GENERIC Treatment of Compressible Two-Phase Flow: Convection Mechanism of Scalar Morphological Variables

Abstract

A two-phase model is considered which resolves both the thermodynamics of the two phases and of the interface, as well as the morphology in terms of Minkowski functionals, as scalar morphological variables, assuming equal velocities of the phases. In order to discuss whether, in compressible flow, the morphological variables should transform as scalars, as scalar densities or as a mixture of both, the two-phase model is cast into the GENERIC framework of non-equilibrium thermodynamics. The Jacobi identity, representing the time structure invariance of the reversible dynamics, is found not to impose any restrictions on the convection of the morphological variables, i.e., on the divergence terms of the velocity field appearing in their evolution equations. As an application of the general compressible two-phase model, the implications of assuming both equal velocities and equal temperatures of the phases are elaborated. In particular, it is found that in such a description the volume fraction and the amount of interface per unit volume are neither scalars nor scalar densities, their intermediate convection mechanism being completely determined in terms of the material properties of the phases.