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On the Existence and Stability of Limit Cycles for Longitudinal Acoustic Modes in a Combustion Chamber

Awad, E. and Culick, F. E. C. (1986) On the Existence and Stability of Limit Cycles for Longitudinal Acoustic Modes in a Combustion Chamber. Combustion Science and Technology, 46 (3-6). pp. 195-222. ISSN 0010-2202. doi:10.1080/00102208608959800.

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Unsteady motions in combustion chambers have previously been treated with an approximate analysis in which an acoustic field is represented as a collection of coupled nonlinear oscillators constructed in one-to-one correspondence to the acoustic modes. Two parameters characterize the linear behavior of each oscillator; a single parameter arises from the nonlinear acoustics carried out to second order in small fluctuations. The formal results are used here as the basis for studying the existence and stability of limit cycles for longitudinal modes. Owing to the special structure of the equations, explicit and precise conclusions can be reached. Existence and stability depend only on the parameters defining the linear motions. The nonlinear gasdynamics influence the amplitudes of motion in the limit cycle. At least one of the acoustic modes must be linearly unstable to produce a nontrivial limit cycle. Generally, energy flows both up and down among the modes, but there are exceptional cases when limit cycles exist only if the fundamental mode is unstable. Explicit results are given for the special cases of two and three modes; the analysis is extendible to any number of modes.

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Additional Information:© 1986 Gordon and Breach Science Publishers, Inc. Received April 8, 1985; in final form July 8, 1985. This work was supported partly by the California Institute of Technology, partly by the Air Force Office of Scientific Research, Grant No. AFOSR-80-G-0137, and partly by the Department of the Navy, ONR Contract NOOO14-84-K-0434.
Group:Guggenheim Jet Propulsion Center, GALCIT
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)AFOSR-80-G-0137
Department of NavyNOOO14-84-K-0434
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Other Numbering System NameOther Numbering System ID
Guggenheim Jet Propulsion CenterUNSPECIFIED
Issue or Number:3-6
Record Number:CaltechAUTHORS:20101201-083223351
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Official Citation:Combustion Science and Technology Awad, E., Culick, F. E. C. On the Existence and Stability of Limit Cycles.for Longitudinal Acoustic Modes in a Combustion Chamber 1986, vol.46, #3, pp.195-222
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:21084
Deposited By: Ruth Sustaita
Deposited On:01 Dec 2010 17:18
Last Modified:09 Nov 2021 00:05

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