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Shock splitting in single-phase gases

Published online by Cambridge University Press:  26 April 2006

M. S. Cramer
M. S. Cramer
Affiliation:
Department of Engineering Science & Mechanics, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061, USA
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Abstract

We consider single-phase gases in which the fundamental derivative is negative over a finite range of pressures and temperatures and show that inadmissible discontinuities give rise to shock splitting. The precise conditions under which splitting occurs are delineated and the formation of the split-shock configuration from smooth initial conditions is described. Specific numerical examples of shock splitting are also provided through use of exact inverse solutions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 199 , February 1989 , pp. 281 - 296
Copyright
© 1989 Cambridge University Press

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References

Bethe, H. A.: 1942 The theory of shock waves for an arbitrary equation of state. Office Sci. Res. & Dev. Rep. 545.Google Scholar
Cramer, M. S.: 1987a Structure of weak shocks in fluids having embedded regions of negative nonlinearity. Phys. Fluids 30, 3034–3044.Google Scholar
Cramer, M. S.: 1987b Dynamics of shock waves in certain dense gases. In Proc. 16th Intl Symp. on Shock Tubes and Waves, Aachen, West Germany, pp. 139–144.Google Scholar
Cramer, M. S.: 1987c Dynamics of shock waves in gases having large specific heats. In Proc. 20th Midwestern Mechanics Conf., Purdue University, W. Lafayette, Indiana, pp. 207–211.Google Scholar
Cramer, M. S. & Kluwick, A., 1984 On the propagation of waves exhibiting both positive and negative nonlinearity. J. Fluid Mech. 142, 9–37.Google Scholar
Cramer, M. S., Kluwick, A., Watson, L. T. & Pelz, W., 1986 Dissipative waves in fluids having both positive and negative nonlinearity. J. Fluid Mech. 169, 323–336.Google Scholar
Cramer, M. S. & Sen, R., 1986a Sonic shocks in certain dense gases. Bull. Am. Phys. Soc. 31, 1720.Google Scholar
Cramer, M. S. & Sen, R., 1986b Shock formation in fluids having embedded regions of negative nonlinearity. Phys. Fluids 29, 2181–2191.Google Scholar
Cramer, M. S. & Sen, R., 1987 Exact solutions for sonic shocks in van der Waals gases. Phys. Fluids 30, 377–385.Google Scholar
Gilbarg, D.: 1951 The existence and limit behavior of the one-dimensional shock layer. Am. J. Maths 73, 256–274.Google Scholar
Kynch, G. J.: 1952 A theory of sedimentation. Trans. Faraday Soc. 48, 166–176.Google Scholar
Lambrakis, K. & Thompson, P. A., 1972 Existence of real fluids with a negative fundamental derivative Γ. Phys. Fluids 5, 933–935.
Landau, L. D. & Lifshitz, E. M., 1959 Fluid Mechanics. Addison-Wesley.
Lax, P. D.: 1971 Shock waves and entropy. In Contributions to Nonlinear Functional Analysis (ed. E. H. Zarantonello). Academic.
Lee-Bapty, I. P.: 1981 Nonlinear wave propagation in stratified and viscoelastic media. Ph.D. dissertation, Leeds University, England.
Lee-Bapty, I. P. & Crighton, D. G. 1987 Nonlinear wave motion governed by the modified Burger's equation. Phil. Trans. R. Soc. Lond. A 323, 173–209.Google Scholar
Shannon, P. T. & Tory, E. M., 1965 Settling of slurries. Ind. Engng Chem. 57, 18–25.Google Scholar
Thompson, P. A.: 1971 A fundamental derivative in gasdynamics. Phys. Fluids. 14, 1843–1849.Google Scholar
Thompson, P. A., Chaves, H., Meier, G. E. A., Kim, Y.-G. & Speckmann, H.-D. 1987 Wave splitting in a fluid of large heat capacity. J. Fluid Mech. 185, 385–414.Google Scholar
Thompson, P. A. & Kim, Y.-G. 1983 Direct observation of shock splitting in a vapor–liquid system. Phys. Fluids 26, 3211–3215.Google Scholar
Thompson, P. A. & Lambrakis, K., 1973 Negative shock waves. J. Fluid Mech. 60, 187–208.Google Scholar
Turner, T. N.: 1979 Second-sound shock waves and critical velocities in liquid helium II. Ph.D. Dissertation, California Institute of Technology, Pasadena, Ca.
Turner, T. N.: 1981 New experimental results obtained with second-sound shock waves. Physica 107B, 701–702.Google Scholar
Zel'dovich, Ya. B. 1946 On the possibility of rarefaction shock waves. Zh. Eksp. Teor. Fiz. 4, 363–364.Google Scholar