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Research Papers: Fundamental Issues and Canonical Flows

Roughness Corrections for the k–ω Shear Stress Transport Model: Status and Proposals

[+] Author and Article Information
B. Aupoix

ONERA,
The French Aerospace Lab,
Toulouse F-31055, France
e-mail: bertrand.aupoix@onera.fr

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 16, 2014; final manuscript received July 25, 2014; published online September 24, 2014. Assoc. Editor: Sharath S. Girimaji.

J. Fluids Eng 137(2), 021202 (Sep 24, 2014) (10 pages) Paper No: FE-14-1025; doi: 10.1115/1.4028122 History: Received January 16, 2014; Revised July 25, 2014

Various corrections were previously proposed to account for wall roughness with the k–ω and shear stress transport (SST) models. A simplified analysis, based upon the wall region analysis, is proposed to characterize the behavior of these roughness corrections. As this analysis points out some deficiencies for each correction, two new corrections are proposed for the SST model, to reproduce different behaviors, mainly in the transition regime. The correction development is based upon a previously developed strategy. A large set of boundary layer experiments is used to compare the different roughness corrections, confirm the failures of previous proposals, and validate the present ones. Moreover, it assesses the proposed simplified analysis. It also evidences the difficulty to determine the equivalent sand grain roughness for a given surface. The Colebrook based correction is recommended while the Nikuradse based one can add information about the envelope of possible behaviors in the transition regime.

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Figures

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Fig. 1

Velocity profiles over smooth and rough walls plotted in wall variables

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Fig. 2

Comparison of correlations for the shift of the logarithmic region proposed by Nikuradse, Ligrani, and Moffat for sand grain (Ligrani) and hemispheres (Ligrani 2) and Grigson for Colebrook's experiments

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Fig. 3

Velocity shift of the logarithmic region—Wilcox’ k–ω model and roughness correction (1998)

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Fig. 4

Velocity shift of the logarithmic region—Wilcox’ k–ω model and Wilcox’ roughness correction (2008)

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Fig. 5

Velocity shift of the logarithmic region—Menter's k–ω SST model and Wilcox’ roughness correction (1988)

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Fig. 6

Reduction of the eddy viscosity by the SST limiter—Menter's k–ω SST model and Wilcox’ roughness correction (1988)

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Fig. 7

Velocity shift of the logarithmic region—Menter's k–ω SST model and Hellsten and Laine roughness correction

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Fig. 8

Velocity shift of the logarithmic region—Menter's k–ω SST model and Knopp et al. roughness correction

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Fig. 9

Velocity shift of the logarithmic region—Menter's k–ω SST model and present roughness correction for the Colebrook's data representation by Grigson

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Fig. 10

MSU experiments—external velocity 12 ms−1—spacing over diameter ratio of 4

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Fig. 11

MSU experiments—external velocity 58 ms−1—spacing over diameter ratio of 4

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Fig. 12

MSU experiments—external velocity 58 ms−1—spacing over diameter ratio of 2

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Fig. 13

Acharya et al. experiments—SRS1 surface

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Fig. 14

Blanchard's experiments—roughness of 0.425 mm—zero pressure gradient

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Fig. 15

Blanchard's experiments—roughness of 0.425 mm—adverse pressure gradient

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Fig. 16

Coleman et al. experiments—most densely packed hemispheres of 1.27 mm diameter—case 3: equilibrium flow under negative pressure gradient

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