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F-1513 Non-selfsimilar nature of Mach reflection over a flat smooth wedge
Abstract
In order to investigate a later stage of Mach reflection and to check the non-selfsimilar and unsteady behavior, we performed experiments in a shock tube with a cross-section of 185 mm square in Karlsruhe University. The reflection configuration was visualized by means of the infinite fringe spacing interferometry, which is similar to the Schlieren method. The angle between incident and reflected waves were measured as well as the location of triple point. The results showed that these physical properties vary as the incident shock proceeds even in the later stage of shock reflection. For some case, the angles of incidence and reflection, which exhibited the so-called von Neumann paradox at an early stage, moved on the three-shock theory curve to resolve the paradox. For other cases, they varied toward the three-shock theory curve but the paradox was yet to be resolved.
... According to Henderson et al.'s numerical experiment [3], the condition on the solid boundary plays a key role in the phenomenon. The authors' experiment in Karlsruhe found different wave angles from those obtained in Saitama [4]. In the Karlsruhe experiment, the initial pressure p 1 of the driven section was below atmospheric pressure and ranges from 280 mmHg to 610 mmHg depending on shock Mach number M i . ...
... This means the surface is not hydraulically smooth according to Ben-Dor et al [5]. In contrast, the surface roughness in past experiments [4] was 12 µm maximum, and the wedge surface was hydraulically smooth. The incident shock Mach number M i was 1.10, 1.20, 1.30 and 1.40. ...
... This negative result leads to the conclusion that the effect of viscosity is dominant in non-self-similar phenomena of Mach reflection. Consequently, the difference in the two kinds of experiments [4] should be ascribed solely to viscosity. ...
This paper deals with the von Neumann paradox, an as yet unsolved major problem in supersonic gas dynamics. We conduct a series of experiments using a conventional shock tube and focus attention on the flow-field around the triple point at various locations of the incident shock wave. By measuring the position of the triple point and the angle made by the incident and reflected shocks for propagating shock waves, we prove that the flow-field around the triple point is not self-similar. The von Neumann paradox is at least partly ascribed to non-self-similarity because classical theory assumes pseudo-steadiness that results from self-similarity for shock reflection over a wedge in a shock tube. The non-self-similarity revealed here clarifies the classical experiments by Smith (Photographic investigation of the reflection of plane Shocks in air. OSRD Report 6271, Washington, USA, 1945) and Bleakney and Taub (Rev. Mod. Phys. 21 (1949) 584). Specifically, since they implicitly assumed self-similarity, they only measured the wave angles at some particular location for each reflecting wedge angle, and their relations between angles of incidence and reflection were recovered by the present experiment.
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