Stochastic simulation of free turbulent premixed flames in isotropic turbulence

Abstract

A theoretical investigation of free turbulent permixed flames in isotropic turbulence is described, limited to the wrinkled thin laminar flamelet regime at neutrally-stable preferential diffusion conditions with negligible effects of quenching. The objective was to develop a computationally tractable three-dimensional time-dependent simulation of flame surface properties, capable of treating turbulence Reynolds numbers typical of experiments and practical flames. The approach involved statistical time series simulation of unburned gas velocities in conjunction with a flame advection and propagation algorithm. The following properties of the unburned gas were simulated, assuming that unburned gas turbulence properties were not affected by the flame: mean velocities due to volumetric expansion at the flame surface, and the Gaussian probability density functions and the spatial and temporal correlations of velocity fluctuations, while satisfying the requirement that cross correlations of velocity fluctuations are zero for isotropic turbulence. Predictions were evaluated using existing measurements for free flames propagating in hydrogen/oxygen/nitrogen mixtures having turbulence intensities relative to laminar burning velocities of 0.48–1.60 and turbulence Reynolds numbers of 1965–4195. Both two- and three-dimensional/time-dependent simulations yielded correct trends of measured flame surface statistics. This included the temporal variation of mean flame radius, r.m.s. flame radius fluctuations, and the average perimeter and fractal dimensions of the wrinkled flame surfaces for various relative turbulence intensities. However, performance of the two-dimensional simulation was less satisfactory because flame surface distortion by turbulence in one coordinate direction was suppressed. Additionally, the three-dimensional simulations underestimated effects of turbulence to some extent, a deficiency attributed to effects of volumetric expansion at the flame surface on unburned gas velocities, with approximations used to treat spatial and temporal correlations of velocity fluctuations in the unburned gas being possible contributing factors. Nevertheless, extension of the three-dimensional/time-dependent simulation to treat other flame configurations, as well as effects of quenching and preferential diffusion, appears to be warranted and is feasible due to the computational efficiency of the velocity simulation.