Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T08:28:35.037Z Has data issue: false hasContentIssue false
  • English
  • Français

Application to radiative acoustics of Whitham's method for the analysis of non-equilibrium wave phenomena

Published online by Cambridge University Press:  29 March 2006

A. C. Cogley  and
W. G. Vincenti
A. C. Cogley
Affiliation:
Department of Aeronautics and Astronautics, Stanford University Present address: Department of Energy Engineering, University of Illinois, Chicago. 41
W. G. Vincenti
Affiliation:
Department of Aeronautics and Astronautics, Stanford University
Get access Rights & Permissions [Opens in a new window]

Abstract

An approximate method due originally to Whitham is applied to the study of acoustic waves propagating in a non-grey radiating and absorbing gas, assumed in local molecular equilibrium. The method, which has general applicability in the study of non-equilibrium wave phenomena, replaces the exact governing equation by a set of lower-order equations that can be solved analytically in many cases. The use of the method is demonstrated by reconsidering the onedimensional problems of (i) harmonic waves driven by a harmonic variation in either position or temperature of a planar wall and (ii) the discrete wave produced by the impulsive motion of a constant-temperature wall. The method greatly simplifies the mathematics for these problems, and comparaison of the results with those of earlier investigators shows the approximate method to be accurate. Moreover, the method allows us to obtain a more systematic and complete analytical solution of the second problem than has been obtained by more conventional methods.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 39 , Issue 4 , 15 December 1969 , pp. 641 - 666
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

Baldwin, B. S. 1962 The propagation of plane acoustic waves in a radiating gas. NASA TR R-138.
Cheng, P. 1966 Dynamics of a radiating gas with application to flow over a wavy wall AIAA J. 4, 238.Google Scholar
Cogley, A. C. 1968 An approximate method of analyzing non-equilibrium acoustic phenomena with application to discrete radiation-driven waves. Ph.D. Thesis, Dept. of Aero, and Astro., Stanford University.
Cogley, A. C. 1969 The radiatively driven discrete acoustic wave J. Fluid Mech. 39, 667.Google Scholar
Courant, R. & Hilbert, D. 1962 Methods of Mathematical Physics. vol. II. New York: Interscience.
Erdelyi, A. et al. 1954 Tables of Integral Transforms. New York: McGraw Hill.
Gilles, S. E., Cogley, A. C. & Vincenti, W. G. 1969 A substitute-kernel approximation for radiative transfer in a non-grey gas near equilibrium, with application to radiative acoustics Int. J. Heat and Mass Transfer, 12, 445.Google Scholar
Khosla, P. K. & Murgai, M. P. 1965 Small amplitude wave propagation in hot ionized gases. Phys: Fluids, 8, 2087.Google Scholar
Lick, W. J. 1964 The propagation of small disturbances in a radiating gas J. Fluid Mech. 18, 274.Google Scholar
Lick, W. J. 1967 Wave propagation in real gases Advan. Appl. Mech. 10, Fasc. 1.Google Scholar
Long, H. R. & Vincenti, W. G. 1967 Radiation-driven acoustic waves in a confined gas Phys. Fluids, 10, 1365.Google Scholar
Moore, F. K. 1966 Effect of radiative transfer on a sound wave travelling in a gas having γ near one Phys. Fluids, 9, 70.Google Scholar
Vincenti, W. G. & Baldwin, B. S. 1962 Effect of thermal radiation on the propagation of plane acoustic waves J. Fluid Mech. 12, 449.Google Scholar
Vincenti, W. G. & Kruger, C. H. 1965 Introduction to Physical Gas Dynamics. New York: Wiley.
Whitham, G. B. 1959 Some comments on wave propagation and shock wave structure with application to magnetohydrodynamics Comm. Pure Appl. Math. 12, 113.Google Scholar