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

Abstract

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.