Resolution requirements in stochastic field simulation of turbulent premixed flames

The spatial resolution requirements of the Stochastic Fields probability density function approach are investigated in the context of turbulent premixed combustion simulation. The Stochastic Fields approach is an attractive way to implement transported Probability Density Function modelling into Large Eddy Simulations of turbulent combustion. In premixed combustion LES, the numerical grid should resolve flame-like structures that arise from solution of the Stochastic Fields equation. Through analysis of Stochastic Fields simulations of a freely-propagating planar turbulent premixed flame, it is shown that the flame-like structures in the Stochastic Fields simulations can be orders of magnitude narrower than the LES filter length scale, implying that the usual practice of setting the LES filter length scale equal to grid spacing leads to severe under-resolution, to numerical thickening of the flame, and to substantial error in the turbulent flame speed. The under-resolution is worst for low Karlovitz number combustion, where the thickness of the Stochastic Fields flame structures is similar to the laminar flame thickness. The effect of resolution on LES predictions is then assessed by performing LES of a laboratory Bunsen flame and comparing the effect of refining the grid spacing and filter length scale independently. The Bunsen flame LES results confirm that setting the LES filter length scale equal to the grid spacing gives substantial numerical error, and that this error affects the Stochastic Fields solution to a greater extent than it affects the flow field solution. The present results have important implications for application of the Stochastic Fields approach to simulation of high-pressure industrial premixed combustion systems where the grid spacing is necessarily much larger than the laminar flame thickness and suggests that some amount of artificial flame thickening might be needed in order to make such simulations numerically accurate