Modelling the response of a turbulent jet flame to acoustic forcing in a linearized framework using an active flame approach

This study performs a linear mean field analysis of a turbulent reacting methane-air jet flame, with the goal of predicting the response of the reacting flow to upstream acoustic actuation. Unlike previous studies, this work develops and applies an active flame approach by taking the heat release oscillations of the flame resulting from the acoustic fluctuations into account. For an active flame approach in the linear mean field analysis, a linearized combustion model is necessary. Linearizing Large Eddy Simulations (LESs) and Direct Numerical Simulations (DNSs) combustion models leads to closure problems, making their application in this context troublesome, whereas Reynolds-averaged Navier Stokess (RANSs) combustion models prove to circumvent this problem making them suitable candidates for this purpose. The RANSs combustion models are linearized around the temporal mean state variables of the turbulent jet flame, which is obtained by LESs. An a priori analysis shows that a linearized RANSs–Eddy Break Ups (EBUs) model is the best suited among all investigated combustion models for the investigated set-up and reproduces with high accuracy the fluctuations in reaction rate obtained in the LESs. Furthermore, the linearized governing equations of the flow including the linearized EBUs model for the reaction rate are solved for incoming acoustic perturbations. The response modes show that the reaction rate oscillations are caused by Kelvin–Helmholtz vortex rings, which perturb the jet flame. The results are in good agreement with the LESs simulations in terms of the mode shapes of both reaction rate and velocity fluctuations. This study represents a basis for linear mean field analysis of turbulent flames and monolithic modelling approaches for thermoacoustic instabilities in gas turbine combustors.