On Certain Peculiarities of the Shock Wave Reflection
The present paper discusses the results, both theoretical and experimental, in author's opinion most important for understanding the formation of a quasi-stationary reflection of a plane shock wave at a wedge. The peculiarities of the behaviour of the shock wave in close vicinity of the leading edge of the wedge are reported. The differences between the stationary shock reflection in the wind tunnel, and the quasi-stationary one in a shock tube, are specified. It is concluded that these two kinds of reflection can be equivalent only in the case of strong shocks.
References
E.MACH. Akad. Wiss., Wien, 77, II, 1228, 1878.
H.HORNUNG, Regular and Mach reflection of shock waves, Ann. Rev. Fluid. Mech., 18, 33-58, 1986.
G.I.TAYLOR, The conditions necessary for discontinuous motion in gases, Proc. Roy. Soc. A, 84, 371-377, 1910.
W.FISZDON, R.HERCZYŃSKI, Z.WALENTA, The structure of a plane shock wave of a monatomic gas. Theory and experiment, Proc. 9-th Int. RGD Symp., Gottingen 1974.
G.BEN-DOR, Regions and transitions of nonstationary oblique shock-wave diffractions in perfect and imperfect gases, UTJAS Rept., No.232, 1978.
J. VON NEUMANN, Collected works, 6, Pergamon, 1963.
H.G.HORNUNG, H.OERTEL, R.J.SANDEMAN, Transition to Mach reflexion of shock waves in steady and pseudo-steady flow with and without relaxation, J. Fluid Mech., 90, 3, 541-560, 1979,
W.BLEAKNEY, An experimental study of the interaction of shock waves, Symp. on Shock-Wave Phenomena, White Oak, Maryland, 30. 06. 1949.
L.G.SMITH, Photographic investigation of the reflection of plane shocks in air, O. S. R. D. Rept. No 6271.
J.M.DEWEY, D.J.MCMILLIN, Observation and analysis of the Mach reflection of weak, uniform plane shock waves. Part 1. Observations, Part .2. Analysis., J. Fluid Mech., 152, 49-81, 1985.
K.G.GUDERLEY, Theorie schallnaher Stromungen, Springer Verlag, Berlin, Gottingen, Heidelberg 1957.
A.SAKURAI, On the problem of weak Mach reflection, J. Phys. Soc. Japan, 19, 1440-1450, 1964.
J.STERNBERG, Triple-shock-wave intersections, Phys. Fluids, 2, 2, 179-206, 1959.
H.M.GLAZ, P.COLELLA, I.I.GLASS, R.L.DESCHAMBAULT, A numerical study of oblique shock wave reflections with experimental comparisons, Proc. Roy. Soc. Lond., A 398, 117-140, 1985.
P.COLELLA, L.F.HENDERSON, The von Neumann paradox for the diffraction of weak shock waves, J. Fluid Mech., 213, 71-94, 1990.
H.N.BALLARD, D.VENABLE, Shock front thickness measurement by an electron "beam technique, Phys. Fluids, 1, 3, 225-229, 1958.
G.SMEETS, A.GEORGE, Gasdynamische Untersuchungen im Stossrohr mit einem hochempfindlichen Laserinterferometer, ISL-R, 14/71, 1971.
J.FUCHS, B.SCHMIDT, Shock wave interaction with the leading edge of a wedge, Proc. 17-th Int. RGD Symp., Aachen 1990, and private communication.
Z.A.WALENTA, Regular reflection of the plane shock wave from an inclined wall, Arch. Mech., 26, 5, 825-832, 1974.
Z.A.WALENTA, Formation of the Mach-type reflection of shock waves, Arch. Mech., 35, 2, 187-196, 1983.
Z.A.WALENTA, Mach reflection of a moving, plane shock wave under rarefied flow conditions, Proc. 16-th Int. Symp. on Shock Tubes and Waves, Aachen, 1987.
L.F.HENDERSON, A.SIEGENTIIALER, Experiments on the diffraction of weak blast waves: the von Neumann paradox, Proc. Roy. Soc. Lond., A 369, 537-555, 1980.
Z.A.WALENTA, Microscopic structure of the Mach-type reflection of the shock wave, Arch. Mech., 32, 5, 819-825, 1980.
H.HORNUNG, The effect of viscosity on the Mach stem length in unsteady strong shock reflection, Lecture Notes in Physics 235, Flow of Real Fluids, 1985.
D.Q.XU, H.HONMA, T.ABE, Kinetic model approach to nonstationary Mach reflection of shock waves, Proc. 17-th Int. Symp. on Shoclt Waves and Shock Tubes, Bethlehem, Pa, 1989.
A.SAKURAI, L.F.HENDERSON, K.TAKAYAMA, Z.A.WALENTA, P.COLELLA, On the von Neumann parodox of weak Mach reflection, Fluid Dynamics Research, 4, 5/6, 333-345, 1989.
Z.A.WALENTA, Microscopic structure of the Mach-type reflection of weak shock waves, Proc. 13-th Int. Symp. on Shock Tubes and Waves, Niagara Falls, 1981.
G.BEN-DOR, K.TAKAYAMA, C.E.NEEDHAM, The thermal nature of the triple point of a Mach reflection, Phys. Fluids, 30, 5, 1287-1293, 1987.
Z.A.WALENTA, Formation of the Mach reflection in polyatomic gases, Proc. 17-th Int. RGD Symp., Aachen, 1990.