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The linearized treatment of general forced gas oscillations in tubes

Published online by Cambridge University Press:  19 April 2006

Peter A. Monkewitz
Peter A. Monkewitz
Affiliation:
Institute of Aerodynamics, Federal Institute of Technology (ETH), Zürich, Switzerland Present address: Department of Aerospace Engineering, University of Southern California, Los Angeles.
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Abstract

A general linear theory is presented to describe oscillatory flows of gases and liquids in a tube of circular cross-section, including the effects of radial and tangential pressure gradients as well as the temperature. The basic equations are solved by separation of variables. The resulting eigenvalue equation is extensively discussed whereby the splitting of the eigenvalues into ‘bands’ is obtained in a natural way. A systematic analysis of a number of simplified cases leads to analytic approximations for the eigenvalues over an extended domain of parameter variation (frequency, friction) so that a complete survey of all the eigenvalues is established. Then the problem of satisfying simultaneously arbitrary end-conditions for all flow variables with the obtained bands of eigenfunctions is formulated in a way to allow the application of Galerkin's method. Finally the theory is applied to a few examples of ‘end-layers’ and radial resonance, which cannot be treated by previous theories.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 91 , Issue 2 , 23 March 1979 , pp. 357 - 397
Copyright
© 1979 Cambridge University Press

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