Swirling Flame Dynamics and Describing Function

Abstract

The present article focuses on the dynamics and response of lean premixed confined swirling flames submitted to plane acoustic perturbations. The axial velocity disturbances and the heat release rate are recorded to determine the flame transfer function. Effects of the amplitude of the velocity perturbations are systematically investigated leading to the determination of the flame describing function (FDF) which generalizes the transfer function concept to the case where the gain and phase depend on the input amplitude level. The flame describing function of swirling flame differs from previously determined FDFs as it exhibits a local minimum with a small gain and a maximum response in the same frequency range. In the case studied in this article the minimum is located at 60 Hz while the maximum is reached at 90 Hz. Abel transformed phase conditioned average images are used to described the flame dynamics and explain the different responses. The flame motion and the heat release rate response at these two frequencies are due to a combination of two mechanisms. The first is associated with the vortex roll-up of the flame while the second is associated with swirl number fluctuations. This second mechanism involves the flame response to incoming perturbations which in the case of a swirler comprise an axial acoustic disturbance and a convective azimuthal velocity perturbation.