Hostname: page-component-669899f699-2mbcq Total loading time: 0 Render date: 2025-04-25T14:46:32.951Z Has data issue: false hasContentIssue false
  • English
  • Français

On the near-equilibrium and near-frozen regions in an expansion wave in a relaxing gas

Published online by Cambridge University Press:  28 March 2006

J. G. Jones
J. G. Jones
Affiliation:
Royal Aircraft Establishment, Bedford
Get access Rights & Permissions [Opens in a new window]

Abstract

A weak expansion wave propagating in a relaxing gas is discussed with particular reference to the ‘near-equilibrium’ and ‘near-frozen’ regions. The concept of bulk viscosity is used in conjunction with Burger's equation in the near-equilibrium region. The asymptotic equilibrium simple wave is modified by diffusive regions in the neighbourhood of the first and last rays. It is shown that in the case of a weak expansion wave, Chu's asymptotic solution of the acoustic equation describes the wave-form for a finite time interval before convection effects become noticeable. In the near-frozen region a characteristic perturbation method is used to describe the flow near the wave-front.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 19 , Issue 1 , May 1964 , pp. 81 - 102
Copyright
© 1964 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.)

Article purchase

Temporarily unavailable

References

Appleton, J. P. 1960 The structure of a centred rarefaction wave in an ideal dissociating gas. Aero. Res. Counc. Rep. no. 22095. Also Univ. Southampton, U.S.A.A. Rep. no. 136.Google Scholar
Chu, B-T. 1958 Wave propagation in a reacting mixture. Heat Transf. Fluid Mech. Inst. pp. 80–90.Google Scholar
Clarke, J. F. 1960 The linearized flow of a dissociating gas. J. Fluid Mech. 7, 577–595.Google Scholar
Erdelyi, A. 1956 Asymptotic Expansions. New York: Dover.
Kantrowitz, A. 1958 One dimensional treatment of non-steady gas dynamics. Fundamentals of Gas Dynamics (ed. Emmons, H. W.). Princeton University Press.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. London: Pergamon.
Lighthill, M. J. 1956 Viscosity effects in sound waves of finite amplitude. Surveys in Mechanics (ed. Batchelor, G. K. & Davies, R. M.), p. 250. Cambridge University Press.
Moore, F. K. & Gibson, W. E. 1959 Propagation of weak disturbances in a gas subject to relaxation effects. Inst. Aero. Sci. Rep. no. 59-64.Google Scholar
Napolitano, L. G. 1960 Non-equilibrium centred rarefaction for a reacting mixture. Arnold Engng Dev. Center Rep. AEDC-TN-60-129.Google Scholar
Stulov, V. P. 1962 The flow of an ideal dissociating gas about a convex angle corner with non-equilibrium taken into account. Unpublished R.A.E. Library Translation by B. A. Woods, from Iz. Akad. Nauk SSSR Otdelenie Tech. Nauk Mekh. i Mashin. 3, 4–10.Google Scholar
Whitham, G. B. 1959 Some comments on wave propagation and shock wave structure with applications to magnetohydrodynamics. Comm. Pure Appl. Math. 12, 113–158.Google Scholar
Wood, W. W. & Parker, F. R. 1958 Structure of a centred rarefaction wave in a relaxing gas. Phys. Fluids, 1, 230–241.Google Scholar