Research Papers: Fundamental Issues and Canonical Flows

Review of Hydraulic Roughness Scales in the Fully Rough Regime

[+] Author and Article Information
Karen A. Flack

Department of Mechanical Engineering, United States Naval Academy, Annapolis, MD 21402flack@usna.edu

Michael P. Schultz

Department of Naval Architecture and Ocean Engineering, United States Naval Academy, Annapolis, MD 21402mschultz@usna.edu

J. Fluids Eng 132(4), 041203 (Apr 20, 2010) (10 pages) doi:10.1115/1.4001492 History: Received July 03, 2009; Revised March 12, 2010; Published April 20, 2010; Online April 20, 2010

A review of predictive methods used to determine the frictional drag on a rough surface is presented. These methods utilize a wide range of roughness scales, including roughness height, pitch, density, and shape parameters. Most of these scales were developed for regular roughness, limiting their applicability to predict the drag for many engineering flows. A new correlation is proposed to estimate the frictional drag for a surface covered with three-dimensional, irregular roughness in the fully rough regime. The correlation relies solely on a measurement of the surface roughness profile and builds on previous work utilizing moments of the surface statistics. A relationship is given for the equivalent sandgrain roughness height as a function of the root-mean-square roughness height and the skewness of the roughness probability density function. Boundary layer similarity scaling then allows the overall frictional drag coefficient to be determined as a function of the ratio of the equivalent sandgrain roughness height to length of the surface.

Copyright © 2010This material is declared a work of the US government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.
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Figure 1

Mean velocity profiles for mesh and sandpaper surfaces from Ref. 18

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Figure 2

Mean velocity profiles in velocity-defect form from Ref. 18

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Figure 3

Roughness function results for a variety of rough surfaces

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Figure 4

Roughness function results for a variety of rough surfaces using ks

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Figure 5

Scaled-up procedure from CF smooth to CF rough

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Figure 6

Overall frictional drag coefficient in the fully rough regime

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Figure 7

Surface topography map and pdf of r, distance above the mean roughness elevation, for a honed surface

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Figure 8

Predicted ks versus actual ks using Eq. 27



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