A numerical study of velocity-pressure gradient and pressure-dilatation terms in transport equations for subfilter turbulent kinetic energy in premixed flames

Pressure-dilatation and velocity-pressure-gradient terms in transport equations for subfilter turbulent kinetic energy are a priori explored by analyzing published three-dimensional direct numerical simulation (DNS) data obtained from a lean (the equivalence ratio Φ = 0.81) complex-chemistry hydrogen-air flame propagating in a box. The DNS conditions are associated with moderately intense (Kolmogorov timescale is shorter than flame timescale by a factor of above two), small-scale (Kolmogorov length scale is smaller than laminar flame thickness by a factor of about 20) turbulence. The studied terms are computed by filtering out the DNS fields of velocity, pressure, and fuel mass fraction and adopting top hat filters of different widths, which are smaller or comparable with the laminar flame thickness. Moreover, gradient models of the second-order generalized central moments (joint cumulants) are extended to close the explored pressure terms. Reported results show that filtered pressure terms conditioned to filtered combustion progress variable change their sign with variations in the sampling variable. Moreover, magnitudes of the conditioned terms are much higher than magnitudes of the counterpart time- and transverse-averaged terms. In addition, spatial variations of time- and transverse averaged velocity-pressure-gradient or pressure-dilatation term within mean flame brush are well predicted by the newly introduced gradient models in all studied cases. While the sole model constant tuned to get the best prediction increases gradually with filter width, the constant remains of unity order in all cases. These results encourage further assessment of gradient models as a promising tool for large eddy simulation of premixed turbulent combustion.