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Experimental and theoretical study of the stability of plane shock waves reflected normally from perturbed flat walls

  • M. G. Briscoe (a1) and A. A. Kovitz (a1)
Abstract

The rate of damping of perturbations on a shock wave reflected from a perturbed flat wall was measured in a shock tube. Incident shock wave Mach numbers of 1·45 and 1·09 in air together with sinusoidal and Gaussian wall perturbations were employed. These measurements were compared with a modified form of a linearized theory due to Zaidel (1960). The linearization was performed about the basic solution of a plane shock wave reflected normally from a flat wall.

The rate of decay and the frequency and phase of oscillations agreed very well with the theoretical predictions; the amplitudes of the oscillations were some-what larger than predicted. The reflected shock shape was initially in good agreement with theory, but higher frequency perturbations on the reflected shock front caused deviations from the predicted shape after the shock front had travelled about one wall-wavelength away from the wall.

The generally satisfactory agreement between theory and experiment supports the use of linearized analysis in predicting shock wave stability.

Copyright
© 1968 Cambridge University Press
References
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Blackburn, D. 1953 Unsteady perturbations of strong shock waves. Ph.D. Thesis, Manchester University.
Briscoe, M. G. 1967 Normal shock reflection from nearly flat walls. Ph.D. Thesis, Northwestern University.
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. New York: Interscience.
Freeman, N. C. 1955 A theory of the stability of plane shock waves. Proc. Roy. Soc A 228, 341–62.
Freeman, N. C. 1957 On the stability of plane shock waves J. Fluid Mech. 2, 397–411.
Lapworth, K. C. 1957 An experimental investigation of the stability of plane shock waves J. Fluid Mech. 2, 341–62.
Lighthill, M. J. 1949 The diffraction of blast. I. Proc. Roy. Soc A 198, 454–70.
Lighthill, M. J. 1950 The diffraction of blast. II. Proc. Roy. Soc A 200, 554–65.
Mark, H. 1957 The interaction of a reflected shock wave with the boundary layer in a shock tube. Ph.D. Thesis, Cornell University. NACA-TM-1418 (1958). AFOSR-TN-57-345, AD-132-418.
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. New York: McGraw-Hill.
Nikolaev, IU. M. 1965 Solution for a plane shock wave moving through a lightly curved interface of two media J. Appl. Math. Mech. 29, 785–94.
Sakharnov, A. D., Zaidel, R. M., Mineev, V. N. & Oleinik, A. G. 1965 Experimental investigation of shock waves and the mechanical properties of substances at high pressures and temperatures Soviet Physics-Doklady, 9, 1091–4.
Watson, G. N. 1966 A Treatise on the Theory of Bessel Functions. 2nd edition. Cambridge University Press.
Zaidel, R. M. 1960 Shock wave from a slightly curved piston J. Appl. Math. Mech. 24, 316–27.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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