A new spectral method for calculation of the time-varying area of a laminar flame in homogeneous turbulence

Abstract

A novel approach to flame area simulation is presented, based on the physical processes of chaotic mixing. The “wrinkled” flame front is represented by a length-scale distribution of distortions of the surface, bounded by the chamber or flame kernel size, and the laminar flame thickness. The turbulent fluid in which the flame propagates is modelled as a length scale spectrum of vortices, with the contribution of each scale to the total turbulent kinetic energy being obtained from a prescribed energy spectrum function. Vortex-flame interaction is modelled by: (a) flame area generation by the vortices at their length scale, (b) stretching and folding by generation of flame area at larger scales. The effect of flame propagation on the radius of curvature of the flame constitutes the third mechanism for altering the “wrinkle” spectrum. The resulting integro-differential equation is solved numerically by a time-marching procedure to yield the evolution of surface area and asymptotic (equilibrium) limit for given conditions of turbulence and prescribed laminar flame speed. Good agreement with experimental results is obtained for the fractal dimension of passive scalar and flame surfaces, and also with turbulent flame speed data over a wide range of conditions. The model also makes predictions of flame-speed trends in the near-wall region in agreement with observed behaviour, and also shows that there is a weak dependence of turbulent flame speed on S l additional to that on u′ /S l used in the Bradley correlations. The effects of turbulent flame stretch and vortices smaller than the laminar flame thickness are not modelled, leading to reduced agreement in the high u′ /S l limit. The physical nature of the modelling means that these, and other phenomena such as holes in the flame front caused by rapid local stretching, can be easily included in future work.