Formation of Shock Wave Reflection Configurations in Unsteady Flows
In spite of the fact that the process of shock wave reflection has been the subject of considerable research effort over the last few decades [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], the question of the transition between the so-called regular and irregular reflection types is still of particular interest. The analytical approach to describing regular (RR) and Mach (MR) reflection pattern was initiated by von Neumann . He developed the local theory of two- and three-shock configurations that are valid in the vicinity of the intersection point of shock waves. Von Neumann’s theory has been successfully applied to shock wave reflection in steady flows. As for the reflection in pseudo-steady flows, this case is more adequately described by a model proposed by Cabannes  for the reflection of a shock wave off an immobile wedge. The main assumption of the theory is that the Mach stem is rectilinear along all its length and perpendicular to the wedge surface. The Cabannes’s theory of pseudo-steady Mach reflection is valid in the finite flow domain. Both theories are mathematically equivalent to each other, and the formal difference is that the given and unknown variables swap places. In the case of the pseudo-steady straight wedge reflection, the given parameters are the Mach number \(M_s\) of an incident shock wave (or the ratio of densities at the shock front), the wedge angle \(\beta \) and the gas specific heat ratio \(\gamma \). Note that in the absence of experimental data one can describe the pseudo-steady reflection process using exclusively Cabannes’s theory, since without experimental data, only two initial parameters, the incident shock Mach number and the wedge angle, are known.
This work has been partially supported by RFBR grant 15-01-04635.
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