modelling atomization with phase change · 2017. 1. 17. · modelling atomization with phase...
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CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 1/20
B. Duret, J. Reveillon and Demoulin F.X.www.cfdandco.com
CORIA – UMR CNRS 6614 – Univ. & INSA de ROUEN
Modelling atomization with phase change
ARCHER codeCORIAA. BerlemontT. Ménard
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 2/20
MARIE SKŁODOWSKA-CURIE ACTIONSInnovative Training Networks (ITN)
“HAoS”Holistic Approach of Spray Injection
through a generalized multi-phase framework
Understand the underlying physics of turbulent atomization
Elaborate atomization models from DNS data
DNS [1]Direct simulation and modelling
RANS [3-4]
ELSA model
LES [2]
ELSA model[1] T. Menard et al, International Journal of Multiphase Flow, 2007.[2] J. Chesnel et al, Atomization and Spray, 2011[3] R. Lebas et al, International Journal of Multiphase Flow, 2009[4] A.Vallet, R. Borghi, C. R. Acad. Sci., Paris, Sér. II b, 1999.
3
A. Berlemont, T. Ménard, S. Tanguy
P.A. Beau, R. Lebas
J. Chesnel, N. Hecht
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 4/20
ARCHER code : T. Ménard, A. Berlemont– DNS/LES code, MPI parallelization– Level Set/VOF/Ghost Fluid method coupling– Solve incompressible NS equations
– Consistent mass (VOF)-momentum fluxes 𝜌𝜌𝑙𝑙𝜌𝜌𝑔𝑔
ARCHER code
Triple disk Liquid Film
Die
sel i
njec
tion
[1] T. Menard et al, International Journal of Multiphase Flow, 2007.
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 5/201/ 1
Comparison with experiment
Experiment on left, simulation on right
The agreement on the shape of the jet is very satisfactory
LEGI - A. Delon, A. CartellierUg=22.6m/s, Ul=0.27m/s
Air/Eau
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 6/20
ELSA RANS
A. Sou et al, ILASS Europe 2011
𝜑𝜑𝑙𝑙: liquid volume fraction
𝜕𝜕𝜑𝜑𝑙𝑙𝜕𝜕𝑡𝑡
: Turbulent diffusion + (Slip vel.)
∑: surface density
𝜕𝜕∑𝜕𝜕𝑡𝑡
: turbulent stretching, collision, breakup, vaporization
ℎ𝑙𝑙: liquid enthalpy variation
R. Lebas et al., Intern. J. of Multiphase Flow, 2009F.X. Demoulin J. Réveillon
𝜑𝜑𝑙𝑙
∑
[A.Vallet, R. Borghi, C. R. Acad. Sci., Paris, Sér. II b, 1999.]
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 7/20
Low resolution Numerical interface stabilization
LES: under-resolved dynamic and ICM [1] 1282x1024
322x256
Low resolution Low dispersion
[1] J. Chesnel, J. Reveillon, T. Menard, and F.X. Demoulin, Large eddy simulation of liquid jet atomization. Atomization and Sprays, 21(9): p. 711-736, 2011
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 8/20
𝜕𝜕𝜑𝜑𝑙𝑙𝜕𝜕𝑡𝑡
+ 𝜕𝜕𝑢𝑢𝑗𝑗 𝜑𝜑𝑙𝑙𝜕𝜕𝑥𝑥𝑗𝑗
=𝜕𝜕𝜏𝜏𝜑𝜑𝑗𝑗𝜕𝜕𝑥𝑥𝑗𝑗
But:
A priori test on phase function equation
iso- =0.5, neglectediso- =0.5, 𝜏𝜏𝜑𝜑𝑖𝑖 considered
iϕτ
Atomized zones
𝜏𝜏𝜑𝜑𝑗𝑗 = 𝑢𝑢𝑗𝑗 𝜑𝜑 − �𝑢𝑢𝑗𝑗 �𝜑𝜑 = �𝑢𝑢𝑗𝑗 𝑙𝑙− �𝑢𝑢𝑗𝑗 ≪ �𝑢𝑢𝑗𝑗 �𝜑𝜑
𝜏𝜏𝜑𝜑𝑗𝑗 ≠ 0
𝜏𝜏𝜑𝜑𝑗𝑗 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑚𝑚𝑚𝑚𝑅𝑅𝑅𝑅𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑢𝑢𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷
+ 𝐶𝐶𝑅𝑅ℎ𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑚𝑚 𝑅𝑅𝑅𝑅𝑚𝑚𝑚𝑚𝑅𝑅𝑅𝑅𝑆𝑆𝑙𝑙𝐷𝐷𝑆𝑆
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 9/20
To combine resolved and under resolved approaches
J. Chesnel et al., Atomization and Spray, 2011
𝜏𝜏𝜑𝜑𝑗𝑗 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑚𝑚𝑚𝑚𝑅𝑅𝑅𝑅𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑢𝑢𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷
! Incompatibility issue !Subgrid term ICM
𝜕𝜕𝜑𝜑𝑙𝑙𝜕𝜕𝑡𝑡
+ 𝜕𝜕𝑢𝑢𝑗𝑗 𝜑𝜑𝑙𝑙𝜕𝜕𝑥𝑥𝑗𝑗
=𝜕𝜕𝜏𝜏𝜑𝜑𝑗𝑗𝜕𝜕𝑥𝑥𝑗𝑗
ICM Method VOF, Level Set
Subgrid Term
𝜕𝜕𝜑𝜑𝑙𝑙𝜕𝜕𝑡𝑡
+ 𝜕𝜕𝑢𝑢𝑗𝑗𝜑𝜑𝑙𝑙𝜕𝜕𝑥𝑥𝑗𝑗
+ 𝜕𝜕𝐶𝐶𝛼𝛼𝑢𝑢𝐶𝐶𝑗𝑗𝜑𝜑𝑙𝑙(1−𝜑𝜑𝑙𝑙)
𝜕𝜕𝑥𝑥𝑗𝑗ICM−interFoam
= (1- 𝐶𝐶𝛼𝛼)𝜏𝜏𝜑𝜑𝑗𝑗
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 10/20
Curvature κ :
𝐼𝐼𝑅𝑅𝑄𝑄𝑘𝑘 =1
2𝜅𝜅∆𝑥𝑥
Sensor: Interface Resolution Quality (IRQ)
Surface density 𝚺𝚺 :
IRQ∑ =∑𝑚𝑚𝑖𝑖𝑚𝑚∑ : Resolved interface
Total interface(ELSA)
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 11/20
ICM combined with subgrid modelling
Unresolved ICM
ELSA- LES𝑪𝑪𝜶𝜶 �𝟏𝟏𝟎𝟎
𝑪𝑪𝜶𝜶 = 𝟏𝟏
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 12/20
ICM + ELSA + LagrangeDynamic adaptive numerical methods
Subgrid Spray
ResolvedInterface
Under ResolvedInterface
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 13/20
Mass transfer: Evaporation, Cavitation, Flash Boiling
Cavitation
Flash Atomization
Evaporation
P.G. Aleiferis et al. Int. J. of Heat and Mass Transfer, 2010
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 14/20
Numerical Issues
Mass Transfer
)(saturationYYZ
v
v=
Ghost Fluid method [2]
DNS Analysis RunningModelling [3]
[2] T. Aslam, Journal of Computational Physics, 2004[3] Duret et al., Int. J. of Multiphase Flow, 2011[4] A. Sou et al. Int. J. Heat Mass Transfer, 2007[5] F. Örley et al., Physics of Fluids, 2015
𝛻𝛻.𝑈𝑈 ≠ 0
At the interface𝛻𝛻.𝑈𝑈 𝛻𝛻𝑇𝑇, 𝛻𝛻Y
B. Duret
Tanguy et al, J.Comp. Physics, 2007, [1] G. Huber et al., J. Comp. Physics, 2015
Bulk compressibility𝛻𝛻.𝑈𝑈 𝛻𝛻P
[4]
[5]
Pressure based
Density based + Equilibrium ? Pr. Saurel tomorrow 10h00
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 15/20
Liquid volume fraction =5%
Scalar field, 𝛁𝛁.𝐔𝐔 = 𝟎𝟎B. Duret et al., Int. J. of Multiphase Flow, 2011
Distance to Interface [m]
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 16/20
Volume production, 𝛻𝛻 � 𝑼𝑼 and pressure
• Based on compressible OpenFOAM® solver + source term• Recast mass to volume fraction equations
𝜕𝜕𝑡𝑡𝛼𝛼𝑙𝑙 + 𝛻𝛻 � 𝛼𝛼𝑙𝑙𝑼𝑼 = −𝛼𝛼𝑙𝑙𝜌𝜌𝑙𝑙𝐷𝐷𝑡𝑡𝜌𝜌𝑙𝑙 + ��𝑅
𝜌𝜌𝑙𝑙𝜕𝜕𝑡𝑡𝛼𝛼𝑣𝑣 + 𝛻𝛻 � 𝛼𝛼𝑣𝑣𝑼𝑼 = −𝛼𝛼𝑣𝑣𝜌𝜌𝑣𝑣
𝐷𝐷𝑡𝑡𝜌𝜌𝑣𝑣 −��𝑅𝜌𝜌𝑣𝑣
𝜕𝜕𝑡𝑡𝛼𝛼𝐷𝐷𝑛𝑛 + 𝛻𝛻 � 𝛼𝛼𝐷𝐷𝑛𝑛𝑼𝑼 = −𝛼𝛼𝐷𝐷𝑛𝑛𝜌𝜌𝐷𝐷𝑛𝑛𝐷𝐷𝑡𝑡𝜌𝜌𝐷𝐷𝑛𝑛
• Velocity divergence (assuming linear compressibility: 𝜌𝜌𝐷𝐷 = 𝜌𝜌i0 + 𝜓𝜓𝐷𝐷𝑝𝑝 )
𝛻𝛻 � 𝑼𝑼 = −𝛼𝛼𝑙𝑙𝜓𝜓𝑙𝑙𝜌𝜌𝑙𝑙
+𝛼𝛼𝑣𝑣𝜓𝜓𝑣𝑣𝜌𝜌𝑣𝑣
+𝛼𝛼𝐷𝐷𝑛𝑛𝜓𝜓𝐷𝐷𝑛𝑛𝜌𝜌𝐷𝐷𝑛𝑛
𝐷𝐷𝑡𝑡𝑝𝑝 +
��𝑅1𝜌𝜌𝑙𝑙−
1𝜌𝜌𝑣𝑣
• Solve velocity field 𝑼𝑼 with approximate pressure 𝑼𝑼∗
• Pressures correction : 𝑼𝑼−𝑼𝑼∗
∆𝑡𝑡= − 1
𝜌𝜌𝛻𝛻𝑝𝑝∗
𝛻𝛻 � 𝑼𝑼∗ + 𝛻𝛻 � ∆𝒕𝒕𝝆𝝆𝛻𝛻𝑝𝑝∗ = 𝛻𝛻 � 𝑼𝑼=− 𝛼𝛼𝑙𝑙𝜓𝜓𝑙𝑙
𝜌𝜌𝑙𝑙+ 𝛼𝛼𝑣𝑣𝜓𝜓𝑣𝑣
𝜌𝜌𝑣𝑣+ 𝛼𝛼𝑚𝑚𝑛𝑛𝜓𝜓𝑚𝑚𝑛𝑛
𝜌𝜌𝑚𝑚𝑛𝑛𝐷𝐷𝑡𝑡𝑝𝑝∗ + ��𝑅 1
𝜌𝜌𝑙𝑙− 1
𝜌𝜌𝑣𝑣
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 17/2017
Diffusion between gaseous phasesVs interface tracking method
• Transport equation of specie volume fraction:𝜕𝜕𝑡𝑡φ𝐷𝐷 + 𝛻𝛻 � 𝑈𝑈φ𝐷𝐷 + 𝛻𝛻 � φ𝐷𝐷 1 −φ𝐷𝐷 𝑈𝑈𝐷𝐷𝑛𝑛 = 𝛻𝛻 � D𝛻𝛻 φ𝐷𝐷
Gasliquid
𝑈𝑈𝐷𝐷𝑛𝑛
CG (compressed gradient) Diffusion
liquid
vapor
air
CG Diff = 0
CG Diff = 0
CG =0Diff
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 18/20
Water injection in a chamber with half vaporand half air: volume fraction
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 19/20
Water injection in a chamber with half vaporand half air: liquid mass transfer rate
Cavitation areas : - local pressure < psat- mAlphal < 0 means thatthe liquid is destructed to be transformed into vapor
Air side Vapor side
At the interface betweenair and liquid, we takeinto account a weakproduction of vapor
When the liquid is injected in a vapor chamber, the vapor is condensed at the interface since the atmospheric pressure > psat
CNRS – UNIVERSITE et INSA de Rouen
Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows 20/20
Conclusion and perspectives
• HAoS :Holistic Approach of Spray Injection through a generalized multi-phase framework
• Possible Project ? To take advantage of both : Advance multiphase flow
compressible method Advance interface treatment
for multiphase flow