Pressure Gradient Effects on Smooth and Rough Surface Turbulent Boundary Layers

Abstract

The present study investigates the effects of streamwise pressure gradients on turbulent boundary layers over smooth and rough surfaces. For smooth surfaces, even with a higher wall shear stress, favorable pressure gradient barely changes friction coefficient due to the increases freestream velocity. Adverse pressure gradient decreases friction coefficient slightly. For smooth surfaces, favorable pressure gradient increases streamwise normal Reynolds stress near the surface because FPG confines high-turbulence vortices to a narrow region near the surface and reduces outward movement of vortices. On the contrary, adverse pressure gradient decreases streamwise normal Reynolds stress near the surface by enhancing the outward movement of near-surface vortices. Under zero pressure gradient, by generating additional coherent unsteady vortices, surface roughness increases mean velocity defect throughout the boundary layer. The surface roughness also increases streamwise normal Reynolds stress and friction coefficient. Combined effects of roughness and pressure gradients have been investigated. For rough surfaces, favorable pressure gradient enhances the roughness effects of increasing mean velocity defect, streamwise normal Reynolds stress, and friction coefficient. Also, favorable pressure gradient increases roughness-induced streamwise turbulent kinetic energy production. The FPG effects are due to 1) near-surface confinement of roughness-generated vortices and 2) strengthened roughness-induced vortices due to an increased velocity gradient. On the contrary, near the surface, adverse pressure gradient reduces the roughness effects on mean velocity defect, streamwise normal Reynolds stress because APG enhances outward convection of roughness-induced vortices and decreases the velocity gradient. Consistently, adverse pressure gradient decreases friction coefficient and streamwise turbulent kinetic energy production in the rough surface boundary layer. The results show that favorable pressure gradient increases the roughness effects while adverse pressure gradient decreases the roughness effects. From the results, mean velocity and friction coefficient estimation methods are proposed. Irrespective of the Reynolds number, pressure gradient, and surface roughness, the ratio of displacement thickness to boundary layer thickness provides appropriate scaling for collapsing the mean velocity profiles in flat plates, axial compressor blade boundary layers, and axial turbine blade boundary layers. A new power law mean velocity estimation method, applicable to smooth and rough flat plate boundary layers with and without pressure gradient, is proposed. The new power law can also accurately estimate mean velocity profiles in axial compressor and turbine blade boundary layers. Finally, a new friction coefficient correlation is proposed for smooth and rough surface turbulent boundary layers with and without pressure gradient. The proposed correlation can also estimate the friction coefficients in smooth axial turbine blades.