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Nonlinear self-excited acoustic oscillations within fixed boundaries

Published online by Cambridge University Press:  20 April 2006

Jakob J. Keller
Jakob J. Keller
Affiliation:
Brown Boveri Research Centre, CH-5405 Baden-Dättwil. Switzerland
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Abstract

In §1 a brief discussion of the general problem of self-excited acoustic oscillations within fixed boundaries is given. I n §2 a second-order analysis is developed for the special case of rectangular cavities. A nonlinear wave equation is derived for essentially arbitrary boundary conditions. The analysis can be extended to other cavity geometries provided that the first-order solutions can be expressed in closed form. Various applications of the analysis are discussed in §3. It turns out that two-dimensional problems of self-excited oscillations generally lead to nonlinear equations containing terms with a time lag. It is anticipated that the time lag (rather than viscous effects or sound radiation) represents the key to a fundamental understanding of the character of the oscillations and the variety of modes appearing in self-excited resonators.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 123 , October 1982 , pp. 267 - 281
Copyright
© 1982 Cambridge University Press

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References

Chester, W. 1964 Resonant oscillations in closed tubes. J. Fluid Mech. 18, 44.Google Scholar
Crocco, L. & Cheng, S. I. 1956 Theory of combustion instability in liquid propellant rocket motors. AGARDograph no. 8.Google Scholar
Chu, B. T. 1963 Analysis of a self-sustained nonlinear vibration in a pipe containing a heater. Phys. Fluids 6, 1638.Google Scholar
Keller, J. J. 1976a Resonant oscillations in closed tubes: the solution of Chester's equation. J. Fluid Mech. 77, 279.Google Scholar
Keller, J. J. 1976b Third order resonances in closed tubes. Z. angew. Math. Phys. 27, 303.Google Scholar
Keller, J. J. 1977 Resonant oscillations in open tubes. Z. angew. Math. Phys. 28, 237.Google Scholar
Keller, J. J. 1978a Nonlinear self-excited acoustic oscillations. Z. angew. Math. Phys. 29, 934.Google Scholar
Keller, J. J. 1978b A note on nonlinear acoustic resonances in rectangular cavities. J. Fluid Mech. 87, 299.Google Scholar
Mitchell, C. E. 1967 Axial mode shock wave combustion instability in liquid propellant rocket engines. Princeton University Dept. of Aerospace and Mech. Sci. Tech. Rep. no. 798 (NASA CR-72259).Google Scholar
Mitchell, C. E., Crocco, L. & Sirignano, W. A. 1969 Nonlinear longitudinal instability in rocket motors with concentrated combustion. Combust. Sci. Tech. 1, 35.Google Scholar
Mortell, M. P. & Seymour, B. R. 1973 The evolution of a self-sustained oscillation in a nonlinear continuous system. Trans. A.S.M.E. E: J. Appl. Mech. 40, 53.Google Scholar