Analysis of Space-Time Correlations to Support the Development of Wall-Modeled LES

Wall models reduce the computational cost of large eddy simulations (LES) by modeling the near-wall energetic scales and enable the application of LES to complex flow configurations of engineering interest. However, most wall models assume that the boundary layer is fully turbulent, at equilibrium, and attached. Such models have also been successfully applied to turbulent boundary layers under moderated adverse pressure gradients. When the adverse pressure gradient becomes too strong, and the boundary layer separates, equilibrium wall models are no longer applicable. In this work, the relations between the instantaneous wall shear stress, velocity field, and pressure gradients are evaluated using space-time correlations for the purpose of analyzing the near-wall physics in different flow configurations. These correlations are extracted from two wall-resolved LES: a channel flow at a friction Reynolds number Re_τ of 950 and the two-dimensional periodic hill at a bulk Reynolds number Re _b of 10595. This analysis highlights that no instantaneous and local correlation is observed in the vicinity of the separation. The domain of high correlation appears to be shifted downstream. This study of the near-wall physics is a step for developing a data-driven wall model applied to separated flows and, in particular, selecting suitable input parameters for the training of neural networks.