Scaling of Flame Describing Functions in Premixed Swirling Flames

Predicting the response of swirling flames subjected to acoustic perturbations poses significant challenges due to the complex nature of the flow. In this work, the effect of swirl number on the Flame Describing Function (FDF) is explored through a computational study of four bluff-body stabilised premixed flames with swirl numbers ranging between 0.44 and 0.97 and at forcing amplitudes of 7% and 25% of the mean bulk velocity. The LES model used for the simulations is validated by comparing two of those flames to experiments. The comparison is observed to be good with the computations capturing the unforced flow structure, flame height and FDF behaviour. It is found that changes in the swirl number can affect the location of the minima and maxima of the FDF gain in the frequency space. These locations are not affected by changes in the forcing amplitude, but the gain difference between the minima and the maxima is reduced as the forcing amplitude is increased. It is then attempted to scale the FDF using Strouhal numbers based on two different flame length scales. A length scale based on the axial height of the maximum heat release rate per unit length leads to a good collapse of the FDF gain curves. However, it is also observed that flow instabilities present in the flow can affect the FDF scaling leading to an imperfect collapse.