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

Rafik Absi

doi:10.1016/j.crme.2009.03.010

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

Présenté par : Jean-Baptiste Leblond

Rafik Absi ¹

¹ EBI, Inst. Polytech. St-Louis, 32, boulevard du Port, 95094 Cergy-Pontoise cedex, France

Comptes Rendus. Mécanique, Volume 337 (2009) no. 3, pp. 158-165.

Résumé

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).

Reçu le : 2009-01-23
Accepté le : 2009-03-18
Publié le : 2009-03-01

DOI : 10.1016/j.crme.2009.03.010

Mots clés : Fluid mechanics, Eddy viscosity formulation

Affiliations des auteurs :

Rafik Absi ¹

¹ EBI, Inst. Polytech. St-Louis, 32, boulevard du Port, 95094 Cergy-Pontoise cedex, France

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     title = {A simple eddy viscosity formulation for turbulent boundary layers near smooth walls},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {158--165},
     publisher = {Elsevier},
     volume = {337},
     number = {3},
     year = {2009},
     doi = {10.1016/j.crme.2009.03.010},
     language = {en},
}

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Rafik Absi. A simple eddy viscosity formulation for turbulent boundary layers near smooth walls. Comptes Rendus. Mécanique, Volume 337 (2009) no. 3, pp. 158-165. doi : 10.1016/j.crme.2009.03.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.03.010/

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