Center for Multiphase Research CMR -...

Center for Multiphase ResearchRensselaer Polytechnic Institute

CMRCMRCMR


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Recent Advances in Multiphase Flow Recent Advances in Multiphase Flow and Heat Transfer;and Heat Transfer;

Nuclear Engineering PerspectiveNuclear Engineering Perspective

Michael Z. PodowskiMichael Z. PodowskiCenter for Multiphase ResearchCenter for Multiphase ResearchRensselaer Polytechnic InstituteRensselaer Polytechnic Institute

Oak Ridge National LaboratoryOak Ridge National LaboratoryNovember 29, 2006November 29, 2006


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Presentation OutlinePresentation Outline

BackgroundBackground

Multiphase Flow Modeling IssuesMultiphase Flow Modeling Issues

Illustrations of Recent Advances Illustrations of Recent Advances

SummarySummary


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BackgroundBackground

Efficiency of power generationEfficiency of power generation

Development of next generation reactorsDevelopment of next generation reactors

Design and operation of chemical processing Design and operation of chemical processing equipment equipment

Increasing safety requirements Increasing safety requirements

Needs for advanced twoNeeds for advanced two--phase flow phase flow modeling methods and computational modeling methods and computational tools: tools:


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Multiphase Flow Multiphase Flow Modeling IssuesModeling Issues


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Mechanistic Multidimensional Mechanistic Multidimensional Modeling of Multiphase FlowModeling of Multiphase Flow

Direct NumericalSimulations

EulerianFramework

Eulerian-LagrangianFramework

Averaging concepts usedto predict fluid/fluid interactions

Modeling concepts


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Mechanistic Multidimensional Modeling of Mechanistic Multidimensional Modeling of Multiphase Flow (Multiphase Flow (continuedcontinued))

Two-Field (Two-Fluid)

Three-Field

Four-Field

N-Field

Multifield Conservation Equations

Time-averaged

Space/volume-averaged

Ensemble/statistically-averaged

Local Closure Laws

Multifield Modeling Concept


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Steps Toward Multiphase Model Steps Toward Multiphase Model DevelopmentDevelopmentUnderstand dominant Understand dominant physical phenomenaphysical phenomena

Identify interface Identify interface tracking methodtracking method

Use appropriate Use appropriate averaging conceptaveraging concept

Dispersed “particle” flow

Deformable interface flow

First-principle “virtual” database


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Multifield Conservation EquationsMultifield Conservation Equations

MassMass

MomentumMomentum

EnergyEnergy

( )k kkk k kt

∂+ ⋅ =

∂

α ρ∇ α ρ Γv

( ) ( ) ( )

( )

k k kk k k k k ki k

kR

k ke

k

kk

k

k

pppt

−+ ∇ ⋅ = − ∇

+∇ ⋅ +

∇∂ α ρ

α ρ − α∂α ρ

α

α + Mg

v v v

+ ττ

( ) ( ) ( )( )

Rek k kk k k k

Rek k

k k k

k

k k

k k k

pe e

t+ ⋅ = − ⋅ − ⋅

− ⋅ + ⋅

∂ α ρ ∇ α ρ ∇

′′ ′′

α + ∂ ∇ α + α ρ

I

q gq

v v

v

+τ τ


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Major Interfacial Transfer MechanismsMajor Interfacial Transfer MechanismsInterfacial mass transfer: Interfacial mass transfer: -- bubble coalescence and breakupbubble coalescence and breakup-- droplet entrainment and depositiondroplet entrainment and deposition-- particle/particle collisionsparticle/particle collisions

Interfacial momentum transfer: Interfacial momentum transfer: -- turbulence (particleturbulence (particle--induced)induced)-- interfacial forces: drag, virtual mass, lift, interfacial forces: drag, virtual mass, lift,

turbulent dispersion (diffusion), wallturbulent dispersion (diffusion), wall--induced, induced, ““particleparticle””--rotationrotation--rotationrotation

Interfacial energy transfer: Interfacial energy transfer: -- (turbulent) heat convection (turbulent) heat convection -- local phase change (evaporation/condensation)local phase change (evaporation/condensation)-- inelastic collisionsinelastic collisions


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Major Multiphase Flow Modeling IssuesMajor Multiphase Flow Modeling IssuesConsistency of formulation Consistency of formulation -- Interpenetrating media vs. dispersed particle Interpenetrating media vs. dispersed particle modelsmodels-- Force balance at equilibriumForce balance at equilibrium-- Limitations of Limitations of Eulerian/EulerialEulerian/Eulerial frame of referenceframe of reference

Flow regimeFlow regime--dependent closure laws dependent closure laws -- local vs. local vs. ““particleparticle””--sizesize--scale modelsscale models-- flowflow--regime transitionregime transition-- coupling between flow topology and heat transfer coupling between flow topology and heat transfer

modes (CHF)modes (CHF)

Multiscale phenomenaMultiscale phenomena-- thin liquid filmthin liquid film-- gas/liquid/solid interactionsgas/liquid/solid interactions-- effect of surfactants and effect of surfactants and nanoparticlesnanoparticles


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SingleSingle--Phase Flow Modeling IssuesPhase Flow Modeling IssuesTurbulence Turbulence -- PrandtlPrandtl mixing lengthmixing length-- High High Re Re kk--εε-- Low Low ReRe kk--εε

Effect of variable fluid propertiesEffect of variable fluid properties–– Flow and heat transfer at supercritical pressure:Flow and heat transfer at supercritical pressure:

ρρ, , µµ, , ccpp, k, Pr, k, Pr

Compressible flowCompressible flow–– Critical flowCritical flow–– Wave propagationWave propagation


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Computational IssuesComputational IssuesConvergence and robustness of numerical solversConvergence and robustness of numerical solvers-- residual trackingresidual tracking-- consistency of numerical vs. physical limitations consistency of numerical vs. physical limitations

Multiple field modeling capabilities Multiple field modeling capabilities -- maximum number of fieldsmaximum number of fields

Accuracy and duration of simulations for transients Accuracy and duration of simulations for transients and oscillatory flows and oscillatory flows -- dual timedual time--step convergence criteriastep convergence criteria

ComputationalComputational--gridgrid--independence of results independence of results

Ability to capture flow in complex geometriesAbility to capture flow in complex geometries


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NPHASE CodeNPHASE CodeNPHASE is a pressureNPHASE is a pressure--based finite volume CMFD based finite volume CMFD (Computational Multiphase (Computational Multiphase Fluid Dynamics) codeFluid Dynamics) codeDevelopment focused on Development focused on improving robustness and improving robustness and convergence characteristics convergence characteristics of multiphase flow of multiphase flow simulasimula--tionstionsBuiltBuilt--in generic interfacial in generic interfacial closure laws (on RHS of closure laws (on RHS of discretizeddiscretized equationsequationsArbitrary (N) number of Arbitrary (N) number of fieldsfields

Major features of NPHASE:Major features of NPHASE:choice of either segregated or choice of either segregated or coupled solverscoupled solversprimitive variables are: primitive variables are: pressure, velocity, enthalpy, pressure, velocity, enthalpy, turbulent kinetic energy, and turbulent kinetic energy, and turbulence dissipation rateturbulence dissipation rateartificial dissipation used to artificial dissipation used to control numerical pressure control numerical pressure oscillationsoscillationscontinuity satisfied through continuity satisfied through pressure correction equation, pressure correction equation, based on SIMPLECbased on SIMPLEC


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Recent Upgrades of NPHASERecent Upgrades of NPHASE

Implementation of efficient and accurate Implementation of efficient and accurate models of the properties of models of the properties of supecriticalsupecriticalwater and COwater and CO22

Encoding and coupling with NPHASE of a Encoding and coupling with NPHASE of a modified Levelmodified Level--Set Method Set Method

Encoding and coupling with NPHASE of Encoding and coupling with NPHASE of spacespace--dependent model of reactor dependent model of reactor neutronicsneutronics


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Other CFD Codes Used in the Past by Other CFD Codes Used in the Past by CMR ResearchersCMR Researchers

PHOENICSPHOENICS

FIDAP FIDAP

CFXCFX

FLUENTFLUENT


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Illustrations of Recent Illustrations of Recent Advances*Advances*

__________________________________________________________________________________________________

(*)(*) details of recent research accomplishments at CMR can details of recent research accomplishments at CMR can be found in the papers listed at the end of this presentationbe found in the papers listed at the end of this presentation


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Consistency of Multifield Consistency of Multifield Model Formulation for Model Formulation for Dilute Dispersed FlowsDilute Dispersed Flows


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pp p p p p c p

dV

dt − −ρ = ρ + −v

g F F

Formulation of Fluid/Particle Model (Podowski, 2006)Formulation of Fluid/Particle Model (Podowski, 2006)

Particle motion (Particle motion (LagrangeanLagrangean frame of reference)frame of reference)

average flow direction

uniform average flow conditions(no lateral velocity gradients)

( ) ( ) ( ) ( )tot tot ic c cc c c c c c c ci c c c c c c c c cp p p

t− −+ ∇ ⋅ = − ∇ ∇ + ∇ ⋅ + ∇

∂ α ρα ρ α − α α ⋅ α + α ρ

∂+g Mv v v τ τ τ

( ) ( ) ( ) ( )tot tot id d dd d d d d d d di d d d d d d d d dp p p

t− −+ ∇ ⋅ = − ∇ ∇ + ∇ ⋅ ∇ +

∂ α ρα ρ α − α α + ⋅ α α ρ

∂+g Mv v v τ τ τ

Averaged equations (Averaged equations (EulerianEulerian frame of reference)frame of reference)

Typical twoTypical two--fluid fluid formulation, formulation, applicable to applicable to packed particlespacked particles


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Dilute particles do not constitute a complete Dilute particles do not constitute a complete ““fieldfield””

pp p p c p

dV

dtρ ρ −= −

vg F

( ) ( )d d dd d d d d m d d dt

α ρα ρ α ρ α ρ+ ∇ ⋅ = +

∂−

∂+g g Mv v v

d di cip p p Kσ= = +IS tot totd d c= =τ τ τ

ForceForce--balance on particlesbalance on particles

LagrangianLagrangian formform

EulerianEulerian formform

( ) ( ) ISd d dd d d d d d d d d d dp

tα ρ

α ρ α α α ρ+ ∇ ⋅ = − ∇ + ∇ ⋅ +∂

∂+g M

v v v τ

TwoTwo--fluid form of dispersedfluid form of dispersed--phase momentum equationphase momentum equation

can be obtained if extra terms are defined as can be obtained if extra terms are defined as

average flow direction

uniform average flow conditions(no lateral velocity gradients)


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FullyFully--Developed Dispersed Particle FlowDeveloped Dispersed Particle Flow((TiwariTiwari et al., 2003)et al., 2003)

(a) NPHASE result using standard Two(a) NPHASE result using standard Two--Field Model (with Field Model (with ττdd = 0)= 0)

Radial velocity profiles: Radial velocity profiles: vvll , , vvpp

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-0.00015 -0.0001 -0.00005 0 0.00005 0.0001 0.00015

Radius (R)

Velo

city

(m/s

ec)

vlvl averagevpvp average

0

0.05

0.1

0.15

0.2

0.25

0.3

-0.00015 -0.0001 -0.00005 0 0.00005 0.0001 0.00015

Radius (R)R

elat

ive

velo

city

(Vr)

α = 0.1α = 0.2

Relative velocity (Relative velocity (vvrr = = vvpp -- vvll))

(b) NPHASE result with correct dispersed field model: (b) NPHASE result with correct dispersed field model: vvpp = = vvll


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Example: RELAP5/MOD3.3 1-D model of gas/liquid vertical flow Operating conditions: G = 1000 kg/m3-s, D = 2 cm,

RELAP wall-friction partitioning

Predicted wall partitioning

Correct wall shear partitioning

Impact on 1-D Simulations (Podowski, 2004)

3

2

/ 1000 , 0.1 , 900 N/mf gpz φ

α ∂ ρ ρ = = ≈ − ∂

222

2 2 22 2

v1(1 ) , , (1 ) (1 ) v

f f g g f f f

g g g

p pp Z p ZA z Z A z Zφ φ

τ τ λ ρα α

α α α α λ ρ∂ ∂ = − = = ∂ + − ∂ + −

, ,2 2 2

0.9998 , 0.0002 0f f g gs sf RELAP g RELAP

p pp p pF FA z z A zφ φ φ

τ τ∂ ∂ ∂ = − = − ≈ − = − = − ≈ ∂ ∂ ∂

3 3

2 2

800 N/m , 100 N/m1

s Indf g

p pF Fz zφ φ

αα

∂ ∂ = − ≈ = − = ∂ − ∂


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Modeling of Modeling of Gas/Liquid/Solid Gas/Liquid/Solid

InterfacesInterfaces


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LevelLevel--Set/NPHASE Simulation of Cap Bubbles Set/NPHASE Simulation of Cap Bubbles in Airin Air--Water Systems (Water Systems (WierzbickiWierzbicki et al., 2006)et al., 2006)

st 6.0=st 2.0= st 4.0=


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Bubble Rising in Converging Channel ((WierzbickiWierzbicki et al., 2006)et al., 2006)

Velocity vectors andzero level set

Unstructured grid andtransition region


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Inclination Effect on Maximum Bubble Rise Velocity at Small Inclination Angle (Wierzbicki et al., 2006)

Air – glycerin system, 2D simulations

scmu 25.14= s

cmu 02.15=

st 4.0= st 8.0= st 4.0= st 8.0=


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Importance of Understanding Dominant Importance of Understanding Dominant Physical PhenomenaPhysical Phenomena

Long air bubble flowing in distilled water along inclined tubeLong air bubble flowing in distilled water along inclined tube

Clean inner tube surface (uB=10 cm/s) Nano-particle coated surface (uB=8 cm/s)

ExperimentExperiment

LevelLevel--Set/NPHASE Set/NPHASE SimulationSimulation


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SuperSuper--Thin Liquid Film on Inclined Wall Thin Liquid Film on Inclined Wall (Podowski & (Podowski & KumbaroKumbaro, 2004), 2004)

Film momentum equation isFilm momentum equation is ( )yxx

K gy x

∂τ ∂ σ + Φ= − + ρ

∂ ∂

θ

δ(z)

liquid

solid plate

g

zx

y

Uo

2 3/ 2

''(1 ' )

K δ=

+ δ n

BΦ =

δ

Hamaker constantHamaker constantwhere:where:


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Effect of Wall Velocity on Thickness of Effect of Wall Velocity on Thickness of Moving Film (Podowski & Moving Film (Podowski & KumbaroKumbaro, 2004), 2004)

( )0.667 0.946 Ca∆ =

( ) Ca ωβ∆ =

0UCa µ=

σ

ga∞

∞δ ρ

∆ = = δσ

Liquid film profileLiquid film profile

( )0.542 0.834 Ca∆ =

wherewhere

Simplified model (Simplified model (ProbsteinProbstein, 1994):, 1994):

Complete flow model (Podowski & Complete flow model (Podowski & KumbaroKumbaro, 2004):, 2004):

0 0.00040.00080.00120.00160.0020.00240.00280.00320.00360.0040.0040

0.001

0.002

0.003

0.004

0.005

0

0.001

0.002

0.003

0.004

0.005

x

δ

Uo= 0.05 m/s

Uo= 0.10 m/s

Uo= 0.15 m/s


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Theoretical Predictions of Droplet ShapeTheoretical Predictions of Droplet Shape

-0.003 -0.002 -0.001 0 0.001 0.002 0.0030

0.0005

0.001

0.0015

0.002

x (m)

z (m

)

α = 0α= 30α= 30

((VafaeiVafaei & Podowski, 2004; 2005)& Podowski, 2004; 2005)


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Multidimensional Modeling Multidimensional Modeling of Particulate Flows in of Particulate Flows in Complex GeometriesComplex Geometries


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NPHASE Predictions of Velocity Field and Particle NPHASE Predictions of Velocity Field and Particle Concentration in UConcentration in U--Bend (Bend (TiwariTiwari et al., 2004)et al., 2004)

without gravitywithout gravity

(a) (b) (c)

(d) (e) (f)

with gravitywith gravity


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33--D Simulation of Particle Flow in Helical D Simulation of Particle Flow in Helical MicroMicro--Tube (Tube (TiwariTiwari et al., 2006)et al., 2006)


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Multidimensional Modeling Multidimensional Modeling of Flow and Heat Transfer of Flow and Heat Transfer

in Supercritical Fluidsin Supercritical Fluids


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Typical Property Variation in a Heated Channel Typical Property Variation in a Heated Channel with Supercritical Water (with Supercritical Water (GallawayGallaway et al., 2006)et al., 2006)

Density [kg/m3] Temperature [oC] Specific heat [J/kg-oC]

x = 3x = 2

x = 2x = 3

x = 2

x = 3

q”


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Multidimensional Modeling of Multidimensional Modeling of Various Flow RegimesVarious Flow Regimes


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Predictions of Void Distribution in Adiabatic Bubbly Flow (Anglart & Podowski, 1999)

Voi

d fr

actio

n

Distance from centerline [mm]


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3-D VOF Predictions of Slug Flow (Anglart & Podowski, 2001)

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1Distance from wall, y/R

UL/

UC

MeasuredCalculatedSingle phase

0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1Distance from wall, y/R

Voi

d fr

actio

n

MeasuredCalculated


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LTBLC

L(r)

r

x

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

r/R

u [m

/s]

0 0.2 0.4 0.6 0.8 1-400

-350

-300

-250

-200

-150

-100

-50

0

r/RF L

[N/m

3 ]

D L BID excessk k k k k= + +M M M M + M

2tBI l

uly

µ ρ ∂=

∂

ThreeThree--Field Model Field Model of Slug Flow of Slug Flow

((Podowski at al., 2004Podowski at al., 2004))

TaylorTaylor--bubble/liquid forcebubble/liquid force

BubbleBubble--induced turbulenceinduced turbulence

2 2

0.142 1.8 25l y y yR R R R

α = + +

*

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

r/R

α

* * * * * **

*

*

*


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0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0 .8 1 1.2RISO Measured Film Thickness (mm)

P

redi

cted

Film

T

hick

ness

(m

m)

+25%

-25%

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

RISO Measured Pressure Gradient (kPa/m)

P

redi

cted

Pre

ssur

e +25%

-25%

Points in RED are for

Gra

dien

t (kP

a/m

)

the 600 series data

z

δl f

wlfdeposition

entrainment

DROPLETS

FILM CORE REGION

Outside Tube Wall

Inside Rod

Film Waviness on Rod Surface

Film Waviness onOutside Tube Surface

Surface

Annular Flow in AnnulusAnnular Flow in Annulus (Antal et al., 2001)(Antal et al., 2001)


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Annular Flow in BWR Fuel Assembly Annular Flow in BWR Fuel Assembly (Antal & Podowski, 1999)(Antal & Podowski, 1999)


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Effect of Local Flow ObstaclesEffect of Local Flow Obstacles


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zone 1: OD 29.2

zone 2: OD 57.2

zone 3: OD 71

heated rod: OD 13.8

supporting part of a spacer

shroud: ID 71

modeled section 36o

(all dimensions in mm)

_ _ _ _ _ _

_

_

__

0.1

0.3

0.4

0.5

0.2

0.09 0.1 0.11 0.12 0.13 0.14

at 30 0 nm elev atio n

at 1 00 mm elev atio n

cross-section averagenea r-w all

Voi

d frac

tion

Axial distance [m]

Two-Phase Bubbly Flow around Spacers in Rod Bundles (Anglart et al., 1997)


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-5 0 0

0

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0

0 0 .0 2 0 .0 4 0 .06 0 .0 8 0 .1 0 .1 2 0 .1 4

Pre ss u re A lo n g C en te rlin e

Pr es su r e o n R od Su r fa ce

0 .0 2 5

0 .0 3

0 .0 3 5

0 .0 4

0 .0 4 5

0 .0 5

0 .0 5 5

0 .0 6

0 .0 6 5

0 0 .0 2 0 .0 4 0 .06 0 .0 8 0 .1 0 .1 2 0 .14

F ilm Th ic k n es s o n R od Su r fa ce

Pre

ssu

re [

Pa]

Film

thic

knes

s [m

m]

Distance from inlet [m]

D istance from inle t [m]

Droplet concentration

Annular Two-Phase Flow Around Spacer (Antal et al., 2001)


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BubblyBubbly--toto--ChurnChurn--Turbulent Turbulent Flow Regime TransitionFlow Regime Transition


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Velocity (U/Uavg) Volume Fraction

1

2

3

4

5

6

7

8 12

11

10

9 13

14

15

16

1

2

3

4

5

6

7

8 12

11

10

9 13

14

15

16

Low Power Fuel Bundle

High Power Fuel Bundle

NPHASE Simulation of TwoNPHASE Simulation of Two--Phase Flow in Adiabatic Phase Flow in Adiabatic Chimney of Advanced BWR (Antal et al., 2005)Chimney of Advanced BWR (Antal et al., 2005)

Uniform Inlet Profile

Base Case Nonuniform Inlet Profile

Cro

ss-s

ectio

nal A

vera

ged

Tot

al G

as V

olum

e Fr

actio

n

Nondimensional distance from inlet (z/DH) along centerline10 13.36.63.30

Total Gas Fraction

Small Bubble Field

Large Bubble Field


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MultipleMultiple--SizeSize--Group Model of Group Model of BoilingBoiling ChannelChannel((KumbaroKumbaro & Podowski, 2006& Podowski, 2006))

0 1 2 3z [m]

380

400

420

440

460

Inte

rfac

ial a

rea

[1/m

]

ExperimentMultifield model

Effect of number of bubble sizes on voidfraction0 1 2 3

x (m)

0

0.1

0.2

0.3

0.4

0.5

0.6

Vap

or v

olum

e fr

actio

n

1−group model (4mm)2−group model (1.5;5mm)3−group model (1;4;8mm)4−group model (1;3;5;8mm)5−group model (0.5;2;4;6;8mm)

0 1 2 3x (m)

0

0.1

0.2

0.3

0.4

0.5

Vap

or v

olum

e fr

actio

n

group−1group−2

0 1 2 3x (m)

0

0.1

0.2

0.3

0.4

0.5

Vap

or v

olum

e fr

actio

n

group−1group−2group−3group−4group−5


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ThreeThree Component Flow Component Flow (Gas/Liquid/Solid)(Gas/Liquid/Solid)


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NPHASE Prediction of Volume Fractions in Bubble Column

Tank Centerline

liquid bubbles solids

(Antal et al., 2000)(Antal et al., 2000)


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Flow in Branching ConduitsFlow in Branching Conduits


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Tee InflowDirection

Branch FlowDirection Run Flow

Direction

Gridgen Grid of 3D Equal Diameter Tee (Antal & Podowski, 2001)

Orthogonal, Wall Resolved Grid

UnstructuredGrid

Structured Grid


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3D Simulation of Flow in 90o Tee (Antal & Podowski, 2001)

Branch facing upward Branch facing downward


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Modeling of ForcedModeling of Forced--Convection Convection LowLow--Quality BoilingQuality Boiling


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(a) local void and temperature distributions along the channel ((a) local void and temperature distributions along the channel (KurulKurul et al., 1996),et al., 1996),(b) comparison between calculations and data for radial distribu(b) comparison between calculations and data for radial distributions of majortions of major

parameters at channel exit (parameters at channel exit (AlajbegovicAlajbegovic et al., 1996)et al., 1996)

Predicted and Measured Local Hydrodynamic and Thermal Predicted and Measured Local Hydrodynamic and Thermal Parameters for Parameters for SubcooledSubcooled Boiling in Annular Channel Heated Boiling in Annular Channel Heated

from Insidefrom Inside

-10.0

-15.0

-20.0

-25.0

-30.0

TEM

PER

ATU

RE

0.80

0.60

0.40

0.20

0.00

VO

ID F

RA

CT

ION

(a)

-10. 0

-15. 0

-20. 0

-25. 0

-30. 0

TEM

PER

ATU

RE

0 .80

0.60

0.40

0.20

0.00

VO

ID F

RA

CTI

ON

(b)(a)


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CHF in CHF in SubcooledSubcooled BoilingBoiling

Flow visualization near heated (Flow visualization near heated (MoudawarMoudawar et al., 2002)et al., 2002)


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Predictions using ThreePredictions using Three--Field ModelField Model

z1

z2

(a)

y

q

Temperature [K] Temperature [K] and void fraction and void fraction contourscontours

8833233230530530301236123616162112111721722020512512222412412412413030512512

Error Error [%][%]

Measured Measured CHF [kW]CHF [kW]

Predicted Predicted CHF [kW]CHF [kW]

Liquid Liquid SubcoolingSubcooling [K][K]

Mass FluxMass Flux[kg/m[kg/m22s]s]

(Podowski & (Podowski & Antal, 2002)Antal, 2002)


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Steam/Water Mixture Injection Steam/Water Mixture Injection into Large Liquid Poolinto Large Liquid Pool


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APAP--600 Reactor System600 Reactor System


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2.5 m

2.5 m

2.5 m

1.5 m

0.5 m

0.5 m

Sparger

Symmetry Plane

Wall

Wall

Wall

Location of CenterCut Plane

Location of Edgeof Sparger Cut Plane

Location of EndWall Cut Plane

33--D Model of IRWST PoolD Model of IRWST Pool


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Prediction of Pool Temperature in IRWSTIRWSTFollowing Steam/Water Injection through Sparger

(Antal et al., 2000)

12.5 s

5 s

37.5 s

50 s

30 s

62.5 s

75 s

55 s

25 s


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33--D Void Profiles in IRWST (Antal et al., 2001)D Void Profiles in IRWST (Antal et al., 2001)

CFXCFX NPHASENPHASE


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PlanaryPlanary Velocity Profiles in IRWST Velocity Profiles in IRWST Calculated by CFX, Fluent and NPHASE Calculated by CFX, Fluent and NPHASE for 40% Inlet Vapor Volumetric Fraction for 40% Inlet Vapor Volumetric Fraction

(Antal et al., 2001)(Antal et al., 2001)


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NPHASE Simulation of VHTR Outlet Plenum NPHASE Simulation of VHTR Outlet Plenum ((GallawayGallaway et al., 2007)et al., 2007)


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Transients and InstabilitiesTransients and Instabilities


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Uni

form

Hea

t Add

ition

Liquid Flow

Unh

eate

d R

iser S

ectio

n Constant Exit

Constant Inlet

3m3m

Pressure

Pressure

0.62

0.64

0.66

0.68

0.7

0.72

0.74

0.76

0.78

0.8

300 350 400 450 500 550 600 650

Voi

d Fr

actio

n

Time [s]

Volume Fraction Exiting Heater

(a)

0.6

0.62

0.64

0.66

0.68

0.7

0.72

0.74

0.76

0.78

0.8

0.82

300 310 320 330 340 350 360 370 380 390

Voi

d Fr

actio

n

Time [s]


(b)

0.66

0.68

0.7

0.72

0.74

300 320 340 360 380 400

Voi

d Fr

actio

n

Time [s]


(c)

Complete model

Constant vapor density model

Constant properties of both phases

(Antal & Podowski, 2003)(Antal & Podowski, 2003)DensityDensity--Wave Oscillations in CoreWave Oscillations in Core--Riser of BWRRiser of BWR


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Coupled ThermalCoupled Thermal--Hydraulics/Hydraulics/NeutronicsNeutronics ModelModel

0

0.5

1

1.5

2

2.5

3

3.5

4

0 50 100 150 200 250 300 350 400

elevation (cm)

rela

tive

linea

r pow

er

2.25 (m/s)2.75 (m/s)

0

1

2

3

4

5

6

0 50 100 150 200 250 300 350 400

elevation (cm)

velo

city

(m/s

)

2.25 m/s2.75 m/s

Superficial velocity

Relative power

10 10.4 10.8 11.2 11.6 120.245

0.246

0.247

0.248

0.249

0.25

x out

t [s]

Stable limitStable limit--cycle oscillations in cycle oscillations in twotwo--zone/twozone/two--parallelparallel--channel channel point kinetics core modelpoint kinetics core model

(Podowski & (Podowski & AnielAniel--BuchheitBuchheit, 2006), 2006)


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SummarySummary

Selected multiphase flow modeling and Selected multiphase flow modeling and computational issues have been discussedcomputational issues have been discussed

Details can be found in published papersDetails can be found in published papers

MostMost--recent results have been submitted recent results have been submitted for publication (journals and/or 2007 for publication (journals and/or 2007 conferences)conferences)


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Recent PublicationsRecent Publications“On the Modeling of Dispersed Particulate Flows using a Multifield Model”, P. Tiwari, S.P. Antal and M.Z. Podowski, Computational Solids and Fluids Mechanics, Elsevier (2003) “Multifield Computational Fluid Dynamics Model of Particulate Flow in Curved Circular Tubes” P. Tiwari, S.P. Antal, G. Belfort, A. Burgoyne and M.Z. Podowski, Theoretical and Computational Fluid Dynamics (2004)“The Modeling of Thin Liquid Films along Inclined Surfaces”, M.Z. Podowski and A. Kumbaro, Journal of Fluids Engineering (2004)"Theoretical Model of Contact Angle and Shape of Dropletson Solid Substrates", S. Vafaei and M.Z. Podowski, Nuclear Engineering and Design (2005)


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Recent Publications (Recent Publications (continuedcontinued))"Understanding Multiphase Flow and Heat Transfer: Perception, Reality, Future Needs", M.Z. Podowski,Archives of Thermodynamics (2005)"Three-Dimensional Fluid Mechanics of Particulate Two-Phase Flows in U-bend and Helical Conduits", P. Tiwari, S.P. Antal and M.Z. Podowski, Physics of Fluids (2006)“On the Modeling of Bubble Evolution and Transport using Coupled Level-Set/CFD Method”, B.W. Wierzbicki, S,P. Antal and M.Z. Podowski, Proc NURETH-11 (2005), also: Nuclear Technology (2006, in print)“Multidimensional Modeling of Developing Two-Phase Flowsin a Large Adiabatic Riser Channel”, S. P. Antal, M.Z. Podowski, R.T. Lahey, D. Barber and C. Delfino, Proc NURETH-11 (2005) ““Development of Mechanistic Modeling Capabilities for Development of Mechanistic Modeling Capabilities for GenerationGeneration--IV IV Supercritical WaterSupercritical Water--Cooled ReactorCooled Reactor””, , M.Z. M.Z. Podowski, S.P. Antal and H. Podowski, S.P. Antal and H. AnglartAnglart, , Proc. ICAPPProc. ICAPP (2006)(2006)


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Recent Publications (Recent Publications (continuedcontinued))"Multidimensional Model of Fluid Flow and Heat Transfer "Multidimensional Model of Fluid Flow and Heat Transfer in Generationin Generation--IV IV Supercritical Water ReactorsSupercritical Water Reactors", T. ", T. GallawayGallaway, S.P. Antal and M.Z. Podowski, , S.P. Antal and M.Z. Podowski, Proc. ICONEProc. ICONE--1414(2006). Also: (2006). Also: Nuclear Engineering and DesignNuclear Engineering and Design (in print)(in print)““On The Modeling of Local On The Modeling of Local NeutronicallyNeutronically--Coupled FlowCoupled Flow--Induced OscillationsInduced Oscillations in Advanced Boiling Water Reactorsin Advanced Boiling Water Reactors””, , S. S. AnielAniel--BuchheitBuchheit andand M.Z. Podowski, M.Z. Podowski, Proc. Proc. ICONEICONE--1414(2006)(2006)The Effect of Bubble/Bubble Interactions on Local Void Distribution in Two-Phase Flows”, A. Kumbaro and M.Z. Podowski, Proc. 13th IHTC (2006)“On the Consistency of Multifield Formulation for Modeling Two-Phase Flow and Heat Transfer”, M.Z. Podowski, Proc. 13th IHTC (2006)

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