Matveev, K. I. and Culick, F. E. C. (2003) A study of the transition to instability in a Rijke tube with axial temperature gradient. Journal of Sound and Vibration , 264 (3). pp. 689-706. ISSN 0022-460X. http://resolver.caltech.edu/CaltechAUTHORS:20101118-102239874
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A horizontal Rijke tube with an electric heat source is a system convenient for studying the fundamental principles of thermoacoustic instabilities both experimentally and theoretically. Given the long history of the device, there is a surprising lack of accurate data defining its behavior. In this work, the main system parameters are varied in a quasi-steady fashion in order to find stability boundaries accurately. The chief purposes of this study are to obtain precise values of the system parameters at the transition to instability with specified uncertainties and to determine how well the experimental results can be explained with existing theory. Measurement errors are reported, and the influence of experimental procedures on the results is discussed. A form of hysteresis effect at stability boundaries has been observed. Mathematical modelling is based on a thermal analysis determining the temperature of the heater and the temperature field in the air inside the tube, which, consequently, affects acoustical mode shapes. Solutions of the linearized wave equation for a non-uniform medium, including losses and a heat source term, determine the stability properties of the eigen modes. Calculated results are compared with experimental data and with results of the modelling based on the common assumption of a constant temperature in the tube. The mathematical model developed here can be applied to designing thermal devices with low Mach number flows, where thermoacoustic issue is a concern.
|Additional Information:||© 2002 Elsevier Science Ltd. Received 16 January 2002; accepted 10 July 2002. ; Available online 8 April 2003. Mr. Dylan Hixon, formerly a graduate student at Caltech, designed and constructed the original version of the apparatus used in this work. The authors wish to thank Dr. Winston Pun and Mr. Steve Palm for the help with recent improvements of the apparatus, instrumentation, and data processing. 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. Daniel Fant & Dr. Larry Golan, Program Managers), and partly by the Air Force Office of Scientific Research (AFOSR) under Grant No. F49620-99-1-0118 (Dr. Mitat Birkan, Program Manager).|
|Group:||Guggenheim Jet Propulsion Center|
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|Official Citation:||A study of the transition to instability in a Rijke tube with axial temperature gradient Original Research Article Pages 689-706 K. I. Matveev, F. E. C. Culick|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||18 Nov 2010 18:38|
|Last Modified:||26 Dec 2012 12:39|
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