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

Paper in proceeding, 2025

In the paper, pressure-dilatation and velocity-pressure-gradient terms in transport equations for subfilter turbulent kinetic energy are a priori explored by analyzing three-dimensional Direct Numerical Simulation (DNS) data obtained earlier from a moderately lean (the equivalence ratio F=0.81) complex-chemistry hydrogen-air flame propagating in a box. The DNS conditions are associated with moderately intense (Kolmogorov time scale is shorter than flame time scale by a factor of above two), small-scale (Kolmogorov length scale is smaller than thermal laminar flame thickness by a factor of about 20) turbulence. The studied terms are computed by filtering out the DNS fields of velocity, density, pressure, and fuel mass fraction and adopting Gaussian or top hat filters of different widths, which are smaller or comparable with laminar flame thickness. Moreover, gradient models of the second order generalized central moments (joint cumulants), which are mainly applied to subfiter turbulent stresses and scalar fluxes in various flows, are extended to close the explored pressure-containing terms. Obtained results give priority to using the velocity-pressure-gradient term when compared to the pressure-dilatation term. Specifically, first, the former term is weakly sensitive to filter shape, whereas the latter term evaluated adopting the Gaussian filter is significantly larger than the same term yielded by the top-hat filter of the same width. Second, spatial variations of time- and transverse averaged velocity-pressure-gradient term within mean flame brush are well predicted by the newly introduced gradient model 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.