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The flow past a flat plate of finite width

Published online by Cambridge University Press:  28 March 2006

J. W. Elder
J. W. Elder
Affiliation:
Geophysics Division, D.S.I.R., Wellington, New Zealand
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Abstract

An experimental study of the incompressible flow near the side edge of a finite flat plate at zero incidence is reported for the Reynolds number range 104 to 106, but comparison with data already published shows that the conclusions are quantitatively valid for Reynolds numbers up to 109. The laminar velocity field is everywhere convex and does not contain any secondary flow other than that of the normal diffusive growth of the layer, but has a logarithmic singularity at the edge where the stress is controlled by the local radius of curvature. The excess skin friction due to the edge is considerably greater than that given by calculations based on the Rayleigh approximation but agrees with a recent Pohlhausen calculation by Varley (1958). Near the edge the high stress and ease of momentum diffusion makes the flow very unstable and turbulent spots occur well upstream of the normal transition zone in the middle of the plate. The spots originate from a nearly point-like region at the edge of the plate and grow linearly in time at the same rate as ordinary turbulent spots to sweep out a narrow tongue of turbulent fluid near the edge until they merge with the normal transition zone. Within this tongue a weak secondary flow of Prandtl's second kind, driven by the anisotropic Reynolds stresses, begins to develop. In fully turbulent flow when the secondary flow is largely localized to within a few boundary-layer thicknesses of the edge the secondary flow velocities are everywhere less than 0.04 of the free-stream velocity. Nevertheless, the secondary flows from each of the side edges interact, regardless of the width of the plate, to increase the total drag coefficient by an amount 0·0004 which is independent both of the Reynolds number and the width of the plate except when it is very narrow. This simple result allows apparent discrepancies between various formulations of the drag coefficient of a finite plate to be reduced to less than ± 1% S.D. Of these formulations Schoenherr's (1932) empirical relation agrees best with the present data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 9 , Issue 1 , September 1960 , pp. 133 - 153
Copyright
© 1960 Cambridge University Press

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