Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures

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.

/pdf/modelling-phase-transition-in-metastable-liquids-application-3q040zs8m5.pdf

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

Modeling phase transition for compressible two-phase flows applied to metastable liquids

A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems

Solid-fluid diffuse interface model in cases of extreme deformations

A relaxation-projection method for compressible flows. Part II: Artificial heat exchanges for multiphase shocks

In nuclear reactor safety and optimization there are key issues that rely on in-depth understanding of basic two-phase flow phenomena with heat and mass transfer. For many reasons, to be discussed, there is growing interest in the application of two-phase flow models to provide diffuse, but nevertheless resolved, simulation of interfaces between two immiscible compressible fluids – diffuse interface method (DIM). Because of its ability to dynamically create interfaces and to solve interfaces separating pure media and mixtures for DNS-like (Direct Numerical Simulation) simulations of interfacial flows, we examine the construction of a simple, robust, fast, and accurate numerical formulation for the 5-equation Kapila et al. [1] reduced two-phase model. Though apparently simple, the Kapila et al. model contains a volume fraction differential transport equation containing a nonlinear, non-conservative term which poses serious computational challenges. To circumvent the difficulties encountered with the single velocity and single pressure Kapila et al. [1] multiphase flow model, a 6-equation relaxation hyperbolic model is built to solve interface problems with compressible fluids. In this approach, pressure non-equilibrium is first restored, followed by a relaxation to an asymptotic solution which is convergent to the solutions of the Kapila et al. reduced model. The apparent complexity introduced with this extended hyperbolic model actually leads to considerable simplifications regarding numerical resolution, and the various ingredients used by this method are general enough to consider future extensions to problems involving complex physics.

/pdf/a-simple-and-efficient-diffuse-interface-method-for-ripb0xa9sq.pdf

A simple and efficient diffuse interface method for compressible two-phase flows

This paper presents a new multiphase flow code, cast under an open-source GNU license. The main characteristics of the different flow models are given, then the numerical method used is briefly presented: it includes temporal flow solvers, meshing features (like AMR technics), results visualization.Two examples of flows solutions are presented: the interaction of a high-speed flow with a droplet and the second concerns the attenuation of a propagating shock wave.

ECOGEN, an open-source tool dedicated to multiphase compressible multiphysics flows

This paper presents a new multiphase flow code, cast under an open-source GNU license. The main characteristics of the different flow models are given, then the numerical method used is briefly presented: it includes temporal flow solvers, meshing features (like AMR technics), results visualization.
Two examples of flows solutions are presented: the interaction of a high-speed flow with a droplet and the second concerns the attenuation of a propagating shock wave.

https://hal.archives-ouvertes.fr/hal-01781830/document

Fabien Petitpas

Papers

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

A relaxation-projection method for compressible flows. Part II: Artificial heat exchanges for multiphase shocks

A simple and efficient diffuse interface method for compressible two-phase flows

ECOGEN, an open-source tool dedicated to multiphase compressible multiphysics flows

ECOGEN, an open-source tool dedicated to multiphase compressible multiphysics flows