Abstract
The distinguished philosopher Ernst Mach published the first known paper on the phenomenon of planar shock-wave reflections over straight wedges over 125 years ago in 1878. In his publication he presented two wave configurations that could result from this reflection process, a regular reflection (RR) and a configuration that was later named after him and called Mach reflection (MR) in the early 1940s. In 1945, Smith reported on an additional wave configuration, which had a reflected shock wave that was slightly different from that of the just-mentioned Mach reflection. Smith (OSRD Rep. 6271, Off. Sci. Res. Dev., 1945) did not ascribe any special importance to the wave configuration that he observed. The wave configuration that was observed and reported by Smith (OSRD Rep. 6271, Off. Sci. Res. Dev., 1945) was recognized as an independent one only about 5 years later when White (Tech. Rep. II-10, Princeton Univ. Dept. Phys., 1951) reported on the discovery of a new wave configuration that was named double-Mach reflections (DMR) because it had similar features to that of the Mach reflection wave configuration but all the features were doubled. For this reason the Mach reflection wave configuration has been re-named single-Mach reflection (SMR). (Until the late 1970s it was called simple-Mach reflection although nothing is simple about it.). The discovery of the double-Mach reflection revealed that the wave configuration that was first observed by Smith was an intermediate wave configuration between the SMR and the DMR wave configurations. For this reason it was named transitional-Mach reflection (TMR) (Until the early 1980s it was called complex-Mach reflection although it is not the most complex one.). Since the discovery of the DMR many investigations were aimed at elucidating the exact transition criteria between the above-mentioned four different wave configurations as well as some additional configurations and sub-configurations that were discovered later. In 1991 Ben-Dor published a monograph, entitled “Shock Wave Reflection Phenomena”, that was, in fact, a state-of-the-knowledge review of the phenomena. This state-of-the-knowledge will be referred to in the followings as the “old”-state-of-the-knowledge (This state-of-the-knowledge existed until the mid 1990s. A few years later Li and Ben-Dor (Shock Wave 5(1/2), 59–73, 1995) modified the analytical approach for evaluating the transition criteria from the single-Mach to the transitional- Mach reflection (SMR, \(\rightleftarrows\),TMR) and from the transitional-Mach to the double-Mach reflection (TMR, \(\rightleftarrows\) ,DMR) and presented some modified and new criteria for the formation and termination of both the TMR and DMR wave configurations. Experimental results from various sources revealed that the transition boundaries between the SMR, TMR and DMR wave configurations that were based on the modified analytical approach were better than those of the “old” state-of-the-knowledge that as mentioned earlier was summarized in Ben-Dor’s (Shock Wave Reflection Phenomena, Springer, 1991) monograph. Unfortunately, however, the results of Li and Ben-Dor’s (Shock Wave 5(1/2), 59–73, 1995) modified analytical approach have not been internalized, and publications by various scientists in the past decade neglected the revised and better transition criteria and kept on referring to the old and wrong criteria that appeared in Ben-Dor’s (Shock Wave Reflection Phenomena, Springer, 1991) monograph. For this reason, a state-of-the-knowledge review that is based on the above-mentioned 10-year-old findings of Li and Ben-Dor (Shock Wave 5(1/2), 59–73, 1995) is presented herein. At the first step, the “old” state-of-the-knowledge is presented.
Similar content being viewed by others
References
Smith L.G. (1945) Photographic investigation of the reflection of plane shocks in air. OSRD Rep. 6271, Off. Sci. Res. Dev. Washington, D.C. U.S.A., or NDRC Rep. A-350
White D.R. (1951) An experimental survey of the Mach reflection of shock waves, Tech. Rep. II-10. Princeton Univ. Dept. Phys. Princeton, New Jersey, NJ, USA
Ben-Dor G. (1991) Shock Wave Reflection Phenomena. Springer, Berlin Heidelberg New York
Li H., Ben-Dor G. (1995) Reconsideration of pseudo-steady shock wave reflections and the transition criteria between them. Shock Waves 5(1/2): 59–73
Courant R., Friedrichs K.O. (1948) Supersonic Flow and Shock Waves. Wiley Interscience, New York
Mach E. (1978) Uber den verlauf von funkenwellen in der ebene und im raume. Sitzungsbr Akad. Wiss Wien 78, 819–838
Ben-Dor G. (1981) Relations between first and second triple point trajectory angles in double-Mach reflection. AIAA J. 19, 531–533
Lee J.-H., Glass I.I. (1984) Pseudo-stationary oblique-shock wave reflections in frozen and equilibrium air. Prog. Aerosp. Sci. 21, 33–80
Colella P., Henderson L.F. (1990) The von Neumann paradox for the diffraction of week shock waves. J. Fluid Mech. 213, 71–94
Ben-Dor G., Takayama K. (1986) The dynamics of the transition from Mach to regular reflection over concave cylinders. Isr. J. Tech. 23, 71–74
Ben-Dor G., Takayama K. (1992) The phenomena of shock wave reflection—a review of unsolved problems and future research needs. Shock Waves 21, 211–223
Hornung H.G., Oertal H. Jr., Sandeman R.J. (1979) Transitions to Mach reflection of shock waves in steady and pseudo-steady flow with and without relaxation. J. Fluid Mech. 90, 541–560
Shirouzu M., Glass I.I. (1982) An assessment of recent results on pseudo-stationary oblique-shock-wave reflection. UTIAS Rept. 264
Ben-Dor G. (1978) Regions and transitions of nonstationary oblique shock wave diifractions in perfect and imperfect gases. UTIAS Rept. 232
Law C.K., Glass I.I. (1971) Diffraction of strong shock waves by a sharp compressive corner, CASI Trans. 4, 2–12
Semenov A.N., Syshchikova M.P. (1975) Properties of Mach reflection in the interaction of shock waves with a stationary wedge. Combust Explos Shock Waves. 11, 506–515
Olim M., Dewey J.M. (1992) A revised three-shock solution for the Mach reflection of weak shock waves. Shock Waves 2, 167–176
Guderley K.G. (1947) Considerations on the structure of mixed subsonic-supersonic flow patterns, Tech. Rep. F-TR-2168-ND. Wright Field, USA
Skews B. Ashworth J.T. (2005) The physical nature of weak shock wave reflection. J. Fluid Mech. 542, 105–114
Bazhenova T.V., Fokeev V.P., Gvozdeva L.G. (1976) Regions of various forms of Mach reflection and its transition to regular reflection. Acta Astroraut, 3, 131–140
Shirouzu M., Glass I.I. (1986) Evaluation of assumptions and criteria in pseudo-stationary oblique shock wave reflections, Proc. R. Soc. Lond. Ser. A 406, 75–92
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by K. Takayama.
This paper was based on work that was presented at the 2nd International Symposium on Interdisciplinary Shock Wave Research, Sendai, Japan, 1–3 March 2005.
Rights and permissions
About this article
Cite this article
Ben-Dor, G. A State-of-the-Knowledge Review on Pseudo-Steady Shock-Wave Reflections and their Transition Criteria. Shock Waves 15, 277–294 (2006). https://doi.org/10.1007/s00193-006-0036-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00193-006-0036-z