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Weak steady Mach reflections are numerically simulated using unstructured grids by means of either “shock-fitting” or “shock-capturing” techniques. It is shown that shock-fitting allows using coarser meshes than those required by shock-capturing, since the latter needs mesh refinement in the direction normal to the discontinuities, which is not needed using the former approach. The shock-fitted solution is also free from the numerical disturbances that arise along the captured discontinuities and pollute the captured solution in the smooth flowfield region. Finally, the shock-fitting solutions show the presence of a small region next to the Mach stem and the reflected shock downstream of the triple point, characterized by very high gradients.

The problem of transition of planar shock waves over straight wedges in steady flows from regular to Mach reflection and back was numerically studied by the DSMC method for solving the Boltzmann equation and finite difference method with FCT algorithm for solving the Euler equations. It is shown that the transition from regular to Mach reflection takes place in accordance with detachment criterion while the opposite transition occurs at smaller angles. The hysteresis effect was observed at increasing and decreasing shock wave angle.

In studying the detonation phenomenon in gas mixtures, much attention is traditionally paid to investigation of the multifront (cellular) structure of a self-sustained unsteady detonation wave (DW) propagating in a mixture at rest, determination of the critical conditions of detonation initiation (critical value of the initiation energy), and marginal regimes of DW propagation.

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.

The influence of relaxation associated with the excitation of vibrational degrees of freedom and chemical reactions, and flow rarefaction on the shock wave reflection phenomena in steady flows is studied in the present paper. The main attention is paid to the impact of the change in the relaxation length, which occurs due to changing Mach number, on the angle of transition from regular to Mach reflection and on the Mach stem height. The Direct Simulation Monte Carlo method is used in the computations. The computational results are compared with predictions obtained using an analytical model that takes into account the change in specific heat ratio behind the shock wave. A substantial effect of relaxation and rarefaction on regular and Mach reflections and on the RR—»MR transition angle is shown.

An impact of vibrational and chemical relaxation and flow rarefaction on the transition from regular to Mach reflection in steady supersonic flows is examined numerically with the direct simulation Monte Carlo method. Wedge-generated shock reflection in N-Nj gas is studied for M — 7.5 and Kn = 3.5 • 1CT and 9.0 • 1CT at fixed and moving wedges. Three different models of molecular collisions were considered, the first allows translationrotation energy exchanges only, the second also takes account of molecular vibrations, and the third is the general case with translation-rotation-vibration exchanges and dissociation reactions. A significant influence of real gas effects both on regular and Mach reflections is shown, and a delay of regular-to-Mach reflection transition is observed.