Burnley, Victor S. and Culick, Fred E. C. (1999) On the Energy Transfer between Transverse Acoustic Modes in a Cylindrical Combustion Chamber. Combustion Science and Technology, 144 (1-6). pp. 1-19. ISSN 0010-2202. http://resolver.caltech.edu/CaltechAUTHORS:20101118-135546896
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Most of the previous work on periodic limit cycles in linearly unstable combustors has been carried out for the case of purely longitudinal classical modes whose natural frequencies are integral multiples of the fundamental. The contrary situation of transverse modes in a cylindrical chamber has led to unexpectedly high amplitudes in the periodic limit cycles, the reasons for which have not been thoroughly understood. Some results reported here serve to clarify the two chief consequences of nonlinear coupling between modes: the first is obvious, for the nonlinear coupling causes excitation of higher modes, and hence energy transfer, when, say, the first mode is unstable; the second has long been known, namely that the coupling must also cause shifts of the frequencies from their linear non-integral values to the integral values required for a periodic limit cycle, but part of the significance of this property has been unclear. In particular, the necessity for the frequency shifts reduces the efficiency at which energy is transfered between modes and leads to higher amplitude oscillations. Our analysis shows that the larger are the differences of the linear frequencies from perfect integral values, the larger are the amplitudes in the limit cycle. These conclusions suggest a way to reduce the amplitudes of transverse oscillations, and examples are presented showing this possibility.
|Additional Information:||© 1999 OPA (Overseas Publishers Association) N.V. This work was sponsored partly by the United States Air Force and partly by the Caltech Multidisciplinary University Research Initiative under ONR Grant No. N00014-95-1-1338, Program Manager Dr. Judah Goldwasser.|
|Group:||Guggenheim Jet Propulsion Center|
|Subject Keywords:||Instability and Pulsating and Unsteady Combustion; Liquid Propellant Rockets; Fluid Dynamics Aspects in Combustion|
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|Official Citation:||On the Energy Transfer between Transverse Acoustic Modes in a Cylindrical Combustion Chamber Victor S. Burnley; Fred E. C. Culic Combustion Science and Technology, 1563-521X, Volume 144, Issue 1, 1999, Pages 1 – 19|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||02 Dec 2010 23:08|
|Last Modified:||26 Dec 2012 12:39|
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