590 (119911)) times 1198761015840(119899)
120590 (119909) =2
Δ119909
1003816100381610038161003816100381610038161003816100381610038161 minus
119909119887
minus 119871119887119909
119871119887119909
100381610038161003816100381610038161003816100381610038161003816
2
120590 (119910) =2
Δ119910
1003816100381610038161003816100381610038161003816100381610038161003816
1 minus119910119887
minus 119871119887119910
119871119887119910
1003816100381610038161003816100381610038161003816100381610038161003816
2
120590 (119911) =2
Δ119911
1003816100381610038161003816100381610038161003816100381610038161 minus
119911119887
minus 119871119887119911
119871119887119911
100381610038161003816100381610038161003816100381610038161003816
2
(5)
Here 1198761015840(119899) is the fluctuation vector at each iteration and
with respect to each direction 1198761015840(119899)119909 1198761015840(119899)
119910 and 1198761015840(119899)
119911are
the damped fluctuation vectors 120590(119909) 120590(119910) and 120590(119911) are thedamping coefficients in the buffer zone Δ119909 Δ119910 and Δz arethe mesh spaces 119871
119887119909 119871119887119910 and 119871
119887119911are the widths of the
buffer zone and119909119887 119910119887 and 119911
119887are the distances from the inner
end of buffer zone Figure 5 shows the buffer zone (illustratedas the hatched area) and an expanded view of the bottom leftcorner in a two-dimensional case
3 Evaluation of the Order of Accuracy
The order of accuracy of the present computational methodis evaluated by the one-dimensional wave propagation prob-lem The IBM and Lagrange interpolation are employed intheir three-dimensional forms Equations (6) are the one-dimensional wave equationsThe initial pressure distributionis given by
1205971199011015840
120597119905+
1205971199061015840
1
120597119909= 0
1205971199061015840
1
120597119905+
1205971199011015840
120597119909= 0
(6)
1199011015840
(initial) = 05 times exp [minus(ln 2)
2(1199092
+ 1199102
+ 1199112)] (7)
The root mean square error (RMSE) between the analyticalsolution and the computed solution is computed by
RMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161199011015840(computed) minus 1199011015840
(analytical)100381610038161003816100381610038161003816
2
(8)
The RMSE is computed for two meshes Figure 6 illustratesthe computational cubes with and without cube refinementThe size of the computational domain is 16119863 times 4119863 times 4119863The periodic boundary condition is set at the end of the 119909-directional boundaries The RMSE is also computed in thecase where a wall boundary exists When the wall boundaryexists the wave reflects at the end of the 119909-directionalboundaries
The RMSE and the order of accuracy are listed in Table 1The order of accuracy of each mesh is computed using theRMSEof onemesh and that of a coarsermesh Case 1 employsno wall boundary and is conducted without cube refinementTherefore the prescribed order of accuracy is as shown InCase 2 the order of accuracy is slightly reduced becausethe spatial derivative at the fluid cell adjacent to the GCis conducted using the second-order central difference Theorder of accuracy of Case 3 is approximately two becausethe accuracy of the cube boundary is dominated by theinterpolation from a larger to smaller cube Case 4 providesa slightly smaller order of accuracy than that of Case 3because of the existence of the wall boundary These resultsindicate that the general order of accuracy of the presentcomputational method is approximately two
4 Acoustic Scattering around a Sphere
Acoustic scattering around a sphere [32] is computed undervarious mesh conditions in this section The magnitude oferror relative to an analytical solution and the computational
6 International Journal of Aerospace Engineering
Cube boundary
Fluid cellOverlap cellStencil
Stencils (4 times 4)
Stencils (2 times 2)
(a) From a smaller to larger cube
Cube boundary
Fluid cellOverlap cellStencil
Stencils (3 times 3)
(b) From a larger to smaller cube
Figure 4 Stencils used for Lagrange interpolation in two dimensions
Buffer zone
(a) Buffer zone in the computational domain
Lbx
xb
yb
Lby
Buffer zone
(b) Expanded view of the bottom left corner of (a)
Figure 5 Buffer zone boundary condition
time are compared A sphere is located at the origin of a three-dimensional domain The reference length 119863 is the diameterof the sphere A monopole Gaussian sound source 119878 is givenby the following equation as a function of time t
119878 = exp[minus (ln 2) ((119909 minus 4119863)
2+ 1199102
+ 1199112
(02119863)2
)] sin (6120587) 119905 (9)
The influence of three important parameters on the erroris investigated the minimum cell size around the spherepoints per wavelength (PPW) in the computational domainand the size of the buffer zoneTheminimum cell size aroundthe sphere has an effect on the error generated from the wall
boundary A small cell size not only suppresses the errorbut also restricts the time step size and results in greatercomputational time The PPW is an important factor foracoustic simulations because insufficient PPW introducesdissipation and dispersion errors in wave propagation Thesize of the buffer domain is important for setting the outerboundary condition If the width of the buffer zone is shortthe reflected wave is generated at the outer boundary and thereflected wave disturbs the inner sound field
Figure 7 shows computational domains of the CoarseBCM Middle2 and BCM Fine3meshes listed in Table 2Thegray lines indicate the cube boundaries Table 2 summarizesthe mesh information of all the cases used for the parametric
International Journal of Aerospace Engineering 7
y x
z
(a) Cubes without cube refinement
y x
z
(b) Cubes with cube refinement
Figure 6 Computational cubes for the one-dimensional wave propagation problem
8D
16D
8D
8D
y
x
y
z
(a) Coarse
16D
32D
16D
16D
y
x
y
z
(b) BCM Middle2
16D
32D
16D
16D
y
x
y
z
(c) BCM Fine3
Figure 7 Computational domains and cube boundaries for acoustic scattering around a sphere of diameter D
8 International Journal of Aerospace Engineering
Table 1 Root mean square error and the order of accuracy
Wall Cube refinement Number of cells in one cube Root mean square error Order of accuracy
Case 1 Without Without36 times 36 times 36 1063 times 10minus5 mdash48 times 48 times 48 3422 times 10minus6 394172 times 72 times 72 6887 times 10minus7 3954
Case 2 With Without36 times 36 times 36 1269 times 10minus5 mdash48 times 48 times 48 4145 times 10minus6 389072 times 72 times 72 8326 times 10minus7 3959
Case 3 Without With36 times 36 times 36 1200 times 10minus4 mdash48 times 48 times 48 6574 times 10minus5 209372 times 72 times 72 2890 times 10minus5 2027
Case 4 With With36 times 36 times 36 1258 times 10minus4 mdash48 times 48 times 48 7086 times 10minus5 199572 times 72 times 72 3156 times 10minus5 1995
Table 2 Mesh information for acoustic scattering around a sphere of diameter 119863
Minimum cellsize
Number ofcubes Number of cells in one cube PPW Width of buffer zone
[119909 119910 119911]Coarse 00415D 128 48 times 48 times 48 8 1D 1D 1DUniform Middle 00277D 128 72 times 72 times 72 12 1D 1D 1DBCM Middle1 00208D 184 48 times 48 times 48 8 16 1D 1D 1DBCM Middle2 00208D 296 48 times 48 times 48 4 8 16 9D 5D 5DBCM Middle3 00208D 408 48 times 48 times 48 4 8 16 9D 5D 5DUniform Fine 00208D 128 96 times 96 times 96 16 1D 1D 1DBCM Fine1 00104D 240 48 times 48 times 48 8 16 32 1D 1D 1DBCM Fine2 00104D 352 48 times 48 times 48 4 8 16 32 9D 5D 5DBCM Fine3 00104D 464 48 times 48 times 48 4 8 16 32 9D 5D 5D
study Coarse mesh forms the base mesh of the other meshesemployedThe size of the computational domain is 16119863times8119863times
8119863 referring to [33] where 128 cubes of a size 1119863 times 1119863 times 1119863
constitute the domain as shown in Figure 7(a) The numberof cells in one cube is 48 times 48 times 48 and the PPW is eight Inthe Uniform Middle and Uniform Fine meshes the domainsize and the number of cubes are the same as those of theCoarse mesh The number of cells in one cube is 72 times 72times 72 in the Uniform Middle mesh and 96 times 96 times 96 in theUniform Fine mesh thus the PPW is 12 and 16 respectivelyIn the BCM Middle1 mesh the eight cubes in the Coarsemesh surrounding the sphere are subdivided into half sizecubes Similarly the eight cubes surrounding the sphere aresubdivided from the BCM Middle1 mesh in the BCM Fine1mesh The number of cubes is 184 in the BCM Middle1mesh and 240 in the BCM Fine1 mesh and the maximumPPW is 16 and 32 respectively In the BCM Middle2 meshshown in Figure 7(b) and BCM Fine2 meshes the bufferzone is expanded to add 112 cubes to the BCM Middle1 andBCM Fine1 meshes In the BCM Middle3 and BCM Fine3(shown in Figure 7(c)) meshes eight cubes located at 2 le xle 6 minus2 le y le 2 and minus2 le z le 2 and eight cubes located at minus6le x le minus2 minus2 le y le 2 and minus2 le z le 2 are subdivided from theBCM Middle2 and BCM Fine2 meshes to increase the PPWof the computational domain The inner end of the buffer
zone is set at x = [minus7D 7D] y = [minus3D 3D] and z = [minus3D3D] in all meshes to compare the sizes of the buffer zones
Figure 8 shows the instantaneous pressure distributionaround the sphere computed using the Coarse mesh In thisfigure the buffer zone is not drawn Waves generated fromthe sound source are scattered by the sphere and interferencefringes appear The computation is executed in nondimen-sional time 119879 = 15 and a periodic steady state is observedafter119879 = 11 Figure 9 shows the pressure distributionnear theinner end of the buffer zone and the time history of the pres-sure near the sphere for all meshes The pressure distributionis sampled at minus6119863 le 119909 le minus4119863 on the 119909-axisThe time historyof the pressure is sampled at (minus2D 0 0) and 14 le 119879 le 15
In Figures 9(a) and 9(b) the uniform meshes arecompared The pressure distributions do not follow thedecreasing trend of the analytical solution in Figure 9(a)Reflection occurs at the outer boundary because of theinsufficient width of the buffer zone Additionally theUniform Middle and Uniform Fine meshes show a higherpressure amplitude compared with the pressure distributionof the Coarse mesh It is assumed that the sound wave isdamped at the Coarse mesh because of the insufficient PPWThe time histories of the uniform meshes provide loweramplitudes than the analytical solution
International Journal of Aerospace Engineering 9
Table 3 Comparison of errors relative to an analytical solution and respective computational times for the meshes listed in Table 2
Total number ofcells
Normalized root meansquare error []
Normalizedmaximum error []
Computational time[120583sectimestepcell]
Real time [sec](128 CPUs)
Coarse 14155776 1197 2382 008454 302Uniform Middle 47775744 502 1131 008631 1388BCM Middle1 20348928 362 1486 010891 1088BCM Middle2 32735232 307 714 011027 1710BCM Middle3 45121536 289 734 009665 2172Uniform Fine 113246208 357 1093 007329 4240BCM Fine1 26542080 614 2224 008851 2654BCM Fine2 38928384 304 700 008777 3358BCM Fine3 51314688 162 500 009019 4794
Non
dim
ensio
nal p
ress
ure
000E + 000
minus500E minus 005
500E minus 005
minus100E minus 004
100E minus 004
Figure 8 Instantaneous pressure distribution (Coarse mesh) around a sphere of diameter D
In Figures 9(c) and 9(d) the BCM Middle meshes arecompared The BCM Middle2 and BCM Middle3 meshesfollow the analytical solution in Figure 9(c) These mesheshave a buffer zone of width 9D in the 119909 direction andoutgoing waves are damped appropriately However theBCM Middle2 mesh provides a lower amplitude This isowing to the insufficient PPW at the sampling points On theother hand phase error is not observed in the BCM Middle2mesh In Figure 9(d) the amplitude of the pressure convergesto the analytical solution for the BCM Middle2 mesh Onlythe BCM Middle1 mesh provides a lower amplitude Thisamplitude is the same as that of the uniform meshes There-fore it is confirmed that the amplitude of the inner soundfieldis diminished when using a buffer zone of short width
In Figures 9(e) and 9(f) the BCM Fine meshes arecompared The pressure distributions and the time historiesof the BCM Fine meshes exhibit similar tendencies as thoseof the BCM Middle meshes
To compare the magnitude of errors more quantitativelythe root mean square pressure 119875rms of the scattered soundis computed and the normalized RMSE (NRMSE) and thenormalized maximum error (MME) between the analytical
solution and the solutions of each mesh are compared asgiven by
NRMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
2
NME = max1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
(10)
The number of sampling points 119873 are set clockwise ata radius 119903 = 2D from the origin The points (minus2D 00) and (2D 0 0) correspond to 0 deg and 180 deg Theerrors are summarized in Table 3 As shown in the table therefined meshes provide lower errors than the coarser meshand the meshes that utilize a large buffer zone also providelower errors The minimum cell size around the sphere alsoaffects the errors The smallest errors are provided by theBCM Fine3 mesh A comparison of the uniform and BCMmeshes indicates that the BCM Middle3 and BCM Fine3meshes which use cubes of different sizes at the appropriatelocations provide lower errors than Uniform Middle meshes
10 International Journal of Aerospace Engineering
Non
dim
ensio
nal p
ress
ure
AnalyticalCoarse
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
Uniform_MiddleUniform_Fine
minus6 minus55 minus5 minus45 minus4
x coordinate
(a) Pressure distributions of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
100E minus 04
150E minus 04
AnalyticalCoarse
Uniform_MiddleUniform_Fine
500E minus 05
14 142 144 146 148 15Nondimensional time
(b) Time histories of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
minus6 minus55 minus5 minus45 minus4
x coordinate
(c) Pressure distributions of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
14 142 144 146 148 15Nondimensional time
(d) Time histories of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
minus6 minus55 minus5 minus45 minus4
x coordinate
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(e) Pressure distributions of BCM Fine meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
14 142 144 146 148 15Nondimensional time
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(f) Time histories of BCM Fine meshes
Figure 9 Pressure distributions (minus6119863 le 119909 le minus4119863) and time histories at (minus2D 0 0) and (14 le 119879 le 15) around a sphere of diameter 119863 forthe meshes listed in Table 2
International Journal of Aerospace Engineering 11
that utilize a similar number of mesh points Moreover theerrors of the BCM Fine3 mesh are about one-half the errorsof the Uniform Fine mesh which has twice the number ofmesh points as the BCM Fine3 mesh These results indicatethe effectiveness of the BCM arrangement
The computational wall-clock times for a single timestep per cell and the total wall-clock time required toreach a nondimensional time 119879 = 15 are also listed inTable 3 All meshes were computed using 128CPUs of anSGI AltixUV1000 computer Regarding the wall-clock timeper one time step per cell the computational times of theuniformandBCMmeshes are comparableHowever the totalwall-clock times of the BCM meshes are slightly longer thanthose of the uniform meshes The BCM meshes employ alarger number of cubes than the number of CPUs used in theevaluationThemismatch between the numbers of cubes andCPUs can degrade the load balance Computations using anequivalent number of CPUs and cubes are more effective forBCMmeshes
5 Noise Propagation from the JT15D Nacelle
Noise propagation from the JT15D [34] nacelle is computedand the far-field sound pressure level (SPL) is compared withdata derived from experiment and the computational resultsof others The JT15D is a small Pratt and Whitney turbofanenginewith a bellmouth inletThe sound source is introducedvia a discrete frequency spinning mode The spinning modeinput [35] is a typical sound source generated by the fan orrotor-stator intersections in the engine The sound source ofa single spinning mode (119898 119899) is defined by
119878 = [119869119898
(119896119903119903) + 1198881119884119898
(119896119903119903)] cos (119896119905 minus 119896
119886119909 minus 119898120579) (11)
Here 119869119898and119884119898are themth order Bessel functions of the first
and second kind respectively 119896 is the angular frequency 119896119886
is the axial wavenumber 119896119903is the radial wavenumber and 120579
is the phase The 119899th solution 119896119903of the following equation is
determined by the hard-wall boundary condition of the duct
119889 [119869119898
(119903outer119896119903)]
119889119903
119889 [119884119898
(119903inner119896119903)]
119889119903
minus119889 [119869119898
(119903inner119896119903)]
119889119903
119889 [119884119898
(119903outer119896119903)]
119889119903= 0
(12)
Here 119903outer and 119903inner are the bypass duct inner wall radius andthe inner hub radius respectively The axial wave number 119896
119886
is computed from
119896119886
=119896
1 minus 1198722119895
(minus119872119895
plusmnradic
1 minus1198962
119903(1 minus 119872
2
119895)
1198962) (13)
where 119872119895is the Mach number at the fan face The selection
of plus or minus signs in the parentheses is determined bythe propagation direction of the sound wave where plus(+) represents the positive propagation direction along the
axial coordinate and vice versa The constant 1198881satisfies the
following relation
1198881
= minus(119889119889119903) [119869
119898(119903outer119896119903)]
(119889119889119903) [119884119898
(119903outer119896119903)]
= minus(119889119889119903) [119869
119898(119903inner119896119903)]
(119889119889119903) [119884119898
(119903inner119896119903)]
(14)
Parameters are set from experimental data (119898 119899) =
(minus13 0) 119903outer = 02667m and 119903inner = 00998m Thereference length D = 06223mis the length from the fanface to the leading edge of the nacelle The blade passingfrequency (BPF) is set to 3150Hz which is derived fromthe fan rotating speed of 6750 rpm The experiments wereconducted in the static condition and the fan face axial Machnumber is 0175 The present computation is also conductedin the static condition In the present computation the axialflow velocity of the ghost cell at the fan face boundary isdirectly modified to this Mach number The pressure andthe density are the same values as those of the adjacent fluidcells The SPL is measured at a radius of 49D The integrationmethod of Ffowcs-Williams and Hawkings (FW-H) [36] isemployed to estimate the far-field pressure from thenear-fieldpressure
Figure 10 shows the computational domain and Table 4lists the mesh information The computations of the com-pressible Euler solver and the LEEs solver are conductedusing the samemeshThePPW inTable 4 is the PPWreducedby the Doppler effect of the fan face axial Mach number Thecomputational domain is set at minus1119863 le 119909 le 7119863 minus8119863 le 119910 le
8119863 and minus8119863 le 119911 le 8119863The fan face is at 119909 = 05119863The innerend of the buffer zone is set at 119909 = [0 4119863] 119910 = [minus4119863 4119863]and 119911 = [minus4119863 4119863] The FW-H surfaces are located at thecube boundaries between the smallest size cubes and thelarger size cubes
Figure 11 shows theMachnumber distribution around theJT15D nacelle In Figure 11 the acceleration region near theinternal wall of the nacelle lip and the stagnation at the spikeare shown Because the experiments and computations wereconducted under the static condition the mean flow fieldexists only near the nacelle
Figure 12 shows the instantaneous pressure distributionsat the planes defined at 119911 = 0 and 119909 = 17119863 In the figure onlythe distributions of the smallest sized cubes are drawn Thefan noise is diffracted at the inlet of the nacelle and propagatesalong the radial direction The 13 peaks and valleys of theswirling fan noise at the 119909 = 17119863 plane are clearly capturedwhich is equivalent to the number of spinning modes Thetime history of the pressure is sampled at the establishedpoints on the FW-H surface and the periodic steady state isobserved after 119879 = 8
Figure 13 shows a comparison of the predicted SPL withthe experimental results conducted by Heidmann et al [37]and the computational results computed by Lan et al [34]The horizontal axis in the figure is the angle from the +119909-axialdirection In the figure the predicted SPL using the presentsolver shows good agreement with the computational resultof Lan et al (within 1 dB) Compared with the experimental
12 International Journal of Aerospace Engineering
Table 4 Mesh information for the JT15D nacelle
JT15D Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWCase 1 00166D 1544 30 times 30 times 30 41688000 87Case 2 00125D 1544 40 times 40 times 40 98816000 116
16D
8D
16D
16D
y
x
yzy
x z
Figure 10 Computational domain for the JT15D nacelle
Mac
h nu
mbe
r
02000100
0000
Figure 11 Mach number distribution around the JT15D nacelle
data a difference of about 3 dB is found at 60 deg Howeverthis discrepancy is also shown between the experimental dataand the result of Lan et al The SPL peak obtained near55 deg is equivalent to that obtained by Lan et al and thatobtained experimentally
6 Noise Propagation arounda Fuselage-Wing-Nacelle Configuration
The noise propagation around a fuselage-wing-nacelle con-figuration is computed as a realistic exampleThe focus of theexample was that of the OWN configuration [38] where theengine nacelle is mounted over the main wing which servesas one of the configurations designed to achieve substantialairport noise reduction The main feature of this configu-ration is that the main wing serves as a shield between the
ground and the noise generated by the engine To investigatethe effect of the OWN configuration the propagation of fannoise of both the conventional DLR-F6 aircraft configuration[39] and the OWN configuration is computed and the SPLbelow the aircraft for both configurations is comparedTheseconfigurations have complex geometry with large curvaturesnear the wing-body and the nacelle-pylon junctions In theOWN configuration the nacelle is moved 11D in the +119909
direction and 06D in the +y direction relative to its locationin the DLR-F6 configuration Here the reference length 119863 =
49m is the longitudinal length of the nacelle The cross-sectional geometry of the pylon is used without any changesand has a sweepback angle of 40 deg A mean flow fieldof Mach number 03 with zero angle of attack is computedusing the compressible Euler solver The sound source isintroduced via a discrete frequency spinning mode As anexample of a modern turbofan engine the CFM56-7B engineis considered The bypass ratio is 55 the fan diameter is154m the number of blades is 24 the maximum rotationalrate is 5382 rpm and the fundamental BPF is 21528HzTheBPF is used as the input frequency of the spinning modeThespinning mode (119898 119899) is set to (minus24 0) The SPL is measuredat a radius of 10D using the FW-H method
Figure 14 shows the computational domain of each con-figuration The black dot shows the origin of coordinatesystem The computations of the compressible Euler andLEEs solvers are conducted using an equivalent mesh Thesize of the computational domains is 4119863 times 2119863 times 2119863 Thesymmetric boundary condition is set at the minusz boundaryThe computational domains are set to ensure that sufficientcomputational domains surround the nacelle It is assumedthat the geometry out of the computational domain has littleinfluence on the noise directivity below the aircraft The
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
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International Journal of
2 International Journal of Aerospace Engineering
address scattering diffraction and reflection by objects LEEsare often solved on body-fitted structured and unstruc-tured meshes [14ndash17] From a practical point of view thesemeshes have some drawbacks in the computation of realisticcomplex geometries Body-fitted structured mesh is fit tothe object and is able to adapt to detailed componentsprecisely however the computational cost of mesh gener-ation around an entire aircraft or more complex geometryis quite high Unstructured mesh is applicable to complexgeometry however it generally achieves low-order accuracyin space In addition high-order unstructuredmethods incurconsiderable computational cost Due to these reasons asimple Cartesian mesh is the focus of the present researchGeneration of Cartesian mesh is based on the simple divisionof the computational domain and thus it can easily accom-modate complex geometries Furthermore a high-orderscheme is easily employed by the extension of stencils Rapidcomputation is achieved owing to the simple computationalstructure of the Cartesian mesh However the main problemassociated with Cartesian mesh is numerical error causedby the staircase wall boundary In this research a block-structured Cartesian mesh method denoted as the building-cube method (BCM) [18ndash22] and the immersed boundarymethod (IBM) are applied to solve the abovementionedproblemUsing the BCM an appropriatemesh resolution canbe locally assigned over the entire computational domainIBM helps to maintain a practical minimum mesh size andto achieve highly accurate wall boundary conditions
The purpose of this research is to develop the LEEs solverto compute noise propagation around complex geometryeasily and robustly To achieve this purpose the BCM isemployed in conjunction with IBM First a one-dimensionalwave propagation problem is evaluated Second acousticscattering around a sphere is computed Third noise prop-agation from the JT15D nacelle is computed and comparedwith results obtained from other sources At last noisepropagation around fuselage-wing-nacelle configurations iscomputed and the noise shielding effect of the over-the-wing nacelle (OWN) configuration is estimated as a realisticcomputation around complex geometry
2 Computational Method
21 Linearized Euler Equations In the Euler equations thephysical quantities 119876 are divided into a mean flow fieldvector 119876
0and fluctuation vector 119876
1015840 By linearization of theEuler equations around 119876
0= 119876 minus 119876
1015840 the time evolutionequations of 119876
1015840 are obtained in (1) These are the LEEs Inthe LEEs the sound source term 119878 is added to incorporatea realistic sound source For computation of the LEEs Sand the mean flow field vector 119876
0are introduced The time
evolution of 1198761015840 is then computed The governing equations
are nondimensionalized by the mean flow density 1205880 speed
of sound c and reference length D
1205971198761015840
120597119905+ 11986010
1205971198761015840
120597119909+ 11986020
1205971198761015840
120597119910+ 11986030
1205971198761015840
120597119911+ 1198601015840
1
1205971198760
120597119909
+ 1198601015840
2
1205971198760
120597119910+ 1198601015840
3
1205971198760
120597119911= 119878
1198761015840
=
[[[[[[[[[
[
1205881015840
1199061015840
1
1199061015840
2
1199061015840
3
1199011015840
]]]]]]]]]
]
1198760
=
[[[[[[[[
[
1205880
11990610
11990620
11990630
1199010
]]]]]]]]
]
1198601198950
=
[[[[[[[[[[[[[[
[
1199061198950
1205751119895
1205880
1205752119895
1205880
1205753119895
1205880
0
0 1199061198950
0 01205751119895
1205880
0 0 1199061198950
01205752119895
1205880
0 0 0 1199061198950
1205753119895
1205880
0 1205741205751119895
1199010
1205741205752119895
1199010
1205741205753119895
1199010
1199061198950
]]]]]]]]]]]]]]
]
1198601015840
119895=
[[[[[[[[[[[[[[[
[
1199061015840
1198951205751119895
1205881015840
1205752119895
1205881015840
1205753119895
1205881015840
0
0 1199061015840
1198950 0 minus120575
1119895
1205881015840
12058820
0 0 1199061015840
1198950 minus120575
2119895
1205881015840
12058820
0 0 0 1199061015840
119895minus1205753119895
1205881015840
12058820
0 1205741205751119895
1199011015840
1205741205752119895
1199011015840
1205741205753119895
1199011015840
1199061015840
119895
]]]]]]]]]]]]]]]
]
(1)
Here 120574 = 14 is the specific heat ratio 120575119894119895is the Kronecker
delta In the computations with mean flow field 1205971198760120597119909
1205971198760120597119910 and 120597119876
0120597119911 are neglected to avoid the instability
waves caused by the shear mean flow field The effect ofneglecting the terms about the gradient of themean flow fieldis discussed in [23]
22 Computational Mesh of the BCM The computationalmesh of BCM is generated by the following procedures intwo dimensions [24] The computational domain is dividedinto an aggregation of square areas (cubic areas in threedimensions) where each area is denoted as a ldquocuberdquo as shownin Figure 1(a) Each cube is then divided by an equispacedCartesianmesh as shown in Figure 1(b) Cells located outsidethe wall boundary are defined as fluid cells On the otherhand cells located inside the wall boundary are defined aswall cells In this method all cubes have the same number ofcells so that the computational effort required for all cubes isessentially equivalent in parallel computation and excellentparallel efficiency is achieved Each cube has three overlapcells as shown by the hatched cells in Figure 1(b) for data
International Journal of Aerospace Engineering 3
Cube
(a) Computational domain and cube boundary (b) Computational cells in a cube (15 times 15 cells 3 overlap cells)
Figure 1 Computational mesh of the building-cube method (BCM) in two dimensions
exchange When a cube is locally refined the cube selectedfor refinement is divided into four cubes (eight cubes in threedimensions) and each cube is subdivided by prescribed cellsAfter the refinement the size of the cube is smoothed so thatthe sizes of adjacent cubes are restricted to the same doubleor half that size The sizes of adjacent cubes are checked forall cubes If the size of an adjacent cube is larger than doublethe size of a focusing cube the adjacent cube is divided intofour cubes (eight cubes in three dimensions) and each cubeis subdivided by prescribed cells
23 Computational Algorithm of the LEEs Solver Figure 2shows the computational algorithm of the LEEs solverAt the beginning mesh information object shape initialconditions and the mean flow field are given The meanflow field is computed by the compressible Euler solver inthis research The details of the compressible Euler solverare provided in [25] The computational scheme of inviscidflux is changed from that of the reference to the simple low-dissipative advection upstream splitting (SLAU) [26] scheme
The spatial derivative of the LEEs solver is computedby the dispersion relation preserving (DRP) scheme [27]Through the use of the overlap cells a fourth-order DRPscheme using seven-point stencils can be implemented overthe entire area of the computational domain Time integra-tion is computed by a six-stage fourth-order Runge-Kuttascheme [28] In the time integral six subiterations constituteone time step In addition artificial selective damping [27] ofthe seven-point stencils is applied at each iteration to elim-inate the nonphysical oscillation The above computationsincluding boundary treatments are parallelized for all cubesusing Open Multi-Processing (OpenMP)
24 Wall Boundary For computation by Cartesian mesh itis important to apply mesh to wall boundaries realistically
because real surfaces have curvature Therefore variousIBMs have been proposed for diverse implementations Inthe present solver an IBM that employs a ghost cell (GC)approach using an image point (IP) [29] is applied Wallcells adjacent to fluid cells are defined as GCs The IP isdefined from the GC in the direction normal to the closestwall boundary as shown in Figure 3(a) In this processsurface stereo lithography (STL) data is used to determinethe intersection point of the normal vector with the wallboundary The physical quantities of the IP are interpolatedby the inverse distance weighting method of (2) using 3 times 3 times
3 = 27 stencils as illustrated in Figure 3(b)
119876IP =
27
sum
119894=1
119908 (119894) times 119876119904
(119894) times mask (119894)
119908 (119894) =ℎ (119894)minus2
sum27
119895=1ℎ (119895)minus2
(2)
Here 119876IP is the physical quantities of the IP 119876119904isthe physical
quantities of stencils 119908 is the weight function based on thedistance ℎ between the IP and stencils and mask is a valuethat reflects whether the stencil is a fluid cell or wall cell Fluidcells have mask = 1 and wall cells have mask = 0
The physical quantities of a GC are computed by thefollowing equations so that the slip condition is satisfied usingthe physical quantities of the IP
VGC = VIP minus (1 + (119889IP119889GC
)) times (VIP sdot n)n
119901GC = 119901IP
120588GC = 120588IP
(3)
Here 119889IP is the distance from the IP to the wall surface 119889GCis the distance from the GC to the wall surface n is the unit
4 International Journal of Aerospace Engineering
Input mesh initial condition and mean flow field
Data exchange at cube boundary
Compute spatial derivative and input
Damping in buffer zone
Output data
Para
llel f
or cu
bes
Subi
tera
tion
Upd
ate t
ime s
tep
Update of Q998400sub(n)
Q998400sub(n)
Fluctuation vector Q998400(n+1)
Fluctuation vector Q998400(n)
120655Q998400120655x 120655Q
998400120655y 120655Q
998400120655z 120655Q0120655x 120655Q0120655y 120655Q0120655z S
Figure 2 Computational algorithm of the linearized Euler equations (LEEs) solver
Fluid cell
Ghost cell
Wall cell
Wall boundary
Image point
(a) Definition of GC and IP
Fluid cell
Ghost cell
Qs(1)
Qs(2)
Qs(3)
Qs(4)
Qs(5)
Qs(6)
Qs(7)
Qs(8)
Qs(9)
QIP
mask(1) = 1
mask(6) = 0
h(1)
(b) Interpolation to IP
Figure 3 The immersed boundary method (IBM) using an image point (IP) based on a ghost cell (GC)
normal vector of the wall surface and VIP 119901IP and 120588IP arethe velocity vector pressure and density at the IP and VGC119901GC and 120588GC are those at the GC respectively In this study119889GC + 119889IP = 175Δ119909 to avoid the instability caused by thewall boundary condition The spatial derivative at the fluidcell adjacent to the GC is conducted using the second-ordercentral difference based on the physical quantities of the GC
25 Cube Boundary At the boundaries between cubes withdifferent sizes the three overlap cells are hanging nodesTherefore data exchange with interpolation is needed In
the solver Lagrange interpolation [30] is employed for dataexchange at the boundary as given by
119876119900
(119909119900 119910119900 119911119900)
= sum
119895119896119897
119876119904
(119909119895 119910119896 119911119897) times 119908119895
(119909119900) times 119908119896
(119910119900) times 119908119897(119911119900)
119908119895
(119909119900) = prod
119894 =119895
(119909119900
minus 119909119894)
(119909119895
minus 119909119894)
International Journal of Aerospace Engineering 5
119908119896
(119910119900) = prod
119894 =119896
(119910119900
minus 119910119894)
(119910119896
minus 119910119894)
119908119897(119911119900) = prod
119894 =119897
(119911119900
minus 119911119894)
(119911119897
minus 119911119894)
(4)
Here 119876119900represents the physical quantities of an overlap
cell 119876119904represents the physical quantities of stencils 119908
119895 119908119896
and 119908119897are computed weight functions based on the distance
between an overlap cell and stencils and 119909119900 119910119900 and 119911
119900are the
coordinates of an overlap cellFigure 4(a) illustrates the stencils used for data exchange
from smaller to larger cubes in two dimensions In this figureblack points are the fluid cells of a larger cube The shadedfluid cells of the larger cube are the overlap cells The whitecircles are stencils of the smaller cube and are used for theinterpolation Interpolation to three overlap cells per one rowis needed The stencils of the overlap cell that is closest to theboundary are 2 times 2 times 2 = 8 points and those of the other twocells are 4 times 4 times 4 = 64 points so that the location of stencils issymmetrical For interpolation from larger to smaller cubesas shown in Figure 4(b) stencils of 3 times 3 times 3 = 27 points areused for four rows in three dimensions which achieves third-order accuracy
26 Outer Boundary In LEEs computation outgoing wavesshould be damped so that the inner sound field is notdisturbed by reflected waves To this end the buffer zoneboundary condition [31] is implemented in the presentsolver To damp the outgoing waves gradually the magnitudeof the damping coefficients varies as a quadratic functionof the coordinates toward the outer boundary Equations(5) provide the damping equation in the buffer zone Thefluctuation vector is damped in each direction individually
1198761015840(119899)119909
= (1 minus 120590 (119909)) times 1198761015840(119899)
1198761015840(119899)119910
= (1 minus 120590 (119910)) times 1198761015840(119899)
1198761015840(119899)119911
= (1 minus 120590 (119911)) times 1198761015840(119899)
120590 (119909) =2
Δ119909
1003816100381610038161003816100381610038161003816100381610038161 minus
119909119887
minus 119871119887119909
119871119887119909
100381610038161003816100381610038161003816100381610038161003816
2
120590 (119910) =2
Δ119910
1003816100381610038161003816100381610038161003816100381610038161003816
1 minus119910119887
minus 119871119887119910
119871119887119910
1003816100381610038161003816100381610038161003816100381610038161003816
2
120590 (119911) =2
Δ119911
1003816100381610038161003816100381610038161003816100381610038161 minus
119911119887
minus 119871119887119911
119871119887119911
100381610038161003816100381610038161003816100381610038161003816
2
(5)
Here 1198761015840(119899) is the fluctuation vector at each iteration and
with respect to each direction 1198761015840(119899)119909 1198761015840(119899)
119910 and 1198761015840(119899)
119911are
the damped fluctuation vectors 120590(119909) 120590(119910) and 120590(119911) are thedamping coefficients in the buffer zone Δ119909 Δ119910 and Δz arethe mesh spaces 119871
119887119909 119871119887119910 and 119871
119887119911are the widths of the
buffer zone and119909119887 119910119887 and 119911
119887are the distances from the inner
end of buffer zone Figure 5 shows the buffer zone (illustratedas the hatched area) and an expanded view of the bottom leftcorner in a two-dimensional case
3 Evaluation of the Order of Accuracy
The order of accuracy of the present computational methodis evaluated by the one-dimensional wave propagation prob-lem The IBM and Lagrange interpolation are employed intheir three-dimensional forms Equations (6) are the one-dimensional wave equationsThe initial pressure distributionis given by
1205971199011015840
120597119905+
1205971199061015840
1
120597119909= 0
1205971199061015840
1
120597119905+
1205971199011015840
120597119909= 0
(6)
1199011015840
(initial) = 05 times exp [minus(ln 2)
2(1199092
+ 1199102
+ 1199112)] (7)
The root mean square error (RMSE) between the analyticalsolution and the computed solution is computed by
RMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161199011015840(computed) minus 1199011015840
(analytical)100381610038161003816100381610038161003816
2
(8)
The RMSE is computed for two meshes Figure 6 illustratesthe computational cubes with and without cube refinementThe size of the computational domain is 16119863 times 4119863 times 4119863The periodic boundary condition is set at the end of the 119909-directional boundaries The RMSE is also computed in thecase where a wall boundary exists When the wall boundaryexists the wave reflects at the end of the 119909-directionalboundaries
The RMSE and the order of accuracy are listed in Table 1The order of accuracy of each mesh is computed using theRMSEof onemesh and that of a coarsermesh Case 1 employsno wall boundary and is conducted without cube refinementTherefore the prescribed order of accuracy is as shown InCase 2 the order of accuracy is slightly reduced becausethe spatial derivative at the fluid cell adjacent to the GCis conducted using the second-order central difference Theorder of accuracy of Case 3 is approximately two becausethe accuracy of the cube boundary is dominated by theinterpolation from a larger to smaller cube Case 4 providesa slightly smaller order of accuracy than that of Case 3because of the existence of the wall boundary These resultsindicate that the general order of accuracy of the presentcomputational method is approximately two
4 Acoustic Scattering around a Sphere
Acoustic scattering around a sphere [32] is computed undervarious mesh conditions in this section The magnitude oferror relative to an analytical solution and the computational
6 International Journal of Aerospace Engineering
Cube boundary
Fluid cellOverlap cellStencil
Stencils (4 times 4)
Stencils (2 times 2)
(a) From a smaller to larger cube
Cube boundary
Fluid cellOverlap cellStencil
Stencils (3 times 3)
(b) From a larger to smaller cube
Figure 4 Stencils used for Lagrange interpolation in two dimensions
Buffer zone
(a) Buffer zone in the computational domain
Lbx
xb
yb
Lby
Buffer zone
(b) Expanded view of the bottom left corner of (a)
Figure 5 Buffer zone boundary condition
time are compared A sphere is located at the origin of a three-dimensional domain The reference length 119863 is the diameterof the sphere A monopole Gaussian sound source 119878 is givenby the following equation as a function of time t
119878 = exp[minus (ln 2) ((119909 minus 4119863)
2+ 1199102
+ 1199112
(02119863)2
)] sin (6120587) 119905 (9)
The influence of three important parameters on the erroris investigated the minimum cell size around the spherepoints per wavelength (PPW) in the computational domainand the size of the buffer zoneTheminimum cell size aroundthe sphere has an effect on the error generated from the wall
boundary A small cell size not only suppresses the errorbut also restricts the time step size and results in greatercomputational time The PPW is an important factor foracoustic simulations because insufficient PPW introducesdissipation and dispersion errors in wave propagation Thesize of the buffer domain is important for setting the outerboundary condition If the width of the buffer zone is shortthe reflected wave is generated at the outer boundary and thereflected wave disturbs the inner sound field
Figure 7 shows computational domains of the CoarseBCM Middle2 and BCM Fine3meshes listed in Table 2Thegray lines indicate the cube boundaries Table 2 summarizesthe mesh information of all the cases used for the parametric
International Journal of Aerospace Engineering 7
y x
z
(a) Cubes without cube refinement
y x
z
(b) Cubes with cube refinement
Figure 6 Computational cubes for the one-dimensional wave propagation problem
8D
16D
8D
8D
y
x
y
z
(a) Coarse
16D
32D
16D
16D
y
x
y
z
(b) BCM Middle2
16D
32D
16D
16D
y
x
y
z
(c) BCM Fine3
Figure 7 Computational domains and cube boundaries for acoustic scattering around a sphere of diameter D
8 International Journal of Aerospace Engineering
Table 1 Root mean square error and the order of accuracy
Wall Cube refinement Number of cells in one cube Root mean square error Order of accuracy
Case 1 Without Without36 times 36 times 36 1063 times 10minus5 mdash48 times 48 times 48 3422 times 10minus6 394172 times 72 times 72 6887 times 10minus7 3954
Case 2 With Without36 times 36 times 36 1269 times 10minus5 mdash48 times 48 times 48 4145 times 10minus6 389072 times 72 times 72 8326 times 10minus7 3959
Case 3 Without With36 times 36 times 36 1200 times 10minus4 mdash48 times 48 times 48 6574 times 10minus5 209372 times 72 times 72 2890 times 10minus5 2027
Case 4 With With36 times 36 times 36 1258 times 10minus4 mdash48 times 48 times 48 7086 times 10minus5 199572 times 72 times 72 3156 times 10minus5 1995
Table 2 Mesh information for acoustic scattering around a sphere of diameter 119863
Minimum cellsize
Number ofcubes Number of cells in one cube PPW Width of buffer zone
[119909 119910 119911]Coarse 00415D 128 48 times 48 times 48 8 1D 1D 1DUniform Middle 00277D 128 72 times 72 times 72 12 1D 1D 1DBCM Middle1 00208D 184 48 times 48 times 48 8 16 1D 1D 1DBCM Middle2 00208D 296 48 times 48 times 48 4 8 16 9D 5D 5DBCM Middle3 00208D 408 48 times 48 times 48 4 8 16 9D 5D 5DUniform Fine 00208D 128 96 times 96 times 96 16 1D 1D 1DBCM Fine1 00104D 240 48 times 48 times 48 8 16 32 1D 1D 1DBCM Fine2 00104D 352 48 times 48 times 48 4 8 16 32 9D 5D 5DBCM Fine3 00104D 464 48 times 48 times 48 4 8 16 32 9D 5D 5D
study Coarse mesh forms the base mesh of the other meshesemployedThe size of the computational domain is 16119863times8119863times
8119863 referring to [33] where 128 cubes of a size 1119863 times 1119863 times 1119863
constitute the domain as shown in Figure 7(a) The numberof cells in one cube is 48 times 48 times 48 and the PPW is eight Inthe Uniform Middle and Uniform Fine meshes the domainsize and the number of cubes are the same as those of theCoarse mesh The number of cells in one cube is 72 times 72times 72 in the Uniform Middle mesh and 96 times 96 times 96 in theUniform Fine mesh thus the PPW is 12 and 16 respectivelyIn the BCM Middle1 mesh the eight cubes in the Coarsemesh surrounding the sphere are subdivided into half sizecubes Similarly the eight cubes surrounding the sphere aresubdivided from the BCM Middle1 mesh in the BCM Fine1mesh The number of cubes is 184 in the BCM Middle1mesh and 240 in the BCM Fine1 mesh and the maximumPPW is 16 and 32 respectively In the BCM Middle2 meshshown in Figure 7(b) and BCM Fine2 meshes the bufferzone is expanded to add 112 cubes to the BCM Middle1 andBCM Fine1 meshes In the BCM Middle3 and BCM Fine3(shown in Figure 7(c)) meshes eight cubes located at 2 le xle 6 minus2 le y le 2 and minus2 le z le 2 and eight cubes located at minus6le x le minus2 minus2 le y le 2 and minus2 le z le 2 are subdivided from theBCM Middle2 and BCM Fine2 meshes to increase the PPWof the computational domain The inner end of the buffer
zone is set at x = [minus7D 7D] y = [minus3D 3D] and z = [minus3D3D] in all meshes to compare the sizes of the buffer zones
Figure 8 shows the instantaneous pressure distributionaround the sphere computed using the Coarse mesh In thisfigure the buffer zone is not drawn Waves generated fromthe sound source are scattered by the sphere and interferencefringes appear The computation is executed in nondimen-sional time 119879 = 15 and a periodic steady state is observedafter119879 = 11 Figure 9 shows the pressure distributionnear theinner end of the buffer zone and the time history of the pres-sure near the sphere for all meshes The pressure distributionis sampled at minus6119863 le 119909 le minus4119863 on the 119909-axisThe time historyof the pressure is sampled at (minus2D 0 0) and 14 le 119879 le 15
In Figures 9(a) and 9(b) the uniform meshes arecompared The pressure distributions do not follow thedecreasing trend of the analytical solution in Figure 9(a)Reflection occurs at the outer boundary because of theinsufficient width of the buffer zone Additionally theUniform Middle and Uniform Fine meshes show a higherpressure amplitude compared with the pressure distributionof the Coarse mesh It is assumed that the sound wave isdamped at the Coarse mesh because of the insufficient PPWThe time histories of the uniform meshes provide loweramplitudes than the analytical solution
International Journal of Aerospace Engineering 9
Table 3 Comparison of errors relative to an analytical solution and respective computational times for the meshes listed in Table 2
Total number ofcells
Normalized root meansquare error []
Normalizedmaximum error []
Computational time[120583sectimestepcell]
Real time [sec](128 CPUs)
Coarse 14155776 1197 2382 008454 302Uniform Middle 47775744 502 1131 008631 1388BCM Middle1 20348928 362 1486 010891 1088BCM Middle2 32735232 307 714 011027 1710BCM Middle3 45121536 289 734 009665 2172Uniform Fine 113246208 357 1093 007329 4240BCM Fine1 26542080 614 2224 008851 2654BCM Fine2 38928384 304 700 008777 3358BCM Fine3 51314688 162 500 009019 4794
Non
dim
ensio
nal p
ress
ure
000E + 000
minus500E minus 005
500E minus 005
minus100E minus 004
100E minus 004
Figure 8 Instantaneous pressure distribution (Coarse mesh) around a sphere of diameter D
In Figures 9(c) and 9(d) the BCM Middle meshes arecompared The BCM Middle2 and BCM Middle3 meshesfollow the analytical solution in Figure 9(c) These mesheshave a buffer zone of width 9D in the 119909 direction andoutgoing waves are damped appropriately However theBCM Middle2 mesh provides a lower amplitude This isowing to the insufficient PPW at the sampling points On theother hand phase error is not observed in the BCM Middle2mesh In Figure 9(d) the amplitude of the pressure convergesto the analytical solution for the BCM Middle2 mesh Onlythe BCM Middle1 mesh provides a lower amplitude Thisamplitude is the same as that of the uniform meshes There-fore it is confirmed that the amplitude of the inner soundfieldis diminished when using a buffer zone of short width
In Figures 9(e) and 9(f) the BCM Fine meshes arecompared The pressure distributions and the time historiesof the BCM Fine meshes exhibit similar tendencies as thoseof the BCM Middle meshes
To compare the magnitude of errors more quantitativelythe root mean square pressure 119875rms of the scattered soundis computed and the normalized RMSE (NRMSE) and thenormalized maximum error (MME) between the analytical
solution and the solutions of each mesh are compared asgiven by
NRMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
2
NME = max1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
(10)
The number of sampling points 119873 are set clockwise ata radius 119903 = 2D from the origin The points (minus2D 00) and (2D 0 0) correspond to 0 deg and 180 deg Theerrors are summarized in Table 3 As shown in the table therefined meshes provide lower errors than the coarser meshand the meshes that utilize a large buffer zone also providelower errors The minimum cell size around the sphere alsoaffects the errors The smallest errors are provided by theBCM Fine3 mesh A comparison of the uniform and BCMmeshes indicates that the BCM Middle3 and BCM Fine3meshes which use cubes of different sizes at the appropriatelocations provide lower errors than Uniform Middle meshes
10 International Journal of Aerospace Engineering
Non
dim
ensio
nal p
ress
ure
AnalyticalCoarse
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
Uniform_MiddleUniform_Fine
minus6 minus55 minus5 minus45 minus4
x coordinate
(a) Pressure distributions of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
100E minus 04
150E minus 04
AnalyticalCoarse
Uniform_MiddleUniform_Fine
500E minus 05
14 142 144 146 148 15Nondimensional time
(b) Time histories of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
minus6 minus55 minus5 minus45 minus4
x coordinate
(c) Pressure distributions of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
14 142 144 146 148 15Nondimensional time
(d) Time histories of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
minus6 minus55 minus5 minus45 minus4
x coordinate
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(e) Pressure distributions of BCM Fine meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
14 142 144 146 148 15Nondimensional time
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(f) Time histories of BCM Fine meshes
Figure 9 Pressure distributions (minus6119863 le 119909 le minus4119863) and time histories at (minus2D 0 0) and (14 le 119879 le 15) around a sphere of diameter 119863 forthe meshes listed in Table 2
International Journal of Aerospace Engineering 11
that utilize a similar number of mesh points Moreover theerrors of the BCM Fine3 mesh are about one-half the errorsof the Uniform Fine mesh which has twice the number ofmesh points as the BCM Fine3 mesh These results indicatethe effectiveness of the BCM arrangement
The computational wall-clock times for a single timestep per cell and the total wall-clock time required toreach a nondimensional time 119879 = 15 are also listed inTable 3 All meshes were computed using 128CPUs of anSGI AltixUV1000 computer Regarding the wall-clock timeper one time step per cell the computational times of theuniformandBCMmeshes are comparableHowever the totalwall-clock times of the BCM meshes are slightly longer thanthose of the uniform meshes The BCM meshes employ alarger number of cubes than the number of CPUs used in theevaluationThemismatch between the numbers of cubes andCPUs can degrade the load balance Computations using anequivalent number of CPUs and cubes are more effective forBCMmeshes
5 Noise Propagation from the JT15D Nacelle
Noise propagation from the JT15D [34] nacelle is computedand the far-field sound pressure level (SPL) is compared withdata derived from experiment and the computational resultsof others The JT15D is a small Pratt and Whitney turbofanenginewith a bellmouth inletThe sound source is introducedvia a discrete frequency spinning mode The spinning modeinput [35] is a typical sound source generated by the fan orrotor-stator intersections in the engine The sound source ofa single spinning mode (119898 119899) is defined by
119878 = [119869119898
(119896119903119903) + 1198881119884119898
(119896119903119903)] cos (119896119905 minus 119896
119886119909 minus 119898120579) (11)
Here 119869119898and119884119898are themth order Bessel functions of the first
and second kind respectively 119896 is the angular frequency 119896119886
is the axial wavenumber 119896119903is the radial wavenumber and 120579
is the phase The 119899th solution 119896119903of the following equation is
determined by the hard-wall boundary condition of the duct
119889 [119869119898
(119903outer119896119903)]
119889119903
119889 [119884119898
(119903inner119896119903)]
119889119903
minus119889 [119869119898
(119903inner119896119903)]
119889119903
119889 [119884119898
(119903outer119896119903)]
119889119903= 0
(12)
Here 119903outer and 119903inner are the bypass duct inner wall radius andthe inner hub radius respectively The axial wave number 119896
119886
is computed from
119896119886
=119896
1 minus 1198722119895
(minus119872119895
plusmnradic
1 minus1198962
119903(1 minus 119872
2
119895)
1198962) (13)
where 119872119895is the Mach number at the fan face The selection
of plus or minus signs in the parentheses is determined bythe propagation direction of the sound wave where plus(+) represents the positive propagation direction along the
axial coordinate and vice versa The constant 1198881satisfies the
following relation
1198881
= minus(119889119889119903) [119869
119898(119903outer119896119903)]
(119889119889119903) [119884119898
(119903outer119896119903)]
= minus(119889119889119903) [119869
119898(119903inner119896119903)]
(119889119889119903) [119884119898
(119903inner119896119903)]
(14)
Parameters are set from experimental data (119898 119899) =
(minus13 0) 119903outer = 02667m and 119903inner = 00998m Thereference length D = 06223mis the length from the fanface to the leading edge of the nacelle The blade passingfrequency (BPF) is set to 3150Hz which is derived fromthe fan rotating speed of 6750 rpm The experiments wereconducted in the static condition and the fan face axial Machnumber is 0175 The present computation is also conductedin the static condition In the present computation the axialflow velocity of the ghost cell at the fan face boundary isdirectly modified to this Mach number The pressure andthe density are the same values as those of the adjacent fluidcells The SPL is measured at a radius of 49D The integrationmethod of Ffowcs-Williams and Hawkings (FW-H) [36] isemployed to estimate the far-field pressure from thenear-fieldpressure
Figure 10 shows the computational domain and Table 4lists the mesh information The computations of the com-pressible Euler solver and the LEEs solver are conductedusing the samemeshThePPW inTable 4 is the PPWreducedby the Doppler effect of the fan face axial Mach number Thecomputational domain is set at minus1119863 le 119909 le 7119863 minus8119863 le 119910 le
8119863 and minus8119863 le 119911 le 8119863The fan face is at 119909 = 05119863The innerend of the buffer zone is set at 119909 = [0 4119863] 119910 = [minus4119863 4119863]and 119911 = [minus4119863 4119863] The FW-H surfaces are located at thecube boundaries between the smallest size cubes and thelarger size cubes
Figure 11 shows theMachnumber distribution around theJT15D nacelle In Figure 11 the acceleration region near theinternal wall of the nacelle lip and the stagnation at the spikeare shown Because the experiments and computations wereconducted under the static condition the mean flow fieldexists only near the nacelle
Figure 12 shows the instantaneous pressure distributionsat the planes defined at 119911 = 0 and 119909 = 17119863 In the figure onlythe distributions of the smallest sized cubes are drawn Thefan noise is diffracted at the inlet of the nacelle and propagatesalong the radial direction The 13 peaks and valleys of theswirling fan noise at the 119909 = 17119863 plane are clearly capturedwhich is equivalent to the number of spinning modes Thetime history of the pressure is sampled at the establishedpoints on the FW-H surface and the periodic steady state isobserved after 119879 = 8
Figure 13 shows a comparison of the predicted SPL withthe experimental results conducted by Heidmann et al [37]and the computational results computed by Lan et al [34]The horizontal axis in the figure is the angle from the +119909-axialdirection In the figure the predicted SPL using the presentsolver shows good agreement with the computational resultof Lan et al (within 1 dB) Compared with the experimental
12 International Journal of Aerospace Engineering
Table 4 Mesh information for the JT15D nacelle
JT15D Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWCase 1 00166D 1544 30 times 30 times 30 41688000 87Case 2 00125D 1544 40 times 40 times 40 98816000 116
16D
8D
16D
16D
y
x
yzy
x z
Figure 10 Computational domain for the JT15D nacelle
Mac
h nu
mbe
r
02000100
0000
Figure 11 Mach number distribution around the JT15D nacelle
data a difference of about 3 dB is found at 60 deg Howeverthis discrepancy is also shown between the experimental dataand the result of Lan et al The SPL peak obtained near55 deg is equivalent to that obtained by Lan et al and thatobtained experimentally
6 Noise Propagation arounda Fuselage-Wing-Nacelle Configuration
The noise propagation around a fuselage-wing-nacelle con-figuration is computed as a realistic exampleThe focus of theexample was that of the OWN configuration [38] where theengine nacelle is mounted over the main wing which servesas one of the configurations designed to achieve substantialairport noise reduction The main feature of this configu-ration is that the main wing serves as a shield between the
ground and the noise generated by the engine To investigatethe effect of the OWN configuration the propagation of fannoise of both the conventional DLR-F6 aircraft configuration[39] and the OWN configuration is computed and the SPLbelow the aircraft for both configurations is comparedTheseconfigurations have complex geometry with large curvaturesnear the wing-body and the nacelle-pylon junctions In theOWN configuration the nacelle is moved 11D in the +119909
direction and 06D in the +y direction relative to its locationin the DLR-F6 configuration Here the reference length 119863 =
49m is the longitudinal length of the nacelle The cross-sectional geometry of the pylon is used without any changesand has a sweepback angle of 40 deg A mean flow fieldof Mach number 03 with zero angle of attack is computedusing the compressible Euler solver The sound source isintroduced via a discrete frequency spinning mode As anexample of a modern turbofan engine the CFM56-7B engineis considered The bypass ratio is 55 the fan diameter is154m the number of blades is 24 the maximum rotationalrate is 5382 rpm and the fundamental BPF is 21528HzTheBPF is used as the input frequency of the spinning modeThespinning mode (119898 119899) is set to (minus24 0) The SPL is measuredat a radius of 10D using the FW-H method
Figure 14 shows the computational domain of each con-figuration The black dot shows the origin of coordinatesystem The computations of the compressible Euler andLEEs solvers are conducted using an equivalent mesh Thesize of the computational domains is 4119863 times 2119863 times 2119863 Thesymmetric boundary condition is set at the minusz boundaryThe computational domains are set to ensure that sufficientcomputational domains surround the nacelle It is assumedthat the geometry out of the computational domain has littleinfluence on the noise directivity below the aircraft The
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
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International Journal of
International Journal of Aerospace Engineering 3
Cube
(a) Computational domain and cube boundary (b) Computational cells in a cube (15 times 15 cells 3 overlap cells)
Figure 1 Computational mesh of the building-cube method (BCM) in two dimensions
exchange When a cube is locally refined the cube selectedfor refinement is divided into four cubes (eight cubes in threedimensions) and each cube is subdivided by prescribed cellsAfter the refinement the size of the cube is smoothed so thatthe sizes of adjacent cubes are restricted to the same doubleor half that size The sizes of adjacent cubes are checked forall cubes If the size of an adjacent cube is larger than doublethe size of a focusing cube the adjacent cube is divided intofour cubes (eight cubes in three dimensions) and each cubeis subdivided by prescribed cells
23 Computational Algorithm of the LEEs Solver Figure 2shows the computational algorithm of the LEEs solverAt the beginning mesh information object shape initialconditions and the mean flow field are given The meanflow field is computed by the compressible Euler solver inthis research The details of the compressible Euler solverare provided in [25] The computational scheme of inviscidflux is changed from that of the reference to the simple low-dissipative advection upstream splitting (SLAU) [26] scheme
The spatial derivative of the LEEs solver is computedby the dispersion relation preserving (DRP) scheme [27]Through the use of the overlap cells a fourth-order DRPscheme using seven-point stencils can be implemented overthe entire area of the computational domain Time integra-tion is computed by a six-stage fourth-order Runge-Kuttascheme [28] In the time integral six subiterations constituteone time step In addition artificial selective damping [27] ofthe seven-point stencils is applied at each iteration to elim-inate the nonphysical oscillation The above computationsincluding boundary treatments are parallelized for all cubesusing Open Multi-Processing (OpenMP)
24 Wall Boundary For computation by Cartesian mesh itis important to apply mesh to wall boundaries realistically
because real surfaces have curvature Therefore variousIBMs have been proposed for diverse implementations Inthe present solver an IBM that employs a ghost cell (GC)approach using an image point (IP) [29] is applied Wallcells adjacent to fluid cells are defined as GCs The IP isdefined from the GC in the direction normal to the closestwall boundary as shown in Figure 3(a) In this processsurface stereo lithography (STL) data is used to determinethe intersection point of the normal vector with the wallboundary The physical quantities of the IP are interpolatedby the inverse distance weighting method of (2) using 3 times 3 times
3 = 27 stencils as illustrated in Figure 3(b)
119876IP =
27
sum
119894=1
119908 (119894) times 119876119904
(119894) times mask (119894)
119908 (119894) =ℎ (119894)minus2
sum27
119895=1ℎ (119895)minus2
(2)
Here 119876IP is the physical quantities of the IP 119876119904isthe physical
quantities of stencils 119908 is the weight function based on thedistance ℎ between the IP and stencils and mask is a valuethat reflects whether the stencil is a fluid cell or wall cell Fluidcells have mask = 1 and wall cells have mask = 0
The physical quantities of a GC are computed by thefollowing equations so that the slip condition is satisfied usingthe physical quantities of the IP
VGC = VIP minus (1 + (119889IP119889GC
)) times (VIP sdot n)n
119901GC = 119901IP
120588GC = 120588IP
(3)
Here 119889IP is the distance from the IP to the wall surface 119889GCis the distance from the GC to the wall surface n is the unit
4 International Journal of Aerospace Engineering
Input mesh initial condition and mean flow field
Data exchange at cube boundary
Compute spatial derivative and input
Damping in buffer zone
Output data
Para
llel f
or cu
bes
Subi
tera
tion
Upd
ate t
ime s
tep
Update of Q998400sub(n)
Q998400sub(n)
Fluctuation vector Q998400(n+1)
Fluctuation vector Q998400(n)
120655Q998400120655x 120655Q
998400120655y 120655Q
998400120655z 120655Q0120655x 120655Q0120655y 120655Q0120655z S
Figure 2 Computational algorithm of the linearized Euler equations (LEEs) solver
Fluid cell
Ghost cell
Wall cell
Wall boundary
Image point
(a) Definition of GC and IP
Fluid cell
Ghost cell
Qs(1)
Qs(2)
Qs(3)
Qs(4)
Qs(5)
Qs(6)
Qs(7)
Qs(8)
Qs(9)
QIP
mask(1) = 1
mask(6) = 0
h(1)
(b) Interpolation to IP
Figure 3 The immersed boundary method (IBM) using an image point (IP) based on a ghost cell (GC)
normal vector of the wall surface and VIP 119901IP and 120588IP arethe velocity vector pressure and density at the IP and VGC119901GC and 120588GC are those at the GC respectively In this study119889GC + 119889IP = 175Δ119909 to avoid the instability caused by thewall boundary condition The spatial derivative at the fluidcell adjacent to the GC is conducted using the second-ordercentral difference based on the physical quantities of the GC
25 Cube Boundary At the boundaries between cubes withdifferent sizes the three overlap cells are hanging nodesTherefore data exchange with interpolation is needed In
the solver Lagrange interpolation [30] is employed for dataexchange at the boundary as given by
119876119900
(119909119900 119910119900 119911119900)
= sum
119895119896119897
119876119904
(119909119895 119910119896 119911119897) times 119908119895
(119909119900) times 119908119896
(119910119900) times 119908119897(119911119900)
119908119895
(119909119900) = prod
119894 =119895
(119909119900
minus 119909119894)
(119909119895
minus 119909119894)
International Journal of Aerospace Engineering 5
119908119896
(119910119900) = prod
119894 =119896
(119910119900
minus 119910119894)
(119910119896
minus 119910119894)
119908119897(119911119900) = prod
119894 =119897
(119911119900
minus 119911119894)
(119911119897
minus 119911119894)
(4)
Here 119876119900represents the physical quantities of an overlap
cell 119876119904represents the physical quantities of stencils 119908
119895 119908119896
and 119908119897are computed weight functions based on the distance
between an overlap cell and stencils and 119909119900 119910119900 and 119911
119900are the
coordinates of an overlap cellFigure 4(a) illustrates the stencils used for data exchange
from smaller to larger cubes in two dimensions In this figureblack points are the fluid cells of a larger cube The shadedfluid cells of the larger cube are the overlap cells The whitecircles are stencils of the smaller cube and are used for theinterpolation Interpolation to three overlap cells per one rowis needed The stencils of the overlap cell that is closest to theboundary are 2 times 2 times 2 = 8 points and those of the other twocells are 4 times 4 times 4 = 64 points so that the location of stencils issymmetrical For interpolation from larger to smaller cubesas shown in Figure 4(b) stencils of 3 times 3 times 3 = 27 points areused for four rows in three dimensions which achieves third-order accuracy
26 Outer Boundary In LEEs computation outgoing wavesshould be damped so that the inner sound field is notdisturbed by reflected waves To this end the buffer zoneboundary condition [31] is implemented in the presentsolver To damp the outgoing waves gradually the magnitudeof the damping coefficients varies as a quadratic functionof the coordinates toward the outer boundary Equations(5) provide the damping equation in the buffer zone Thefluctuation vector is damped in each direction individually
1198761015840(119899)119909
= (1 minus 120590 (119909)) times 1198761015840(119899)
1198761015840(119899)119910
= (1 minus 120590 (119910)) times 1198761015840(119899)
1198761015840(119899)119911
= (1 minus 120590 (119911)) times 1198761015840(119899)
120590 (119909) =2
Δ119909
1003816100381610038161003816100381610038161003816100381610038161 minus
119909119887
minus 119871119887119909
119871119887119909
100381610038161003816100381610038161003816100381610038161003816
2
120590 (119910) =2
Δ119910
1003816100381610038161003816100381610038161003816100381610038161003816
1 minus119910119887
minus 119871119887119910
119871119887119910
1003816100381610038161003816100381610038161003816100381610038161003816
2
120590 (119911) =2
Δ119911
1003816100381610038161003816100381610038161003816100381610038161 minus
119911119887
minus 119871119887119911
119871119887119911
100381610038161003816100381610038161003816100381610038161003816
2
(5)
Here 1198761015840(119899) is the fluctuation vector at each iteration and
with respect to each direction 1198761015840(119899)119909 1198761015840(119899)
119910 and 1198761015840(119899)
119911are
the damped fluctuation vectors 120590(119909) 120590(119910) and 120590(119911) are thedamping coefficients in the buffer zone Δ119909 Δ119910 and Δz arethe mesh spaces 119871
119887119909 119871119887119910 and 119871
119887119911are the widths of the
buffer zone and119909119887 119910119887 and 119911
119887are the distances from the inner
end of buffer zone Figure 5 shows the buffer zone (illustratedas the hatched area) and an expanded view of the bottom leftcorner in a two-dimensional case
3 Evaluation of the Order of Accuracy
The order of accuracy of the present computational methodis evaluated by the one-dimensional wave propagation prob-lem The IBM and Lagrange interpolation are employed intheir three-dimensional forms Equations (6) are the one-dimensional wave equationsThe initial pressure distributionis given by
1205971199011015840
120597119905+
1205971199061015840
1
120597119909= 0
1205971199061015840
1
120597119905+
1205971199011015840
120597119909= 0
(6)
1199011015840
(initial) = 05 times exp [minus(ln 2)
2(1199092
+ 1199102
+ 1199112)] (7)
The root mean square error (RMSE) between the analyticalsolution and the computed solution is computed by
RMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161199011015840(computed) minus 1199011015840
(analytical)100381610038161003816100381610038161003816
2
(8)
The RMSE is computed for two meshes Figure 6 illustratesthe computational cubes with and without cube refinementThe size of the computational domain is 16119863 times 4119863 times 4119863The periodic boundary condition is set at the end of the 119909-directional boundaries The RMSE is also computed in thecase where a wall boundary exists When the wall boundaryexists the wave reflects at the end of the 119909-directionalboundaries
The RMSE and the order of accuracy are listed in Table 1The order of accuracy of each mesh is computed using theRMSEof onemesh and that of a coarsermesh Case 1 employsno wall boundary and is conducted without cube refinementTherefore the prescribed order of accuracy is as shown InCase 2 the order of accuracy is slightly reduced becausethe spatial derivative at the fluid cell adjacent to the GCis conducted using the second-order central difference Theorder of accuracy of Case 3 is approximately two becausethe accuracy of the cube boundary is dominated by theinterpolation from a larger to smaller cube Case 4 providesa slightly smaller order of accuracy than that of Case 3because of the existence of the wall boundary These resultsindicate that the general order of accuracy of the presentcomputational method is approximately two
4 Acoustic Scattering around a Sphere
Acoustic scattering around a sphere [32] is computed undervarious mesh conditions in this section The magnitude oferror relative to an analytical solution and the computational
6 International Journal of Aerospace Engineering
Cube boundary
Fluid cellOverlap cellStencil
Stencils (4 times 4)
Stencils (2 times 2)
(a) From a smaller to larger cube
Cube boundary
Fluid cellOverlap cellStencil
Stencils (3 times 3)
(b) From a larger to smaller cube
Figure 4 Stencils used for Lagrange interpolation in two dimensions
Buffer zone
(a) Buffer zone in the computational domain
Lbx
xb
yb
Lby
Buffer zone
(b) Expanded view of the bottom left corner of (a)
Figure 5 Buffer zone boundary condition
time are compared A sphere is located at the origin of a three-dimensional domain The reference length 119863 is the diameterof the sphere A monopole Gaussian sound source 119878 is givenby the following equation as a function of time t
119878 = exp[minus (ln 2) ((119909 minus 4119863)
2+ 1199102
+ 1199112
(02119863)2
)] sin (6120587) 119905 (9)
The influence of three important parameters on the erroris investigated the minimum cell size around the spherepoints per wavelength (PPW) in the computational domainand the size of the buffer zoneTheminimum cell size aroundthe sphere has an effect on the error generated from the wall
boundary A small cell size not only suppresses the errorbut also restricts the time step size and results in greatercomputational time The PPW is an important factor foracoustic simulations because insufficient PPW introducesdissipation and dispersion errors in wave propagation Thesize of the buffer domain is important for setting the outerboundary condition If the width of the buffer zone is shortthe reflected wave is generated at the outer boundary and thereflected wave disturbs the inner sound field
Figure 7 shows computational domains of the CoarseBCM Middle2 and BCM Fine3meshes listed in Table 2Thegray lines indicate the cube boundaries Table 2 summarizesthe mesh information of all the cases used for the parametric
International Journal of Aerospace Engineering 7
y x
z
(a) Cubes without cube refinement
y x
z
(b) Cubes with cube refinement
Figure 6 Computational cubes for the one-dimensional wave propagation problem
8D
16D
8D
8D
y
x
y
z
(a) Coarse
16D
32D
16D
16D
y
x
y
z
(b) BCM Middle2
16D
32D
16D
16D
y
x
y
z
(c) BCM Fine3
Figure 7 Computational domains and cube boundaries for acoustic scattering around a sphere of diameter D
8 International Journal of Aerospace Engineering
Table 1 Root mean square error and the order of accuracy
Wall Cube refinement Number of cells in one cube Root mean square error Order of accuracy
Case 1 Without Without36 times 36 times 36 1063 times 10minus5 mdash48 times 48 times 48 3422 times 10minus6 394172 times 72 times 72 6887 times 10minus7 3954
Case 2 With Without36 times 36 times 36 1269 times 10minus5 mdash48 times 48 times 48 4145 times 10minus6 389072 times 72 times 72 8326 times 10minus7 3959
Case 3 Without With36 times 36 times 36 1200 times 10minus4 mdash48 times 48 times 48 6574 times 10minus5 209372 times 72 times 72 2890 times 10minus5 2027
Case 4 With With36 times 36 times 36 1258 times 10minus4 mdash48 times 48 times 48 7086 times 10minus5 199572 times 72 times 72 3156 times 10minus5 1995
Table 2 Mesh information for acoustic scattering around a sphere of diameter 119863
Minimum cellsize
Number ofcubes Number of cells in one cube PPW Width of buffer zone
[119909 119910 119911]Coarse 00415D 128 48 times 48 times 48 8 1D 1D 1DUniform Middle 00277D 128 72 times 72 times 72 12 1D 1D 1DBCM Middle1 00208D 184 48 times 48 times 48 8 16 1D 1D 1DBCM Middle2 00208D 296 48 times 48 times 48 4 8 16 9D 5D 5DBCM Middle3 00208D 408 48 times 48 times 48 4 8 16 9D 5D 5DUniform Fine 00208D 128 96 times 96 times 96 16 1D 1D 1DBCM Fine1 00104D 240 48 times 48 times 48 8 16 32 1D 1D 1DBCM Fine2 00104D 352 48 times 48 times 48 4 8 16 32 9D 5D 5DBCM Fine3 00104D 464 48 times 48 times 48 4 8 16 32 9D 5D 5D
study Coarse mesh forms the base mesh of the other meshesemployedThe size of the computational domain is 16119863times8119863times
8119863 referring to [33] where 128 cubes of a size 1119863 times 1119863 times 1119863
constitute the domain as shown in Figure 7(a) The numberof cells in one cube is 48 times 48 times 48 and the PPW is eight Inthe Uniform Middle and Uniform Fine meshes the domainsize and the number of cubes are the same as those of theCoarse mesh The number of cells in one cube is 72 times 72times 72 in the Uniform Middle mesh and 96 times 96 times 96 in theUniform Fine mesh thus the PPW is 12 and 16 respectivelyIn the BCM Middle1 mesh the eight cubes in the Coarsemesh surrounding the sphere are subdivided into half sizecubes Similarly the eight cubes surrounding the sphere aresubdivided from the BCM Middle1 mesh in the BCM Fine1mesh The number of cubes is 184 in the BCM Middle1mesh and 240 in the BCM Fine1 mesh and the maximumPPW is 16 and 32 respectively In the BCM Middle2 meshshown in Figure 7(b) and BCM Fine2 meshes the bufferzone is expanded to add 112 cubes to the BCM Middle1 andBCM Fine1 meshes In the BCM Middle3 and BCM Fine3(shown in Figure 7(c)) meshes eight cubes located at 2 le xle 6 minus2 le y le 2 and minus2 le z le 2 and eight cubes located at minus6le x le minus2 minus2 le y le 2 and minus2 le z le 2 are subdivided from theBCM Middle2 and BCM Fine2 meshes to increase the PPWof the computational domain The inner end of the buffer
zone is set at x = [minus7D 7D] y = [minus3D 3D] and z = [minus3D3D] in all meshes to compare the sizes of the buffer zones
Figure 8 shows the instantaneous pressure distributionaround the sphere computed using the Coarse mesh In thisfigure the buffer zone is not drawn Waves generated fromthe sound source are scattered by the sphere and interferencefringes appear The computation is executed in nondimen-sional time 119879 = 15 and a periodic steady state is observedafter119879 = 11 Figure 9 shows the pressure distributionnear theinner end of the buffer zone and the time history of the pres-sure near the sphere for all meshes The pressure distributionis sampled at minus6119863 le 119909 le minus4119863 on the 119909-axisThe time historyof the pressure is sampled at (minus2D 0 0) and 14 le 119879 le 15
In Figures 9(a) and 9(b) the uniform meshes arecompared The pressure distributions do not follow thedecreasing trend of the analytical solution in Figure 9(a)Reflection occurs at the outer boundary because of theinsufficient width of the buffer zone Additionally theUniform Middle and Uniform Fine meshes show a higherpressure amplitude compared with the pressure distributionof the Coarse mesh It is assumed that the sound wave isdamped at the Coarse mesh because of the insufficient PPWThe time histories of the uniform meshes provide loweramplitudes than the analytical solution
International Journal of Aerospace Engineering 9
Table 3 Comparison of errors relative to an analytical solution and respective computational times for the meshes listed in Table 2
Total number ofcells
Normalized root meansquare error []
Normalizedmaximum error []
Computational time[120583sectimestepcell]
Real time [sec](128 CPUs)
Coarse 14155776 1197 2382 008454 302Uniform Middle 47775744 502 1131 008631 1388BCM Middle1 20348928 362 1486 010891 1088BCM Middle2 32735232 307 714 011027 1710BCM Middle3 45121536 289 734 009665 2172Uniform Fine 113246208 357 1093 007329 4240BCM Fine1 26542080 614 2224 008851 2654BCM Fine2 38928384 304 700 008777 3358BCM Fine3 51314688 162 500 009019 4794
Non
dim
ensio
nal p
ress
ure
000E + 000
minus500E minus 005
500E minus 005
minus100E minus 004
100E minus 004
Figure 8 Instantaneous pressure distribution (Coarse mesh) around a sphere of diameter D
In Figures 9(c) and 9(d) the BCM Middle meshes arecompared The BCM Middle2 and BCM Middle3 meshesfollow the analytical solution in Figure 9(c) These mesheshave a buffer zone of width 9D in the 119909 direction andoutgoing waves are damped appropriately However theBCM Middle2 mesh provides a lower amplitude This isowing to the insufficient PPW at the sampling points On theother hand phase error is not observed in the BCM Middle2mesh In Figure 9(d) the amplitude of the pressure convergesto the analytical solution for the BCM Middle2 mesh Onlythe BCM Middle1 mesh provides a lower amplitude Thisamplitude is the same as that of the uniform meshes There-fore it is confirmed that the amplitude of the inner soundfieldis diminished when using a buffer zone of short width
In Figures 9(e) and 9(f) the BCM Fine meshes arecompared The pressure distributions and the time historiesof the BCM Fine meshes exhibit similar tendencies as thoseof the BCM Middle meshes
To compare the magnitude of errors more quantitativelythe root mean square pressure 119875rms of the scattered soundis computed and the normalized RMSE (NRMSE) and thenormalized maximum error (MME) between the analytical
solution and the solutions of each mesh are compared asgiven by
NRMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
2
NME = max1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
(10)
The number of sampling points 119873 are set clockwise ata radius 119903 = 2D from the origin The points (minus2D 00) and (2D 0 0) correspond to 0 deg and 180 deg Theerrors are summarized in Table 3 As shown in the table therefined meshes provide lower errors than the coarser meshand the meshes that utilize a large buffer zone also providelower errors The minimum cell size around the sphere alsoaffects the errors The smallest errors are provided by theBCM Fine3 mesh A comparison of the uniform and BCMmeshes indicates that the BCM Middle3 and BCM Fine3meshes which use cubes of different sizes at the appropriatelocations provide lower errors than Uniform Middle meshes
10 International Journal of Aerospace Engineering
Non
dim
ensio
nal p
ress
ure
AnalyticalCoarse
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
Uniform_MiddleUniform_Fine
minus6 minus55 minus5 minus45 minus4
x coordinate
(a) Pressure distributions of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
100E minus 04
150E minus 04
AnalyticalCoarse
Uniform_MiddleUniform_Fine
500E minus 05
14 142 144 146 148 15Nondimensional time
(b) Time histories of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
minus6 minus55 minus5 minus45 minus4
x coordinate
(c) Pressure distributions of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
14 142 144 146 148 15Nondimensional time
(d) Time histories of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
minus6 minus55 minus5 minus45 minus4
x coordinate
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(e) Pressure distributions of BCM Fine meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
14 142 144 146 148 15Nondimensional time
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(f) Time histories of BCM Fine meshes
Figure 9 Pressure distributions (minus6119863 le 119909 le minus4119863) and time histories at (minus2D 0 0) and (14 le 119879 le 15) around a sphere of diameter 119863 forthe meshes listed in Table 2
International Journal of Aerospace Engineering 11
that utilize a similar number of mesh points Moreover theerrors of the BCM Fine3 mesh are about one-half the errorsof the Uniform Fine mesh which has twice the number ofmesh points as the BCM Fine3 mesh These results indicatethe effectiveness of the BCM arrangement
The computational wall-clock times for a single timestep per cell and the total wall-clock time required toreach a nondimensional time 119879 = 15 are also listed inTable 3 All meshes were computed using 128CPUs of anSGI AltixUV1000 computer Regarding the wall-clock timeper one time step per cell the computational times of theuniformandBCMmeshes are comparableHowever the totalwall-clock times of the BCM meshes are slightly longer thanthose of the uniform meshes The BCM meshes employ alarger number of cubes than the number of CPUs used in theevaluationThemismatch between the numbers of cubes andCPUs can degrade the load balance Computations using anequivalent number of CPUs and cubes are more effective forBCMmeshes
5 Noise Propagation from the JT15D Nacelle
Noise propagation from the JT15D [34] nacelle is computedand the far-field sound pressure level (SPL) is compared withdata derived from experiment and the computational resultsof others The JT15D is a small Pratt and Whitney turbofanenginewith a bellmouth inletThe sound source is introducedvia a discrete frequency spinning mode The spinning modeinput [35] is a typical sound source generated by the fan orrotor-stator intersections in the engine The sound source ofa single spinning mode (119898 119899) is defined by
119878 = [119869119898
(119896119903119903) + 1198881119884119898
(119896119903119903)] cos (119896119905 minus 119896
119886119909 minus 119898120579) (11)
Here 119869119898and119884119898are themth order Bessel functions of the first
and second kind respectively 119896 is the angular frequency 119896119886
is the axial wavenumber 119896119903is the radial wavenumber and 120579
is the phase The 119899th solution 119896119903of the following equation is
determined by the hard-wall boundary condition of the duct
119889 [119869119898
(119903outer119896119903)]
119889119903
119889 [119884119898
(119903inner119896119903)]
119889119903
minus119889 [119869119898
(119903inner119896119903)]
119889119903
119889 [119884119898
(119903outer119896119903)]
119889119903= 0
(12)
Here 119903outer and 119903inner are the bypass duct inner wall radius andthe inner hub radius respectively The axial wave number 119896
119886
is computed from
119896119886
=119896
1 minus 1198722119895
(minus119872119895
plusmnradic
1 minus1198962
119903(1 minus 119872
2
119895)
1198962) (13)
where 119872119895is the Mach number at the fan face The selection
of plus or minus signs in the parentheses is determined bythe propagation direction of the sound wave where plus(+) represents the positive propagation direction along the
axial coordinate and vice versa The constant 1198881satisfies the
following relation
1198881
= minus(119889119889119903) [119869
119898(119903outer119896119903)]
(119889119889119903) [119884119898
(119903outer119896119903)]
= minus(119889119889119903) [119869
119898(119903inner119896119903)]
(119889119889119903) [119884119898
(119903inner119896119903)]
(14)
Parameters are set from experimental data (119898 119899) =
(minus13 0) 119903outer = 02667m and 119903inner = 00998m Thereference length D = 06223mis the length from the fanface to the leading edge of the nacelle The blade passingfrequency (BPF) is set to 3150Hz which is derived fromthe fan rotating speed of 6750 rpm The experiments wereconducted in the static condition and the fan face axial Machnumber is 0175 The present computation is also conductedin the static condition In the present computation the axialflow velocity of the ghost cell at the fan face boundary isdirectly modified to this Mach number The pressure andthe density are the same values as those of the adjacent fluidcells The SPL is measured at a radius of 49D The integrationmethod of Ffowcs-Williams and Hawkings (FW-H) [36] isemployed to estimate the far-field pressure from thenear-fieldpressure
Figure 10 shows the computational domain and Table 4lists the mesh information The computations of the com-pressible Euler solver and the LEEs solver are conductedusing the samemeshThePPW inTable 4 is the PPWreducedby the Doppler effect of the fan face axial Mach number Thecomputational domain is set at minus1119863 le 119909 le 7119863 minus8119863 le 119910 le
8119863 and minus8119863 le 119911 le 8119863The fan face is at 119909 = 05119863The innerend of the buffer zone is set at 119909 = [0 4119863] 119910 = [minus4119863 4119863]and 119911 = [minus4119863 4119863] The FW-H surfaces are located at thecube boundaries between the smallest size cubes and thelarger size cubes
Figure 11 shows theMachnumber distribution around theJT15D nacelle In Figure 11 the acceleration region near theinternal wall of the nacelle lip and the stagnation at the spikeare shown Because the experiments and computations wereconducted under the static condition the mean flow fieldexists only near the nacelle
Figure 12 shows the instantaneous pressure distributionsat the planes defined at 119911 = 0 and 119909 = 17119863 In the figure onlythe distributions of the smallest sized cubes are drawn Thefan noise is diffracted at the inlet of the nacelle and propagatesalong the radial direction The 13 peaks and valleys of theswirling fan noise at the 119909 = 17119863 plane are clearly capturedwhich is equivalent to the number of spinning modes Thetime history of the pressure is sampled at the establishedpoints on the FW-H surface and the periodic steady state isobserved after 119879 = 8
Figure 13 shows a comparison of the predicted SPL withthe experimental results conducted by Heidmann et al [37]and the computational results computed by Lan et al [34]The horizontal axis in the figure is the angle from the +119909-axialdirection In the figure the predicted SPL using the presentsolver shows good agreement with the computational resultof Lan et al (within 1 dB) Compared with the experimental
12 International Journal of Aerospace Engineering
Table 4 Mesh information for the JT15D nacelle
JT15D Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWCase 1 00166D 1544 30 times 30 times 30 41688000 87Case 2 00125D 1544 40 times 40 times 40 98816000 116
16D
8D
16D
16D
y
x
yzy
x z
Figure 10 Computational domain for the JT15D nacelle
Mac
h nu
mbe
r
02000100
0000
Figure 11 Mach number distribution around the JT15D nacelle
data a difference of about 3 dB is found at 60 deg Howeverthis discrepancy is also shown between the experimental dataand the result of Lan et al The SPL peak obtained near55 deg is equivalent to that obtained by Lan et al and thatobtained experimentally
6 Noise Propagation arounda Fuselage-Wing-Nacelle Configuration
The noise propagation around a fuselage-wing-nacelle con-figuration is computed as a realistic exampleThe focus of theexample was that of the OWN configuration [38] where theengine nacelle is mounted over the main wing which servesas one of the configurations designed to achieve substantialairport noise reduction The main feature of this configu-ration is that the main wing serves as a shield between the
ground and the noise generated by the engine To investigatethe effect of the OWN configuration the propagation of fannoise of both the conventional DLR-F6 aircraft configuration[39] and the OWN configuration is computed and the SPLbelow the aircraft for both configurations is comparedTheseconfigurations have complex geometry with large curvaturesnear the wing-body and the nacelle-pylon junctions In theOWN configuration the nacelle is moved 11D in the +119909
direction and 06D in the +y direction relative to its locationin the DLR-F6 configuration Here the reference length 119863 =
49m is the longitudinal length of the nacelle The cross-sectional geometry of the pylon is used without any changesand has a sweepback angle of 40 deg A mean flow fieldof Mach number 03 with zero angle of attack is computedusing the compressible Euler solver The sound source isintroduced via a discrete frequency spinning mode As anexample of a modern turbofan engine the CFM56-7B engineis considered The bypass ratio is 55 the fan diameter is154m the number of blades is 24 the maximum rotationalrate is 5382 rpm and the fundamental BPF is 21528HzTheBPF is used as the input frequency of the spinning modeThespinning mode (119898 119899) is set to (minus24 0) The SPL is measuredat a radius of 10D using the FW-H method
Figure 14 shows the computational domain of each con-figuration The black dot shows the origin of coordinatesystem The computations of the compressible Euler andLEEs solvers are conducted using an equivalent mesh Thesize of the computational domains is 4119863 times 2119863 times 2119863 Thesymmetric boundary condition is set at the minusz boundaryThe computational domains are set to ensure that sufficientcomputational domains surround the nacelle It is assumedthat the geometry out of the computational domain has littleinfluence on the noise directivity below the aircraft The
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
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DistributedSensor Networks
International Journal of
4 International Journal of Aerospace Engineering
Input mesh initial condition and mean flow field
Data exchange at cube boundary
Compute spatial derivative and input
Damping in buffer zone
Output data
Para
llel f
or cu
bes
Subi
tera
tion
Upd
ate t
ime s
tep
Update of Q998400sub(n)
Q998400sub(n)
Fluctuation vector Q998400(n+1)
Fluctuation vector Q998400(n)
120655Q998400120655x 120655Q
998400120655y 120655Q
998400120655z 120655Q0120655x 120655Q0120655y 120655Q0120655z S
Figure 2 Computational algorithm of the linearized Euler equations (LEEs) solver
Fluid cell
Ghost cell
Wall cell
Wall boundary
Image point
(a) Definition of GC and IP
Fluid cell
Ghost cell
Qs(1)
Qs(2)
Qs(3)
Qs(4)
Qs(5)
Qs(6)
Qs(7)
Qs(8)
Qs(9)
QIP
mask(1) = 1
mask(6) = 0
h(1)
(b) Interpolation to IP
Figure 3 The immersed boundary method (IBM) using an image point (IP) based on a ghost cell (GC)
normal vector of the wall surface and VIP 119901IP and 120588IP arethe velocity vector pressure and density at the IP and VGC119901GC and 120588GC are those at the GC respectively In this study119889GC + 119889IP = 175Δ119909 to avoid the instability caused by thewall boundary condition The spatial derivative at the fluidcell adjacent to the GC is conducted using the second-ordercentral difference based on the physical quantities of the GC
25 Cube Boundary At the boundaries between cubes withdifferent sizes the three overlap cells are hanging nodesTherefore data exchange with interpolation is needed In
the solver Lagrange interpolation [30] is employed for dataexchange at the boundary as given by
119876119900
(119909119900 119910119900 119911119900)
= sum
119895119896119897
119876119904
(119909119895 119910119896 119911119897) times 119908119895
(119909119900) times 119908119896
(119910119900) times 119908119897(119911119900)
119908119895
(119909119900) = prod
119894 =119895
(119909119900
minus 119909119894)
(119909119895
minus 119909119894)
International Journal of Aerospace Engineering 5
119908119896
(119910119900) = prod
119894 =119896
(119910119900
minus 119910119894)
(119910119896
minus 119910119894)
119908119897(119911119900) = prod
119894 =119897
(119911119900
minus 119911119894)
(119911119897
minus 119911119894)
(4)
Here 119876119900represents the physical quantities of an overlap
cell 119876119904represents the physical quantities of stencils 119908
119895 119908119896
and 119908119897are computed weight functions based on the distance
between an overlap cell and stencils and 119909119900 119910119900 and 119911
119900are the
coordinates of an overlap cellFigure 4(a) illustrates the stencils used for data exchange
from smaller to larger cubes in two dimensions In this figureblack points are the fluid cells of a larger cube The shadedfluid cells of the larger cube are the overlap cells The whitecircles are stencils of the smaller cube and are used for theinterpolation Interpolation to three overlap cells per one rowis needed The stencils of the overlap cell that is closest to theboundary are 2 times 2 times 2 = 8 points and those of the other twocells are 4 times 4 times 4 = 64 points so that the location of stencils issymmetrical For interpolation from larger to smaller cubesas shown in Figure 4(b) stencils of 3 times 3 times 3 = 27 points areused for four rows in three dimensions which achieves third-order accuracy
26 Outer Boundary In LEEs computation outgoing wavesshould be damped so that the inner sound field is notdisturbed by reflected waves To this end the buffer zoneboundary condition [31] is implemented in the presentsolver To damp the outgoing waves gradually the magnitudeof the damping coefficients varies as a quadratic functionof the coordinates toward the outer boundary Equations(5) provide the damping equation in the buffer zone Thefluctuation vector is damped in each direction individually
1198761015840(119899)119909
= (1 minus 120590 (119909)) times 1198761015840(119899)
1198761015840(119899)119910
= (1 minus 120590 (119910)) times 1198761015840(119899)
1198761015840(119899)119911
= (1 minus 120590 (119911)) times 1198761015840(119899)
120590 (119909) =2
Δ119909
1003816100381610038161003816100381610038161003816100381610038161 minus
119909119887
minus 119871119887119909
119871119887119909
100381610038161003816100381610038161003816100381610038161003816
2
120590 (119910) =2
Δ119910
1003816100381610038161003816100381610038161003816100381610038161003816
1 minus119910119887
minus 119871119887119910
119871119887119910
1003816100381610038161003816100381610038161003816100381610038161003816
2
120590 (119911) =2
Δ119911
1003816100381610038161003816100381610038161003816100381610038161 minus
119911119887
minus 119871119887119911
119871119887119911
100381610038161003816100381610038161003816100381610038161003816
2
(5)
Here 1198761015840(119899) is the fluctuation vector at each iteration and
with respect to each direction 1198761015840(119899)119909 1198761015840(119899)
119910 and 1198761015840(119899)
119911are
the damped fluctuation vectors 120590(119909) 120590(119910) and 120590(119911) are thedamping coefficients in the buffer zone Δ119909 Δ119910 and Δz arethe mesh spaces 119871
119887119909 119871119887119910 and 119871
119887119911are the widths of the
buffer zone and119909119887 119910119887 and 119911
119887are the distances from the inner
end of buffer zone Figure 5 shows the buffer zone (illustratedas the hatched area) and an expanded view of the bottom leftcorner in a two-dimensional case
3 Evaluation of the Order of Accuracy
The order of accuracy of the present computational methodis evaluated by the one-dimensional wave propagation prob-lem The IBM and Lagrange interpolation are employed intheir three-dimensional forms Equations (6) are the one-dimensional wave equationsThe initial pressure distributionis given by
1205971199011015840
120597119905+
1205971199061015840
1
120597119909= 0
1205971199061015840
1
120597119905+
1205971199011015840
120597119909= 0
(6)
1199011015840
(initial) = 05 times exp [minus(ln 2)
2(1199092
+ 1199102
+ 1199112)] (7)
The root mean square error (RMSE) between the analyticalsolution and the computed solution is computed by
RMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161199011015840(computed) minus 1199011015840
(analytical)100381610038161003816100381610038161003816
2
(8)
The RMSE is computed for two meshes Figure 6 illustratesthe computational cubes with and without cube refinementThe size of the computational domain is 16119863 times 4119863 times 4119863The periodic boundary condition is set at the end of the 119909-directional boundaries The RMSE is also computed in thecase where a wall boundary exists When the wall boundaryexists the wave reflects at the end of the 119909-directionalboundaries
The RMSE and the order of accuracy are listed in Table 1The order of accuracy of each mesh is computed using theRMSEof onemesh and that of a coarsermesh Case 1 employsno wall boundary and is conducted without cube refinementTherefore the prescribed order of accuracy is as shown InCase 2 the order of accuracy is slightly reduced becausethe spatial derivative at the fluid cell adjacent to the GCis conducted using the second-order central difference Theorder of accuracy of Case 3 is approximately two becausethe accuracy of the cube boundary is dominated by theinterpolation from a larger to smaller cube Case 4 providesa slightly smaller order of accuracy than that of Case 3because of the existence of the wall boundary These resultsindicate that the general order of accuracy of the presentcomputational method is approximately two
4 Acoustic Scattering around a Sphere
Acoustic scattering around a sphere [32] is computed undervarious mesh conditions in this section The magnitude oferror relative to an analytical solution and the computational
6 International Journal of Aerospace Engineering
Cube boundary
Fluid cellOverlap cellStencil
Stencils (4 times 4)
Stencils (2 times 2)
(a) From a smaller to larger cube
Cube boundary
Fluid cellOverlap cellStencil
Stencils (3 times 3)
(b) From a larger to smaller cube
Figure 4 Stencils used for Lagrange interpolation in two dimensions
Buffer zone
(a) Buffer zone in the computational domain
Lbx
xb
yb
Lby
Buffer zone
(b) Expanded view of the bottom left corner of (a)
Figure 5 Buffer zone boundary condition
time are compared A sphere is located at the origin of a three-dimensional domain The reference length 119863 is the diameterof the sphere A monopole Gaussian sound source 119878 is givenby the following equation as a function of time t
119878 = exp[minus (ln 2) ((119909 minus 4119863)
2+ 1199102
+ 1199112
(02119863)2
)] sin (6120587) 119905 (9)
The influence of three important parameters on the erroris investigated the minimum cell size around the spherepoints per wavelength (PPW) in the computational domainand the size of the buffer zoneTheminimum cell size aroundthe sphere has an effect on the error generated from the wall
boundary A small cell size not only suppresses the errorbut also restricts the time step size and results in greatercomputational time The PPW is an important factor foracoustic simulations because insufficient PPW introducesdissipation and dispersion errors in wave propagation Thesize of the buffer domain is important for setting the outerboundary condition If the width of the buffer zone is shortthe reflected wave is generated at the outer boundary and thereflected wave disturbs the inner sound field
Figure 7 shows computational domains of the CoarseBCM Middle2 and BCM Fine3meshes listed in Table 2Thegray lines indicate the cube boundaries Table 2 summarizesthe mesh information of all the cases used for the parametric
International Journal of Aerospace Engineering 7
y x
z
(a) Cubes without cube refinement
y x
z
(b) Cubes with cube refinement
Figure 6 Computational cubes for the one-dimensional wave propagation problem
8D
16D
8D
8D
y
x
y
z
(a) Coarse
16D
32D
16D
16D
y
x
y
z
(b) BCM Middle2
16D
32D
16D
16D
y
x
y
z
(c) BCM Fine3
Figure 7 Computational domains and cube boundaries for acoustic scattering around a sphere of diameter D
8 International Journal of Aerospace Engineering
Table 1 Root mean square error and the order of accuracy
Wall Cube refinement Number of cells in one cube Root mean square error Order of accuracy
Case 1 Without Without36 times 36 times 36 1063 times 10minus5 mdash48 times 48 times 48 3422 times 10minus6 394172 times 72 times 72 6887 times 10minus7 3954
Case 2 With Without36 times 36 times 36 1269 times 10minus5 mdash48 times 48 times 48 4145 times 10minus6 389072 times 72 times 72 8326 times 10minus7 3959
Case 3 Without With36 times 36 times 36 1200 times 10minus4 mdash48 times 48 times 48 6574 times 10minus5 209372 times 72 times 72 2890 times 10minus5 2027
Case 4 With With36 times 36 times 36 1258 times 10minus4 mdash48 times 48 times 48 7086 times 10minus5 199572 times 72 times 72 3156 times 10minus5 1995
Table 2 Mesh information for acoustic scattering around a sphere of diameter 119863
Minimum cellsize
Number ofcubes Number of cells in one cube PPW Width of buffer zone
[119909 119910 119911]Coarse 00415D 128 48 times 48 times 48 8 1D 1D 1DUniform Middle 00277D 128 72 times 72 times 72 12 1D 1D 1DBCM Middle1 00208D 184 48 times 48 times 48 8 16 1D 1D 1DBCM Middle2 00208D 296 48 times 48 times 48 4 8 16 9D 5D 5DBCM Middle3 00208D 408 48 times 48 times 48 4 8 16 9D 5D 5DUniform Fine 00208D 128 96 times 96 times 96 16 1D 1D 1DBCM Fine1 00104D 240 48 times 48 times 48 8 16 32 1D 1D 1DBCM Fine2 00104D 352 48 times 48 times 48 4 8 16 32 9D 5D 5DBCM Fine3 00104D 464 48 times 48 times 48 4 8 16 32 9D 5D 5D
study Coarse mesh forms the base mesh of the other meshesemployedThe size of the computational domain is 16119863times8119863times
8119863 referring to [33] where 128 cubes of a size 1119863 times 1119863 times 1119863
constitute the domain as shown in Figure 7(a) The numberof cells in one cube is 48 times 48 times 48 and the PPW is eight Inthe Uniform Middle and Uniform Fine meshes the domainsize and the number of cubes are the same as those of theCoarse mesh The number of cells in one cube is 72 times 72times 72 in the Uniform Middle mesh and 96 times 96 times 96 in theUniform Fine mesh thus the PPW is 12 and 16 respectivelyIn the BCM Middle1 mesh the eight cubes in the Coarsemesh surrounding the sphere are subdivided into half sizecubes Similarly the eight cubes surrounding the sphere aresubdivided from the BCM Middle1 mesh in the BCM Fine1mesh The number of cubes is 184 in the BCM Middle1mesh and 240 in the BCM Fine1 mesh and the maximumPPW is 16 and 32 respectively In the BCM Middle2 meshshown in Figure 7(b) and BCM Fine2 meshes the bufferzone is expanded to add 112 cubes to the BCM Middle1 andBCM Fine1 meshes In the BCM Middle3 and BCM Fine3(shown in Figure 7(c)) meshes eight cubes located at 2 le xle 6 minus2 le y le 2 and minus2 le z le 2 and eight cubes located at minus6le x le minus2 minus2 le y le 2 and minus2 le z le 2 are subdivided from theBCM Middle2 and BCM Fine2 meshes to increase the PPWof the computational domain The inner end of the buffer
zone is set at x = [minus7D 7D] y = [minus3D 3D] and z = [minus3D3D] in all meshes to compare the sizes of the buffer zones
Figure 8 shows the instantaneous pressure distributionaround the sphere computed using the Coarse mesh In thisfigure the buffer zone is not drawn Waves generated fromthe sound source are scattered by the sphere and interferencefringes appear The computation is executed in nondimen-sional time 119879 = 15 and a periodic steady state is observedafter119879 = 11 Figure 9 shows the pressure distributionnear theinner end of the buffer zone and the time history of the pres-sure near the sphere for all meshes The pressure distributionis sampled at minus6119863 le 119909 le minus4119863 on the 119909-axisThe time historyof the pressure is sampled at (minus2D 0 0) and 14 le 119879 le 15
In Figures 9(a) and 9(b) the uniform meshes arecompared The pressure distributions do not follow thedecreasing trend of the analytical solution in Figure 9(a)Reflection occurs at the outer boundary because of theinsufficient width of the buffer zone Additionally theUniform Middle and Uniform Fine meshes show a higherpressure amplitude compared with the pressure distributionof the Coarse mesh It is assumed that the sound wave isdamped at the Coarse mesh because of the insufficient PPWThe time histories of the uniform meshes provide loweramplitudes than the analytical solution
International Journal of Aerospace Engineering 9
Table 3 Comparison of errors relative to an analytical solution and respective computational times for the meshes listed in Table 2
Total number ofcells
Normalized root meansquare error []
Normalizedmaximum error []
Computational time[120583sectimestepcell]
Real time [sec](128 CPUs)
Coarse 14155776 1197 2382 008454 302Uniform Middle 47775744 502 1131 008631 1388BCM Middle1 20348928 362 1486 010891 1088BCM Middle2 32735232 307 714 011027 1710BCM Middle3 45121536 289 734 009665 2172Uniform Fine 113246208 357 1093 007329 4240BCM Fine1 26542080 614 2224 008851 2654BCM Fine2 38928384 304 700 008777 3358BCM Fine3 51314688 162 500 009019 4794
Non
dim
ensio
nal p
ress
ure
000E + 000
minus500E minus 005
500E minus 005
minus100E minus 004
100E minus 004
Figure 8 Instantaneous pressure distribution (Coarse mesh) around a sphere of diameter D
In Figures 9(c) and 9(d) the BCM Middle meshes arecompared The BCM Middle2 and BCM Middle3 meshesfollow the analytical solution in Figure 9(c) These mesheshave a buffer zone of width 9D in the 119909 direction andoutgoing waves are damped appropriately However theBCM Middle2 mesh provides a lower amplitude This isowing to the insufficient PPW at the sampling points On theother hand phase error is not observed in the BCM Middle2mesh In Figure 9(d) the amplitude of the pressure convergesto the analytical solution for the BCM Middle2 mesh Onlythe BCM Middle1 mesh provides a lower amplitude Thisamplitude is the same as that of the uniform meshes There-fore it is confirmed that the amplitude of the inner soundfieldis diminished when using a buffer zone of short width
In Figures 9(e) and 9(f) the BCM Fine meshes arecompared The pressure distributions and the time historiesof the BCM Fine meshes exhibit similar tendencies as thoseof the BCM Middle meshes
To compare the magnitude of errors more quantitativelythe root mean square pressure 119875rms of the scattered soundis computed and the normalized RMSE (NRMSE) and thenormalized maximum error (MME) between the analytical
solution and the solutions of each mesh are compared asgiven by
NRMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
2
NME = max1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
(10)
The number of sampling points 119873 are set clockwise ata radius 119903 = 2D from the origin The points (minus2D 00) and (2D 0 0) correspond to 0 deg and 180 deg Theerrors are summarized in Table 3 As shown in the table therefined meshes provide lower errors than the coarser meshand the meshes that utilize a large buffer zone also providelower errors The minimum cell size around the sphere alsoaffects the errors The smallest errors are provided by theBCM Fine3 mesh A comparison of the uniform and BCMmeshes indicates that the BCM Middle3 and BCM Fine3meshes which use cubes of different sizes at the appropriatelocations provide lower errors than Uniform Middle meshes
10 International Journal of Aerospace Engineering
Non
dim
ensio
nal p
ress
ure
AnalyticalCoarse
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
Uniform_MiddleUniform_Fine
minus6 minus55 minus5 minus45 minus4
x coordinate
(a) Pressure distributions of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
100E minus 04
150E minus 04
AnalyticalCoarse
Uniform_MiddleUniform_Fine
500E minus 05
14 142 144 146 148 15Nondimensional time
(b) Time histories of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
minus6 minus55 minus5 minus45 minus4
x coordinate
(c) Pressure distributions of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
14 142 144 146 148 15Nondimensional time
(d) Time histories of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
minus6 minus55 minus5 minus45 minus4
x coordinate
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(e) Pressure distributions of BCM Fine meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
14 142 144 146 148 15Nondimensional time
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(f) Time histories of BCM Fine meshes
Figure 9 Pressure distributions (minus6119863 le 119909 le minus4119863) and time histories at (minus2D 0 0) and (14 le 119879 le 15) around a sphere of diameter 119863 forthe meshes listed in Table 2
International Journal of Aerospace Engineering 11
that utilize a similar number of mesh points Moreover theerrors of the BCM Fine3 mesh are about one-half the errorsof the Uniform Fine mesh which has twice the number ofmesh points as the BCM Fine3 mesh These results indicatethe effectiveness of the BCM arrangement
The computational wall-clock times for a single timestep per cell and the total wall-clock time required toreach a nondimensional time 119879 = 15 are also listed inTable 3 All meshes were computed using 128CPUs of anSGI AltixUV1000 computer Regarding the wall-clock timeper one time step per cell the computational times of theuniformandBCMmeshes are comparableHowever the totalwall-clock times of the BCM meshes are slightly longer thanthose of the uniform meshes The BCM meshes employ alarger number of cubes than the number of CPUs used in theevaluationThemismatch between the numbers of cubes andCPUs can degrade the load balance Computations using anequivalent number of CPUs and cubes are more effective forBCMmeshes
5 Noise Propagation from the JT15D Nacelle
Noise propagation from the JT15D [34] nacelle is computedand the far-field sound pressure level (SPL) is compared withdata derived from experiment and the computational resultsof others The JT15D is a small Pratt and Whitney turbofanenginewith a bellmouth inletThe sound source is introducedvia a discrete frequency spinning mode The spinning modeinput [35] is a typical sound source generated by the fan orrotor-stator intersections in the engine The sound source ofa single spinning mode (119898 119899) is defined by
119878 = [119869119898
(119896119903119903) + 1198881119884119898
(119896119903119903)] cos (119896119905 minus 119896
119886119909 minus 119898120579) (11)
Here 119869119898and119884119898are themth order Bessel functions of the first
and second kind respectively 119896 is the angular frequency 119896119886
is the axial wavenumber 119896119903is the radial wavenumber and 120579
is the phase The 119899th solution 119896119903of the following equation is
determined by the hard-wall boundary condition of the duct
119889 [119869119898
(119903outer119896119903)]
119889119903
119889 [119884119898
(119903inner119896119903)]
119889119903
minus119889 [119869119898
(119903inner119896119903)]
119889119903
119889 [119884119898
(119903outer119896119903)]
119889119903= 0
(12)
Here 119903outer and 119903inner are the bypass duct inner wall radius andthe inner hub radius respectively The axial wave number 119896
119886
is computed from
119896119886
=119896
1 minus 1198722119895
(minus119872119895
plusmnradic
1 minus1198962
119903(1 minus 119872
2
119895)
1198962) (13)
where 119872119895is the Mach number at the fan face The selection
of plus or minus signs in the parentheses is determined bythe propagation direction of the sound wave where plus(+) represents the positive propagation direction along the
axial coordinate and vice versa The constant 1198881satisfies the
following relation
1198881
= minus(119889119889119903) [119869
119898(119903outer119896119903)]
(119889119889119903) [119884119898
(119903outer119896119903)]
= minus(119889119889119903) [119869
119898(119903inner119896119903)]
(119889119889119903) [119884119898
(119903inner119896119903)]
(14)
Parameters are set from experimental data (119898 119899) =
(minus13 0) 119903outer = 02667m and 119903inner = 00998m Thereference length D = 06223mis the length from the fanface to the leading edge of the nacelle The blade passingfrequency (BPF) is set to 3150Hz which is derived fromthe fan rotating speed of 6750 rpm The experiments wereconducted in the static condition and the fan face axial Machnumber is 0175 The present computation is also conductedin the static condition In the present computation the axialflow velocity of the ghost cell at the fan face boundary isdirectly modified to this Mach number The pressure andthe density are the same values as those of the adjacent fluidcells The SPL is measured at a radius of 49D The integrationmethod of Ffowcs-Williams and Hawkings (FW-H) [36] isemployed to estimate the far-field pressure from thenear-fieldpressure
Figure 10 shows the computational domain and Table 4lists the mesh information The computations of the com-pressible Euler solver and the LEEs solver are conductedusing the samemeshThePPW inTable 4 is the PPWreducedby the Doppler effect of the fan face axial Mach number Thecomputational domain is set at minus1119863 le 119909 le 7119863 minus8119863 le 119910 le
8119863 and minus8119863 le 119911 le 8119863The fan face is at 119909 = 05119863The innerend of the buffer zone is set at 119909 = [0 4119863] 119910 = [minus4119863 4119863]and 119911 = [minus4119863 4119863] The FW-H surfaces are located at thecube boundaries between the smallest size cubes and thelarger size cubes
Figure 11 shows theMachnumber distribution around theJT15D nacelle In Figure 11 the acceleration region near theinternal wall of the nacelle lip and the stagnation at the spikeare shown Because the experiments and computations wereconducted under the static condition the mean flow fieldexists only near the nacelle
Figure 12 shows the instantaneous pressure distributionsat the planes defined at 119911 = 0 and 119909 = 17119863 In the figure onlythe distributions of the smallest sized cubes are drawn Thefan noise is diffracted at the inlet of the nacelle and propagatesalong the radial direction The 13 peaks and valleys of theswirling fan noise at the 119909 = 17119863 plane are clearly capturedwhich is equivalent to the number of spinning modes Thetime history of the pressure is sampled at the establishedpoints on the FW-H surface and the periodic steady state isobserved after 119879 = 8
Figure 13 shows a comparison of the predicted SPL withthe experimental results conducted by Heidmann et al [37]and the computational results computed by Lan et al [34]The horizontal axis in the figure is the angle from the +119909-axialdirection In the figure the predicted SPL using the presentsolver shows good agreement with the computational resultof Lan et al (within 1 dB) Compared with the experimental
12 International Journal of Aerospace Engineering
Table 4 Mesh information for the JT15D nacelle
JT15D Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWCase 1 00166D 1544 30 times 30 times 30 41688000 87Case 2 00125D 1544 40 times 40 times 40 98816000 116
16D
8D
16D
16D
y
x
yzy
x z
Figure 10 Computational domain for the JT15D nacelle
Mac
h nu
mbe
r
02000100
0000
Figure 11 Mach number distribution around the JT15D nacelle
data a difference of about 3 dB is found at 60 deg Howeverthis discrepancy is also shown between the experimental dataand the result of Lan et al The SPL peak obtained near55 deg is equivalent to that obtained by Lan et al and thatobtained experimentally
6 Noise Propagation arounda Fuselage-Wing-Nacelle Configuration
The noise propagation around a fuselage-wing-nacelle con-figuration is computed as a realistic exampleThe focus of theexample was that of the OWN configuration [38] where theengine nacelle is mounted over the main wing which servesas one of the configurations designed to achieve substantialairport noise reduction The main feature of this configu-ration is that the main wing serves as a shield between the
ground and the noise generated by the engine To investigatethe effect of the OWN configuration the propagation of fannoise of both the conventional DLR-F6 aircraft configuration[39] and the OWN configuration is computed and the SPLbelow the aircraft for both configurations is comparedTheseconfigurations have complex geometry with large curvaturesnear the wing-body and the nacelle-pylon junctions In theOWN configuration the nacelle is moved 11D in the +119909
direction and 06D in the +y direction relative to its locationin the DLR-F6 configuration Here the reference length 119863 =
49m is the longitudinal length of the nacelle The cross-sectional geometry of the pylon is used without any changesand has a sweepback angle of 40 deg A mean flow fieldof Mach number 03 with zero angle of attack is computedusing the compressible Euler solver The sound source isintroduced via a discrete frequency spinning mode As anexample of a modern turbofan engine the CFM56-7B engineis considered The bypass ratio is 55 the fan diameter is154m the number of blades is 24 the maximum rotationalrate is 5382 rpm and the fundamental BPF is 21528HzTheBPF is used as the input frequency of the spinning modeThespinning mode (119898 119899) is set to (minus24 0) The SPL is measuredat a radius of 10D using the FW-H method
Figure 14 shows the computational domain of each con-figuration The black dot shows the origin of coordinatesystem The computations of the compressible Euler andLEEs solvers are conducted using an equivalent mesh Thesize of the computational domains is 4119863 times 2119863 times 2119863 Thesymmetric boundary condition is set at the minusz boundaryThe computational domains are set to ensure that sufficientcomputational domains surround the nacelle It is assumedthat the geometry out of the computational domain has littleinfluence on the noise directivity below the aircraft The
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Active and Passive Electronic Components
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
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Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 5
119908119896
(119910119900) = prod
119894 =119896
(119910119900
minus 119910119894)
(119910119896
minus 119910119894)
119908119897(119911119900) = prod
119894 =119897
(119911119900
minus 119911119894)
(119911119897
minus 119911119894)
(4)
Here 119876119900represents the physical quantities of an overlap
cell 119876119904represents the physical quantities of stencils 119908
119895 119908119896
and 119908119897are computed weight functions based on the distance
between an overlap cell and stencils and 119909119900 119910119900 and 119911
119900are the
coordinates of an overlap cellFigure 4(a) illustrates the stencils used for data exchange
from smaller to larger cubes in two dimensions In this figureblack points are the fluid cells of a larger cube The shadedfluid cells of the larger cube are the overlap cells The whitecircles are stencils of the smaller cube and are used for theinterpolation Interpolation to three overlap cells per one rowis needed The stencils of the overlap cell that is closest to theboundary are 2 times 2 times 2 = 8 points and those of the other twocells are 4 times 4 times 4 = 64 points so that the location of stencils issymmetrical For interpolation from larger to smaller cubesas shown in Figure 4(b) stencils of 3 times 3 times 3 = 27 points areused for four rows in three dimensions which achieves third-order accuracy
26 Outer Boundary In LEEs computation outgoing wavesshould be damped so that the inner sound field is notdisturbed by reflected waves To this end the buffer zoneboundary condition [31] is implemented in the presentsolver To damp the outgoing waves gradually the magnitudeof the damping coefficients varies as a quadratic functionof the coordinates toward the outer boundary Equations(5) provide the damping equation in the buffer zone Thefluctuation vector is damped in each direction individually
1198761015840(119899)119909
= (1 minus 120590 (119909)) times 1198761015840(119899)
1198761015840(119899)119910
= (1 minus 120590 (119910)) times 1198761015840(119899)
1198761015840(119899)119911
= (1 minus 120590 (119911)) times 1198761015840(119899)
120590 (119909) =2
Δ119909
1003816100381610038161003816100381610038161003816100381610038161 minus
119909119887
minus 119871119887119909
119871119887119909
100381610038161003816100381610038161003816100381610038161003816
2
120590 (119910) =2
Δ119910
1003816100381610038161003816100381610038161003816100381610038161003816
1 minus119910119887
minus 119871119887119910
119871119887119910
1003816100381610038161003816100381610038161003816100381610038161003816
2
120590 (119911) =2
Δ119911
1003816100381610038161003816100381610038161003816100381610038161 minus
119911119887
minus 119871119887119911
119871119887119911
100381610038161003816100381610038161003816100381610038161003816
2
(5)
Here 1198761015840(119899) is the fluctuation vector at each iteration and
with respect to each direction 1198761015840(119899)119909 1198761015840(119899)
119910 and 1198761015840(119899)
119911are
the damped fluctuation vectors 120590(119909) 120590(119910) and 120590(119911) are thedamping coefficients in the buffer zone Δ119909 Δ119910 and Δz arethe mesh spaces 119871
119887119909 119871119887119910 and 119871
119887119911are the widths of the
buffer zone and119909119887 119910119887 and 119911
119887are the distances from the inner
end of buffer zone Figure 5 shows the buffer zone (illustratedas the hatched area) and an expanded view of the bottom leftcorner in a two-dimensional case
3 Evaluation of the Order of Accuracy
The order of accuracy of the present computational methodis evaluated by the one-dimensional wave propagation prob-lem The IBM and Lagrange interpolation are employed intheir three-dimensional forms Equations (6) are the one-dimensional wave equationsThe initial pressure distributionis given by
1205971199011015840
120597119905+
1205971199061015840
1
120597119909= 0
1205971199061015840
1
120597119905+
1205971199011015840
120597119909= 0
(6)
1199011015840
(initial) = 05 times exp [minus(ln 2)
2(1199092
+ 1199102
+ 1199112)] (7)
The root mean square error (RMSE) between the analyticalsolution and the computed solution is computed by
RMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161199011015840(computed) minus 1199011015840
(analytical)100381610038161003816100381610038161003816
2
(8)
The RMSE is computed for two meshes Figure 6 illustratesthe computational cubes with and without cube refinementThe size of the computational domain is 16119863 times 4119863 times 4119863The periodic boundary condition is set at the end of the 119909-directional boundaries The RMSE is also computed in thecase where a wall boundary exists When the wall boundaryexists the wave reflects at the end of the 119909-directionalboundaries
The RMSE and the order of accuracy are listed in Table 1The order of accuracy of each mesh is computed using theRMSEof onemesh and that of a coarsermesh Case 1 employsno wall boundary and is conducted without cube refinementTherefore the prescribed order of accuracy is as shown InCase 2 the order of accuracy is slightly reduced becausethe spatial derivative at the fluid cell adjacent to the GCis conducted using the second-order central difference Theorder of accuracy of Case 3 is approximately two becausethe accuracy of the cube boundary is dominated by theinterpolation from a larger to smaller cube Case 4 providesa slightly smaller order of accuracy than that of Case 3because of the existence of the wall boundary These resultsindicate that the general order of accuracy of the presentcomputational method is approximately two
4 Acoustic Scattering around a Sphere
Acoustic scattering around a sphere [32] is computed undervarious mesh conditions in this section The magnitude oferror relative to an analytical solution and the computational
6 International Journal of Aerospace Engineering
Cube boundary
Fluid cellOverlap cellStencil
Stencils (4 times 4)
Stencils (2 times 2)
(a) From a smaller to larger cube
Cube boundary
Fluid cellOverlap cellStencil
Stencils (3 times 3)
(b) From a larger to smaller cube
Figure 4 Stencils used for Lagrange interpolation in two dimensions
Buffer zone
(a) Buffer zone in the computational domain
Lbx
xb
yb
Lby
Buffer zone
(b) Expanded view of the bottom left corner of (a)
Figure 5 Buffer zone boundary condition
time are compared A sphere is located at the origin of a three-dimensional domain The reference length 119863 is the diameterof the sphere A monopole Gaussian sound source 119878 is givenby the following equation as a function of time t
119878 = exp[minus (ln 2) ((119909 minus 4119863)
2+ 1199102
+ 1199112
(02119863)2
)] sin (6120587) 119905 (9)
The influence of three important parameters on the erroris investigated the minimum cell size around the spherepoints per wavelength (PPW) in the computational domainand the size of the buffer zoneTheminimum cell size aroundthe sphere has an effect on the error generated from the wall
boundary A small cell size not only suppresses the errorbut also restricts the time step size and results in greatercomputational time The PPW is an important factor foracoustic simulations because insufficient PPW introducesdissipation and dispersion errors in wave propagation Thesize of the buffer domain is important for setting the outerboundary condition If the width of the buffer zone is shortthe reflected wave is generated at the outer boundary and thereflected wave disturbs the inner sound field
Figure 7 shows computational domains of the CoarseBCM Middle2 and BCM Fine3meshes listed in Table 2Thegray lines indicate the cube boundaries Table 2 summarizesthe mesh information of all the cases used for the parametric
International Journal of Aerospace Engineering 7
y x
z
(a) Cubes without cube refinement
y x
z
(b) Cubes with cube refinement
Figure 6 Computational cubes for the one-dimensional wave propagation problem
8D
16D
8D
8D
y
x
y
z
(a) Coarse
16D
32D
16D
16D
y
x
y
z
(b) BCM Middle2
16D
32D
16D
16D
y
x
y
z
(c) BCM Fine3
Figure 7 Computational domains and cube boundaries for acoustic scattering around a sphere of diameter D
8 International Journal of Aerospace Engineering
Table 1 Root mean square error and the order of accuracy
Wall Cube refinement Number of cells in one cube Root mean square error Order of accuracy
Case 1 Without Without36 times 36 times 36 1063 times 10minus5 mdash48 times 48 times 48 3422 times 10minus6 394172 times 72 times 72 6887 times 10minus7 3954
Case 2 With Without36 times 36 times 36 1269 times 10minus5 mdash48 times 48 times 48 4145 times 10minus6 389072 times 72 times 72 8326 times 10minus7 3959
Case 3 Without With36 times 36 times 36 1200 times 10minus4 mdash48 times 48 times 48 6574 times 10minus5 209372 times 72 times 72 2890 times 10minus5 2027
Case 4 With With36 times 36 times 36 1258 times 10minus4 mdash48 times 48 times 48 7086 times 10minus5 199572 times 72 times 72 3156 times 10minus5 1995
Table 2 Mesh information for acoustic scattering around a sphere of diameter 119863
Minimum cellsize
Number ofcubes Number of cells in one cube PPW Width of buffer zone
[119909 119910 119911]Coarse 00415D 128 48 times 48 times 48 8 1D 1D 1DUniform Middle 00277D 128 72 times 72 times 72 12 1D 1D 1DBCM Middle1 00208D 184 48 times 48 times 48 8 16 1D 1D 1DBCM Middle2 00208D 296 48 times 48 times 48 4 8 16 9D 5D 5DBCM Middle3 00208D 408 48 times 48 times 48 4 8 16 9D 5D 5DUniform Fine 00208D 128 96 times 96 times 96 16 1D 1D 1DBCM Fine1 00104D 240 48 times 48 times 48 8 16 32 1D 1D 1DBCM Fine2 00104D 352 48 times 48 times 48 4 8 16 32 9D 5D 5DBCM Fine3 00104D 464 48 times 48 times 48 4 8 16 32 9D 5D 5D
study Coarse mesh forms the base mesh of the other meshesemployedThe size of the computational domain is 16119863times8119863times
8119863 referring to [33] where 128 cubes of a size 1119863 times 1119863 times 1119863
constitute the domain as shown in Figure 7(a) The numberof cells in one cube is 48 times 48 times 48 and the PPW is eight Inthe Uniform Middle and Uniform Fine meshes the domainsize and the number of cubes are the same as those of theCoarse mesh The number of cells in one cube is 72 times 72times 72 in the Uniform Middle mesh and 96 times 96 times 96 in theUniform Fine mesh thus the PPW is 12 and 16 respectivelyIn the BCM Middle1 mesh the eight cubes in the Coarsemesh surrounding the sphere are subdivided into half sizecubes Similarly the eight cubes surrounding the sphere aresubdivided from the BCM Middle1 mesh in the BCM Fine1mesh The number of cubes is 184 in the BCM Middle1mesh and 240 in the BCM Fine1 mesh and the maximumPPW is 16 and 32 respectively In the BCM Middle2 meshshown in Figure 7(b) and BCM Fine2 meshes the bufferzone is expanded to add 112 cubes to the BCM Middle1 andBCM Fine1 meshes In the BCM Middle3 and BCM Fine3(shown in Figure 7(c)) meshes eight cubes located at 2 le xle 6 minus2 le y le 2 and minus2 le z le 2 and eight cubes located at minus6le x le minus2 minus2 le y le 2 and minus2 le z le 2 are subdivided from theBCM Middle2 and BCM Fine2 meshes to increase the PPWof the computational domain The inner end of the buffer
zone is set at x = [minus7D 7D] y = [minus3D 3D] and z = [minus3D3D] in all meshes to compare the sizes of the buffer zones
Figure 8 shows the instantaneous pressure distributionaround the sphere computed using the Coarse mesh In thisfigure the buffer zone is not drawn Waves generated fromthe sound source are scattered by the sphere and interferencefringes appear The computation is executed in nondimen-sional time 119879 = 15 and a periodic steady state is observedafter119879 = 11 Figure 9 shows the pressure distributionnear theinner end of the buffer zone and the time history of the pres-sure near the sphere for all meshes The pressure distributionis sampled at minus6119863 le 119909 le minus4119863 on the 119909-axisThe time historyof the pressure is sampled at (minus2D 0 0) and 14 le 119879 le 15
In Figures 9(a) and 9(b) the uniform meshes arecompared The pressure distributions do not follow thedecreasing trend of the analytical solution in Figure 9(a)Reflection occurs at the outer boundary because of theinsufficient width of the buffer zone Additionally theUniform Middle and Uniform Fine meshes show a higherpressure amplitude compared with the pressure distributionof the Coarse mesh It is assumed that the sound wave isdamped at the Coarse mesh because of the insufficient PPWThe time histories of the uniform meshes provide loweramplitudes than the analytical solution
International Journal of Aerospace Engineering 9
Table 3 Comparison of errors relative to an analytical solution and respective computational times for the meshes listed in Table 2
Total number ofcells
Normalized root meansquare error []
Normalizedmaximum error []
Computational time[120583sectimestepcell]
Real time [sec](128 CPUs)
Coarse 14155776 1197 2382 008454 302Uniform Middle 47775744 502 1131 008631 1388BCM Middle1 20348928 362 1486 010891 1088BCM Middle2 32735232 307 714 011027 1710BCM Middle3 45121536 289 734 009665 2172Uniform Fine 113246208 357 1093 007329 4240BCM Fine1 26542080 614 2224 008851 2654BCM Fine2 38928384 304 700 008777 3358BCM Fine3 51314688 162 500 009019 4794
Non
dim
ensio
nal p
ress
ure
000E + 000
minus500E minus 005
500E minus 005
minus100E minus 004
100E minus 004
Figure 8 Instantaneous pressure distribution (Coarse mesh) around a sphere of diameter D
In Figures 9(c) and 9(d) the BCM Middle meshes arecompared The BCM Middle2 and BCM Middle3 meshesfollow the analytical solution in Figure 9(c) These mesheshave a buffer zone of width 9D in the 119909 direction andoutgoing waves are damped appropriately However theBCM Middle2 mesh provides a lower amplitude This isowing to the insufficient PPW at the sampling points On theother hand phase error is not observed in the BCM Middle2mesh In Figure 9(d) the amplitude of the pressure convergesto the analytical solution for the BCM Middle2 mesh Onlythe BCM Middle1 mesh provides a lower amplitude Thisamplitude is the same as that of the uniform meshes There-fore it is confirmed that the amplitude of the inner soundfieldis diminished when using a buffer zone of short width
In Figures 9(e) and 9(f) the BCM Fine meshes arecompared The pressure distributions and the time historiesof the BCM Fine meshes exhibit similar tendencies as thoseof the BCM Middle meshes
To compare the magnitude of errors more quantitativelythe root mean square pressure 119875rms of the scattered soundis computed and the normalized RMSE (NRMSE) and thenormalized maximum error (MME) between the analytical
solution and the solutions of each mesh are compared asgiven by
NRMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
2
NME = max1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
(10)
The number of sampling points 119873 are set clockwise ata radius 119903 = 2D from the origin The points (minus2D 00) and (2D 0 0) correspond to 0 deg and 180 deg Theerrors are summarized in Table 3 As shown in the table therefined meshes provide lower errors than the coarser meshand the meshes that utilize a large buffer zone also providelower errors The minimum cell size around the sphere alsoaffects the errors The smallest errors are provided by theBCM Fine3 mesh A comparison of the uniform and BCMmeshes indicates that the BCM Middle3 and BCM Fine3meshes which use cubes of different sizes at the appropriatelocations provide lower errors than Uniform Middle meshes
10 International Journal of Aerospace Engineering
Non
dim
ensio
nal p
ress
ure
AnalyticalCoarse
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
Uniform_MiddleUniform_Fine
minus6 minus55 minus5 minus45 minus4
x coordinate
(a) Pressure distributions of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
100E minus 04
150E minus 04
AnalyticalCoarse
Uniform_MiddleUniform_Fine
500E minus 05
14 142 144 146 148 15Nondimensional time
(b) Time histories of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
minus6 minus55 minus5 minus45 minus4
x coordinate
(c) Pressure distributions of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
14 142 144 146 148 15Nondimensional time
(d) Time histories of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
minus6 minus55 minus5 minus45 minus4
x coordinate
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(e) Pressure distributions of BCM Fine meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
14 142 144 146 148 15Nondimensional time
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(f) Time histories of BCM Fine meshes
Figure 9 Pressure distributions (minus6119863 le 119909 le minus4119863) and time histories at (minus2D 0 0) and (14 le 119879 le 15) around a sphere of diameter 119863 forthe meshes listed in Table 2
International Journal of Aerospace Engineering 11
that utilize a similar number of mesh points Moreover theerrors of the BCM Fine3 mesh are about one-half the errorsof the Uniform Fine mesh which has twice the number ofmesh points as the BCM Fine3 mesh These results indicatethe effectiveness of the BCM arrangement
The computational wall-clock times for a single timestep per cell and the total wall-clock time required toreach a nondimensional time 119879 = 15 are also listed inTable 3 All meshes were computed using 128CPUs of anSGI AltixUV1000 computer Regarding the wall-clock timeper one time step per cell the computational times of theuniformandBCMmeshes are comparableHowever the totalwall-clock times of the BCM meshes are slightly longer thanthose of the uniform meshes The BCM meshes employ alarger number of cubes than the number of CPUs used in theevaluationThemismatch between the numbers of cubes andCPUs can degrade the load balance Computations using anequivalent number of CPUs and cubes are more effective forBCMmeshes
5 Noise Propagation from the JT15D Nacelle
Noise propagation from the JT15D [34] nacelle is computedand the far-field sound pressure level (SPL) is compared withdata derived from experiment and the computational resultsof others The JT15D is a small Pratt and Whitney turbofanenginewith a bellmouth inletThe sound source is introducedvia a discrete frequency spinning mode The spinning modeinput [35] is a typical sound source generated by the fan orrotor-stator intersections in the engine The sound source ofa single spinning mode (119898 119899) is defined by
119878 = [119869119898
(119896119903119903) + 1198881119884119898
(119896119903119903)] cos (119896119905 minus 119896
119886119909 minus 119898120579) (11)
Here 119869119898and119884119898are themth order Bessel functions of the first
and second kind respectively 119896 is the angular frequency 119896119886
is the axial wavenumber 119896119903is the radial wavenumber and 120579
is the phase The 119899th solution 119896119903of the following equation is
determined by the hard-wall boundary condition of the duct
119889 [119869119898
(119903outer119896119903)]
119889119903
119889 [119884119898
(119903inner119896119903)]
119889119903
minus119889 [119869119898
(119903inner119896119903)]
119889119903
119889 [119884119898
(119903outer119896119903)]
119889119903= 0
(12)
Here 119903outer and 119903inner are the bypass duct inner wall radius andthe inner hub radius respectively The axial wave number 119896
119886
is computed from
119896119886
=119896
1 minus 1198722119895
(minus119872119895
plusmnradic
1 minus1198962
119903(1 minus 119872
2
119895)
1198962) (13)
where 119872119895is the Mach number at the fan face The selection
of plus or minus signs in the parentheses is determined bythe propagation direction of the sound wave where plus(+) represents the positive propagation direction along the
axial coordinate and vice versa The constant 1198881satisfies the
following relation
1198881
= minus(119889119889119903) [119869
119898(119903outer119896119903)]
(119889119889119903) [119884119898
(119903outer119896119903)]
= minus(119889119889119903) [119869
119898(119903inner119896119903)]
(119889119889119903) [119884119898
(119903inner119896119903)]
(14)
Parameters are set from experimental data (119898 119899) =
(minus13 0) 119903outer = 02667m and 119903inner = 00998m Thereference length D = 06223mis the length from the fanface to the leading edge of the nacelle The blade passingfrequency (BPF) is set to 3150Hz which is derived fromthe fan rotating speed of 6750 rpm The experiments wereconducted in the static condition and the fan face axial Machnumber is 0175 The present computation is also conductedin the static condition In the present computation the axialflow velocity of the ghost cell at the fan face boundary isdirectly modified to this Mach number The pressure andthe density are the same values as those of the adjacent fluidcells The SPL is measured at a radius of 49D The integrationmethod of Ffowcs-Williams and Hawkings (FW-H) [36] isemployed to estimate the far-field pressure from thenear-fieldpressure
Figure 10 shows the computational domain and Table 4lists the mesh information The computations of the com-pressible Euler solver and the LEEs solver are conductedusing the samemeshThePPW inTable 4 is the PPWreducedby the Doppler effect of the fan face axial Mach number Thecomputational domain is set at minus1119863 le 119909 le 7119863 minus8119863 le 119910 le
8119863 and minus8119863 le 119911 le 8119863The fan face is at 119909 = 05119863The innerend of the buffer zone is set at 119909 = [0 4119863] 119910 = [minus4119863 4119863]and 119911 = [minus4119863 4119863] The FW-H surfaces are located at thecube boundaries between the smallest size cubes and thelarger size cubes
Figure 11 shows theMachnumber distribution around theJT15D nacelle In Figure 11 the acceleration region near theinternal wall of the nacelle lip and the stagnation at the spikeare shown Because the experiments and computations wereconducted under the static condition the mean flow fieldexists only near the nacelle
Figure 12 shows the instantaneous pressure distributionsat the planes defined at 119911 = 0 and 119909 = 17119863 In the figure onlythe distributions of the smallest sized cubes are drawn Thefan noise is diffracted at the inlet of the nacelle and propagatesalong the radial direction The 13 peaks and valleys of theswirling fan noise at the 119909 = 17119863 plane are clearly capturedwhich is equivalent to the number of spinning modes Thetime history of the pressure is sampled at the establishedpoints on the FW-H surface and the periodic steady state isobserved after 119879 = 8
Figure 13 shows a comparison of the predicted SPL withthe experimental results conducted by Heidmann et al [37]and the computational results computed by Lan et al [34]The horizontal axis in the figure is the angle from the +119909-axialdirection In the figure the predicted SPL using the presentsolver shows good agreement with the computational resultof Lan et al (within 1 dB) Compared with the experimental
12 International Journal of Aerospace Engineering
Table 4 Mesh information for the JT15D nacelle
JT15D Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWCase 1 00166D 1544 30 times 30 times 30 41688000 87Case 2 00125D 1544 40 times 40 times 40 98816000 116
16D
8D
16D
16D
y
x
yzy
x z
Figure 10 Computational domain for the JT15D nacelle
Mac
h nu
mbe
r
02000100
0000
Figure 11 Mach number distribution around the JT15D nacelle
data a difference of about 3 dB is found at 60 deg Howeverthis discrepancy is also shown between the experimental dataand the result of Lan et al The SPL peak obtained near55 deg is equivalent to that obtained by Lan et al and thatobtained experimentally
6 Noise Propagation arounda Fuselage-Wing-Nacelle Configuration
The noise propagation around a fuselage-wing-nacelle con-figuration is computed as a realistic exampleThe focus of theexample was that of the OWN configuration [38] where theengine nacelle is mounted over the main wing which servesas one of the configurations designed to achieve substantialairport noise reduction The main feature of this configu-ration is that the main wing serves as a shield between the
ground and the noise generated by the engine To investigatethe effect of the OWN configuration the propagation of fannoise of both the conventional DLR-F6 aircraft configuration[39] and the OWN configuration is computed and the SPLbelow the aircraft for both configurations is comparedTheseconfigurations have complex geometry with large curvaturesnear the wing-body and the nacelle-pylon junctions In theOWN configuration the nacelle is moved 11D in the +119909
direction and 06D in the +y direction relative to its locationin the DLR-F6 configuration Here the reference length 119863 =
49m is the longitudinal length of the nacelle The cross-sectional geometry of the pylon is used without any changesand has a sweepback angle of 40 deg A mean flow fieldof Mach number 03 with zero angle of attack is computedusing the compressible Euler solver The sound source isintroduced via a discrete frequency spinning mode As anexample of a modern turbofan engine the CFM56-7B engineis considered The bypass ratio is 55 the fan diameter is154m the number of blades is 24 the maximum rotationalrate is 5382 rpm and the fundamental BPF is 21528HzTheBPF is used as the input frequency of the spinning modeThespinning mode (119898 119899) is set to (minus24 0) The SPL is measuredat a radius of 10D using the FW-H method
Figure 14 shows the computational domain of each con-figuration The black dot shows the origin of coordinatesystem The computations of the compressible Euler andLEEs solvers are conducted using an equivalent mesh Thesize of the computational domains is 4119863 times 2119863 times 2119863 Thesymmetric boundary condition is set at the minusz boundaryThe computational domains are set to ensure that sufficientcomputational domains surround the nacelle It is assumedthat the geometry out of the computational domain has littleinfluence on the noise directivity below the aircraft The
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
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6 International Journal of Aerospace Engineering
Cube boundary
Fluid cellOverlap cellStencil
Stencils (4 times 4)
Stencils (2 times 2)
(a) From a smaller to larger cube
Cube boundary
Fluid cellOverlap cellStencil
Stencils (3 times 3)
(b) From a larger to smaller cube
Figure 4 Stencils used for Lagrange interpolation in two dimensions
Buffer zone
(a) Buffer zone in the computational domain
Lbx
xb
yb
Lby
Buffer zone
(b) Expanded view of the bottom left corner of (a)
Figure 5 Buffer zone boundary condition
time are compared A sphere is located at the origin of a three-dimensional domain The reference length 119863 is the diameterof the sphere A monopole Gaussian sound source 119878 is givenby the following equation as a function of time t
119878 = exp[minus (ln 2) ((119909 minus 4119863)
2+ 1199102
+ 1199112
(02119863)2
)] sin (6120587) 119905 (9)
The influence of three important parameters on the erroris investigated the minimum cell size around the spherepoints per wavelength (PPW) in the computational domainand the size of the buffer zoneTheminimum cell size aroundthe sphere has an effect on the error generated from the wall
boundary A small cell size not only suppresses the errorbut also restricts the time step size and results in greatercomputational time The PPW is an important factor foracoustic simulations because insufficient PPW introducesdissipation and dispersion errors in wave propagation Thesize of the buffer domain is important for setting the outerboundary condition If the width of the buffer zone is shortthe reflected wave is generated at the outer boundary and thereflected wave disturbs the inner sound field
Figure 7 shows computational domains of the CoarseBCM Middle2 and BCM Fine3meshes listed in Table 2Thegray lines indicate the cube boundaries Table 2 summarizesthe mesh information of all the cases used for the parametric
International Journal of Aerospace Engineering 7
y x
z
(a) Cubes without cube refinement
y x
z
(b) Cubes with cube refinement
Figure 6 Computational cubes for the one-dimensional wave propagation problem
8D
16D
8D
8D
y
x
y
z
(a) Coarse
16D
32D
16D
16D
y
x
y
z
(b) BCM Middle2
16D
32D
16D
16D
y
x
y
z
(c) BCM Fine3
Figure 7 Computational domains and cube boundaries for acoustic scattering around a sphere of diameter D
8 International Journal of Aerospace Engineering
Table 1 Root mean square error and the order of accuracy
Wall Cube refinement Number of cells in one cube Root mean square error Order of accuracy
Case 1 Without Without36 times 36 times 36 1063 times 10minus5 mdash48 times 48 times 48 3422 times 10minus6 394172 times 72 times 72 6887 times 10minus7 3954
Case 2 With Without36 times 36 times 36 1269 times 10minus5 mdash48 times 48 times 48 4145 times 10minus6 389072 times 72 times 72 8326 times 10minus7 3959
Case 3 Without With36 times 36 times 36 1200 times 10minus4 mdash48 times 48 times 48 6574 times 10minus5 209372 times 72 times 72 2890 times 10minus5 2027
Case 4 With With36 times 36 times 36 1258 times 10minus4 mdash48 times 48 times 48 7086 times 10minus5 199572 times 72 times 72 3156 times 10minus5 1995
Table 2 Mesh information for acoustic scattering around a sphere of diameter 119863
Minimum cellsize
Number ofcubes Number of cells in one cube PPW Width of buffer zone
[119909 119910 119911]Coarse 00415D 128 48 times 48 times 48 8 1D 1D 1DUniform Middle 00277D 128 72 times 72 times 72 12 1D 1D 1DBCM Middle1 00208D 184 48 times 48 times 48 8 16 1D 1D 1DBCM Middle2 00208D 296 48 times 48 times 48 4 8 16 9D 5D 5DBCM Middle3 00208D 408 48 times 48 times 48 4 8 16 9D 5D 5DUniform Fine 00208D 128 96 times 96 times 96 16 1D 1D 1DBCM Fine1 00104D 240 48 times 48 times 48 8 16 32 1D 1D 1DBCM Fine2 00104D 352 48 times 48 times 48 4 8 16 32 9D 5D 5DBCM Fine3 00104D 464 48 times 48 times 48 4 8 16 32 9D 5D 5D
study Coarse mesh forms the base mesh of the other meshesemployedThe size of the computational domain is 16119863times8119863times
8119863 referring to [33] where 128 cubes of a size 1119863 times 1119863 times 1119863
constitute the domain as shown in Figure 7(a) The numberof cells in one cube is 48 times 48 times 48 and the PPW is eight Inthe Uniform Middle and Uniform Fine meshes the domainsize and the number of cubes are the same as those of theCoarse mesh The number of cells in one cube is 72 times 72times 72 in the Uniform Middle mesh and 96 times 96 times 96 in theUniform Fine mesh thus the PPW is 12 and 16 respectivelyIn the BCM Middle1 mesh the eight cubes in the Coarsemesh surrounding the sphere are subdivided into half sizecubes Similarly the eight cubes surrounding the sphere aresubdivided from the BCM Middle1 mesh in the BCM Fine1mesh The number of cubes is 184 in the BCM Middle1mesh and 240 in the BCM Fine1 mesh and the maximumPPW is 16 and 32 respectively In the BCM Middle2 meshshown in Figure 7(b) and BCM Fine2 meshes the bufferzone is expanded to add 112 cubes to the BCM Middle1 andBCM Fine1 meshes In the BCM Middle3 and BCM Fine3(shown in Figure 7(c)) meshes eight cubes located at 2 le xle 6 minus2 le y le 2 and minus2 le z le 2 and eight cubes located at minus6le x le minus2 minus2 le y le 2 and minus2 le z le 2 are subdivided from theBCM Middle2 and BCM Fine2 meshes to increase the PPWof the computational domain The inner end of the buffer
zone is set at x = [minus7D 7D] y = [minus3D 3D] and z = [minus3D3D] in all meshes to compare the sizes of the buffer zones
Figure 8 shows the instantaneous pressure distributionaround the sphere computed using the Coarse mesh In thisfigure the buffer zone is not drawn Waves generated fromthe sound source are scattered by the sphere and interferencefringes appear The computation is executed in nondimen-sional time 119879 = 15 and a periodic steady state is observedafter119879 = 11 Figure 9 shows the pressure distributionnear theinner end of the buffer zone and the time history of the pres-sure near the sphere for all meshes The pressure distributionis sampled at minus6119863 le 119909 le minus4119863 on the 119909-axisThe time historyof the pressure is sampled at (minus2D 0 0) and 14 le 119879 le 15
In Figures 9(a) and 9(b) the uniform meshes arecompared The pressure distributions do not follow thedecreasing trend of the analytical solution in Figure 9(a)Reflection occurs at the outer boundary because of theinsufficient width of the buffer zone Additionally theUniform Middle and Uniform Fine meshes show a higherpressure amplitude compared with the pressure distributionof the Coarse mesh It is assumed that the sound wave isdamped at the Coarse mesh because of the insufficient PPWThe time histories of the uniform meshes provide loweramplitudes than the analytical solution
International Journal of Aerospace Engineering 9
Table 3 Comparison of errors relative to an analytical solution and respective computational times for the meshes listed in Table 2
Total number ofcells
Normalized root meansquare error []
Normalizedmaximum error []
Computational time[120583sectimestepcell]
Real time [sec](128 CPUs)
Coarse 14155776 1197 2382 008454 302Uniform Middle 47775744 502 1131 008631 1388BCM Middle1 20348928 362 1486 010891 1088BCM Middle2 32735232 307 714 011027 1710BCM Middle3 45121536 289 734 009665 2172Uniform Fine 113246208 357 1093 007329 4240BCM Fine1 26542080 614 2224 008851 2654BCM Fine2 38928384 304 700 008777 3358BCM Fine3 51314688 162 500 009019 4794
Non
dim
ensio
nal p
ress
ure
000E + 000
minus500E minus 005
500E minus 005
minus100E minus 004
100E minus 004
Figure 8 Instantaneous pressure distribution (Coarse mesh) around a sphere of diameter D
In Figures 9(c) and 9(d) the BCM Middle meshes arecompared The BCM Middle2 and BCM Middle3 meshesfollow the analytical solution in Figure 9(c) These mesheshave a buffer zone of width 9D in the 119909 direction andoutgoing waves are damped appropriately However theBCM Middle2 mesh provides a lower amplitude This isowing to the insufficient PPW at the sampling points On theother hand phase error is not observed in the BCM Middle2mesh In Figure 9(d) the amplitude of the pressure convergesto the analytical solution for the BCM Middle2 mesh Onlythe BCM Middle1 mesh provides a lower amplitude Thisamplitude is the same as that of the uniform meshes There-fore it is confirmed that the amplitude of the inner soundfieldis diminished when using a buffer zone of short width
In Figures 9(e) and 9(f) the BCM Fine meshes arecompared The pressure distributions and the time historiesof the BCM Fine meshes exhibit similar tendencies as thoseof the BCM Middle meshes
To compare the magnitude of errors more quantitativelythe root mean square pressure 119875rms of the scattered soundis computed and the normalized RMSE (NRMSE) and thenormalized maximum error (MME) between the analytical
solution and the solutions of each mesh are compared asgiven by
NRMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
2
NME = max1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
(10)
The number of sampling points 119873 are set clockwise ata radius 119903 = 2D from the origin The points (minus2D 00) and (2D 0 0) correspond to 0 deg and 180 deg Theerrors are summarized in Table 3 As shown in the table therefined meshes provide lower errors than the coarser meshand the meshes that utilize a large buffer zone also providelower errors The minimum cell size around the sphere alsoaffects the errors The smallest errors are provided by theBCM Fine3 mesh A comparison of the uniform and BCMmeshes indicates that the BCM Middle3 and BCM Fine3meshes which use cubes of different sizes at the appropriatelocations provide lower errors than Uniform Middle meshes
10 International Journal of Aerospace Engineering
Non
dim
ensio
nal p
ress
ure
AnalyticalCoarse
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
Uniform_MiddleUniform_Fine
minus6 minus55 minus5 minus45 minus4
x coordinate
(a) Pressure distributions of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
100E minus 04
150E minus 04
AnalyticalCoarse
Uniform_MiddleUniform_Fine
500E minus 05
14 142 144 146 148 15Nondimensional time
(b) Time histories of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
minus6 minus55 minus5 minus45 minus4
x coordinate
(c) Pressure distributions of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
14 142 144 146 148 15Nondimensional time
(d) Time histories of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
minus6 minus55 minus5 minus45 minus4
x coordinate
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(e) Pressure distributions of BCM Fine meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
14 142 144 146 148 15Nondimensional time
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(f) Time histories of BCM Fine meshes
Figure 9 Pressure distributions (minus6119863 le 119909 le minus4119863) and time histories at (minus2D 0 0) and (14 le 119879 le 15) around a sphere of diameter 119863 forthe meshes listed in Table 2
International Journal of Aerospace Engineering 11
that utilize a similar number of mesh points Moreover theerrors of the BCM Fine3 mesh are about one-half the errorsof the Uniform Fine mesh which has twice the number ofmesh points as the BCM Fine3 mesh These results indicatethe effectiveness of the BCM arrangement
The computational wall-clock times for a single timestep per cell and the total wall-clock time required toreach a nondimensional time 119879 = 15 are also listed inTable 3 All meshes were computed using 128CPUs of anSGI AltixUV1000 computer Regarding the wall-clock timeper one time step per cell the computational times of theuniformandBCMmeshes are comparableHowever the totalwall-clock times of the BCM meshes are slightly longer thanthose of the uniform meshes The BCM meshes employ alarger number of cubes than the number of CPUs used in theevaluationThemismatch between the numbers of cubes andCPUs can degrade the load balance Computations using anequivalent number of CPUs and cubes are more effective forBCMmeshes
5 Noise Propagation from the JT15D Nacelle
Noise propagation from the JT15D [34] nacelle is computedand the far-field sound pressure level (SPL) is compared withdata derived from experiment and the computational resultsof others The JT15D is a small Pratt and Whitney turbofanenginewith a bellmouth inletThe sound source is introducedvia a discrete frequency spinning mode The spinning modeinput [35] is a typical sound source generated by the fan orrotor-stator intersections in the engine The sound source ofa single spinning mode (119898 119899) is defined by
119878 = [119869119898
(119896119903119903) + 1198881119884119898
(119896119903119903)] cos (119896119905 minus 119896
119886119909 minus 119898120579) (11)
Here 119869119898and119884119898are themth order Bessel functions of the first
and second kind respectively 119896 is the angular frequency 119896119886
is the axial wavenumber 119896119903is the radial wavenumber and 120579
is the phase The 119899th solution 119896119903of the following equation is
determined by the hard-wall boundary condition of the duct
119889 [119869119898
(119903outer119896119903)]
119889119903
119889 [119884119898
(119903inner119896119903)]
119889119903
minus119889 [119869119898
(119903inner119896119903)]
119889119903
119889 [119884119898
(119903outer119896119903)]
119889119903= 0
(12)
Here 119903outer and 119903inner are the bypass duct inner wall radius andthe inner hub radius respectively The axial wave number 119896
119886
is computed from
119896119886
=119896
1 minus 1198722119895
(minus119872119895
plusmnradic
1 minus1198962
119903(1 minus 119872
2
119895)
1198962) (13)
where 119872119895is the Mach number at the fan face The selection
of plus or minus signs in the parentheses is determined bythe propagation direction of the sound wave where plus(+) represents the positive propagation direction along the
axial coordinate and vice versa The constant 1198881satisfies the
following relation
1198881
= minus(119889119889119903) [119869
119898(119903outer119896119903)]
(119889119889119903) [119884119898
(119903outer119896119903)]
= minus(119889119889119903) [119869
119898(119903inner119896119903)]
(119889119889119903) [119884119898
(119903inner119896119903)]
(14)
Parameters are set from experimental data (119898 119899) =
(minus13 0) 119903outer = 02667m and 119903inner = 00998m Thereference length D = 06223mis the length from the fanface to the leading edge of the nacelle The blade passingfrequency (BPF) is set to 3150Hz which is derived fromthe fan rotating speed of 6750 rpm The experiments wereconducted in the static condition and the fan face axial Machnumber is 0175 The present computation is also conductedin the static condition In the present computation the axialflow velocity of the ghost cell at the fan face boundary isdirectly modified to this Mach number The pressure andthe density are the same values as those of the adjacent fluidcells The SPL is measured at a radius of 49D The integrationmethod of Ffowcs-Williams and Hawkings (FW-H) [36] isemployed to estimate the far-field pressure from thenear-fieldpressure
Figure 10 shows the computational domain and Table 4lists the mesh information The computations of the com-pressible Euler solver and the LEEs solver are conductedusing the samemeshThePPW inTable 4 is the PPWreducedby the Doppler effect of the fan face axial Mach number Thecomputational domain is set at minus1119863 le 119909 le 7119863 minus8119863 le 119910 le
8119863 and minus8119863 le 119911 le 8119863The fan face is at 119909 = 05119863The innerend of the buffer zone is set at 119909 = [0 4119863] 119910 = [minus4119863 4119863]and 119911 = [minus4119863 4119863] The FW-H surfaces are located at thecube boundaries between the smallest size cubes and thelarger size cubes
Figure 11 shows theMachnumber distribution around theJT15D nacelle In Figure 11 the acceleration region near theinternal wall of the nacelle lip and the stagnation at the spikeare shown Because the experiments and computations wereconducted under the static condition the mean flow fieldexists only near the nacelle
Figure 12 shows the instantaneous pressure distributionsat the planes defined at 119911 = 0 and 119909 = 17119863 In the figure onlythe distributions of the smallest sized cubes are drawn Thefan noise is diffracted at the inlet of the nacelle and propagatesalong the radial direction The 13 peaks and valleys of theswirling fan noise at the 119909 = 17119863 plane are clearly capturedwhich is equivalent to the number of spinning modes Thetime history of the pressure is sampled at the establishedpoints on the FW-H surface and the periodic steady state isobserved after 119879 = 8
Figure 13 shows a comparison of the predicted SPL withthe experimental results conducted by Heidmann et al [37]and the computational results computed by Lan et al [34]The horizontal axis in the figure is the angle from the +119909-axialdirection In the figure the predicted SPL using the presentsolver shows good agreement with the computational resultof Lan et al (within 1 dB) Compared with the experimental
12 International Journal of Aerospace Engineering
Table 4 Mesh information for the JT15D nacelle
JT15D Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWCase 1 00166D 1544 30 times 30 times 30 41688000 87Case 2 00125D 1544 40 times 40 times 40 98816000 116
16D
8D
16D
16D
y
x
yzy
x z
Figure 10 Computational domain for the JT15D nacelle
Mac
h nu
mbe
r
02000100
0000
Figure 11 Mach number distribution around the JT15D nacelle
data a difference of about 3 dB is found at 60 deg Howeverthis discrepancy is also shown between the experimental dataand the result of Lan et al The SPL peak obtained near55 deg is equivalent to that obtained by Lan et al and thatobtained experimentally
6 Noise Propagation arounda Fuselage-Wing-Nacelle Configuration
The noise propagation around a fuselage-wing-nacelle con-figuration is computed as a realistic exampleThe focus of theexample was that of the OWN configuration [38] where theengine nacelle is mounted over the main wing which servesas one of the configurations designed to achieve substantialairport noise reduction The main feature of this configu-ration is that the main wing serves as a shield between the
ground and the noise generated by the engine To investigatethe effect of the OWN configuration the propagation of fannoise of both the conventional DLR-F6 aircraft configuration[39] and the OWN configuration is computed and the SPLbelow the aircraft for both configurations is comparedTheseconfigurations have complex geometry with large curvaturesnear the wing-body and the nacelle-pylon junctions In theOWN configuration the nacelle is moved 11D in the +119909
direction and 06D in the +y direction relative to its locationin the DLR-F6 configuration Here the reference length 119863 =
49m is the longitudinal length of the nacelle The cross-sectional geometry of the pylon is used without any changesand has a sweepback angle of 40 deg A mean flow fieldof Mach number 03 with zero angle of attack is computedusing the compressible Euler solver The sound source isintroduced via a discrete frequency spinning mode As anexample of a modern turbofan engine the CFM56-7B engineis considered The bypass ratio is 55 the fan diameter is154m the number of blades is 24 the maximum rotationalrate is 5382 rpm and the fundamental BPF is 21528HzTheBPF is used as the input frequency of the spinning modeThespinning mode (119898 119899) is set to (minus24 0) The SPL is measuredat a radius of 10D using the FW-H method
Figure 14 shows the computational domain of each con-figuration The black dot shows the origin of coordinatesystem The computations of the compressible Euler andLEEs solvers are conducted using an equivalent mesh Thesize of the computational domains is 4119863 times 2119863 times 2119863 Thesymmetric boundary condition is set at the minusz boundaryThe computational domains are set to ensure that sufficientcomputational domains surround the nacelle It is assumedthat the geometry out of the computational domain has littleinfluence on the noise directivity below the aircraft The
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Active and Passive Electronic Components
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
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Civil EngineeringAdvances in
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Electrical and Computer Engineering
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Navigation and Observation
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DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 7
y x
z
(a) Cubes without cube refinement
y x
z
(b) Cubes with cube refinement
Figure 6 Computational cubes for the one-dimensional wave propagation problem
8D
16D
8D
8D
y
x
y
z
(a) Coarse
16D
32D
16D
16D
y
x
y
z
(b) BCM Middle2
16D
32D
16D
16D
y
x
y
z
(c) BCM Fine3
Figure 7 Computational domains and cube boundaries for acoustic scattering around a sphere of diameter D
8 International Journal of Aerospace Engineering
Table 1 Root mean square error and the order of accuracy
Wall Cube refinement Number of cells in one cube Root mean square error Order of accuracy
Case 1 Without Without36 times 36 times 36 1063 times 10minus5 mdash48 times 48 times 48 3422 times 10minus6 394172 times 72 times 72 6887 times 10minus7 3954
Case 2 With Without36 times 36 times 36 1269 times 10minus5 mdash48 times 48 times 48 4145 times 10minus6 389072 times 72 times 72 8326 times 10minus7 3959
Case 3 Without With36 times 36 times 36 1200 times 10minus4 mdash48 times 48 times 48 6574 times 10minus5 209372 times 72 times 72 2890 times 10minus5 2027
Case 4 With With36 times 36 times 36 1258 times 10minus4 mdash48 times 48 times 48 7086 times 10minus5 199572 times 72 times 72 3156 times 10minus5 1995
Table 2 Mesh information for acoustic scattering around a sphere of diameter 119863
Minimum cellsize
Number ofcubes Number of cells in one cube PPW Width of buffer zone
[119909 119910 119911]Coarse 00415D 128 48 times 48 times 48 8 1D 1D 1DUniform Middle 00277D 128 72 times 72 times 72 12 1D 1D 1DBCM Middle1 00208D 184 48 times 48 times 48 8 16 1D 1D 1DBCM Middle2 00208D 296 48 times 48 times 48 4 8 16 9D 5D 5DBCM Middle3 00208D 408 48 times 48 times 48 4 8 16 9D 5D 5DUniform Fine 00208D 128 96 times 96 times 96 16 1D 1D 1DBCM Fine1 00104D 240 48 times 48 times 48 8 16 32 1D 1D 1DBCM Fine2 00104D 352 48 times 48 times 48 4 8 16 32 9D 5D 5DBCM Fine3 00104D 464 48 times 48 times 48 4 8 16 32 9D 5D 5D
study Coarse mesh forms the base mesh of the other meshesemployedThe size of the computational domain is 16119863times8119863times
8119863 referring to [33] where 128 cubes of a size 1119863 times 1119863 times 1119863
constitute the domain as shown in Figure 7(a) The numberof cells in one cube is 48 times 48 times 48 and the PPW is eight Inthe Uniform Middle and Uniform Fine meshes the domainsize and the number of cubes are the same as those of theCoarse mesh The number of cells in one cube is 72 times 72times 72 in the Uniform Middle mesh and 96 times 96 times 96 in theUniform Fine mesh thus the PPW is 12 and 16 respectivelyIn the BCM Middle1 mesh the eight cubes in the Coarsemesh surrounding the sphere are subdivided into half sizecubes Similarly the eight cubes surrounding the sphere aresubdivided from the BCM Middle1 mesh in the BCM Fine1mesh The number of cubes is 184 in the BCM Middle1mesh and 240 in the BCM Fine1 mesh and the maximumPPW is 16 and 32 respectively In the BCM Middle2 meshshown in Figure 7(b) and BCM Fine2 meshes the bufferzone is expanded to add 112 cubes to the BCM Middle1 andBCM Fine1 meshes In the BCM Middle3 and BCM Fine3(shown in Figure 7(c)) meshes eight cubes located at 2 le xle 6 minus2 le y le 2 and minus2 le z le 2 and eight cubes located at minus6le x le minus2 minus2 le y le 2 and minus2 le z le 2 are subdivided from theBCM Middle2 and BCM Fine2 meshes to increase the PPWof the computational domain The inner end of the buffer
zone is set at x = [minus7D 7D] y = [minus3D 3D] and z = [minus3D3D] in all meshes to compare the sizes of the buffer zones
Figure 8 shows the instantaneous pressure distributionaround the sphere computed using the Coarse mesh In thisfigure the buffer zone is not drawn Waves generated fromthe sound source are scattered by the sphere and interferencefringes appear The computation is executed in nondimen-sional time 119879 = 15 and a periodic steady state is observedafter119879 = 11 Figure 9 shows the pressure distributionnear theinner end of the buffer zone and the time history of the pres-sure near the sphere for all meshes The pressure distributionis sampled at minus6119863 le 119909 le minus4119863 on the 119909-axisThe time historyof the pressure is sampled at (minus2D 0 0) and 14 le 119879 le 15
In Figures 9(a) and 9(b) the uniform meshes arecompared The pressure distributions do not follow thedecreasing trend of the analytical solution in Figure 9(a)Reflection occurs at the outer boundary because of theinsufficient width of the buffer zone Additionally theUniform Middle and Uniform Fine meshes show a higherpressure amplitude compared with the pressure distributionof the Coarse mesh It is assumed that the sound wave isdamped at the Coarse mesh because of the insufficient PPWThe time histories of the uniform meshes provide loweramplitudes than the analytical solution
International Journal of Aerospace Engineering 9
Table 3 Comparison of errors relative to an analytical solution and respective computational times for the meshes listed in Table 2
Total number ofcells
Normalized root meansquare error []
Normalizedmaximum error []
Computational time[120583sectimestepcell]
Real time [sec](128 CPUs)
Coarse 14155776 1197 2382 008454 302Uniform Middle 47775744 502 1131 008631 1388BCM Middle1 20348928 362 1486 010891 1088BCM Middle2 32735232 307 714 011027 1710BCM Middle3 45121536 289 734 009665 2172Uniform Fine 113246208 357 1093 007329 4240BCM Fine1 26542080 614 2224 008851 2654BCM Fine2 38928384 304 700 008777 3358BCM Fine3 51314688 162 500 009019 4794
Non
dim
ensio
nal p
ress
ure
000E + 000
minus500E minus 005
500E minus 005
minus100E minus 004
100E minus 004
Figure 8 Instantaneous pressure distribution (Coarse mesh) around a sphere of diameter D
In Figures 9(c) and 9(d) the BCM Middle meshes arecompared The BCM Middle2 and BCM Middle3 meshesfollow the analytical solution in Figure 9(c) These mesheshave a buffer zone of width 9D in the 119909 direction andoutgoing waves are damped appropriately However theBCM Middle2 mesh provides a lower amplitude This isowing to the insufficient PPW at the sampling points On theother hand phase error is not observed in the BCM Middle2mesh In Figure 9(d) the amplitude of the pressure convergesto the analytical solution for the BCM Middle2 mesh Onlythe BCM Middle1 mesh provides a lower amplitude Thisamplitude is the same as that of the uniform meshes There-fore it is confirmed that the amplitude of the inner soundfieldis diminished when using a buffer zone of short width
In Figures 9(e) and 9(f) the BCM Fine meshes arecompared The pressure distributions and the time historiesof the BCM Fine meshes exhibit similar tendencies as thoseof the BCM Middle meshes
To compare the magnitude of errors more quantitativelythe root mean square pressure 119875rms of the scattered soundis computed and the normalized RMSE (NRMSE) and thenormalized maximum error (MME) between the analytical
solution and the solutions of each mesh are compared asgiven by
NRMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
2
NME = max1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
(10)
The number of sampling points 119873 are set clockwise ata radius 119903 = 2D from the origin The points (minus2D 00) and (2D 0 0) correspond to 0 deg and 180 deg Theerrors are summarized in Table 3 As shown in the table therefined meshes provide lower errors than the coarser meshand the meshes that utilize a large buffer zone also providelower errors The minimum cell size around the sphere alsoaffects the errors The smallest errors are provided by theBCM Fine3 mesh A comparison of the uniform and BCMmeshes indicates that the BCM Middle3 and BCM Fine3meshes which use cubes of different sizes at the appropriatelocations provide lower errors than Uniform Middle meshes
10 International Journal of Aerospace Engineering
Non
dim
ensio
nal p
ress
ure
AnalyticalCoarse
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
Uniform_MiddleUniform_Fine
minus6 minus55 minus5 minus45 minus4
x coordinate
(a) Pressure distributions of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
100E minus 04
150E minus 04
AnalyticalCoarse
Uniform_MiddleUniform_Fine
500E minus 05
14 142 144 146 148 15Nondimensional time
(b) Time histories of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
minus6 minus55 minus5 minus45 minus4
x coordinate
(c) Pressure distributions of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
14 142 144 146 148 15Nondimensional time
(d) Time histories of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
minus6 minus55 minus5 minus45 minus4
x coordinate
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(e) Pressure distributions of BCM Fine meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
14 142 144 146 148 15Nondimensional time
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(f) Time histories of BCM Fine meshes
Figure 9 Pressure distributions (minus6119863 le 119909 le minus4119863) and time histories at (minus2D 0 0) and (14 le 119879 le 15) around a sphere of diameter 119863 forthe meshes listed in Table 2
International Journal of Aerospace Engineering 11
that utilize a similar number of mesh points Moreover theerrors of the BCM Fine3 mesh are about one-half the errorsof the Uniform Fine mesh which has twice the number ofmesh points as the BCM Fine3 mesh These results indicatethe effectiveness of the BCM arrangement
The computational wall-clock times for a single timestep per cell and the total wall-clock time required toreach a nondimensional time 119879 = 15 are also listed inTable 3 All meshes were computed using 128CPUs of anSGI AltixUV1000 computer Regarding the wall-clock timeper one time step per cell the computational times of theuniformandBCMmeshes are comparableHowever the totalwall-clock times of the BCM meshes are slightly longer thanthose of the uniform meshes The BCM meshes employ alarger number of cubes than the number of CPUs used in theevaluationThemismatch between the numbers of cubes andCPUs can degrade the load balance Computations using anequivalent number of CPUs and cubes are more effective forBCMmeshes
5 Noise Propagation from the JT15D Nacelle
Noise propagation from the JT15D [34] nacelle is computedand the far-field sound pressure level (SPL) is compared withdata derived from experiment and the computational resultsof others The JT15D is a small Pratt and Whitney turbofanenginewith a bellmouth inletThe sound source is introducedvia a discrete frequency spinning mode The spinning modeinput [35] is a typical sound source generated by the fan orrotor-stator intersections in the engine The sound source ofa single spinning mode (119898 119899) is defined by
119878 = [119869119898
(119896119903119903) + 1198881119884119898
(119896119903119903)] cos (119896119905 minus 119896
119886119909 minus 119898120579) (11)
Here 119869119898and119884119898are themth order Bessel functions of the first
and second kind respectively 119896 is the angular frequency 119896119886
is the axial wavenumber 119896119903is the radial wavenumber and 120579
is the phase The 119899th solution 119896119903of the following equation is
determined by the hard-wall boundary condition of the duct
119889 [119869119898
(119903outer119896119903)]
119889119903
119889 [119884119898
(119903inner119896119903)]
119889119903
minus119889 [119869119898
(119903inner119896119903)]
119889119903
119889 [119884119898
(119903outer119896119903)]
119889119903= 0
(12)
Here 119903outer and 119903inner are the bypass duct inner wall radius andthe inner hub radius respectively The axial wave number 119896
119886
is computed from
119896119886
=119896
1 minus 1198722119895
(minus119872119895
plusmnradic
1 minus1198962
119903(1 minus 119872
2
119895)
1198962) (13)
where 119872119895is the Mach number at the fan face The selection
of plus or minus signs in the parentheses is determined bythe propagation direction of the sound wave where plus(+) represents the positive propagation direction along the
axial coordinate and vice versa The constant 1198881satisfies the
following relation
1198881
= minus(119889119889119903) [119869
119898(119903outer119896119903)]
(119889119889119903) [119884119898
(119903outer119896119903)]
= minus(119889119889119903) [119869
119898(119903inner119896119903)]
(119889119889119903) [119884119898
(119903inner119896119903)]
(14)
Parameters are set from experimental data (119898 119899) =
(minus13 0) 119903outer = 02667m and 119903inner = 00998m Thereference length D = 06223mis the length from the fanface to the leading edge of the nacelle The blade passingfrequency (BPF) is set to 3150Hz which is derived fromthe fan rotating speed of 6750 rpm The experiments wereconducted in the static condition and the fan face axial Machnumber is 0175 The present computation is also conductedin the static condition In the present computation the axialflow velocity of the ghost cell at the fan face boundary isdirectly modified to this Mach number The pressure andthe density are the same values as those of the adjacent fluidcells The SPL is measured at a radius of 49D The integrationmethod of Ffowcs-Williams and Hawkings (FW-H) [36] isemployed to estimate the far-field pressure from thenear-fieldpressure
Figure 10 shows the computational domain and Table 4lists the mesh information The computations of the com-pressible Euler solver and the LEEs solver are conductedusing the samemeshThePPW inTable 4 is the PPWreducedby the Doppler effect of the fan face axial Mach number Thecomputational domain is set at minus1119863 le 119909 le 7119863 minus8119863 le 119910 le
8119863 and minus8119863 le 119911 le 8119863The fan face is at 119909 = 05119863The innerend of the buffer zone is set at 119909 = [0 4119863] 119910 = [minus4119863 4119863]and 119911 = [minus4119863 4119863] The FW-H surfaces are located at thecube boundaries between the smallest size cubes and thelarger size cubes
Figure 11 shows theMachnumber distribution around theJT15D nacelle In Figure 11 the acceleration region near theinternal wall of the nacelle lip and the stagnation at the spikeare shown Because the experiments and computations wereconducted under the static condition the mean flow fieldexists only near the nacelle
Figure 12 shows the instantaneous pressure distributionsat the planes defined at 119911 = 0 and 119909 = 17119863 In the figure onlythe distributions of the smallest sized cubes are drawn Thefan noise is diffracted at the inlet of the nacelle and propagatesalong the radial direction The 13 peaks and valleys of theswirling fan noise at the 119909 = 17119863 plane are clearly capturedwhich is equivalent to the number of spinning modes Thetime history of the pressure is sampled at the establishedpoints on the FW-H surface and the periodic steady state isobserved after 119879 = 8
Figure 13 shows a comparison of the predicted SPL withthe experimental results conducted by Heidmann et al [37]and the computational results computed by Lan et al [34]The horizontal axis in the figure is the angle from the +119909-axialdirection In the figure the predicted SPL using the presentsolver shows good agreement with the computational resultof Lan et al (within 1 dB) Compared with the experimental
12 International Journal of Aerospace Engineering
Table 4 Mesh information for the JT15D nacelle
JT15D Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWCase 1 00166D 1544 30 times 30 times 30 41688000 87Case 2 00125D 1544 40 times 40 times 40 98816000 116
16D
8D
16D
16D
y
x
yzy
x z
Figure 10 Computational domain for the JT15D nacelle
Mac
h nu
mbe
r
02000100
0000
Figure 11 Mach number distribution around the JT15D nacelle
data a difference of about 3 dB is found at 60 deg Howeverthis discrepancy is also shown between the experimental dataand the result of Lan et al The SPL peak obtained near55 deg is equivalent to that obtained by Lan et al and thatobtained experimentally
6 Noise Propagation arounda Fuselage-Wing-Nacelle Configuration
The noise propagation around a fuselage-wing-nacelle con-figuration is computed as a realistic exampleThe focus of theexample was that of the OWN configuration [38] where theengine nacelle is mounted over the main wing which servesas one of the configurations designed to achieve substantialairport noise reduction The main feature of this configu-ration is that the main wing serves as a shield between the
ground and the noise generated by the engine To investigatethe effect of the OWN configuration the propagation of fannoise of both the conventional DLR-F6 aircraft configuration[39] and the OWN configuration is computed and the SPLbelow the aircraft for both configurations is comparedTheseconfigurations have complex geometry with large curvaturesnear the wing-body and the nacelle-pylon junctions In theOWN configuration the nacelle is moved 11D in the +119909
direction and 06D in the +y direction relative to its locationin the DLR-F6 configuration Here the reference length 119863 =
49m is the longitudinal length of the nacelle The cross-sectional geometry of the pylon is used without any changesand has a sweepback angle of 40 deg A mean flow fieldof Mach number 03 with zero angle of attack is computedusing the compressible Euler solver The sound source isintroduced via a discrete frequency spinning mode As anexample of a modern turbofan engine the CFM56-7B engineis considered The bypass ratio is 55 the fan diameter is154m the number of blades is 24 the maximum rotationalrate is 5382 rpm and the fundamental BPF is 21528HzTheBPF is used as the input frequency of the spinning modeThespinning mode (119898 119899) is set to (minus24 0) The SPL is measuredat a radius of 10D using the FW-H method
Figure 14 shows the computational domain of each con-figuration The black dot shows the origin of coordinatesystem The computations of the compressible Euler andLEEs solvers are conducted using an equivalent mesh Thesize of the computational domains is 4119863 times 2119863 times 2119863 Thesymmetric boundary condition is set at the minusz boundaryThe computational domains are set to ensure that sufficientcomputational domains surround the nacelle It is assumedthat the geometry out of the computational domain has littleinfluence on the noise directivity below the aircraft The
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
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8 International Journal of Aerospace Engineering
Table 1 Root mean square error and the order of accuracy
Wall Cube refinement Number of cells in one cube Root mean square error Order of accuracy
Case 1 Without Without36 times 36 times 36 1063 times 10minus5 mdash48 times 48 times 48 3422 times 10minus6 394172 times 72 times 72 6887 times 10minus7 3954
Case 2 With Without36 times 36 times 36 1269 times 10minus5 mdash48 times 48 times 48 4145 times 10minus6 389072 times 72 times 72 8326 times 10minus7 3959
Case 3 Without With36 times 36 times 36 1200 times 10minus4 mdash48 times 48 times 48 6574 times 10minus5 209372 times 72 times 72 2890 times 10minus5 2027
Case 4 With With36 times 36 times 36 1258 times 10minus4 mdash48 times 48 times 48 7086 times 10minus5 199572 times 72 times 72 3156 times 10minus5 1995
Table 2 Mesh information for acoustic scattering around a sphere of diameter 119863
Minimum cellsize
Number ofcubes Number of cells in one cube PPW Width of buffer zone
[119909 119910 119911]Coarse 00415D 128 48 times 48 times 48 8 1D 1D 1DUniform Middle 00277D 128 72 times 72 times 72 12 1D 1D 1DBCM Middle1 00208D 184 48 times 48 times 48 8 16 1D 1D 1DBCM Middle2 00208D 296 48 times 48 times 48 4 8 16 9D 5D 5DBCM Middle3 00208D 408 48 times 48 times 48 4 8 16 9D 5D 5DUniform Fine 00208D 128 96 times 96 times 96 16 1D 1D 1DBCM Fine1 00104D 240 48 times 48 times 48 8 16 32 1D 1D 1DBCM Fine2 00104D 352 48 times 48 times 48 4 8 16 32 9D 5D 5DBCM Fine3 00104D 464 48 times 48 times 48 4 8 16 32 9D 5D 5D
study Coarse mesh forms the base mesh of the other meshesemployedThe size of the computational domain is 16119863times8119863times
8119863 referring to [33] where 128 cubes of a size 1119863 times 1119863 times 1119863
constitute the domain as shown in Figure 7(a) The numberof cells in one cube is 48 times 48 times 48 and the PPW is eight Inthe Uniform Middle and Uniform Fine meshes the domainsize and the number of cubes are the same as those of theCoarse mesh The number of cells in one cube is 72 times 72times 72 in the Uniform Middle mesh and 96 times 96 times 96 in theUniform Fine mesh thus the PPW is 12 and 16 respectivelyIn the BCM Middle1 mesh the eight cubes in the Coarsemesh surrounding the sphere are subdivided into half sizecubes Similarly the eight cubes surrounding the sphere aresubdivided from the BCM Middle1 mesh in the BCM Fine1mesh The number of cubes is 184 in the BCM Middle1mesh and 240 in the BCM Fine1 mesh and the maximumPPW is 16 and 32 respectively In the BCM Middle2 meshshown in Figure 7(b) and BCM Fine2 meshes the bufferzone is expanded to add 112 cubes to the BCM Middle1 andBCM Fine1 meshes In the BCM Middle3 and BCM Fine3(shown in Figure 7(c)) meshes eight cubes located at 2 le xle 6 minus2 le y le 2 and minus2 le z le 2 and eight cubes located at minus6le x le minus2 minus2 le y le 2 and minus2 le z le 2 are subdivided from theBCM Middle2 and BCM Fine2 meshes to increase the PPWof the computational domain The inner end of the buffer
zone is set at x = [minus7D 7D] y = [minus3D 3D] and z = [minus3D3D] in all meshes to compare the sizes of the buffer zones
Figure 8 shows the instantaneous pressure distributionaround the sphere computed using the Coarse mesh In thisfigure the buffer zone is not drawn Waves generated fromthe sound source are scattered by the sphere and interferencefringes appear The computation is executed in nondimen-sional time 119879 = 15 and a periodic steady state is observedafter119879 = 11 Figure 9 shows the pressure distributionnear theinner end of the buffer zone and the time history of the pres-sure near the sphere for all meshes The pressure distributionis sampled at minus6119863 le 119909 le minus4119863 on the 119909-axisThe time historyof the pressure is sampled at (minus2D 0 0) and 14 le 119879 le 15
In Figures 9(a) and 9(b) the uniform meshes arecompared The pressure distributions do not follow thedecreasing trend of the analytical solution in Figure 9(a)Reflection occurs at the outer boundary because of theinsufficient width of the buffer zone Additionally theUniform Middle and Uniform Fine meshes show a higherpressure amplitude compared with the pressure distributionof the Coarse mesh It is assumed that the sound wave isdamped at the Coarse mesh because of the insufficient PPWThe time histories of the uniform meshes provide loweramplitudes than the analytical solution
International Journal of Aerospace Engineering 9
Table 3 Comparison of errors relative to an analytical solution and respective computational times for the meshes listed in Table 2
Total number ofcells
Normalized root meansquare error []
Normalizedmaximum error []
Computational time[120583sectimestepcell]
Real time [sec](128 CPUs)
Coarse 14155776 1197 2382 008454 302Uniform Middle 47775744 502 1131 008631 1388BCM Middle1 20348928 362 1486 010891 1088BCM Middle2 32735232 307 714 011027 1710BCM Middle3 45121536 289 734 009665 2172Uniform Fine 113246208 357 1093 007329 4240BCM Fine1 26542080 614 2224 008851 2654BCM Fine2 38928384 304 700 008777 3358BCM Fine3 51314688 162 500 009019 4794
Non
dim
ensio
nal p
ress
ure
000E + 000
minus500E minus 005
500E minus 005
minus100E minus 004
100E minus 004
Figure 8 Instantaneous pressure distribution (Coarse mesh) around a sphere of diameter D
In Figures 9(c) and 9(d) the BCM Middle meshes arecompared The BCM Middle2 and BCM Middle3 meshesfollow the analytical solution in Figure 9(c) These mesheshave a buffer zone of width 9D in the 119909 direction andoutgoing waves are damped appropriately However theBCM Middle2 mesh provides a lower amplitude This isowing to the insufficient PPW at the sampling points On theother hand phase error is not observed in the BCM Middle2mesh In Figure 9(d) the amplitude of the pressure convergesto the analytical solution for the BCM Middle2 mesh Onlythe BCM Middle1 mesh provides a lower amplitude Thisamplitude is the same as that of the uniform meshes There-fore it is confirmed that the amplitude of the inner soundfieldis diminished when using a buffer zone of short width
In Figures 9(e) and 9(f) the BCM Fine meshes arecompared The pressure distributions and the time historiesof the BCM Fine meshes exhibit similar tendencies as thoseof the BCM Middle meshes
To compare the magnitude of errors more quantitativelythe root mean square pressure 119875rms of the scattered soundis computed and the normalized RMSE (NRMSE) and thenormalized maximum error (MME) between the analytical
solution and the solutions of each mesh are compared asgiven by
NRMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
2
NME = max1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
(10)
The number of sampling points 119873 are set clockwise ata radius 119903 = 2D from the origin The points (minus2D 00) and (2D 0 0) correspond to 0 deg and 180 deg Theerrors are summarized in Table 3 As shown in the table therefined meshes provide lower errors than the coarser meshand the meshes that utilize a large buffer zone also providelower errors The minimum cell size around the sphere alsoaffects the errors The smallest errors are provided by theBCM Fine3 mesh A comparison of the uniform and BCMmeshes indicates that the BCM Middle3 and BCM Fine3meshes which use cubes of different sizes at the appropriatelocations provide lower errors than Uniform Middle meshes
10 International Journal of Aerospace Engineering
Non
dim
ensio
nal p
ress
ure
AnalyticalCoarse
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
Uniform_MiddleUniform_Fine
minus6 minus55 minus5 minus45 minus4
x coordinate
(a) Pressure distributions of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
100E minus 04
150E minus 04
AnalyticalCoarse
Uniform_MiddleUniform_Fine
500E minus 05
14 142 144 146 148 15Nondimensional time
(b) Time histories of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
minus6 minus55 minus5 minus45 minus4
x coordinate
(c) Pressure distributions of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
14 142 144 146 148 15Nondimensional time
(d) Time histories of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
minus6 minus55 minus5 minus45 minus4
x coordinate
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(e) Pressure distributions of BCM Fine meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
14 142 144 146 148 15Nondimensional time
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(f) Time histories of BCM Fine meshes
Figure 9 Pressure distributions (minus6119863 le 119909 le minus4119863) and time histories at (minus2D 0 0) and (14 le 119879 le 15) around a sphere of diameter 119863 forthe meshes listed in Table 2
International Journal of Aerospace Engineering 11
that utilize a similar number of mesh points Moreover theerrors of the BCM Fine3 mesh are about one-half the errorsof the Uniform Fine mesh which has twice the number ofmesh points as the BCM Fine3 mesh These results indicatethe effectiveness of the BCM arrangement
The computational wall-clock times for a single timestep per cell and the total wall-clock time required toreach a nondimensional time 119879 = 15 are also listed inTable 3 All meshes were computed using 128CPUs of anSGI AltixUV1000 computer Regarding the wall-clock timeper one time step per cell the computational times of theuniformandBCMmeshes are comparableHowever the totalwall-clock times of the BCM meshes are slightly longer thanthose of the uniform meshes The BCM meshes employ alarger number of cubes than the number of CPUs used in theevaluationThemismatch between the numbers of cubes andCPUs can degrade the load balance Computations using anequivalent number of CPUs and cubes are more effective forBCMmeshes
5 Noise Propagation from the JT15D Nacelle
Noise propagation from the JT15D [34] nacelle is computedand the far-field sound pressure level (SPL) is compared withdata derived from experiment and the computational resultsof others The JT15D is a small Pratt and Whitney turbofanenginewith a bellmouth inletThe sound source is introducedvia a discrete frequency spinning mode The spinning modeinput [35] is a typical sound source generated by the fan orrotor-stator intersections in the engine The sound source ofa single spinning mode (119898 119899) is defined by
119878 = [119869119898
(119896119903119903) + 1198881119884119898
(119896119903119903)] cos (119896119905 minus 119896
119886119909 minus 119898120579) (11)
Here 119869119898and119884119898are themth order Bessel functions of the first
and second kind respectively 119896 is the angular frequency 119896119886
is the axial wavenumber 119896119903is the radial wavenumber and 120579
is the phase The 119899th solution 119896119903of the following equation is
determined by the hard-wall boundary condition of the duct
119889 [119869119898
(119903outer119896119903)]
119889119903
119889 [119884119898
(119903inner119896119903)]
119889119903
minus119889 [119869119898
(119903inner119896119903)]
119889119903
119889 [119884119898
(119903outer119896119903)]
119889119903= 0
(12)
Here 119903outer and 119903inner are the bypass duct inner wall radius andthe inner hub radius respectively The axial wave number 119896
119886
is computed from
119896119886
=119896
1 minus 1198722119895
(minus119872119895
plusmnradic
1 minus1198962
119903(1 minus 119872
2
119895)
1198962) (13)
where 119872119895is the Mach number at the fan face The selection
of plus or minus signs in the parentheses is determined bythe propagation direction of the sound wave where plus(+) represents the positive propagation direction along the
axial coordinate and vice versa The constant 1198881satisfies the
following relation
1198881
= minus(119889119889119903) [119869
119898(119903outer119896119903)]
(119889119889119903) [119884119898
(119903outer119896119903)]
= minus(119889119889119903) [119869
119898(119903inner119896119903)]
(119889119889119903) [119884119898
(119903inner119896119903)]
(14)
Parameters are set from experimental data (119898 119899) =
(minus13 0) 119903outer = 02667m and 119903inner = 00998m Thereference length D = 06223mis the length from the fanface to the leading edge of the nacelle The blade passingfrequency (BPF) is set to 3150Hz which is derived fromthe fan rotating speed of 6750 rpm The experiments wereconducted in the static condition and the fan face axial Machnumber is 0175 The present computation is also conductedin the static condition In the present computation the axialflow velocity of the ghost cell at the fan face boundary isdirectly modified to this Mach number The pressure andthe density are the same values as those of the adjacent fluidcells The SPL is measured at a radius of 49D The integrationmethod of Ffowcs-Williams and Hawkings (FW-H) [36] isemployed to estimate the far-field pressure from thenear-fieldpressure
Figure 10 shows the computational domain and Table 4lists the mesh information The computations of the com-pressible Euler solver and the LEEs solver are conductedusing the samemeshThePPW inTable 4 is the PPWreducedby the Doppler effect of the fan face axial Mach number Thecomputational domain is set at minus1119863 le 119909 le 7119863 minus8119863 le 119910 le
8119863 and minus8119863 le 119911 le 8119863The fan face is at 119909 = 05119863The innerend of the buffer zone is set at 119909 = [0 4119863] 119910 = [minus4119863 4119863]and 119911 = [minus4119863 4119863] The FW-H surfaces are located at thecube boundaries between the smallest size cubes and thelarger size cubes
Figure 11 shows theMachnumber distribution around theJT15D nacelle In Figure 11 the acceleration region near theinternal wall of the nacelle lip and the stagnation at the spikeare shown Because the experiments and computations wereconducted under the static condition the mean flow fieldexists only near the nacelle
Figure 12 shows the instantaneous pressure distributionsat the planes defined at 119911 = 0 and 119909 = 17119863 In the figure onlythe distributions of the smallest sized cubes are drawn Thefan noise is diffracted at the inlet of the nacelle and propagatesalong the radial direction The 13 peaks and valleys of theswirling fan noise at the 119909 = 17119863 plane are clearly capturedwhich is equivalent to the number of spinning modes Thetime history of the pressure is sampled at the establishedpoints on the FW-H surface and the periodic steady state isobserved after 119879 = 8
Figure 13 shows a comparison of the predicted SPL withthe experimental results conducted by Heidmann et al [37]and the computational results computed by Lan et al [34]The horizontal axis in the figure is the angle from the +119909-axialdirection In the figure the predicted SPL using the presentsolver shows good agreement with the computational resultof Lan et al (within 1 dB) Compared with the experimental
12 International Journal of Aerospace Engineering
Table 4 Mesh information for the JT15D nacelle
JT15D Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWCase 1 00166D 1544 30 times 30 times 30 41688000 87Case 2 00125D 1544 40 times 40 times 40 98816000 116
16D
8D
16D
16D
y
x
yzy
x z
Figure 10 Computational domain for the JT15D nacelle
Mac
h nu
mbe
r
02000100
0000
Figure 11 Mach number distribution around the JT15D nacelle
data a difference of about 3 dB is found at 60 deg Howeverthis discrepancy is also shown between the experimental dataand the result of Lan et al The SPL peak obtained near55 deg is equivalent to that obtained by Lan et al and thatobtained experimentally
6 Noise Propagation arounda Fuselage-Wing-Nacelle Configuration
The noise propagation around a fuselage-wing-nacelle con-figuration is computed as a realistic exampleThe focus of theexample was that of the OWN configuration [38] where theengine nacelle is mounted over the main wing which servesas one of the configurations designed to achieve substantialairport noise reduction The main feature of this configu-ration is that the main wing serves as a shield between the
ground and the noise generated by the engine To investigatethe effect of the OWN configuration the propagation of fannoise of both the conventional DLR-F6 aircraft configuration[39] and the OWN configuration is computed and the SPLbelow the aircraft for both configurations is comparedTheseconfigurations have complex geometry with large curvaturesnear the wing-body and the nacelle-pylon junctions In theOWN configuration the nacelle is moved 11D in the +119909
direction and 06D in the +y direction relative to its locationin the DLR-F6 configuration Here the reference length 119863 =
49m is the longitudinal length of the nacelle The cross-sectional geometry of the pylon is used without any changesand has a sweepback angle of 40 deg A mean flow fieldof Mach number 03 with zero angle of attack is computedusing the compressible Euler solver The sound source isintroduced via a discrete frequency spinning mode As anexample of a modern turbofan engine the CFM56-7B engineis considered The bypass ratio is 55 the fan diameter is154m the number of blades is 24 the maximum rotationalrate is 5382 rpm and the fundamental BPF is 21528HzTheBPF is used as the input frequency of the spinning modeThespinning mode (119898 119899) is set to (minus24 0) The SPL is measuredat a radius of 10D using the FW-H method
Figure 14 shows the computational domain of each con-figuration The black dot shows the origin of coordinatesystem The computations of the compressible Euler andLEEs solvers are conducted using an equivalent mesh Thesize of the computational domains is 4119863 times 2119863 times 2119863 Thesymmetric boundary condition is set at the minusz boundaryThe computational domains are set to ensure that sufficientcomputational domains surround the nacelle It is assumedthat the geometry out of the computational domain has littleinfluence on the noise directivity below the aircraft The
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Active and Passive Electronic Components
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RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Submit your manuscripts athttpwwwhindawicom
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Shock and Vibration
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Civil EngineeringAdvances in
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Electrical and Computer Engineering
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 9
Table 3 Comparison of errors relative to an analytical solution and respective computational times for the meshes listed in Table 2
Total number ofcells
Normalized root meansquare error []
Normalizedmaximum error []
Computational time[120583sectimestepcell]
Real time [sec](128 CPUs)
Coarse 14155776 1197 2382 008454 302Uniform Middle 47775744 502 1131 008631 1388BCM Middle1 20348928 362 1486 010891 1088BCM Middle2 32735232 307 714 011027 1710BCM Middle3 45121536 289 734 009665 2172Uniform Fine 113246208 357 1093 007329 4240BCM Fine1 26542080 614 2224 008851 2654BCM Fine2 38928384 304 700 008777 3358BCM Fine3 51314688 162 500 009019 4794
Non
dim
ensio
nal p
ress
ure
000E + 000
minus500E minus 005
500E minus 005
minus100E minus 004
100E minus 004
Figure 8 Instantaneous pressure distribution (Coarse mesh) around a sphere of diameter D
In Figures 9(c) and 9(d) the BCM Middle meshes arecompared The BCM Middle2 and BCM Middle3 meshesfollow the analytical solution in Figure 9(c) These mesheshave a buffer zone of width 9D in the 119909 direction andoutgoing waves are damped appropriately However theBCM Middle2 mesh provides a lower amplitude This isowing to the insufficient PPW at the sampling points On theother hand phase error is not observed in the BCM Middle2mesh In Figure 9(d) the amplitude of the pressure convergesto the analytical solution for the BCM Middle2 mesh Onlythe BCM Middle1 mesh provides a lower amplitude Thisamplitude is the same as that of the uniform meshes There-fore it is confirmed that the amplitude of the inner soundfieldis diminished when using a buffer zone of short width
In Figures 9(e) and 9(f) the BCM Fine meshes arecompared The pressure distributions and the time historiesof the BCM Fine meshes exhibit similar tendencies as thoseof the BCM Middle meshes
To compare the magnitude of errors more quantitativelythe root mean square pressure 119875rms of the scattered soundis computed and the normalized RMSE (NRMSE) and thenormalized maximum error (MME) between the analytical
solution and the solutions of each mesh are compared asgiven by
NRMSE = radic1
119873
119873
sum
119894=1
1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
2
NME = max1003816100381610038161003816100381610038161003816100381610038161003816
119875rms(computed) minus 119875rms(analytical)
119875rms(analytical)
1003816100381610038161003816100381610038161003816100381610038161003816
(10)
The number of sampling points 119873 are set clockwise ata radius 119903 = 2D from the origin The points (minus2D 00) and (2D 0 0) correspond to 0 deg and 180 deg Theerrors are summarized in Table 3 As shown in the table therefined meshes provide lower errors than the coarser meshand the meshes that utilize a large buffer zone also providelower errors The minimum cell size around the sphere alsoaffects the errors The smallest errors are provided by theBCM Fine3 mesh A comparison of the uniform and BCMmeshes indicates that the BCM Middle3 and BCM Fine3meshes which use cubes of different sizes at the appropriatelocations provide lower errors than Uniform Middle meshes
10 International Journal of Aerospace Engineering
Non
dim
ensio
nal p
ress
ure
AnalyticalCoarse
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
Uniform_MiddleUniform_Fine
minus6 minus55 minus5 minus45 minus4
x coordinate
(a) Pressure distributions of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
100E minus 04
150E minus 04
AnalyticalCoarse
Uniform_MiddleUniform_Fine
500E minus 05
14 142 144 146 148 15Nondimensional time
(b) Time histories of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
minus6 minus55 minus5 minus45 minus4
x coordinate
(c) Pressure distributions of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
14 142 144 146 148 15Nondimensional time
(d) Time histories of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
minus6 minus55 minus5 minus45 minus4
x coordinate
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(e) Pressure distributions of BCM Fine meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
14 142 144 146 148 15Nondimensional time
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(f) Time histories of BCM Fine meshes
Figure 9 Pressure distributions (minus6119863 le 119909 le minus4119863) and time histories at (minus2D 0 0) and (14 le 119879 le 15) around a sphere of diameter 119863 forthe meshes listed in Table 2
International Journal of Aerospace Engineering 11
that utilize a similar number of mesh points Moreover theerrors of the BCM Fine3 mesh are about one-half the errorsof the Uniform Fine mesh which has twice the number ofmesh points as the BCM Fine3 mesh These results indicatethe effectiveness of the BCM arrangement
The computational wall-clock times for a single timestep per cell and the total wall-clock time required toreach a nondimensional time 119879 = 15 are also listed inTable 3 All meshes were computed using 128CPUs of anSGI AltixUV1000 computer Regarding the wall-clock timeper one time step per cell the computational times of theuniformandBCMmeshes are comparableHowever the totalwall-clock times of the BCM meshes are slightly longer thanthose of the uniform meshes The BCM meshes employ alarger number of cubes than the number of CPUs used in theevaluationThemismatch between the numbers of cubes andCPUs can degrade the load balance Computations using anequivalent number of CPUs and cubes are more effective forBCMmeshes
5 Noise Propagation from the JT15D Nacelle
Noise propagation from the JT15D [34] nacelle is computedand the far-field sound pressure level (SPL) is compared withdata derived from experiment and the computational resultsof others The JT15D is a small Pratt and Whitney turbofanenginewith a bellmouth inletThe sound source is introducedvia a discrete frequency spinning mode The spinning modeinput [35] is a typical sound source generated by the fan orrotor-stator intersections in the engine The sound source ofa single spinning mode (119898 119899) is defined by
119878 = [119869119898
(119896119903119903) + 1198881119884119898
(119896119903119903)] cos (119896119905 minus 119896
119886119909 minus 119898120579) (11)
Here 119869119898and119884119898are themth order Bessel functions of the first
and second kind respectively 119896 is the angular frequency 119896119886
is the axial wavenumber 119896119903is the radial wavenumber and 120579
is the phase The 119899th solution 119896119903of the following equation is
determined by the hard-wall boundary condition of the duct
119889 [119869119898
(119903outer119896119903)]
119889119903
119889 [119884119898
(119903inner119896119903)]
119889119903
minus119889 [119869119898
(119903inner119896119903)]
119889119903
119889 [119884119898
(119903outer119896119903)]
119889119903= 0
(12)
Here 119903outer and 119903inner are the bypass duct inner wall radius andthe inner hub radius respectively The axial wave number 119896
119886
is computed from
119896119886
=119896
1 minus 1198722119895
(minus119872119895
plusmnradic
1 minus1198962
119903(1 minus 119872
2
119895)
1198962) (13)
where 119872119895is the Mach number at the fan face The selection
of plus or minus signs in the parentheses is determined bythe propagation direction of the sound wave where plus(+) represents the positive propagation direction along the
axial coordinate and vice versa The constant 1198881satisfies the
following relation
1198881
= minus(119889119889119903) [119869
119898(119903outer119896119903)]
(119889119889119903) [119884119898
(119903outer119896119903)]
= minus(119889119889119903) [119869
119898(119903inner119896119903)]
(119889119889119903) [119884119898
(119903inner119896119903)]
(14)
Parameters are set from experimental data (119898 119899) =
(minus13 0) 119903outer = 02667m and 119903inner = 00998m Thereference length D = 06223mis the length from the fanface to the leading edge of the nacelle The blade passingfrequency (BPF) is set to 3150Hz which is derived fromthe fan rotating speed of 6750 rpm The experiments wereconducted in the static condition and the fan face axial Machnumber is 0175 The present computation is also conductedin the static condition In the present computation the axialflow velocity of the ghost cell at the fan face boundary isdirectly modified to this Mach number The pressure andthe density are the same values as those of the adjacent fluidcells The SPL is measured at a radius of 49D The integrationmethod of Ffowcs-Williams and Hawkings (FW-H) [36] isemployed to estimate the far-field pressure from thenear-fieldpressure
Figure 10 shows the computational domain and Table 4lists the mesh information The computations of the com-pressible Euler solver and the LEEs solver are conductedusing the samemeshThePPW inTable 4 is the PPWreducedby the Doppler effect of the fan face axial Mach number Thecomputational domain is set at minus1119863 le 119909 le 7119863 minus8119863 le 119910 le
8119863 and minus8119863 le 119911 le 8119863The fan face is at 119909 = 05119863The innerend of the buffer zone is set at 119909 = [0 4119863] 119910 = [minus4119863 4119863]and 119911 = [minus4119863 4119863] The FW-H surfaces are located at thecube boundaries between the smallest size cubes and thelarger size cubes
Figure 11 shows theMachnumber distribution around theJT15D nacelle In Figure 11 the acceleration region near theinternal wall of the nacelle lip and the stagnation at the spikeare shown Because the experiments and computations wereconducted under the static condition the mean flow fieldexists only near the nacelle
Figure 12 shows the instantaneous pressure distributionsat the planes defined at 119911 = 0 and 119909 = 17119863 In the figure onlythe distributions of the smallest sized cubes are drawn Thefan noise is diffracted at the inlet of the nacelle and propagatesalong the radial direction The 13 peaks and valleys of theswirling fan noise at the 119909 = 17119863 plane are clearly capturedwhich is equivalent to the number of spinning modes Thetime history of the pressure is sampled at the establishedpoints on the FW-H surface and the periodic steady state isobserved after 119879 = 8
Figure 13 shows a comparison of the predicted SPL withthe experimental results conducted by Heidmann et al [37]and the computational results computed by Lan et al [34]The horizontal axis in the figure is the angle from the +119909-axialdirection In the figure the predicted SPL using the presentsolver shows good agreement with the computational resultof Lan et al (within 1 dB) Compared with the experimental
12 International Journal of Aerospace Engineering
Table 4 Mesh information for the JT15D nacelle
JT15D Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWCase 1 00166D 1544 30 times 30 times 30 41688000 87Case 2 00125D 1544 40 times 40 times 40 98816000 116
16D
8D
16D
16D
y
x
yzy
x z
Figure 10 Computational domain for the JT15D nacelle
Mac
h nu
mbe
r
02000100
0000
Figure 11 Mach number distribution around the JT15D nacelle
data a difference of about 3 dB is found at 60 deg Howeverthis discrepancy is also shown between the experimental dataand the result of Lan et al The SPL peak obtained near55 deg is equivalent to that obtained by Lan et al and thatobtained experimentally
6 Noise Propagation arounda Fuselage-Wing-Nacelle Configuration
The noise propagation around a fuselage-wing-nacelle con-figuration is computed as a realistic exampleThe focus of theexample was that of the OWN configuration [38] where theengine nacelle is mounted over the main wing which servesas one of the configurations designed to achieve substantialairport noise reduction The main feature of this configu-ration is that the main wing serves as a shield between the
ground and the noise generated by the engine To investigatethe effect of the OWN configuration the propagation of fannoise of both the conventional DLR-F6 aircraft configuration[39] and the OWN configuration is computed and the SPLbelow the aircraft for both configurations is comparedTheseconfigurations have complex geometry with large curvaturesnear the wing-body and the nacelle-pylon junctions In theOWN configuration the nacelle is moved 11D in the +119909
direction and 06D in the +y direction relative to its locationin the DLR-F6 configuration Here the reference length 119863 =
49m is the longitudinal length of the nacelle The cross-sectional geometry of the pylon is used without any changesand has a sweepback angle of 40 deg A mean flow fieldof Mach number 03 with zero angle of attack is computedusing the compressible Euler solver The sound source isintroduced via a discrete frequency spinning mode As anexample of a modern turbofan engine the CFM56-7B engineis considered The bypass ratio is 55 the fan diameter is154m the number of blades is 24 the maximum rotationalrate is 5382 rpm and the fundamental BPF is 21528HzTheBPF is used as the input frequency of the spinning modeThespinning mode (119898 119899) is set to (minus24 0) The SPL is measuredat a radius of 10D using the FW-H method
Figure 14 shows the computational domain of each con-figuration The black dot shows the origin of coordinatesystem The computations of the compressible Euler andLEEs solvers are conducted using an equivalent mesh Thesize of the computational domains is 4119863 times 2119863 times 2119863 Thesymmetric boundary condition is set at the minusz boundaryThe computational domains are set to ensure that sufficientcomputational domains surround the nacelle It is assumedthat the geometry out of the computational domain has littleinfluence on the noise directivity below the aircraft The
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
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DistributedSensor Networks
International Journal of
10 International Journal of Aerospace Engineering
Non
dim
ensio
nal p
ress
ure
AnalyticalCoarse
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
Uniform_MiddleUniform_Fine
minus6 minus55 minus5 minus45 minus4
x coordinate
(a) Pressure distributions of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
100E minus 04
150E minus 04
AnalyticalCoarse
Uniform_MiddleUniform_Fine
500E minus 05
14 142 144 146 148 15Nondimensional time
(b) Time histories of uniform meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
minus6 minus55 minus5 minus45 minus4
x coordinate
(c) Pressure distributions of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
AnalyticalBCM_Middle1
BCM_Middle2BCM_Middle3
14 142 144 146 148 15Nondimensional time
(d) Time histories of BCM Middle meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
minus6 minus55 minus5 minus45 minus4
x coordinate
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(e) Pressure distributions of BCM Fine meshes
Non
dim
ensio
nal p
ress
ure
minus150E minus 04
minus100E minus 04
minus500E minus 05
000E + 00
500E minus 05
100E minus 04
150E minus 04
14 142 144 146 148 15Nondimensional time
AnalyticalBCM_Fine1
BCM_ Fine2BCM_ Fine3
(f) Time histories of BCM Fine meshes
Figure 9 Pressure distributions (minus6119863 le 119909 le minus4119863) and time histories at (minus2D 0 0) and (14 le 119879 le 15) around a sphere of diameter 119863 forthe meshes listed in Table 2
International Journal of Aerospace Engineering 11
that utilize a similar number of mesh points Moreover theerrors of the BCM Fine3 mesh are about one-half the errorsof the Uniform Fine mesh which has twice the number ofmesh points as the BCM Fine3 mesh These results indicatethe effectiveness of the BCM arrangement
The computational wall-clock times for a single timestep per cell and the total wall-clock time required toreach a nondimensional time 119879 = 15 are also listed inTable 3 All meshes were computed using 128CPUs of anSGI AltixUV1000 computer Regarding the wall-clock timeper one time step per cell the computational times of theuniformandBCMmeshes are comparableHowever the totalwall-clock times of the BCM meshes are slightly longer thanthose of the uniform meshes The BCM meshes employ alarger number of cubes than the number of CPUs used in theevaluationThemismatch between the numbers of cubes andCPUs can degrade the load balance Computations using anequivalent number of CPUs and cubes are more effective forBCMmeshes
5 Noise Propagation from the JT15D Nacelle
Noise propagation from the JT15D [34] nacelle is computedand the far-field sound pressure level (SPL) is compared withdata derived from experiment and the computational resultsof others The JT15D is a small Pratt and Whitney turbofanenginewith a bellmouth inletThe sound source is introducedvia a discrete frequency spinning mode The spinning modeinput [35] is a typical sound source generated by the fan orrotor-stator intersections in the engine The sound source ofa single spinning mode (119898 119899) is defined by
119878 = [119869119898
(119896119903119903) + 1198881119884119898
(119896119903119903)] cos (119896119905 minus 119896
119886119909 minus 119898120579) (11)
Here 119869119898and119884119898are themth order Bessel functions of the first
and second kind respectively 119896 is the angular frequency 119896119886
is the axial wavenumber 119896119903is the radial wavenumber and 120579
is the phase The 119899th solution 119896119903of the following equation is
determined by the hard-wall boundary condition of the duct
119889 [119869119898
(119903outer119896119903)]
119889119903
119889 [119884119898
(119903inner119896119903)]
119889119903
minus119889 [119869119898
(119903inner119896119903)]
119889119903
119889 [119884119898
(119903outer119896119903)]
119889119903= 0
(12)
Here 119903outer and 119903inner are the bypass duct inner wall radius andthe inner hub radius respectively The axial wave number 119896
119886
is computed from
119896119886
=119896
1 minus 1198722119895
(minus119872119895
plusmnradic
1 minus1198962
119903(1 minus 119872
2
119895)
1198962) (13)
where 119872119895is the Mach number at the fan face The selection
of plus or minus signs in the parentheses is determined bythe propagation direction of the sound wave where plus(+) represents the positive propagation direction along the
axial coordinate and vice versa The constant 1198881satisfies the
following relation
1198881
= minus(119889119889119903) [119869
119898(119903outer119896119903)]
(119889119889119903) [119884119898
(119903outer119896119903)]
= minus(119889119889119903) [119869
119898(119903inner119896119903)]
(119889119889119903) [119884119898
(119903inner119896119903)]
(14)
Parameters are set from experimental data (119898 119899) =
(minus13 0) 119903outer = 02667m and 119903inner = 00998m Thereference length D = 06223mis the length from the fanface to the leading edge of the nacelle The blade passingfrequency (BPF) is set to 3150Hz which is derived fromthe fan rotating speed of 6750 rpm The experiments wereconducted in the static condition and the fan face axial Machnumber is 0175 The present computation is also conductedin the static condition In the present computation the axialflow velocity of the ghost cell at the fan face boundary isdirectly modified to this Mach number The pressure andthe density are the same values as those of the adjacent fluidcells The SPL is measured at a radius of 49D The integrationmethod of Ffowcs-Williams and Hawkings (FW-H) [36] isemployed to estimate the far-field pressure from thenear-fieldpressure
Figure 10 shows the computational domain and Table 4lists the mesh information The computations of the com-pressible Euler solver and the LEEs solver are conductedusing the samemeshThePPW inTable 4 is the PPWreducedby the Doppler effect of the fan face axial Mach number Thecomputational domain is set at minus1119863 le 119909 le 7119863 minus8119863 le 119910 le
8119863 and minus8119863 le 119911 le 8119863The fan face is at 119909 = 05119863The innerend of the buffer zone is set at 119909 = [0 4119863] 119910 = [minus4119863 4119863]and 119911 = [minus4119863 4119863] The FW-H surfaces are located at thecube boundaries between the smallest size cubes and thelarger size cubes
Figure 11 shows theMachnumber distribution around theJT15D nacelle In Figure 11 the acceleration region near theinternal wall of the nacelle lip and the stagnation at the spikeare shown Because the experiments and computations wereconducted under the static condition the mean flow fieldexists only near the nacelle
Figure 12 shows the instantaneous pressure distributionsat the planes defined at 119911 = 0 and 119909 = 17119863 In the figure onlythe distributions of the smallest sized cubes are drawn Thefan noise is diffracted at the inlet of the nacelle and propagatesalong the radial direction The 13 peaks and valleys of theswirling fan noise at the 119909 = 17119863 plane are clearly capturedwhich is equivalent to the number of spinning modes Thetime history of the pressure is sampled at the establishedpoints on the FW-H surface and the periodic steady state isobserved after 119879 = 8
Figure 13 shows a comparison of the predicted SPL withthe experimental results conducted by Heidmann et al [37]and the computational results computed by Lan et al [34]The horizontal axis in the figure is the angle from the +119909-axialdirection In the figure the predicted SPL using the presentsolver shows good agreement with the computational resultof Lan et al (within 1 dB) Compared with the experimental
12 International Journal of Aerospace Engineering
Table 4 Mesh information for the JT15D nacelle
JT15D Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWCase 1 00166D 1544 30 times 30 times 30 41688000 87Case 2 00125D 1544 40 times 40 times 40 98816000 116
16D
8D
16D
16D
y
x
yzy
x z
Figure 10 Computational domain for the JT15D nacelle
Mac
h nu
mbe
r
02000100
0000
Figure 11 Mach number distribution around the JT15D nacelle
data a difference of about 3 dB is found at 60 deg Howeverthis discrepancy is also shown between the experimental dataand the result of Lan et al The SPL peak obtained near55 deg is equivalent to that obtained by Lan et al and thatobtained experimentally
6 Noise Propagation arounda Fuselage-Wing-Nacelle Configuration
The noise propagation around a fuselage-wing-nacelle con-figuration is computed as a realistic exampleThe focus of theexample was that of the OWN configuration [38] where theengine nacelle is mounted over the main wing which servesas one of the configurations designed to achieve substantialairport noise reduction The main feature of this configu-ration is that the main wing serves as a shield between the
ground and the noise generated by the engine To investigatethe effect of the OWN configuration the propagation of fannoise of both the conventional DLR-F6 aircraft configuration[39] and the OWN configuration is computed and the SPLbelow the aircraft for both configurations is comparedTheseconfigurations have complex geometry with large curvaturesnear the wing-body and the nacelle-pylon junctions In theOWN configuration the nacelle is moved 11D in the +119909
direction and 06D in the +y direction relative to its locationin the DLR-F6 configuration Here the reference length 119863 =
49m is the longitudinal length of the nacelle The cross-sectional geometry of the pylon is used without any changesand has a sweepback angle of 40 deg A mean flow fieldof Mach number 03 with zero angle of attack is computedusing the compressible Euler solver The sound source isintroduced via a discrete frequency spinning mode As anexample of a modern turbofan engine the CFM56-7B engineis considered The bypass ratio is 55 the fan diameter is154m the number of blades is 24 the maximum rotationalrate is 5382 rpm and the fundamental BPF is 21528HzTheBPF is used as the input frequency of the spinning modeThespinning mode (119898 119899) is set to (minus24 0) The SPL is measuredat a radius of 10D using the FW-H method
Figure 14 shows the computational domain of each con-figuration The black dot shows the origin of coordinatesystem The computations of the compressible Euler andLEEs solvers are conducted using an equivalent mesh Thesize of the computational domains is 4119863 times 2119863 times 2119863 Thesymmetric boundary condition is set at the minusz boundaryThe computational domains are set to ensure that sufficientcomputational domains surround the nacelle It is assumedthat the geometry out of the computational domain has littleinfluence on the noise directivity below the aircraft The
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
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DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 11
that utilize a similar number of mesh points Moreover theerrors of the BCM Fine3 mesh are about one-half the errorsof the Uniform Fine mesh which has twice the number ofmesh points as the BCM Fine3 mesh These results indicatethe effectiveness of the BCM arrangement
The computational wall-clock times for a single timestep per cell and the total wall-clock time required toreach a nondimensional time 119879 = 15 are also listed inTable 3 All meshes were computed using 128CPUs of anSGI AltixUV1000 computer Regarding the wall-clock timeper one time step per cell the computational times of theuniformandBCMmeshes are comparableHowever the totalwall-clock times of the BCM meshes are slightly longer thanthose of the uniform meshes The BCM meshes employ alarger number of cubes than the number of CPUs used in theevaluationThemismatch between the numbers of cubes andCPUs can degrade the load balance Computations using anequivalent number of CPUs and cubes are more effective forBCMmeshes
5 Noise Propagation from the JT15D Nacelle
Noise propagation from the JT15D [34] nacelle is computedand the far-field sound pressure level (SPL) is compared withdata derived from experiment and the computational resultsof others The JT15D is a small Pratt and Whitney turbofanenginewith a bellmouth inletThe sound source is introducedvia a discrete frequency spinning mode The spinning modeinput [35] is a typical sound source generated by the fan orrotor-stator intersections in the engine The sound source ofa single spinning mode (119898 119899) is defined by
119878 = [119869119898
(119896119903119903) + 1198881119884119898
(119896119903119903)] cos (119896119905 minus 119896
119886119909 minus 119898120579) (11)
Here 119869119898and119884119898are themth order Bessel functions of the first
and second kind respectively 119896 is the angular frequency 119896119886
is the axial wavenumber 119896119903is the radial wavenumber and 120579
is the phase The 119899th solution 119896119903of the following equation is
determined by the hard-wall boundary condition of the duct
119889 [119869119898
(119903outer119896119903)]
119889119903
119889 [119884119898
(119903inner119896119903)]
119889119903
minus119889 [119869119898
(119903inner119896119903)]
119889119903
119889 [119884119898
(119903outer119896119903)]
119889119903= 0
(12)
Here 119903outer and 119903inner are the bypass duct inner wall radius andthe inner hub radius respectively The axial wave number 119896
119886
is computed from
119896119886
=119896
1 minus 1198722119895
(minus119872119895
plusmnradic
1 minus1198962
119903(1 minus 119872
2
119895)
1198962) (13)
where 119872119895is the Mach number at the fan face The selection
of plus or minus signs in the parentheses is determined bythe propagation direction of the sound wave where plus(+) represents the positive propagation direction along the
axial coordinate and vice versa The constant 1198881satisfies the
following relation
1198881
= minus(119889119889119903) [119869
119898(119903outer119896119903)]
(119889119889119903) [119884119898
(119903outer119896119903)]
= minus(119889119889119903) [119869
119898(119903inner119896119903)]
(119889119889119903) [119884119898
(119903inner119896119903)]
(14)
Parameters are set from experimental data (119898 119899) =
(minus13 0) 119903outer = 02667m and 119903inner = 00998m Thereference length D = 06223mis the length from the fanface to the leading edge of the nacelle The blade passingfrequency (BPF) is set to 3150Hz which is derived fromthe fan rotating speed of 6750 rpm The experiments wereconducted in the static condition and the fan face axial Machnumber is 0175 The present computation is also conductedin the static condition In the present computation the axialflow velocity of the ghost cell at the fan face boundary isdirectly modified to this Mach number The pressure andthe density are the same values as those of the adjacent fluidcells The SPL is measured at a radius of 49D The integrationmethod of Ffowcs-Williams and Hawkings (FW-H) [36] isemployed to estimate the far-field pressure from thenear-fieldpressure
Figure 10 shows the computational domain and Table 4lists the mesh information The computations of the com-pressible Euler solver and the LEEs solver are conductedusing the samemeshThePPW inTable 4 is the PPWreducedby the Doppler effect of the fan face axial Mach number Thecomputational domain is set at minus1119863 le 119909 le 7119863 minus8119863 le 119910 le
8119863 and minus8119863 le 119911 le 8119863The fan face is at 119909 = 05119863The innerend of the buffer zone is set at 119909 = [0 4119863] 119910 = [minus4119863 4119863]and 119911 = [minus4119863 4119863] The FW-H surfaces are located at thecube boundaries between the smallest size cubes and thelarger size cubes
Figure 11 shows theMachnumber distribution around theJT15D nacelle In Figure 11 the acceleration region near theinternal wall of the nacelle lip and the stagnation at the spikeare shown Because the experiments and computations wereconducted under the static condition the mean flow fieldexists only near the nacelle
Figure 12 shows the instantaneous pressure distributionsat the planes defined at 119911 = 0 and 119909 = 17119863 In the figure onlythe distributions of the smallest sized cubes are drawn Thefan noise is diffracted at the inlet of the nacelle and propagatesalong the radial direction The 13 peaks and valleys of theswirling fan noise at the 119909 = 17119863 plane are clearly capturedwhich is equivalent to the number of spinning modes Thetime history of the pressure is sampled at the establishedpoints on the FW-H surface and the periodic steady state isobserved after 119879 = 8
Figure 13 shows a comparison of the predicted SPL withthe experimental results conducted by Heidmann et al [37]and the computational results computed by Lan et al [34]The horizontal axis in the figure is the angle from the +119909-axialdirection In the figure the predicted SPL using the presentsolver shows good agreement with the computational resultof Lan et al (within 1 dB) Compared with the experimental
12 International Journal of Aerospace Engineering
Table 4 Mesh information for the JT15D nacelle
JT15D Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWCase 1 00166D 1544 30 times 30 times 30 41688000 87Case 2 00125D 1544 40 times 40 times 40 98816000 116
16D
8D
16D
16D
y
x
yzy
x z
Figure 10 Computational domain for the JT15D nacelle
Mac
h nu
mbe
r
02000100
0000
Figure 11 Mach number distribution around the JT15D nacelle
data a difference of about 3 dB is found at 60 deg Howeverthis discrepancy is also shown between the experimental dataand the result of Lan et al The SPL peak obtained near55 deg is equivalent to that obtained by Lan et al and thatobtained experimentally
6 Noise Propagation arounda Fuselage-Wing-Nacelle Configuration
The noise propagation around a fuselage-wing-nacelle con-figuration is computed as a realistic exampleThe focus of theexample was that of the OWN configuration [38] where theengine nacelle is mounted over the main wing which servesas one of the configurations designed to achieve substantialairport noise reduction The main feature of this configu-ration is that the main wing serves as a shield between the
ground and the noise generated by the engine To investigatethe effect of the OWN configuration the propagation of fannoise of both the conventional DLR-F6 aircraft configuration[39] and the OWN configuration is computed and the SPLbelow the aircraft for both configurations is comparedTheseconfigurations have complex geometry with large curvaturesnear the wing-body and the nacelle-pylon junctions In theOWN configuration the nacelle is moved 11D in the +119909
direction and 06D in the +y direction relative to its locationin the DLR-F6 configuration Here the reference length 119863 =
49m is the longitudinal length of the nacelle The cross-sectional geometry of the pylon is used without any changesand has a sweepback angle of 40 deg A mean flow fieldof Mach number 03 with zero angle of attack is computedusing the compressible Euler solver The sound source isintroduced via a discrete frequency spinning mode As anexample of a modern turbofan engine the CFM56-7B engineis considered The bypass ratio is 55 the fan diameter is154m the number of blades is 24 the maximum rotationalrate is 5382 rpm and the fundamental BPF is 21528HzTheBPF is used as the input frequency of the spinning modeThespinning mode (119898 119899) is set to (minus24 0) The SPL is measuredat a radius of 10D using the FW-H method
Figure 14 shows the computational domain of each con-figuration The black dot shows the origin of coordinatesystem The computations of the compressible Euler andLEEs solvers are conducted using an equivalent mesh Thesize of the computational domains is 4119863 times 2119863 times 2119863 Thesymmetric boundary condition is set at the minusz boundaryThe computational domains are set to ensure that sufficientcomputational domains surround the nacelle It is assumedthat the geometry out of the computational domain has littleinfluence on the noise directivity below the aircraft The
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Active and Passive Electronic Components
Control Scienceand Engineering
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
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Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
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Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
12 International Journal of Aerospace Engineering
Table 4 Mesh information for the JT15D nacelle
JT15D Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWCase 1 00166D 1544 30 times 30 times 30 41688000 87Case 2 00125D 1544 40 times 40 times 40 98816000 116
16D
8D
16D
16D
y
x
yzy
x z
Figure 10 Computational domain for the JT15D nacelle
Mac
h nu
mbe
r
02000100
0000
Figure 11 Mach number distribution around the JT15D nacelle
data a difference of about 3 dB is found at 60 deg Howeverthis discrepancy is also shown between the experimental dataand the result of Lan et al The SPL peak obtained near55 deg is equivalent to that obtained by Lan et al and thatobtained experimentally
6 Noise Propagation arounda Fuselage-Wing-Nacelle Configuration
The noise propagation around a fuselage-wing-nacelle con-figuration is computed as a realistic exampleThe focus of theexample was that of the OWN configuration [38] where theengine nacelle is mounted over the main wing which servesas one of the configurations designed to achieve substantialairport noise reduction The main feature of this configu-ration is that the main wing serves as a shield between the
ground and the noise generated by the engine To investigatethe effect of the OWN configuration the propagation of fannoise of both the conventional DLR-F6 aircraft configuration[39] and the OWN configuration is computed and the SPLbelow the aircraft for both configurations is comparedTheseconfigurations have complex geometry with large curvaturesnear the wing-body and the nacelle-pylon junctions In theOWN configuration the nacelle is moved 11D in the +119909
direction and 06D in the +y direction relative to its locationin the DLR-F6 configuration Here the reference length 119863 =
49m is the longitudinal length of the nacelle The cross-sectional geometry of the pylon is used without any changesand has a sweepback angle of 40 deg A mean flow fieldof Mach number 03 with zero angle of attack is computedusing the compressible Euler solver The sound source isintroduced via a discrete frequency spinning mode As anexample of a modern turbofan engine the CFM56-7B engineis considered The bypass ratio is 55 the fan diameter is154m the number of blades is 24 the maximum rotationalrate is 5382 rpm and the fundamental BPF is 21528HzTheBPF is used as the input frequency of the spinning modeThespinning mode (119898 119899) is set to (minus24 0) The SPL is measuredat a radius of 10D using the FW-H method
Figure 14 shows the computational domain of each con-figuration The black dot shows the origin of coordinatesystem The computations of the compressible Euler andLEEs solvers are conducted using an equivalent mesh Thesize of the computational domains is 4119863 times 2119863 times 2119863 Thesymmetric boundary condition is set at the minusz boundaryThe computational domains are set to ensure that sufficientcomputational domains surround the nacelle It is assumedthat the geometry out of the computational domain has littleinfluence on the noise directivity below the aircraft The
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 13
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(a) 119911 = 0 plane
Pressure
5000E minus 003
0000E + 000
minus5000E minus 003
(b) 119909 = 17119863 plane
Figure 12 Instantaneous pressure distributions of two cross-sectional surfaces
0deg
90deg
45deg
y
x70
75
80
85
90
95
0 10 20 30 40 50 60 70 80 90 100
SPL
(dB)
Angle (deg)
Heidmann et al (1979)Lan et al (2004)
Case 1Case 2
Figure 13 The sound pressure level (SPL) distributions at a radius of 119903 = 49D
minimum size cubes are located within the domain whereinthe reflection and diffraction by the aircraftmust be resolvedThe inner end of the buffer zone is set at 119909 = [minus075119863 175119863]119910 = [minus05119863 05119863] and 119911 = 175119863 in the DLR-F6 calculationand at 119909 = [0119863 275119863] 119910 = [minus025119863 075119863] and 119911 = 175119863
in the OWN calculation FW-H surfaces are located at theinner end of the buffer zone and the symmetrical plane Thesize of the buffer zones of the DLR-F6 calculation is 075D inthe minus119909 and +119909 directions 05D in the minusy and +y directionsand 025D in the +z direction The size of the buffer zonesof the OWN calculation is 05D in the minusx direction 075Din the +x direction 025D in the minusy direction 075D in +ydirection and 025D in the+z direction Table 5 lists themeshinformation of the computations The PPW in Table 5 is thePPW reduced by the Doppler effect of the mean flow fieldMach number
Figure 15 shows the Mach number distributions at thenacelle center for the two configurations In Figure 15 the
acceleration region over the wing and the stagnation at theinlet of the nacelle are shown A Mach number greater than03 is shown in the acceleration region Figure 16 showsthe SPL distributions on the aircraft surface for the twoconfigurations Noise from the nacelle propagates in theradial direction and the noise is shielded by the main wingin the OWN configuration On the other hand noise fromthe inlet reaches the fuselage and generates a high SPL in theOWN configuration compared to the DLR-F6 configuration
To check the propriety of the computations the SPLdistribution computed for the OWN configuration on thesuction side of themain wing is compared with data capturedduring flight and the computations of others [40] The flightdata of a twin-engine business jet aircraft was acquired ata flight Mach number of 03 at an altitude of 1500m Thisaircraft has the aft fuselage nacelle configuration that the inletof the engine nacelle is located over themain wingThereforequalitative comparisons can be conducted The SPL on thesuction side of the main wing was measured using Kulite
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
14 International Journal of Aerospace Engineering
2D
2D
2D
4D
y
z
x
z
(a) DLR-F6 configuration
2D
2D
2D
4D
y
z
x
z
(b) OWN configuration
Figure 14 Computational domains for the fuselage-wing-nacelle configurations (black dot origin of coordinate system)
Mac
h nu
mbe
r
0100
0300
0000
0200
0400
(a) DLR-F6 configurationM
ach
num
ber
0100
0300
0000
0200
0400
(b) OWN configuration
Figure 15 Mach number distributions at the nacelle center
minus27500
minus2500
minus40000
minus15000
10000
SPL
(a) DLR-F6 configuration
minus27500
minus2500
minus40000
minus15000
10000
SPL
(b) OWN configuration
Figure 16 The sound pressure level (SPL) distributions on the aircraft surfaces
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 15
Table 5 Mesh information for calculations of noise propagation around the fuselage-wing-nacelle configurations
Minimum cell size Number of cubes Number of cells in one cube Total number of cells PPWDLR-F6 00025D 3474 50 times 50 times 50 434250000 90OWN 00025D 3425 50 times 50 times 50 428125000 90
120579n
0
10
20
30
40 45 50 55 60 65 70SP
L (d
B)Angle from inlet axis (deg)
Flight dataXu et al (2003)
OWN configuration
minus30
minus20
minus10
Figure 17 Sound pressure level (SPL) distributions on the main wing surface
microphones The computation of Xu et al was conductedusing the discrete frequency spinning mode (20 0) without amean flow field The computed SPL is normalized so that thepeak SPL is equal to that of the flight data Figure 17 showsthe SPL versus the angle from the inlet axis The computedSPL agrees with the flight data from 50 to 70 deg within 3 dBThe peak SPL is at 63 deg This is similar to the peak given bythe flight data which has a peak at 60 deg The discrepancyat an angle of 40 deg is caused by the different clearancesbetween the engine and the main wing where the clearanceof the aircraft employed in the experiment is smaller than thatof the present computation
Figure 18 shows the estimated SPL distribution at a radiusof 10D based on the center of the front face of nacelle Basedon International Civil Aviation Organization rules aircraftnoise is determined by the noise levels at the side and thebottom locations relative to the fuselage Therefore the SPLdistribution below the aircraft is estimated From Figure 18the SPL of the OWN configuration is lower than that ofthe DLR-F6 configuration by about 10 dB over the range of40 deg to 70 deg This represents significant noise reductionrelative to conventional aircraft design Using the proposedmethod it would be possible to optimize the position of thenacelle to obtain maximum noise shielding performance
7 Conclusion
The linearized Euler equationssolver on block-structuredCartesianmesh of the building-cubemethod (BCM) coupledwith the immersed boundary method (IBM) has been devel-oped to compute noise propagation around complex geome-try The accuracy and effectiveness of the solver for practical
problems were validated by application to one-dimensionaland three-dimensional noise propagation problems and theapplication of fan noise propagation around fuselage-wing-nacelle configurations
For the one-dimensional noise propagation problem theIBM slightly decreased the order of accuracy of the systembecause the second-order central difference is employed atfluid cells adjacent to ghost cells However a fourth orderof accuracy is nearly retained even when employing theIBM Interpolation between cubes of different sizes causesdegradation to a second order of accuracy
For the problem of acoustic scattering around a spherethe error was suppressed by mesh refinement near the sphereand by expansion of the buffer zone The results computedon the BCM meshes provided quantitative agreement withthe analytical solution A normalized root mean square errorof 162 and a normalized maximum error of 5 for theresults computed by the BCM Fine3 mesh were about one-half of the errors computed by theUniform Finemesh whichhas twice as many mesh points as the BCM Fine3 mesh Thecomputational time required for the BCM mesh was slightlylonger than that required for the uniformmesh because of themismatch between the number of CPUs and cubes
The estimated sound pressure level (SPL) from the JT15Dnacelle provided good agreement with experimental dataand with other computational results The present solverdemonstrated accurate computations for a curved object likean axisymmetric nacelle
Noise propagation around two fuselage-wing-nacelleconfigurations was computed as a realistic example to verifythe capability of the present solver and to estimate thenoise shielding effect of the OWN configurationThe aircraftconfiguration has complicated geometries especially near the
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
16 International Journal of Aerospace Engineering
3540455055606570758085
40 50 60 70 80 90 100 110 120 130 140
SPL
(dB)
Angle (deg)
DLR-F6OWN configuration
0deg 180deg
90deg
y
x
Figure 18 The sound pressure level (SPL) distributions at a radius of 119903 = 10D based on the center of front face of nacelle
wing-body and the nacelle-pylon junctions and the presentsolver demonstrated a robust treatment of these geometriesFor the OWN configuration the noise from the nacelle inletwas shielded effectively by the main wing because the noisediffracted strongly in the radial directionThe computed SPLat the suction side of themain wing agrees with data obtainedduring flightThe SPL distribution of theOWNconfigurationbelow the aircraft was lower by about 10 dB than that of theconventional DLR-F6 configuration
Through application to simple test cases and realisticcases the effectiveness of the solver was confirmed Usingthe present solver noise propagation around next-generationunconventional aircraft can be estimated and the method isexpected to contribute to the future of aircraft design
Nomenclature
119894 119895 119896 119897 Cell index coordinates119909 119910 119911 Coordinates in the computational domainΔ119909 Δ119910 Δ119911 Mesh spacing119876 Physical quantities vector1198761015840 Fluctuation vector
1199061 1199062 1199063 Velocity fluctuation of 119909 119910 and 119911
direction1198760 Mean flow field vector
11990610
11990620
11990630 Mean velocity of 119909 119910 and 119911 direction
119878 Sound source vector120574 Specific heat ratio120575 Kronecker deltan Unit normal vectorVIP Velocity vector at the image pointVGC Velocity vector at the ghost cell119889IP Distance from the image point to the wall
surface119889GC Distance from the ghost cell to the wall
surface119876119900 Physical quantities at an overlap cell
119876119904 Physical quantities at a surrounding cell
119909119900 119910119900 119911119900 119909 119910 119911 coordinates of an overlap cell
120590 Damping coefficient in the buffer zone119909119887 119910119887 119911119887 Distance from the inner end of the buffer
zone119871119887119909
119871119887119910
119871119887119911 Width of the buffer zone
119863 Reference length1199011015840
(initial) Initial pressure1199011015840
(computed) Computed pressure1199011015840
(analytical) Analytical solution of the pressure119879 Nondimensional time119875rms Root mean square pressure119888 Speed of sound(119898 119899) Input spinning mode119869119898
119884119898 119898th order Bessel functions of the first and
second kind
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by JSPS KAKENHI Grant nos21226018 and 25sdot9225 The computation in this research wasconducted using an SGI AltixUV1000 of the Institute ofFluid Science Tohoku University The Ffowcs-Williams andHawkings code used in this research was provided by theAviation Program Group of Japan Aerospace ExplorationAgency (JAXA)
References
[1] D-Y Kwak T Hirotani M Noguchi and T Ito ldquoExperimen-tal research for aerodynamic interference by upper mountedengine exhaust jet on sst configurationsrdquo in Proceedings of the27th Congress of the International Council of the AeronauticalSciences 2010 (ICAS rsquo10) pp 1211ndash1219 Nice France September2010
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 17
[2] H Ishikawa K Tanaka Y Makino and K YamamotoldquoSonic-boom prediction using euler CFD codes with struc-turedunstrucutured overset methodrdquo in Proceedings of the 27thCongress of the International Council of the Aeronautical Sciences(ICAS rsquo10) pp 744ndash751 September 2010
[3] A Murakami ldquoSilent supersonic technology demonstrationprogramrdquo in Proceedings of the 25th Congress of InternationalCouncil of the Aeronautical Sciences Hamburg GermanySeptember 2006
[4] E Envia ldquoEmerging community noise reduction approachesrdquoin Proceedings of the 3rd AIAA Atmospheric Space EnvironmentsConference AIAA Paper 2011-3532 June 2011
[5] T Russell B Casey and O Erik ldquoHybrid wing body aircraftsystem noise assessment with propulsion airframe aeroacousticexperimentsrdquo in Proceedings of the 16th AIAACEAS Aeroacous-tic Conference AIAAPaper 2010-3913 Stockholm Sweden June2010
[6] J L Felder H D Kim and G V Brown ldquoTurboelectric dis-tributed propulsion engine cycle analysis for hybrid-wing-bodyaircraftrdquo in Proceedings of the 47th AIAA Aerospace SciencesMeeting including the New Horizons Forum and AerospaceExposition January 2009 AIAA paper 2009-1132
[7] S Redonnet G Desquesnes E Manoha and C ParzanildquoNumerical study of acoustic installation effects with a compu-tational aeroacoustics methodrdquoAIAA Journal vol 48 no 5 pp929ndash937 2010
[8] M Hepperle ldquoEnvironmental friendly transport aircraftrdquo inNewResults in Numerical and Experimental FluidMechanics IVvol 87 of Notes on Numerical Fluid Mechanics and Multidisci-plinary Design Springer 2004
[9] A B Nagy ldquoAeroacoustics research in Europe the CEAS-ASCreport on 2010 highlightsrdquo Journal of Sound and Vibration vol330 no 21 pp 4955ndash4980 2011
[10] S Powell A Sobester and P Joseph ldquoPerformance and noisetrade-offs on a civil airliner with over-the-wing enginesrdquo inProceedings of the 49th AIAA Aerospace Sciences Meeting AIAApaper 2011-0266 Orlando Fla USA 2011
[11] S Fukata K Hayama G Sylvand S Alestra and T AxumaldquoStudy of jet noise source modeling and shielding effect forfuture aircraftrdquo Inter-Noise 2011 2011
[12] M Czech R Thomas and R Elkoby ldquoPropulsion airframeaeroacoustic integration effects for a hybrid wing body aircraftconfiguraionrdquo inProceedings of the 16thAIAACEASAeroacous-tics Conference AIAA Paper 2010-3912 Stockholm SwedenJune 2010
[13] X Huang X Chen Z Ma and X Zhang ldquoEfficient compu-tation of spinning modal radiation through an engine bypassductrdquo AIAA Journal vol 46 no 6 pp 1413ndash1423 2008
[14] K Chiba T Imamura K Amemiya and K Yamamoto ldquoDesignoptimization of shielding effect for aircraft engine noiserdquoJournal of Environment and Engineering vol 2 no 3 pp 567ndash577 2007
[15] T Kamatsuchi ldquoComputational aeroacoustic analysis aroundan airfoil using linearized Euler equationsrdquo Journal of JapanSociety of Fluid Mechanics vol 23 pp 285ndash294 2004
[16] X Chen X Huang and X Zhang ldquoSound radiation from abypass duct with bifurcationsrdquo AIAA Journal vol 47 no 2 pp429ndash436 2009
[17] M Bauer J Dierke and R Ewert ldquoApplication of a discon-tinuous Galerkin method to discretize acoustic perturbationequationsrdquo AIAA Journal vol 49 no 5 pp 898ndash908 2011
[18] H Onda R Sakai D Sasaki and K Nakahashi ldquoUnsteadyflow and aerodynamic noise analysis around JAXA landing gearmodel by building-cube methodrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting AIAA Paper 2011-1081 2011
[19] D Sasaki H Onda A Deguchi R Sakai and K NakahashildquoLanding gear aerodynamic noise prediction using building-cube methodrdquo in Proceedings of the 29th AIAA Applied Aero-dynamics Conference June 2011 AIAA Paper 2011-3366
[20] A Deguchi D Sasaki K Nakahashi M Murayama KYamamoto and Y Yokokawa ldquoAeroacoustic simulation ofJAXA landing gear by building-cube method and non-compactCurlersquos equationrdquo in Proceedings of the 50th AIAA AerospaceSciences Meeting AIAA Paper 2012-0388 2012
[21] K Nakahashi and L-S Kim ldquoHigh-density mesh flow com-putations by building-cube methodrdquo in Computational FluidDynamics 2004 C Groth and D W Zinggm Eds pp 121ndash126Springer Berlin Germany 2006
[22] K Nakahashi ldquoBuilding-cube method for flow problemswith broadband characteristic lengthrdquo in Computational FluidDynamics 2002 S Armfield R Morgan and K Srinivas Edspp 77ndash81 Springer 2003
[23] C Bogey C Bailly and D Juve ldquoComputation of flow noiseusing source terms in linearized Eulerrsquos equationsrdquo AIAAJournal vol 40 no 2 pp 235ndash243 2002
[24] T Ishida S Takahashi and K Nakahashi ldquoEfficient and robustCartesian mesh generation for building-cube methodrdquo Journalof Computational Science and Technology vol 2 pp 33ndash45 2011
[25] K Nakahashi ldquoImmersed boundary method for compressibleEuler equations in the building-cube methodrdquo in Proceedingsof the 20th AIAA Computational Fluid Dynamics ConferenceAIAA Paper 2011-3386 2011
[26] E Shima and K Kitamura ldquoOn new simple low-dissipationscheme of AUSM-family for all speedsrdquo in Proceedings of the47th AIAA Aerospace Sciences Meeting AIAA Paper 2009-136January 2009
[27] C K W Tam ldquoRecent advances in computational aeroacous-ticsrdquo Fluid Dynamics Research vol 38 pp 591ndash615 2006
[28] V Allampalli R HixonM Nallasamy and S D Sawyer ldquoHigh-accuracy large-step explicit Runge-Kutta (HALE-RK) schemesfor computational aeroacousticsrdquo Journal of ComputationalPhysics vol 228 no 10 pp 3837ndash3850 2009
[29] R Mittal H Dong M Bozkurttas F M Najjar A Vargasand A von Loebbecke ldquoA versatile sharp interface immersedboundary method for incompressible flows with complexboundariesrdquo Journal of Computational Physics vol 227 no 10pp 4825ndash4852 2008
[30] T Ishida S Kawai and K Nakahashi ldquoA high-resolutionmethod for flow simulations on block-structured Cartesianmeshesrdquo in Proceedings of the 6th International Conference onComputational Fluid Dynamics (ICCFD6 rsquo10) Saint PetersburgRussia July 2010
[31] B Wasistho B J Geurts and J G M Kuerten ldquoSimulationtechniques for spatially evolving instabilities in compressibleflow over a flat platerdquo Computers and Fluids vol 26 no 7 pp713ndash739 1997
[32] C K W Tam and J C Hardin Second Computational Aeroa-coustics (CAA) Workshop on Benchmark Problems NASA Con-ference Publication 3352 1997
[33] J H Seo and R Mittal ldquoA high-order immersed boundarymethod for acoustic wave scattering and low-Mach numberflow-induced sound in complex geometriesrdquo Journal of Com-putational Physics vol 230 no 4 pp 1000ndash1019 2011
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
18 International Journal of Aerospace Engineering
[34] J H Lan Y Guo and C Breard ldquoValidation of acousticpropagation code with JT15D static and flight test datardquo inProceedings of the 10th AIAACEAS Aeroacoustic ConferenceAIAA paper 2004-2986 May 2004
[35] J M Tyler and T G Sofrin ldquoAxial flow compressor noisestudiesrdquo SAE Transactions vol 70 pp 309ndash332 1962
[36] A S Lyrintzis ldquoSurface integral methods in computationalaeroacousticsmdashfrom the (CFD) near-field to the (Acoustic) far-fieldrdquo International Journal of Aeroacoustics vol 2 no 2 pp 95ndash128 2003
[37] M F Heidmann A V Saule and J G McArdle ldquoAnalysis ofradiation patterns of interaction tones generated by inlet rods inthe JT15D enginerdquo in Proceedings of the 5th AIAA AeroacousticsConference AIAA paper 79-0581 1979
[38] D Sasaki and K Nakahashi ldquoAerodynamic optimization ofan over-the-wing-nacelle-mount configurationrdquoModelling andSimulation in Engineering vol 2011 Article ID 293078 13 pages2011
[39] K R Laflin SM Klausmeyer T Zickuhr et al ldquoData summaryfrom second AIAA computational fluid dynamics drag predic-tion workshoprdquo Journal of Aircraft vol 42 no 5 pp 1165ndash11782005
[40] J XuD StanescuMYHussaini and F Farassat ldquoComputationof engine noise propagation and scattering off an aircraftrdquo inProceedings of the 41th AIAA Aerospace Sciences Meeting AIAAPaper 2003-0542 Reno Nev USA January 2003
International Journal of
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Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of