A hierarchy of non-equilibrium two-phase flow models

Abstract

We consider a hierarchy of relaxation models for two-phase flow. The models are derived from the non-equilibrium Baer-Nunziato model, which is endowed with relaxation source terms to drive it towards equilibrium. The source terms cause transfer of volume, heat, mass and momentum due to differences between the phases in pressure, temperature, chemical potential and velocity, respectively. The subcharacteristic condition is closely linked to the stability of such relaxation systems, and in the context of two-phase flow models, it implies that the sound speed of an equilibrium system can never exceed that of the relaxation system. Here, previous work by Flåtten and Lund [Math. Models ] is extended to encompass two-fluid models, i.e. models with separately governed velocities for the two phases. Each remaining model in the hierarchy is derived, and analytical expressions for the sound speeds are presented. Given only physically fundamental assumptions, the subcharacteristic condition is shown to be satisfied in the entire hierarchy, either in a weak or in a strong sense.

Arbitrary-rate relaxation techniques for the numerical modeling of compressible two-phase flows with heat and mass transfer

“…The seven-equation two-phase flow model of Baer-Nunziato [4] (and the variant of Saurel-Abgrall [57]) is the most general model able to account for velocity, pressure, temperature and chemical potential disequilibria between the phases. From this full non-equilibrium seven-equation model endowed with relaxation source terms a hierarchy of relaxed models can be established by considering combinations of infinite-rate relaxation processes driving the flow to different levels of equilibrium [41]. The six-equation model considered in the present work represents the relaxed velocity equilibrium model obtained from the seven-equation Baer-Nunziato model in the limit of instantaneous kinetic equilibrium.…”

A pressure-based diffuse interface method for low-Mach multiphase flows with mass transfer

“…This model is often characterised as a non-equilibrium model, meaning that in the regions where both phases coexist, there is no requirement for kinetic equilibrium (same velocity), mechanical equilibrium (same pressure), thermal equilibrium (same temperature) or chemical equilibrium (same Gibbs free energy). From this parent model, a hierarchy of models arises via relaxation processes that drive the system to specific equilibrium states [16], such as,…”

News on Baer–Nunziato-type model at pressure equilibrium

“…In [6,12], a hierarchy of two-fluid models derived from the Baer-Nunziato model [1] is investigated where mechanical, thermal and chemical relaxation is assumed to proceed in different order. This hierarchy splits into two branches of models distinguished by the assumption of dynamical velocity equilibrium and local velocity equilibrium where either both fluids have the same velocity or the fluids have different velocities that coincide for a particular state.…”