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CFD-Modeling of Boiling Processes
© 2011 ANSYS, Inc. August 9, 20131
C. Lifante1, T. Frank1, A. Burns2,
E. Krepper3, R. Rzehak3
1ANSYS Germany, 2ANSYS UK, 3HZDR
Outline
• Introduction
• Motivation
• Mathematical Formulation− Wall Boiling model (RPI)−
© 2011 ANSYS, Inc. August 9, 20132
− Wall Boiling model (RPI)− Population Balance approach (MUSIG)
• Validation− Roy et al. case− DEBORA cases
• Summary & Outlook
ANSYS Germany
TUD, Dept. Fluid
Mechanics
Karlsruhe Inst. of
Technology (KIT)
• R&D Initiative:“Modeling, Simulation &
Experiments for Boiling
Processes in Fuel
Assemblies of PWR”
• Sept 2009-Sept 2012
Introduction: R&D Consortium
© 2011 ANSYS, Inc. August 9, 20133
HZ Dresden/Rossen-
dorf
TUD, Dept. Nucl. Eng.
TUD Medical Faculty
Univ. Appl. Sciences Zittau/ Görlitz
Univ.Bochum,
Dept. Energy Systems
TUM, Dept. Thermo-dynamics
Material PropertiesMaterial PropertiesWall Boiling Wall Boiling & &
Bulk CondensationBulk Condensation
Conjugate Heat Conjugate Heat
Introduction: CFD Simulation for Fuel Assemblies in Nuclear Reactors
© 2011 ANSYS, Inc. August 9, 20134
Multiphase Flow Multiphase Flow
ModelingModeling
Conjugate Heat Conjugate Heat
Transfer (CHT)Transfer (CHT)
FSI: Stresses & FSI: Stresses &
DeformationsDeformations
Validation againstValidation against
ExperimentsExperiments
TurbulenceTurbulence
Coalescence
Condensation
Saute
r dia
m
Siz
e D
istr
.
Motivation
© 2011 ANSYS, Inc. August 9, 20135
0 0
1 0 0 11 0
1 0
1 1
( ) ( )
Kurul&Podowski
sub
sub subB sub
sub
d T T
d T T d T Td T T T
T T
d T T
∆ > ∆
∆ − ∆ + ∆ − ∆= ∆ < ∆ < ∆
∆ − ∆ ∆ < ∆
MUSIG
Departure
min( , )
sub
ref
T
T
w ref maxd d e d
−∆
∆= ⋅
R
Saute
r dia
m
di
Siz
e D
istr
.
Modelling of Sub-cooled Boiling at a Heated Wall
The RPI Wall Boiling Model:
• Constant pressure � given Tsat
• Overall heat flux Qw given
• Heat flux partitioning:
Qw = Qf + Qe + Qq Qw
all
QE
© 2011 ANSYS, Inc. August 9, 20136
Qw = Qf + Qe + Qq
Qf- single phase convection
Qe - evaporation
Qq - quenching
(departure of a bubble from the
heated surface � cooling of the
surface by fresh water)
Qw
all
G
QF
Wall Boiling Sub-models
The RPI model contains
sub-models for:
• Heat Flux Partitioning
• Bubble Dynamics
• MPF Turbulence interaction
• Interfacial heat and mass transfer
•
Heat Flux Partitioning:
�Convective turbulent liquid heat flux
�Quenching heat flux
�Evaporative heat flux
�Convective turbulent vapor heat flux, DNB+CHF
Bubble Dynamics:
� Nucleation site density
� Bubble departure frequency
� Bubble departure diameter
� Area of bubble influence
© 2011 ANSYS, Inc. August 9, 20137
• Coupled to CHT (1÷1, GGI)
• Coupled to population banlance
Sub-models for non-
equilibrium DNB and CHF
• Include convective turbulent
heat flux to vapor
• Topological function for flow
regime transition
� Area of bubble influence
� Coupled to MUSIG population balance model
Turbulence Interaction:
� Turbulent dispersion
� Bubble induced turbulence
Interfacial Heat and Mass Transfer:
� Condensation in the subcooled liquid
� Heat flux to vapour heat transfer
� Wall vapour mass transfer
� Interfacial heat transfer / volume condensation
Flow Regime:
�Flow regime transition from bubbly flow to droplets
Flows with Subcooled Boiling (DNB) –RPI Wall Boiling Model
RPI wall boiling model available in ANSYS CFX and ANSYS Fluent
• activated per boundary patch @ individual wall heat flux
Submodels:
• Nucleation site density: Lemmert & Chawla , User Defined
• Bubble departure diameter:
© 2011 ANSYS, Inc. August 9, 20138
• Bubble departure diameter:
Tolubinski & Kostanchuk, Unal, Fritz, User Defined
• Bubble detachment frequency:
Terminal velocity over Departure Diameter, User Defined
• Bubble waiting time:
Proportional to Detachment Period, User Defined
• Quenching heat transfer: Del Valle & Kenning, User Defined
• Turbulent Wall Function for liquid convective heat transfer coefficient
• Mean bubble diameter Kurul & Podowski correlation via CCL/UDF or coupling to
population balance model (homog. or inhomog. MUSIG model)
• Wall boiling & CHT in the solid (1:1 and GGI interfaces)
• Bartolomei et al. (1967,1982) • Bartolomei with recondensation
(1980)R = 7.7 mm
Z=
2 m
q=
0.5
7M
W/
m2
Investigated Boiling Validation Test Cases
© 2011 ANSYS, Inc. August 9, 20139
• Lee et al. (ICONE-16, 2008) • OECD NEA PSBT subchannel
benchmark (1987-1995, 2009)
Gin=900 kg/(s m2)
• FRIGG-6a Test Case (Anglart & Nylund,
1967, 1996 & 1997)• Roy et al. (2002)
Investigated Boiling Validation Test Cases
© 2011 ANSYS, Inc. August 9, 201310
• Size fraction equations derived from mass balance
• RPI wall heat partitioning
B B C C
j
i d i i d i i B D B D ij( r f ) ( r U f ) S S S S S
t x
∂ ∂ρ + ρ = − + − +
∂ ∂
Std. MUSIG Mass transfer due
to phase change
extension
Coupling Between Wall Boiling Modelling and Population Balance
© 2011 ANSYS, Inc. August 9, 201311
• RPI wall heat partitioning
• At the heated walls one more source term is added to one size
fract. Eq.
lgwall convl quench evapQ Q Q m h= + + &
23 2
3
[ ]/ [ / ]
[ ]W evap
S mS kg m s m kg m s
V m = & RPI: Evaporation rate
• Inhomogeneous MUSIG:
Gas 2Gas 2-Active Phase
Active class
Gas 1
Coupling Between Wall Boiling Modelling and Population Balance
© 2011 ANSYS, Inc. August 9, 201312
Bubble at departure
18 7 6 5 4 3 2
• � Size fraction class 5
• � Mass conservation Gas 2
• Derived Source Terms � Momentum Gas 2
evapm&
evapm&
outlet
sym
metr
y
heate
d w
all
(L=
2.7
5m
)
ro=19.01mm
Me
asu
rem
en
t
pla
ne
Co
mp
uta
tio
na
l D
om
ain
Test geometry (Roy et al., 2002)
Validation: RPI & homog. MUSIG
© 2011 ANSYS, Inc. August 9, 201313 inlet
ad
iab
ati
c w
all
(L=
0.9
1m
)
sym
metr
y
ad
iab
ati
c w
all
ri=7.89mm
Fluid: R-113
Pressure Inlet Temp. Mass Flux Power
2.69 bar 50.2 C 784 kg m-2 s-1 116 kW m-2
L=2
.2 m
Co
mp
uta
tio
na
l D
om
ain
Main setup parameters:
• Steady state
• High resolution advection scheme
• Turbulence model: SST• Morel model for source terms in turb. eq.’s (Cε,3 = 1.0)
• Turbulent dispersion (FAD) & drag force
Roy test case: Setup
© 2011 ANSYS, Inc. August 9, 201314
• Turbulent dispersion (FAD) & drag force
���� Grace with correction coefficient -0.5
• Constant value for wall roughness
• Wall Contact Model: AFliquid = 1; AFgas = 0
• Heat transfer correlation: Tomiyama
1 0.575convl quench
r W
wall
Q Qk d mm
Q
ζ
η+
= − =
Main setup parameters:
• RPI model & bubble departure diameter: 1.3 mm
• Homogenous MUSIG model, 15 bubble classes− dmin = 0.25 mm, dmax = 3.75 mm
− Prince/Blanch for coalescence (FC=4); no breakup (FB=0)
Roy test case: Setup
© 2011 ANSYS, Inc. August 9, 201315
− Prince/Blanch for coalescence (FC=4); no breakup (FB=0)
• For comparison: monodisperse simulation with Kurul & Podowski
assumption on dB=f(TSub)=f(TSat-TL)
• Spatial grid hierarchy:
Mesh 1 Mesh 2 Mesh 3 Mesh 4
Radial cells 8 16 32 64
Axial cells 220 440 880 1760
Total Cells 1760 7040 28160 112640
Spatial Grid Independence Analysis
© 2011 ANSYS, Inc. August 9, 201316
Total Cells 1760 7040 28160 112640
y+max 381 199 104 86
Mesh3 Single phase
y+max 34
* i
o i
R RR
R R
−=
−R* dimensionless radius
Spatial Grid Independence Analysis
© 2011 ANSYS, Inc. August 9, 201317
• Bubble size class discretization hierarchy:
Discret. 1 Discret. 2 Discret. 3 Discret. 4
Number of
classes7 15 30 60
Diameter 0.50 0.23 0.12 0.06
Analysis of Independence from Bubble Size Class Discretization
© 2011 ANSYS, Inc. August 9, 201318
Diameter
step [mm]0.50 0.23 0.12 0.06
Analysis of Independence from Bubble Size Class Discretization
© 2011 ANSYS, Inc. August 9, 201319
Analysis of Independence from Bubble Size Class Discretization
© 2011 ANSYS, Inc. August 9, 201320
Mesh 3
15 Classes
Comparison to K&P Correlation
© 2011 ANSYS, Inc. August 9, 201321
Mesh 3
15 Classes
Comparison to K&P Correlation
© 2011 ANSYS, Inc. August 9, 201322
Validation: RPI & Inhomog. MUSIG
Water R12
Pressure [MPa] 15.7 2.6
Tsat [°C] 345 87
Density Liquid [kg/m3] 590 1020
Density Gas [kg/m3] 104 172
Viscosity [kg/ms] 6.8e-5 9.0e-5
• DEBORA test cases
• Scaling conditions:
– Density relation
Liquid/Gas
– Reynolds Number
– Weber Number
© 2011 ANSYS, Inc. August 9, 201323
Surface Tension [N/m] 4.5e-3 1,8e-3
D [m] 0.012 0.02
V [m/s] 5 2.3
DenLiquid/DenGas 5.6 5.9
Re 5.2e+5 5.2e+5
We 3.3e+3 3.3e+3
– Weber Number
• Replacing water by R12
• More convenient
experimental conditions:
– Pressure
– Temperature
– Tube diameter
• Measurement of profiles
becomes possible
Example: DEBORA Tests (CEA)
flow
he
at
• Fluid Dichlorodifluoromethane = R12
• Heated tube D = 19.2 mm over 3.5 m
• Measurement of profiles for gas fraction, liquid and gas velocities, temperatures, bubble sizes
• Validation of
– non drag forces
– turbulent wall functions
© 2011 ANSYS, Inc. August 9, 201324
0 0.002 0.004 0.006 0.008 0.01r [m]
1.5
2.0
2.5
3.0
U [m
/s]
DEBORA1UGAS Exp
UGAS
ULIQUID
0 0.002 0.004 0.006 0.008 0.01r [m]
0.0
0.2
0.4
0.6
αG [
-]
Exp
CFX-12
flow– turbulent wall functions
gas fraction liquid and gas velocity
Application of Inhomog. MUSIG
• P = 1.49 MPa; G = 2000 kg m-2 s-1; Q = 75 kW m-2; TSAT
– TIN
= 13.9 K
• 2 disperse phases, 35 MUSIG size groups
0.0015
0.0020
m]
200
300
mm
-1]
x=3.5 mP1: R=0.0095 m
P2: R=0.007 m
P3: R=0.0045 m
P : R=0.001 m
© 2011 ANSYS, Inc. August 9, 201325
0 0.002 0.004 0.006 0.008 0.01r [m]
0.0000
0.0005
0.0010
dB [m
]
Exp
MUSIG
monodispersed approach
Gas1 Gas2Bubble size
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5dB [mm]
0
100dα
G/d
dB [m P4: R=0.001 m
P4 P3 P2 P1
Gas Volume Fraction DistributionGas1Gas2
© 2011 ANSYS, Inc. August 9, 201326
2 dispersed gaseous phases, 10 &15 MUSIG size fractions
CFD Simulation Results for Variation of Inlet Temperature Tin
0.4
0.6
0.8
1.0
[-]
TSAT-TIN [K]
13.8918.43
23.19
26.94
29.58
0.0005
0.0010
0.0015
0.0020
[m]
TSAT-TIN [K]
13.89
18.43
23.19
26.94
29.58
© 2011 ANSYS, Inc. August 9, 201327
• All tests were calculated with the same model parameters
• Shifting of void fraction maximum towards the core can be
reproduced
0 0.002 0.004 0.006 0.008 0.01R [m]
0.0
0.2
0 0.002 0.004 0.006 0.008 0.01R [m]
0.0000
0.0005
bubble sizegas volume fraction
Summary & Outlook • MUSIG-RPI coupling
− Implemented in ANSYS CFX
− Improves the accuracy of the simulations
− Provides more detailed information about bubble size distribution
− Shift of gas void fraction maximum from wall peak to core peak
with increased inlet temperature
• Homog. model (here) & inhomog. (HZDR) were validated
© 2011 ANSYS, Inc. August 9, 201328
• Homog. model (here) & inhomog. (HZDR) were validated
• Open questions, further work necessary:
− Bubble coalescence and fragmentation
− Bubble induced turbulence
The work was funded by
German Federal Ministry of
Education and Research
© 2011 ANSYS, Inc. August 9, 201329
Thank You!