Consequences of flame geometry for the acoustic response of premixed flames

This study investigates the consequences of flame geometry for the linear response of laminar premixed flames to acoustic perturbations, as expressed by the flame transfer function (FTF). Analytical G-equation-based response models are derived for Slit, Bunsen and Wedge type flames; their respective characteristics are analyzed and validated against data obtained from high fidelity numerical simulations. Motivated by the poor agreement between numerical and analytical flame response predictions, particularly for Slit flames, an extension to the well-established incompressible-convective velocity model is proposed, which employs a Gaussian kernel function. Such a kernel disperses the flame response in time and leads to very good agreement with high fidelity numerical simulations. The validity of the model is further confirmed by comparing model predictions with experimental data taken from the literature. Analyzing the analytical flame response modeling concepts in detail, we find that the surface integration, which is required to compute the change of the global heat-release rate from the instantaneous flame front deflections, constitutes the most significant geometry-related property affecting the FTF. The linearized global heat-release rate of stiffly anchored Slit flames reacts only to movements of the flame tip and, hence, these flames respond time delayed to imposed flame front perturbations. Bunsen flames continuously transform convected flame front deflections to changes in the heat-release rate and, therefore, show a more pronounced low-pass behavior than Slit flames. The heat-release rate of Wedge flames reacts to both movements of the flame tip and the integral of instantaneous flame front deflections. Hence, perturbations of the flame front initially have a rather weak effect until they reach the flame tip, where a sudden and strong response is provoked. This leads to the occurrence of high peak gain values in the corresponding FTF.