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Turbulent Poiseuille flow with near‐critical wall transpiration
Author(s) -
Vigdorovich Igor,
Oberlack Martin
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010221
Subject(s) - hagen–poiseuille equation , mechanics , turbulence , laminar flow , reynolds number , physics , open channel flow , law of the wall , shear velocity , shear stress , enstrophy , laminar sublayer , boundary layer , mathematics , classical mechanics , flow (mathematics) , vorticity , vortex
An incompressible, pressure‐driven, fully developed turbulent flow between two parallel walls, with an extra constant transverse velocity component, is considered. A closure condition is formulated, which relates the shear stress with the first and the second derivatives of the longitudinal mean velocity. The closure condition is derived without invoking any special hypotheses on the nature of turbulent motion, only taking advantage of the fact that the flow depends on a finite number of governing parameters. By virtue of the closure condition, the momentum equation is reduced to the boundary‐value problem for a second‐order differential equation, which is solved by the method of matched asymptotic expansions at high values of the logarithm of the Reynolds number based on the friction velocity. The case of near‐critical transpiration, when the shear stress at the injection wall vanishes, is considered. It is shown that the maximum point on the mean velocity profile lies in a thin sublayer near the suction wall in this case. A formula for the position of the maximum point as a function of the transpiration factor is obtained. The mean velocity profiles near the suction wall are calculated. A friction law for Poiseuille flow with near‐critical transpiration is found, which makes it possible to describe the relation between the shear stress at the wall, the Reynolds number, and the transpiration velocity by a single function of one variable. Direct numerical simulation of the flow for some transpiration factors is performed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)