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Steady and unsteady separation in an approximately two-dimensional indented channel

Published online by Cambridge University Press:  20 April 2006

C. D. Bertram  and
T. J. Pedley
C. D. Bertram
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW Present address: Centre for Biomedical Engineering, University of New South Wales, P.O. Box 1, Kensington, Australia 2033.
T. J. Pedley
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
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Abstract

Experiments are performed on steady and impulsively started flow in an approximately two-dimensional closed channel, with one wall locally indented. In plan the indentation is a long trapezium which halves the channel width: the inclination of the sloping walls is approximately 5.7°, and these tapered sections merge smoothly into the narrowest section via rounded corners. The Reynolds number $ Re = a_0\overline{u}_0/\nu $ (a0 = unindented channel width, $\overline{u}_0$ = steady mean velocity in the unindented channel) lies in the range 300 [les ] Re [les ] 1800. In steady flow, flow visualization reveals that separation occurs on the lee slope of the indentation, at a distance downstream of the convex corner which decreases (tending to a non-zero value) as Re increases. There is no upstream separation, and there is some evidence of three-dimensionality of the flow in the downstream separated eddy. Pressure measurements agree qualitatively but not quantitatively with theoretical predictions. Unsteady flow visualization reveals that, as in external flow, wall-shear reversal occurs over much of the lee slope (at dimensionless time $\tau = \overline{u}_0t/a_0 \approx 4$) before there is any evidence of severe boundary-layer thickening and breakaway. Then, at τ ≈ 5.5, a separated eddy develops, and its nose moves gradually upstream from the downstream end of the indentation to its eventual (τ ≈ 75) steady-state position on the lee slope. At about the same time as the wall-shear reversal, wavy vortices appear at the edge of the boundary layer on both walls of the channel, and (for Re < 750) subsequently disappear again; these are interpreted as manifestations of inflection-point instability and not as intrinsic aspects of boundary-layer separation. Pressure measurements are made to investigate the discrepancy between the actual pressure drop across the lee slope and that predicted on the assumption that energy dissipation is quasi-steady. This discrepancy has a maximum value of approximately $1.5\rho \overline{u}^2_0$ (ρ = fluid density), and decays to zero by the time τ ≈ 7.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 130 , May 1983 , pp. 315 - 345
Copyright
© 1983 Cambridge University Press

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