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Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

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Abstract

As the Reynolds number increases, the skin friction has been identified as the dominant drag in many practical applications. In the present paper, the effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows up to Reτ= 5 200 are investigated based on two different methods, i.e., the Fukagata-Iwamoto-Kasagi (FIK) identity (FUKAGATA, K., IWAMOTO, K., and KASAGI, N. Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Physics of Fluids, 14(11), L73–L76 (2002)) and the Renard-Deck (RD) identity (DECK, S., RENARD, N., LARAUFIE, R., and WEISS, P. É. Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Reθ= 13 650. Journal of Fluid Mechanics, 743, 202–248 (2014)). The direct numerical simulation (DNS) data provided by Lee and Moser (LEE, M. and MOSER, R. D. Direct numerical simulation of turbulent channel flow up to Reτ≈ 5 200. Journal of Fluid Mechanics, 774, 395–415 (2015)) are used. For these two skin friction decomposition methods, their decomposed constituents are discussed and compared for different Reynolds numbers. The integrands of the decomposed constituents are locally analyzed across the boundary layer to assess the actions associated with the inhomogeneity and multi-scale nature of turbulent motion. The scaling of the decomposed constituents and their integrands are presented. In addition, the boundary layer is divided into three sub-regions to evaluate the contributive proportion of each sub-region with an increase in the Reynolds number.

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Acknowledgements

The large-scale computations were supported by the Center for High-Performance Computing, Shanghai Jiao Tong University.

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Yitong Fan, Cheng Cheng & Weipeng Li

  2. Engineering Research Center of Gas Turbine and Civil Aero Engine, Shanghai, 200240, China

    Weipeng Li

Authors
  1. Yitong Fan
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  2. Cheng Cheng
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  3. Weipeng Li
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Correspondence to Weipeng Li.

Additional information

Project supported by the National Basic Research Program of China (973 Program) (No. 2014CB744802) and the National Natural Science Foundation of China (No. 11772194)

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Fan, Y., Cheng, C. & Li, W. Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows. Appl. Math. Mech.-Engl. Ed. 40, 331–342 (2019). https://doi.org/10.1007/s10483-019-2442-8

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  • DOI: https://doi.org/10.1007/s10483-019-2442-8

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