低普朗特数强制对流中湍流传热的雷诺平均 Navier-Stokes 模型的批判性评估
Critical assessment of RANS Models for Turbulent Heat Transfer in Low-Prandtl-Number Forced Convection
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中文总结 AI 辅助
研究液态金属低普朗特数强制对流中湍流传热的 RANS 模型，用 OpenFOAM v2212 评估多种模型组合，对比 DNS 数据等，发现部分模型可靠，如 k-ω SST 模型性能最佳，还统一公式并验证了模型特性。
中文摘要 AI 辅助
液态金属中湍流传热的雷诺平均 Navier-Stokes（RANS）建模仍然具有挑战性，因为极低的普朗特数削弱了动量和热传输之间的相似性。使用 OpenFOAM v2212 评估了几种用于液态金属强制对流的热湍流封闭模型。这些组合包括具有凯斯（Kays）普朗特数关联的 k-ω SST 模型、四方程 k-ε-kθ-εθ 模型、对数 k-Ω-kθ-Ωθ 模型以及两种用于湍流动能通量的代数热通量公式与低雷诺数 k-ε 模型或椭圆混合雷诺应力模型（EBRSM）相结合。它们在通道流、管道流和加热后向台阶流中针对直接数值模拟（DNS）数据和原始出版物的结果进行评估，重点关注可重复性、鲁棒性和准确性。只有有限的模型子集被证明对低普朗特数流动可靠。具有凯斯关联的 k-ω SST 模型在所有情况下都给出了最稳健的性能和准确的温度预测。k-ε-kθ-εθ模型显示出良好的可重复性和与参考数据的满意一致性，仍然是最一致的多方程替代方案。对数四方程模型表现出数值鲁棒性降低，而与 k-ε 封闭相结合的代数热通量模型尽管正确预测了动量场，但未能再现已发表的热结果。基于 EBRSM 的代数热通量公式再现了选定的参考结果，但存在显著的鲁棒性限制。该研究建立了所研究封闭模型的统一公式，纠正了其已发表形式中的不一致性，并验证了它们的可重复性和鲁棒性。
英文摘要
RANS modeling of turbulent heat transfer in liquid metals remains challenging because the very low Prandtl number weakens the similarity between momentum and thermal transport. Several thermal turbulence closures for forced convection in liquid metals are assessed using OpenFOAM v2212. The combinations include the $k$--$ω$ SST model with the Kays correlation for $\mathrm{Pr}_t$, the four-equation $k$--$ε$--$k_θ$--$ε_θ$ model, the logarithmic $k$--$Ω$--$k_θ$--$Ω_θ$ model, and two algebraic heat-flux formulations for $\overline{u_i'θ'}$ coupled with either a low-Reynolds $k$--$ε$ model or an elliptic blending Reynolds-stress model (EBRSM). They are evaluated in channel flow, pipe flow, and heated backward-facing step flow against DNS data and results from the original publications, focusing on reproducibility, robustness, and accuracy. Only a limited subset of models proves reliable for low-$\mathrm{Pr}$ flows. The $k$--$ω$ SST model with the Kays correlation gives the most robust performance and accurate temperature predictions in all cases. The $k$--$ε$--$k_θ$--$ε_θ$ model shows good reproducibility and satisfactory agreement with reference data, remaining the most consistent multi-equation alternative. The logarithmic four-equation model exhibits reduced numerical robustness, while the algebraic heat-flux model coupled with the $k$--$ε$ closure fails to reproduce published thermal results despite correct prediction of the momentum field. The EBRSM-based algebraic heat-flux formulation reproduces selected reference results but suffers from significant robustness limitations. The study establishes a unified formulation of the examined closures, correcting inconsistencies in their published forms, and verifies their reproducibility and robustness.
