Analysis of turbulent skin friction generated in flow along a cylinder

Abstract

This paper presents an extension of FIK identity [K. Fukagata et al., Phys. Fluids 14, L73 (2002)] to turbulent axial flow along a cylinder. This relation gives the contributions of both the mean flow and the turbulent fluctuating flow to the skin friction coefficient. The later contribution is then further decomposed more precisely as proposed by B. Frohnapfel, Y. Hasegawa, and N. Kasagi, “Reactive Flow Control for Skin Friction Drag Reduction based on Sensing of the Streamwise Wall-Shear Stress,” Euromech Fluid Mechanics Conference 8 (EFMC8), Bad Reichenhall, Germany, 13–16 Sept. 2010, S4-30. The Reynolds shear stress can be linked to the eigenvalues of the anisotropy tensor, the angle between the principal axis of the Reynolds stress tensor, and the mean flow direction and the turbulent kinetic energy. These eigenvalues and the alignment are important elements of the Reynolds stress profile. The present analysis is based on high-fidelity Reynolds-Stress-Model-based simulations. The results are first validated using available DNS and experimental data. Then, results are used in order to investigate the variations of the skin friction componential contributions with respect to characteristic dimensionless radius a+, Reynolds numbers, Rea (cylinder-radius-based Reynolds number) and Reδ (boundary-layer-thickness-based Reynolds number), or curvature ratio δ/a, and anisotropic decomposition of the Reynolds stress. Explicit empirical formula for surface responses of skin friction and its turbulent component is given.