Abstract
A new criterion is suggested to define the point of transition between regular and Mach reflection. The suggested criterion is based on the natural tendency of a physical system to minimize its energy. The increases of the specific energy behind the reflected shock of a regular reflection and behind the Mach stem of a Mach reflection are calculated. It is hypothesized that the type of reflection that will occur is that which produces the smaller change of specific energy. The transition angles predicted using this criterion show better agreement with experimental results than those predicted using the detachment criterion for incident shock waves with Mach numbers between 1.1 and 2.0.
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References
Bazhenova TV, Gvozdeva LG, Nettleton MA (1984) Unsteady interactions of shock waves. Prog Aerospace Sci 21:249–331
Ben-Dor G (1978) Regions and transitions of non-stationary oblique shock wave diffractions in perfect and imperfect gases. UTIAS Rept 232, Univ Toronto, Canada
Ben-Dor G, Takayama K, Dewey JM (1987) Further analytical considerations of weak planar shock wave reflections over a concave wedge. Fluid Dynamics Research 2(2):77–85
Ben-Dor G (1988) Steady, pseudo-steady and unsteady shock wave reflections. Prog Aerospace Sci 25:329–412
Book D, Boris J, Kuhl A, Oran E, Picone M, Zalesak S (1981) Simulation of complex shock reflection from wedges in inert and reactive gas mixtures. Proc 7th Int Conf Numerical Methods in Fluid Dynamics pp 84–90
Colella P, Glaz HM (1984) Numerical calculation of complex shock reflections in gases. Proc 8th Int Conf Numerical Methods in Fluid Dynamics 218:154–158
Deschambault RL (1982) Nonstationary oblique shock wave reflections in air. UTIAS Rept 270, Univ Toronto, Canada
Dewey JM, McMillin DJ, Classen DF (1977) Photogrammetry of spherical shocks reflected from real and ideal surfaces. J Fluid Mech 81:701–717
Dewey JM, McMillin DJ (1985) Observation and analysis of the Mach reflection of weak uniform plane shock waves. Part 2 Analysis. J Fluid Mech 152:67–81
Dewey JM, Lock GD (1989) An experimental investigation of the sonic criterion for transition from regular to Mach reflection of weak shock waves. Expt Fluids 7:289–292
Dewey JM (1989) Explosive flows: shock tubes and blast waves. In: Yang WJ (ed) Handbook of flow visualization, Hemisphere, New York, Chap 29
Glaz HM, Colella P, Glass II, Deschambault RL (1985) A detailed numerical, graphical and experimental study of oblique shock reflections. UTIAS Rept 285, Univ Toronto, Canada
Heilig WH (1969) Diffraction of a shock wave by a cylinder. Phys Fluids 1(I):154–157
Henderson LF, Lozzi A (1975) Experiments on transition of Mach reflections. J Fluid Mech 68:139–155
Henderson LF, Gray PM (1981) Experiments on the diffraction of strong shock waves. Proc Roy Soc Lond A 377:363–378
Henderson LF (1987) Regions and boundaries for diffraction shock wave systems. Zamm Z Angew Math Mech 67:73–86
Hornung HG, Oertel H Jr, Sandeman J (1979) Transition to Mach reflection of shock waves in steady and pseudosteady flow with and without relaxation. J Fluid Mech 90:541–560
Hornung HG (1985) Regular and Mach reflection of shock waves. Ann Rev Fluid Mech 18:33–58
Itoh K, Takayama K (1987) Transonic shock tube flow over a NACA 0012 aerofoil and elliptical cylinders. In: Grönig H (ed) Proc 16th Int Symp Shock Tubes and Waves pp 693–699
Lee JH, Glass II (1982) Domains and boundaries of pseudo-stationary oblique shock-wave reflections in air. UTIAS Rept 262, Univ Toronto, Canada
von Neumann J (1943) Oblique reflection of shocks. Explosive Research Rept 12, Navy Dept, Bureau of Ordnance, Washington DC
Sakurai A (1964) On the problem of weak Mach reflection. J Phys Soc Jap 19:1440–1450
Smith LG (1945) Photographic investigation of the reflection of plane shocks in air. OSRD Rept 6271
White DR (1951) An experimental survey of the Mach reflection of shock waves. PhD Thesis, Princeton University
Zhilin YV, Bazhenova TV, Gvozdeva LG (1978) Bifurcation of shock waves upon reflecting from end wall of shock tube. Archives of Mech 30:675–681
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Olim, M., Dewey, J.M. Least energy as a criterion for transition between regular and Mach reflection. Shock Waves 1, 243–249 (1991). https://doi.org/10.1007/BF01418881
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DOI: https://doi.org/10.1007/BF01418881