Effect of local variations of the laminar flame speed on the global finger-flame acceleration scenario

Abstract

Numerous formulations describing the dynamics and morphology of corrugated flames, including the scenarios of flame acceleration, are based on a “geometrical consideration”, where the wrinkled-to-planar flame velocities ratio, Sw/SL, is evaluated as the scaled flame surface area, while the entire combustion chemistry is immersed into the planar flame speed SL, which is assumed to be constant. However, SL may experience noticeable spatial/temporal variations in practice, in particular, due to pressure/temperature variations as well as non-uniform distribution of the equivalence ratio and/or that of combustible or inert dust impurities. The present work initiates the systematic study of the impact of the local SL-variations on the global flame evolution scenario. The variations are assumed to be imposed externally, in a manner being a free functional of the formulation. Specifically, the linear, parabolic and hyperbolic spatial SL-distributions are incorporated into the formulations of finger flame acceleration in pipes, and they are compared to the case of constant SL. Both two-dimensional channels and cylindrical tubes are considered. The conditions promoting or moderating flame acceleration are identified, and the revisited equations for the flame shape, velocity and acceleration rate are obtained for various SL-distributions. The theoretical findings are validated by the computational simulations of the reacting flow equations, with agreement between the theory and modelling demonstrated.