A wall-layer model for large-eddy simulations of turbulent flows with/out pressure gradient

In this work, modeling of the near-wall region in turbulent flows is addressed. A new wall-layer model is proposed with the goal to perform high-Reynolds number large-eddy simulations of wall bounded flows in the presence of a streamwise pressure gradient. The model applies both in the viscous sublayer and in the inertial region, without any parameter to switch from one region to the other. An analytical expression for the velocity field as a function of the distance from the wall is derived from the simplified thin-boundary equations and by using a turbulent eddy coefficient with a damping function. This damping function relies on a modified van Driest formula to define the mixing-length taking into account the presence of a streamwise pressure gradient. The model is first validated by a priori comparisons with direct numerical simulation data of various flows with and without streamwise pressure gradient and with eventual flow separation. Large-eddy simulations are then performed using the present wall model as wall boundary condition. A plane channel flow and the flow over a periodic arrangement of hills are successively considered. The present model predictions are compared with those obtained using the wall models previously proposed by Spalding, Trans. ASME, J. Appl. Mech 28, 243 (2008) and Manhart at al., Theor. Comput. Fluid Dyn. 22, 243 (2008). It is shown that the new wall model allows for a good prediction of the mean velocity profile both with and without streamwise pressure gradient. It is shown than, conversely to the previous models, the present model is able to predict flow separation even when a very coarse grid is used. (c) 2011 American Institute of Physics. [doi:10.1063/1.3529358]