Separating shear flow past a surface-mounted blunt obstacle

The planar flow of incompressible fluid past a blunt obstacle mounted on a flat (horizontal) fixed solid surface of infinite extent is examined in the presence of an incident linear velocity profile, modelling the fluid behaviour close to a small surface roughness for instance. The motion is taken to be steady and laminar. The obstacle is blunt in the sense that its typical surface slopes are not small, a feature which here always induces flow separation both upstream and downstream of the obstacle. Computations and nonlinear theory are applied, together with comparisons. The direct computations of the Navier-Stokes equations, using for example a higher order upwind-difference scheme, deal with a moderate range of Reynolds numbers up to 200, based on the obstacle height and the incident uniform shear. In addition the accuracy is necessarily limited as the Reynolds number increases. The theory is for large Reynolds numbers and is based on viscous-inviscid reasoning, back-pressure effects from the obstacle and slender-layer separation locally, among other influences. The comparisons nevertheless yield encouragingly close agreement, for the present computed cases of a vertical flap or a rectangular block. This is both quantitatively, in terms of the upstream separation and downstream reattachment positions in particular, and generally, in terms of the separating flow structure, even at the notably moderate Reynolds numbers covered accurately by the computations.