The flow fields associated with Mach reflection wave configurations in steady flows are analysed, and an analytical model for predicting the wave configurations is proposed. It is found that provided the flow field is free of far-field downstream influences, the Mach stem heights are solely determined by the set-up geometry for given incoming-flow Mach numbers. It is shown that the point at which the Mach stem height equals zero is exactly at the von Neumann transition. For some parameters, the flow becomes choked before the Mach stem height approaches zero. It is suggested that the existence of a Mach reflection not only depends on the strength and the orientation of the incident shock wave, as prevails in von Neumann's three-shock theory, but also on the set-up geometry to which the Mach reflection wave configuration is attached. The parameter domain, beyond which the flow gets choked and hence a Mach reflection cannot be established, is calculated. Predictions based on the present model are found to agree well both with experimental and numerical results.

The reflection of asymmetric shock waves in steady flows is studied both theoretically and experimentally. While the analytical model was two-dimensional, threedimensional edge effects influenced the experiments. In addition to regular and Mach reflection wave configurations, an inverse-Mach reflection wave configuration, which has been observed so far only in unsteady flows (e.g. shock wave reflection over concave surfaces or over double wedges) has been recorded. A hysteresis phenomenon similar to the one that exists in the reflection of symmetric shock waves has been found to also exist in the reflection of asymmetric shock waves. The domains and transition boundaries of the various types of overall reflection wave configurations are analytically predicted.

The reflection of shock waves over straight reflecting surfaces in steady flows was investigated experimentally using the supersonic wind tunnel of Laboratoire d'Aerothermique du CNRS, Meudon, France. The results for a flow Mach number M0 = 4.96 contradict the state of the art regarding the regular [harr ] Mach reflection transition in steady flows. Not only was a hysteresis found to exist in this transition, but, unlike previous reports, regular reflection configurations were found to be stable in the dual-solution domain in which theoretically both regular and Mach reflection are possible.

The properties of curved oblique shocks associated with the reflection of weak shock waves AIP Conf.Based on new experimental results of Chpoun, Passerel, Li, and Ben-Dor ͓J. Fluid Mech. 301, 19 ͑1995͔͒ and numerical results of Vuillon, Zeitoun, and Ben-Dor ͓J. Fluid Mech. 301, 37 ͑1995͔͒ regarding the shock wave reflection transitions from regular to Mach reflection and from Mach to regular reflection in steady flows of perfect gases which contradicted the present understanding regarding these processes ͓Hornung and Robinson, J. Fluid Mech. 123, 155 ͑1982͔͒, we present a new approach for better understanding the supersonic flow deflection over straight wedges and the transition of steady shock wave reflections over straight wedges. The new approach is based on the principle of minimum entropy production which enables one to choose the physical ͑stable͒ solutions out of a variety of possible mathematical ones. To the best of our knowledge the new transition criteria which are proposed in this study agree with all the available experimental results.

The unsteady inviscid two-dimensional flow field and the wave configurations which result when a supersonic vehicle strikes a planar oblique shock wave were modelled and analytically predicted using some approximations and simplifying assumptions. Based on the two- and three-shock theories together with the geometric shock dynamics theory, both regular (windward) and irregular (leeward) shock-on-shock (S-O-S) interactions were investigated, and the transition criterion between them was suggested. For the case of regular S-O-S interaction, the transmitted shock wave reflects over the vehicle body surface either as a regular (RR) or a Mach reflection (MR) depending on the inclination angle and the strength of the impingement shock wave. A pronounced peak surface pressure jump was found to exist during the transition from RR to MR. A RR[harr ]MR transition criterion when the flow ahead of the shock pattern is not quiescent was proposed. Predictions based on the model developed here are superior to those of approximate theories when compared to the available experimental data and numerical simulations.

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Abstract, The shock wave reflection phenomenon in pseudosteady flows was reconsidered by replacing the Law-Glass assumption by models accounting for the interaction of the shock wave reflection and the shock induced flow deflection processes. As a result, the analytical predictions of the location of the kink of a transitional-Mach reflection and the second triple point of a double-Mach reflection improved tremendously. It has also been proven that based on gas dynamic considerations a triple-Mach reflection wave configuration is physically impossible. In addition, the transition lines between the various reflection configurations were also found to better agree with the experimental results when they were calculated using the proposed models.

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