Direct numerical simulation of two boundary layers with the same pressure distribution but different surface curvatures

Abstract

A pair of Direct Numerical Simulations is used to investigate curvature and pressure effects. One has a Gaussian test bump and a straight opposite wall, while the other has a straight test wall and a blowing/suction distribution on an opposite porous boundary, adjusted to produce the same pressure distribution. The calculation of the transpiration distribution is made in potential flow, ignoring the boundary layer. This problem of specifying a pressure distribution is known to be ill-posed for short waves. We address this issue by considering a pressure distribution that is very smooth compared with the distance from wall to opposite boundary. It is also ill-posed once separation occurs. The pressure distribution of the viscous flow nevertheless ended up very close to the specified one, upstream of separation, and comparisons are confined to that region. In the entry region the boundary layers have essentially the same thicknesses and are well-developed turbulence-wise, which is essential for a valid comparison. The focus is on the attached flow in the favorable and adverse gradients. The convex curvature is strong enough compared with the boundary-layer thickness to make the strain-rate tensor drop to near zero over the top of the bump. An intense internal layer forms in the favorable gradient, an order of magnitude thinner than the incoming boundary layer. The effect of curvature follows expectations: concave curvature moderately raises the skin friction, although without creating Gortler vortices, and convex curvature reduces it. The pressure gradient still dominates the physics. Common turbulence models unfortunately over-predict the skin friction in both flows near its peak, and under-predict the curvature effect even when curvature corrections are included.