Numerical treatment of multi-phase flow equations with chemistry and stiff source terms

A computational model suitable for multiphase/multispecies flows has been developed. The source term containing the inter-phase interaction and species production/destruction terms can be numerically stiff, due to near-equilibrium chemistry, mass/momentum and energy exchange terms among phases. An Eulerian-Eulerian (E 2) formulation for the conservation equations has been chosen. The chemistry model is described through a multi-step, finite-rate chemical kinetics model with third body reactions. The inviscid fluxes for the right and left states are evaluated using the Total Variation Diminishing (TVD) method. Lax-Friedrichs (LF) and Steger-Warming (SW) numerical fluxes are used to calculate the full flux in the gaseous and liquid phases, respectively. The TVD-LF-SW scheme proved to be robust and suitable for liquid rocket engine applications.