Investigation of wall function formulations for the large eddy simulation method using direct numerical simulation data

Direct numerical simulation (DNS) databases of developed turbulent channel flows are used for a priori and a posteriori testing of various formulations of wall-modeled large eddy simulation (WMLES). Average wall friction values and their root-mean-square deviations are compared with the exact data of the filtered DNS field; in addition, correlation coefficients between the exact friction field and that obtained using the wall function method are calculated. The equilibrium wall functions of Spalding, Werner and Wengle, Li et al. are considered, as well as various options for taking into account nonequilibrium effects in the approach of Li et al.: the contribution of the mean pressure gradient, the contribution of the total pressure gradient; additional inclusion of convective terms in the momentum equation are also considered. Conclusions are drawn on the applicability of wall functions when using instantaneous and time-averaged input data in LES simulations of wall-bounded flows.