基于k-ε-kθ-εθ模型的液态金属三角形棒束数值传热研究

Numerical Heat Transfer Study of Liquid Metal in Triangular Rod Bundle Based on k-ε-kθ-εθ Model

  • 摘要: 相比恒定的湍流普朗特数(Prt)模型,四方程模型通过引入湍流时间尺度来考虑液态金属的速度和温度边界层之间的差异性,有望提高具有低普朗特数(Pr)传热特性的液态金属数值传热精度。然而四方程模型的输运形式受限于其复杂的边界条件。为简化湍流变量的边界条件,本研究基于泰勒级数展开和近壁湍流分析方法建立了各向同性四方程kkθεθ模型。基于开源计算流体力学程序OpenFOAM数值计算了液态金属(Pr=0.01)在三角形排列棒束内不同贝克莱数(Pe)、不同栅距比(P/D)的充分发展流动传热过程。将kkθεθ模型、Prt=0.85模型和Kays模型的数值结果与实验关系式进行了对比,结果表明:Prt=0.85模型过高估计了液态金属的努塞尔数,Kays模型和kkθεθ模型传热结果介于实验关联式之间;低Pe下Kays模型和kkθεθ模型预测结果相近,而高Pe下kkθεθ模型较Kays模型保守;随着雷诺数的增加,平均湍流普朗特数减小;随着栅距比的增加,平均湍流普朗特数增加。基于各向同性四方程kkθεθ模型,可为简化湍流边界条件和计算液态金属流动传热提供参考。

     

    Abstract: Compared with the constant turbulent Prandtl number (Prt) model, a fourequation model considers the difference between the velocity and temperature boundary layer of liquid metals by introducing the turbulence timescale, which is expected to improve the numerical heat transfer accuracy of liquid metals with low Prandtl number (Pr) heat transfer characteristics. However, the transport form of a fourequation model is limited by its complex turbulent boundary conditions. In order to simplify the boundary conditions of turbulent variables and improve numerical stability for a fourequation model, an isotropic fourequation model that can use natural nearwall boundary conditions was considered in the present work. So, based on Taylor series expansion and nearwall turbulence analysis method, an isotropic fourequation kkθεθ model was established and the kkθεθ model coefficients and key damping functions for liquid metals were obtained. Based on the opensource computational fluid dynamics program OpenFOAM and the kkθεθ model solver, the fullydeveloped flow and heat transfer processes of liquid metals (Pr=0.01) in triangular rod bundles with different Peclet numbers (Pe=2504 000) and different pitchdiameter ratios (P/D=1.251.46) were numerically calculated. The numerical Nusselt number results of the isotropic fourequation kkθεθ model, Prt=0.85 model and Kays model were compared with the available experimental and derivation correlations. The results show that Prt=0.85 model and Friedland correlation overestimate the Nusselt number of liquid metals, and the heat transfer results of the Kays model and the kkθεθ model are almost between the experimental correlation. The prediction Nusselt number results of the Kays model and the kkθεθ model are similar at low Peclet numbers, but the isotropic kkθεθ model is conservative compared with Kays model at high Peclet numbers. With the increase of P/D, the kkθεθ model gradually intersects with the Subbotin correlation at a certain Peclet number. If P/D is constant, the Nusselt number increases with the increase of the Peclet number. While the Peclet number is not changed, the Nusselt number increases with the increase of P/D. Then detailed local heat transfer phenomena for liquid metals in triangular rod bundles were analyzed, including dimensionless temperature, dimensionless temperature fluctuation, dimensionless thermal diffusion coefficient and dimensionless turbulent Prandtl number. Due to the large thermal conductivity and thick thermal boundary layer of liquid metals, the molecular heat conduction nearwall is stronger than the turbulent heat diffusion. When the Peclet number reaches a certain degree, the inflection point of turbulent heat diffusion greater than molecular heat conduction begins to appear. With the increase of Peclet number, the mean turbulent Prandtl number decreases. With the increase of P/D, the average turbulent Prandtl number increases. Based on the isotropic fourequation kkθεθ model, simple turbulent boundary conditions can be used and more references can be provided for the calculation of liquid metal flow and heat transfer.

     

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