On skin friction in wall-bounded turbulence

• Published in: Acta mechanica Sinica Vol. 37; no. 4; pp. 589 - 598
• Main Authors: Xia, Zhenhua, Zhang, Peng, Yang, Xiang I. A.
• Format: Journal Article
• Language: English
• Published: Beijing The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences 01.04.2021; Springer Nature B.V; Department of Engineering Mechanics,Zhejiang University,Hangzhou 310027,China%Mechanical Engineering,Pennsylvania State University,State College,PA 16802,USA
• Edition: English ed.
• Subjects: Boundary layer flow; Classical and Continuum Physics; Coefficient of friction; Computational fluid dynamics; Computational Intelligence; Direct numerical simulation; Empirical equations; Engineering; Engineering Fluid Dynamics; Fluid flow; Formulas (mathematics); Friction; High Reynolds number; Research Paper; Shear stress; Skin friction; Theoretical and Applied Mechanics; Turbulence; Turbulent boundary layer; Skin friction; Wall-bounded turbulence; Integral formula
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-020-01024-4

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. Graphic abstract