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Forced Convection

Prediction of Turbulent Heat Transfer in Rotating and Nonrotating Channels With Wall Suction and Blowing

[+] 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

A. Laqua2

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

1

Present address: Alstom Switzerland, Brown Boveri Strasse 7, 5401 Baden, Switzerland.

2

Corresponding author.

J. Heat Transfer 134(7), 071702 (May 22, 2012) (9 pages) doi:10.1115/1.4006014 History: Received February 23, 2011; Revised November 17, 2011; Published May 22, 2012; Online May 22, 2012

This paper reports on the prediction of heat transfer in a fully developed turbulent flow in a straight rotating channel with blowing and suction through opposite walls. The channel is rotated about its spanwise axis; a mode of rotation that amplifies the turbulent activity on one wall and suppresses it on the opposite wall leading to reverse transition at high rotation rates. The present predictions are based on the solution of the Reynolds-averaged forms of the governing equations using a second-order accurate finite-volume formulation. The effects of turbulence on momentum transport were accounted for by using a differential Reynolds-stress transport closure. A number of alternative formulations for the difficult fluctuating pressure–strain correlations term were assessed. These included a high turbulence Reynolds-number formulation that required a “wall-function” to bridge the near-wall region as well as three alternative low Reynolds-number formulations that permitted integration through the viscous sublayer, directly to the walls. The models were assessed by comparisons with experimental data for flows in channels at Reynolds-numbers spanning the range of laminar, transitional, and turbulent regimes. The turbulent heat fluxes were modeled via two very different approaches: one involved the solution of a modeled differential transport equation for each of the three heat-flux components, while in the other, the heat fluxes were obtained from an explicit algebraic model derived from tensor representation theory. The results for rotating channels with wall suction and blowing show that the algebraic model, when properly extended to incorporate the effects of rotation, yields results that are essentially identically to those obtained with the far more complex and computationally intensive heat-flux transport closure. This outcome argues in favor of incorporation of the algebraic model in industry-standard turbomachinery codes.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Flow considered and coordinates system

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Figure 2

Variation of skin-friction coefficient with Reynolds-number in stationary channel. Equation (16), - - - predictions; Gerolymos and Vallet [9], ○; Launder and Shima [20], △; Kebede [11], ◊; Gibson and Launder [12], ▽; DNS of Tomita [20], □.

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Figure 3

Variation of Nusselt number with Reynolds-number in stationary channel. Laminar solution: - - -, Turbulent correlations Eq. (17: —-. Predictions: Gerolymos and Vallet [9]: Algebraic ○, Differential □; Kebede [11]: Algebraic ◊, Differential ▷. DNS of Tomita [22]: ▵.

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Figure 4

Mean velocity and Reynolds stresses in stationary channel. DNS of Tomita [22]: ○. Predictions: Gerolymos and Vallet [9]: —-, Launder and Shima [10]: -·-·-, Gibson and Launder [12]: - - - -.

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Figure 5

Mean temperature and heat fluxes in stationary channel. DNS of Tomita [22]: ○. Predictions: Algebraic flux model - - - -, Differential flux model -·-·-.

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Figure 6

Mean velocity and Reynolds stresses in stationary channel with blowing and suction (Vw  = 0.05). DNS of Kasagi [23]: ○. Predictions: Gerolymos and Vallet [9]: —-, Launder and Shima [10]: -·-·-, Gibson and Launder [12]:- - - -.

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Figure 7

Mean temperature and heat fluxes in stationary channel with blowing and suction (Vw  = 0.05). DNS of Kasagi [23]: ○. Predictions: Algebraic flux model - - - -, Differential flux model -·-·-.

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Figure 8

Variation of friction velocity with Rotation number. Data of Johnston [24]: ○. Predictions: Gerolymos and Vallet [9]: —-, Gibson and Launder [12]: - - - -.

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Figure 9

Mean velocity and Reynolds stresses in rotating channel (Ro = 0.159). DNS of Nishimura [25]: ○. Predictions: Gerolymos and Vallet [9]: —-, Gibson and Launder [12]: - - - -.

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Figure 10

Mean temperature and heat fluxes in rotating channel (Ro = 0.159). DNS of Nishimura [25]: ○. Predictions: Algebraic flux model: - - - -, Differential flux model: -·-·-·-, Fourier’s law: ·· · ·.

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