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Analysis of Instantaneous Turbulent Velocity Vector and Temperature Profiles in Transitional Rough Channel Flow

[+] Author and Article Information
Noor Afzal

Faculty of Engineering, Aligarh Muslim University, Aligarh 202002, India

J. Heat Transfer 131(6), 064503 (Apr 10, 2009) (7 pages) doi:10.1115/1.3085827 History: Received February 23, 2008; Revised December 16, 2008; Published April 10, 2009

The instantaneous velocity vector and instantaneous temperature in a turbulent flow in a transitionally rough channel have been analyzed from unsteady Navier–Stokes equations and unsteady thermal energy equation for large Reynolds numbers. The inner and outer layers asymptotic expansions for the instantaneous velocity vector and instantaneous temperature have been matched in the overlap region by the Izakson–Millikan–Kolmogorov hypothesis. The higher order effects and implications of the intermediate (or meso) layer are analyzed for the instantaneous velocity vector and instantaneous temperature. Uniformly valid solutions for instantaneous velocity vector have been decomposed into the mean velocity vector, and fluctuations in velocity vector, as well as the instantaneous temperature, have been decomposed into mean temperature and fluctuations in temperature. It is shown in the present work that if the mean velocity vector in the work of Afzal (1976, “Millikan Argument at Moderately Large Reynolds Numbers,” Phys. Fluids, 16, pp. 600–602) is replaced by instantaneous velocity vector, we get the results of Lundgren (2007, “Asymptotic Analysis of the Constant Pressure Turbulent Boundary Layer,” Phys. Fluids, 19, pp. 055105) for instantaneous velocity vector. The comparison of the predictions for momentum and thermal mesolayers is supported by direct numerical simulation (DNS) and experimental data.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Velocity fluctuations (um+′,vm+′) versus η in the mesolayer from DNS data of Hoyas and Jimenez (30)

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Figure 2

Comparison of the Reynolds shear stress peak location y+m and peak value τ+m with the DNS and experimental data for fully developed flow in a fully smooth channel and pipe. The first, second, and third order predictions based on higher order logarithmic law velocity profile.

Grahic Jump Location
Figure 3

Comparison of the thermal Reynolds heat flux peak location yt+m and peak value τt+m with the DNS data of Abe (32) for molecular Prandtl number σ=0.71 for fully developed flow in a fully smooth channel and pipe. The first and third order predictions based on higher order logarithmic law for temperature profile.

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