On the near-wall structure in reverse-flow and post-reattachment recovery regions of separated flow and its equivalence to the structure in wall and free-surface jets

Abstract

The statistical and structural properties of two wall jets, one developing along a real wall and the other along a shear-free wall, are contrasted with the equivalent properties in the post-reattachment- recovery and reverse-flow regions of a separated backward-facing step flow, respectively. The study was motivated, principally, by the wish to isolate and understand the mechanisms responsible for the poor representation of the post-reattachment recovery returned by most RANS closures. It demonstrates a substantive commonality in the turbulent processes between, on the one hand, the real wall jet and post- reattachment recovery, and on the other hand, between the zero-wall-shear jet and the reattachment zone, as well as the reverse-flowing near-wall layer in the backward-facing-step flow. All regions under consideration are found to be characterised by an influential interaction between an outer shear layer and the wall, but an important distinction arises from the presence or absence of strong near-wall shear which introduces significant changes to the nature of this interaction: in the absence or near- absence of wall shear, the interaction is largely inviscid, associated with wall-blocking, while strong shear tends to shield the wall from the outer flow. The commonality between the two sets of flow conditions is explored by way of mean-flow properties, budgets, anisotropy maps, departures from local equilibrium, non-dimensional strain parameter, length-scale variations and structural properties. The study shows that the post-reattachment-recovery region, like the real wall jet, is far from the state of local equilibrium found in a standard boundary layer, that the recovery of the flow towards a state of equilibrium is slow, and that the near-wall region is strongly affected by turbulent diffusion associated with the migration of large-scale structures towards the wall. In statistical terms, this last process is represented by the importance of turbulent transport by third moments and pressure–velocity correlations. Within the reattachment and reverse–flow layer, near-wall shear is weak, and so is the shielding of the wall from the outer layer. In these regions, the flow shares many of the properties of the zero-wall-shear jet.