Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-14T21:05:20.126Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-fluid Euler theory of sound dispersion in gas mixtures of disparate masses

Published online by Cambridge University Press:  21 April 2006

J. Fernandez De La Mora  and
A. Puri
J. Fernandez De La Mora
Affiliation:
Yale University, Department of Mechanical Engineering, New Haven, CT 06520, USA
A. Puri
Affiliation:
Yale University, Department of Mechanical Engineering, New Haven, CT 06520, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The suitability of an Euler-level two-fluid theory to describe the behaviour of gas mixtures with disparate masses is explored for the problem of sound propagation at frequencies high enough that dispersion effects are important. The determination of the speed of propagation is reduced to solving a quadratic equation in the complex plane. The model leads to small errors of the order of the molecular mass ratio M when the molar fraction xp of the heavy gas is small (xp = O(M)), becoming increasingly inaccurate at larger values of xp. Yet agreement with He-Xe experiments is excellent for the whole range of frequencies tested, up to values of xp = 0.4. For values of xp above 0.5 our quantitative results become poorer but they still agree qualitatively with experiments, predicting small and negative dispersion coefficients and the presence of a bifurcation at critical values of the frequency and the composition. It is concluded that this generalized Euler theory provides an excellent framework within which to develop a two-fluid boundary-layer description of the peculiar dynamics of disparate-mass mixtures in the region of parameters of greatest industrial interest.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 168 , July 1986 , pp. 369 - 382
Copyright
© 1986 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

Bowler J. R.1984 Ph.D. thesis, University of Surrey (UK).
Bowler, J. R. & Johnson E. A.1985 Phys. Rev. Lett. 54, 329–332.
Burgers J. M.1969 Flow Equations for Composite Gases. Academic.
Fernandez De La Mora J.1984 J. Phys. Chem. 88, 4557.
Fernandez De La Mora J.1985 J. Chem. Phys. 82, 3453.
Fernandez de la Mora, J. & Rosner, D. E. 1981 Physicochem. Hydrod. 2, 1.
Foch, J. D. & Fuentes Losa M.1972 Phys. Rev. Lett. 28, 1315.
Foch J. D., Uhlenbeck, G. E. & Fuentes Losa M.1972 Phys. Fluids 15, 1224.
Fuentes Losa M.1972 Ph.D. thesis, University of Colorado.
Fuentes Losa, M. & Foch, J. D. 1972 Phys. Rev. Lett. 29, 209.
Goebel C. J., Harris, S. M. & Johnson E. A.1976 Phys. Fluids 19, 627.
Goldman, E. & Sirovich L.1967 Phys. Fluids 10, 1928.
Grad H.1960 In Rarefied Gas Dynamics (ed. F. M. Devienne), p. 127. Pergamon.
Hamel B.1966 Phys. Fluids 9, 12.
Huck, R. J. & Johnson E. A.1980 Phys. Rev. Lett. 44, 142.
Prangsma G. J., Jonkman, R. M. & Beenakker J. J.1970 Physica 48, 323.
Vargaftik N. B.1975 Tables on the Thermophysical Properties of Gases and Liquids, p. 464, Hemisphere.
Wang Chang, C. W. & Uhlenbeck, G. E. 1970 In Studies in Statistical Mechanics (eds. J. De Boer & G. E. Uhlenbeck), vol. 5. North Holland.