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The Two-Mode Approximation to Nonlinear Acoustics in Combustion Chambers. I. Exact Solution for Second Order Acoustics

Paparizos, Leonidas G. and Culick, F. E. C. (1989) The Two-Mode Approximation to Nonlinear Acoustics in Combustion Chambers. I. Exact Solution for Second Order Acoustics. Combustion Science and Technology, 65 (1-3). pp. 39-65. ISSN 0010-2202. http://resolver.caltech.edu/CaltechAUTHORS:20101203-081753345

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Abstract

The behavior of unsteady pressure fluctuations in combustion chambers is examined. An approximate method used in the derivation of the amplitude equations is based on the spatial and time domain averaging of the conservation equations, and follows the analytical framework introduced by Culick (1976a,b). The first order perturbation terms retained in the analysis correspond to linear contributions from the combustion processes, gas/particle interactions, mean flow and boundary conditions, as well as second order nonlinear gas dynamics terms. Further simplification of these equations is obtained by an appropriate change of variables. Following this step, the analysis based on two longitudinal modes is reduced to the solution of a three-dimensional system of nonlinear equations. This enables derivation of exact results for the existence, stability and the amplitude of the limit cycle, in the general case of frequency shifted periodic oscillations. Consideration is also given to the transfer of energy within the spectrum of the acoustic modes. In agreement with experimental observations, it is shown analytically that the preferred direction of energy transfer is from the lower to the higher acoustic modes. Validation of the results is accomplished by comparison with numerical results obtained when higher numbers of modes are treated. Finally, it is shown that combustion instabilities can be treated analytically using the center manifold theory.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1080/00102208908924041 DOIUNSPECIFIED
http://www.informaworld.com/10.1080/00102208908924041PublisherUNSPECIFIED
Additional Information:© 1989 Gordon and Breach Science Publishers, Inc. Received, 14 September, 1987; in final form 24 April, 1989. This investigation was sponsored by the Department of Navy, ONR Contract N0014-84-K-0434.
Group:Guggenheim Jet Propulsion Center
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Funding AgencyGrant Number
Department of the NavyN0014-84-K-0434
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Guggenheim Jet Propulsion CenterUNSPECIFIED
Record Number:CaltechAUTHORS:20101203-081753345
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20101203-081753345
Official Citation:The Two-Mode Approximation to Nonlinear Acoustics in Combustion Chambers I. Exact Solution for Second Order Acoustics Leonidas G. Paparizos; F. E. C. Culick Pages 39 – 65
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:21140
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:03 Dec 2010 16:45
Last Modified:26 Dec 2012 12:42

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