✍ Scribed by W. POLIFKE; A. PONCET; C.O. PASCHEREIT; K. DÖBBELING
No coin nor oath required. For personal study only.
Thermoacoustic combustion instabilities are a frequently encountered problem in the operation of combustion equipment. The &&brute-force'' application of computational #uid dynamics to the analysis of thermoacoustic instabilities is estimated to be forbiddingly expensive for many systems of technical interest due to the high computational demands of a time-and space-accurate simulation of a (low Mach number) compressible reacting #ow in a complex geometry. Thermoacoustic systems can be modelled e$ciently as networks of acoustic multi-ports, where each multi-port corresponds to a certain component of the system, e.g., air or fuel supply, burner, #ame, combustor and suitable terminations, and is represented mathematically by its transfer matrix. For some multi-ports, the transfer matrix can be derived analytically from "rst principles: i.e., the equations of #uid motions and suitable approximations. However, the acoustic behavior of more complicated components, e.g., a burner or a #ame, has to be determined by empirical methods, by using a &&black box'' approach common in communications engineering. In this work, a method is introduced which allows one to reconstruct the transfer matrix of an acoustic two-port from an instationary computation of the response of the two-port to an imposed perturbation of the steady state. Firstly, from the time series data of #uctuating velocity and pressure on both sides of the two-port, the auto-and cross-correlations of the #uctuations are estimated. Then, the unit impulse responses of the multi-port are computed by inverting the Wiener}Hopf equation. Finally, the unit impulse responses are z-transformed to yield the coe$cients of the transfer matrix. The method is applied to the one-dimensional model of a heat source with time delay placed in a low-Mach-number compressible #ow, for which an analytical description can be derived from "rst principles. Computational predictions of the transfer matrix have been validated successfully against these analytical results. Furthermore, a comparison of the novel approach presented in this paper with a method for computing the frequency response of a #ame by Laplace-transforming its step response is carried out.
2001 Academic Press
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