From Pressure Time Series Data to Flame Transfer Functions: A Framework for Perfectly-Premixed Swirling Flames

Abstract

Abstract We present a two-step optimization (TSO) framework, which uses the pressure data of an unstable combustion process to estimate the Flame Transfer Function (FTF). From the pressure time series, we obtain the instability frequency and the amplitudes of the pressure fluctuations. The first optimization step is based on an acoustic network model of the combustor: the TSO approach uses the pressure data to find a simplified n-tau model, which reproduces the unstable combustion process. This step has already been validated for the Rijke tube, a laminar and a turbulent flame in Ghani et al. (2020). The major contribution of this work adds a second optimization loop to extend the n-tau model to the FTF: the gain and phase obtained by the n-tau model are used to fit a distributed time delay model. Our proposed method is applied to a turbulent, premixed, swirl-stabilized flame operated at two power ratings and two swirler positions. The model results for the FTFs are compared against experimentally measured FTFs for these four configurations and all agree well. To the best of our knowledge, this is the first attempt to estimate the complex-valued FTF solely based on pressure measurements. Compared to classical methods for FTF determination such as experimental tests or numerical simulations, our TSO approach is fast and accurate. The proposed framework is suitable for perfectly-premixed flames stabilized by a swirling flow field, requires two pressure sensors and is easy to implement.