This paper describes the behaviour of a turbulent boundary layer on a smooth, axisymmetric body exposed to an adverse pressure gradient of sufficient strength to cause a short region of mean reverse flow ('separation’). The pressure distribution is tailored such that the boundary layer reattaches and then develops in a nominally zero pressure gradient. Hot-wire and pulsed-wire measurements are presented over the separated region and downstream of reattachment. The response of the turbulence quantities to separation and to reattachment is discussed, with emphasis on the relaxation behaviour after reattachment. Over the separation bubble, the response is characteristic of that seen by other workers: the Reynolds stresses in the inner region are reduced and stress peaks develop away from the wall. At reattachment, the skewness of the fluctuating wall shear stress vanishes, as it is known to do at separation. After reattachment, the outer-layer stresses decay towards levels typical of unperturbed boundary layers. But the inner-layer relaxation is unusual. As the viscous wall stress increases downstream of reattachment, the recovery does not start at the wall and travel outward via the formation of an ‘internal’ layer, the process observed in many other relaxing flows. In fact, the inner layer responds markedly more slowly than the outer layer, even though response times are shortest near the wall. It is concluded that the large-scale, outer structures in the turbulent boundary layer survive the separation process and interfere with the regeneration of Reynolds stresses in the inner region after reattachment. This behaviour continues for at least six bubble lengths (20 boundary-layer thicknesses) after reattachment and is believed to have profound implications for our understanding of the interaction between inner and outer layers in turbulent boundary layers.
A comparison of the turbulence structure of subsonic and supersonic boundary layers reveals that, despite broad similarities, significant differences exist. The length scales derived from space-time correlations indicate that the spanwise scales are almost identical but that the streamwise scales in the supersonic flow are about half the size of those in subsonic flow. The large-scale structures in the subsonic boundary layer appear to move slightly slower, and lean more toward the wall than those observed in supersonic flows, and their shear stress content is distributed differently among the four quadrants. These observations should have a strong impact on deriving turbulence models for high Reynolds number supersonic flows.
A non-similar boundary layer theory for air blowing over a water layer on a flat plate is formulated and studied as a two-fluid problem in which the position of the interface is unknown. The problem is considered at large Reynolds number (based on x), away from the leading edge. We derive a simple non-similar analytic solution of the problem for which the interface height is proportional to x1/4 and the water and air flow satisfy the Blasius boundary layer equations, with a linear profile in the water and a Blasius profile in the air. Numerical studies of the initial value problem suggest that this asymptotic non-similar air–water boundary layer solution is a global attractor for all initial conditions.
A study was undertaken to examine the flat plate relaxation behaviour of a turbulent boundary layer recovering from 90° of strong convex curvature (δ0/R = 0.08), for a length of ≈ 90δ0 after the end of curvature, where δ0 is the boundary layer thickness at the start of the curvature. The results show that the relaxation behaviour of the mean flow and the turbulence are quite different. The mean velocity profile and skin friction coefficient asymptotically approach the unperturbed state and at the last measuring station appear to be fully recovered. The turbulence relaxation, however, occurs in several stages over a much longer distance. In the first stage, a stress ‘bore’ (a region of elevated stress) is generated near the wall, and the bore thickens with distance downstream. Eventually it fills the whole boundary layer, but the stress levels continue to rise beyond their self-preserving values. Finally the stresses begin a gradual decline, but at the last measuring station they are still well above the unperturbed levels, and the ratios of the Reynolds stresses are distorted. These results imply a reorganization of the large-scale structure into a new quasi-stable state. The long-lasting effects of curvature highlight the sensitivity of a boundary layer to its condition of formation.
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