The work reported here describes a portion of the development of a finite element model of thermoacoustic oscillations in ducted flows, including three dimensional geometries and nonuniform mean flows with steady heat addition. The thermoacoustic problem is not modeled by a form of the convected wave equation but instead by the conservation equations in primitive form. In this paper the three-dimensional model is reduced to one dimension, applicable to a uniform geometry, but allowing an axially nonuniform flow with sharp gradients in temperature, density, and Mach number. The steady mean flow is computed as a Rayleigh flow. Calculations are shown for standing waves in several flows with different heating rates and acoustically rigid upstream and downstream conditions to emphasize the effect of the heat input on the modal structure in the cavity. Limited comparisons are made to relevant experimental work available in the literature. It is found that some of the features of modal structure in unstable oscillations reported in the literature can be reproduced using the FEM model.


Mechanical and Aerospace Engineering

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Open Access

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Article - Conference proceedings

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Publication Date

01 Jan 1996