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On skin friction in wall-bounded turbulence

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Abstract

In this paper, we derive mathematical formulas for the skin friction coefficient in wall-bounded turbulence based on the Reynolds averaged streamwise momentum equation and the total stress. Specifically, with a theoretical or empirical relation of the total stress, the skin friction coefficient is expressed in terms of the mean velocity and the Reynolds shear stress in an arbitrary wall-normal region \([h_0, h_1]\). The formulas are validated using direct numerical simulation data of turbulent channel and boundary layer flows, and the results show that our formulas estimate the skin friction coefficient very accurately with an error less than \(2\%\). The present integral formula can be used to determine the skin friction in turbulent channel and boundary layer flows at high Reynolds numbers where the near-wall statistics are very difficult to measure accurately.

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Acknowledgements

The works of Xia and Zhang were supported by the National Natural Science Foundation of China (Grants 11822208, 11772297, and 91852205) and the Fundamental Research Funds for the central Universities.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Zhejiang University, Hangzhou, 310027, China

    Zhenhua Xia & Peng Zhang

  2. Mechanical Engineering, Pennsylvania State University, State College, PA, 16802, USA

    Xiang I. A. Yang

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  1. Zhenhua Xia
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  2. Peng Zhang
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  3. Xiang I. A. Yang
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Correspondence to Zhenhua Xia.

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Xia, Z., Zhang, P. & Yang, X.I.A. On skin friction in wall-bounded turbulence. Acta Mech. Sin. 37, 589–598 (2021). https://doi.org/10.1007/s10409-020-01024-4

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  • DOI: https://doi.org/10.1007/s10409-020-01024-4

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