Effect of flame-to-flame interaction on the flame describing function of a turbulent swirling flame in an annular combustor

This article reports a numerical study of the impact of flame-to-flame interaction on the flame response to oncoming acoustic perturbations in an annular combustor. This refers to experiments performed at the Cambridge University involving an annular rig equipped with a variable number of C 2 H 4 -air bluff-body stabilised swirling flames (Worth N. and Dawson J., Proc. Combust. Inst. 2013). A sector of this annular device comprising 3 independent burners is considered. Simulations are performed using incompressible Large Eddy Simulations (LES) via the open source CFD toolbox, OpenFOAM. The unperturbed flame structures of two configurations characterised by a different angular distance between neighbouring flames (∆ θ ), i.e. ∆ θ = 30 ◦ and 20 ◦ , are firstly simulated, both of which are validated by available experimental data. The existence of flame-to-flame interaction largely affects the unforced flame shape and flow-field, compared to those of an independent single flame. Subsequently, the three flames are forced simultaneously by the same harmonic velocity perturbation located at three domain inlets, with the perturbation frequency varied from 300 Hz to 2,000 Hz across multiple perturbation amplitudes (|u 01 /U|=0.025-0.3). The flame response of only the central flame is recorded and used to construct the Flame Describing Function (FDF). For a given forcing amplitude, it is found that the strong flame-to-flame interaction achieved in the ∆ θ =20 ◦ configuration enhances the gain of FDF in the low frequency regime but reduces it at higher forcing frequencies. When increasing the perturbation amplitude, the saturation of FDF-gain is predicted for both configurations, while a more complex behaviour is achieved for the phase - when the interaction between flames is weak (i.e. the ∆ θ =30 ◦ case), the increase of time delay (i.e. phase) between velocity perturbation and heat release response, which is typical of independent flames, is observed. On the contrary, a reduction of the phase is predicted for the ∆ θ =20 ◦ FDF. These differences in FDF's gain and phase highlight the importance of correctly accounting for the flame-to-flame interaction when simulating the FDF for a non-independent flame in an annular combustor.