Computational Study of Mach Reflection in Chemically Reacting Steady Flows

Abstract

Numerical simulations have been performed to study regular and Mach reflections of oblique shock waves (SW) in a steady supersonic flow of a homogeneous combustible hydrogen-oxygen gas mixture and different inflow Mach numbers Min. The dynamics of the compressible medium was described by two-dimensional unsteady Euler equations. Chemical transformations in the gas mixture were described by a two-stage reaction model. The resultant hyperbolic system of equations was solved numerically using the finite-volume scheme with the fourth-order MUSCL TVD reconstruction and the advanced HLLC algorithm for an approximate solution of the Riemann problem. Integration in time was performed with a second-order accuracy by using recently developed, additive semi-implicit Runge-Kutta methods. It was found that, as for nonreacting SW, there is a dual solution domain, where the existence of both regular reflection (RR) and Mach reflection (MR) is possible under identical flow parameters and geometry. In the case of the MR, the Mach stem (MS) is a section of the front of an overdriven stationary detonation wave (DW). A hysteresis phenomenon was obtained for a varied wedge angle θ.The dependence of the Mach stem height on the value of θ was found. It was showed ∗ Senior Research Scientist, Computational Aerodynamics Lab. † Senior Research Scientist, Computational Aerodynamics Lab. ‡ Professor, Head, Computational Aerodynamics Lab. Associate Fellow AIAA. E-mail: ivanov@itam.nsc.ru that for some values of Min there may exist a standing MS with a system of unsteady transverse waves on its front. The flow structure behind the Mach stem is similar to the flow structure behind the front of a multifront (cellular) freely propagating DW. Despite the motion of the transverse shocks along the MS and periodic changes in the stem shape, MS, on the average, is a standing wave that slightly oscillates near some equilibrium point. The effect of an existence of strong transverse waves on the MS front to steadiness of Mach reflection was investigated. The present study showed that the Mach stem height for the case of a chemically reacting mixture is greater than that for an inert mixture. For a model combustible mixture with variable amount of heat release, the dependence of the MS height on chemical reaction heat was found. The present study showed that certain types of local perturbations of the free-stream flow might initiate the transition from RR to MR in the dual-solution domain.