Paschereit O., Moeck J., Bothien M.

Modelling the acoustic field in confined geometries is a crucial task for the prediction and control of thermoacoustic instabilities in gas turbine combustors. The traditional approach, making use of relations for the acoustic wave propagation in frequency domain, has proven its usefulness in stability analysis and control design. However, it suffers from certain drawbacks. Assessing stability characteristics requires the solution of transcendental dispersion relations which becomes a nontrivial task with growing system complexity. In addition to that, time-domain simulations of the combustion chamber’s acoustic field based on the traditional frequency domain relations are not feasible. This is due to the fact that parts of the system model are described by dynamics of infinite order, e.g. the simple duct or an n-tau flame. Low-dimensional state-space models do not suffer from these disadvantages. Thermoacoustic stability analysis only requires the solution of a matrix eigenvalue problem and time-domain simulations and the incorporation of nonlinearities become a much easier task. The state-space approach is applied to thermoacoustic model systems and results are compared to frequency domain calculations and experimental data.