Friction factor from velocity profiles in smooth turbulent channel flows

¹ EBI, EBInnov-Lab, 9 avenue des Genottes, CS 90009, 95895 Cergy cedex, France
² ECAM-EPMI, LR2E-Lab, Quartz-Lab (EA 7393), 13 boulevrad de l’Hautil, 95094 Cergy-Pontoise cedex, France

^* Corresponding author: s.marchandon@hubebi.com
^† Corresponding author: r.absi@ecam-epmi.com

Abstract

Fluid dynamics plays an important role in many Renewable energies studies, i.e. wind and tidal turbines, wave energy geothermal and solar power, …). Friction factor f is an important parameter for the determination of pressure drop in different processes and systems. In this study, we use DNS data of turbulent smooth channels to evaluate different methods. First, a recalibration of Dean’s correlation (Dean, 1978) is proposed. The aim of the study is to obtain accurate wall friction factors from velocity profiles. On the one hand, we obtained two implicit analytical relations based on the law-of-the-wall: a logarithmic friction relation similar to that of pipes and a linear-logarithmic friction relation. On the other hand, we obtained f from the computation of the average velocity. It is first calculated from the law-of-the-wall and allows a good prediction of f for Re_τ > 395 but presents a gap for low Re_τ which is related to inaccurate velocities. Low-Reynolds number effect in channel flows has been previously observed in different experimental and computational studies. In order to provide suitable friction factor values, it is important to predict velocities accurately on the overall channel height. We used therefore a more appropriate method which consists to use for y⁺ < 20 the momentum equation with an eddy viscosity formulation (Absi, 2019) and the log-wake law for high y⁺ values. This method provides accurate friction factor values and allows good agreement with DNS data.