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Research Papers: Forced Convection

Modeling the Effects of System Rotation on the Turbulent Scalar Fluxes

[+] Author and Article Information
B. A. Younis1

Department of Civil and Environmental Engineering, University of California, Davis, CA 95616bayounis@ucdavis.edu

B. Weigand

Institut für Thermodynamik der Luft- und Raumfahrt, Universität Stuttgart, 70569 Stuttgart, Germany

F. Mohr, M. Schmidt2

Institut für Thermodynamik der Luft- und Raumfahrt, Universität Stuttgart, 70569 Stuttgart, Germany

1

Corresponding author.

2

Present address: ALSTOM (Switzerland) Ltd., Brown Boveri Strasse 7, 5401 Baden, Switzerland.

J. Heat Transfer 132(5), 051703 (Mar 08, 2010) (14 pages) doi:10.1115/1.4000446 History: Received March 09, 2009; Revised August 28, 2009; Published March 08, 2010; Online March 08, 2010

A proposal for modeling the effects of system rotation on the turbulent scalar fluxes is presented. It is based on extension to rotating frames of an explicit algebraic model derived using tensor-representation theory. The model is formulated to allow for the turbulent scalar fluxes to depend on the details of the turbulence field and on the gradients of both the mean-velocity and the scalar. Such dependence, which is absent from conventional models, is required by the exact equations governing the transport of the scalar fluxes. The model’s performance is assessed, both a priori and by actual computations, by comparisons with results from recent direct numerical simulations (DNS) of flows in heated channels rotated about their streamwise, spanwise, and wall-normal axes. To place the new model’s performance in context, additional comparisons are made with predictions obtained from three alternative models, namely, the conventional gradient-transport model, a model that is implicit in the scalar fluxes derived by simplification of the modeled transport equations for the scalar fluxes, and a differential scalar-flux transport model. The results show that the present model yields predictions that are substantially in better agreement with the DNS results than the algebraic models, and which are indistinguishable from those obtained with the more complex differential model. However, important differences remain and reasons for these are discussed.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Geometry and coordinates system

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Figure 2

DNS results for spatial variation of time-scale ratio R with and without rotation: no rotation (○) (13), streamwise (△) (15), wall-normal (◆) (17), and average value (—)

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Figure 3

uθ¯ in stationary channel. DNS of Debusschere and Rutland (13). DNS (○), explicit (—), and implicit (⋅–⋅).

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Figure 4

vθ¯ in stationary channel. DNS of Debusschere and Rutland (13). DNS (○), explicit (—), implicit (⋅–⋅), and gradient-transport (– – –).

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Figure 5

Prt in stationary channel. DNS of Debusschere and Rutland (13). DNS (○), explicit (—), and Prt=0.85(–––).

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Figure 6

uθ¯ in channel with streamwise rotation. DNS of Wu and Kasagi (16) for Roτ=2.5. DNS (○), explicit (—), and implicit (⋅–⋅).

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Figure 7

vθ¯ in channel with streamwise rotation. DNS of Wu and Kasagi (16) for Roτ=2.5. DNS (○), explicit (—), implicit (⋅–⋅), and gradient-transport (– – –).

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Figure 8

Prt in channel with streamwise rotation. DNS of Wu and Kasagi (16) for Roτ=2.5. DNS (○), explicit (—), and Prt=0.85(–––).

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Figure 9

uθ¯ in channel with streamwise rotation. DNS of El-Samni and Kasagi (15) for Roτ=15. DNS (○), explicit (—), and implicit (⋅–⋅).

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Figure 10

vθ¯ in channel with streamwise rotation. DNS of El-Samni and Kasagi (15) for Roτ=15. DNS (○), explicit (—), implicit (⋅–⋅), and gradient-transport (– – –).

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Figure 11

wθ¯ in channel with streamwise rotation. DNS of El-Samni and Kasagi (15) for Roτ=15. DNS (○), explicit (—), and implicit (⋅–⋅).

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Figure 12

uθ¯ in channel with wall-normal rotation. DNS of El-Samni and Kasagi (17) for Roτ=0.04. DNS (○), explicit (—), and implicit (⋅–⋅).

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Figure 13

vθ¯ in channel with wall-normal rotation. DNS of El-Samni and Kasagi (17) for Roτ=0.04. DNS (○), explicit (—), implicit (⋅–⋅), and gradient-transport (– – –).

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Figure 14

uθ¯ in channel with spanwise rotation. DNS of Wu and Kasagi (16) for Roτ=2.5. DNS (○), explicit (—), and implicit (⋅–⋅).

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Figure 15

vθ¯ in channel with spanwise rotation. DNS of Wu and Kasagi (16) for Roτ=2.5. DNS (○), explicit (—), implicit (⋅–⋅), and gradient-transport (– – –).

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Figure 16

Prt in channel with spanwise rotation. DNS of Wu and Kasagi (16) for Roτ=2.5. DNS (○), explicit (—), and Prt=0.85(–––).

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Figure 17

Skin-friction coefficient in stationary channel. Laminar solution (- -) and Turbulent correlations (20) (- -). Predictions: Gerolymos and Vallet (18) (○).

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Figure 18

Nusselt number in stationary channel. Laminar solution (- -), turbulent correlations (21) (—), explicit (○), and differential flux model (△).

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Figure 19

Friction velocities in spanwise-rotating channel. Data of Johnston (1) (○) and Gerolymos and Vallet (18) (—).

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Figure 20

Rotating channel flow with Reτ=150 and Ro=0.159. DNS (○), explicit (—), differential flux model (–⋅–⋅–), and gradient-transport (⋯).

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