A simple eddy viscosity formulation for turbulent boundary layers near smooth walls

Abstract

The aim of this study is to improve the prediction of near-wall mean streamwise velocity profile U + by using a simple method. The U + profile is obtained by solving the momentum equation which is written as an ordinary differential equation. An eddy viscosity formulation based on a near-wall turbulent kinetic energy k + function [R. Absi, Analytical solutions for the modeled k-equation, ASME J. Appl. Mech. 75 (2008) 044501] and the van Driest mixing length equation [E.R. van Driest, On turbulent flow near a wall, J. Aero. Sci. 23 (1956) 1007] is used. The parameters obtained from the k + profiles are used for the computation of U + (variables with the superscript of + are those nondimensionalized by the wall friction velocity u τ and the kinematic viscosity ν). Comparisons with DNS data of fully-developed turbulent channel flows for 109 < Re τ < 2003 show good agreement (where Re τ denotes the friction Reynolds number defined by u τ , ν and the channel half-width δ). To cite this article: R. Absi, C. R. Mecanique 337 (2009).