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Modelling phase transition in metastable liquids: application to cavitating and flashing flows

Published online by Cambridge University Press:  30 June 2008

RICHARD SAUREL ,
FABIEN PETITPAS  and
REMI ABGRALL
RICHARD SAUREL*
Affiliation:
Polytech'Marseille, Aix-Marseille Université and SMASH Project UMR CNRS 6595 - IUSTI - INRIA, 5 rue E. Fermi, 13453 Marseille Cedex 13, France University Institute of France
FABIEN PETITPAS
Affiliation:
Polytech'Marseille, Aix-Marseille Université and SMASH Project UMR CNRS 6595 - IUSTI - INRIA, 5 rue E. Fermi, 13453 Marseille Cedex 13, France
REMI ABGRALL
Affiliation:
SCALAPPLIX Project, INRIA and Institut de Mathématiques, Université de Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France University Institute of France
*
†Author to whom correspondence should be addressed: [email protected]
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Abstract

A hyperbolic two-phase flow model involving five partial differential equations is constructed for liquid–gas interface modelling. The model is able to deal with interfaces of simple contact where normal velocity and pressure are continuous as well as transition fronts where heat and mass transfer occur, involving pressure and velocity jumps. These fronts correspond to extra waves in the system. The model involves two temperatures and entropies but a single pressure and a single velocity. The closure is achieved by two equations of state that reproduce the phase diagram when equilibrium is reached. Relaxation toward equilibrium is achieved by temperature and chemical potential relaxation terms whose kinetics is considered infinitely fast at specific locations only, typically at evaporation fronts. Thus, metastable states are involved for locations far from these fronts. Computational results are compared to the experimental ones. Computed and measured front speeds are of the same order of magnitude and the same tendency of increasing front speed with initial temperature is reported. Moreover, the limit case of evaporation fronts propagating in highly metastable liquids with the Chapman–Jouguet speed is recovered as an expansion wave of the present model in the limit of stiff thermal and chemical relaxation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 607 , 25 July 2008 , pp. 313 - 350
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Abgrall, R. & Saurel, R. 2003 Discrete equations for physical and numerical compressible multiphase mixtures. J. Comput. Phys. 186, 361–396.CrossRefGoogle Scholar
Baer, M. R. & Nunziato, J. W. 1986 A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Intl J. Multiphase Flows 12, 861–889.CrossRefGoogle Scholar
Butler, P. B., Lambeck, M. F. & Krier, H. 1982 Modeling of shock development and transition to detonation initiated by burning in porous propellant beds. Combust. Flame 46, 75–93.CrossRefGoogle Scholar
Cahn, J. W. & Hilliard, J. E. 1958 Free energy of a nonuniform system i: Interfacial free energy. J. Chem. Phys. 28, 258–267.CrossRefGoogle Scholar
Chaves, H. 1984 Changes of phase and waves on depressurization of liquids with high specific heat. Ph D thesis, Georg-August-Universitat, Gottingen.Google Scholar
Chinnayya, A., Daniel, E. & Saurel, R. 2004 Computation od detonation waves in heterogeneous energetic materials. J. Comput. Phys. 196, 490–538.CrossRefGoogle Scholar
Delhaye, J. M. & Boure, J. A. 1982 General equations and two-phase flow modeling. In Handbook of Multiphase Systems (ed. Hestroni, G.), Hemisphere.Google Scholar
Faucher, E., Herard, J. M., Barret, M. & Toulemonde, C. 2000 Computation of flashing flows in variable cross section ducts. Intl J. Comput. Fluid Dyn. 13, 365–391.CrossRefGoogle Scholar
Frost, D. L., Lee, J. H. S. & Ciccarelli, G. 1991 The use of hugoniot analysis for the propagation of vapor explosion waves. Shock Waves 1, 99–110.CrossRefGoogle Scholar
Grolmes, M. A. & Fauske, H. K. 1974 Axial propagation of free surface boiling into superheated liquids in vertical tubes. Heat Transfer 4, 30–34.CrossRefGoogle Scholar
Hill, L. G. & Sturtevant, B. 1990 An experimental study of evaporation waves in a superheated liquid. In Adiabatic Waves in Liquid-Vapor Systems (ed. Meier, G. E. A. & Thompson, P. A.), pp. 25–37. Springer.CrossRefGoogle Scholar
Ishii, M. 1975 Thermo-Fluid Dynamic Theory of Two-Phase Flow. Eyrolles, Paris.Google Scholar
Jamet, D., Lebaigue, O., Coutris, N. & Delhaye, J. M. 2001 The second gradient method for the direct numerical simulation of liquid-vapor flows with phase change. J. Comput. Phys. 169, 624–651.CrossRefGoogle Scholar
Kapila, A., Menikoff, R., Bdzil, J., Son, S. & Stewart, D. 2001 Two-phase modeling of DDT in granular materials: reduced equations. Phys. Fluids 13, 3002–3024.CrossRefGoogle Scholar
Kurschat, Th., Chaves, H. & Meier, G. E. A. 1992 Complete adiabatic evaporation of highly superheated liquid jets. J. Fluid Mech. 236, 43–59.CrossRefGoogle Scholar
Le Metayer, O., Massoni, J. & Saurel, R. 2004 Elaborating equations of state of a liquid and its vapor for two-phase flow models. Intl J. Therm. Sci. 43, 265–276.Google Scholar
Le Metayer, O., Massoni, J. & Saurel, R. 2005 Modeling evaporation fronts with reactive Riemann solvers. J. Comput. Phys. 205, 567–610.CrossRefGoogle Scholar
Liou, M. S. & Edwards, J. R. 1999 AUSM schemes and extensions for low Mach and multiphase flows. 30th Computational Fluid Dynamics Conf., March 8-12. Lecture Series 1999-03, Von Karman Institute for Fluid Dynamics.Google Scholar
Menikoff, R. & Plohr, B. J. 1989 The Riemann problem for fluid flow of real materials. Rev. Mod. Phys. 61, 75–130.CrossRefGoogle Scholar
Muller, S. & Voss, A. 2006 The riemann problem for the Euler equations with nonconvex and nonsmooth equations of state: Construction of the waves curves. SIAM J. Sci. Comput. 28, 651–681.CrossRefGoogle Scholar
Murrone, A. & Guillard, H. 2004 A five equations reduced model for compressible two-phase flow problems. J. Comput. Phys. 202, 664–698.CrossRefGoogle Scholar
Oldenbourg, R. 1989 Properties of Water and Steam in SI-units. Springer.Google Scholar
Perigaud, G. & Saurel, R. 2005 A compressible flow model with capillary effects. J. Comput. Phys. 209, 139–178.CrossRefGoogle Scholar
Petitpas, F., Franquet, E., Saurel, R. & Le Metayer, O. 2007 A relaxation-projection method for compressible flows. Part 2: Artificial heat exchange for multiphase shocks. J. Comput. Phys. 225, 2214–2248.CrossRefGoogle Scholar
Reinke, P. & Yadigaroglu, G. 2001 Explosive vaporization of superheated liquids by boiling fronts. Intl J. Multiphase Flows 27, 1487–1516.CrossRefGoogle Scholar
Saurel, R. & Abgrall, R. 1999 A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150, 425–467.CrossRefGoogle Scholar
Saurel, R., Cocchi, J. P. & Butler, P. B. 1999 A numerical study of cavitation in the wake of a hypervelocity underwater projectile. J. Propulsion Power 15, 513–522.CrossRefGoogle Scholar
Saurel, R., Franquet, E., Daniel, E. & Le Metayer, O. 2007 a A relaxation-projection method for compressible flows. Part 1: The numerical equation of state for the Euler Equations. J. Comput. Phys. 223, 822–845.CrossRefGoogle Scholar
Saurel, R., Gavrilyuk, S. & Renaud, F. 2003 A multiphase model with internal degrees of freedom: application to shock-bubble interaction. J. Fluid Mech. 495, 283–321.CrossRefGoogle Scholar
Saurel, R. & Le Metayer, O. 2001 A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation. J. Fluid Mech. 431, 239–271.CrossRefGoogle Scholar
Saurel, R., Le Metayer, O., Massoni, J. & Gavrilyuk, S. 2007 b Shock jump relations for multiphase mixtures with stiff mechanical relaxation. Shock Waves 16, 209–232.CrossRefGoogle Scholar
Simoes-Moreira, J. R. 1994 Adiabatic evaporation waves. PhD Thesis, Rensselaer Polytechnic Institute, Troy.Google Scholar
Simoes-Moreira, J. R. & Shepherd, J. E. 1999 Evaporation waves in superheated dodecane. J. Fluid Mech. 382, 63–86.CrossRefGoogle Scholar
Thompson, P. A., Chaves, H., Meier, G. E. A, Kim, Y. G. & Speckmann, H. D. 1987 Wave splitting in a fluid of large heat capacity. J. Fluid Mech. 185, 385–414.CrossRefGoogle Scholar
Wood, A. B. 1930 A Textbook of Sound. G. Bell and Sons Ltd, London.Google Scholar