A priori assessment of gradient models of joint cumulants for large eddy simulations of premixed turbulent flames

The paper aims at exploring gradient models of joint cumulants for large eddy simulations of premixed turbulent combustion. These are joint cumulants between (i) filtered density and velocity, (ii) two components of Favre-filtered velocity vector, i.e., subfilter-scale stress tensor, (iii) Favre-filtered velocity and combustion progress variable, c̃, i.e., subfilter-scale scalar flux, (iv) c̃ and c̃, i.e., subfilter-scale scalar variance, and (v) filtered density and combustion progress. The model equations are derived for all these cumulants in a unified manner, with each equation involving a single constant. The equations are tested by filtering out Direct Numerical Simulation (DNS) data obtained from three weakly turbulent single-step-chemistry flames characterized by significantly different density ratios and from a lean H2/air complex-chemistry flame propagating in moderately intense small-scale turbulence. (A ratio of laminar flame thickness to Kolmogorov length scale is about 20.) Four box filters are applied to each dataset, with the filter width Δ being equal to 4, 8, 16, and 30 or 32 DNS mesh steps Δx. In all studied cases (four filters and four flames), the tested gradient models yield countergradient subfilter-scale scalar flux and backscatter, in line with the DNS data. If the theoretically evaluated constant 1/12 is adopted, all joint cumulants can be predicted in all flames, but only at Δ=4Δx or/and Δ=8Δx. If a single model constant is tuned for a single cumulant, most cumulants are quantitatively predicted using all four filters in all four analyzed flames, with the tuned model constants being increased with Δ.