Modeling transfer matrices of premixed flames and comparison with experimental results

A combined analytical/experimental investigation of the thermoacoustic properties of a gas turbine burner with a premixed, turbulent, swirl-stabilized flame is presented. In an enclosed flame, an interaction occurs between acoustic fluctuations and non-steady heat release, which may lead to thermoacoustic instabilities. This interaction may be characterized by the transfer 'matrix of the burner with flame. The transfer matrix describes the coupling between fluctuations of acoustic pressure and velocity on both sides of burner and flame, incorporating also the effects of heat release fluctuations on the acoustic quantities. The transfer matrix has been modeled and validated with experimental results. For the burner, an analytical model is proposed, which is based on the Bernoulli equation for instationary flow through compact elements. The model is based on the Rankine-Hugoniot relations across a thin heat source. The fundamental assumption underlying the model is that acoustic fluctuations cause modulations of fuel concentrations at the fuel injector, which result, after a certain time lag, in a fluctuating heat release rate at the flame. The oscillating heat release couples with pressure and velocity fluctuations in the combustion chamber, thereby to creating a feedback loop between combustor acoustics and flame dynamics which may result in self-excited combustion instability. The transfer matrix of the burner with flame has been determined experimentally in an atmospheric combustion test facility. The test rig was equipped with loudspeakers and microphones in order to measure Notations: the response to an acoustical excitation. Our new flame model shows to be in agreement with the measured results.