A seven-equation diffused interface method for resolved multiphase flows

TL;DR

This paper introduces a novel seven-equation diffused interface method for simulating resolved multiphase flows, incorporating surface tension, viscosity, multi-species, and reactions, with validation through various test cases.

Contribution

The paper presents an advanced multiphase flow model that allows for pressure and velocity disequilibrium, improving numerical stability and flexibility over existing models.

Findings

Accurately models non-equilibrium pressure and velocity in multiphase flows.

Validates the method with shock tube, droplet oscillation, and shock interaction tests.

Demonstrates stability and applicability in complex multiphase scenarios.

Abstract

The seven-equation model is a compressible multiphase formulation that allows for phasic velocity and pressure disequilibrium. These equations are solved using a diffused interface method that models resolved multiphase flows. Novel extensions are proposed for including the effects of surface tension, viscosity, multi-species, and reactions. The allowed non-equilibrium of pressure in the seven-equation model provides numerical stability in strong shocks and allows for arbitrary and independent equations of states. A discrete equations method (DEM) models the fluxes. We show that even though stiff pressure- and velocity-relaxation solvers have been used, they are not needed for the DEM because the non-conservative fluxes are accurately modeled. An interface compression scheme controls the numerical diffusion of the interface, and its effects on the solution are discussed. Test cases are used to validate the computational method and demonstrate its applicability. They include multiphase shock tubes, shock propagation through a material interface, a surface-tension-driven oscillating droplet, an accelerating droplet in a viscous medium, and shock-detonation interacting with a deforming droplet. Simulation results are compared against exact solutions and experiments when possible.