Many two-phase flow situations, from engineering science to astrophysics, deal with transition from dense (high concentration of the condensed phase) to dilute concentration (low concentration of the same phase), covering the entire range of volume fractions. Some models are now well accepted at the two limits, but none is able to cover accurately the entire range, in particular regarding waves propagation. In the present work an alternative to the Baer and Nunziato (1986) (BN for short) model, initially designed for dense flows, is built. The corresponding model is hyperbolic and thermodynamically consistent. Contrarily to the BN model that involves 6 wave speeds, the new formulation involves 4 waves only, in agreement with the Marble (1963) model based on pressureless Euler equations for the dispersed phase, a well-accepted model for low particle volume concentrations. In the new model, the presence of pressure in the momentum equation of the particles and consideration of volume fractions in the two phases render the model valid for large particle concentrations. A symmetric version of the new model is derived as well for liquids containing gas bubbles. This model version involves 4 wave speeds as well, but with different wave's speeds. Last, the two sub-models with 4 waves are combined in a unique formulation, valid for the full range of volume fractions. It involves the same 6 wave's speeds as the BN model, but at a given point of space 4 waves only emerge, depending on the local volume fractions. The non-linear pressure waves propagate only in the phase with dominant volume fraction. The new model is tested numerically on various test problems ranging from separated phases in a shock tube to shock -particle cloud interaction. Its predictions are compared to BN and Marble models as well as against experimental data.Key words: hyperbolic, two-phase, compressible, shocks Emails: Richard.Saurel@univ-amu.fr; Ashwin.Chinnayya@ensma.fr; Quentin.Carmouze@rs2n.eu 2 I. IntroductionIt is well accepted that hyperbolic models are mandatory to deal with phenomena involving wave propagation. This is the case for multiphase flow mixtures in many situations such as in particular shocks and detonations propagation in granular explosives and in fuel suspensions, as well as liquid-gas mixtures with bubbles, cavitation and flashing, as soon as motion is intense and governed by pressure gradients. This is thus the case of most unsteady two-phase flows situations. Wave propagation is important as it carries pressure, density and velocity disturbances. Sound propagation is also very important as it determines critical (choked) flow conditions and associated mass flow rates. It has also fundamental importance on sonic conditions of detonation waves when the twophase mixture is exothermically reacting (Petitpas et al., 2009). Hyperbolicity is also related to the causality principle, meaning that initial and boundary conditions are responsible of time evolution of the solution. When dealing with first-order partial different...

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The propagation of two-dimensional cellular gaseous detonation bounded by an inert layer is examined via computational simulations. The analysis is based on the high-order integration of the reactive Euler equations with a one-step irreversible reaction. To assess whether the cellular instabilities have a significant influence on a detonation yielding confinement, we achieved numerical simulations for several mixtures from very stable to mildly unstable. The cell regularity was controlled through the value of the activation energy, while keeping constant the ideal Zel’dovich - von Neumann - Döring (ZND) half-reaction length. For stable detonations, the detonation velocity deficit and structure are in accordance with the generalized ZND model, which incorporates the losses due to the front curvature. The deviation with this laminar solution is clear as the activation energy is more significant, increasing the flow field complexity, the variations of the detonation velocity, and the transverse wave strength. The chemical length scale gets thicker, as well as the hydrodynamic thickness. The sonic location is delayed due to the presence of hydrodynamic fluctuations, for which the intensity is increased with the activation energy as well as with the losses to a lesser extent. The flow field has been studied through numerical soot foils, detonation velocities, and 2D detonation front profiles, which are consistent with experimental findings. The velocity deficit increases with the cell irregularity. Moreover, the relation between the detonation limits obtained numerically and in detonation experiments with losses is discussed.

This paper deals with pressure relaxation procedures for multiphase compressible flow models. Such models have nice mathematical properties (hyperbolicity) and are able to solve a wide range of applications: interface problems, detonation physics, shock waves in mixtures, cavitating flows, etc. The numerical solution of such models involves several ingredients. One of those ingredients is the instantaneous pressure relaxation process and is of particular importance. In this article, we present and compare existing and new pressure relaxation procedures in terms of both accuracy and computational efficiency. Among these procedures we enhance an exact one in the particular case of fluids governed by the stiffened gas equation of state, and approximate procedures for general equations of state, which are particularly well suited for problems with large pressure variations. We also present some generalizations of these procedures in the context of multiphase flows with an arbitrary number of fluids. Some tests are provided to illustrate these comparisons. Copyright © 2005 John Wiley & Sons, Ltd.

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