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Nonlinear behavior of acoustic waves in combustion chambers—I

Culick, F. E. C. (1976) Nonlinear behavior of acoustic waves in combustion chambers—I. Acta Astronautica, 3 (9). pp. 715-734. ISSN 0094-5765. http://resolver.caltech.edu/CaltechAUTHORS:20101217-100432116

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Abstract

This paper is concerned with the general problem of the nonlinear growth and limiting amplitude of acoustic waves in a combustion chamber. The analysis is intended to provide a formal framework within which practical problems can be treated with a minimum of effort and expense. There are broadly three parts. First, the general conservation equations are expanded in two small parameters, one characterizing the mean flow field and one measuring the amplitude of oscillations, and then combined to yield a nonlinear inhomogeneous wave equation. Second, the unsteady pressure and velocity fields are expressed as syntheses of the normal modes of the chamber, but with unknown time-varying amplitudes. This procedure yields a representation of a general unsteady field as a system of coupled nonlinear oscillators. Finally, the system of nonlinear equations is treated by the method of averaging to produce a set of coupled nonlinear first order differential equations for the amplitudes and phases of the modes. These must be solved numerically, but results can be obtained quite inexpensively. Subject to the approximations used, the analysis is applicable to any combustion chamber. The most interesting applications are probably to solid rockets, liquid rockets, or thrust augmentors on jet engines. The discussion of this report is oriented towards solid propellant rockets.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/0094-5765(76)90107-7DOIUNSPECIFIED
Additional Information:© 1976, Pergamon Press. Received 25 August 1975; revised 4 March 1976. Available online 26 February 2003. This work was supported partly by Hercules, Inc., Magna, Utah; by the Aerojet Solid Propulsion Co., Sacramento, California; and by the National Aeronautics and Space Administration under the Jet Propulsion Laboratory Contract NAS 7-100. Manuscript received at ASME Headquarters December 2, 1974. Paper No. 75-GT-40.
Group:Guggenheim Jet Propulsion Center
Funders:
Funding AgencyGrant Number
Hercules, Inc.UNSPECIFIED
Magna, UtahUNSPECIFIED
Aerojet Propulsion Co. UNSPECIFIED
NASA/JPLNAS 7-100
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Guggenheim Jet Propulsion CenterUNSPECIFIED
ASME 75-GT-40
Record Number:CaltechAUTHORS:20101217-100432116
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20101217-100432116
Official Citation:Culick, F. E. C. "Nonlinear behavior of acoustic waves in combustion chambers--I." Acta Astronautica 3(9-10): 715-734.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:21422
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:20 Dec 2010 19:42
Last Modified:26 Dec 2012 12:46

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