Response of Laminar Premixed Flame to Mass Flow Rate and Pressure Fluctuations

Abstract

In this work, we develop an analytical model to describe laminar premixed flame response to an oscillating flow and use this model to predict the relationship between the heat release rate and the instantaneous flow field. Fully developed pulsating flow through a channel is considered. The flow is driven by pressure gradients. To facilitate direct comparison with experiments, the transient velocity profile is obtained in terms of mass flow rate fluctuations. The flame is anchored at the channel wall. The flame is assumed to be a thin surface, separating the reactants and the products. Flame displacement speed is assumed to be constant. The flame displacement is described by a single-valued function of the transverse coordinate. The flame dynamics is represented by a kinematic equation describing the displacement of the surface. The assumption of constant flame speed and fully developed flow allows closed-form solution of the flame response. The temporal variation of the mass flow rate and the flame surface area are compared to determine the gain and phase difference of the flame transfer function, relating the fluctuations in flame surface area to fluctuations in the mass flow rate.