Sound wave structures downstream of pseudo-steady weak and strong Mach reflections

Abstract

Sound wave structures, downstream of moving incident shocks reflecting from straight compressive wedges, are analysed for both weak and strong Mach reflections (MR) using existing experiments. It is shown that the reflected waves can be well described by using the acoustic criterion or the weak oblique shock approximation, when the classical three-shock theory gives forward-facing reflected shock solutions. The predicted triple-point trajectory angles are found to be in close agreement with the experiments. The distinction between the applicabilities of the two methods is given by an analytically defined ‘smallness’ for the angle of reflecting wedges. The physics of the success of the two methods is discussed. It is concluded that forward-facing reflected shock solutions of pseudo-steady MR should be ruled out physically because sound waves cannot coalesce into Mach waves that propagate upstream of the triple point. In their place, MR-like phenomena occur with the reflected waves being normal Mach waves or finite compression waves for ‘small’ or ‘not-small’ reflecting wedge angles, respectively, and they are classified as the first- or second-king von Neumann reflections, respectively. Boundaries separating regimes between the first and second kinds of von Neumann reflections, and backward-facing MR are determined.