Turbulent boundary layer relaxation from convex curvature

Abstract

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.

Numerical investigation of the turbulent boundary layer over a bump

“…The behaviour of the shear stress and normal stress ratio in the present flow is quite different than that measured in previous experiments on boundary layers experiencing extended convex curvature (in the absence of an external pressure gradient), in which the shear stress is strongly reduced and the normal stresses approach isotropy (e.g. see So & Mellor 1973;Gillis & Johnston 1983;Alving et al 1990). Thus, it should be expected that the relaxation process will be different than the slow recovery observed in boundary layers recovering from convex curvature (see also Webster et al 1996).…”

“…For example, in a related study by Alving et al (1990), although the criterion established by Baskaran et al (1987) for generation of an internal layer due to curvature change was satisfied in their experiments, signatures of an internal layer could not be found. Alving et al (1990) suggested that the concept of an internal layer growing from the wall with its origin at the curvature discontinuity and remaining uninfluenced by the flow in the parent boundary layer for significant distances, might be too simplistic (see Patel & Sotiropoulos 1997 for further discussion). On the other hand, recent measurements by Webster et al (1996) clearly show distinct 'knees' in profiles of the streamwise intensity downstream of the bump trailing edge and imply the generation of an internal layer.…”

“…In addition to the issues directly linked to the existence, cause, and evolution of internal layers, two important and unusual features emerge from the experiments of Webster et al (1996). They found that, unlike the experiments of Gillis & Johnston (1983) and Alving et al (1990), the boundary layer over the flat plate downstream of the trailing edge exhibits a surprisingly rapid return to equilibrium. The rate of recovery has profound implications on the use of curvature as a means for the control of boundary layer development (e.g.…”

Resolution effects in compressible, turbulent boundary layer simulations

“…(c) (d) Figure 4: Effect of spatial resolution on boundary layer profiles at x 1 /δ 0 = 100. Experimental data of Elena and Lacharme [79], Alving [78], and Konrad [80], and computational data of Pirozzoli and Bernardini [48] are shown for comparison. …”

Experimental investigation of vortex properties in a turbulent boundary layer

“…Moin and Kim 6 and Kim and Moin 7 performed correlation studies on vorticity fields in channel flows and concluded that the most probable inclination angle of a vortex is 45 ‫ؠ‬ to the streamwise direction. Experimental studies of structure angle using two-point correlation measurements 8 have found that the "inferred" angle is seldom equal to 45 ‫ؠ‬ . Marusic 9 performed attached eddy calculations and showed that such a result is consistent with the presence of individual eddies inclined at 45 ‫ؠ‬ , given that, however, these 45 ‫ؠ‬ eddies exist over a range of length scales and population densities.…”