Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T18:37:13.915Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence and uniqueness of normal shock waves in gas-particle mixtures

Published online by Cambridge University Press:  29 March 2006

Barbara Schmitt-Von Schubert
Barbara Schmitt-Von Schubert
Affiliation:
Institut für Mechanik, Technische Hochschule, Darmstadt
Get access Rights & Permissions [Opens in a new window]

Abstract

A mixture of a gas and small solid particles is considered which, far upstream, is in a constant equilibrium state, and moves with a constant velocity. The existence of shock waves is investigated in the four possible cases, namely for frozen flow, for two kinds of partly frozen flow, and for equilibrium flow. It is shown that, in all these cases, compressive shocks may exist, if the upstream velocity exceeds the velocity of sound appropriate to the type of flow. Rarefaction shocks are impossible in each case. Moreover, it is shown that the downstream values of the flow parameters are determined uniquely, and the direction of their change is given. Only rather general assumptions concerning the behaviour of the gas are needed. The paper takes into account the influence of the finite particle volume fraction unlike most previous papers on the topic.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 3 , 18 September 1969 , pp. 633 - 655
Copyright
© 1969 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Becker, E. 1968 Gas Dynamics. New York: Academic Press.
Garrier, G. F. 1958 Shock waves in a dusty gas J. Fluid Mech. 4, 376–382.Google Scholar
Cowan, R. D. 1958 Properties of the Hugoniot function J. Fluid Mech. 3, 531–545.Google Scholar
Kraiko, A. N. & Sternin, L. E. 1965 Theory of flows of a two-velocity continuous medium containing solid or liquid particles PMM 29, 418–429. (English translation 1966.)Google Scholar
Rudinger, G. 1964 Some properties of shock relaxation in gas flows carrying small particles Phys. Fluids, 7, 658–663.Google Scholar
Rudinger, G. 1965 Some effects of finite particle volume on the dynamics of gasparticle mixtures AIAA J. 3, 1217–1222.Google Scholar
Schmitt-Von Schubert, B. 1969 Schallwellen in Gasen mit festen Teilchen. To be published in Z. angew. Math. Phys.Google Scholar
Serrin, J. 1959 Mathematical principles of classical fluid mechanics. Encyclopaedia of Physics, vol. viii, no. 1. Berlin: Springer.