Validation of flame transfer function reconstruction for perfectly premixed swirl flames

The introduction of lean premix combustion increases the susceptibility of the combustor to thermoacoustic instabilities. To control these instabilities, information about the dynamic behavior of the combustion process is necessary. The flame transfer function offers one possibility to describe the dynamic behavior of the combustion process. It relates velocity fluctuations through the burner to an overall heat release fluctuation caused by the flame. As the transfer function for turbulent premix swirl flames can not be derived accurately from first principles, an alternative approach is needed. This paper introduces and validates a method, based on computational fluid dynamics (CFD), to reconstruct flame transfer functions. A transient simulation of the turbulent reacting flow is performed with broad band excitation of the flow variables on the boundaries. On the basis of the resulting time series for velocity and heat release, the transfer function of the flame is reconstructed by application of a system identification procedure based on the Wiener-Hopf equation. This method is applied to a lean perfectly premixed swirl burner. The resulting transfer function is validated with experimental data up to frequencies of f = 400 Hz. Good qualitative agreement is observed between the two approaches. Remarkably, the absolute value of the flame transfer function (the 'gain' of the flame) is found to be larger than unity over a range of frequencies, even though fluctuations of heat release and velocity are normalized with their mean flow values. To gain insight into this phenomenon, the dynamic behavior of the flame is investigated in detail. This concerns in particular the interaction of velocity, heat release fluctuations, the swirl number, and fluctuations of flame position and shape. Instead of broad band excitation, single frequency excitation is applied on the boundary for these investigations. It is found that swirl number fluctuations are convected into the flame. At the frequency where the wavelength of those fluctuations agrees with the length scale of the flame, unburned gases accumulate in the combustor. The excess heat is released periodically, which causes the overshoot in the absolute value of the flame transfer function.