Nonlinear corrections to Rott's equations of thermoacoustics
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The goal of this research project is to develop a method for examining the frequency components present a thermoacoustic device based upon perturbation analysis. This paper documents the evolution of the linear thermoacoustic solver developed in 1960s by Nicholas Rott to a higher order approximation of the thermoacoustic equations by the author. The method will be carried out to third order to provide a means to compute the nonlinear corrections to the fundamental mode. The method developed will utilize symmetries in the computational region to reduce the required solution to a one-dimensional problem along the axis of the resonator. The result of this project is a description of the method employed, the development of a tool for numerically computing the higher order terms in the perturbation scheme, and the impact of the perturbation terms on the output of the thermoacoustic device.