Discrete Equation Method (DEM) for the simulation of viscous, compressible, two-phase flows

A numerical approximation of a five equations model for the simulation of two-phase flows, including viscous effects is illustrated. A DEM approach is developed obtaining a clear formulation of viscous fluxes and an accurate resolution method for all terms. Starting from a system composed by the Navier-Stokes equations for each phase, a final 1D semi-discrete equation for the discretization of pressure and velocity equilibrium model is obtained. First, the influence of viscous terms is studied comparing viscous and inviscid solutions in two-phase configurations. This analysis allows to identify the thermodynamic quantities, such as pressure, velocity, phase densities and volume fraction that are influenced by the viscous effects. Then, several gas/liquid mixtures, obtained modifying the gas/liquid viscosity ratio, are compared in order to study the influence of viscous effects in terms of phase volume fraction, density and entropy. Finally, the influence of mesh on the viscosity, in terms of minimum mesh size needed to evaluate the viscous effects in the simulation, is shown. (C) 2013 Elsevier Ltd. All rights reserved.