Validation of CFD algorithms for unsteady shock-induced combustion

Abstract

A numerical experiment was performed to investigate the characteristics of the various numerical approaches in the analysis of periodically unstable shock-induced combustion. Inviscid Euler equations and species conservation equations are used as the governing equations for the chemically reacting flow around a blunt body in stoichiometric hydrogen-air mixture. The baseline numerical methods are the MUSCL-type TVD scheme based on Roe's approximate Riemann solver and the second order time accurate LU-SGS scheme using Newton sub-iteration method and Steger-Warming flux Jacobian splitting. As a first step of validation procedure, simulations of experimental results were carried out to confirm the reliability of base-lined method. In next step, the general aspects of baseline methods were examined including order of time integration, number of sub-iteration and use of approximate flux Jacobian splitting. Appropriateness of grid is also examined by grid refinement study. In view of spatial discretization, effects of limiter functions, entropy fixing and different upwind schemes were examined. As a final step, the efficiency and accuracy of different time integration approaches were tested for the present problem via time step refinement study. In this study, four-step explicit Runge-Kutta method, point-implicit method, CrankNicolson method and dual time stepping method were examined in addition to the base line method.