Computation of acoustic transfer matrices of swirl burner with finite element and acoustic network method

For a gas turbine combustor, an accurate transfer matrix of the burner is an essential prerequisite for stability analysis of combustion instability. This paper describes two numerical methods for the computation of burner transfer matrix (BTM) derived from the experimental method and an experimental validation. In the numerical study, Helmholtz equation with the boundaries of plane wave radiation is solved by employing a finite element code. As alternative to the finite element method (FEM), the BTM is also assessed through using acoustic network method (ANM). In the experimental study, complex acoustic pressure at the combustion chamber firstly can be evaluated based on multi-microphone method (MMM) from three measurement points in the plenum and BTM calculated by the FEM or ANM, then be compared with the measurement for the BTM validation at resonance frequency self-excited by the combustion instability of the combustor consisting of a supply plenum, a premixed swirl-stabilized burner and a combustor chamber. The validation shows that the three calculated values are essentially the same as the experimental data, when resonance frequency approximately equal to194, 243 and 290Hz. The results indicate that acoustic behavior of the complex swirl burner can be evaluated successfully by mapping the burner to a network consisting of simple elements.