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Prandtl's Mixing Length Model ‐ Revisited
Author(s) -
Obermeier Frank
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610269
Subject(s) - prandtl number , turbulent prandtl number , reynolds number , mechanics , turbulence , mixing (physics) , reynolds stress , mixing length model , physics , flow (mathematics) , reynolds stress equation model , mathematics , classical mechanics , turbulence kinetic energy , heat transfer , nusselt number , k omega turbulence model , quantum mechanics
Abstract The paper is concerned with a modification of Prandtl's mixing length model of Reynolds stresses in fully developed turbulent channel flows. Here it is a well established fact that Prandtl's model falls short to describe the Reynolds stresses correctly very close to the wall. Furthermore, the resulting solution of the time averaged velocity fails to describe the channel flow correctly from the wall to its center. To overcome these shortcomings, the only characteristic mixing length in Prandtl's model is replaced by separate mixing lengths for velocity fluctuations parallel to the wall and normal to the wall, respectively. The modified model describes the mean velocity, all Reynolds stresses, and the functional dependence between Reynolds number based on the mean velocity and the one based on the friction velocity. For all Reynolds numbers these results ‐ and corresponding results for the production terms of Reynolds stresses and the energy balance of the mean flow ‐ agree quantitatively with experimental data and with data obtained by numerical simulations. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)