Abstract
Although the phenomenon of shock wave reflection was discovered more than a hundred years ago, active research related to this phenomenon still goes on in many countries in the world (e.g., Australia, Canada, China, Germany, Israel, Japan, Poland, Russia and United States of America). As a matter of fact the research activity increased so drastically in the past decade and a half that a special scientific meeting dedicated to better understanding the reflection phenomena of shock waves, namely “The International Mach Reflection Symposium” was initiated in 1981 and was held since then in the major research centers actively involved in the research of shock wave reflections. In the present paper the status of the research of the phenomenon of shock wave reflection will be discussed in general, and unresolved problems and future research needs will be pointed out.
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Azevedo DJ (1989) Analytic prediction of shock patterns in a high-speed, wedge-bounded duct. Ph.D. Thesis, Dept Mech and Aero Eng, State Univ, N.Y., Buffalo, N.Y., USA
Bazhenova TV, Fokeev VP, Gvozdeva LG (1976) Regions of various forms of Mach reflection and its transition to regular reflection. Acta Astro 3:131–140
Ben-Dor G (1978) Regions and transitions of nonstationary oblique shock wave diffractions in prefect and imperfect gases. UTIAS Rept 232
Ben-Dor G (1981) Relation between first and second triple point trajectory angles in double Mach reflection. AIAA J 19:531–533
Ben-Dor G (1987) A reconsideration of the three shock theory of a pseudo steady Mach reflection. J Fluid Mech 181:467–484
Ben-Dor G (1990) Structure of the contact discontinuity of nonstationary Mach reflections. AIAA J 28:1314–1316
Ben-Dor G (1991) Shock wave reflection phenomena. Springer-Verlag, New York, N.Y., USA
Ben-Dor G, Dewey JM, Takayama K (1987) The reflection of a plane shock wave over a double wedge. J Fluid Mech 176:483–520
Ben-Dor G, Elperin T (1991) Analysis of the wave configuration resulting from the termination of an inverse Mach reflection. Shock Waves 1:237–241
Ben-Dor G, Glass II (1979) Domains and boundaries of nonstationary oblique shock wave reflections. 1 Diatomic gas. J Fluid Mech 92:459–496
Ben-Dor G, Rayevski D, Shock wave interaction with a high density layer. submitted for publication
Ben-Dor G, Takayama K (1985) Analytical prediction of the transition from Mach to regular reflection over cylindrical concave wedges. J Fluid Mech 158:365–380
Ben-Dor G, Takayama K (1986/7) The dynamics of the transition from Mach to regular reflection over concave cylinders. Israel J Tech 23:71–74
Ben-Dor G, Takayama K, Dewey JM (1987) Further analytical considerations of the reflection of weak shock waves over concave wedges. Fluid Dynamics Research 20:77–85
Ben-Dor G, Takayama K, Needham CE (1987) The thermal nature of the triple point of a Mach reflection. Physics Fluids 30:1287–1293
Birkhoff G (1950) Hydrodynamics, a study in Logic, fact and similitude. Princeton University Press, N.J., USA
Colella P, Henderson LF (1990) The von Neumann paradox for the diffraction of weak shock waves. J Fluid Mech 213:71–94
Dewey JM, McMillan DJ (1985a) Observation and analysis of the Mach reflection of weak uniform planar shock waves. Pt. I. Observation. J Fluid Mech 152:49–66
Dewey JM, McMillan DJ (1985b) Observation and analysis of the Mach reflection of weak uniform planar shock waves. Pt. II. Analysis. J Fluid Mech 152:67–81
Homung HG, Oertel H Jr, Sandeman RJ (1979) Transition to Mach reflection of shock waves in steady and pseudo-steady flow with and without relaxation. J Fluid Mech 90:541–560
Homung HG, Robinson ML (1982) Transition from regular to Mach reflection of shock waves. Part 2. The steady-flow criterion. J Fluid Mech 123:155–164
Krehl P, van der Geest (1991) The discovery of the Mach reflection effect and its demonstration in an auditorium. Shock Waves 1:3–15
Law CK, Glass II (1971) Diffraction of strong shock waves by a sharp compressive comer. CASI Trans 4:2–12
Lee J-H, Glass II (1984) Pseudo-stationary oblique-shock wave reflections in frozen and equilibrium air. Prog Aerospace Sci 21:33–80
Lock GD, Dewey JM (1989) An experimental investigation of the sonic criterion for transition from regular to Mach reflection of weak shock waves. Exp in Fluids 7:289–292
Mach E (1878) Uber den Verlauf von Funkenwellen in der Ebene und im Raume. Sitzungsbr Akad Wiss Wien 78:819–838
Neumann J von (1943a) Oblique reflection of shocks. Explos Res Rep 12, Navy Dept Bureau of ordinance, Washington, DC, USA
Neumann J von (1943b) Reflection, intersection and reflection of shock waves. NAVORD Rep 203-45, Navy Dept, Bureau of Ordinance, Washington, DC, USA
Reichenbach H (1985) Roughness and heated layer effects on shock-wave propagation and reflection — experimental results. Ernst Mach Int, Rep E24/85, Freiburg, West Germany
Schmidt B (1989) Structure of incipient triple point at the transition from regular reflection to Mach reflection. In: Muntz EP, Weaver DP, Campbell DH (eds) Rarefied Gas Dynamics: Theoretical and Computational Techniques, Progress in Astronautic and Aeronautics 118:597–607
Shirouzu M, Glass II (1986) Evaluation of assumptions and criteria in pseudo-stationary oblique shock wave reflections. Proc Roy Soc London, Ser A 406:75–92
Skews BW (1972) A departmental note from McMaster University by private communication
Smith LG (1945) Photographic investigation of the reflection of plane shocks in air. OSRD Rep 6271, Off Sci Res Dev, Washington, D.C., USA, or NDRC Rep A-350
Sternberg J (1959) Triple shock wave interactions. Phys Fluids 2:179–206
Takayama K (1992) Optical flow visualization of shock wave phenomena. Springer Verlag, New York, N.Y., USA
Takayama K, Ben-Dor G (1989) A reconsideration of transition criterion from Mach to regular reflection over cylindrical concave surfaces. KSME J 3:6–9
White DR (1951) An experimental survey of the Mach reflection of shock waves. Princeton Univ, Dept Phys Tech Rep II-10, Princeton, N.J., USA
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Ben-Dor, G., Takayama, K. The phenomena of shock wave reflection — a review of unsolved problems and future research needs. Shock Waves 2, 211–223 (1992). https://doi.org/10.1007/BF01414757
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DOI: https://doi.org/10.1007/BF01414757