The Importance of the Mean Elevation in Predicting Skin Friction for Flow Over Closely Packed Surface Roughness

[+] Author and Article Information
Stephen T. McClain

Department of Mechanical Engineering,  The University of Alabama at Birmingham, 1530 3rd Ave. S., BEC 358B, Birmingham, AL 35294-4461

S. Patrick Collins

Department of Mechanical Engineering,  The University of Alabama at Birmingham, 1530 3rd Ave. S., BEC 257, Birmingham, AL 35294-4461

B. Keith Hodge

Department of Mechanical Engineering,  Mississippi State University, P.O. Box ME, Mississippi State, MS 39762

Jeffrey P. Bons

Department of Mechanical Engineering,  Brigham Young University, 435 CTB, P.O. Box 24201, Provo, UT 84602-4201

J. Fluids Eng 128(3), 579-586 (Oct 25, 2005) (8 pages) doi:10.1115/1.2175164 History: Received February 04, 2005; Revised October 25, 2005

The discrete-element surface roughness model is used to provide insight into the importance of the mean elevation of surface roughness in predicting skin friction over rough surfaces. Comparison of experimental data and extensive computational results using the discrete-element model confirm that the appropriate surface for the imposition of the no-slip condition is the mean elevation of the surface roughness. Additionally, the use of the mean elevation in the Sigal-Danberg approach relating their parameter to the equivalent sand-grain roughness height results in replacing three different piecewise expressions with a single relation. The appropriate mean elevation for closely-packed spherical roughness is also examined.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

The discrete-element roughness model control volume schematic

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Figure 2

A randomly rough surface

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Figure 3

Mean elevation of the cone surfaces

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Figure 4

Comparison of mean elevation for the random and cone roughness panels

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Figure 5

ks∕k vs Λs for three-dimensional roughness elements

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Figure 6

ks∕keff vs Λs evaluated using the characteristics of the roughness elements above the mean elevation

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Figure 7

Variation of skin friction coefficient and effective roughness height as functions of the roughness element spacing

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Figure 8

Flow over closely packed spheres




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