Identification of High-Frequency Transverse Acoustic Modes In Multi-Nozzle Can Combustors
Lieuwen, Timothy C.
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High frequency thermoacoustic instabilities are problematic for lean-premixed gas turbines. Identifying which acoustic mode is being excited is important, in that it provides insight into potential mitigation measures, as well as input into mechanical stress/lifing calculations. However, the frequency spacing between modes becomes significantly narrower for high frequency instabilities in a can combustor. This makes it difficult to distinguish between the modes (e.g., the first transverse mode vs. a higher order axial/mixed mode) based upon frequency calculations alone, which inevitably have uncertainties in boundary conditions, temperature profiles, and combustion response. This paper presents a methodology to simultaneously identify the acoustic mode shapes in the axial and azimuthal directions from acoustic pressure measurements. Multiple high temperature pressure transducers, located at distinct axial and azimuthal positions, are flush mounted in the combustor wall. The measured pressure oscillations from each sensor are then used to reconstruct the pressure distributions by using a least squares method in conjunction with a solution of a three dimensional wave equation. In order to validate the methodology, finite element method (FEM) with estimated post-flame temperature is used to provide the candidate frequencies and corresponding mode shapes. The results demonstrate the reconstructed mode shapes and standing/spinning character of transverse waves, as well as the associated frequencies, both of which are consistent with the FEM predictions. Nodal line location was also extracted from the experimental data during the instabilities in the pressure data. It was found that the line was wandering at fixed location for one mode, whereas the line was rotating in one direction for the other mode. This paper details these experimental measurements and analysis methodologies for high frequency modal identification in self-excited can combustors.