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Reduced-order modeling and dynamics of nonlinear acoustic waves in a combustion chamber

Ananthkrishnan, N. and Deo, Shardul and Culick, Fred E. C. (2005) Reduced-order modeling and dynamics of nonlinear acoustic waves in a combustion chamber. Combustion Science and Technology, 177 (2). pp. 221-247. ISSN 0010-2202 . http://resolver.caltech.edu/CaltechAUTHORS:20110207-072124993

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Abstract

For understanding the fundamental properties of unsteady motions in combustion chambers, and for applications of active feedback control, reduced-order models occupy a uniquely important position. A framework exists for transforming the representation of general behavior by a set of infinite-dimensional partial differential equations to a finite set of nonlinear second-order ordinary differential equations in time. The procedure rests on an expansion of the pressure and velocity fields in modal or basis functions, followed by spatial averaging to give the set of second-order equations in time. Nonlinear gasdynamics is accounted for explicitly, but all other contributing processes require modeling. Reduced-order models of the global behavior of the chamber dynamics, most importantly of the pressure, are obtained simply by truncating the modal expansion to the desired number of terms. Central to the procedures is a criterion for deciding how many modes must be retained to give accurate results. Addressing that problem is the principal purpose of this paper. Our analysis shows that, in case of longitudinal modes, a first mode instability problem requires a minimum of four modes in the modal truncation whereas, for a second mode instability, one needs to retain at least the first eight modes. A second important problem concerns the conditions under which a linearly stable system becomes unstable to sufficiently large disturbances. Previous work has given a partial answer, suggesting that nonlinear gasdynamics alone cannot produce pulsed or 'triggered' true nonlinear instabilities; that suggestion is now theoretically established. Also, a certain form of the nonlinear energy addition by combustion processes is known to lead to stable limit cycles in a linearly stable system. A second form of nonlinear combustion dynamics with a new velocity coupling function that naturally displays a threshold character is shown here also to produce triggered limit cycle behavior.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1080/00102200590900219 DOIUNSPECIFIED
http://www.informaworld.com/10.1080/00102200590900219PublisherUNSPECIFIED
Additional Information:© 2005 Taylor & Francis Inc. Received 18 November 2003; accepted 29 July 2004. This work was supported in part by the California Institute of Technology, partly by the Caltech Multidisciplinary University Research Initiative under Grant No. N00014-95-1- 1338 (Dr. Judah Goldwasser, Program Manager), partly by the Department of Energy Advanced Gas Turbine Systems Research (AGTSR) Program under Subcontract No. 98-02- SR072 (Dr. Larry Golan, Program Manager), and partly by the Air Force Office of Scientific Research under Grant No. F49620-99-1-0118 (Dr. Mitat Birkan, Program Manager).
Group:Guggenheim Jet Propulsion Center
Funders:
Funding AgencyGrant Number
Caltech Multidisciplinary University Research InitiativeN00014-95-1-1338
Department of Energy (DOE) Advanced Gas Turbine Systems Research (AGTSR)98-02-SR072
Air Force Office of Scientific Research (AFOSR)F49620-99-1-0118
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Other Numbering System NameOther Numbering System ID
Guggenheim Jet Propulsion Center UNSPECIFIED
Record Number:CaltechAUTHORS:20110207-072124993
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20110207-072124993
Official Citation:REDUCED-ORDER MODELING AND DYNAMICS OF NONLINEAR ACOUSTIC WAVES IN A COMBUSTION CHAMBER Authors: N. Ananthkrishnana; Shardul Deoa; Fred E. C. Culick
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22031
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:07 Feb 2011 16:23
Last Modified:26 Dec 2012 12:54

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