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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

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