An analytical model for the transversely forced flame transfer functions of conical and V-flame dynamics

Heat release rate perturbations of two-dimensional asymmetric premixed slot flames subjected to transverse perturbations, so called flame transfer functions (FTFs), are theoretically studied in this paper. The proposed models of both the two-dimensional conical flame and V-flame are studied based upon the linear analysis. The flame front dynamic response under the transverse disturbance is captured and solved using the G-equation model. The analytical solution of the FTF is derived using different oncoming velocity perturbation models, in order to reveal the flame heat release rate response mechanism to the transverse disturbances. In the two-dimensional conical flame model, the flame front tip moves with the transverse perturbations, which in turn also affects the FTF. In the two-dimensional V-flame model, the flame front tips are intersected by the flame branches and the unburned gas boundaries; this also contributes to the different behaviours of the FTF. The linear flame tip dynamics and the explicit analytical models of the FTFs of both the conical flame model and the V-flame model are proposed and validated. Results show that the transverse disturbance propagation velocity model has a significant effect on the FTF. The movement of the flame tip is also affected by the transverse convection models.