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The development of weak waves in the unsteady one-dimensional flow of a vibrationally relaxing gas ahead of an impulsively started piston

Published online by Cambridge University Press:  29 March 2006

C. G. Dain  and
J. P. Hodgson
C. G. Dain
Affiliation:
Department of the Mechanics of Fluids, University of Manchester, England Present address: Logica Limited, 31-36 Foley Street, London W1P 7LB.
J. P. Hodgson
Affiliation:
Department of the Mechanics of Fluids, University of Manchester, England
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Abstract

The method of characteristics is used to calculate the flow ahead of an impulsively started piston moving at constant velocity. Particular attention is paid to the development of weak shock waves which are either fully or partly dispersed at very large distances from the piston. It is found that the global features of the flows may be represented in similarity form, and the graphs obtained allow extrapolation to very weak waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 69 , Issue 1 , 13 May 1975 , pp. 129 - 144
Copyright
© 1975 Cambridge University Press

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References

Blythe, P. A. 1969 Nonlinear wave propagation in a relaxing gas J. Fluid Mech. 37, 31.Google Scholar
Clarke, J. F. 1960 The linearized flow of a dissociating gas J. Fluid Mech. 7, 529.Google Scholar
Hodgson, J. P. & Johannesen, N. H. 1971 Real-gas effects in very weak shock waves in the atmosphere and the structure of sonic bangs J. Fluid Mech. 50, 17.Google Scholar
Hornby, R. P. & Johannesen, N. H. 1975 The development of weak waves in the steady two-dimensional flow of a gas with vibrational relaxation past a thin wedge J. Fluid Mech. 69, 109.CrossRefGoogle Scholar
Johannesen, N. H., Bird, G. A. & Zienkiewicz, H. K. 1967 Theoretical and experimental investigation of the reflexion of normal shock waves with vibrational relaxation J. Fluid Mech. 30, 51.Google Scholar
Lick, W. 1967 Wave propagation in real gases Adv. in Appl. Mech. 10, 1.Google Scholar
Lighthill, M. J. 1956 Viscosity effects in sound waves of finite amplitude. In Surveys in Mechanics (ed. Batchelor & Davies), pp. 250–351. Cambridge University Press.
Moore, F. K. & Gibson, W. E. 1960 Propagation of weak disturbances in a gas subject to relaxation effects J.A.S.S. 27, 117.Google Scholar
Ockendon, H. & Spence, D. A. 1969 Non-linear wave propagation in a relaxing gas J. Fluid Mech. 39, 329.Google Scholar
Sedney, R. 1970 The method of characteristics. In Nonequilibrium Flows, part 2 (ed. Wegener), pp. 160–225. Dekker.
Zhukov, A. I. 1960 Application of the characteristics method to numerical solution of uni-dimensional problems in gas dynamics. N.A.S.A. Trans. (1967) TT-F-298.Google Scholar