On Predicting the Effects of Streamline Curvature on the Turbulent Prandtl Number

[+] Author and Article Information
Bassam A. Younis

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

Stanley A. Berger

Department of Mechanical Engineering,  University of California, Berkeley, CA 94720-1740saberger@me.berkeley.edu

J. Appl. Mech 73(3), 391-396 (Nov 01, 2005) (6 pages) doi:10.1115/1.2151208 History: Received February 10, 2004; Revised November 01, 2005

Streamline curvature in the plane of the mean flow is known to exert a proportionately greater effect on the turbulent mixing processes than might be expected from inspection of the conservation equations governing the evolution of the turbulence field. For the case of momentum transport, streamline curvature in the destabilizing sense increases the Reynolds stresses throughout all regions of the flow while the effects of stabilizing curvature are to reduce these parameters relative to their plane flow values. In the limit of strong stabilizing effects, the turbulence activity is suppressed altogether with the mean flow and turbulence parameters asymptoting to their laminar-flow limits. When heat transfer is present, the experimental findings appear to suggest that the rate of heat transfer by the turbulent motions is more sensitive to the effects of curvature than that of momentum transfer. This is equivalent to an increase in the value of the turbulent Prandtl number with increasing stabilizing curvature. The conventional gradient-transport model, with its built-in assumption of constant Prandtl number, cannot reproduce this result. The purpose of the work reported in this paper was to investigate whether the use of alternative, explicit, and nonlinear models for the turbulent scalar fluxes results in the prediction of a more realistic response of the turbulent Prandtl number to stabilizing curvature effects.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Predicted and measured evolution of thermal eddy diffusivity in decaying grid turbulence. Symbols are data of Sirivat and Warhaft (22) for (a) U=3.4m∕s; (b) U=6.3m∕s. Predictions: —, Younis (18); ---, Rogers (16); -. -. -, Gibson (13); --- Rubinstein and Barton (17); ⋯. Gradient transport (Eq. 1).

Grahic Jump Location
Figure 2

Predicted variation of relative stress levels with curvature parameter (data of Champagne (26))

Grahic Jump Location
Figure 3

Variation of relative stress levels (top) and the turbulent Prandtl number with curvature parameter, lines as in Fig. 1



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