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

Abstract

We present a two-step optimization (TSO) framework, which uses the pressure data of an unstable combustion process to estimate the complex-valued 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 makes use of the pressure data to find a simplified n–τ 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, Data-Driven Identification of Nonlinear Flame Models,” ASME J. Eng. Gas Turbines Power, 142(12)). The major contribution of this work adds a second optimization loop to extend the n–τ model to the complex-valued FTF: the gain and phase obtained by the n–τ model are used to fit a distributed time delay model based on the work of Komarek and Polifke (2010, “Impact of Swirl Fluctuations on the Flame Response of a Perfectly Premixed Swirl Burner,” ASME J. Eng. Gas Turbines Power, 132(6)). Our proposed method is applied to a turbulent, premixed, swirl-stabilized flame operated at two power ratings (30 kW and 70 kW) 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 placed at distinct axial locations, and is easy to implement.