Direct numerical simulation of self-similar turbulent boundary layers in adverse pressure gradients

Abstract

Direct numerical simulations of the Navier–Stokes equations have been carried out with § the objective of studying turbulent boundary layers in adverse pressure gradients. The boundary layer flows concerned are of the equilibrium type which makes the analysis simpler and the results ¨can be compared with earlier experiments and simulations. This type of turbulent boundary layers © also permits an analysis of the equation of motion to predict separation. The linear analysis based �on the assumption of asymptotically high Reynolds number gives results that are not applicable § to finite Reynolds number flows. A different non-linear approach is presented to obtain a useful relation between the freestream variation and other mean flow parameters. Comparison of turbulent �statistics from the zero pressure gradient case and two adverse pressure gradient cases shows the �development of an outer peak in the turbulent energy in agreement with experiment. The turbulent �flows have also been investigated using a differential Reynolds stress model. Profiles for velocity and § turbulence quantities obtained from the direct numerical simulations were used as initial data. The initial transients in the model predictions vanished rapidly. The model predictions are compared with § the direct simulations and low Reynolds number effects are investigated