Reconstruction of acoustic transfer matrices by instationary computationalfluid dynamics

Thermoacoustic combustion instabilities are a frequently encountered proble m in the operation of combustion equipment. The "brute-force" application o f computational fluid dynamics to the analysis of thermoacoustic instabilit ies is estimated to be forbiddingly expensive for many systems of technical interest due to the high computational demands of a time- and space-accura te simulation of a (low Mach number) compressible reacting flow in a comple x geometry. Thermoacoustic systems can be modelled efficiently as networks of acoustic multi-ports, where each multi-port corresponds to a certain com ponent of the system, e.g., air or fuel supply, burner, flame, combustor an d suitable terminations, and is represented mathematically by its transfer matrix. For some multi-ports, the transfer matrix can be derived analytical ly from first principles: i.e., the equations of fluid motions and suitable approximations. However, the acoustic behavior of more complicated compone nts, e.g., a burner or a flame, has to be determined by empirical methods, by using a "black box" approach common in communications engineering. In th is work, a method is introduced which allows one to reconstruct the transfe r matrix of an acoustic two-port from an instationary computation of the re sponse of the two-port to an imposed perturbation of the steady state. Firs tly, from the time series data of fluctuating velocity and pressure on both sides of the two-port, the auto- and cross-correlations of the fluctuation s are estimated. Then, the unit impulse responses of the multi-port are com puted by inverting the Wiener-Hopf equation. Finally, the unit impulse resp onses are z-transformed to yield the coefficients of the transfer matrix. T he method is applied to the one-dimensional model of a heat source with tim e delay placed in a low-Mach-number compressible flow, for which an analyti cal description can be derived from first principles. Computational predict ions of the transfer matrix have been validated successfully against these analytical results. Furthermore, a comparison of the novel approach present ed in this paper with a method for computing the frequency response of a fl ame by Laplace-transforming its step response is carried out. (C) 2001 Acad emic Press.