Direct Numerical Simulation of Self-Similar Turbulent Boundary Layers in Adverse Pressure Gradients

Direct numerical simulations of the Navier–Stokes equations have been carried out with t § he 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 a © lso 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 t § o 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 st atistics from the zero pressure gradient case and two adverse pressure gradient cases shows the de velopment of an outer peak in the turbulent energy in agreement with experiment. The turbulent fl ows have also been investigated using a differential Reynolds stress model. Profiles for velocity and tu § rbulence 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 t § he direct simulations and low Reynolds number effects are investigated.