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Transition to Mach reflexion of shock waves in steady and pseudosteady flow with and without relaxation

Published online by Cambridge University Press:  19 April 2006

H. G. Hornung ,
H. Oertel  and
R. J. Sandeman
H. G. Hornung
Affiliation:
Department of Physics, Australian National University, Canberra, Australia
H. Oertel
Affiliation:
Department of Physics, Australian National University, Canberra, Australia Permanent address: Institut für Strömungslehre und Strömungsmaschinen, Universität Karlsruhe, Federal Republic of Germany.
R. J. Sandeman
Affiliation:
Department of Physics, Australian National University, Canberra, Australia
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Abstract

Experiments were conducted in the free-piston shock tube and shock tunnel with dissociating nitrogen and carbon dioxide, ionizing argon and frozen argon to measure the transition condition in pseudosteady and steady flow. The transition condition in the steady flow, in which the wall was eliminated by symmetry, agrees with the calculated von Neumann condition. In the real gases this calculation assumed thermo-dynamic equilibrium after the reflected shock. In the pseudosteady flow of reflexion from a wedge the measured transition angle lies on the Mach-reflexion side of the calculated detachment condition by an amount which may be explained in terms of the displacement effect of the boundary layer on the wedge surface. A single criterion based on the availability of a length scale at the reflexion point explains the difference between the pseudosteady and steady flow transition condition and predicts a hysteresis effect in the transition angle when the shock angle is varied during steady flow. No significant effects on the transition condition due to finite relaxation length could be detected. However, new experiments in which interesting relaxation effects should be evident are suggested.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 90 , Issue 3 , 13 February 1979 , pp. 541 - 560
Copyright
© 1979 Cambridge University Press

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References

Bleakney, W. & Taub, A. H. 1949 Rev. Mod. Phys. 21, 584–605.
Buggisch, H. 1973 J. Fluid Mech. 61, 159–172.
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. Interscience.
Crane, K. C. A. & Stalker, R. J. 1977 J. Phys. D, Appl. Phys. 10, 679.
Ebrahim, N. A. & Hornung, H. G. 1975 A.I.A.A. J. 13, 845–846.
Ebrahim, N. A. & Sandeman, R. J. 1976 J. Chem. Phys. 65, 3446–3453.
Gvozdeva, L. G., Bazhenova, T. V., Predvoditeleva, O. A. & Fokeev, F. P. 1969 Astron. Acta 14, 503–508.
Heilig, W. 1969 Dissertation, University of Karlsruhe. (See also Proc. 11th Int. Symp. Shock Tubes & Wares, Seattle, 1977, pp. 288–295.)
Henderson, L. F. & Lozzi, A. 1975 J. Fluid Mech. 68, 139–155.
Hornung, H. G. 1972 J. Fluid Mech. 53, 149–176.
Hornung, H. G. & Kychakoff, G. 1977 Proc. 11th Int. Symp. Shock Tubes & Waves, Seattle, pp. 296–302.
Hornung, H. G. & Smith, G. 1979 J. Fluid Mech. To appear.
Kewley, D. J. & Hornung, H. G. 1974a Chem. Phys. Lett. 25, 531–536.
Kewley, D. J. & Hornung, H. G. 1974b J. Fluid Mech. 64, 725–736.
Knöös, S. 1968 J. Plasma Phys. 2, 207–242.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Law, C. K. & Glass, I. I. 1971 C.A.S.I. Trans. 4, 2.
Liepmann, H. W. & Roshko, A. 1957 Elements of Gasdynamics. Wiley.
Mach, E. 1878 Akad. Wiss. Wien 77, 1228.
Neumann, J. von 1943 See Collected Works, 1963, vol. 6, pp. 239–299. Pergamon.
Oertel, H. 1974 Dissertation, Karlsruhe.
Oertel, H. 1976 J. Fluid Mech. 74, 477–495.
Smith, W. R. 1959 Phys. Fluids 2, 533–541.
Stalker, R. J. 1967 A.I.A.A. J. 5, 2160.
Takayama, K. & Sekiguchi, H. 1977 Rep. Inst. High Speed Mech. Tohoku Univ. 336, 53–74.