An analytical model for the prediction of the dynamic response of premixed flames stabilized on a heat-conducting perforated plate

Abstract

The dynamic response of a premixed flame stabilized on a heat-conducting perforated plate depends critically on their coupled thermal interaction. The objective of this paper is to develop an analytical model to capture this coupling. The model predicts the mean flame base standoff distance; the flame base area, curvature and speed; and the burner plate temperature given the operating conditions; the mean velocity, temperature and equivalence ratio of the reactants; thermal conductivity and the perforation ratio of the burner. This coupled model is combined with our flame transfer function (FTF) model to predict the dynamic response of the flame to velocity perturbations. We show that modeling the thermal coupling between the flame and the burner, while accounting for the two-dimensionality of the former, is critical to predicting the dynamic response characteristics such as the overshoot in the gain curve (resonant condition) and the phase delay. Good agreement with the numerical and experimental results is demonstrated over a range of conditions.