Analytical solutions for the acoustic field in thin annular combustion chambers with linear gradients of cross-sectional area and mean temperature

Combustion instability frequently occurs in propulsion and power generation systems. It is characterized by large-amplitude acoustic oscillations leading to undesirable consequences. Designing a stable combustor by predicting its stability characteristics is therefore essential. This study centers upon modeling a straight one-dimensional combustor with an acoustically compact heat source, low Mach numbers, and different end point conditions. To predict the stability characteristics, we examine six combustor configurations (open–closed, closed–closed, open–choked, closed–choked, open–open, and closed–open). A Galerkin expansion technique is implemented to capture the acoustic disturbances. The unsteady heat release is modeled using an N−τ formulation. The results show that steepening of the mean temperature gradient causes the eigenfrequency associated with an open outlet to increase more rapidly than that of a choked nozzle. Compared to a choked boundary, an open outlet generates higher eigenfrequencies and lower sound energy when coupled with an open inlet. Conversely, it triggers lower eigenfrequencies and higher sound energy using a closed inlet. The maximum possible growth of sound energy, Gmax, remains positively correlated with the inlet temperature, interaction index N, and inlet Mach number, but inversely proportional to the temperature gradient. The heat source extrema leading to the most and least amplified system energy seem to shift upstream, when the mean temperature gradient is successively increased. Their coordinates are similar in half-open tubes and exhibit a converse relation between the open–open and closed–choked tubes. At sufficiently low Mach numbers, the choked and closed outlets show equivalence in acoustic frequencies, transient energy evolution, and optimal heat source locations.

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Analytical solutions for the acoustic field in thin annular combustion chambers with linear gradients of cross-sectional area and mean temperature

Cited by 4 publications

References 36 publications

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