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Research Papers: Natural and Mixed Convection

Numerical Experiments in Turbulent Natural Convection Using Two-Equation Eddy-Viscosity Models

[+] Author and Article Information
X. Albets-Chico, C. D. Pérez-Segarra

Centre Tecnològic de Transferència de Calor,  Universitat Politècnica de Catalunya (UPC), ETSEIAT, C∕ Colom 11, 08222 Terrassa, Catalunya, Spain

A. Oliva1

Centre Tecnològic de Transferència de Calor,  Universitat Politècnica de Catalunya (UPC), ETSEIAT, C∕ Colom 11, 08222 Terrassa, Catalunya, Spain

1

Corresponding author.

J. Heat Transfer 130(7), 072501 (May 19, 2008) (11 pages) doi:10.1115/1.2907432 History: Received March 05, 2007; Revised October 17, 2007; Published May 19, 2008

This work is focused on the simulation and prediction of turbulent natural convection flows by means of two-equation eddy-viscosity models. In order to show the generality, precision, and numerical issues related to these models under natural convection, three different buoyancy-driven cavities have been simulated: a tall cavity with a 30:1 aspect ratio, a cavity with a 5:1 aspect ratio, and, finally, a 4:1 aspect ratio cavity. All cases are solved under moderate and∕or transitional Rayleigh numbers (2.43×1010, 5×1010, and 1×1010, respectively) and all simulations are compared to experimental and∕or direct numerical simulation data available in literature. These different situations allow to check the applicability of two-equation eddy-viscosity models in buoyancy-driven flows, giving criteria on computational effort∕precision and their physical behavior.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Cavity 1 (A=30, RaH=2.43×1010). Nu¯ prediction (a) and v¯ at y=H∕2 prediction (b) for all the models.

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Figure 2

Cavity 2 (A=5, RaH=5×1010). Comparison of the normalized buoyancy and shear production effects for WX93 and PDH+D model. While for WX93 model, Nkb increases as grid is refined (giving an asymptotic laminar cavity) (a): PHD+D model is able to give an asymptotic prediction, thanks to the stable Nkb prediction for m5 mesh (b).

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Figure 3

(a) Nks, Nkb prediction for m1, m2, and m3 meshes for IL model under Cavity 2 (A=5, RaH=5×1010). (b) Nks, Nkb prediction for m5, m4, and m3 meshes for GPC model under Cavity 3 (A=4, RaH=1×1010).

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Figure 4

Cavity 2 (A=5, RaH=5×1010). Comparison of the Nu evolution for WX93 and PDH+D model. On the one hand, it is shown that the WX93 model is not capable of giving asymptotic behavior in the prediction of transition point when refining the mesh (a). On the other, the PDH+D model is able to give an asymptotic transition point prediction (b).

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Figure 5

Cavity 3 (A=4, RaH=1×1010). (a) Dimensionless temperature profiles: y=H∕2. (b)Nu number prediction for GPC and PDH+D models. Sudden rising of Nu number indicates transition from laminar to turbulent flow.

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Figure 6

Cavity 3 (A=4, RaH=1×1010). Dimensionless v profiles: (a) y=H∕2; (b) y=15H∕16.

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Figure 7

Cavity 3 (A=4, RaH=1×1010). Dimensionless u profiles: (a) y=H∕2; (b) y=15H∕16.

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Figure 8

Cavity 3 (A=4, RaH=1×1010). Dimensionless k profiles: (a) y=H∕2; (b) y=15H∕16.

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Figure 9

Cavity 3 (A=4, RaH=1×1010). Dimensionless ϵ profiles: (a) y=H∕2; (b) y=15H∕16.

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