Gas-Liquid Two-Phase Flow Studies using Three-Field Two ......Gas-Liquid Two-Phase Flow Studies....

.1 School of Nuclear Engineering, Purdue University

May 9, 2019

Gas-Liquid Two-Phase Flow Studiesusing Three-Field Two-Fluid Model and Two-

Group Interfacial Area Transport Equation

Subash L. SharmaMamoru IshiiTakashi Hibiki

School of Nuclear EngineeringPurdue University

.2

Motivation and Objective

Motivation: Computational Fluid Dynamics (CFD) simulation with a goodtwo-phase model can give detailed three dimensional aspects for betterdesign and performance of Two-phase systems (Nuclear Reactor, steamgenerator, heat exchanger, bubble column chemical reactor, electroniccooling system)

Objective:To develop a CFD framework within two-fluid model Formulation

(Three-Field Two-fluid model with two group IATE) which can be usedto predict the bubbly to churn-turbulent flow.

Select the right set of closure relations based on physics of adiabatic two-phase flow

– IATE models (coalescence and breakup models) – Sun et al. (2001) selected –Needs to be tested in 3D form against Non-Uniform Conditions in CFD code

– Existing Hydrodynamics model– Develop appropriate model based on correct physics observed in

experimentsSchool of Nuclear Engineering, Purdue University


Presentation Outline

• Introduction-Theoretical background• Experimental setup and Non-Uniform data• CFD Benchmark preparation• Bubbly flow simulation Results• Two-group Simulations (Cap-bubbly, Cap-Turbulent)• Summary and Future work


Introduction Theoretical Background

3-D two-fluid model (Ishii, 1975; Ishii & Hibiki, 2010)

Interfacial transfer terms due to time average

Conventional approach Flow regime dependent correlations- Static approach, Causes Numerical Bifurcation

during transition Advanced Approach

Interfacial Area Transport Equation (IATE)- Dynamic approach, Multidimensional(1-D, 3-D)

( )k kk kk k v

tΓα ρ α ρ∂

+∇⋅ =∂

( ) ( ) ikki kk tk k

k k kik k k k k k k k kv Γv v v Mp gt

α ρ α ρ α α τ τ α ρ α τ∂+∇ ⋅ = − ∇ +∇⋅ + + + + −∇ ⋅

∂

"( ) ( )tk k k k kkk k k k k k kk ki k i ki

i D pi v q qt D

it

Γ a qα ρ α ρ α α φ∂+∇⋅ = −∇ ⋅ + + + + +

∂

( )Interfacial transfer term = (Driving flux)ia ×

2

22 1( ) ( )3 3

gi i iii g g ph j bc ph

jg g

a a aa v v R D Rt t

αα η π

α α ∂ ∂

+∇ ⋅ = +∇ ⋅ − + + ∂ ∂ Ψ ∑

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One Group IATE

pm j phj

nn R R

t

v

max max

min min

V Vg

g g j phV Vj

dVf dV S S VdV

t V dtV

v

• One Group Void transport:

• One Group number density transport Equation:

max

min

V

gV

dV Vf dV

V dt VV

j phj

f dVf f S S

t V dt

v

• Particle transport equation

1 1

b bg ph g

g

g b gb bb g

g ph g g

g g

dm V.

dt

d V ddm dVV

dt dt dt dtddV

V dt dt

max

min

V

ph phVS VdV

g gg g g gt

v


max max

min min

V Vi

i i i j ph iV Vj

a dVa A f S S AdV

t V dtdV

v

• One Group IATE transport:

23

max

min

V

i iV

dV VA f dV a

V dt V

23

max

min

Vgi i

i i g g ph j ph iVjg

a aa S S AdV

t t

v v

2

22 1( ) ( )3 3


jg g

a a aa v v R D Rt t

αα η π

α α ∂ ∂

+∇ ⋅ = +∇ ⋅ − + + ∂ ∂ Ψ ∑

1

1

2( )3

gi ii gi g ph j

jg

a aa v vt t

αα η φ

α ∂ ∂ +∇ ⋅ = +∇ ⋅ − + ∂ ∂

∑

: particle number density source/sink

: interfacial area concentration source/sink

: void fraction source/sink

j jV

j j jV

j jV

R S dV

S A dV

S VdV

φ

η

≡

≡

≡

∫∫∫


Interfacial Area Transport Equation

Interfacial Area Transport Equation (Kojasoy and Ishii, 1995)

Contribution due to particle volume change

Contribution due to fluid particle interactions: coalescence & breakup

Contribution due to phase change: nucleation & condensation

2

22 1( ) ( )3 3


jg g

a a aa v v R D Rt t

αα η π

α α ∂ ∂

+∇ ⋅ = +∇ ⋅ − + + ∂ ∂ Ψ ∑


Key Bubble Length Scale and Bubble Group Boundary

Description Length scale

Spherical bubble limit

Maximum distorted bubble limit

Maximum cap bubble limit

Critical bubble size at the group boundary in narrow channel

1/324fdsD N

g µ

σ=

∆ρ

,max 4dDgσ

=∆ρ

,max 40cDgσ

=∆ρ

1/31/31.7cD G

g σ

= ∆ρ

1* 21 11 11 1 1

1,1

2( )3

gi ii gi c g

gj

j

a aa v D vt t

φα

χ αα ∂ ∂ +∇ ⋅ = − +∇ ⋅ + ∂ ∂

∑

2 1* 22 2 12 2 12 2 1 1

2 1,2

2( )3

g gi i ii g gi g c g

g gj

j

a a aa v v D vt t t

α αα χ α

αφ

α ∂ ∂ ∂

+∇ ⋅ = +∇ ⋅ + +∇ ⋅ + ∂ ∂ ∂ ∑

Two-Group Approach Group-1 bubbles: spherical and distorted

bubbles Group-2 bubbles: cap, slug and churn

bubbles

Two-Group IATE transport:

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Schematics of Two-Group Bubble Interaction (Ishii et al., 2002)

School of Nuclear Engineering, Purdue University


Two-Group IATE with Three-Field Two-Fluid Model:Two Gas Momentum Equations

Two-group gas continuity equation

Two-group gas momentum equation

Two-group IATE

11 121

( )( )g g

gg g v mt

α ρα ρ

⋅∂+∇ ⋅ = −∆

∂

22 122

( )( )g g

gg g v mt

α ρα ρ

⋅∂+∇ ⋅ = ∆

∂

( )1111 1 1 12 1 11 1 1 1 1 1 1

gg g tigg g g g i g ig g g g g g g g g

vv v p g m v M

tα ρ

α ρ α α τ τ α ρ α τ⋅∂

+∇ ⋅ = − ∇ +∇⋅ + + −∆ + −∇ ⋅∂

( )2222 2 2 12 2 22 2 2 2 2 2 2

gg g tigg g g g i g ig g g g g g g g g

vv v p g m v M

tα ρ

α ρ α α τ τ α ρ α τ⋅∂

+∇ ⋅ = − ∇ +∇⋅ + + + ∆ + −∇ ⋅∂

1* 21 11 11 1 1 ,1

1

2( )3

gi ii gi c g j

jg

a aa v D vt t

αχ α φ

α ∂ ∂ +∇ ⋅ = − +∇ ⋅ + ∂ ∂

∑

2 1* 22 2 12 2 12 2 1 1 ,2

2 1

2( )3

g gi i ii g gi g c g j

jg g

a a aa v v D vt t t

α αα χ α φ

α α ∂ ∂ ∂

+∇ ⋅ = +∇ ⋅ + +∇ ⋅ + ∂ ∂ ∂ ∑

(Driving flux)ia ×

Coalescence and Breakup mechanism

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Momentum closures


( )

D L W TD VM Bdid d d d d d d

dD L W TD VM Bd d d d d d

M F F F F F FB

M M M M M M

α= + + + + +

= + + + + +

Liquid phaseTurbulence:

,

2

;

t f SI BI

fSI f BI BI f b g f

f

kC C Dµ

µ µ µ

µ ρ µ ρ α υ υε

= +

= = −k-ε model, ,

, ,

Gas phase turbulence: zero order

; 1t f g t ft g t g

f

υ ρ µυ µ σ

σ ρ σ= ⇒ = =

Interfacial Forces Phases Nature Coefficient

Drag Force Gas and Liquid Interfacial force Ishii and Zuber (1979)

Wall Lubrication Force Gas and Liquid Interfacial force Antal et al. (1991)

1 0.01WC = − , 2 0.05WC =

Lift force Gas and Liquid Interfacial force Hibiki and Ishii (2007)

, 1 0.01L GC = , , 2 0.5L GC = −

Turbulent dispersion force Gas and Liquid Interfacial force Bertodano (1992)

,1 0.25TDC = Momentum Transfer by

Bubble interaction mechanism (Random

Collision)

Gas and Liquid Interfacial force Sharma et al. (2017, 2019)

Bubble-induced turbulence Liquid

Turbulence Induced by relative

motions of Bubbles in liquid

Sato et al. (1981)

, 1 0.6Sato GC =

, 2 2.1Sato GC = Lee (2010);

Lopez de Bertodano et al.(2006); Prabhudharwadkar et al. (2012)


Experimental Facility

Rectangular channel 200 mm x 10 mm x 2950 mm

Total test section length z/Dh~150

Local instrumentation ports z/Dh=34.8 (Port 2), 88.2 (Port 4),

142 (Port 6) Flow regime of interest

Bubbly Cap-turbulent Churn-turbulent

Measured flow parameters

Experimental database Uniform inlet injection Non-uniform inlet injection

, , , g i g Sma v Dα200 mm

x

yCross Sectional View of Test Section 10 mm


Experimental Database Used for Benchmarking with Non-Uniform Inlet Boundary Conditions

jf

jg jg jg

jf

jf

Double Side jf Profile Single Side jf Profile Center jf Profile

jf

jg

Uniform jf Profile

Non-Uniform inlet injection

jg

jf jf jf

jg

jg

Double Side jg Profile Single Side jg Profile Center jg Profile

jg

jf

Uniform jg Profile

Uniform Liquid Injection Uniform Gas Injection

Uncertainty and Possible Error:Kim et al (2000):Void Fraction: 5%Interfacial Area conc.:10%Le Corre et al (2003):Void Fraction:7%Gas velocity:12%Interfacial Area conc.:25%Factors affecting:

•finite size probe effect (missing bubbles)•data acquisition (sampling frequency, total sampling time)•signal processing (filtering, threshold)

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CFD simulation strategy

B.C Inlet :

Local measured void fraction, gas velocity , IAC at Port 2Liquid velocity Profile variation in x- direction obtained from gas

velocity by subtracting slip velocity, in y- direction 1/7th power lawvariation used

Outlet atmospheric pressureMesh


x

z Mesh Configuration: 60x10x162

Wall B.C. No slip for liquid phase and Free slip for Gas phase

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Bubbly Flow - Run1


jf

jg

Uniform jf Profile

<jg,0>=0.289 m/s<jf>=1.25 m/s

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Bubbly Flow - Run 2


<jg,0>=0.289 m/s<jf>=1.25 m/s

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Bubbly Flow - Run 3


jg

jf

Center jf Profile

<jg,0>=0.289 m/s<jf>=1.25 m/s

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Bubbly Flow - Run 4


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Bubbly Flow - Run 5


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Bubbly Flow - Run 6


-Hydraodynamics model predicting the trend in measured void fraction-Good prediction of development of velocity profile by models

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Two-group case

Cap-bubbly, cap-turbulent, churn-Turbulent flows


,

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Two-Group cases: Run 1


<jg,0>=0.77 m/s<jf>=1.92 m/s

jg

jf

Uniform jg Profile

Good prediction for overall trend and magnitude of each bubble group in transverse direction

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<jg,0>=0.74 m/s<jf>=1.25 m/s

jg

jf

Uniform jg Profile

•Good prediction for overall trend of phase distribution in transverse direction..

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<jg,0>=0.77 m/s<jf>=1.25 m/s

jg

jf

Double Side jg Profile

•Very Good prediction for overall trend of phase distribution in transverse direction.•Underprediction of volume transfer from G-2 to G-1 bubbles

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<jg,0>=0.74 m/s<jf>=0.943 m/s

•Very Good prediction for overall trend of phase distribution in transverse direction.•Underprediction of volume transfer from G-2 to G-1 bubbles

jg

jf

Uniform jg Profile

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<jg,0>=0.74 m/s<jf>=0.942m/s

jg

jf

Center jf Profile

•Very Good prediction for overall trend of phase distribution in transverse direction.•Underprediction of volume transfer from G-1 to G-2 bubbles by coalescence•Underprediction of the increase in G-2 bubble sauter mean diameter.

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Summary :-Hydrodynamics model gives satisfactory prediction in the trend of phase distribution-Discrepancies were found in IATE model prediction in some cases , specially in intergroup transfer model- Need to establish a good set of flow transition experimental

database for IATE benchmarking- Need to improve coalescence model

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CFD Framework with three-field two-fluid model and two-group IATE was prepared

Benchmarking simulations was carried out against uniform and non-uniform inlet test conditions.

In general, Hydrodynamic models along with IATE showing satisfactory prediction of phase distribution Bubble coalescence model will be further investigated


Conclusion


Thank you!!

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Publications Sharma, S. L., Ishii, M., Hibiki, T., Schlegel, J., Liu, Y., Buchanan, Jr., J.R.,

2019, "Beyond Bubbly Two-Phase Flow Investigation using a CFD Three-Field Two-Fluid Model", International Journal of Multiphase Flow, 113, p.1-15.

Sharma, S. L., Hibiki, T., Ishii, M., Brooks, C. S., Schlegel, J., Liu, Y., Buchanan, Jr., J.R., 2017, “Turbulence-induced Bubble Collision Force Modeling and Validation in Adiabatic Two-phase Flow using CFD”, Nuclear Engineering and Design Journal, 312, p.399-409.

Gas-Liquid Two-Phase Flow Studies using Three-Field Two ......Gas-Liquid Two-Phase Flow Studies....

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