Comptes Rendus
A simple turbulent two-fluid model
Comptes Rendus. Mécanique, Volume 344 (2016) no. 11-12, pp. 776-783.

We present in this paper a simple turbulent two-phase flow model using the two-fluid approach. The model, which relies on the classical ensemble averaging, allows the computation of unsteady flows including shock waves, rarefaction waves, and contact discontinuities. It requires the definition of adequate source terms and interfacial quantities. The hyperbolic turbulent two-fluid model is such that unique jump conditions hold within each field. Closure laws for the interfacial velocity and the interfacial pressure comply with a physically relevant entropy inequality. Moreover, source terms that account for mass, momentum and energy interfacial transfer are in agreement with the entropy inequality. Particular attention is also given to the jump conditions when assuming a perfect gas equation of state within each phase; this enables us to recover expected bounds on the mean density through shock waves.

Published online:
DOI: 10.1016/j.crme.2016.10.010
Keywords: Two-fluid model, Turbulence, Entropy inequality, Shocks

Jean-Marc Hérard 1, 2; Hippolyte Lochon 3, 4

1 EDF Lab Chatou, 6 quai Watier, 78400 Chatou, France
2 I2M, UMR CNRS 7373, Technopôle Château-Gombert, 39, rue Joliot Curie, 13453 Marseille, France
3 EDF Lab Saclay, 7 boulevard Gaspard Monge, 91120 Palaiseau, France
4 IMSIA, UMR EDF/CNRS/CEA/ENSTA 9219, Université Paris-Saclay, 828, boulevard des Maréchaux, 91762 Palaiseau, France
     author = {Jean-Marc H\'erard and Hippolyte Lochon},
     title = {A simple turbulent two-fluid model},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {776--783},
     publisher = {Elsevier},
     volume = {344},
     number = {11-12},
     year = {2016},
     doi = {10.1016/j.crme.2016.10.010},
     language = {en},
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TI  - A simple turbulent two-fluid model
JO  - Comptes Rendus. Mécanique
PY  - 2016
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VL  - 344
IS  - 11-12
PB  - Elsevier
DO  - 10.1016/j.crme.2016.10.010
LA  - en
ID  - CRMECA_2016__344_11-12_776_0
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%A Hippolyte Lochon
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Jean-Marc Hérard; Hippolyte Lochon. A simple turbulent two-fluid model. Comptes Rendus. Mécanique, Volume 344 (2016) no. 11-12, pp. 776-783. doi : 10.1016/j.crme.2016.10.010.

[1] M. Ishii Thermo-Fluid Dynamic Theory of Two-Phase Flows, Collection de la direction des études et recherches d'Électricité de France, 1975

[2] D.A. Drew; S.L. Passman Theory of Multicomponent Fluids, Springer-Verlag, 1999

[3] F. Coquel; T. Gallouët; J.-M. Hérard; N. Seguin Closure laws for a two-fluid two-pressure model, C. R. Acad. Sci. Paris, Ser. I, Volume 334 (2002) no. 10, pp. 927-932

[4] R. Berry; L. Zou; H. Zhao; D. Andrs; J. Peterson; H. Zhang; R. Martineau Relap-7: Demonstrating Seven-Equation, Two-Phase Flow Simulation in a Single-Pipe, Two-Phase Reactor Core and Steam Separator/Dryer, Idaho National Laboratory (INL), Idaho Falls, ID, USA, 2013 (Technical Report INL/EXT-13-28750)

[5] M. Baer; J. Nunziato A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials, Int. J. Multiph. Flow, Volume 12 (1986) no. 6, pp. 861-889

[6] J.B. Bdzil; R. Menikoff; S.F. Son; A.K. Kapila; D.S. Stewart Two-phase modeling of deflagration-to-detonation transition in granular materials: a critical examination of modeling issues, Phys. Fluids, Volume 11 (1999) no. 2, pp. 378-402

[7] A.K. Kapila; S.F. Son; J.B. Bdzil; R. Menikoff; D.S. Stewart Two-phase modeling of DDT: structure of the velocity-relaxation zone, Phys. Fluids, Volume 9 (1997) no. 12, pp. 3885-3897

[8] J. Glimm; D. Saltz; D.H. Sharp Renormalization group solution of two-phase flow equations for Rayleigh–Taylor mixing, Phys. Lett. A, Volume 222 (1996) no. 3, pp. 171-176

[9] H. Jin; J. Glimm; D.H. Sharp Compressible two-pressure two-phase flow models, Phys. Lett. A, Volume 353 (2006) no. 6, pp. 469-474

[10] R. Saurel; R. Abgrall A multiphase Godunov method for compressible multifluid and multiphase flows, J. Comput. Phys., Volume 150 (1999) no. 2, pp. 425-467

[11] S. Gavrilyuk; R. Saurel Mathematical and numerical modeling of two-phase compressible flows with micro-inertia, J. Comput. Phys., Volume 175 (2002) no. 1, pp. 326-360

[12] T. Gallouët; J.-M. Hérard; N. Seguin Numerical modeling of two-phase flows using the two-fluid two-pressure approach, Math. Models Methods Appl. Sci., Volume 14 (2004) no. 5, pp. 663-700

[13] J.-M. Hérard Problème de Riemann pour un modèle simple de turbulence monophasique compressible, 2014 Internal EDF report CR-I81-2014-006 (in French)

[14] A. Forestier; J.-M. Hérard; X. Louis Solveur de type Godunov pour simuler les écoulements turbulents compressibles, C. R. Acad. Sci. Paris, Ser. I, Volume 324 (1997) no. 8, pp. 919-926

[15] C. Berthon Contribution à l'analyse numérique des équations de Navier–Stokes compressibles à deux entropies spécifiques. Applications à la turbulence compressible, Université Pierre-et-Marie-Curie, Paris-6, 1999 (PhD thesis)

[16] B. Audebert Contribution à l'analyse des modèles aux tensions de Reynolds pour l'interaction choc turbulence, Université Pierre-et-Marie-Curie, Paris-6, 2006 (PhD thesis)

[17] S. Gavrilyuk; H. Gouin Geometric evolution of the Reynolds stress tensor, Int. J. Eng. Sci., Volume 59 (2012), pp. 65-73

[18] J.-M. Hérard Numerical modelling of turbulent two phase flows using the two fluid approach, 16th AIAA Computational Fluid Dynamics Conference, American Institute of Aeronautics and Astronautics, 2003

[19] P. Spalart; S. Allmaras A one-equation turbulence model for aerodynamic flows, Reno, NV, USA, 6–9 January 1992 (1992)

[20] V. Guillemaud Modélisation et simulation numérique des écoulements diphasiques par une approche bifluide à deux pressions, Université Aix–Marseille-1, 2007 (PhD thesis)

[21] R. Saurel; S. Gavrilyuk; F. Renaud A multiphase model with internal degrees of freedom: application to shock–bubble interaction, J. Fluid Mech., Volume 495 (2003), pp. 283-321

[22] J.-M. Hérard; Y. Liu Une approche bifluide statistique de modelisation des écoulements diphasiques à phases compressibles, 2013 Internal EDF report H-I81-2013-01162-FR (in French)

[23] V.H. Ransom; D.L. Hicks Hyperbolic two-pressure models for two-phase flow, J. Comput. Phys., Volume 53 (1984) no. 1, pp. 124-151

[24] R.A. Berry; R. Saurel; O. LeMetayer The discrete equation method (DEM) for fully compressible, two-phase flows in ducts of spatially varying cross-section, Nucl. Eng. Des., Volume 240 (2010) no. 11, pp. 3797-3818

[25] S. Gavrilyuk The Structure of Pressure Relaxation Terms: the One-Velocity Case, 2014 (EDF report H-I83-2014-00276-EN, January France)

[26] J. Smoller Shock Waves and Reaction Diffusion Equations, Springer-Verlag, 1983

[27] S. Muller; M. Hantke; P. Richter Closure conditions for non-equilibrium multi-component models, Contin. Mech. Thermodyn., Volume 28 (2016) no. 4, pp. 1157-1189

[28] J.-M. Hérard A class of compressible multiphase flow models, C. R. Acad. Sci. Paris, Ser. I, Volume 354 (2016) no. 9, pp. 954-959

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