cfd-modeling of boiling processes - drth.frank · cfd-modeling of boiling processes ... coupled to...

CFD-Modeling of Boiling Processes

© 2011 ANSYS, Inc. August 9, 20131

C. Lifante1, T. Frank1, A. Burns2,

E. Krepper3, R. Rzehak3

conxita.lifante@ansys.com

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

QQ

© 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!