2840
Transcript of 2840
-
University of Tsukuba
Title
Author(s),
Citation
Issue Date2013-03
Text versionauthor
URL http://hdl.handle.net/2241/118900
DOI
Right
-
Rotating Detonation EngineRDERDE
RDE
Multi-frame Short-time Open-shutter PhotographyMSOP
2
ir2
2
2
nD ChapmanJouguet CJD nD
CJn /DD ir 1 CJn /DD CJn /DD C2H4+3O22H2+O2 2C2H2+5O2+7Ar2 CJn /DD 1 ir ir
2
CJn /DD Yao and Stewart Sharpe
2
CJn /DD CJn DD 1 CJn DD
CJn DD
CJn DD
-
__________________________________________________________________________________________________________
i
1 1 1.1. 1
1.1.1. 1
1.1.2. 4
1.2. 6
1.2.1. 6
1.2.2. 7
1.2.3. 11
1.3. 14
1.3.1. 14
1.3.2. 17
2 18
2.1. 18
2.2. Multi-frame Short-time Open-shutter PhotographyMSOP 18
2.3. 22
2.4. 25
2.5. 26
2.5.1. 26
2.5.2. 27
2.5.3. 29
2.5.4. 32
2.6. 34
3 Dn/DCJ 35
3.1. 35
3.2. 35
3.3. 38
3.4. 41
3.5. 43
3.5.1. 43
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__________________________________________________________________________________________________________
ii
3.5.2. 45
3.5.3. 48
3.5.4. 50
3.5.5. 51
3.5.6. Dn/DCJ 55 3.5.7. Dn/DCJ 59 3.5.8. 62
3.6. 66
3.6.1. Dn/DCJ 66 3.6.2. Dn/DCJ 68 3.6.3. 70
3.7. 75
4 1 76
4.1. 76
4.2. 76
4.3. 78
4.4. 80
4.5. 82
4.5.1. 82
4.5.2. 83
4.5.3. 84
4.6. 85
4.7. Dn/DCJ 88 4.8. Dn/DCJ 91 4.9. 95
4.9.1. 95
4.9.2. 100
4.9.3. Dn/DCJ 102 4.10. 105
5 106 5.1. 106
5.2. 109
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__________________________________________________________________________________________________________
iii
111 113 123 A ChapmanJouguetCJ 128 B 131 C 136 D ChapmanJouguetCJ 142 E 148 F 151
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__________________________________________________________________________________________________________
iv
1
1.1
ZND 2
1.2 4 1.3 vp 38) 5
1.4 7
1.5 PBX9502
62) 8
1.6 PBX9502
64) 8
1.7 12
1.8
12
1.9 92) 13
1.10 2 14
2
2.1 Short-time Open-shutter PhotographySOP 19
2.2 2 SOP 19
2.3 Multi-frame Short-time Open-shutter PhotographyMSOP 21
2.4 2MSOP 21
2.5 22
2.6 23
2.7 2 24
2.8 2
25
2.9 2
27
2.10 2
28
2.11 2
40i r mm 29 2.12 MSOP 40i r mm 31
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__________________________________________________________________________________________________________
v
2.13 irMSOP 50.1 mm 33 3
3.1 2 2
37
3.2 2 37
3.3 2
39
3.4 2
C2H4+3O2 44
3.5 2
2H2+O2 44
3.6 2
2C2H2+5O2+7Ar 45
3.7 2
20i r mm2H2+O2 47 3.8 2
C2H4+3O2 48
3.9 2
2H2+O2 49
3.10 2
2C2H2+5O2+7Ar 49
3.11 2
20i r mm 70.0 mmC2H4+3O2 50 3.12 2
20i r mm 70.0 mm C2H4+3O2 51
3.13 2
20i r mm 70.0 mmC2H4+3O2 52 3.14 2
20i r mm 70.0 mmC2H4+3O2 53 3.15 2 33.100.1 i rr
20i r mm 70.0 mmC2H4+3O2 54
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vi
3.16 1 00.200.1 i rr 2 20.100.1 i rr CJn DD 20i r mm 70.0 mmC2H4+3O2 55 3.17 2
CJn DD C2H4+3O2 56 3.18 2
CJn DD 2H2+O2 57 3.19 2
CJn DD 2C2H2+5O2+7Ar 57 3.20 CJn DD 58 3.21 2
CJn DD 20i r mm 70.0 mmC2H4+3O2 60 3.22 2
CJn DD 40i r mm 56.1 mm2H2+O2 60 3.23 2
CJn DD 10i r mm 27.0 mm2C2H2+5O2+7Ar 61 3.24 Marker particle method 61
3.25 2
64
3.26 2
3.36i r C2H4+3O2 ir 65
3.27 2
5.27i r 20i r mm 65
3.28 2
01.3 mm 66 3.29 2
CJn DD 67 3.30 CJn DD
2 69
3.31 2
CJn DD 70
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__________________________________________________________________________________________________________
vii
3.32
71
3.33 w 72
3.34 CJn DD 2
74
4
4.1 77 4.2 CJC 88 4.3 CJn DD
C2H4+3O2 90
4.4 CJn DD 2H2+O2 90
4.5 CJn DD 2C2H2+5O2+7Ar 91
4.6 CJn DD C2H4+3O2 93 4.7 CJn DD a~T
C2H4+3O2 94
4.8 CJn DD C C2H4+3O2 94 4.9 T~C2H4+3O2 96
4.10 ~C2H4+3O2 96 4.11 fr~a C2H4+3O2 97
4.12 n~u C2H4+3O2 97
4.13 p~C2H4+3O2 98
4.14 ~C2H4+3O2 98 4.15 YC2H4+3O2 99
4.16 M C2H4+3O2 99
4.17 CJn DD ~ ~ ~~ C2H4+3O2 101
4.18 CJn DD *Q M C2H4+3O2 102 4.19 CJn DD M
C2H4+3O2 104
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viii
A A.1 C2H4+3O2 129
A.2 2H2+O2 129
A.3 2C2H2+5O2+7Ar 130
B
B.1 Marker particle method 131
B.2 2
133
D
D.1 142
D.2 CJ
C2H4+3O2 144
-
ix
2
2.1 25
3 3.1 36
3.2 38
4
4.1 87
4.2 C2H4+3O2 92
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__________________________________________________________________________________________________________
x
A
a
B
C ChapmanJouguet
c
D
D e
f f f1 ~ f5 6
G
g
h
K C.50
k
L
l
M
M
m 3.5
n
n
P
p
Q* 4.51
q
q* 4.49
R
R 2
r
s
T
T t
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__________________________________________________________________________________________________________
xi
u
v
W
w
X
x
Y
y
Z
Z
D.25 ChapmanJouguet 4.48 4.47 D.24
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__________________________________________________________________________________________________________
xii
a
asy
B
b
CJ ChapmanJouguet
CJp ChapmanJouguet
c
cr
D
eq
exp
f
fr
H
i 2
ig
im
ChapmanJouguet
in
ind
int
j
mt
n
nd
ng
o 2
out
overall
P
p
R
s
u
-
__________________________________________________________________________________________________________
xiii
v
vN von Neumann
w
0
1
2, 2, 2 1.3 22 2 3, 3, 3 1.3 33 3 +
0
m
~ 4.40
-
1
__________________________________________________________________________________________________________
1
1
1.1.
1.1.1.
5 ~ 7
1.1 1.1
1
1)
von NeumannvN
1.1
2)
-
1
__________________________________________________________________________________________________________
2
1) ChapmanJouguetCJCJ 1.1
Zeldovich3)von Neumann4) Dring5)ZND
CJ
CJ CJ
CJ CJ
CJ CJ
CJ
ZND 1
613)
Propagation direction
x
p, T, M,
Pressure, p
Temperature, T
Mach number, MM = 1
Front shock
Induction zone
CJ point
Induction length, lind
Reaction zone
Thermicity,
Propagation direction
x
p, T, M,
Pressure, p
Temperature, T
Mach number, MM = 1
Front shock
Induction zone
CJ point
Induction length, lind
Reaction zone
Thermicity,
1.1
ZND
-
1
__________________________________________________________________________________________________________
3
ZND
1.2
1.2
1.2
3
1.2
CJ 1430)
CJ
CJ
CJ 1.8 CJ
0.6 31,32)
CJ
ZND CJ
2
1.2 3
-
1
__________________________________________________________________________________________________________
4
1.1.2.
Pulse
Detonation EnginePDE 3337)PDE
PDE PDE
1 PDE 1.3 vp
38)
Zeldovich39) Heiser and Pratt40) 1 Wu et al.41) 2
Wintenberger and Shepherd42)
D
Trajectory of triple point Cell width,
Incident shock (weak shock)
Transverse wave
Propagation direction
Mach stem (strong shock)
Triple point
: Front shock: Forward edge of reaction zone
Micro explosion
Trajectory of triple point Cell width,
Incident shock (weak shock)
Transverse wave
Propagation direction
Mach stem (strong shock)
Triple point
: Front shock: Forward edge of reaction zone
Micro explosion
1.2
-
1
__________________________________________________________________________________________________________
5
Humphrey cycleHBrayton cycle
B
Zeldovich39)PDE 1.3 1 PDE PDE
NvN
2CJ
32 13 132N1 PDE 1
1321 121 qhh outin inh outh q
inh
q outh 3h 3h 3 h 333 q333 sTh dd 1.3
222 sss 333 sss sTh dd h s 333 hhh D > H > B
p
v
1
2
von Neumann point
Hugoniot adiabatic curve
Frozen Hugoniot curve with fixed heat release
Isentropic process
CJ point
Rayleigh line
Detonation process
Constant-volume combustion process
Constant-pressure combustion process2'
3'3
2'', 3''
N
p
v
1
2
von Neumann point
Hugoniot adiabatic curve
Frozen Hugoniot curve with fixed heat release
Isentropic process
CJ point
Rayleigh line
Detonation process
Constant-volume combustion process
Constant-pressure combustion process2'
3'3
2'', 3''
N
1.3 vp 38)
-
1
__________________________________________________________________________________________________________
6
1.2.
1.2.1.
1.4
2327,4347)
4856)
1621)
1.4
CJ Kudo et al.57)Maeda et
al.16) Pintgen and Shepherd44)
58)
1.2.2
1.4a
1.4b
52)
59)
CJ
52)
1.4c
-
1
__________________________________________________________________________________________________________
7
1.2.2.
CJ 60,61)
60)
62,63) 1.5
PBX9502PBX Plastic Bonded Explosive
62)
1.5
Projectile
(a)
(b)
(c)
ProjectileProjectile
(a)
(b)
(c)
1.4
-
1
__________________________________________________________________________________________________________
8
1.6 PBX9502
64) 1.5
1.6 PBX9502
64) 2
1.5
1.5 PBX9502
62)
-
1
__________________________________________________________________________________________________________
9
Eyring et al.65) Wood and Kirkwood66)
Bdzil and Stewart67,68)
ZND Wood and Kirkwood
2
3 1
Bdzil and Stewart Whitham
Geometrical Shock DynamicsGSD69) Detonation Shock DynamicsDSD70)
DSD
64,7173)DSD
7476)
70,74)
1.1.1
2 1
Menikoff et al.77)
1
77)
DSD
2
1
-
1
__________________________________________________________________________________________________________
10
53,64,7881)
1 1
53,7779)
Yao and Stewart80)
2 Sharpe81)
1 1
1.2.1
Maeda et al.16)
Maeda et al.
Maeda et al.
Kudo et al.57) C2H4+3O2
2
-
1
__________________________________________________________________________________________________________
11
2 in,D CJ CJD
8.0CJin, DD 8.06.0 CJin, DD 6.0CJin, DD 3 Kudo et al. 2
2
Thomas and Williams82) Edwards et al.83) 2C2H2+5O2Kudo et al.57) 2
59)
Thomas and Williams Edwards et al.Kudo et al. 2
2
2
Thomas and Williams
Edwards et al.
1.2.3. PDE
PDE
PDE
Rotating
Detonation EngineRDE8492)RDE 1.7
1.8 RDE
RDE PDE
4
RDE
1
1.9 RDE 92)
-
1
__________________________________________________________________________________________________________
12
20 92)
1.8
Burnt gasGaseous
detonation wave
Combustible gas injection
Contact surfaceShock wave
Combustible gas layer
Burnt gasGaseous
detonation wave
Combustible gas injection
Contact surfaceShock wave
Combustible gas layer
1.7
-
1
__________________________________________________________________________________________________________
13
RDE RDE
RDE
RDE
CJ 16,44,57)RDE
RDE
1.8 RDE
RDE
RDE
2 1.10 2
1.9 92)
-
1
__________________________________________________________________________________________________________
14
2
2
2
2
1.10
3.5.2
1.3.
1.3.1. 1.10 2
2 2
2 Kudo et
al.57)
3
Inner wall
Outer wall
Gaseous detonation wave
Initial pressure of combustible gas mixtureHigh Low
Shock waveReaction zone
Re-initiation (transverse
detonation wave)
Propagation of detonation waveSteady Unsteady
Gaseous detonation wave
Shock wave
Reaction zone
Gaseous detonation waveInner radius
Inner radius of annular channelLarge Small
Inner wall
Outer wall
Gaseous detonation wave
Initial pressure of combustible gas mixtureHigh LowInitial pressure of combustible gas mixtureHigh Low
Shock waveReaction zone
Re-initiation (transverse
detonation wave)
Propagation of detonation waveSteady UnsteadyPropagation of detonation waveSteady Unsteady
Gaseous detonation wave
Shock wave
Reaction zone
Gaseous detonation waveInner radius
Inner radius of annular channelLarge SmallInner radius of annular channelLarge Small
1.10 2
-
1
__________________________________________________________________________________________________________
15
1 2
1.2.2 Kudo et al.57) 2
2
2
Thomas and Williams82) Edwards et al.83)2
2
RDE
RDE
2
RDE
2 2
1.2.2
62,63)
RDE
-
1
__________________________________________________________________________________________________________
16
RDE
3 1
1.2.2 ZND
1
2
Yao and Stewart80)
2 Sharpe81)
1 1
Yao and Stewart80) Sharpe81)
3
1 Multi-frame
Short-time Open-shutter PhotographyMSOP93)2
-
1
__________________________________________________________________________________________________________
17
2
2
3
2
1.3.2. 1 2 2
93) 3 2
94,95)
4
1 5
-
2
__________________________________________________________________________________________________________
18
2
2.1.
Multi-frame Short-time Open-shutter PhotographyMSOP93)
2
2
MSOP
2.2. Multi-frame Short-time Open-shutter PhotographyMSOP
2
Multi-frame Short-time Open-shutter Photography
MSOP93)MSOP Short-time Open-shutter PhotographySOP
2.1 SOP 2.1 2 expt
expt s expt
SOP
SOP expt
2.2 2 SOP
2 60 mm
20 mm 1 mm C2H4+3O2 30.8 kPa
expt 4 s 2.2 SOP
-
2
__________________________________________________________________________________________________________
19
Outer wall
Inner wall
Triple point trajectories
Strong luminescence by the shock wave reflected over the outer wall
Outer wall
Inner wall
Triple point trajectories
Strong luminescence by the shock wave reflected over the outer wall
2.2 2 SOP
2 60 mm 20 mm
1 mm C2H4+3O2
30.8 kPa 4 s
Detonation wave at t
Detonation wave at t+texp
Reflected shock waves at t+texp
Triple point trajectories recorded in texp(detonation cell structure)
Reflected shock waves at t
: Overexposure due tostrong luminescence by reflected shock waves
Inner wall
Outer wall
Detonation wave at t
Detonation wave at t+texp
Reflected shock waves at t+texp
Triple point trajectories recorded in texp(detonation cell structure)
Reflected shock waves at t
: Overexposure due tostrong luminescence by reflected shock waves
Inner wall
Outer wall
2.1 Short-time Open-shutter PhotographySOP
-
2
__________________________________________________________________________________________________________
20
SOP
SOP SOP
1
Multi-frame Short-time Open-shutter
PhotographyMSOP 2.3 MSOP 2.3a
SOP intt expt intt
expt intt
SOP SOP 2.3
b1 MSOP MSOP
MSOP SOP m SOP
1m SOP SOP
MSOP
MSOP 2
MSOP MSOP
2.4 2 MSOP
2
20 mm 20 mm 1 mm C2H4+3O2 60.3 kPa expt 4 s 2.4 MSOP MSOP
-
2
__________________________________________________________________________________________________________
21
2.4 2 MSOP
2 20 mm 20 mm
1 mm C2H4+3O2
60.3 kPa 4 s
1st frame
2nd frame
3rd frame
Nth frame
tint
texp
tint tint tint
texp
texp
texp
Exposure
Exposure
Exposure
Exposure
1st frame
2nd frame
3rd frame
Nth frame
tint
texp
tint tint tint
texp
texp
texp
Exposure
Exposure
Exposure
Exposure
(a) SOP
1st frame 2nd frame 3rd frame Nth frame
+
Superimposed-photograph
+ + + =
1st frame 2nd frame 3rd frame Nth frame
+
Superimposed-photograph
+ + + =
(b) SOP MSOP
2.3 Multi-frame Short-time Open-shutter PhotographyMSOP
-
2
__________________________________________________________________________________________________________
22
2.3.
2.5
3 MSOP
3
Convex lens
Convex lens
Mirror
Concave mirror
Pinhole
Knife edge
Signal conditioner
Pulse generator
Observation chamber
Dump tank
Mixture tank
Light source
Rotary pump
Vacuum gauge
Pressure gauge
High-speed video camera
Ignition driver
Optical system
MSOP: w/o optical systemShadowgraph photography: w/ optical system (w/o knife edge)Schlieren photography: w/ optical system (w/ knife edge)Direct photography: w/o optical system
Convex lens
Convex lens
Mirror
Concave mirror
Pinhole
Knife edge
Signal conditioner
Pulse generator
Observation chamber
Dump tank
Mixture tank
Light source
Rotary pump
Vacuum gauge
Pressure gauge
High-speed video camera
Ignition driver
Optical system
Convex lens
Convex lens
Mirror
Concave mirror
Pinhole
Knife edge
Signal conditioner
Pulse generator
Observation chamber
Dump tank
Mixture tank
Light source
Rotary pump
Vacuum gauge
Pressure gauge
High-speed video camera
Ignition driver
Ignition driver
Optical system
MSOP: w/o optical systemShadowgraph photography: w/ optical system (w/o knife edge)Schlieren photography: w/ optical system (w/ knife edge)Direct photography: w/o optical system
2.5
-
2
__________________________________________________________________________________________________________
23
2.6 25.8 mm
20 mm x 16 mm 100 mm x 100 mm 2
12 m
CJ 2
2 40 mm
10 mm
(a) (b)
Spark plug Shchelkin spiral
Rectangular cross-section tube(20 mm x 16 mm)
Detonation tube ( 25.8 mm)
To dump tank
Housing
Diaphragm (12 m)
Curved channel(100 mm x 100 mm)
Curved section
Straight section
590 mm
60 mm
Pressure transducer
Detonation wave
(a) (b)
Spark plug Shchelkin spiral
Rectangular cross-section tube(20 mm x 16 mm)
Detonation tube ( 25.8 mm)
To dump tank
Housing
Diaphragm (12 m)
Curved channel(100 mm x 100 mm)
Curved section
Straight section
590 mm
60 mm
Pressure transducer
Detonation wave
Spark plug Shchelkin spiral
Rectangular cross-section tube(20 mm x 16 mm)
Detonation tube ( 25.8 mm)
To dump tank
Housing
Diaphragm (12 m)
Curved channel(100 mm x 100 mm)
Curved section
Straight section
590 mm
60 mm
Pressure transducer
Detonation wave
2.6
-
2
__________________________________________________________________________________________________________
24
2.7 2 2
ir or
2 5 ir 5 mm10 mm20 mm40 mm 60 mm
20 mm MSOP
1 mm
2.1 p T
CJ CJD CJ C2H4+3O2 T
p p A A.1 p CJD
CJ 2
CJD
2
Shimadzu HPV-2
4 s/frame MSOP 312 x 260 0.3 mm
Type 2 (ri = 10 mm, ro = 30 mm)
ri
50 mm
ro
O
Type 3 (ri = 20 mm, ro = 40 mm)
ri
50 mm
ro
O
Type 5 (ri = 60 mm, ro = 80 mm)
ri
10 mm
ro
O
ri
50 mm
ro
O
Type 1 (ri = 5 mm, ro = 25 mm)
Type 4 (ri = 40 mm, ro = 60 mm)
ri
30 mm
ro
O
Channel width: 20 mm
Channel depth: 1 mm
Type 2 (ri = 10 mm, ro = 30 mm)
ri
50 mm
ro
O
Type 2 (ri = 10 mm, ro = 30 mm)
ri
50 mm
ro
O
ri
50 mm
ro
O
Type 3 (ri = 20 mm, ro = 40 mm)
ri
50 mm
ro
O
Type 3 (ri = 20 mm, ro = 40 mm)
ri
50 mm
ro
O
ri
50 mm
ro
O
Type 5 (ri = 60 mm, ro = 80 mm)
ri
10 mm
ro
O
Type 5 (ri = 60 mm, ro = 80 mm)
ri
10 mm
ro
O
ri
10 mm
ro
O
ri
50 mm
ro
O
Type 1 (ri = 5 mm, ro = 25 mm)
ri
50 mm
ro
O
ri
50 mm
ro
O
Type 1 (ri = 5 mm, ro = 25 mm)
Type 4 (ri = 40 mm, ro = 60 mm)
ri
30 mm
ro
O
Type 4 (ri = 40 mm, ro = 60 mm)
ri
30 mm
ro
O
ri
30 mm
ro
O
Channel width: 20 mm
Channel depth: 1 mm
2.7 2
-
2
__________________________________________________________________________________________________________
25
2.1
Gas mixture p [kPa] T [K] [mm] CJD [m/s] C2H4+3O2 20.3 ~ 80.6 298 1 0.51 ~ 2.42 2121 ~ 2316
2.4.
2 2
2.8
2 2
i CJD
nD in,D
i iiin, rD i in,D CJin, DD Kudo et al.57)
1 stable mode: 8.0CJin, DD 2 critical mode: 8.0CJin, DD 6.0CJin, DD 3 unstable mode: 6.0CJin, DD
O Straight section
Curved section
Outer wall
inner wall
Detonation wave
Dn,i = rii
DCJ
ri i
Dn
O Straight section
Curved section
Outer wall
inner wall
Detonation wave
Dn,i = rii
DCJ
ri i
Dn
2.8 2
-
2
__________________________________________________________________________________________________________
26
2.5.
2.5.1. 2
2.9 2
CJD
NASA CEA96)
CJD
p 5%2
1 mm
2
A A.1 Nakayama et al. 93)
A A.1 p
-
2
__________________________________________________________________________________________________________
27
2.5.2. 2.10 ir ir 2 ir
2.10 .i constr .i constr 3 .i constr
.i constr
.i constr ir 1 32i r 21i r 2 3221 i r
10 20 30 40 50 60 70 80 900
500
1000
1500
2000
2500
3000
p- [kPa]
DC
J [m
/s]
: Theoretical (298.15 K): Experimental (ri = 5 mm): Experimental (ri = 10 mm): Experimental (ri = 20 mm): Experimental (ri = 40 mm): Experimental (ri = 60 mm)
2.9 2
-
2
__________________________________________________________________________________________________________
28
2.11 in,D ir 40 mm
in,D CJD CJin, DD
CJin, DD
CJin, DD
0.0 0.5 1.0 1.5 2.0 2.5 3.00
10
20
30
40
50
60
70
80
[mm]
r i [m
m]
: Stable, : Critical, : Unstable
Stablezone
Transitionzone
Unstablezone
ri/ = 32
ri/ = 21
0.0 0.5 1.0 1.5 2.0 2.5 3.00
10
20
30
40
50
60
70
80
[mm]
r i [m
m]
: Stable, : Critical, : Unstable
Stablezone
Transitionzone
Unstablezone
ri/ = 32
ri/ = 21
2.10 2
-
2
__________________________________________________________________________________________________________
29
2.5.3. 2.12 MSOP 2.12a 2.12b 2.12c 2.11 ir 40 mm
2
2.12a
2.11 CJin, DD
2
concave front focusingkinked front evolution wrinkled front
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
1.0
Dn,
i/DC
J [-]
i []
: = 1.10 mm (stable mode): = 1.48 mm (critical mode): = 2.36 mm (unstable mode)
2.11 2
40i r mm
-
2
__________________________________________________________________________________________________________
30
evolution 3
97)
2.12b2
2.11 CJin, DD
2.12c2
2
2.11 CJin, DD 0.4
2
-
2
__________________________________________________________________________________________________________
31
(a) = 1.10 mm
Stable mode
O
(c) = 2.36 mm
Unstable mode
O
(b) = 1.48 mm
Critical mode
O
(a) = 1.10 mm
Stable mode
O
Stable mode
OO
(c) = 2.36 mm
Unstable mode
O
Unstable mode
OO
(b) = 1.48 mm
Critical mode
O
Critical mode
OO
2.12 MSOP 40i r mm
-
2
__________________________________________________________________________________________________________
32
2.5.4. 2.13 ir MSOP 1.50 mm 2.13a 2.13b
2.13c~ 2.13e
2.13a 2
2.13b
2 2.13c~
2.13e 2
ir 2.13c~ 2.13e
2
2
2
2
1.2
-
2
__________________________________________________________________________________________________________
33
(a) ri = 60 mm
O
Stable mode = 1.51 mm
Critical mode
O
= 1.48 mm
(b) ri = 40 mm
O
Unstable mode = 1.54 mm
(c) ri = 20 mm
O
Unstable mode = 1.50 mm
(d) ri = 10 mm
O
Unstable mode = 1.50 mm
(e) ri = 5 mm
(a) ri = 60 mm
O
Stable mode = 1.51 mm
(a) ri = 60 mm
O
Stable mode = 1.51 mm
OO
Stable mode = 1.51 mm
Critical mode
O
= 1.48 mmCritical mode
OO
= 1.48 mm
(b) ri = 40 mm
O
Unstable mode = 1.54 mm
OO
Unstable mode = 1.54 mm
(c) ri = 20 mm
O
Unstable mode = 1.50 mm
OO
Unstable mode = 1.50 mm
(d) ri = 10 mm
O
Unstable mode = 1.50 mm
OO
Unstable mode = 1.50 mm
(e) ri = 5 mm 2.13 ir MSOP 50.1 mm
-
2
__________________________________________________________________________________________________________
34
2.6.
Multi-frame Short-time Open-shutter PhotographyMSOPMSOP 2
ir
2
2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
35
3 Dn/DCJ
3.1.
2 MSOP
2 1 mm
MSOP 1 mm
2
2
2
or 2
3.2.
2.5 2.6
2.7 2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
36
1 mm 16 mm
3.1 C2H4+3O2 2H2+O2
2C2H2+5O2+7Ar 3 2 T
p p A A.1~ A.3 p CJD CJ 2
2 2
Shimadzu HPV-2 2 s/frame C2H4+3O2 2C2H2+5O2+7Ar 2H2+O2
250 ns 312 x 260
0.3 mm
3.1
Gas mixture p [kPa] T [K] [mm] CJD [m/s] C2H4+3O2 20.4 ~ 100.9 298 6 0.40 ~ 2.41 2212 ~ 2387
2H2+O2 30.0 ~ 190.1 296 2 0.73 ~ 4.82 2680 ~ 2932 2C2H2+5O2+7Ar 15.0 ~ 150.1 294 2 0.23 ~ 3.00 1847 ~ 2033
2.5 2.6
2 2
2
3.1 2 2
2
2
3.2 2 20 mm
16 mm 50 mm 24
2
2.7
-
3 Dn/DCJ
__________________________________________________________________________________________________________
37
1 mm 16 mm
3.2 2C2H2+5O2+7Ar 2
T p
p 1 mm 4 A A.3 p CJD CJ
2
Channel depth: 16 mm
20 mm27.7 mm
R = 50 mm
2480 mm
Channel depth: 16 mm
20 mm27.7 mm
R = 50 mm
2480 mm
3.2 2
Transition region
Fully-developed region
Planar detonation wave
Converging detonation wave
(arc-like, negatively-curved)
R = 1/R
(a) 2
Outer wall
Inner wall
Negatively-curved detonation waveDetonation wave
(b) 2
Transition region
Fully-developed region
Planar detonation wave
Converging detonation wave
(arc-like, negatively-curved)
R = 1/R
Transition region
Fully-developed region
Planar detonation wave
Converging detonation wave
(arc-like, negatively-curved)
R = 1/R
(a) 2
Outer wall
Inner wall
Negatively-curved detonation waveDetonation wave
Outer wall
Inner wall
Negatively-curved detonation waveDetonation wave
(b) 2
3.1 2 2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
38
2 2
2
Shimadzu HPV-2 1 s/frame 250 ns 312 x 260
0.1 mm
3.2
Gas mixture p [kPa] T [K] [mm] CJD [m/s] 2C2H2+5O2+7Ar 11.5 ~ 39.9 297 1 1.00 ~ 4.04 1828 ~ 1977
3.3.
2
3.3
3.3 2
r
2
rd td d
,P r rDnsin 3.1
dd1
sin1sintan
2
rr
3.2
nD
iin, rD 3.13.2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
39
rDDr
r n
2n
2
dd 3.3
nD r3.3
r
r
r
rrDDr
i
dn
2n
2
i
3.4
2 nD
nD
nD
nD
9395)
mrrDDDD
iin,asyn,asyn,n 3.5
dr
Dndt
Straight section
Curved section
Outer wall
Inner wall
Initial line
Dndt
rj = 1 rj = 14 rj = 15
rdt
rj = 2 rj = 13
Detonation wave at t
Detonation wave at t+dt(r+dr)dt
P
r
-di
dtri
rj = 0
rdDn,idt
O
dr
Dndt
Straight section
Curved section
Outer wall
Inner wall
Initial line
Dndt
rj = 1 rj = 14 rj = 15
rdt
rj = 2 rj = 13
Detonation wave at t
Detonation wave at t+dt(r+dr)dt
P
r
-di
dtri
rj = 0
rdDn,idt
O
3.3 2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
40
asyn,D m asyn,D r nD
3.53.43.5 nD r nD r in,D asyn,D
3.3
r r 15 asyn,D m
3.43.5 r r 94) asyn,D 0.005 CJD m 0.05 asyn,D
m CJD 2 asyn,D m ir
2 p r CJasyn, DD asyn,D m
asyn,D CJD
2 nD
nD nD in,D
1dd1
dd1 2
n
r
rr
rrD 3.6
3.63.3 nD 3.6 ddr r 2 ddr 93,94)
j1j2j1jj
2
2
j1jj d
d21
dd
rrrr 3.7
3.7 22 dd r 93,94)
22d
d 1jjj1j1jj
1jj
j1j
j1j
j2
2 rrrrr 3.8
3.73.8
-
3 Dn/DCJ
__________________________________________________________________________________________________________
41
ddr 22 dd r 3.43.5 r
23
22
2
222
dd
dd
dd2
rrrrrr 3.9
ddr 3.3 22 dd r 3.3 3.4
3.5
3.9
3.4.
2
nD nD 93)
2
ir
2
rr p T CJD CJD
nD irr CJD 4
CJi1n ,,, DrrfD 3.10 ir r ir irr 2 ir irr
2
3.10
-
3 Dn/DCJ
__________________________________________________________________________________________________________
42
i
i2
CJ
n ,rrrf
DD
3.11 in,D ir 3.43.11
r
r
r
r
r
r
rrr
rrfrrrf
rr
rrD
DDD
rr
rrDDr
i
i
i
d11,,
d11
d
21
2
i
i2
2
i
ii2
2
i
21
2
CJ
n
2
CJ
in,2
i
n
2n
2
i
3.12
3.12 2f ir
3.9 3.12 ddr 22 dd r ir irr r3.12
ddr 22 dd r 3.93.9 ir irr r
rrrrf 1,i
i3 3.13
3.13
i
i4
1
i
1i
i
i3
i
i3 ,,, r
rrfrrr
rrrf
rrrrf
3.14
3.14 irr 3.11
,i
5CJ
n rfDD 3.15
3.15
CJn DD ir CJn DD ir 3 nD CJn DD ir 3 nD
-
3 Dn/DCJ
__________________________________________________________________________________________________________
43
1.2.2
nD 62,63)3.15 CJn DD ir CJn DD
nD ir CJn DD CJn DD ir CJn DD CJD 2
3.5.
3.5.1. 2
3.4 ~ 3.6 CJD
NASA CEA96) CJD
2 16 mm
-
3 Dn/DCJ
__________________________________________________________________________________________________________
44
20 40 60 80 100 120 140 160 180 2000
500
1000
1500
2000
2500
3000
3500
p- [kPa]
DC
J [m
/s]
: Theoretical (298.15 K): Experimental (ri = 5 mm): Experimental (ri = 10 mm): Experimental (ri = 20 mm): Experimental (ri = 40 mm): Experimental (ri = 60 mm)
3.5 2
2H2+O2
10 20 30 40 50 60 70 80 90 100 1100
500
1000
1500
2000
2500
3000
p- [kPa]
DC
J [m
/s]
: Theoretical (298.15 K): Experimental (ri = 5 mm): Experimental (ri = 10 mm): Experimental (ri = 20 mm): Experimental (ri = 40 mm): Experimental (ri = 60 mm)
3.4 2
C2H4+3O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
45
3.5.2. 3.7 2
4 s ir 20 mm 2H2+O2 2.4
3.7a 2
2.12a MSOP
3.7b
2.12b
MSOP
0 20 40 60 80 100 120 140 1600
500
1000
1500
2000
2500
p- [kPa]
DC
J [m
/s]
: Theoretical (298.15 K): Experimental (ri = 5 mm): Experimental (ri = 10 mm): Experimental (ri = 20 mm): Experimental (ri = 40 mm): Experimental (ri = 60 mm)
3.6 2
2C2H2+5O2+7Ar
-
3 Dn/DCJ
__________________________________________________________________________________________________________
46
3.7c 2
2.12c MSOP
-
3 Dn/DCJ
__________________________________________________________________________________________________________
47
(c)
(b)
(a)
O
= 0.73 mm
O
= 1.56 mm
Unburnt gas pockets
O
= 4.09 mm
Transverse detonation wave
Re-initiation
(c)
(b)
(a)
O
= 0.73 mm
OOO
= 0.73 mm
O
= 1.56 mm
Unburnt gas pockets
OOO
= 1.56 mm
Unburnt gas pockets
O
= 4.09 mm
Transverse detonation wave
Re-initiation
OOO
= 4.09 mm
Transverse detonation wave
Re-initiation
3.7 2
20i r mm2H2+O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
48
3.5.3. 3.8 ~ 3.10 ir 2.5.2 2.10 .i constr C2H4+3O2 23i r 2H2+O2 22i r 2C2H2+5O2+7Ar 24i r C2H4+3O2 13i r 2H2+O2 14i r 2C2H2+5O2+7Ar 13i r ir 2 2313 i r
23i r 3.5.8
0.0 0.5 1.0 1.5 2.0 2.5 3.00
10
20
30
40
50
60
70
80
ri/ = 23
[mm]
r i [m
m]
: Stable, : Critical, : Unstable
ri/ = 14
Stablezone
Unstablezone
Transitionzone
0.0 0.5 1.0 1.5 2.0 2.5 3.00
10
20
30
40
50
60
70
80
ri/ = 23
[mm]
r i [m
m]
: Stable, : Critical, : Unstable
ri/ = 14
Stablezone
Unstablezone
Transitionzone
3.8 2
C2H4+3O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
49
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50
10
20
30
40
50
60
70
80
Transitionzone
[mm]
r i [m
m]
ri/ = 24: Stable, : Critical, : Unstable
ri/ = 14Stablezone
Unstablezone
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50
10
20
30
40
50
60
70
80
Transitionzone
[mm]
r i [m
m]
ri/ = 24: Stable, : Critical, : Unstable
ri/ = 14Stablezone
Unstablezone
3.10 2
2C2H2+5O2+7Ar
0 1 2 3 4 50
10
20
30
40
50
60
70
80
[mm]
r i [m
m]
ri/ = 22: Stable, : Critical, : Unstable
ri/ = 13Stablezone
Unstablezone
Transitionzone
0 1 2 3 4 50
10
20
30
40
50
60
70
80
[mm]
r i [m
m]
ri/ = 22: Stable, : Critical, : Unstable
ri/ = 13Stablezone
Unstablezone
Transitionzone
3.9 2
2H2+O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
50
3.5.4. 3.11 2 ir 20 mm 0.70 mm C2H4+3O2 r r ir2
or 2
3.12 2
3.11 r ir
2 i
-35-30-25-20-15-10-501.0
1.2
1.4
1.6
1.8
2.0
-i []
r/r i
[-]
Outer wall
Inner wall
ri = 20 mm, = 0.70 mm: i = 10.7: i = 34.5: i = 57.7: i = 80.9: i = 103.7: i = 127.1: i = 150.0: i = 173.0
3.11 2
20i r mm 70.0 mmC2H4+3O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
51
3.3 2
3.11 3.12
3.5.5. 3.11 3.12 2
3.4
3.4
3.5
3.13 2
3.43.5
3.11 r r ir 3.12 in,D iin, rD
1.0 1.2 1.4 1.6 1.8 2.00.0
0.5
1.0
1.5
r/ri [-]
[1
05 ra
d/s]
ri = 20 mm, = 0.70 mm: Experimental (i = 115.1): Experimental (i = 127.1): Experimental (i = 138.8): Average (= 1.0231105 rad/s)
Inner wall Outer wall
3.12 2 20i r mm 70.0 mmC2H4+3O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
52
asyn,D m CJasyn, 980.0 DD 10.8m 3.13 asyn,D m2
3.43.5
3.14 2
nD 3.11
nD
nD r CJD ir 3.6
3.13 3.5 nD 2 3.14 asyn,D m
2
nD 3.53.5
nD 3.53.4
-35-30-25-20-15-10-501.0
1.2
1.4
1.6
1.8
2.0
r/r i
[-]
-i []
ri = 20 mm, = 0.70 mm: Experimental (i = 115.1): Experimental (i = 127.1): Experimental (i = 138.8): Fitting
(Dn,i = 0.87235DCJ, Dn,asy = 0.980DCJ, m = 8.10, = 1.0231105 rad/s)
Outer wall
Inner wall
3.13 2 20i r mm 70.0 mmC2H4+3O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
53
3.43.52 nD
3.9 nD 3.133.43.5 2
3.15 2 3.43.5
3.13
1 3.13
2 3.13 5 3.3 5j 33.100.1 i rr 2 CJasyn, 995.0 DD 50.7m 12
2 33.100.1 i rr 2 3.16
1.0 1.2 1.4 1.6 1.8 2.00.80
0.85
0.90
0.95
1.00
1.05
r/ri [-]
ri = 20 mm, = 0.70 mm: Experimental (i = 115.1): Experimental (i = 127.1): Experimental (i = 138.8): Fitting
(Dn,i = 0.87235DCJ, Dn,asy = 0.980DCJ, m = 8.10)
Dn/D
CJ [
-]
Inner wall Outer wall
3.14 2
20i r mm 70.0 mmC2H4+3O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
54
12 nD nD CJD 1 CJn DD 00.200.1 i rr 2 CJn DD21 20.100.1 i rr 3.16 CJn DD
CJn DD 0.05 0.003
CJn DD
CJn DD
-7-6-5-4-3-2-101.0
1.1
1.2
1.3
1.4
r/r i
[-]
-i []
ri = 20 mm, = 0.70 mm: Experimental (i = 115.1): Experimental (i = 127.1): Experimental (i = 138.8): Fitting (1)
(Dn,i = 0.87235DCJ, Dn,asy = 0.980DCJ, m = 8.10, = 1.0231105 rad/s)
: Fitting (2)(Dn,i = 0.87235DCJ, Dn,asy = 0.995DCJ, m = 7.50, = 1.0231105 rad/s)
Inner wall
3.15 2 33.100.1 i rr
20i r mm 70.0 mmC2H4+3O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
55
3.5.6. Dn/DCJ 3.17 ~ 3.19 CJn DD 3.8 ~ 3.10 ir
CJn DD C2H4+3O2 10 2H2+O2 9 2C2H2+5O2+7Ar 13 CJn DD
CJn DD ir 2 p ir 1 CJn DD 3.15 CJn DD ir CJn DD ir nD 62,63)
nD p CJn DD
0.00 0.02 0.04 0.06 0.08 0.10 0.120.6
0.7
0.8
0.9
1.0
[-]
Dn/D
CJ [
-]
ri = 20 mm, = 0.70 mm: Fitting (1)
(Dn,i = 0.87235DCJ, Dn,asy = 0.980DCJ, m = 8.10, = 1.0231105 rad/s)
: Fitting (2)(Dn,i = 0.87235DCJ, Dn,asy = 0.995DCJ, m = 7.50, = 1.0231105 rad/s)
)00.200.1( i rr
)20.100.1( i rr
0.00 0.02 0.04 0.06 0.08 0.10 0.120.6
0.7
0.8
0.9
1.0
[-]
Dn/D
CJ [
-]
ri = 20 mm, = 0.70 mm: Fitting (1)
(Dn,i = 0.87235DCJ, Dn,asy = 0.980DCJ, m = 8.10, = 1.0231105 rad/s)
: Fitting (2)(Dn,i = 0.87235DCJ, Dn,asy = 0.995DCJ, m = 7.50, = 1.0231105 rad/s)
)00.200.1( i rr
)20.100.1( i rr
3.16 1 00.200.1 i rr 2 20.100.1 i rr CJn DD 20i r mm
70.0 mmC2H4+3O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
56
0 1CJn DD CJn DD 0 1CJn DD 3.43.5 asyn,D CJD
3.17 ~ 3.19 CJn DD 0 1CJn DD 3.43.5 0
CJn DD 3.5 0 CJn DD
0 1CJn DD CJn DD 3.5
0.00 0.02 0.04 0.06 0.08 0.10 0.120.6
0.7
0.8
0.9
1.0
[-]
Dn/D
CJ [
-]
: ri = 10 mm, = 0.40 mm: ri = 20 mm, = 0.40 mm: ri = 20 mm, = 0.59 mm: ri = 20 mm, = 0.87 mm: ri = 40 mm, = 0.40 mm: ri = 40 mm, = 0.86 mm: ri = 40 mm, = 1.51 mm: ri = 60 mm, = 0.40 mm: ri = 60 mm, = 1.11 mm: ri = 60 mm, = 2.07 mm
3.17 2
CJn DD C2H4+3O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
57
0.00 0.02 0.04 0.06 0.08 0.10 0.120.6
0.7
0.8
0.9
1.0
[-]
Dn/D
CJ [
-] : ri = 5 mm, = 0.23 mm: ri = 10 mm, = 0.23 mm: ri = 10 mm, = 0.36 mm: ri = 10 mm, = 0.46 mm: ri = 20 mm, = 0.23 mm: ri = 20 mm, = 0.53 mm: ri = 20 mm, = 0.90 mm: ri = 40 mm, = 0.23 mm: ri = 40 mm, = 0.78 mm: ri = 40 mm, = 1.55 mm: ri = 60 mm, = 0.23 mm: ri = 60 mm, = 1.38 mm: ri = 60 mm, = 2.16 mm
3.19 2
CJn DD 2C2H2+5O2+7Ar
0.00 0.02 0.04 0.06 0.08 0.10 0.120.6
0.7
0.8
0.9
1.0
[-]
Dn/D
CJ [
-]
: ri = 20 mm, = 0.73 mm: ri = 20 mm, = 0.82 mm: ri = 20 mm, = 0.93 mm: ri = 40 mm, = 0.73 mm: ri = 40 mm, = 1.27 mm: ri = 40 mm, = 1.76 mm: ri = 60 mm, = 0.74 mm: ri = 60 mm, = 1.56 mm: ri = 60 mm, = 2.37 mm
3.18 2
CJn DD 2H2+O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
58
3.20 CJn DD 3.17 ~ 3.19 CJn DD CJn DD CJn DD CJn DD CJn DD
332210CJn aaaa DD 0000.1a0 3017.1a1 089.16a 2 67.169a3 3.20 CJn DD 0 1CJn DD
0 1CJn DD 8.0CJin, DD CJn DD 11614.000000.0 0.18.0 CJn DD
0.00 0.02 0.04 0.06 0.08 0.10 0.120.6
0.7
0.8
0.9
1.0
[-]
Dn/D
CJ [
-]
: C2H4+3O2: 2H2+O2: 2C2H2+5O2+7Ar: Fitting (overall)
Dn/DCJ = aj()j (j = 0~3)a0 = 1.0000, a1 = -1.3017a2 = 16.089, a3 = -169.67
3.20 CJn DD
-
3 Dn/DCJ
__________________________________________________________________________________________________________
59
3.5.7. Dn/DCJ 3.21 ~ 3.23 2 CJn DD 3.21 ir 20 mm 0.70 mm C2H4+3O2 3.22 ir 40 mm 1.56 mm 2H2+O2 3.23 ir 10 mm 0.27 mm 2C2H2+5O2+7Ar marker particle method98)
Marker particle method 3.24
1 2
2
B
2 s 4 s 3.21 ~ 3.23 CJn DD
CJn DD 2 ir p CJn DD CJn DD
CJn DD
CJn DD 1 1.2.2
3.21 ~ 3.23 2 CJn DD
p 11614.000000.0 0.18.0 CJn DD
CJn DD
-
3 Dn/DCJ
__________________________________________________________________________________________________________
60
Photograph: schlieren photography (t = 2 s): Front shock reconstructed with overall Dn/DCJ- relation (t = 4 s)
Photograph: schlieren photography (t = 2 s): Front shock reconstructed with overall Dn/DCJ- relation (t = 4 s)
Photograph: schlieren photography (t = 2 s): Front shock reconstructed with overall Dn/DCJ- relation (t = 4 s)
3.22 2
CJn DD 40i r mm 56.1 mm2H2+O2
Photograph: shadowgraph photography (t = 2 s): Front shock reconstructed with overall Dn/DCJ- relation (t = 4 s)
Photograph: shadowgraph photography (t = 2 s): Front shock reconstructed with overall Dn/DCJ- relation (t = 4 s)
Photograph: shadowgraph photography (t = 2 s): Front shock reconstructed with overall Dn/DCJ- relation (t = 4 s)
3.21 2
CJn DD 20i r mm 70.0 mmC2H4+3O2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
61
Wave front at t
Wave front at t+t
: node
Wave front at t
Wave front at t+t
: node: node
3.24 Marker particle method
Photograph: shadowgraph photography (t = 2 s): Front shock reconstructed with overall Dn/DCJ- relation (t = 4 s)
Photograph: shadowgraph photography (t = 2 s): Front shock reconstructed with overall Dn/DCJ- relation (t = 4 s)
Photograph: shadowgraph photography (t = 2 s): Front shock reconstructed with overall Dn/DCJ- relation (t = 4 s)
3.23 2
CJn DD 10i r mm 27.0 mm 2C2H2+5O2+7Ar
-
3 Dn/DCJ
__________________________________________________________________________________________________________
62
3.5.8. 3.21 ~ 3.23 CJn DD CJn DD x y t irx iry iCJ rtD
3.25 2
ir 2350 108 3 CJn DD 3.25a
3.25b CJn DD
1 2
or
CJn DD
3.14 3.25 CJn DD
2
3.11 3.12 3.25 CJn DD irr CJn DD io rr 2 3.25 ir CJn DD 1 0
ir
3.25 CJn DD ir ir 2 ir ir ir CJn DD 2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
63
ir 3.26 3.27 r r ir 3.26
ir 36.3 C2H4+3O2 ir 20 mm40 mm 60 mm 3 3.27 ir 27.5 ir 20 mm
CJn DD ir ir 2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
64
: Constant Dn/DCJ line : Front shock reconstructed with
overall Dn/DCJ- relation ( = 1)
(b) Dn/DCJ
(a)
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-] [-
]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
0.0000
0.0104
0.0207
0.0414
0.0518
0.0725
0.0829
0.0932
0.1036
0.0622
0.0311
0.8270
0.8443
0.8616
0.8962
0.9135
0.9481
0.9654
0.9827
1.0000
0.9308
0.8789
0.0000
0.0104
0.0207
0.0414
0.0518
0.0725
0.0829
0.0932
0.1036
0.0622
0.0311
0.8270
0.8443
0.8616
0.8962
0.9135
0.9481
0.9654
0.9827
1.0000
0.9308
0.8789
0.0000
0.0104
0.0207
0.0414
0.0518
0.0725
0.0829
0.0932
0.1036
0.0622
0.0311
0.8270
0.8443
0.8616
0.8962
0.9135
0.9481
0.9654
0.9827
1.0000
0.9308
0.8789
: Constant line : Front shock reconstructed with
overall Dn/DCJ- relation ( = 1)
= 0
= 2
= 4 =
6
= 8
= 10
(i) ri/ = 23
= 0.0104
= 0.0104
= 0
= 2
= 4 =
6
= 8
= 10
(i) ri/ = 23
Dn/DCJ = 0.9827
Dn/DCJ = 0.9654
= 0
= 2
= 4 =
6
= 8
= 0
= 2
= 4 =
6
= 8
(iii) ri/ = 108 (iii) ri/ = 108
= 0
= 2
= 4 =
6
= 8
= 10
= 0
= 2
= 4 =
6
= 8
= 10
= 0.0104
= 0.0104(ii) ri/ = 50 (ii) ri/ = 50
Dn/DCJ = 0.9827
Dn/DCJ = 0.9654
: Constant Dn/DCJ line : Front shock reconstructed with
overall Dn/DCJ- relation ( = 1): Constant Dn/DCJ line : Front shock reconstructed with
overall Dn/DCJ- relation ( = 1)
(b) Dn/DCJ
(a)
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-] [
-]-5 -4 -3 -2 -1 0 1 2 3 4 5
-5-4-3-2-1012345
[-] [
-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345
[-]
[-]
0.0000
0.0104
0.0207
0.0414
0.0518
0.0725
0.0829
0.0932
0.1036
0.0622
0.0311
0.0000
0.0104
0.0207
0.0414
0.0518
0.0725
0.0829
0.0932
0.1036
0.0622
0.0311
0.8270
0.8443
0.8616
0.8962
0.9135
0.9481
0.9654
0.9827
1.0000
0.9308
0.8789
0.8270
0.8443
0.8616
0.8962
0.9135
0.9481
0.9654
0.9827
1.0000
0.9308
0.8789
0.0000
0.0104
0.0207
0.0414
0.0518
0.0725
0.0829
0.0932
0.1036
0.0622
0.0311
0.0000
0.0104
0.0207
0.0414
0.0518
0.0725
0.0829
0.0932
0.1036
0.0622
0.0311
0.8270
0.8443
0.8616
0.8962
0.9135
0.9481
0.9654
0.9827
1.0000
0.9308
0.8789
0.8270
0.8443
0.8616
0.8962
0.9135
0.9481
0.9654
0.9827
1.0000
0.9308
0.8789
0.0000
0.0104
0.0207
0.0414
0.0518
0.0725
0.0829
0.0932
0.1036
0.0622
0.0311
0.0000
0.0104
0.0207
0.0414
0.0518
0.0725
0.0829
0.0932
0.1036
0.0622
0.0311
0.8270
0.8443
0.8616
0.8962
0.9135
0.9481
0.9654
0.9827
1.0000
0.9308
0.8789
0.8270
0.8443
0.8616
0.8962
0.9135
0.9481
0.9654
0.9827
1.0000
0.9308
0.8789
: Constant line : Front shock reconstructed with
overall Dn/DCJ- relation ( = 1): Constant line : Front shock reconstructed with
overall Dn/DCJ- relation ( = 1)
= 0
= 2
= 4 =
6
= 8
= 10
(i) ri/ = 23
= 0.0104
= 0.0104
= 0
= 2
= 4 =
6
= 8
= 10
(i) ri/ = 23
Dn/DCJ = 0.9827
Dn/DCJ = 0.9654
= 0
= 2
= 4 =
6
= 8
= 0
= 2
= 4 =
6
= 8
(iii) ri/ = 108 (iii) ri/ = 108
= 0
= 2
= 4 =
6
= 8
= 10
= 0
= 2
= 4 =
6
= 8
= 10
= 0.0104
= 0.0104(ii) ri/ = 50 (ii) ri/ = 50
Dn/DCJ = 0.9827
Dn/DCJ = 0.9654
3.25 2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
65
-35-30-25-20-15-10-501.0
1.2
1.4
1.6
1.8
2.0
-i []
r/ri [
-]
Outer wall
Experimental: C2H4+3O2: 2H2+O2: 2C2H2+5O2+7Ar
Reconstructed: Overall Dn/DCJ- relationInner wall
3.27 2
5.27i r 20i r mm
-35-30-25-20-15-10-501.0
1.2
1.4
1.6
1.8
2.0
-i []
r/ri [
-]
Outer wall
Experimental: ri = 20 mm: ri = 40 mm: ri = 60 mm
Reconstructed: Overall Dn/DCJ- relationInner wall
3.26 2
3.36i r C2H4+3O2 ir
-
3 Dn/DCJ
__________________________________________________________________________________________________________
66
3.6.
3.6.1. Dn/DCJ 2
CJD 3.6
3.28 2
3.01 mm R1 ~ R3 17.5 mm 2
CJn DD
3.29 2 CJn DD CJn DD CJn DD CJn DD 3.19 CJn DD p 1 CJn DD 1CJn DD
CJ
R1
R1 = 17.5 mmR2 = 17.4 mmR3 = 17.5 mm Transition region
Fully-developed region
R3R2R1
R1 = 17.5 mmR2 = 17.4 mmR3 = 17.5 mm Transition region
Fully-developed region
R3R2
3.28 2 01.3 mm
-
3 Dn/DCJ
__________________________________________________________________________________________________________
67
CJ 3.29 CJn DD CJn DD
CJn DD
CJn DD CJn DD
CJn DD 3.29
CJn DD 332210CJn aaaa DD 00000.1a0 41858.0a1 25821.0a 2 13027.0a3 CJn DD 0 1CJn DD CJn DD 0.07.0 2042.10000.1 CJn DD
-0.80 -0.60 -0.40 -0.20 0.00 0.200.80
0.90
1.00
1.10
1.20
1.30
[-]
: FittingDn/DCJ = aj()j (j = 0~3)a0 = 1.00000, a1 = -0.41858a2 = -0.25821, a3 = -0.13027
Dn/D
CJ [
-]
Interpolation limit ofDn/DCJ- relation (negative)
: = 4.02 mm: = 3.01 mm: = 2.00 mm: = 1.00 mm
Positive
Negative
3.29 2
CJn DD
-
3 Dn/DCJ
__________________________________________________________________________________________________________
68
3.6.2. Dn/DCJ 3.30 2
CJn DD 2 marker particle
method98) 2
B
1 s 2 s 2
2
2
3.30 2
CJn DD
CJn DD
CJn DD
-
3 Dn/DCJ
__________________________________________________________________________________________________________
69
CJn DD CJn DD 2 3.31 2 CJn DD
3 cm CJn DD
CJn DD CJn DD 0 0 CJn DD
99) 2C2H2+5O2
CJn DD
(a) = 4.00 mm(), 4.03 mm()
(b) = 3.01 mm(), 3.01 mm()
(c) = 2.00 mm(), 2.00 mm()
(d) = 1.00 mm(), 1.00 mm()
Photograph: direct photography (t = 1 s): Front shock reconstructed with Dn/DCJ- relation (t = 2 s)
(a) = 4.00 mm(), 4.03 mm()
(b) = 3.01 mm(), 3.01 mm()
(c) = 2.00 mm(), 2.00 mm()
(d) = 1.00 mm(), 1.00 mm()
Photograph: direct photography (t = 1 s): Front shock reconstructed with Dn/DCJ- relation (t = 2 s)
Photograph: direct photography (t = 1 s): Front shock reconstructed with Dn/DCJ- relation (t = 2 s)
3.30 CJn DD 2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
70
3.6.3. 2 CJn DD
CJn DD 2
2
3.32 3.32 sM
w
w
w w
Dn/DCJ= 1.08
Dn/DCJ= 1.07
1.191.20
1.181.171.161.151.141.131.121.111.101.091.081.071.061.051.041.031.021.011.00
(a) = 4.00 mm (b) = 3.00 mm (c) = 2.00 mm (d) = 1.00 mm
Dn/DCJ= 1.06
Dn/DCJ= 1.05
Dn/DCJ= 1.04
Dn/DCJ= 1.07
Dn/DCJ= 1.06
Dn/DCJ= 1.05
Dn/DCJ= 1.08
Dn/DCJ= 1.07
1.191.20
1.181.171.161.151.141.131.121.111.101.091.081.071.061.051.041.031.021.011.00
1.191.20
1.181.171.161.151.141.131.121.111.101.091.081.071.061.051.041.031.021.011.00
(a) = 4.00 mm (b) = 3.00 mm (c) = 2.00 mm (d) = 1.00 mm
Dn/DCJ= 1.06
Dn/DCJ= 1.05
Dn/DCJ= 1.04
Dn/DCJ= 1.07
Dn/DCJ= 1.06
Dn/DCJ= 1.05
3.31 2 CJn DD
-
3 Dn/DCJ
__________________________________________________________________________________________________________
71
3.33 w DW RS MS
Vasilev et al. 100) 3.33 2 w von Neumann condition 101) 3.32 w von Neumann condition 3.32 w w 3.33 Skews and Kleine 102) CJn DD 1
1 CJn DD
CJn DD 3.33 2C2H2+5O2+7Ar 9.23w CJn DD
9.23w CJn DD
O
Ms
Planar detonation wave
ww
ro
Outer wall (concave)
Msw
Simplified geometric relationship between the planar detonation wave and the outer wall with fixed wO
Ms
Planar detonation wave
ww
ro
Outer wall (concave)
Msw
Simplified geometric relationship between the planar detonation wave and the outer wall with fixed w
3.32
-
3 Dn/DCJ
__________________________________________________________________________________________________________
72
3.34 2 CJn DD marker particle method98) 2
B 2
3.34c 3.34d CJn DD 3.34a 3.34b 1CJn DD
1 s 0.07.0 2042.10000.1 CJn DD 3.34 CJn DD 2 or p
2
1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
70
80
90
Ms [-]
w [
]
Sonic condition
Detachment criterion(2-shock theory)
von Neumann condition(3-shock theory)
No reflection
Machreflection
Regularreflection
MCJ = 6.3125
w = 23.9
1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
70
80
90
Ms [-]
w [
]
Sonic condition
Detachment criterion(2-shock theory)
von Neumann condition(3-shock theory)
No reflection
Machreflection
Regularreflection
MCJ = 6.3125
w = 23.9
DW
DW
DW
RS
RSMS
1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
70
80
90
Ms [-]
w [
]
Sonic condition
Detachment criterion(2-shock theory)
von Neumann condition(3-shock theory)
No reflection
Machreflection
Regularreflection
MCJ = 6.3125
w = 23.9
1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
70
80
90
Ms [-]
w [
]
Sonic condition
Detachment criterion(2-shock theory)
von Neumann condition(3-shock theory)
No reflection
Machreflection
Regularreflection
MCJ = 6.3125
w = 23.9
DW
DW
DW
RS
RSMS
3.33 w
-
3 Dn/DCJ
__________________________________________________________________________________________________________
73
0.07.0 2042.10000.1 CJn DD CJn DD
CJn DD
-
3 Dn/DCJ
__________________________________________________________________________________________________________
74
Head of expansion wave
w = 23.9 w = 23.9
Head of expansion wave
w = 23.9
w = 23.9
(a) ro = 30 mm, = 4.01 mm
Photograph: direct photography (t = 1 s): Front shock reconstructed with Dn/DCJ- relation (t = 1 s)
(b) ro = 30 mm, = 1.00 mm
(c) ro = 40 mm, = 1.00 mm (d) ro = 80 mm, = 1.00 mm
Head of expansion wave
w = 23.9
Head of expansion wave
w = 23.9 w = 23.9
Head of expansion wave
w = 23.9
Head of expansion wave
w = 23.9w = 23.9
w = 23.9w = 23.9
(a) ro = 30 mm, = 4.01 mm
Photograph: direct photography (t = 1 s): Front shock reconstructed with Dn/DCJ- relation (t = 1 s)
Photograph: direct photography (t = 1 s): Front shock reconstructed with Dn/DCJ- relation (t = 1 s)
(b) ro = 30 mm, = 1.00 mm
(c) ro = 40 mm, = 1.00 mm (d) ro = 80 mm, = 1.00 mm 3.34 CJn DD
2
-
3 Dn/DCJ
__________________________________________________________________________________________________________
75
3.7.
C2H4+3O22H2+O2 2C2H2+5O2+7Ar 3 2
2 2313 i r
23i r 2
CJn DD CJn DD ir 2 p
ir 1 CJn DD CJn DD
CJn DD 1 ir CJn /DD 1 ir ir ir 2
2C2H2+5O2+7Ar CJn DD CJn DD
CJn DD
-
4
__________________________________________________________________________________________________________
76
4
1
4.1.
3 CJn DD ir
Yao and Stewart80)
2 Sharpe81)
1 1
Yao and Stewart80) Sharpe81)
2
CJn DD 3 CJn DD
4.2.
4.1
Menikoff et al. 77)
ZND
Yao and Stewart80)
induction zoneIZreaction zone
RZ 2 Whitham ray tube theory69)
1
-
4
__________________________________________________________________________________________________________
77
4.1 n igl
mtl igl mtl indl
A AnA dd indl 1ind l
IZ RZ 2 ZND CJ CJind,l
CJ CJind,l CJind,Cl C 28) CJn DD CJD CJ 0 NASA CEA96) CJ
CJn DD 2 CJind,CJn lDD CJind,Cl
CJind,CJn lDD CJn DD
Induction zone (IZ)
Reaction zone (RZ)
n
Ray tubeThermicity
Reaction progress
lig
lmt
Front shockPropagation
direction
CJ point
0
Analysis domain (IZ+RZ)
Onset point of ignition
Reaction progressor
Thermicity
Max. thermicity
Reaction progress at CJ point
Induction length: lind = lig+lmtCell width: = Clind,CJCurvature: = (dA/dn)/A
C: ConstantA: Cross-section area of ray tube
lind
Induction zone (IZ)
Reaction zone (RZ)
n
Ray tubeThermicity
Reaction progress
lig
lmt
Front shockPropagation
direction
CJ point
0
Analysis domain (IZ+RZ)
Onset point of ignition
Reaction progressor
Thermicity
Max. thermicity
Reaction progress at CJ point
Induction length: lind = lig+lmtCell width: = Clind,CJCurvature: = (dA/dn)/A
C: ConstantA: Cross-section area of ray tube
lind
4.1
-
4
__________________________________________________________________________________________________________
78
4.3.
1
1
64)
0nnn
uDnu
t 4.1
01nnnn
np
nuu
tuD
4.2
0n2n
n
ut
pneu
te
4.3
wnYu
tY
n 4.4
Yqpe 1 4.5 RTp 4.6
t nu nD peY
0Y 1Y w q RT
80)
80,81)
N21N21 PPPRRR R : , P : 1
1
-
4
__________________________________________________________________________________________________________
79
RTqKYY
TTZw exp1exp a1 4.7
Z aT K4.7 C
4.74.7 aT
aT
4.7 1 4.7 2 K g 1)
YYRTKRTqg
1lnln 4.8
0 CJCJ 1,81,103) CJ CJ 4.8 0g 1) K CJ CJ
CJpeq,CJpeq,
CJpeq, exp1
RTq
YY
K 4.9
eq CJp CJ
eq,CJp CJ CJ
CJpeq,Y
CJ D CJ 2 CJpeq,
2CJpn, au 1,81,103) CJpeq,a CJ CJ
CJ CJ CJpfr,a
1)
-
4
__________________________________________________________________________________________________________
80
CJpeq,CJpeq,2
2CJpfr,
2
2
2CJpfr,
2CJpfr,
2CJpfr,
2CJpeq,
1111
1
1
YYaq
aqa
aa
4.10
fra T
RTpa 2fr 4.11
CJpfr,a 4.11 CJpeq,T CJpfr,a q
q 4.5.2 CJpeq,Y CJpeq,T
4.9 K
4.4.
IZ RZ
4.1~ 4.4 1 t 4.1
~ 4.4
0d
dnn
n uDnu 4.12
0dd1
dd n
n np
nuu 4.13
0dd
dd
2 np
ne
4.14
wnYu
dd
n 4.15
4.5 Ypee ,,
nY
Ye
np
pe
ne
ne
dd
dd
dd
dd
4.16
4.164.14
0dd
dd
dd
2
nY
pe
Ye
np
npeep
4.17 fra
-
4
__________________________________________________________________________________________________________
81
peepa
2
2fr 4.18
1)4.184.17
0dd
dd
dd2
fr
nY
pe
Ye
np
na 4.19
4.124.134.154.19
2n
2fr
nn2fr
n
1
dd
ua
uDawpe
Ye
nu
4.20
4.5
qYe 4.21
1
11
p
e 4.22
4.214.224.20
2
nn2fr
2n
2fr
nn2frn
1
11
dd
M
uDwaq
uauDaqw
nu
4.23
M 2fr2n
2 auM 4.23 1
IZ RZ 80,81)
4.134.14
02d
d 2n
upen 4.24
4.244.5
021dd 2n
Yq
upn
4.25
.212n constYqup
4.26 4.26
4.26
2n2n
21
121DpYqup
4.27 4.27 pa 2fr
-
4
__________________________________________________________________________________________________________
82
YquDpa
21
2n
2n2
fr 4.28
4.28 1 IZ RZ
4.5.
4.5.1. ZND IZ RZ 2 igl
0w CJ 0w CJ
104) 1ind l 1 t 1 CJ
T igt
TT
TT
qZRt a
a
21
ig exp1 4.29
4.29 E
ltnu
l
ig
0n
d1 4.30
ln ln 4.29 igt 4.30 l igl
4.30 0n igln nu T 0w 0Y p nD 4.234.28 0n nu 4.12 0n
-
4
__________________________________________________________________________________________________________
83
1
21 2n
nn,
D
pDu 4.31
n,
n
uD 4.32
105)+T4.11
4.28
4.5.2. CJ 0 CJn DD 4.124.13 CJn Du 4.33 2CJ
2n Dpup 4.34
4.334.34 p CJD fra CJn2CJ
CJ
n2fr DuDpD
upa
4.35
nu w
aq
2fr
1 4.36
58) CJ CJmt,l 4.23 0
mtn,
ig,n
mtn,
ig,n
n
a1
2n
2fr
n
2n
2fr
CJmt,
d
exp1exp1
d1
u
u
u
u
u
RTqKYY
TTZq
ua
uqwual
4.37
CJ ZND
CJ CJig,l
4.30
TT
TT
qZRu
utl aa
21n,
n,,igCJig, exp1 4.38
CJ CJind,l CJig,l CJmt,l
-
4
__________________________________________________________________________________________________________
84
mtn,
i,n
n
a1
2n
2fr
a
a
21n,
CJind,
d
exp1exp1
exp1
u
u g
u
RTqKYY
TTZq
ua
TT
TT
qZRu
l
4.39
p CJD 4.394.35 ign,u mtn,u ind,CJl CJ
0n CJig,ln 1 0w 0Y n,n uu TT
n,ign, uu n,u 4.31 4.324.33 T 4.114.354.39 CJig,ln nu T4.234.35 0 CJig,ln nu n,ign,n uuu nu 4.114.334.35 T CJ D CJ
2CJpeq,
2CJpn, au 1,81,103) p CJpeq,Y
0 CJn DD 4.104.284.35 q NewtonRaphson 106)q4.104.284.35 2 CJpeq,a
CJpfr,a CJpfr,a 4.3 K
4.5.3. l tu pT e
CJ
1
CJind,
~DZl
lll
1~ Ztt
CJ
~Duu
~ 2CJ
~Dpp
2CJ
~DRTT 2
CJ
~Dee 4.40
~4.40 ~ 1 p~
2CJ
2CJ
1~MD
pp
4.41
-
4
__________________________________________________________________________________________________________
85
CJM CJ CJ 1
4.39
mtn,
ig,n
~
~
n
a1
2n
2fr
a
a
21n,
~d
~~
exp1~~
exp~~1
~~
~~
exp~~
~~1
~
u
u
u
TqKYY
TTq
ua
TT
TT
qu
4.42
4.6.
p CJD CJM R nD 0n p T 4.12~ 4.15 aT q CJpeq,Y Z K 4.12~ 4.15 0n CJ pT4.12~ 4.15 0n igln 0w igln CJ 0w
4.54.64.114.28
1 CJ
nD nD
0 CJ D CJ 81,103)4.12~ 4.15 2 CJpfr,
2CJpn, au 4.23 0
4.23 0 81,103)
CJ
4.23 CJ CJ nD
shooting method107) nD nD
-
4
__________________________________________________________________________________________________________
86
nD 4.12~ 4.154 108)
CJ 0 CJ 4.3 2 CJpeq,
2CJpn, au eqfr aa CJ
1,81,103) 0 CJ CJ 2 CJpeq,
2CJpn, au 0 CJ
CJ CJ CJ
0CJ D 0 0n D 81,103)Sharpe
0 0n D CJ 81) 0n D Sharpe 0 0 0CJ D CJ 81) Sharpe
0CJ D CJ 0 CJ CJ 2 CJpfr,2 CJpn, au 0 CJ 0CJ D 0 CJ 2 CJpfr,
2CJpn, au CJ
0CJ D 0n D 0CJ D
0CJ D 0.3% 1) 0n D 0CJ D CJ
nD 3 C2H4+3O22H2+O2 2C2H2+5O2+7Ar 4.1
T 298.15 K 4.40
C p 0.1 MPa
CJM CEA96) CJD CJM CEA96) CJpeq,Y overallCJ qq CJq CJ CJ
0.1 MPa298.15 K CJ
2 Thompson109) CJq CJ CJ
-
4
__________________________________________________________________________________________________________
87
CEA96) overallq
22242 2COO2H3OHC 4.43 O2HO2H 222 4.44 7Ar4COO2H7Ar5OH2C 22222 4.45 0.1 MPa298.15 K 110)C CJind,l A A.1~ A.3 p CJind,l T 298.15
K CJ ZND CJind,Cl 28)C p C2H4+3O2
Konnov mechanism111)2H2+O2 2C2H2+5O2+7Ar GRI-Mech 3.0112) 4.2
CJ p C 4.2 p
3.1 C p
C a~T
Schultz and Shepherd 104) a~T
F p 1 A A.1~ A.3 p 4.1 K 4.3 q~ 4.5.2 4.5.3
4.1
Gas mixture CJM a~T q~ CJpeq,Y K C C2H4+3O2 7.2528 1.3402 0.74480 1.3113 0.45481 1.1893 199.12 2.1270 12.860
2H2+O2 5.2743 1.4016 0.95076 0.91776 0.51881 3.7329 31.134 2.0242 26.986
2C2H2+5O2+7Ar 6.3125 1.4409 0.74701 0.98095 0.44256 0.89014 57.110 2.1173 10.225
4.1 ~~n D 4.40 nD CJD CJind,l
~~n D CJind,CJn lDD nD CJn DD CJind,CJn lDD 4.2 CJind,Cl CJind,CJn lDD CJn DD
-
4
__________________________________________________________________________________________________________
88
4.7. Dn/DCJ 4.3 ~ 4.5 CJn DD
4.3 ~ 4.5 3.17 ~ 3.19
4.1 1 1
Yao and Stewart80) Sharpe81)
1 1 p 1 CJn DD 1 1 p CJn DD 1 CJn DD
CJn DD crCJn DD cr cr CJn DD 4.3 ~ 4.5 CJn DD p 1
0 50 100 150 2000
5
10
15
20
25
30
35
40
p- [kPa]
C [
-]2H2+O2 (average: 26.986)
2C2H2+5O2+7Ar (average: 10.225)
C2H4+3O2 (average: 12.860)
4.2 CJ C
-
4
__________________________________________________________________________________________________________
89
CJn DD CJn DD 1
CJn DD CJn DD 1 crCJn DD 0.83 ~ 0.86
crCJn DD Radulescu and Lee
113,114)
113,114)Radulescu and Lee
CJD
CJn DD 0.80 ~ 0.86 crCJn DD CJn DD 1 Radulescu and Lee 2 3 8.0CJin, DD crCJn DD
CJn DD 1
4.9.3
C2H4+3O2 2H2+O2 CJn DD 1 1 2C2H2+5O2+7Ar 1 CJn DD 1 1 CJn DD CJn DD 1 2
CJn DD
1
CJn DD
-
4
__________________________________________________________________________________________________________
90
0.00 0.05 0.10 0.15 0.20 0.25 0.300.6
0.7
0.8
0.9
1.0
(= C ) [-]
Dn/D
CJ (
= D
n) [-
]
: Experimental (9 cases of ri/): Model ( = 2.0242): Model ( = 1.0000)
(Dn/DCJ)cr= 0.86344
()cr= 0.16429
~
~
0.29333
0.85857
4.4 CJn DD
2H2+O2
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140.6
0.7
0.8
0.9
1.0
(= C ) [-]
Dn/D
CJ (
= D
n) [-
]
: Experimental (10 cases of ri/): Model ( = 2.1270): Model ( = 1.0000)
0.85682
()cr= 0.080327
~
~
0.14237
(Dn/DCJ)cr= 0.86548
4.3 CJn DD C2H4+3O2
-
4
__________________________________________________________________________________________________________
91
4.8. Dn/DCJ CJn DD 1
4.1 CJn DD 1 4.1 a~T C 4.1
CJn DD a~T C
C2H4+3O2 4.1 C2H4+3O2 a~T C10% CJn DD 4.2 a~T C 1 CJM a~T q~ K CJM
a
~T
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140.6
0.7
0.8
0.9
1.0
(= C ) [-]
Dn/D
CJ (
= D
n) [-
]
: Experimental (13 cases of ri/): Model ( = 2.1173): Model ( = 1.0000)
()cr= 0.049173
~
~
0.13109
(Dn/DCJ)cr = 0.83290 ( = 2.1173)
0.83268( = 1.0000)
4.5 CJn DD
2C2H2+5O2+7Ar
-
4
__________________________________________________________________________________________________________
92
CCC CJind,l C
C
4.2 C2H4+3O2
CJM a~T q~ CJpeq,Y K C Baseline 7.2528 1.3402 0.74480 1.3113 0.45481 1.1893 199.12 2.1270 12.860
1.1 7.2528 1.4742 0.67709 0.88619 0.45481 0.22649 39.015 2.1270 12.8609.0 7.2528 1.2062 0.82755 2.3094 0.45481 3.9447 9302.2 2.1270 12.860
a~1.1 T 7.2528 1.3402 0.81928 1.3113 0.45481 1.4601 199.12 2.1270 12.860
a~9.0 T 7.2528 1.3402 0.67032 1.3113 0.45481 0.44295 199.12 2.1270 12.860
C1.1 7.2528 1.3402 0.74480 1.3113 0.45481 1.1893 199.12 2.1270 14.147
C9.0 7.2528 1.3402 0.74480 1.3113 0.45481 1.1893 199.12 2.1270 11.574
4.6 ~ 4.8 CJn DD a~T C CJ 1.2 4.6 0.9 CJn DD 1 CJn DD 1 1 4.7 4.8 CJn DD a
~T C
1 a~T
CJn DD 1 1 0.5 ~ 2.0 115,116)
C CJn DD 1 1
CJn DD
-
4
__________________________________________________________________________________________________________
93
CJn DD
0.00 0.02 0.04 0.06 0.08 0.10 0.120.6
0.7
0.8
0.9
1.0
(= C ) [-]
Dn/D
CJ (
= D
n) [-
]
0.91025
()cr= 0.043275
: (baseline): 1.1: 0.9
(Dn/DCJ)cr= 0.81767
0.85682
0.080327
0.068855
~
~
4.6 CJn DD C2H4+3O2
-
4
__________________________________________________________________________________________________________
94
0.00 0.02 0.04 0.06 0.08 0.10 0.120.6
0.7
0.8
0.9
1.0
(= C ) [-]
Dn/D
CJ (
= D
n) [-
]
()cr= 0.088359
: C (baseline): 1.1C: 0.9C
(Dn/DCJ)cr= 0.85682
0.080327
0.072294
~
~
4.8 CJn DD C C2H4+3O2
0.00 0.02 0.04 0.06 0.08 0.10 0.120.6
0.7
0.8
0.9
1.0
(= C ) [-]
Dn/D
CJ (
= D
n) [-
](Dn/DCJ)cr= 0.87122
()cr= 0.084519
: Ta (baseline): 1.1Ta: 0.9Ta
0.856820.83972
0.0803270.073568
~~~
~
~
4.7 CJn DD a
~T C2H4+3O2
-
4
__________________________________________________________________________________________________________
95
4.9.
4.9.1. C2H4+3O2 1 T~ ~ fr~a n~u p~ ~ YM 4.9 ~ 4.16 0 cr 026776.0 4 n~ 0~ n 0~ n 1~ n CJind,l CJn DD 4.9 T~ cr 4.10 ~ ~ T~ 4.11 fr
~a 4.12 ~ 4.14 p~ ~ 4.15 CJ Y CJpY T~
4.9 T~ CJ 4.16 CJ CJ
CJ CJ
CJ
CJ CJ 10 Vasilev et al. 117,118) CJ CJ
CJ
4.10 CJ 0~ CJ
-
4
__________________________________________________________________________________________________________
96
0.1 0.5 1.0 5.0 10.0 50.00.00
0.05
0.10
0.15
0.20
0.25
0.30
-n [-]
T [-
]
~
: = 0.000000, Dn/DCJ = 1.00000: = 0.026776, Dn/DCJ = 0.97202: = 0.053551, Dn/DCJ = 0.93907: = 0.080327, Dn/DCJ = 0.85682
~
4.9 T~ C2H4+3O2
0.1 0.5 1.0 5.0 10.0 50.0
0.00
0.05
0.10
0.15
-n [-]
[-]
~
: = 0.000000, Dn/DCJ = 1.00000: = 0.026776, Dn/DCJ = 0.97202: = 0.053551, Dn/DCJ = 0.93907: = 0.080327, Dn/DCJ = 0.85682
~
4.10 ~ C2H4+3O2
-
4
__________________________________________________________________________________________________________
97
0.1 0.5 1.0 5.0 10.0 50.00.2
0.3
0.4
0.5
0.6
0.7
0.8
-n [-]
a fr [
-]
~
: = 0.000000, Dn/DCJ = 1.00000: = 0.026776, Dn/DCJ = 0.97202: = 0.053551, Dn/DCJ = 0.93907: = 0.080327, Dn/DCJ = 0.85682
~
4.11 fr~a C2H4+3O2
0.1 0.5 1.0 5.0 10.0 50.00.0
0.2
0.4
0.6
0.8
-n [-]
-un [
-]
~
: = 0.000000, Dn/DCJ = 1.00000: = 0.026776, Dn/DCJ = 0.97202: = 0.053551, Dn/DCJ = 0.93907: = 0.080327, Dn/DCJ = 0.85682
~
4.12 n~u C2H4+3O2
-
4
__________________________________________________________________________________________________________
98
0.1 0.5 1.0 5.0 10.0 50.00.0
0.2
0.4
0.6
0.8
1.0
-n [-]
p [-
]
~
: = 0.000000, Dn/DCJ = 1.00000: = 0.026776, Dn/DCJ = 0.97202: = 0.053551, Dn/DCJ = 0.93907: = 0.080327, Dn/DCJ = 0.85682
~
4.13 p~ C2H4+3O2
0.1 0.5 1.0 5.0 10.0 50.00.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
-n [-]
[-]
~
: = 0.000000, Dn/DCJ = 1.00000: = 0.026776, Dn/DCJ = 0.97202: = 0.053551, Dn/DCJ = 0.93907: = 0.080327, Dn/DCJ = 0.85682
~
4.14 ~ C2H4+3O2
-
4
__________________________________________________________________________________________________________
99
0.1 0.5 1.0 5.0 10.0 50.00.0
0.2
0.4
0.6
0.8
1.0
-n [-]
Y [-
]
~
: = 0.000000, Dn/DCJ = 1.00000: = 0.026776, Dn/DCJ = 0.97202: = 0.053551, Dn/DCJ = 0.93907: = 0.080327, Dn/DCJ = 0.85682
4.15 YC2H4+3O2
0.1 0.5 1.0 5.0 10.0 50.00.0
0.2
0.4
0.6
0.8
1.0
-n [-]
M [-
]
~
: = 0.000000, Dn/DCJ = 1.00000: = 0.026776, Dn/DCJ = 0.97202: = 0.053551, Dn/DCJ = 0.93907: = 0.080327, Dn/DCJ = 0.85682
4.16 M C2H4+3O2
-
4
__________________________________________________________________________________________________________
100
4.9.2. CJn DD 1 CJn DD
p 1 CJn DD
4.284.23
2
fr
nn2
2fr
2
12
1211
dd
Ma
uDMwaqM
nM
4.46
2fr
2fr
2
12
11
Ma
waqM
4.47
2fr nn2
1212
MauDM
4.48
nM4.46 nM dd
C2H4+3O2 CJn DD 1 ~ ~ ~~ 4.17 0~ M
CJ
0w 0~ 0~~ M CJ
0~ 0~~ M
M
M 4.16
-
4
__________________________________________________________________________________________________________
101
*q
RTqq* 4.49
*q q~
qMq ~2CJ* 4.50
*q CJM *q
*Q
** YqQ 4.51 CJ
*CJp
*CJp qYQ C2H4+3O2 CJn DD 1
C2H4+3O2 CJn DD 85682.0crCJn DD 6.2144 C2H4+3O2
CJ CJ CJ 440.30* imCJp, Q 48.345*CJp Q im
0.1 0.5 1.0 5.0 10.0 50.0-0.10
-0.05
0.00
0.05
0.10
0.15
-n [-]
, ,
+
[-]
~
~~
~~
: : : +
~~~ ~
CJ pointOnset of ignition
4.17 CJn DD ~ ~ ~~ C2H4+3O2
-
4
__________________________________________________________________________________________________________
102
CJ
4.18 C2H4+3O2 CJn DD *Q M
440.30* imCJp, Q M 0.6 M 1M
905.17* Q *q
*q CJ
4.9.3. Dn/DCJ 4.3 ~ 4.5 CJn DD C2H4+3O2 CJn DD 1
CJn DD 4.19a cr 0.1% crCJn DD 0.1% 4 4.19bM
0.1 0.5 1.0 5.0 10.0 50.00
10
20
30
40
50
60
70
0.0
0.2
0.4
0.6
0.8
1.0
-n [-]~
Q* [
-] Q*
MQ*CJp
Q*CJp,im
: Q*: M
M [-
]CJ point
4.18 CJn DD *Q M C2H4+3O2
-
4
______________________________________