Response of burner-stabilized flat flames to acoustic perturbations

Abstract

The response of burner-stabilized flat flames to acoustic velocity perturbations is studied numerically and analytically. The numerical setup involves the set of one-dimensional transport equations for the low-Mach number reacting flow using a simple and a more complex reaction mechanism. The physical background of the phenomena observed numerically is explained by a simple analytical model. The model uncouples the unsteady transport equations into two parts: the first part describes the flame motion through the G-equation and the second flamelet part describes the inner flame structure and mass burning rate of the flame. The G-equation can be solved exactly in the case of a quasi-steady flame structure. The mass burning rate is assumed to be directly related to the flame temperature. Relations for the fluctuating heat release and heat loss to the burner are derived, from which the coupling between the velocity fluctuations at both sides of the flame is found. Comparison of the numerical and analytical results with earlier work of McIntosh and with primary experimental results on a lean methane/air flame shows the validity of the models. The origin of the differences encountered is discussed. The resulting transfer function for the velocity perturbation can be applied to the acoustic stability analysis of combustion systems. The most interesting application is the acoustic behaviour of central heating boilers.