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Resonance gas oscillations in closed tubes

Published online by Cambridge University Press:  26 April 2006

A. Goldshtein ,
P. Vainshtein ,
M. Fichman  and
C. Gutfinger
A. Goldshtein
Affiliation:
Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
P. Vainshtein
Affiliation:
Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
M. Fichman
Affiliation:
Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
C. Gutfinger
Affiliation:
Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
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Abstract

The problem of gas motion in a tube closed at one end and driven at the other by an oscillating poston is studied theoretically. When the piston vibrates with a finite amplitude at the first acoustic resonance frequency, periodic shock waves are generated, travelling back and forth in the tube. A perturbation method, based on a small Mach number. M and a global mass conservation condition, is employed to formulate a solution of the problem in the form of two standing waves separated by a jump (shock front). By expanding the equations of motion in a series of a small parameter ε = M½, all hydrodynamic properties are predicted with an accuracy to second-order terms, i.e. to ε2. It is found that the first-order solution coincides with the previous theories of Betchov (1958) and Chester (1964), while additional terms predict a non-homogeneous time-averaged pressure along the tube. This prediction compares favourably with experimental results from the literature. The importance of the phenomenon is discussed in relation to different transport processes in resonance tubes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 322 , 10 September 1996 , pp. 147 - 163
Copyright
© 1996 Cambridge University Press

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