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Existence and stability of limit cycles for pressure oscillations incombustion chambers

Awad, E. and Culick, F. E. C. (1983) Existence and stability of limit cycles for pressure oscillations incombustion chambers. AIAA Papers, AIAA-1983-576 . American Institute of Aeronautics and Astronautics . http://resolver.caltech.edu/CaltechAUTHORS:20101209-094958257

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Abstract

In this paper, we discuss two problems. First, using a second order expansion in the pressure amplitude, some analytical results on the existence, stability and amplitude of limit cycles for pressure oscillations in combusticm chambers are presented. A stable limit cycle seems to be unique. The conditions for existence and stability are found to be dependent only on the linear parameters. The nonlinear parameter affects only the wave amplitude. The imaginary parts of the linear responses, to pressure oscillations, of the different processes in the chamber play an important role in the stability of the limit cycle. They also affect the direction of flow of energy among modes. In the absence of the imaginary parts, in order for an infinitesimal perturbation in the flow to reach a finite amplitude, the lowest mode must be unstable while the highest must be stable; thus energy flows from the lowest mode to the highest one. The same case exists when the imaginary parts are non-zero, but in addition, the contrary situation is possible. There are conditions under which an infinitesimal perturbation may reach a finite amplitude if the lowest mode is stable while the highest is unstable. Thus energy can flow "backward" from the highest mode to the lowest one. It is also shown that the imaginary parts increase the final wave amplitude. Second, the triggering of pressure oscillations in solid propellant rockets is discussed. In order to explain the triggering of the oscillations to a nontrivial stable: limit cycle, the treatment of two modes and the inclusion in the combustion response of either a second order nonlinear velocity coupling or a third order nonlinear pressure coupling seem to be sufficient.


Item Type:Report or Paper (Report)
Additional Information:© 1983, American Institute of Aeronautics and Astronautics. This work was supported by the California Institute of Technology, by the Air Force Office of Scientific Research, Grant No. AFOSR-80-0265, and by the Naval Weapons Center, Contract N 60530-82-C-0137.
Group:Guggenheim Jet Propulsion Center
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Other Numbering System NameOther Numbering System ID
Guggenheim Jet Propulsion CenterUNSPECIFIED
AIAA1983-576
Record Number:CaltechAUTHORS:20101209-094958257
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20101209-094958257
Official Citation:Existence and stability of limit cycles for pressure oscillations incombustion chambers CULICK, F. E. C., California Institute of Technology, Pasadena, CA AIAA-1983-576 American Institute of Aeronautics and Astronautics, Aerospace Sciences Meeting, 21st, Reno, NV, Jan 10-13, 1983. 19 p. Research supported by the California Institute of Technology
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:21258
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:17 Dec 2010 18:17
Last Modified:26 Dec 2012 12:44

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