Uncertainty quantification of combustion noise by generalized polynomial chaos and state-space models

Abstract

Many physical systems are subject to uncertainty in operating regimes, boundary conditions, and physical parameter values. The generalized polynomial chaos (gPC) framework offers methods to represent and propagate uncertainties through the governing equations by means of spectral expansions in random space. The present study combines intrusive gPC with a state-space thermoacoustic model to account for uncertainties in combustion noise prediction of confined flames. The acoustic waves, flame response and acoustic reflection coefficients are modeled as stochastic variables and projected onto a finite set of gPC basis functions. By solving the resulting set of equations once, it is possible to determine probability density functions of acoustic quantities at each node of the discretized domain. Results of the proposed method are satisfactorily validated against Monte Carlo simulation and compared with experiments. We show that the contribution of the flame response uncertainties (magnitude and phase) to the sound pressure level produced by combustion is particularly important within a frequency range, which is close to the frequency characterizing the intrinsic thermoacoustic feedback loop. Additionally, we demonstrate the simplicity of performing global sensitivity analysis once the gPC coefficients are available. Furthermore, non-intrusive gPC is applied to the deterministic state-space model of the system and computational costs are compared with those of the intrusive gPC counterpart.