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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
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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

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