Pseudo-stationary oblique-shock-wave reflections in frozen and equilibrium air

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The reflection of oblique shock waves in air in pseudo-stationary flow was investigated analytically and numerically. Emphasis was placed on air owing to its importance in determining structural loading caused by blast. However, some comparisons are also made with fictitious perfect gases corresponding to γ = 1.290 for CO 2 and γ = 1.093 for SF 6, at room conditions, in order to bring out certain features known to gasdynamicists, helpful for an understanding of the generated flows. The transition boundaries between the four types of shock-wave reflection (regular RR, single Mach SMR, complex Mach CMR and double Mach DMR) were established up to an initial shock Mach number M S = 20 for both frozen (perfect) and imperfect air in thermodynamic equilibrium (rotation-vibration coupling, vibrational excitation, dissociation, electronic excitation and ionization). It was verified that the reflected shock-wave angle ω′ is a very sensitive function of γ, and a decrease in γ lowered the value of ω′ significantly and even shifted ω′ towards negative values under certain conditions of Mach reflection. In the case of a polyatomic gas (SF 6), the reflection angle ω′ can have a steep negative value with increasing shock Mach number, and the reflected shock wave can strike the wedge surface and re-reflect like a RR at high M S and wedge angles. The transition of ω′ from a positive value to a negative value occurred in a perfect gas with γ less than 1.4 and in imperfect air. However, in perfect air with γ = 1.4, ω′ was always positive. This provides a means of identifying real-gas effects. An examination of the perfect and imperfect air results shows no crossing of transition lines and removes the conjecture of possible triple-Mach reflection. The present analytical results were compared with available experimental data for air and nitrogen for shock Mach numbers up to 10. From the available experiments it was shown from the relaxation lengths behind the shock waves that, the flow states behind the shock fronts, which determine the wave systems for shock-wave reflection, were frozen or nearly frozen regarding vibrational excitation and dissociation. Consequently, in general, the present (perfect) frozen-gas analysis agreed with the experiments for air and nitrogen at the tabulated conditions. However, this was not the case for carbon dioxide (CO 2) and sulfur hexafluoride (SF 6) where the vibrational degrees of freedom are readily excited compared with those in O 2 and N 2. Hence, an imperfect-gas analysis taking into account the vibrational excitation is required for those gases. It was confirmed that RR persisted below the frozen gas RR↔MR transition line determined by the von Neumann detachment criterion, as research workers in the Forties and Fifties had shown. This is now known as the “von Neumann paradox”. Some recent work has resolved this paradox as arising from the shock-induced boundary layer on the wedge surface. Also some SMR, CMR and DMR did occur outside their analytically predicted domains. Consequently, the development of more accurate transition criteria for SMR↔CMR and CMR↔DMR, improvements in predicting the first triple-point trajectory angle, accurate locations of the kink and the second triple point, along with the effects of Mach-stem curvature are problems to be resolved in the future. Some progress in this direction has already been made.