Turbulent Streamwise Edge Effects in the Boundary Layer on a Flat Plate Finite Aspect Ratio

A detailed investigation of the turbulent boundary layer on a flat plate of finite aspect ratio at zero incidence has been made, incorporating measurements of mean velocity profiles and skin friction over one surface of the plate. Skin friction was measured using Prof. Preston's surface-tube technique with the N.P.L. calibration, and this is justified by comparison with the measured momentum defect. These results are compared with others recorded on a 'two-dimensional' plate (i.e. one that spanned the wind tunnel), and the effects of the streamwise edges on the boundary-layer flow on the plate surface are shown to be limited to regions of the plate surface near the edges of the order of a boundary-layer thickness in width. The drag results are analysed to provide an indication of the effect of the edges on the drag of the plate, but a more general assessment of this effect follows from an analysis of the spanwise distribution of the boundary-layer parameters near the edges of the plate. The recommended relation that results for the ratio of the skin-friction coefficient of a plate of finite aspect ratio (C:~) to that of a corresponding two-dimensional plate (C • 0) is: cF/C~o = 1 + c~ d/b, where l is the length and b is the span of the plate. This aspect-ratio effect is considerably smaller than that estimated by Hughes (Ref. 2) and, contrary to Hughes' conclusions, is such that the drag results from tests on three-dimensional plates used as a basis for the Schoenherr and Prandtl-Schlichting laws generally require insignificant modification on account of it (never greater than about 4 ~). These, or similar newer laws can therefore continue to be regarded as reliable guides for most engineering purposes to the skin friction in two dimensions. A re-analysis of Hughes' results brings them into line with the present work.