The Development of a Three-Dimensional Turbulent Separated Flow Downstream of Reattachment.

Abstract

A detailed experimental study of three flows downstream of attachment is reported; i) a two-dimensional co-planar flow, ii) a non-coplanar spanwise invariant (swept) flow and iii) a fully three-dimensional flow. These flows were formed on a blunt thick plate where for the last case the separation line was in the shape of a downstream-facing v. A special feature of the last case was that the fully three-dimensional region was bounded on each side by a region of spanwise invariance (as investigated in ii)). Mean velocity and turbulence quantities were measured using hot-wire and pulsed-wire anemometry. The Reynolds number based on plate thickness was 8200. The development downstream of attachment is slow and non-monotonic. A dip in the mean velocity profile could be seen in all cases. The development in ii) is slightly quicker if scaled on the streamwise distance to attachment, Xr, but is similar to i) if scaled on Xr cos(theta), where theta is the sweep angle. The downstream flow in iii) is much thicker than the other two flows because of the inward-flow generated in the separated region (cross flow from each side). The height and width of this 'bulge' grow in approximately constant proportion, and this bulge-like feature persists far downstream, perhaps indefinitely. A logarithmic law of the wall, consistent with independently measured wall shear stress, is established in each case, but curiously, more quickly in the fully three-dimensional case even though the distortion in the outer layer is much stronger and the length scales of the large-scale motion are larger. For ii) the Reynolds stresses are lower than in i), but all the second moments in these two cases fall below the respective levels in the standard boundary layer before rising slowly. In iii) the Reynolds stresses are much higher than in the other two eases, and only u2 and uv fall lower than the standard levels at the last measurement station, u2 and vv are also the first two Reynolds stresses to fall below that of the standard boundary layer in the other two cases. It seems likely that the Reynolds stresses in this case will need a much longer distance before they settle to the standard levels, if ever they do. Balances of the turbulent kinetic energy and shear stress transport equations are also given for each case, at two or more streamwise stations. Low-frequency flapping is seen in each case. In ii) it is closely double that in i), indicating a modification of the entrainment mechanism. The shear-layer frequency (indicative of large-scale structures) in ii) decreases linearly with streamwise distance over the first half of the bubble (scaling on the component of free-stream velocity perpendicular to the separation line), and then becomes constant, as in i). In contrast, in Hi) the shear-layer frequency decreases continually along the bubble (at least as far as 2.1Xr)