Analysis of shock-wave diffraction over double concave cylindrical wedges. Part I: Shock dynamics

Shock-wave diffraction over double concave cylindrical surfaces has been numerically investigated at different flow regimes by varying the incident-shock-wave Mach number from Ms=1.6 (transonic) to Ms=4.5 (supersonic regime). The purpose of this study is to better understand the dynamics of shock-wave structure and the associated wave configurations. A mesh-independent solution is obtained and the flow is assessed through different physical quantities (transition angles, triple points trajectories, wall-pressure and skin-friction distributions, velocity and shock location). It is found that the transition angles, from regular to Mach reflection, increase with the Mach number. This phenomenon remains almost the same over both concave surfaces for weak Mach numbers (up to Ms=2.5) and becomes relatively larger on the second surface for high Mach numbers. In terms of shock dynamics, it is found that by increasing the incident incident-shock-wave Mach number to Ms=4.5, unlike the first reflector, the transition from a single-triple-point (STP) wave configuration to a double-triple-point (DTP) wave configuration and back occurred on the second reflector, indicating that the flow is capable of retaining the memory of the past events over the entire process. For the shock velocity, the velocity deficit is found to be increasing with increase in Ms. A best fitting scaling law is derived, to ensure a universal decay of the shock velocity depending on the flow parameters