Efficient Computation of Thermoacoustic Modes in Industrial Annular Combustion Chambers Based on Bloch-Wave Theory

Most annular combustors feature a discrete rotational symmetry so that the full configuration can be obtained by copying one burner-flame segment a certain number of times around the circumference. A thermoacoustic model based on the Helmholtz equation then admits special solutions of the so-called Bloch type that can be obtained by considering one segment only. We show that a significant reduction in computational effort for the determination of thermoacoustic modes can be achieved by exploiting this concept. The framework is applicable even in complex cases including an inhomogeneous temperature field and a frequency-dependent, spatially distributed flame response. A parametric study on a three-dimensional combustion chamber model is conducted using both the full-scale chamber simulation and a one-segment model with the appropriate Bloch-type boundary conditions. The results for both computations are compared in terms of mode frequencies and growth rates as well as the corresponding mode shapes. The same is done for a more complex industrial configuration. These comparisons demonstrate the benefits of the Bloch-wave based analysis.