Computation of transfer matrices for gas turbine combustors including acoustics/flame interaction

A new method for the computation of acoustic transfer matrices for gas turbine combustor elements is presented. The approach is able to represent both the passive combustor acoustics and the interaction with the reaction zone in a flame. It basically transfers the multimicrophone method, well-known for the determination of four-pole parameters in the experimental field, to numerical simulations. Different acoustically excited test states are simulated in the frequency-domain, employing a finite element code. From these calculations, the amplitudes of the upstream and downstream travelling waves on both sides of the element in question can be obtained, which consequently allows the computation of the transfer matrix. The influence of the flame enters the simulation through a source term, describing the heat of reaction as a function of acoustic quantities. This relation would, for example, be the result of experiments providing the dependence of the fluctuating heat release in terms of the burner exit velocity fluctuations. Such experiments turn out to be much easier to conduct than a direct experimental determination of a transfer matrix, which lacks accuracy due to the extremely noisy environment of a combustion system. The simulation therefore delivers a very useful means to obtain accurate transfer matrices for real and technically relevant combustor elements, and thus to give valuable input for the design and improvement of combustors with respect to combustion instabilities. The method is demonstrated by showing the determination of the four-pole parameters of a swirl burner.