Arbitrary-rate relaxation techniques for the numerical modeling of compressible two-phase flows with heat and mass transfer. (August 2022) - Pelanti, Marica
Abstract: We describe compressible two-phase flows by a single-velocity six-equation flow model, which is composed of the phasic mass and total energy equations, one volume fraction equation, and the mixture momentum equation. The model contains relaxation source terms accounting for volume, heat and mass transfer. The equations are numerically solved via a fractional step algorithm, where we alternate between the solution of the homogeneous hyperbolic portion of the system via a HLLC-type wave propagation scheme, and the solution of a sequence of three systems of ordinary differential equations for the relaxation source terms driving the flow toward mechanical, thermal and chemical equilibrium. In the literature often numerical relaxation procedures are based on simplifying assumptions, namely simple equations of state, such as the stiffened gas one, and instantaneous relaxation processes. These simplifications of the flow physics might be inadequate for the description of the thermodynamical processes involved in various flow problems. In the present work we introduce new numerical relaxation techniques with two significant properties: the capability to describe heat and mass transfer processes of arbitrary relaxation time, and the applicability to a general equation of state. We show the effectiveness of the proposed methods by presenting several numerical experiments. Highlights: A mixture-energy-consistent 2D finite volume scheme for compressible two-phase flows. New relaxation techniques to model arbitrary-rate heat and mass transfer. Simple relaxation techniques applicable to a general equation of state. Simulations of flows with shocks, interfaces, phase transition, metastable states.