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An exact solution of linearized flow of an emitting, absorbing and scattering grey gas

Published online by Cambridge University Press:  29 March 2006

Ping Cheng  and
A. Leonard
Ping Cheng
Affiliation:
NASA-Ames Research Center, Moffett Field, California Present address: Department of Mechanical Engineering, University of Hawaii, Honolulu, Hawaii 96822.
A. Leonard
Affiliation:
Stanford University, Stanford, California
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Abstract

The governing equations for the problem of linearized flow through a normal shock wave in an emitting, absorbing, and scattering grey gas are reduced to two linear coupled integro-differential equations. By separation of variables, these equations are further reduced to an integral equation similar to that which arises in neutron-transport theory. It is shown that this integral equation admits both regular (associated with discrete eigenfunctions) and singular (associated with continuum eigenfunctions) solutions to form a complete set. The exact closed-form solution is obtained by superposition of these eigen-functions. If the gas downstream of a strong shock is absorption–emission dominated, the discrete mode of the solution disappears downstream. The effects of isotropic scattering are discussed. Quantitative comparison between the numerical results based on the exact solution and on the differential approximation are presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 45 , Issue 4 , 26 February 1971 , pp. 673 - 699
Copyright
© 1971 Cambridge University Press

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