Models of the time-averaged heat release rate of laminar premixed conical and V-shape flames subjected to flow disturbances

The time-averaged heat release rates of two-dimensional laminar premixed flames subjected to axial oncoming flow perturbations are theoretically studied in this paper. The proposed models of both the two-dimensional conical flame and V-shape flame are derived from the G-equation method. The weakly nonlinear perturbation analysis has been applied in the present work. The origins of time-averaged flame fronts consist of two parts: the unperturbed flame fronts caused by the balance between the laminar flame burning velocity and the incident normal velocity; the perturbed zero order time-averaged flame fronts caused by the second order nonlinear items in the perturbation analysis. For the conical and V-shape flame models, the analytical solution of the time-averaged flame heat release rate is derived based upon the perturbation method (analytical perturbation model) using different velocity perturbation models, in order to reveal the time-averaged flame heat release rate response mechanism to the axial disturbances. Results show that the velocity perturbation models and the flame aspect ratio have significant effects on the time-averaged flame heat release rates.