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The effective slip length and vortex formation in laminar flow over a rough surface

Phys. Fluids 21, 052105 (2009); doi:10.1063/1.3121305

Published 11 May 2009

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Anoosheh Niavarani and Nikolai V. Priezjev
Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48824, USA
The flow of viscous incompressible fluid over a periodically corrugated surface is investigated numerically by solving the Navier–Stokes equation with the local slip and no-slip boundary conditions. We consider the effective slip length which is defined with respect to the level of the mean height of the surface roughness. With increasing corrugation amplitude the effective no-slip boundary plane is shifted toward the bulk of the fluid, which implies a negative effective slip length. The analysis of the wall shear stress indicates that a flow circulation is developed in the grooves of the rough surface provided that the local boundary condition is no-slip. By applying a local slip boundary condition, the center of the vortex is displaced toward the bottom of the grooves and the effective slip length increases. When the intrinsic slip length is larger than the corrugation amplitude, the flow streamlines near the surface are deformed to follow the boundary curvature, the vortex vanishes, and the effective slip length saturates to a constant value. Inertial effects promote vortex flow formation in the grooves and reduce the effective slip length. ©2009 American Institute of Physics
History: Received 8 October 2008; accepted 6 March 2009; published 11 May 2009
Permalink: http://link.aip.org/link/?PHFLE6/21/052105/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.45.Gx
    Slip flows and accomodation in fluid dynamics
  • 47.15.Rq
    Laminar flows in cavities, channels, ducts, and conduits
  • 47.32.-y
    Vortex dynamics; rotating fluids
  • 83.50.Rp
    Wall slip and apparent slip in rheology
  • 47.10.ad
    Navier-Stokes equations
  • YEAR: 2009

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PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
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