A Thermodynamically Consistent Relaxation Model for Turbulent Binary Mixture Undergoing Phase Transition

Abstract

Non-equilibrium phenomena within a turbulent binary mixture undergoing a phase transition are modelled based on the one fluid, homogeneous approach. The set of governing evolution equations is given and the averaged basic balance laws are considered. The continuum under consideration consists of two constituents of which the first is undergoing a phase transition (vaporisation, cavitation, flashing, condensation) during the flow with turbulent transport of mass, heat and momentum. Starting from the Clausius-Duhem inequality for the recoverable specific entropy, several thermodynamical relationships for equilibrium and non-equilibrium fields are developed. The relaxation-retardation constitutive model for turbulent, phasic and diffusive fluxes are described. It is shown that the resulting model uncovers a few known two-phase models of turbulence and also the classical relaxation models as limiting cases.