On the Existence and Stability of Limit Cycles for Transverse Acoustic Oscillations in a Cylindrical Combustion Chamber. 1: Standing Modes

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Abstract
Nonlinear pressure oscillations in combustion chambers have been studied using an approximate analysis which treats the unsteady motions as a collection of coupled nonlinear oscillators, each corresponding to an acoustic mode of the chamber. Based on spatial and temporal averaging of the conservation equations, the formulation provides a convenient means for analyzing the nonlinear behavior of acoustic wave motions. The work addresses the linear and nonlinear characteristics of transverse acoustic waves in a cylindrical chamber, with attention focused on the conditions for the existence and stability of limit cycles. As a result of the special structure of the equations, both general and precise conclusions can be reached. Explicit results are given for the special cases of two and three standing modes. Spinning wave motions will be treated in a subsequent paper.