Singular spectrum analysis of transient heat release in a premixed swirling combustor

Preprint. Turbulent lean premixed swirling flames are normally accompanied with thermoacoustic issues. Analysis of the heat release rate time series generated by large eddy simulation (LES) is an effective way to determine the flame dynamics during combustor design. In this study, singular spectrum analysis (SSA) is employed to investigate the non-statistically stationary, short, and noisy time series of heat release rate (HRR) in a premixed swirling combustor. This method constructs the HRR trajectory matrix and performs singular value decomposition (SVD) to find decomposed modes of HRR. The flame response of the decomposed SSA modes is defined and identified by the transfer path response (TPR) method. The intrinsic connection between SSA modes and flame structures is further revealed by the dynamic mode decomposition (DMD) method. Results indicate that the reconstructed series by SSA is able to efficiently track the original heat release rate time series. Distinct evolution trends and frequency responses could be found in SSA modes. The heat release rate response of single or grouped SSA modes to the inlet excitation can be reflected more accurately by the TPR analysis than the traditional flame transfer function (FTF) method. In addition, the SSA modes with specific frequencies find the corresponding hydrodynamic structures in DMD analysis. Based on the DMD analysis, frequency responses in SSA-TPR results may be caused by the shear layer instabilities, low-frequency flame motions, and flame superposition by swirl.