Development of Thermoacoustic Network Model Using Transfer Matrix Method

In this paper, one-dimensional thermoacoustic model based on the transfer matrix approach is developed for studying combustion instabilities in a gas turbine combustor. Two different transfer functions are introduced for the closed-loop feedback system analysis. One is acoustic transfer function, which is derived from the conservation equations such as mass, momentum, and energy for a given problem. The other is flame transfer function, which quantifies the heat release response in the combustor to the incoming velocity fluctuations. Combining the acoustic and flame transfer functions, one can analyze the combustion instability in the closed-loop system. The calculated thermoacoustic instability behavior using the current model matches well with the experimental results in the literature.