Flame transfer function measurement and instability frequency prediction using a thermoacoustic model

The dynamic response of a turbulent premixed flame to an acoustic velocity perturbation was experimentally determined in a lean-premixed, swirl-stabilized, lab-scale gas turbine combustor. Fuel was injected far upstream of a choked inlet to eliminate equivalence ratio oscillations. A siren-type modulation device was used to provide acoustic perturbations at the forcing frequency of 100-400 Hz. To measure global heat release rate, OH*, CH*, and CO₂* chemiluminescence emissions were used. The two-microphone method was utilized to estimate inlet velocity fluctuations, and it was calibrated by direct measurements using a hot wire anemometer under cold-flow conditions. Gain of the flame transfer function (FTF) shows a low pass filter behavior, and it is well-fitted by a second-order model. Phase difference increases quasi-linearly with the forcing frequency. Using the n-τ formulation, gain and phase of FTF were incorporated into an analytic thermoacoustic model in order to predict instability frequencies and corresponding modal structures. Self-excited flame response measurements were also performed to verify eigenfrequencies predicted by the thermoacoustic model. Instability frequency predicted by the thermoacoustic model is supported by experimental results. Two instability frequency bands were measured in the investigated gas turbine combustor at all operating conditions: f ∼ 220 Hz and f ∼ 350 Hz. Results show that the self-excited instability frequency of f ∼ 220 Hz results from the fact that the flames amplify flow perturbations with f = 150-250 Hz. This frequency range was observed in the flame transfer function measurements. The other instability frequency of f ∼ 350 Hz occurs because the whole combustion system has an eigenfrequency corresponding to the 1/4-wave eigenmode of the mixing section. This was analytically and experimentally demonstrated. Results also show that the flame length, L _CH*max, plays a critical role in determining self-induced instability frequency.