Evaluating the impact of uncertainty in flame impulse response model on thermoacoustic instability prediction: A dimensionality reduction approach

The flame response to upstream velocity perturbations is properly described by a Finite Impulse Response (FIR) model. When combining an FIR model with acoustic tools to predict thermoacoustic modal growth rates, uncertainties contained in the FIR model coefficients would propagate through the acoustic model, inducing deviations of the modal growth rate from its nominal value. Therefore, an associated uncertainty quantification (UQ) analysis, which focuses on quantifying the impact of FIR model uncertainties on the modal growth rate prediction, is a necessity to obtain a more reliable thermoacoustic instability prediction. To address this UQ problem, our present work proposes an analytical strategy featuring (1) compactly summarizing the causal relationship between variations of FIR model coefficients and variations of modal growth rates; (2) Effectively shrinking the dimension of the UQ problem; (3) Requiring only negligible computational cost; (4) Involving no complex mathematical treatments. Our case studies yielded 5000 times faster yet highly accurate UQ analyses compared with reference Monte Carlo simulations, even though a significant level of FIR model uncertainty is present. The analytical approach brings additional benefits including (1) visualization of the process from the variations of FIR model coefficients to the variations of modal growth rate; (2) Easily-obtainable sensitivity measurement for each FIR model coefficient, which can help identify key mechanisms controlling the thermoacoustic instability; (3) New possibility for robust combustor design, i.e., to minimize the impact of FIR model uncertainty on the thermoacoustic instability prediction.