Modeling Flame Describing Functions Based on Hydrodynamic Linear Stability Analysis

Abstract

Combustion instabilities crucially affect the operational range of modern lean premixed gas turbine combustors and must be avoided or kept at low amplitudes. The main uncertainty of current prediction models is the flame describing function (FDF) that characterizes the flame response to high amplitude acoustic forcing. In this work, we present a new FDF model based on linear hydrodynamic stability analysis. This work is in continuation of an earlier study, where the frequency dependence and saturation of the FDF gain of a perfectly premixed flame was linked to the growth rates of the Kelvin–Helmholtz (KH) instability. In this work, we report on FDF measurements in a newly designed swirl-stabilized combustor. We identify two independent mechanisms that determine the flame response. The first stems from swirl-fluctuations that are generated in the swirler and the second stems from the KH instability. The swirl-fluctuations are approximated by a convective time lag model. The KH instability is predicted from linear hydrodynamic stability analysis based on the time-mean flow measured via PIV. A combination of both models leads to a good quantitative agreement with the measured FDF. Besides the practical advantages of predicting the FDF from stationary flow data, the model reveals the mechanisms driving the saturation of the FDF and guides the way out from the black-box treatment of the nonlinear flame response.