Sound Wave Structures Downstream of Incident Propagating Oblique Shock Waves
Graphical illustration for the sound wave structure downstream of a moving incident oblique shock is presented for weak and strong Mach reflections (MR). For experimentally observed MR-like phenomena, where the classical three-shock theory requires a forward facing reflected shock solution, it is found that the downstream flow velocity is almost sonic relative to the triple point and the path of sound generation centers of the triple point becomes essentially identical to the observed slipstream line. The observed reflected shock emanating from the triple point is shown to degenerate to a normal Mach wave for very small reflecting wedge angle, or be replaced by a backward-facing compression wave for not very small edge angles. Furthermore, forward facing reflected shocks, which were never observed before, are unphysical from the consideration of sound wave structures downstream of incident propagating oblique shocks. When the three-shock theory does provide a backward-facing reflected shock solution, it is shown that the trajectory of sound generation centers of the triple point is no longer along the same line as the observed slipstream. The existence of a non-negligible angle between these two lines explains why a reflected shock is required to turn the downstream flow parallel to the slipstream; thereby a reflected shock solution can be found from the theory.
Key wordsMach reflection Sound wave structure von Neumann paradox
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- Deschambault RL (1984) Nonstationary oblique-shock-wave reflections in air. UTIAS Rep No. 270Google Scholar
- Dewey JM, Ohm M, Van Netten AA, Walker DK (1989) The properties of curved oblique shocks associated with the reflection of weak shock waves. In: Kim YW (ed) 17th Intl. Symp. on Shock Waves and Shock Tubes. Bethlehem, USAGoogle Scholar
- Mach E (1878) Uber den Verlauf der Funkenwellen in der Ebene and in Raume. Vienna Academy Sitzungsberichte 78: 819–538Google Scholar
- von Neumann J (1943) Oblique reflection of shocks. Explosive Research Report No. 12. Navy Dept, Bureau of Ordnance, Washington, DC, USAGoogle Scholar
- Smith LG (1945) Photographic investigation of the reflection of plane shocks in air. Office of Scientific Research and Development, Rep No. 6271, USAGoogle Scholar