Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-17T16:23:55.469Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear resonant wave motion of a radiating gas

Published online by Cambridge University Press:  29 March 2006

James E. Eninger  and
Walter G. Vincenti
James E. Eninger
Affiliation:
Department of Aeronautics and Astronautics, Stanford University Present address: TRW Systems Group, Redondo Beach, California.
Walter G. Vincenti
Affiliation:
Department of Aeronautics and Astronautics, Stanford University
Get access Rights & Permissions [Opens in a new window]

Abstract

A method due to Chester is applied to the theoretical study of resonant wave motion of a radiatively active gas. The inviscid non-conducting grey gas is confined between two infinite parallel walls, and a one-dimensional wave motion is driven by a sinusoidally varying input of black-body radiation from one of the walls. For sufficiently weak driving radiation, the motion can be described by the general solution of the classical wave equation (with the functional form of the solution still undetermined) plus a particular solution due to the driving radiation. When the driving is done at or near a resonant frequency, however, nonlinearities and perturbations in spontaneous emission from the gas must be taken into account before application of the boundary conditions. Such application then leads to a nonlinear integral equation governing the undetermined function in the general solution of the wave equation. This equation is solved numerically by the method of parametric differentiation.

In a frequency range around resonance and for a sufficiently weak relative level of spontaneous emission, the nonlinearities give rise to shock waves (numbering N at the Nth resonant frequency) that are repeatedly reflected at the walls. The perturbations in spontaneous emission give rise to damping, however, and for sufficiently high levels of emission the shock waves disappear. Specific results for various values of optical thickness and various relative levels of spontaneous emission are presented at frequencies in a range around the first resonance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 60 , Issue 1 , 21 August 1973 , pp. 161 - 186
Copyright
© 1973 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

Betchov, R. 1958 Nonlinear oscillations of a column of gas Phys. Fluids, 1, 3.Google Scholar
Chapman, G. T. 1970 Radiatively driven acoustic waves in a gas in a cylindrical tubetheory and experiment for the untuned condition. Ph.D. dissertation, Stanford University.
Chester, W. 1964 Resonant oscillations in closed tubes J. Fluid Mech. 18, 44.Google Scholar
Chester, W. 1968 Resonant oscillations of water waves. Proc. Roy. Soc. A 306, 5.Google Scholar
Chester, W. & Bones, J. A. 1968 Resonant oscillations of water waves. Proc. Roy. Soc. A 306, 23.Google Scholar
Collins, W. D. 1971 Forced oscillations of systems governed by one-dimensional nonlinear wave equations Quart. J. Mech. Appl. Math. 24, 129.Google Scholar
Compton, D. L. 1969 Radiatively driven acoustic waves in a gas in a cylindrical tubetheory and experiment at resonance. Ph.D. dissertation, Stanford University.
Cruikshank, D. B. 1969 An experimental investigation of finite-amplitude oscillations in a closed tube at resonance. Ph.D. dissertation, University of Rochester.
Eninger, J. E. 1971 Nonlinear resonant wave motion of a radiating gas. Ph.D. dissertation, Stanford University.
Jischke, J. C. & Baron, J. R. 1969 Application of the method of parametric differentiation to radiative gasdynamics A.I.A.A. J. 7, 1326.Google Scholar
Lighthill, M. J. 1956 Surveys in Mechanics (ed. G. K. Batchelor & R. M. Davies), pp. 250–351. Cambridge University Press.
Long, H. R. & Vincenti, W. G. 1967 Radiation-driven acoustic waves in a confined gas Phys. Fluids, 10, 1365.Google Scholar
Mortell, M. P. 1971 Resonant oscillations: a regular perturbation approach. J. Math. Phys. 12, 1069.Google Scholar
Rubbert, P. E. & Landahl, M. T. 1967 Solution of nonlinear flow problems through parametric differentiation Phys. Fluids, 10, 831.Google Scholar
Vincenti, W. G. & Kruger, C. H. 1965 Introduction to Physical Gas Dynamics. Wiley.