On the irregular refraction of a plane shock wave at a Mach number interface

Abstract

The paper considers the refraction of a plane shock wave at an interface between two streams of different Mach number. Particular attention is paid to the irregular wave systems. It is found that when the interface is slow-fast, that is when the speed of sound a0 in the first or incident wave medium is less than the speed of sound aB in the second or transmitted wave medium, then there are two irregular systems, one being a double Mach reflexion type and the other being a four-wave confluence type. There are also two irregular systems when the refraction is fast-slow; these are a single Mach reflexion type and an expansion wave type. This last system has a central expansion wave when the flow is steady and a continuous band expansion wave when the flow is self-similar. Only two of the irregular wave systems have been observed experimentally in the fully developed state. Possible degeneracies are discussed.

Irregular self-similar configurations of shock-wave impingement on shear layers

“…The present work is focused on the study of the large-scale structures formed in the interaction of oblique shocks with shear layers. It extends the works of Henderson (1966Henderson ( , 1968 and Abd-El-Fattah (1978a,b) addressing the irregular refraction problem from a combination of theoretical and numerical work. While the theoretical work provides a deeper understanding of the canonical problem and the explanation of its self-similar nature in time, the numerical simulations are used to describe the flow dynamics.…”

“…These two types of regular refractions can only occur in certain ranges of the controlling parameters, beyond which more complicated irregular-refraction patterns may arise. Theoretical considerations indicate that the "atlas" of possible solutions include, in principle, single and double Mach reflections, 4-wave confluences, and continuous expansion bands (Henderson 1966(Henderson , 1968Abd-El-Fattah 1976, 1978a, although only some of these solutions have been observed experimentally.…”

“…By way of contrast, the interaction of oblique shocks with contact surfaces or tangential discontinuities can be addressed from linear theory when the strength of the former is sufficiently low (Ryley 1960;Huete 2016) or the Mach-number tangential discontinuity is weak enough (see appendix C). This type of interactions, despite comprising rich phenomena as bifurcations in the convective Mach number domain, transonic regions, irregular reflections, and unstable structures, has received much less attention to the best of the authors knowledge, with the works of Henderson (1966Henderson ( , 1968; Abd-El-Fattah (1976, 1978a; Skews (2005); Ben-Dor (2007) and Tesdall (2008) being some representative contributions in the limit of extremely thin contact surfaces. These works have established the basis to predict the type of irregular reflections that may arise attending to the structure shape.…”

Interaction of Oblique Shocks and Laminar Shear Layers

“…These two types of regular expansions can occur only in certain ranges of the controlling parameters, outside of which more complicated irregular-refraction patterns may arise. Theoretical considerations indicate that the "atlas" of possible solutions may include in principle single and double Mach reflections, 4-wave confluences, and continuous expansion bands [12], although only some of these solutions have been observed in experiments. The present considerations are restricted to the cases illustrated in Fig.…”

Multi-valued solutions of steady-state supersonic flow. Part 1. Linear analysis

“…While this is successful in some cases, it fails in others. For example it fails to yield any result for Mach reflexion, while for regular refraction of shocks it is occasionally confounded by there being two solutions in the acoustic limit (Henderson & Macpherson 1968). I n the present paper (part 1) an attempt is made to formulate more satisfactory procedures for selecting the correct solution from the ordered set.…”