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RESEARCH PAPERS: Model Development

An Explicit Algebraic Model for Turbulent Heat Transfer in Wall-Bounded Flow With Streamline Curvature

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

Department of Civil & Environmental Engineering, University of California, Davis, CA 95616

B. Weigand, S. Spring

Institut fuer Thermodynamik der Luft- und Raumfahrt, University of Stuttgart, 70569 Stuttgart, Germany

J. Heat Transfer 129(4), 425-433 (Jul 31, 2006) (9 pages) doi:10.1115/1.2709960 History: Received March 06, 2006; Revised July 31, 2006

Fourier’s law, which forms the basis of most engineering prediction methods for the turbulent heat fluxes, is known to fail badly in capturing the effects of streamline curvature on the rate of heat transfer in turbulent shear flows. In this paper, an alternative model, which is both algebraic and explicit in the turbulent heat fluxes and which has been formulated from tensor-representation theory, is presented, and its applicability is extended by incorporating the effects of a wall on the turbulent heat transfer processes in its vicinity. The model’s equations for flows with curvature in the plane of the mean shear are derived and calculations are performed for a heated turbulent boundary layer, which develops over a flat plate before encountering a short region of high convex curvature. The results show that the new model accurately predicts the significant reduction in the wall heat transfer rates wrought by the stabilizing-curvature effects, in sharp contrast to the conventional model predictions, which are shown to seriously underestimate the same effects. Comparisons are also made with results from a complete heat-flux transport model, which involves the solution of differential transport equations for each component of the heat-flux tensor. Downstream of the bend, where the perturbed boundary layer recovers on a flat wall, the comparisons show that the algebraic model yields indistinguishable predictions from those obtained with the differential model in regions where the mean-strain field is in rapid evolution and the turbulence processes are far removed from local equilibrium.

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Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Flow domain and coordinate systems

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Figure 2

Heated channel flow (Pr=0.7). Data of Debusschere. Models: solid line, present; dotted line, (31); dashed line, (32); dotted-dashed line, (33); x-x-x, (34).

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Figure 3

Heated Couette flow (Pr=0.7). Data of Debusschere (Models: solid line, present; dotted line, (31); dashed line, (32); dotted-dashed line, (33); x-x-x, (34))

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Figure 4

Streamwise variation of wall static-pressure coefficient; vertical lines signify location of convex bend

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Figure 5

Predicted and measured variation of freestream velocity (Ue∕Uref)

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Figure 6

Predicted and measured variation of boundary layer thickness

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Figure 7

Predicted and measured streamwise variation of skin-friction coefficient

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Figure 8

Predicted and measured shape factor

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Figure 9

Mean-velocity profiles in wall coordinates

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Figure 10

Predicted and measured profiles of −uv¯

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Figure 11

Predicted and measured variation of Stanton number

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Figure 12

Mean-temperature profiles in wall coordinates

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Figure 13

Predicted and measured profiles of −vt¯

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Figure 14

Predicted and measured profiles of −ut¯

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