Large eddy simulations for the flame describing functionof apremixed turbulent swirling flame

Computational prediction of thermoacoustic instabilities arising in gas turbine and aeroengine combustors is an ongoing challenge. Approaches which couple separate treatments for the acoustic waves and the flame all rely on a model for the response of the flame to oncoming acoustic perturbations. In the frequency domain, in the limit of small perturbations, this function is usually given in terms of the so-called Flame Transfer Function (FTF), i.e., a function that relates the heat release rate perturbation at the flame location with longitudinal velocity fluctuations taken at an upstream reference point. With the increase of the amplitude of oscillations, nonlinear combustion process controls the dynamics of the systems. A flame describing function (FDF) is so-defined introducing a dependence of the gain and phase of the FTF on velocity fluctuations amplitude |u'/ū|. The present work uses numerical simulations to obtain the FDF of a turbulent premixed swirling flame. The swirled burner developed at NTNU university is considered in a longitudinal combustor setup. Simulations are performed using Large Eddy Simulations (LES) via the open source Computational Fluid Dynamics (CFD) code, OpenFOAM. The predicted unperturbed flame structure is at first presented and discussed. Subsequently, the nonlinear flame response is characterised submitting the flame to a harmonically varying longitudinal velocity fluctuation, for which the forcing frequency is varied from 300 Hz to 1900 Hz considering two forcing amplitude levels, |u'/ū|=0.1 and |u'/ū|=0.2. The shape of the gain and the phase of the full FDF is discussed and the main characteristics are investigated.