Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-30T20:27:08.190Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Betchov, B. 1958 Non-linear oscillations of the column of a gas. Phys. Fluids 1, 205–212.Google Scholar
Chester, W. 1964 Resonant oscillations in closed tubes. J. Fluid Mech. 18, 44–64.Google Scholar
Cruikshank, D. B. 1972 Experimental investigation of finite-amplitude acoustic oscillations in a closed tube. J. Acoust. Soc. Am. 52, 1024–1036.Google Scholar
Galiev, Sh. U., Ilhamov, M. A. & Sadykov, A. V. 1970 Gas periodic shock waves. Izv. Akad. Nauk. SSR Mech. Jidcosty i Gasa 2, 57–66.Google Scholar
Keller, J. 1976 Resonant oscillations in closed tubes: The solution of Chester's equation J. Fluid Mech. 77, 279–304.Google Scholar
Klein, R. & Peters, N. 1988 Cumulative effects of weak pressure waves during the induction period of a thermal explosion in a closed cylinder. J. Fluid Mech. 187, 197–230.Google Scholar
Majda, A. & Rosales, R. 1984 Resonantly interacting, weakly nonlinear, hyperbolic waves. I. A single space variable. Stud. Appl. Maths. 71, 149–179.Google Scholar
Majda, A., Rosales, R. & Schonbek, M. 1988 A canonical system of integrodifferential equations arising in resonant nonlinear acoustics. Stud. Appl. Maths 79, 205–262.Google Scholar
Merkli, P. & Thomann, H. 1975 Thermoacoustic effects in a resonance tube. J. Fluid Mech. 70, 161–177.Google Scholar
Ockendon, H., Ockendon, J. R., Peake, M. R. & Chester, W. 1993 Geometrical effects in resonant gas oscillations. J. Fluid Mech. 77, 61–66.Google Scholar
Ochmann, M. 1985 Nonlinear resonant oscillations in closed tubes-An application of the averaging method. J. Acoust. Soc. Am. 32, 961–971.Google Scholar
Saenger, R. A. & Hudson, G. E. 1960 Periodic shock waves in resonating gas columns. J. Acoust. Soc. Am. 32, 961–971.Google Scholar
Wang, M. & Kassoy, D. R. 1990 Evolution of weakly nonlinear waves in a cylinder with a movable piston. J. Fluid Mech. 221, 23–52.Google Scholar
Wang, M. & Kassoy, D. R. 1995 Nonlinear oscillations in a resonant gas column: an initial-boundary-value study. SIAM J. Appl. Maths 55, 923–951.Google Scholar
Zaripov, R. G. & Ilhamov, M. A. 1976 Non-linear gas oscillations in a pipe. J. Sound Vib. 46, 245–257.Google Scholar