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Scaling of rough-wall turbulence by the roughness height and steepness

Published online by Cambridge University Press:  11 August 2020

Guo-Zhen Ma ,
Chun-Xiao Xu Open the ORCID record for Chun-Xiao Xu [Opens in a new window] ,
Hyung Jin Sung Open the ORCID record for Hyung Jin Sung [Opens in a new window]  and
Wei-Xi Huang Open the ORCID record for Wei-Xi Huang [Opens in a new window]
Guo-Zhen Ma
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing100084, PR China
Chun-Xiao Xu
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing100084, PR China
Hyung Jin Sung
Affiliation:
Department of Mechanical Engineering, KAIST, Daejeon34141, Korea
Wei-Xi Huang*
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing100084, PR China
*
†Email address for correspondence: [email protected]
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Abstract

A roughness scaling behaviour is tested by performing the direct numerical simulation (DNS) of a turbulent channel flow over three-dimensional sinusoidal rough walls. By systematically varying the roughness height ${{k}^{+}}$ and the roughness steepness S, the results for three groups of cases are considered and compared with those for flat-wall turbulence. The results show that the mean velocity and Reynolds stresses are highly dependent on both ${{k}^{+}}$ and S. To describe these specific relationships, we define a coupling scale ${{k}^{+}} S$. With this coupling scale, all the simulated data for the roughness function (${\rm \Delta} {{U}^{+}}$), the ratio of the pressure drag to the total wall resistance (${{\gamma }_{p}}$), the normalized bulk mean velocity ($U_{b}^{+}$) and the peak of the streamwise turbulent velocity fluctuations ($\overline {u_{p}^{\prime +}}$) collapse onto single curves, which shows that there is a strong direct correlation between them, i.e. ${\rm \Delta} U^{+}, \gamma _{p}, U_{b}^{+}, \overline {u_{p}^{\prime +}} \propto f(k^{+} S)$. Furthermore, a model for the prediction of wall resistance based on the roughness function can be established by defining a drag increasing ratio (DI). Accordingly, the wall resistance coefficient ${{C}_{f}}$ can be estimated directly from ${{k}^{+}}S$ of a given rough surface. These results suggest that this coupling scale provides a useful alternative to the equivalent sand grain roughness ${{k}_{s}}$.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , R7
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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