Diffuse interface relaxation model for two-phase compressible flows with diffusion processes

TL;DR

This paper introduces a diffuse interface relaxation model for simulating two-phase compressible flows with diffusion processes, incorporating heat conduction, viscosity, and thermal relaxation, along with a high-order numerical solution method.

Contribution

It develops a reduced two-temperature model from the Baer-Nunziato framework that includes diffusion effects and proposes a numerical scheme ensuring PVT equilibrium in complex flow simulations.

Findings

Model accurately captures heat conduction effects in two-phase flows.

Numerical method effectively solves hyperbolic and parabolic equations.

Validated with multiphase shock tube, impact, and Rayleigh-Taylor instability tests.

Abstract

The paper addresses a two-temperature model for simulating compressible two-phase flow taking into account diffusion processes related to the heat conduction and viscosity of the phases. This model is reduced from the two-phase Baer-Nunziato model in the limit of complete velocity relaxation and consists of the phase mass and energy balance equations, the mixture momentum equation, and a transport equation for the volume fraction.Terms describing effects of mechanical relaxation, temperature relaxation, and thermal conduction on volume fraction evolution are derived and demonstrated to be significant for heat conduction problems. The thermal conduction leads to instantaneous thermal relaxation so that the temperature equilibrium is always maintained in the interface region with meeting the entropy relations. A numerical method is developed to solve the model governing equations that ensures the pressure-velocity-temperature (PVT) equilibrium condition in its high-order extension. We solve the hyperbolic part of the governing equations with the Godunov method with the HLLC approximate Riemann solver. The non-linear parabolic part is solved with an efficient Chebyshev explicit iterative method without dealing with large sparse matrices. To verify the model and numerical methods proposed,we demonstrate numerical results of several numerical tests such as the multiphase shock tube problem, the multiphase impact problem, and the planar ablative Rayleigh-Taylor instability problem.