The effect of flame curvature and flame base movement on the frequency response of a conical Bunsen flame

Abstract

We create a general model for the tracking of a premixed flame sheet. This model is based on a Lagrangian formulation of the interface motion, which is more computationally efficient than the level-set formulation solved on a grid. We apply this model to a conical Bunsen flame in which flame-base oscillations and flame stretch effects are also considered. We demonstrate that the flame-front dynamics, the heat release rate perturbations, and the flame transfer function (FTF) are affected by three features: (i) the velocity field locally perturbing the flame-front, (ii) the flame-base oscillations normal to the steady flame-front propagating along the flame and (iii) the flame-base oscillations tangential to the flame-front reducing and increasing the flame-length. We provide a physical explanation for the saturation of the FTF phase shift with increasing forcing frequency, which is found experimentally. We show why a n−τ model with fixed τ cannot model this simple flame and that, when building a quantitatively-accurate model of a thermoacoustic system containing this flame, the flame dynamics need to be simulated directly or modelled more accurately than with the n−τ model. The flame model used in this paper has been designed to be differentiable so that it can be used for rapid data assimilation using Laplace’s method. Code is provided so that the user can generate the FTF of a conical premixed flame with any set of parameters and any flame-base trajectory.