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Resonant oscillations in closed tubes: the solution of Chester's equation

Published online by Cambridge University Press:  11 April 2006

Jakob Keller
Jakob Keller
Affiliation:
Institut für Aerodynamik, Eidgenossiche Technische, Hochschule, Zurich, Switzerland
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Abstract

A closed tube is considered in which the oscillations of a gas column are driven by the sinusoidal motion of a piston. The case where the frequency of the gas column in the tube lies near one of its resonant frequencies is of special interest. The aim of this paper is to extend the theory of Chester (1964), who has given solutions in the inviscid case and for very small boundary-layer friction, to cases of frictional effects of arbitrary strength. This is done by means of a combination of analytical and numerical methods. Different methods are applied for different strengths of the boundary-layer friction. The cases where the influence of the Stokes boundary layer is either very strong or very weak are not especially difficult to treat. The main part of this paper considers cases of intermediate friction, i.e. when the shock strength has grown rather small owing to the influence of the Stokes boundary layer. To obtain an overall view of the phenomena which occur in the Merent regions, a number of solutions have been calculated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 77 , Issue 2 , 24 September 1976 , pp. 279 - 304
Copyright
© 1976 Cambridge University Press

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References

Betchov, R. 1958 Nonlinear oscillations of a column of gas. Phys. Fluids, 1, 205.Google Scholar
Chester, W. 1964 Resonant oscillations in closed tubes. J. Fluid Mech. 18, 44.Google Scholar
Cruikshank, D. B. 1972 Experimental investigations of finite-amplitude acoustic oscillations in a closed tube. J. Acoust. Soc. Am. 52, 1024.Google Scholar
Keller, J. 1975 Subharmonic non-linear acoustic resonances in closed tubes. Z. angew. Math. Phys. 26, 395.Google Scholar
Merkli, P. 1973 Theoretische und experimentelle thermoakustische Untersuchungen am kolbegetriebenen Resonrtnzrohr. Thesis no. 5151, ETH Zurich.
Saenger, R. A. & Hudson, G. E. 1960 Periodic shock waves in resonating gas columns. J. Acoust. Soc. Am. 32, 961.Google Scholar
Seymour, B. R. & Mortell, M. P. 1973 Resonant acoustic oscillations with damping: small rate theory. J. Fluid Mech. 58, 353.Google Scholar
Temkin, S. 1968 Nonlinear oscillations in a resonant tube. Phys. Fluids, 11, 960.Google Scholar