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RESEARCH PAPERS

kϵ Model for the Atmospheric Boundary Layer Under Various Thermal Stratifications

[+] Author and Article Information
Cédric Alinot

École de Technologie Supérieure,  Department of Mechanical Engineering, Montréal, QC H3C 1K3 Canada

Christian Masson1

École de Technologie Supérieure,  Department of Mechanical Engineering, Montréal, QC H3C 1K3 Canadachristian.masson@etsmtl.ca

1

Correspondence to: Christian Masson, École de Technologie Supérieure, 1100 Notre-Dame Ouest, Montréal, Québec, Canada, H3C 1K3. Telephone: (514) 396-8504; fax: (514) 396-8530; e-mail: christian.masson@etsmtl.ca. Holder of the Canada Research Chair in the Aerodynamics of Wind Turbines in Nordic Environment.

J. Sol. Energy Eng 127(4), 438-443 (Jun 02, 2005) (6 pages) doi:10.1115/1.2035704 History: Received November 19, 2004; Revised May 26, 2005; Accepted June 02, 2005

This paper presents a numerical method for predicting the atmospheric boundary layer under stable, neutral, or unstable thermal stratifications. The flow field is described by the Reynolds’ averaged Navier-Stokes equations complemented by the kϵ turbulence model. Density variations are introduced into the momentum equation using the Boussinesq approximation, and appropriate buoyancy terms are included in the k and ϵ equations. An original expression for the closure coefficient related to the buoyancy production term is proposed in order to improve the accuracy of the simulations. The resulting mathematical model has been implemented in FLUENT . The results presented in this paper include comparisons with respect to the Monin-Obukhov similarity theory, measurements, and earlier numerical solutions based on kϵ turbulence models available in the literature. It is shown that the proposed version of the kϵ model significantly improves the accuracy of the simulations for the stable atmospheric boundary layer. In neutral and unstable thermal stratifications, it is shown that the version of the kϵ models available in the literature also produce accurate simulations.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Velocity profiles on a flat terrain with H=35m, u0(H)=10m∕s, and TI(H)=8%

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Figure 2

Temperature profiles on a flat terrain with H=35m, u0(H)=10m∕s, and TI(H)=8%

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Figure 3

Turbulent intensity profiles on a flat terrain with H=35m, u0(H)=10m∕s, and TI(H)=8%

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Figure 4

Turbulent dissipation profiles on a flat terrain with H=35m, u0(H)=10m∕s, and TI(H)=8%

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Figure 5

Neutral atmospheric boundary layer with H=35m, u0(H)=10m∕s, TI(H)=8%, z0=1.88mm, and L→∞

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Figure 6

Stable atmospheric boundary layer with H=35m, u0(H)=10m∕s, TI(H)=8%, z0=6mm, and L=191m

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Figure 7

Unstable atmospheric boundary layer with H=35m, u0(H)=10m∕s, TI(H)=8%, z0=0.4mm, and L=−231m

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Figure 8

Stable atmospheric boundary layer with H=55m, u0(H)=9m∕s, TI(H)=9%, z0=50mm, and L=177m

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Figure 9

Unstable atmospheric boundary layer with H=55m, u0(H)=9m∕s, TI(H)=9%, z0=0.4mm, and L=−121m

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