G-Equation and the vorticity-stream function formulation
Motivation
LES/SI has proved to be an efficient method to model the flame response. Although the insight on the mechanisms involved between input and output is clearer when considering the impulse response of the flame (with respect to the flame frequency response), there are still major questions that can be hardly answered by black-box models. It is therefore necessary to implement analytical models to describe the flame response to velocity perturbations. The G-Equation has proved to be a powerful modeling tool to describe the dynamic response of the flame sheet to incoming flow disturbances. In its linear form, The G-Equation has contributed in the derivation of analytical models of the flame response. These models are based, in addition, on descriptions of the flow which are compact but, unfortunately, very simplistic. This leads to a certain lack of precision in the estimation process in cases such as highly confined flames, among others. In this project, the classical G-Equation is considered together with more realistic models for the flow such as the vorticity-stream function formulation. The first goal is to be able to reproduce numerically, by means of the Finite Volume approach, the response of premixed, laminar flames to incoming velocity perturbations by considering not only the influence of the flow on the flame but also the repercussion that the flame has in the flow. The later could be achieved by developing jump conditions for the flow across the flame in terms of vorticity generation and dissipation along sets of stream-lines. The ultimate goal is to derive realistic analytical models for the response of several flame topologies.