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TECHNICAL PAPERS

A General Strategy to Extend Turbulence Models to Rough Surfaces: Application to Smith’s k-L Model

[+] Author and Article Information
B. Aupoix

ONERA/DMAE/TMP, Centre d’Études et de Recherches de Toulouse, B.P. 74025, 2 Avenue Édouard Belin, 31055 Toulouse Cedex 4, Francebertrand.aupoix@onera.fr

J. Fluids Eng 129(10), 1245-1254 (Apr 27, 2007) (10 pages) doi:10.1115/1.2776960 History: Received June 26, 2006; Revised April 27, 2007

A general procedure to extend turbulence models to account for wall roughness, in the framework of the equivalent sand grain approach, is proposed. It is based on the prescription of the turbulent quantities at the wall to reproduce the shift of the logarithmic profile and hence provide the right increase in wall friction. This approach was previously applied to Spalart and Allmaras one equation (1992, “A One-Equation Turbulence Model for Aerodynamic. Flows  ,” 30th Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA paper No. 92-0439;1994, ibid, Rech. Aerosp.1, pp. 5–21). Here, the strategy is detailed and applied to Smith’s two-equation k-L model (1995, “Prediction of Hypersonic Shock Wave Turbulent Boundary Layer Interactions With The k-l Two Equaton Turbulence Model  ,” 33rd Aerospace Sciences Meeting and Exhibit, Reno, NV, Paper No. 95-0232). The final model form is given. The so-modified Spalart and Allmaras and Smith models were tested on a large variety of test cases, covering a wide range of roughness and boundary layer Reynolds numbers and compared with other models. These tests confirm the validity of the approach to extend any turbulence model to account for wall roughness. They also point out the deficiency of some models to cope with small roughness levels as well as the drawbacks of present correlations to estimate the equivalent sand grain roughness.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Velocity profiles over smooth and rough walls plotted in wall variables

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Figure 2

MSU experiments, hemispherical roughness elements, spacing/diameter ratio of 2, external velocity of 12ms−1, predictions of the skin friction coefficient versus momentum thickness Reynolds number

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Figure 3

MSU experiments, hemispherical roughness elements, spacing/diameter ratio of 4, external velocity of 12ms−1, predictions of the skin friction coefficient versus momentum thickness Reynolds number

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Figure 4

MSU experiments, hemispherical roughness elements, spacing/diameter ratio of 2, external velocity of 58ms−1, predictions of the skin friction coefficient versus momentum thickness Reynolds number

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Figure 5

MSU experiments, hemispherical roughness elements, spacing/diameter ratio of 4, external velocity of 58ms−1, predictions of the skin friction coefficient versus momentum thickness Reynolds number

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Figure 6

Acharya experiments, SRS1 surface, predictions of the skin friction coefficient

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Figure 7

Acharya experiments, SRS1 surface, predictions of the shape factor

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Figure 8

Acharya experiments, SRS2 surface, predictions of the skin friction coefficient

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Figure 9

Acharya experiments, SRS2 surface, predictions of the shape factor

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Figure 10

Blanchard’s experiments, roughness height of 0.425mm, zero pressure gradient flow, predictions of the skin friction coefficient

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Figure 11

Blanchard’s experiments, roughness height of 0.425mm, zero pressure gradient flow, predictions of the shape factor

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Figure 12

Blanchard’s experiments, roughness height of 0.425mm, positive pressure gradient flow, predictions of the skin friction coefficient

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Figure 13

Blanchard’s experiments, roughness height of 0.425mm, positive pressure gradient flow, predictions of the shape factor

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Figure 14

Blanchard’s experiments, roughness height of 0.58mm, zero pressure gradient flow, predictions of the skin friction coefficient

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Figure 15

Blanchard’s experiments, roughness height of 0.58mm, zero pressure gradient flow, predictions of the shape factor

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Figure 16

Blanchard’s experiments, roughness height of 0.58mm, zero pressure gradient flow, predictions of the velocity profile

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