The Existence of a Consistent Stationary Mach Reflection in Shock Tube Flows

A shock wave reflected from a solid wall takes either a regular reflection (RR) or a Mach reflection (MR). In general, the patterns of Mach reflections (MR) are divided into a direct MR, a stationary MR, and an inverted MR [1]. In a direct MR, its triple point moves away from the wedge surface and hence its pattern is locally self-similar. In a stationary MR, its triple point moves exactly parallel to the wedge and hence this pattern exists only in a steady supersonic flow. In an inverted MR, its triple point moves toward the wedge and hence it eventually terminates.. This is a truly unsteady reflection pattern.

In the shock reflection from a straight wedge, the reflected shock pattern is always the direct MR and self-similar, whereas reflection over a concave wall, the abovementioned three shock reflection patterns temporally appears and eventually becomes RR [2]. Therefore, in the shock tube flow, a stationary MR never exits consistently.

We installed a 35° movable wedge in a 60mm × 150mm shock tube and superimposed a 25°wedge on the movable wedge to form a double wedge. We varied the first wedge angle 1 step by step and observed the reflected shock by using double exposure holographic interferometry. Eventually a consistent stationary MR obtained on the second wedge 2. The results so far collected here would be reproduced numerically and could be analyzed based on the shock polar analyses [2].

Figures 1(a)-(c) show a series of interferograms. Adjusting the first wedge angle 1, we visualized, by using double exposure holographic interferometry, reflected shock patterns on the second wedge 2: in Fig. 1(a), a direct MR in which the slip line is directed to the wedge; in Fig.1(b), a stationary MR, in which the slip line is nearly parallel to the wall; and in Fig.1(c), an inverted MR, in which the slip line is directed to the wall.

(a)

(b)

(c)

Fig. 1 Shock reflection over a double wedge, in air at 500hPa and 293K, 21= 25°: (a) 88022306 delay time 75s, Ms = 1.749 1= 24.5°, direct MR; (b) 88022501 delay time 70s, Ms = 1.754　1= 32.5°, stationary MR; and (c) 88022409 delay time 50s, Ms = 1.773 1= 34.2 °, inverted MR

[1] R. Courant and K.O. friedrichs: SupersonicFlow and Shock Waves, Wiley Interscience, 1948

[2] G. Ben-Dor: Reflection of Shock Waves, Springer Verlag, 2008.