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Negative shock waves

Published online by Cambridge University Press:  29 March 2006

P. A. Thompson  and
K. C. Lambrakis
P. A. Thompson
Affiliation:
Division of Fluid, Chemical and Thermal Processes, Rensselaer Polytechnic Institute, Troy, New York
K. C. Lambrakis
Affiliation:
Division of Fluid, Chemical and Thermal Processes, Rensselaer Polytechnic Institute, Troy, New York
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Abstract

Negative or rarefaction shock waves may exist in single-phase fluids under certain conditions. It is necessary that a particular fluid thermodynamic quantity Γ ≡ −½δ In (δP/δν)s/δ In ν be negative: this condition appears to be met for sufficiently large specific heat, corresponding to a sufficient level of molecular complexity. The dynamic formation and evolution of a negative shock is treated, as well as its properties. Such shocks satisfy stability conditions and have a positive, though small, entropy jump. The viscous shock structure is found from an approximate continuum model. Possible experimental difficulties in the laboratory production of negative shocks are briefly discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 60 , Issue 1 , 21 August 1973 , pp. 187 - 208
Copyright
© 1973 Cambridge University Press

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References

Abbott, M. M. 1973 Cubic equations of state. A.I.Ch.E. J. (in press).Google Scholar
Barker, L. M. & Hollenbach, R. E. 1970 Shock-wave studies of PMMA, fused silica, and sapphire J. Appl. Phys. 41, 4208–4226.Google Scholar
Bethe, H. A. 1942 The theory of shock waves for an arbitrary equation of state. Office Sci. Res. & Dev., Washington, Rep. no. 545.Google Scholar
Duhem, P. 1909 Sur la propagation des ondes de choc au sein des fluides Z. Phys. Chem., Leipzig, 69, 169–186.Google Scholar
Hatsopoulos, G. N. & Keenan, J. H. 1965 Principles of General Thermodynamics. Wiley.
Hayes, W. D. 1958 The basic theory of gasdynamic discontinuities. In. Fundamentals of Gasdynamics (ed. H. W. Emmons), pp. 416–481. Princeton University Press.
Hirschfelder, J. O., Buehler, R. J., McGee, H. A. & Sutton, J. R. 1958 Generalized thermodynamic excess functions for gases and liquids Ind. Engng Chem. 50, 386.Google Scholar
Jouguet, E. 1901 Sur la propagation des discontinuités dans les fluides C. R. Acad. Sci., Paris, 132, 673–676.Google Scholar
Kline, S. J. & Shapiro, A. H. 1953 On the normal shock wave in any single-phase fluid substance. Heat Transfer and Fluid Mechanics Institute, pp. 193–210. Stanford University Press.
Lambert, J. D. 1972 Vibration-translation and vibration-rotation energy transfer in polyatomic molecules. J. Chem. Soc. Faraday Trans. 2 (II), 364–373.Google Scholar
Lambrakis, K. C. & Thompson, P. A. 1972 Existence of real fluids with a negative fundamental derivative Phys. Fluids, 15, 933–935.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Lighthill, M. J. 1956 Viscosity effects in waves of finite amplitude. In Surveys in Mechanics (ed. G. K. Batchelor & R. M. Davies), pp. 250–351. Cambridge University Press.
Martin, J. J. & Hou, Y. C. 1955 Development of an equation of state for gases A.I.Ch.E. J. 1, 142.Google Scholar
Rankine, W. J. M. 1870 On the thermodynamic theory of waves of finite longitudinal disturbance. Proc. Roy. Soc A 160, 277–286.Google Scholar
Rayleigh, Lord 1910 Aerial plane waves of finite amplitude. Proc. Roy. Soc A 84, 247–284.Google Scholar
Taylor, G. I. 1910 The conditions necessary for discontinuous motion in gases. Proc. Roy. Soc A 84, 371–377.Google Scholar
Thompson, P. A. 1971 A fundamental derivative in gasdynamics Phys. Fluids 14, 1843–1849.Google Scholar
Thompson, P. A. 1972 Compressible Fluid Dynamics. McGraw-Hill.
Zel'dovich, Ya. B. 1946 On the possibility of rarefaction shock waves Zh. Eksp. Teor. Fiz. 4, 363–364.Google Scholar
Zel'dovich, Ya. B. & Raizer, Yu. P. 1966 Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, vol. 1 (ed. W. D. Hayes & R. F. Probstein), pp. 67–69. Academic.
Zel'dovich, Ya. B. & Raizer, Yu. P. 1967 Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, vol. 2 (ed. W. D. Hayes & R. F. Probstein), pp. 757–762. Academic.
Zemplén, G. 1905 Sur l'impossibilité des ondes de choc negatives dans les gaz C.R. Acad. Sci., Paris, 141, 710–712.Google Scholar