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This study performs a linear analysis of a turbulent reacting methane-air jetflame, with the goal of predicting the response of the reacting flow toupstream acoustic actuation. Accounting for heat release fluctuations is avital component when investigating thermoacoustic instabilities and flame noisein a linearized framework. Unlike previous studies this work develops andapplies an active flame approach, meaning the heat release oscillations of theflame resulting from the acoustic fluctuations are taken into account. To yieldan active flame approach in the linear framework, a combustion model needs tobe linearized. It is demonstrated that linearizing Large Eddy Simulation (LES)and Direct Numerical Simulation (DNS) combustion models leads to closureproblems, making their application in the linearized framework troublesome.Reynolds-averaged Navier Stokes (RANS) combustion models, however, prove tocircumvent this problem, which makes them suitable candidates for this purpose.The RANS combustion models are linearized around the temporal mean flow of theturbulent jet flame, which is obtained by LES. An a priori analysis shows thata linearized RANS-Eddy Break Up (EBU) model is the best suited among allinvestigated combustion models for the investigated set-up and reproduces withhigh accuracy the fluctuations in reaction rate obtained in the LES.Furthermore, the linearized governing equations of the flow including thelinearized EBU model for the reaction rate are solved for incoming acousticperturbations. The response modes show that the reaction rate oscillations arecaused by Kelvin-Helmholtz vortex rings, which perturb the jet flame. Theresults are in good agreement with the LES simulations in terms of the modeshapes of both reaction rate and velocity fluctuations.

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