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TFAWS Paper Session
Analytical Approach in DeCoM
Presented ByDeepak Patel
NASA/ Goddard Space Flight Center
Thermal & Fluids Analysis WorkshopTFAWS 2011August 15-19, 2011NASA Langley Research CenterNewport News, VA
• Hume Peabody • Matt Garrison • Dr. Jentung Ku• Tamara O'Connell • Thermal Engineering Branch at Goddard Space
Flight Center
TFAWS 2011 – August 15-19, 2011 2
Acknowledgments
Outline
• Introduction• Governing Equations• Develop 1D Computer Code
– DeCoM• Conclusion
– Summary
3TFAWS 2011 – August 15-19, 2011
Introduction:Purpose
• Purpose
–To develop a model which efficiently and accurately simulates LHP Condenser
–Understand basic principles of two-phase flow–Correlation method for two-phase convection value–Governing equations to obtain quality change
4TFAWS 2011 – August 15-19, 2011
Introduction:Introduction to LHP
• Compensation Chamber, QCC – Excess fluid is stored here,
from which the LHP can increase its performance by accessing or storing the excess fluid.
• Evaporator, QE
– Liquid from the bayonet is flown into the wick where it is converted to vapor, from the heat that is conducted from the instrument.
• Vapor Line– Vapor from evaporator is
transferred to the condenser, adiabatically.
5
• Liquid Line, LL – Subcooled liquid from the condenser is
returned to the evaporator. • Condenser – QC (Condenser), QSC (Subcooled)
– QC is the amount of heat rejected when the fluid is in two-phase, and QSC is for condensed Subcooled liquid section (1-phase fluid).
Bayonet Tube
TFAWS 2011 – August 15-19, 2011
Introduction:Condenser Basics
• Condenser:– Vapor generated travels from vapor transport line and enters the
heat exchanger (condenser). – Vapor enters as saturated vapor and phase change occurs, after
which it is condensed to liquid.
6
Condenser and Subcooler
TFAWS 2011 – August 15-19, 2011
Outline
• Introduction• Governing Equations• Develop 1D Computer Code
– DeCoM• Conclusion
– Summary
7TFAWS 2011 – August 15-19, 2011
8
in outQ Q Conservation of Energy
• Condenser source code is based on the Conservation of Energy equation. Applied on each node.
Governing Equations: Control Volume Analysis
Radiative Tsink
Node, Inlet Node, Outlet
FLUID
WALL
iQ2 or scQ
1iQ
• The thermodynamic plot above describes the regions (arrows) that the equations are derived for.
• A fluid is defined by its any two thermodynamic property (e.g. temperature and pressure)
to wall radQRADIATOR
Control Volume for which Equations are formulated
Pressure = co
nstant
Superheated VaporSubcooled
Liquid
2 1T1 = T2
T (oC)
v (m3/kg)
Two-Phase Envelope
Sat’d Liquid and
Sat’d Vapor
TFAWS 2011 – August 15-19, 2011
9
2 * *Q m x
* *sc lQ m Cp T
2-Phase section
Subcooled section
UNKNOWNS KNOWNS
xout
if 2φ
Twi, Tfi
Xin
G2φ(xin)Q2φ(G2φ ,Twi)
TOUT
if SC
TW i TIN GSC
QSC(GSC,TWi)
• Inlet conditions are known• Equations can vary depending upon the state of the fluid
(2φ or SC), as shown above. • Lockhart-Martinelli equations are used to solve for the G2φ
value.
FLUID
WALL ,w iT
* * in
in SAT
m xT T
(2 )Two Phase
* * out
out SAT
m xT T
* *0.0L in
in
m Cp Tx
( )Subcooled SC
* *0.0L out
out
m Cp Tx
2 or scG
IF
2
SC
TRADIATOR
2 or scQ
Governing Equations: Control Volume Analysis
TFAWS 2011 – August 15-19, 2011
10
• Flow regimes of the fluid inside a tube– Two-Phase Lockhart-Martinelli calculations are based on an Annular Flow regime– This is a general case in all simple condensers, and a safe assumption
Governing Equations: Fluid flow regimes
TFAWS 2011 – August 15-19, 2011
11
Calculate , two-phase heat transfer coefficient multiplier.
Lockhart – Martinelli correlationAn empirically formulated two-phase multiplier equation
X – Lockhart-Martinelli parameter
2 = f(X)
1-xx
1 12 2w,v l
w,l v
f ρX =f ρ
Governing Equations: 2φ Lockhart-Martinelli Calculations
• Lockhart-Martinelli correlation is based upon an annular flow regime.
x
w,v w,l
v l 3
f , f = Wall friction factor, vapor / liquid
kgρ ,ρ = Vapor / liquid density, m
= Quality
Wall
FluidVapor
TFAWS 2011 – August 15-19, 2011
12
00.10.20.30.40.50.60.70.80.91
0.0499999999999999
0.499999999999999
4.99999999999999
49.9999999999999
499.999999999999Heat Transfer Convection value vs.
Quality
Fluid QualityFilm
Coe
ffici
ent,
W/in
2K ,
Log
Sca
le
Thermodynamic Plot highlights the
region being analyzed (arrow).
The plot on the right shows
behavior of the convection value in
relation to the fluid quality for
saturation temperature at -4 degC
@ 216W.
Background Theory / Governing Equations: 2φ Heat Transfer Calculations
Solving for the convection value using Lockhart-Martinelli multiplier1/2
2
2 2
*
*l
S
h h
G h A
l 2
2S
Wh = liquid phase convection, m K
A = heat transfer surface area , m
Pressure = co
nstant
Superheated VaporSubcooled
Liquid
2 1T1 = T2
T (oC)
v (m3/kg)
Two-Phase Envelope
Sat’d Liquid and Sat’d Vapor
99.5
TFAWS 2011 – August 15-19, 2011
13
• Equations here are based upon 1-phase, subcooled liquid. Using the flow characteristics, either turbulent or laminar, the heat transfer coefficient is calculated.
• Thermodynamic plot above shows (the blue arrow) section being analyzed.
Background Theory / Governing Equations: Liquid Phase Heat Transfer Calculations
*SC LIQG h A
4*Re* *LIQ
LIQ
mflowDc
Re 2300LIQ
Turbulent Laminar
Re 2300LIQ
10.8 30.027*Re *PrLIQ LIQ LIQNu 3.66LIQNu
*LIQ LIQLIQ
Nu Kh
Dc
Pressure = co
nstant
Superheated VaporSubcooled
Liquid
2 1T1 = T2
T (oC)
v (m3/kg)
Two-Phase Envelope
Sat’d Liquid and Sat’d Vapor
TFAWS 2011 – August 15-19, 2011
Outline
• Introduction• Governing Equations• Develop 1D Computer Code
– DeCoM• Conclusion
– Summary
14TFAWS 2011 – August 15-19, 2011
DECOM Implementation
• DeCoM (Deepak Condenser Model) Implementation
– Code based on FORTRAN language. – Model works for transient and steady state conditions
• Response time to transient is part of future work. – Calculate condenser fluid quality, temperature values, and fluid – wall convection
value.• Radiator and wall temperatures are calculated by SINDA.
– Input DECOM in VAR 1 of SINDA, in order for the logic to be executed at every time step.
15
**Equations based on Governing Theory from previous slides.
TFAWS 2011 – August 15-19, 2011
DECOM Implementation: Nodal network
16
• DECOM Internal– The above diagram shows the network of nodes in the solution
(code).
Nodal Network
Fluid Boundary Nodes
Radiator Nodes
Wall Nodes
Fluid – Wall Conductor
These temperatures and conductor values are calculated by EXCEL/DECOM
Wall – Rad Conductor
TFAWS 2011 – August 15-19, 2011
DECOM Implementation: Calculations Flow Chart
17TFAWS 2011 – August 15-19, 2011
i SAT
in out
T Tx x
( )Power W1T Tsat
0.001ix
2-Phase Fluid
2 , 2 *i cG h A
Subcooled Liquid
SCG
wT
,LIQ iOUT w
SC
QT T
G 2 , ,( )
*i SAT wall i
out infg
G T Tx x
m
Solve for, φi (as shown in Equation Slides)
( )2
in outi
x xx
YES NO
Initial Conditions
i= 1 , N
Read Input Values
Determine Fluid Stage
Calculate Fluid to Wall Heat Transfer Value
Calculate Fluid Parameters
Output Fluid Parameters
0.0out
OUT
Tx
SAT W in 2f,SCT ,T , x ,G
Outline
• Introduction• Governing Equations• Develop 1D Computer Code
– DeCoM• Conclusion
– Summary
18TFAWS 2011 – August 15-19, 2011
19
Summary
• Alternative LHP Condenser modeling method– Purpose of explicit condenser modeling
• Understand condenser governing equation– Implement two-phase correlation method– Fluid to Wall interaction modeling
• Developed FORTRAN code based on governing equations.
TFAWS 2011 – August 15-19, 2011
BACKUPSymbols & Acronyms
20
Subscripts, Loop count
L / LIQ, Liquid/ , Vapor
SAT, SaturationH, enthalpy2 , two-phase
i
V VAP
2
, Conductance
, Heat Rate (W), Fluid Quality , Temperature (C)
, Area (in ), Length (in), Diameter (in)
, Mass Flowrate sec
, Two-Phase
flow
WGK
QxT
ALD
kgm
heat transfer multiplierXM, Lockhart-Martinelli parameter~ Approximate
Superscripts
2
, Latent Heat of Vaporization
, Specific Heat Capacity *
, Dynamic Viscosity *sec
, Thermal Conductivity *
, Heat transfer coefficient *
Re, Reynold
Jkg
JCpkg K
kgin
Wkin K
Whin K
s NumberPr, Prandlt Number
, Nusslett NumberNu
Acronyms
SINDA: Systems Improved Numerical Differencing Analyzer)FLUINT: Fluid Integrator)SC: SubCooledLL: Liquid LineLHP: Loop Heat PipeSTOP: Structural-Thermal-Optical
Performance
TFAWS 2011 – August 15-19, 2011