di usion inertia model for simulation multiphase turbulent ......governing equations interfacial...

Diffusion Inertia Model for SimulationMultiphase Turbulent Flows andimplementation into OpenFOAM

Roman Mukin

Nuclear Safety Institute Russian Academy of Science

Riga, Latvia, October 20-21, 2011

1 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM

Introduction

Contents

1 Aerosols TransportDIM and flow rate of depositing particlesAerosol deposition in straight tubeAlgebraic Reynolds Stress ModelDeposition of aerosol particles in tube bendFeedback of Particles on Turbulence

2 Bubbly flowsGoverning equationsInterfacial forcesCoagulation and break-up of bubblesMonodisperse bubbly flowPolydisperse bubbly flow

3 Subcooled Boiling flows

Introduction

Contents

Introduction

Contents

Aerosols Transport

Mathematical formulation of DIM

The model is based on the kinetic equation for the probability density function(PDF) of the particles velocity distribution, and is valid for two-phase flowswith particles, which dynamic relaxation time does not exceed the Lagrangianintegral timescale of the turbulence.

Particle mass concentration equation∂M

∂t+∂UiM

∂xi︸︷︷︸transport

(Fi −

]︸︷︷︸

inertia

[(DBδij +DTp ij

) ∂M∂xj

]︸︷︷︸

turbulent dispersion

(M∂quDTp ij

)︸︷︷︸

turbulent migration

Relative velocity

Vri = Ui − Vi =(DBδij +DTp ij

)∂ lnM∂xj

(Fi − DUi

Dt− ∂(quDTp ij)

Aerosols Transport

Flow rate of depositing particles

Boundary condition, a relation between the flow rate of depositing particles JW andthe particle concentration in the near-wall region outside the viscous sub-layer ΦW :

Jw =V +CFu∗Φ1

1− exp(−V +

/V +DT

) ,V +CF = UW + τp

(FW −

)– convection-force component

V +DT =

[ScTκ

ln y+ +(V +DF + V +

)−1]−1

– the diffusion-turbulence component

V +DF =

Sc3/4B

– diffusion term

V +TR =

2 · 10−4τ2.5+

1 + 10−3τ2.5+

– turbophoresis term

Aerosols Transport

Aerosol Deposition in Straight Tube

j+ – dimensionless deposition velocityτ+ – dimensionless relaxation time dp=10 µm, Re = 10000

Aerosols Transport

Explicit Self-Consistent Algebraic RSMS.S. Girimaji, Fully Explicit and Self-Consistent ARSM // Theoret. Comput. Fluid Dynamics 8, 387 (1996).

Reynolds stress

〈u′iu′j〉 =2k

3δij − 2C∗µ

{S∗ij −

(S∗ikS

∗jk −

3S∗knS

∗knδij

(S∗ikW

∗jk + S∗jkW

) ]}C∗µ =

3A21 − 2A2

3S̄∗II − 6A2

4W̄∗II

, B1 = 2A3A1

, B2 = A4A1

A31 −

1 − 2)A2

1 −{[

1 + 2)

]S̄∗II + 2A2

4W̄∗II

+ 2(C0

1 − 2)(A2

3S̄∗II

4W̄∗II

S∗ij = (1 +Mfu1)Sij W ∗ij = (1 +Mfu1)Wij

Sij = 12

(∂Ui∂xj

+∂Uj∂xi

)Wij = 1

(∂Ui∂xj− ∂Uj

)A2 = 4

3− C2, A3 = 2− C3, A4 = 2− C4,

Aerosols Transport

Turbulence model

Turbulent energy balance equation

(1 +Mfu1)

∂t+ Ui

{[ν + (1 +Mfu1)

C∗µk2

− (1 +Mfu1) 〈u′iu′j〉∂Ui

∂xj− (ε+ εp + Gp)

Turbulence dissipation balance equation

(1 +Mfu1)

(∂ε

∂t+ Ui

{[ν + (1 +Mfu1)

C∗µk2

σεε

]∂ε

[Cε1 (1 +Mfu1) 〈u′iu′j〉

∂xj+ Cε2 (ε+ εp + Gp)

Aerosols Transport

Deposition of aerosol particles in tube bend

Aerosols Transport

Experiment: D.Y.H. Pui et al. // Aerosol Sci. Technol. 7 (1987) 301315.

Aerosols Transport

Experiment: A.R. McFarland et al. // Environ. Sci. Technol. 31 (1997) 33713377.

Aerosols Transport

Experiment: T.M. Peters, D. Leith // Ann. Occup. Hyg. 48 (2004) 483490.

Aerosols Transport

Deposition of aerosol particles in mouth-throat geometry

CAD files of the Alberta mouth-throat geometry proposed by Professor W. Finlay (University of Alberta, Canada)

Schematic of the Alberta mouth-throat geometry

Aerosols Transport

Circular Tube FlowExperiment: Varaksin A.Yu. et al. // High Temperature. 1998. 36, N5, P.767.

Mean velocity profiles

Re = 25600

D = 64 mm

U0 = 6.4 m/s

L/D > 20

1 0 1 0 01 0

dp, µm Minput Φinput, 10−5 τp, ms

Al2O3 50 ± 6 0.12, 0.18, 0.26 3.66, 5.49, 7.93 30.5

SiO2 50 ± 2 0.12, 0.18, 0.26, 0.39 5.67, 8.5, 12.23, 18.42 19.7

SiO2 100 ± 2 0.12, 0.18, 0.26, 0.39 5.67, 8.5, 12.23, 18.42 78.7

Aerosols Transport

SiO2: dp = 50 µm, taup = 19.7 ms

0 . 0 0 . 2 0 . 4 0 . 6 0 . 82468

E x p . S i m .0 . 1 2 0 . 1 8 0 . 2 6 0 . 3 9

0 . 0 0 . 2 0 . 4 0 . 6 0 . 82345678

E x p . S i m .0 . 1 2 0 . 1 8 0 . 2 6 0 . 3 9

√⟨u′2x

⟩〈uc〉

√⟨u′2y

⟩〈uc〉

Streamwise fluctuating velocity Radial fluctuating velocity

Aerosols Transport

Al2O3: dp = 50 µm, taup = 30.5 ms

0 . 0 0 . 2 0 . 4 0 . 6 0 . 82468

E x p . S i m .0 . 1 2 0 . 1 8 0 . 2 6

r / R 0 . 0 0 . 2 0 . 4 0 . 6 0 . 82345678

E x p . S i m .0 . 1 2 0 . 1 8 0 . 2 6

√⟨u′2x

⟩〈uc〉

√⟨u′2y

⟩〈uc〉

Aerosols Transport

SiO2: dp = 100 µm, taup = 78.7 ms

0 . 0 0 . 2 0 . 4 0 . 6 0 . 82468

E x p . S i m .0 . 1 2 0 . 1 8 0 . 2 6 0 . 3 9

0 . 0 0 . 2 0 . 4 0 . 6 0 . 82345678

E x p . S i m .0 . 1 2 0 . 1 8 0 . 2 6 0 . 3 9

√⟨u′2x

⟩〈uc〉

√⟨u′2y

⟩〈uc〉

Bubbly flows

Diffusion Inertia Model

Equation for numerical concentration of bubbles

∂Nα

∂t+∂NαWi

∂xi+

{τpαNα

[(1−A)

(gi −

)+ FLαi + FWαi

∂Nα

∂xi+Nα

∂qαDT

)]+ Scoα + Sbrα

Equation for mass concentration of bubbles

∂Mα

∂t+∂MαWi

∂xi+

{τpαMα

[(1−A)

(gi −

)+ FLαi + FWαi

∂Mα

∂xi+Mα

∂qαDT

)]Φα = Mα

ρp– volume concentration

Bubbly flows

Turbulence Model

Turbulent energy balance equation

∂ρk

∂t+∂ρkWi

∂xi=

{[(1− Φ)µf +

(1− Φ) ρf +A∑α=1

Mαfpα

]〈u′iu′j〉

∂xj− ρε+ Sk1 − Sk2

Turbulence dissipation balance equation

∂ρε

∂t+∂ρεWi

∂xi=

{[(1− Φ)µf +

]∂ε

−Cε1ε

[(1− Φ) ρf +

A∑α=1

Mαfpα

]〈u′iu′j〉

∂xj−Cε2ρε2

k(Cε3Sk1 − Cε4Sk2)

Sk1 – TKE source term due to the particle hydrodynamic resistanceSk2 – additional dissipation owing to particle involvement in turbulent motion

Bubbly flows

Drag coefficient

τp =4(ρp+CAρf )d3ρfCD|Vr| – particle response time

Loth E. // Int. J. Multiphase Flow. 2008. V. 34. P. 523.

CD = CWep→0

D + ∆CD

Wep→∞D − CWep→0

)– drag coefficient for

deformable bubbles

CWep→∞D = 8

Rep– drag coefficient for high Weber number

CWep→0

(1 + 0.15Re0.687

)if Rep ≤ 103

0.44 if Rep > 103– drag coefficient of

spherical bubbles

∆CD = tanh[0.0038

(WepRe0.2p

Bubbly flows

Lift coefficient

FLi =CLρfV

ρp + CAρf

(∂Ui∂xj− ∂Uj∂xi

)– lift force

CL = max

(−0.27, FL(Wep)C

Wep→0

)– lift coefficient

Legendre D., Magnaudet J. // J. Fluid Mech. 1998. V. 368. P. 81.

CWep→0

RepSrp(1+0.2Rep/ Srp)3+

(1+16Re−1

1+29Re−1p

)2]1/2

Hibiki T., Ishii M. // Chem. Eng. Sc. 2007. V.62. P. 6457.

FL(Wep) = 2− exp(0.0295 ·We2.21

FWi =CW ρf |Vr|2ni(ρp + CAρf ) d

– wall force

CW = max(Cw1 + Cw2

dpyw, 0) 0 1 2 3 4 5 6 7 8

- 0 . 4

- 0 . 2

T o m i y a m a ��

L e g a n d r e M a g n a d u e t

Bubbly flows

Coagulation and Break-Up of bubbles

Scoα = −Nα2

A∑α1=1

βαα1Nα1 – coagulation term

βαα1 – coagulation kernel function

Zaichik L.I. et al. // Int. J. H&MT. 2010. V. 53. P. 1613.

βαα1 = 4π1/2d2αα1

Vtφ(Σ)Γηco

We∗cr =3

1 + 2ρp/ρf

Sbrα =Nα,cr −Nα

τbrαH(We∗α −We∗cr)ηbr

Yao M., Morel C. // Int. J. H&MT. 2004. V. 47. P. 307.

βαα1 =πd

7/3αα1ε

1/3Γηco

6[1 +KcΦ

(We∗αα1

/We∗cr

)1/2Γ]

We∗cr = 1.24

Sbrα =Kb1Φ (1− Φ) ε1/3ηbr

3d11/3α

[1 +Kb2 (1− Φ) (We∗α/We∗cr)

Bubbly flows

Monodisperse bubbly flow

Flow condition

Case Jinc , m/s α dp, mm Flow direction Pipe diam, mm

Wang 1 0.43 0.132 2.8 Up 57.15

Wang 2 0.43 0.310 3.0 Up 57.15

Wang 3 0.43 0.383 3.2 Up 57.15

Wang 4 0.71 0.145 2.8 Down 57.15

Wang 5 0.71 0.288 3.0 Down 57.15

Wang 6 0.71 0.371 3.2 Down 57.15

Serizawa 1 1.03 0.0397 4.0 Up 60

Serizawa 2 1.03 0.1023 4.0 Up 60

Serizawa 3 1.03 0.1627 4.0 Up 60

Liu 4 1.0 0.087 6.6 Up 57.2

Liu 5 1.0 0.095 3.7 Up 57.2

Liu 6 1.0 0.106 2.81 Up 57.2

Bubbly flows

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 10 . 20 . 30 . 40 . 50 . 60 . 7

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 00 . 10 . 20 . 30 . 40 . 50 . 6

r / R Void fraction

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 20 . 40 . 60 . 81 . 01 . 2

r / RLiquid velocity

Wang 1

Wang 2

Wang 3

Wang 4

Wang 5

Wang 6

Bubbly flows

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

Void fraction

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 40 . 60 . 81 . 01 . 21 . 4

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 40 . 60 . 81 . 01 . 21 . 4

Liquid velocity

Serizawa 1

Serizawa 2

Serizawa 3

Bubbly flows

Polydisperse bubbly flow

Flow pattern map of MTLOOP experiments

Case Jinc , m/s Jing , m/s

MTLOOP-074 1.017 0.0368

MTLOOP-071 0.255 0.0368

MTLOOP-095 0.641 0.0898

MTLOOP-107 1.017 0.140

MTLOOP-118 1.017 0.219D. Lucas, E. Krepper, H.-M. Prasser // Int. J. Multiphase Flow 31 (2005) P.1304

Bubbly flows

MTLOOP-071

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 0

0 . 0 4

0 . 0 8

0 . 1 2

0 . 1 6

��

Void fraction

0 2 4 6 8 1 0 1 20

8 o u t l e t i n l e t

h(dp),

d p , [ m m ]Comparison bubble size distribution at the inlet and

outlet

0 . 0 1 0 . 1 14

7 1 d e l t a 2 d e l t a 4 d e l t a E x p e r i m e n t

D32, [

L , [ m ]

Comparison of the spatial averaged Sauter mean diameter

Bubbly flows

MTLOOP-074

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 0

0 . 0 3

0 . 0 6

0 . 0 9

0 . 1 2��

��

Void fraction

MTLOOP-095

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 00 . 0 50 . 1 00 . 1 50 . 2 00 . 2 50 . 3 0

��

Void fraction

MTLOOP-107

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 00 . 0 50 . 1 00 . 1 50 . 2 00 . 2 5

��

Void fraction

MTLOOP-118

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0

��

Void fraction

MTLOOP-118

0 . 0 1 0 . 1 15

2 0 1 d e l t a 2 d e l t a 4 d e l t a E x p e r i m e n t

L , [ m ]

D32, [

Spatial averaged Sauter mean diameter

Bubbly flows

Validation matrix of polydisperse bubbly flows

Flow parameters

Jinc , m/s α Ref Tube diam., mm

Hibiki 1 0.986 0.203 4.3× 104 50.8

Hibiki 2 0.986 0.108 4.3× 104 50.8

Hibiki 3 0.986 0.0512 4.3× 104 50.8

MTLOOP 071 0.255 0.155 1.1× 104 51.2

MTLOOP 074 1.017 0.04 4.5× 104 51.2

MTLOOP 095 0.641 0.14 2.8× 104 51.2

MTLOOP 107 1.017 0.13 4.5× 104 51.2

MTLOOP 118 1.017 0.172 4.5× 104 51.2

TOPFLOW 074 1.017 0.04 2.6× 105 195.3

TOPFLOW 107 1.017 0.13 2.6× 105 195.3

Bubbly flows

Polydisperse bubbly flow in vertical tube

Upward flowRef = 4.99× 104, D = 50.8 , 〈Φ〉 = 5%

Local void fraction Liquid and gas velocities Bubbles diameter

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0

Z a i c h i k m o d i f i e d Y a o M o r e l

E x p e r i m e n t : z / D = 5 3 . 5

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 60 . 81 . 01 . 21 . 41 . 6

E x p e r i m e n t : z / D = 5 3 . 5 l i q u i d z / D = 5 3 . 5 g a s s i n g l e p h a s e

G a s v e l o c i t y : L i q u i d v e l o c i t y : Y a o M o r e l Y a o M o r e l Z a i c h i k m o d i f i e d Z a i c h i k m o d i f i e d s i n g l e p h a s e

r / R0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 02 . 0

2 . 42 . 83 . 23 . 64 . 0

d bubble

Z a i c h i k m o d i f i e d E x p e r i m e n t : Y a o M o r e l z / D = 5 3 . 5 i n l e t z / D = 6

Experiment T. Hibiki et al. Int. J. Heat Mass Transfer, 44 (2001) 1869-1888

Bubbly flows

Polydisperse bubbly flow in vertical tube

Upward flow in vertical tubeRef = 4.99× 104, D = 50.8 mm, 〈Φ〉 = 10%

Local void fraction Liquid and gas velocities Bubbles diameter

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0

Z a i c h i k m o d i f i e d Y a o M o r e l

E x p e r i m e n t : z / D = 5 3 . 5

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 60 . 81 . 01 . 21 . 41 . 6

E x p e r i m e n t : s i n g l e p h a s e z / D = 5 3 . 5 l i q u i d z / D = 5 3 . 5 g a s s i n g l e p h a s e

G a s v e l o c i t y : L i q u i d v e l o c i t y : Y a o M o r e l Y a o M o r e l Z a i c h i k m o d i f i e d Z a i c h i k m o d i f i e d

r / R0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 02 . 0

2 . 42 . 83 . 23 . 64 . 0

d bubble

Z a i c h i k m o d i f i e d E x p e r i m e n t : Y a o M o r e l z / D = 5 3 . 5 i n l e t z / D = 6

Experiment T. Hibiki et al. Int. J. Heat Mass Transfer, 44 (2001) 1869-1888

Bubbly flows

Experiments MTLOOP and TOPFLOW

Flow pattern in MTLOOP experiments

Bubbly flows

MTLOOP-074

Ref = 4.99× 104, D = 51.2 , 〈Φ〉 = 4%

Radial gas volume fraction Bubble size distribution

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 00 . 0 20 . 0 40 . 0 60 . 0 80 . 1 00 . 1 2

M T L O O P - 0 7 4

r / R2 3 4 5 6 70

1 02 03 04 05 06 07 0

H(d p ),

d p , m m

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 00 . 0 20 . 0 40 . 0 60 . 0 80 . 1 00 . 1 2

M T L O O P - 0 7 4

r / R2 3 4 5 6 70

H(d p ),

d p , m m

H(dp) = dΦddp

Φ =∫∞0 H(dp)ddp

Bubbly flows

MTLOOP-074

Ref = 4.99× 104, D = 51.2 , 〈Φ〉 = 4%

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 00 . 0 20 . 0 40 . 0 60 . 0 80 . 1 00 . 1 2

M T L O O P - 0 7 4

r / R2 3 4 5 6 70

1 02 03 04 05 06 07 0

H(d p ),

d p , m m

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 00 . 0 20 . 0 40 . 0 60 . 0 80 . 1 00 . 1 2

M T L O O P - 0 7 4

r / R2 3 4 5 6 70

H(d p ),

d p , m m

Bubbly flows

MTLOOP-074

Ref = 4.99× 104, D = 51.2 , 〈Φ〉 = 4%

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 00 . 0 20 . 0 40 . 0 60 . 0 80 . 1 00 . 1 2

Z a i c h i k m o d i f i e d , 2 m o m e n t s Y a o M o r e l , 2 m o m e n t s M T L O O P - 0 7 4

r / R2 3 4 5 6 70

1 02 03 04 05 06 07 0

H(d p ),

d p , m m 2 3 4 5 6 701 02 03 04 05 06 07 0

H(d p ),

d p , m m

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 00 . 0 20 . 0 40 . 0 60 . 0 80 . 1 00 . 1 2

Z a i c h i k m o d i f i e d , 4 m o m e n t s Y a o M o r e l , 4 m o m e n t s M T L O O P - 0 7 4

r / R2 3 4 5 6 70

H(d p ),

d p , m m 2 3 4 5 6 70

H(d p ),

d p , m m

Bubbly flows

MTLOOP-107

Ref = 4.99× 104, D = 51.2 , 〈Φ〉 = 13%

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 00 . 0 50 . 1 00 . 1 50 . 2 00 . 2 50 . 3 0

M T L O O P - 1 0 7

r / R2 4 6 8 1 0 1 20

H(d p ),

d p , m m

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 0 00 . 0 50 . 1 00 . 1 50 . 2 00 . 2 50 . 3 0

M T L O O P - 1 0 7

r / R2 4 6 8 1 0 1 20

H(d p ),

d p , m m

H(dp) = dΦddp

Φ =∫∞0 H(dp)ddp

Bubbly flows

MTLOOP-107

Ref = 4.99× 104, D = 51.2 , 〈Φ〉 = 13%

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 00 . 0 50 . 1 00 . 1 50 . 2 00 . 2 50 . 3 0

M T L O O P - 1 0 7

r / R2 4 6 8 1 0 1 20

H(d p ),

d p , m m

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 0 00 . 0 50 . 1 00 . 1 50 . 2 00 . 2 50 . 3 0

M T L O O P - 1 0 7

r / R2 4 6 8 1 0 1 20

H(d p ),

d p , m m

Bubbly flows

MTLOOP-107

Ref = 4.99× 104, D = 51.2 , 〈Φ〉 = 13%

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 00 . 0 50 . 1 00 . 1 50 . 2 00 . 2 50 . 3 0

M T L O O P - 1 0 7 Y a o M o r e l Z a i c h i k m o d i f i e d

r / R2 4 6 8 1 0 1 20

H(d p ),

d p , m m

2 4 6 8 1 0 1 20

H(d p ),

d p , m m

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 00 . 0 50 . 1 00 . 1 50 . 2 00 . 2 50 . 3 0

M T L O O P - 1 0 7 Y a o M o r e l Z a i c h i k m o d i f i e d

r / R2 4 6 8 1 0 1 20

H(d p ),

d p , m m

2 4 6 8 1 0 1 20

H(d p ),

md p , m m

Bubbly flows

TOPFLOW-074 TOPFLOW-107

Ref = 2.6× 105, D = 195.3 , 〈Φ074〉 = 4%, 〈Φ107〉 = 13%

Radial gas volume fraction Gas velocity Bubble size distribution

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

0 . 0 4

T O P F L O W 0 7 4

void f

ractio

r / R0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

T O P F L O W 0 7 4

2 4 6 8 1 0 1 20

H(d p ),

d p , m m

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 0

0 . 0 4

0 . 0 8

0 . 1 2

0 . 1 6

T O P F L O W 1 0 7

void f

ractio

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 4

T O P F L O W 1 0 70 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 50

H(d p ),

d p , m m

Bubbly flows

TOPFLOW-074 TOPFLOW-107

Ref = 2.6× 105, D = 195.3 , 〈Φ074〉 = 4%, 〈Φ107〉 = 13%

Radial gas volume fraction Gas velocity Bubble size distribution

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

0 . 0 4

1 m o m e n t 2 m o m e n t s T O P F L O W 0 7 4

void f

ractio

r / R0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

s g a s l i q u i d T O P F L O W 0 7 4

2 4 6 8 1 0 1 20

H(d p ),

d p , m m

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0 0

0 . 0 4

0 . 0 8

0 . 1 2

0 . 1 6

1 m o m e n t 2 m o m e n t s T O P F L O W 1 0 7

void f

ractio

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 4

g a s l i q u i d T O P F L O W 1 0 7

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 50

H(d p ),

d p , m m

Subcooled Boiling flows

Vertical annular flowExperiment: T.H. Lee , G.C. Park, D.J. Lee // , Int. J. of Multiphase Flow 28 (2002) 1351–1368

Subcooled Boiling flows

Diffusion-Inertia Model (DIM) of a dispersed flow

DIM is 1-fluid Eulerian mixture approach to modeling ofmultiphase flows in complex geometry for 3D simulation of:

aerosols (drops) transport and deposition (NPP’s primary circuitand containment)

bubbles(vessel outer cooling)

It was specially designed to account for particle-turbulenceinteraction.Why DIM among other existing multiphase models?

universal description of particles, droplets, and bubbles withreasonable accuracy

actually claims to be a self-consistent description ofparticles/bubbles interaction with the turbulence

robust and effective

developable to expansion of its application field

di usion inertia model for simulation multiphase turbulent ......governing equations interfacial...

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sedimentation of a polydisperse non- brownian...

youth ideas - bubbly christians

viscoelasticity of mono-and polydisperse inverse ferrofluids

measuring combustion emissions down to 10 nm with...

polydisperse turbidity currents propagating over...

monodisperse magnetic nanoparticles: effects of

start-up rheometry of highly polydisperse

cadbury bubbly bar advertising

1-0016 bubbly

transient superdiffusion of polydisperse vacuoles in...

understanding the polydisperse behavior of asphaltenes...

bubbly- share your voice

network morphologies in monodisperse and polydisperse

highly monodisperse zwitterion functionalized non

evaluation of filter media for particle number, surface...

morphological investigation of polydisperse asymmetric block...

studi fluidisasi dan pembakaran batubara polydisperse di

compression and flowback in polydisperse composite

incipient flu1dization of polydisperse beds