Improved Simulations of Heat Transfer in Liquid-Metal Flows

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Abstract
In liquid-metal flows, the predictions of the Nusselt number (heat transfer) by Reynolds-averaged Navier–Stokes models of turbulence that use the assumption of a constant turbulent Prandtl number can be significantly off. Heat transfer analyses were performed with a number of turbulence models for flows in a triangular rod bundle and in a pipe, and model predictions were compared with experimental data. Emphasis was placed on the low Reynolds (low-Re) number k-ε model that resolves the boundary layer and does not use “logarithmic wall functions.” The high Reynolds (high-Re) number k-ε model underpredicts the Nusselt number up to 30%, while the low-Re number model overpredicts it up to 34%. For high Peclet number values, the low-Re number model provides better predictions than the high-Re number model. For Peclet numbers higher than 1500, the predictions of the Reynolds stress model (RSM) are in very good agreement with experimental measurements, but for lower Peclet number values its predictions are significantly off. A relationship was developed that expresses the turbulent Prandtl number as a function of the ratio of the turbulent viscosity to the molecular viscosity. With this modified turbulent Prandtl number, for the flow in the rod bundle the predictions of the low-Re number model are well within the spread of the experimental measurements. For pipe flow, the model predictions are not as sensitive to the correction of the turbulent Prandtl number as they are in the case of the flow in a bundle. The modified low-Re number model underpredicts the limited experimental data by 4%.

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