Assessment and improvement on the applicability of turbulent-Prandtl-number models in RANS for liquid metals

Purpose The purpose of this paper is to develop new semi-empirical heat transfer correlations for turbulent flow of liquid metals in the tubes, and then to compare these correlations with the experimental data. The Prandtl and Reynolds numbers can vary in the ranges: 0.0001 ≤ Pr ≤ 0.1 and 3000 ≤ Re ≤ 106. Design/methodology/approach The energy conservation equation averaged by Reynolds was integrated using the universal velocity profile determined experimentally by Reichardt for the turbulent tube flow and four different models for the turbulent Prandtl number. Turbulent heat transfer in the circular tube was analyzed for a constant heat flux at the inner surface. Some constants in different models for the turbulent Prandtl number were adjusted to obtain good agreement between calculated and experimentally obtained Nusselt numbers. Subsequently, new correlations for the Nusselt number as a function of a Peclet number was proposed for different models of the turbulent Prandtl number. Findings The inclusion of turbulent Prandtl number greater than one and the experimentally determined velocity profile of the fluid in the tube while solving the energy conservation equation improved the compatibility of calculated Nusselt numbers, with Nusselt numbers determined experimentally. The correlations proposed in the paper have a sound theoretical basis and give Nusselt number values that are in good agreement with the experimental data. Research limitations/implications Heat transfer correlations proposed in this paper were derived assuming a constant heat flux at the inner surface of the tube. However, they can also be used for a constant wall temperature, as for the turbulent flow (Re > 3,000), the relative difference between the Nusselt number for uniform wall heat flux and uniform wall temperature is very low. Originality/value Unified, systematic approach to derive correlations for the Nusselt number for liquid metals was proposed in the paper. The Nusselt number was obtained from the solution of the energy conservation equation using the universal velocity profile and eddy diffusivity determined experimentally, and various models for the turbulent Prandtl number. Four different relationships for the Nusselt number proposed in the paper were compared with the experimental data.

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Turbulent Heat Transfer to Heavy Liquid Metals in Circular Tubes

Volume 4 ◽

10.1115/ht-fed2004-56562 ◽

2004 ◽

Cited By ~ 2

Author(s):

X. Cheng ◽

A. Batta ◽

H. Y. Chen ◽

N. I. Tak

Keyword(s):

Heat Transfer ◽

Prandtl Number ◽

Liquid Metals ◽

Turbulence Models ◽

Numerical Results ◽

Heavy Liquid ◽

Turbulent Heat Transfer ◽

Turbulent Heat ◽

Turbulent Prandtl Number ◽

Mesh Structure

The present paper gives a brief literature review on turbulent heat transfer in heavy liquid metals (HLM), especially liquid lead-bismuth eutectic (LBE). Some models available in the open literature on heat transfer and turbulent Prandtl number are assessed. In addition, CFD analysis is carried out for circular tube geometries. The effect of turbulence models, mesh structure and turbulent Prandtl number on the numerical results is studied. Application of ε-type turbulence models with scalable wall function shows less dependence of the numerical results on mesh structure than the ω-type turbulence models with automatic wall treatment. The turbulent Prandtl number affects strongly the heat transfer performance. Comparison between the CFD results, heat transfer correlations and heat transfer test data reveals a decrease in turbulent Prandtl number by increasing Reynolds number. Based on the results achieved, recommendations are made on correlations of heat transfer and turbulent Prandtl number for LBE flows.

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