Direct numerical simulation of a turbulent boundary layer over a bump with strong pressure gradients

The turbulent boundary layer over a Gaussian-shaped bump is computed by direct numerical simulation of the incompressible Navier-Stokes equations. The two-dimensional bump causes a series of strong pressure gradients alternating in rapid succession. At the inflow, the momentum thickness Reynolds number is approximately 1000 and the boundary layer thickness is 1/8 of the bump height. Direct numerical simulation results show that the strong favourable pressure gradient (FPG) causes the boundary layer to enter a relaminarization process. The near-wall turbulence is significantly weakened and becomes intermittent, however, relaminarization does not complete. The streamwise velocity profiles deviate above the standard logarithmic law and the Reynolds shear stress is reduced. The strong acceleration also suppresses the wall-shear normalized turbulent kinetic energy production rate. At the bump peak, where the FPG switches to an adverse gradient (APG), the near-wall turbulence is suddenly enhanced through a partial retransition process. This results in a new highly energized internal layer which is more resilient to the strong APG and only produces incipient flow separation on the downstream side. In the strong FPG and APG regions, the inner and outer layers become largely independent of each other. The near-wall region responds to the pressure gradients and determines the skin friction. The outer layer behaves similarly to a free shear layer subject to pressure gradients and mean streamline curvature effects. Results from a RANS simulation of the bump are also discussed and clearly show the lack of predictive capacity of the near-wall pressure gradient effects on the mean flow.

Automated summary

Direct numerical simulation shows that the strong favorable pressure gradient on the bump causes the boundary layer to enter a relaminarization process, significantly weakening near-wall turbulence. However, at the bump peak, when the favorable pressure gradient switches to an adverse gradient, near-wall turbulence is suddenly enhanced through a partial retransition process.