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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
N
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
2 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
2 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
2 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
+∂
∂xi
[τp
(Fi −
DUi
Dt
)M
]︸ ︷︷ ︸
inertia
=∂
∂xi
[(DBδij +DTp ij
) ∂M∂xj
]︸ ︷︷ ︸
turbulent dispersion
+
+∂
∂xi
(M∂quDTp ij
∂xj
)︸ ︷︷ ︸
turbulent migration
Relative velocity
Vri = Ui − Vi =(DBδij +DTp ij
)∂ lnM∂xj
+ τp
(Fi − DUi
Dt− ∂(quDTp ij)
∂xj
)
3 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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 +
CF
/V +DT
) ,V +CF = UW + τp
(FW −
[DU
Dt
]W
)– convection-force component
V +DT =
[ScTκ
ln y+ +(V +DF + V +
TR
)−1]−1
– the diffusion-turbulence component
V +DF =
0.115
Sc3/4B
– diffusion term
V +TR =
2 · 10−4τ2.5+
1 + 10−3τ2.5+
– turbophoresis term
4 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
5 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Aerosols Transport
Aerosol Deposition in Straight Tube
j+ – dimensionless deposition velocityτ+ – dimensionless relaxation time dp=10 µm, Re = 10000
6 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
7 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
k2
ε
{S∗ij −
k
ε
[B1
(S∗ikS
∗jk −
1
3S∗knS
∗knδij
)+
+B2
(S∗ikW
∗jk + S∗jkW
∗ik
) ]}C∗µ =
3A1A2
3A21 − 2A2
3S̄∗II − 6A2
4W̄∗II
, B1 = 2A3A1
, B2 = A4A1
A31 −
(C0
1 − 2)A2
1 −{[
2A2
(C1
1 + 2)
+2A2
3
3
]S̄∗II + 2A2
4W̄∗II
}A1+
+ 2(C0
1 − 2)(A2
3S̄∗II
3+A2
4W̄∗II
)= 0
S∗ij = (1 +Mfu1)Sij W ∗ij = (1 +Mfu1)Wij
Sij = 12
(∂Ui∂xj
+∂Uj∂xi
)Wij = 1
2
(∂Ui∂xj− ∂Uj
∂xi
)A2 = 4
3− C2, A3 = 2− C3, A4 = 2− C4,
8 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Aerosols Transport
Turbulence model
Turbulent energy balance equation
(1 +Mfu1)
(∂k
∂t+ Ui
∂k
∂xi
)=
∂
∂xi
{[ν + (1 +Mfu1)
C∗µk2
σkε
]∂k
∂xi
}−
− (1 +Mfu1) 〈u′iu′j〉∂Ui
∂xj− (ε+ εp + Gp)
Turbulence dissipation balance equation
(1 +Mfu1)
(∂ε
∂t+ Ui
∂ε
∂xi
)=
∂
∂xi
{[ν + (1 +Mfu1)
C∗µk2
σεε
]∂ε
∂xi
}−
−ε
k
[Cε1 (1 +Mfu1) 〈u′iu′j〉
∂Ui
∂xj+ Cε2 (ε+ εp + Gp)
]
9 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
10 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Aerosols Transport
Deposition of aerosol particles in tube bend
11 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Aerosols Transport
Deposition of aerosol particles in tube bend
Experiment: D.Y.H. Pui et al. // Aerosol Sci. Technol. 7 (1987) 301315.
12 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Aerosols Transport
Deposition of aerosol particles in tube bend
Experiment: A.R. McFarland et al. // Environ. Sci. Technol. 31 (1997) 33713377.
13 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Aerosols Transport
Deposition of aerosol particles in tube bend
Experiment: T.M. Peters, D. Leith // Ann. Occup. Hyg. 48 (2004) 483490.
14 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
15 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
16 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
1 5
2 0
y +
u +
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
17 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Aerosols Transport
SiO2: dp = 50 µm, taup = 19.7 ms
0 . 0 0 . 2 0 . 4 0 . 6 0 . 82468
1 0
r / R
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
r / R
√⟨u′2x
⟩〈uc〉
,%
√⟨u′2y
⟩〈uc〉
,%
Streamwise fluctuating velocity Radial fluctuating velocity
18 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Aerosols Transport
Al2O3: dp = 50 µm, taup = 30.5 ms
0 . 0 0 . 2 0 . 4 0 . 6 0 . 82468
1 0
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
r / R
E x p . S i m .0 . 1 2 0 . 1 8 0 . 2 6
√⟨u′2x
⟩〈uc〉
,%
√⟨u′2y
⟩〈uc〉
,%
Streamwise fluctuating velocity Radial fluctuating velocity
19 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Aerosols Transport
SiO2: dp = 100 µm, taup = 78.7 ms
0 . 0 0 . 2 0 . 4 0 . 6 0 . 82468
1 0
r / R
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
r / R
√⟨u′2x
⟩〈uc〉
,%
√⟨u′2y
⟩〈uc〉
,%
Streamwise fluctuating velocity Radial fluctuating velocity
20 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
21 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Bubbly flows
Diffusion Inertia Model
Equation for numerical concentration of bubbles
∂Nα
∂t+∂NαWi
∂xi+
∂
∂xi
{τpαNα
1 +m
[(1−A)
(gi −
DWi
Dt
)+ FLαi + FWαi
]}=
=∂
∂xi
[1
1 +m
(DT
∂Nα
∂xi+Nα
∂qαDT
∂xi
)]+ Scoα + Sbrα
Equation for mass concentration of bubbles
∂Mα
∂t+∂MαWi
∂xi+
∂
∂xi
{τpαMα
1 +m
[(1−A)
(gi −
DWi
Dt
)+ FLαi + FWαi
]}=
=∂
∂xi
[1
1 +m
(DT
∂Mα
∂xi+Mα
∂qαDT
∂xi
)]Φα = Mα
ρp– volume concentration
22 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Bubbly flows
Turbulence Model
Turbulent energy balance equation
∂ρk
∂t+∂ρkWi
∂xi=
∂
∂xi
{[(1− Φ)µf +
ρνT
σk
]∂k
∂xi
}−
−[
(1− Φ) ρf +A∑α=1
Mαfpα
]〈u′iu′j〉
∂Wi
∂xj− ρε+ Sk1 − Sk2
Turbulence dissipation balance equation
∂ρε
∂t+∂ρεWi
∂xi=
∂
∂xi
{[(1− Φ)µf +
ρνT
σε
]∂ε
∂xi
}−
−Cε1ε
k
[(1− Φ) ρf +
A∑α=1
Mαfpα
]〈u′iu′j〉
∂Wi
∂xj−Cε2ρε2
k+
+ε
k(Cε3Sk1 − Cε4Sk2)
Sk1 – TKE source term due to the particle hydrodynamic resistanceSk2 – additional dissipation owing to particle involvement in turbulent motion
23 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
24 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
(C
Wep→∞D − CWep→0
D
)– drag coefficient for
deformable bubbles
CWep→∞D = 8
3+ 24
Rep– drag coefficient for high Weber number
CWep→0
D =
{24
Rep
(1 + 0.15Re0.687
p
)if Rep ≤ 103
0.44 if Rep > 103– drag coefficient of
spherical bubbles
∆CD = tanh[0.0038
(WepRe0.2p
)1.6]
25 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Bubbly flows
Lift coefficient
FLi =CLρfV
rj
ρp + CAρf
(∂Ui∂xj− ∂Uj∂xi
)– lift force
CL = max
(−0.27, FL(Wep)C
Wep→0
L
)– lift coefficient
Legendre D., Magnaudet J. // J. Fluid Mech. 1998. V. 368. P. 81.
CWep→0
L =
[1.88
RepSrp(1+0.2Rep/ Srp)3+
(1+16Re−1
p
)24(
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
p
)
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
0 . 0
0 . 2
0 . 4
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
26 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
27 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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)
1/2]
28 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
29 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
30 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Bubbly flows
Monodisperse bubbly flow
Φ
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0
0 . 10 . 20 . 30 . 40 . 50 . 60 . 7
r / R
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 00 . 10 . 20 . 30 . 40 . 50 . 6
r / R Void fraction
U,m/s
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
r / R
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
31 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Bubbly flows
Monodisperse bubbly flow
Φ
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0
0 . 1
0 . 2
0 . 3
r / R
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0
0 . 1
0 . 2
0 . 3
r / R
Void fraction
U,m/s
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0
0 . 40 . 60 . 81 . 01 . 21 . 4
r / R
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0
0 . 40 . 60 . 81 . 01 . 21 . 4
r / R
Liquid velocity
Serizawa 1
Serizawa 2
Serizawa 3
Liu 6
Liu 7
Liu 8
32 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
33 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
34 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Bubbly flows
Polydisperse bubbly flow
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
2
4
6
8 o u t l e t i n l e t
h(dp),
[%/m
m]
d p , [ m m ]Comparison bubble size distribution at the inlet and
outlet
0 . 0 1 0 . 1 14
5
6
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, [
mm]
L , [ m ]
Comparison of the spatial averaged Sauter mean diameter
35 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
Bubbly flows
Polydisperse bubbly flow
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
0 . 1
0 . 2
0 . 3
0 . 4
���������������������������� ��
�
����
�
Void fraction
MTLOOP-118
0 . 0 1 0 . 1 15
1 0
1 5
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, [
mm]
Spatial averaged Sauter mean diameter
36 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
37 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
N
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
0 . 1
0 . 2
0 . 3
0 . 4
�
r / R
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
U, m/
s
r / R0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 02 . 0
2 . 42 . 83 . 23 . 64 . 0
d bubble
, mm
r / R
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
38 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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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
0 . 1
0 . 2
0 . 3
0 . 4
�
r / R
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
U, m/
s
r / R0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 02 . 0
2 . 42 . 83 . 23 . 64 . 0
d bubble
, mm
r / R
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
39 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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Bubbly flows
Experiments MTLOOP and TOPFLOW
Flow pattern in MTLOOP experiments
40 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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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 ),
%/m
m
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
1 0
2 0
3 0
4 0
H(d p ),
%/mm
d p , m m
H(dp) = dΦddp
Φ =∫∞0 H(dp)ddp
41 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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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 ),
%/m
m
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
1 0
2 0
3 0
4 0
H(d p ),
%/mm
d p , m m
41 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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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
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 ),
%/m
m
d p , m m 2 3 4 5 6 701 02 03 04 05 06 07 0
H(d p ),
%/m
m
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
1 0
2 0
3 0
4 0
H(d p ),
%/mm
d p , m m 2 3 4 5 6 70
1 0
2 0
3 0
4 0
H(d p ),
%/mm
d p , m m
41 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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Bubbly flows
MTLOOP-107
Ref = 4.99× 104, D = 51.2 , 〈Φ〉 = 13%
Radial gas volume fraction Bubble size distribution
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
2
4
6
8
1 0
H(d p ),
%/m
m
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
2
4
6
8
1 0
H(d p ),
%/m
m
d p , m m
H(dp) = dΦddp
Φ =∫∞0 H(dp)ddp
42 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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Bubbly flows
MTLOOP-107
Ref = 4.99× 104, D = 51.2 , 〈Φ〉 = 13%
Radial gas volume fraction Bubble size distribution
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
2
4
6
8
1 0
H(d p ),
%/m
m
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
2
4
6
8
1 0
H(d p ),
%/m
m
d p , m m
42 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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Bubbly flows
MTLOOP-107
Ref = 4.99× 104, D = 51.2 , 〈Φ〉 = 13%
Radial gas volume fraction Bubble size distribution
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
2
4
6
8
1 0
H(d p ),
%/m
m
d p , m m
2 4 6 8 1 0 1 20
2
4
6
8
1 0
H(d p ),
%/m
m
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
2
4
6
8
1 0
H(d p ),
%/m
m
d p , m m
2 4 6 8 1 0 1 20
2
4
6
8
1 0
H(d p ),
%/m
md p , m m
42 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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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
n
r / R0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0
0 . 4
0 . 8
1 . 2
1 . 6
r / R
U, m/
s
T O P F L O W 0 7 4
2 4 6 8 1 0 1 20
1 0
2 0
3 0
4 0
H(d p ),
%/m
m
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
r / R
T O P F L O W 1 0 7
void f
ractio
n
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 4
0 . 8
1 . 2
1 . 6
r / R
U, m/
s
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
5
1 0
1 5
2 0
H(d p ),
%/m
m
d p , m m
43 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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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
n
r / R0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0
0 . 4
0 . 8
1 . 2
1 . 6
r / R
U, m/
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
1 0
2 0
3 0
4 0
H(d p ),
%/m
m
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
r / R
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
n
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00 . 4
0 . 8
1 . 2
1 . 6
r / R
U, m/
s
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
5
1 0
1 5
2 0
H(d p ),
%/m
m
d p , m m
43 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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Subcooled Boiling flows
Vertical annular flowExperiment: T.H. Lee , G.C. Park, D.J. Lee // , Int. J. of Multiphase Flow 28 (2002) 1351–1368
44 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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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
45 / 45Diffusion Inertia Model for Simulation Multiphase Turbulent Flows and implementation into OpenFOAM
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