Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-12T17:36:47.856Z Has data issue: false hasContentIssue false
  • English
  • Français

The radiatively driven discrete acoustic wave

Published online by Cambridge University Press:  29 March 2006

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

Abstract

A complete and detailed study of a radiatively driven plane acoustic wave in a non-grey radiating and absorbing gas is carried out on the assumption of local molecular equilibrium. Specifically, the response of the gas in a semi-infinite space to a step input of radiation from a stationary black wall is investigated. The problem is physically interesting because radiative heat addition is the only driving mechanism, and this mechanism is unique and fundamental to the field of radiative gas dynamics. The solution shows that the heat addition gives rise initially to a compression-expansion wave in the gas, with the wave front controlled by radiation. This wave-front disturbance, though caused initially by the direct effect of radiative transfer, eventually outruns the region of appreciable heating near the wall and becomes a modified-classical disturbance that propagates away from the wall at the isentropic speed of sound. The radiative heat addition continues directly to affect the gas near the wall and in this manner drives the modified-classical wave indirectly by causing the formation of an ‘effective gas piston’. The solution thus exhibits a linearized phenomenology corresponding to that observed in the non-linear leading wave associated with the nuclear fireball.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 39 , Issue 4 , 15 December 1969 , pp. 667 - 694
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.
Brode, H. L. 1964 Fireball phenomenology. RAND Corp., Report P-3026.
Cogley, A. C. 1968 An approximate method for 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. & Vincenti, W. G. 1969 Application to radiative acoustics of Whitham's method for the analysis of non-equilibrium wave phenomena J. Fluid Mech. 39, 641.Google Scholar
Courant, R. & Hilbert, D. 1962 Methods of Mathematical Physics. II. New York: Interscience.
Erdélyi, 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
Long, H. R. & Vincenti, W. G. 1967 Radiation-driven acoustic waves in a confined gas Phys. Fluids, 10, 1365.Google Scholar
Solan, A. & Cohen, I. M. 1966 Weakly radiative acoustic flow induced by radiation from a stationary wall Phys. Fluids, 9, 2365.Google Scholar
Solan, A. & Cohen, I. M. 1967a Rayleigh problem in a radiating compressible gas. Part 1. Plate mach number finite Phys. Fluids, 10, 108.Google Scholar
Solan, A. & Cohen, I. M. 1967b Rayleigh problem in a radiating compressible gas. Part 2. Plate mach number large Phys. Fluids, 10, 257.Google Scholar
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