A thickened stochastic fields approach for turbulent combustion simulation

The Stochastic Fields approach is an effective way to implement transported Probability Density Function modelling into Large Eddy Simulation of turbulent combustion. In premixed turbulent combustion however, thin flame-like structures arise in the solution of the Stochastic Fields equations that require grid spacing much finer than the filter scale used for the Large Eddys Simulation. The conventional approach of using grid spacing equal to the filter scale yields substantial numerical error, whereas using grid spacing much finer than the filter length scale is computationally-unaffordable for most industrially-relevant combustion systems. A Partially-Thickened Stochastic Fields approach is developed in this study in order to provide physically accurate and numerically-converged solutions of the Stochastic Fields equations with reduced compute time. The Partially-Thickened Stochastic Fields formulation bridges between the conventional Stochastic Fields and conventional Thickened-Flame approaches depending on the numerical grid spacing utilised, and converges towards Direct Numerical Simulation in the limit of full-resolution. One-dimensional Stochastic Fields simulations of freely-propagating turbulent premixed flames are used in order to obtain criteria for the thickening factor required, as a function of relevant physical and numerical parameters, and to obtain a model for an efficiency function that accounts for the loss of resolved flame surface area caused by applying the thickening transformation to the Stochastic Fields equations. The Thickened Stochastic Fields formulation is tested by performing LES of a laboratory Bunsen flame, demonstrating that the method leads to numerically-converged simulations that agree with results of conventional Stochastic Fields simulations using orders of magnitude more grid points. The present development therefore facilitates the accurate application of the Stochastic Fields approach to industrially-relevant combustion systems