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Application of dynamical systems theory to nonlinear combustion instabilities

Jahnke, Craig C. and Culick, F. E. C. (1994) Application of dynamical systems theory to nonlinear combustion instabilities. Journal of Propulsion and Power, 10 (4). pp. 508-517. ISSN 0748-4658.

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Two important approximations have been incorporated in much or the work with approximate analysis or unsteady motions in combustion chambers: 1) truncation of the series expansion to a finite number or modes, and 2) time-averaging. A major purpose or the present analysis is to investigate the limitations or those approximations. A continuation method Is used to determine the limit cycle behavior or the time-dependent amplitudes or the longitudinal acoustic modes in a combustion chamber. The results show that time-averaging works well only when the system Is slightly unstable. In addition, the stability boundaries predicted by the twomode approximation are shown to be artifacts of the truncation of the system. Systems of two, four. and six modes are analyzed and show that more modes are needed to analyze more unstable systems. For the six-mode approximation with an unstable second-mode, two birurcations are found to exist: 1) a pitchfork bifurcation leading to a new branch of limit cycles, and 2) a torus bifurcation leading to quasiperiodic motions.

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Additional Information:© 1994 by the American Institute of Aeronautics and Astronautics, Inc. Presented as Paper 93-0114 at the AIAA 31st Aerospace Sciences Meeting and Exhibit, Reno, NY, Jan. 11-14, 1993; received Aug. 5, 1993; revision received Nov. 4, 1993; accepted for publication Nov. 19.1993.
Group:Guggenheim Jet Propulsion Center, GALCIT
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Guggenheim Jet Propulsion Center376
Issue or Number:4
Record Number:CaltechAUTHORS:20101124-101555564
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Official Citation:Application of dynamical systems theory to nonlinear combustion instabilities pages 508-517 Jahnke, Craig C. (Clarkson Univ., Potsdam, NY);Culick, F. E. C. (California Inst. of Technology, Pasadena) Journal of Propulsion and Power (0748-4658) 1994 vol. 10 no. 4
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:21017
Deposited By: Ruth Sustaita
Deposited On:24 Nov 2010 18:50
Last Modified:03 Oct 2019 02:18

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