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