Shock waves at a fast-slow gas interface

Abstract

This paper presents the results of experiments on plane shock waves refracting at air/SF6and He/CO2interfaces. These are called fast-slow gas combinations because the speed of sound in the incident shock gas is greater than that in the transmitting shock gas. Our work was based on a generalization of the von Neumann (1943) classification of shocks into two classes called weak and strong. We introduced two subclasses of each of these, giving in all four groups of phenomena for study. This is possibly an exhaustive list, at least for conditions where the gases are approximately perfect. We present data on all four groups and study various transition conditions both within and across the groups. Our results appear to conflict with a previously reported irregular refraction; in fact we could apparently completely suppress this wave system by attention to our gas purity and boundary conditions. In its place we found a different system which appears to be a new phenomenon. We found another new system which has the appearance of a Mach-reflexion type of refraction but with its shock dispersed into a band of wavelets. It is interesting that the wavelets remain intense enough to induce identifiable vortex sheets in the flow. Finally we found yet another refraction of the Mach-reflexion type which had no detectable vortex sheet emanating from the triple point: such a system was foreshadowed by von Neumann.

Shock wave refraction patterns at interfaces

“…For the slow-fast case we have Takayama and co-authors who employed doubleexposure holographic interferometry to visualize shock interaction with planar (Takayama, 1987) and cylindrical (Igra and Takayama, 2003) gas-liquid (slow-fast) interfaces. In the planar geometry they observed a sequence of three refraction patterns that can be recognized (see Table 2) as RRR, FPR, and FNR, in the Abd-El-Fattah and Henderson (1978b) classification scheme Table 1 Refraction pattern sequences in gas-gas systems according to the experiments of (Abd- El-Fattah et al (1976), Abd-ElFattah and Henderson (1978a) and Abd-El-Fattah and Henderson, 1978b). All patterns could be reproduced in our simulations.…”

“…Simulations were performed varying the angle of the attack b for incident shock strengths corresponding to the Very Weak (M sh = 1.12 and v i = 0.78), Weak (M sh = 1.34 and v i = 0.53), and Strong shock (M sh = 2.25 and v i = 0.18) sequences in the experiments. Comparisons are made in two ways: (a) directly with experimental images, which are legible enough only in a followup (the simulation) paper (Henderson et al, 1991), and only for the selected cases of FNR (Very Weak), TRR and TNR (Weak) and TMR (Strong), and (b) indirectly, by using the definitions and maps of Abd-El-Fattah and Henderson (1978b) for all cases shown in Table 1, since the experimental images are not of sufficient clarity in the original publications.…”

“…Based on the combinations of materials across the interface, the shock-interface interactions were separated into two major groups: ''slow-fast'' and ''fast-slow'', the speeds referring to the acoustic impedances (qc) of the materials involved, while the order is to denote the direction of propagation of the shock. Within each group, the interactions were further subdivided into sub-classes, in terms of (i) Very Weak, (ii) Weak, (iii) Strong and (iv) Stronger incident shocks for fast-slow interfaces (Abd-El-Fattah and Henderson, 1978a); and (i) Very Weak, (ii) Weak and (iii) Strong incident shocks for slow-fast interfaces (Abd-El-Fattah and Henderson, 1978b). Running experiments under different conditions, Abd-El-Fattah and Henderson have observed eight and four distinct patterns for slow-fast (Abd-El-Fattah and Henderson, 1978b) and fast-slow (Abd-ElFattah and Henderson, 1978a) interfaces, respectively, as summarized in Table 1.…”

“…Within each group, the interactions were further subdivided into sub-classes, in terms of (i) Very Weak, (ii) Weak, (iii) Strong and (iv) Stronger incident shocks for fast-slow interfaces (Abd-El-Fattah and Henderson, 1978a); and (i) Very Weak, (ii) Weak and (iii) Strong incident shocks for slow-fast interfaces (Abd-El-Fattah and Henderson, 1978b). Running experiments under different conditions, Abd-El-Fattah and Henderson have observed eight and four distinct patterns for slow-fast (Abd-El-Fattah and Henderson, 1978b) and fast-slow (Abd-ElFattah and Henderson, 1978a) interfaces, respectively, as summarized in Table 1. The results were depicted in regime maps, which define the domains of a particular patternÕs existence on the (strength of the shock) À (incident shock angle of attack) plane.…”

Shock refraction from classical gas to relativistic plasma environments

“…Mach number M ) at the left hand end of the tube, which traverses the tube and interacts, or refracts, with this initial contact interface. From extensive experimental campaigns, a whole zoology of shock refraction patterns is known (Abd-El-Fattah & Henderson, 1978). A recurring aspect, irrespective of whether the impinging shock is (very) weak to strong, is the transition from an irregular to a regular refraction pattern, when the angle α is varied from shallow to large values (up to 90 • inclination angles, at which point the problem is a 1D shock-CD interaction problem).…”