New Mixing-Length Approach for the Mean Velocity Profile of Turbulent Boundary Layers

[+] Author and Article Information
M. H. Buschmann

Institut für Strömungsmechanik,  Technische Universität Dresden, 01060 Dresden, Germany hanno@ism.mw.tu-dresden.de

M. Gad-el-Hak

Department of Mechanical Engineering,  Virginia Commonwealth University, Richmond, VA 23284, USA gadelhak@vcu.edu

J. Fluids Eng 127(2), 393-396 (Jan 17, 2005) (4 pages) doi:10.1115/1.1881701 History: Received June 11, 2004; Revised January 17, 2005

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Copyright © 2005 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Parameters of the velocity profile 3. Solid lines represent formulas in the small boxes. Dashed lines show parameters for simple log law according to (7), κ=0.38 and A=4.1, and according to (5), D=5.0.

Grahic Jump Location
Figure 2

Damping factor of the proposed mixing-length expression and first coefficient of the Taylor series expansion of Reynolds shear stress in the vicinity of the wall. Solid lines represent formulas in the small boxes. Dashed lines show the range of first coefficient values according to (18), FC=4×10−4−8×10−4.

Grahic Jump Location
Figure 3

Mean velocity and velocity gradient profiles for different Kármán numbers. Solid lines result from the proposed mixing-length theory and numerically integrating Eq. 8. Dashed lines are according to Eq. 3, without mixing-length approach. Data from Ref. 7, ◆ δ+=1,092(Reθ=4,312); ∎ δ+=1,661(Reθ=6,930); and ▴δ+=6,147(Reθ=27,320).

Grahic Jump Location
Figure 4

Comparison of experimental mean velocity profiles and the new mixing-length theory. Data from Ref. 19, ⩾δ+=7,274(Reθ=20,920); ∎ δ+=19,926(Reθ=57,720). Data from Ref. 20, ◆ δ+=10,022(Reθ=30,850).




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