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Resonant acoustic oscillations with damping: small rate theory

Published online by Cambridge University Press:  29 March 2006

Brian R. Seymour  and
Michael P. Mortell
Brian R. Seymour
Affiliation:
Department of Mathematics, New York University
Michael P. Mortell
Affiliation:
Center for the Application of Mathematics, Lehigh University Present address: Department of Mathematical Physics, University College, Cork, Ireland.
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Abstract

A gas in a tube is excited by a reciprocating piston operating at or near a resonant frequency. Damping is introduced into the system by two means: radiation of energy from one end of the tube and rate dependence of the gas. These define a lumped damping coefficient. It is shown that in the small rate limit the signal in the periodic state suffers negligible distortion in one travel time, and hence its propagation according to acoustic theory is valid. The shape of the signal is determined by a nonlinear ordinary differential equation. The small rate condition provides a test of the applicability of the theory to given experimental conditions. When there is no damping, shocks are a feature of the flow for frequencies in the resonant band. For a given amount of damping an upper bound on the piston acceleration which ensures shockless motion is given. The resonant band is analysed for both damped and undamped cases. The predictions of the theory are compared with experiment.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 2 , 17 April 1973 , pp. 353 - 373
Copyright
© 1973 Cambridge University Press

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