Turbulent boundary layers subjected to multiple curvatures and pressure gradients

Abstract

The effects of abruptly applied cycles of curvatures and pressure gradients on turbulent boundary layers are examined experimentally. Two two-dimensional curved test surfaces are considered: one has a sequence of concave and convex longitudinal surface curvatures and the other has a sequence of convex and concave curvatures. The choice of the curvature sequences were motivated by a desire to study the asymmetric response of turbulent boundary layers to convex and concave curvatures. The relaxation of a boundary layer from the effects of these two opposite sequences has been compared. The effect of the accompanying sequences of pressure gradient has also been examined but the effect of curvature dominates. The growth of internal layers at the curvature junctions have been studied. Measurements of the Górtler and corner vortex systems have been made. The boundary layer recovering from the sequence of concave to convex curvature has a sustained lower skin friction level than in that recovering from the sequence of convex to concave curvature. The amplification and suppression of turbulence due to the curvature sequences have also been studied.

Numerical investigation of the turbulent boundary layer over a bump

“…They also noted the formation of internal layers related to the step changes in curvature. Signatures of an internal layer caused by a step change in curvature were also reported in the experimental investigation of Bandyopadhyay & Ahmed (1993). Parallel to the departure from equilibrium caused by changes in streamwise pressure gradient and surface curvature, the return to equilibrium of a turbulent boundary layer following the removal of these perturbations is also of interest.…”

“…The rate of recovery has profound implications on the use of curvature as a means for the control of boundary layer development (e.g. see Bandyopadhyay & Ahmed 1993). Thus, additional insight is needed to explain the driving mechanism behind such an unusually fast return as observed in the experiments.…”

“…The constant shape factor on the downstream flat plate indicates that the flow is relaxing towards equilibrium (see also Bandyopadhyay & Ahmed 1993). This relaxation process is more clearly shown in figure 9(b) where the Clauser parameter G is plotted against the streamwise pressure gradient parameter β following Bandyopadhyay & Ahmed (1993),…”

“…Parallel to the departure from equilibrium caused by changes in streamwise pressure gradient and surface curvature, the return to equilibrium of a turbulent boundary layer following the removal of these perturbations is also of interest. Bandyopadhyay & Ahmed (1993) found that the skin friction in a boundary layer recovering from a sequence of concave-convex curvature was low and proposed that viscous drag reduction might therefore be accomplished using curvature. Their measurements were similar to the earlier work of Gillis & Johnston (1983) which showed that the recovery of the skin friction is slow in a boundary layer following the removal of prolonged convex curvature (in the absence of external pressure gradients).…”

“…The complex response of boundary layers subjected to multiple external perturbations in turn complicates modelling of these non-equilibrium flows. The situation is well described by Bandyopadhyay & Ahmed (1993): 'The modeling is fraught with difficulty because the lag behaviour of large eddies in the simultaneous presence of repeatedly applied complex strains of curvature, pressure gradient, lateral divergence and compressibility, is unknown'. Gibson, Jones & Younis (1981) found, for example, that predictive methods based on modelling the full Reynolds-stress transport equations fail to reproduce the convex-flat relaxation process measured by Gillis & Johnston (1983).…”