Critical assessment of RANS models for turbulent heat transfer in low-Prandtl-number forced convection

Reliable modeling of turbulent heat transfer in liquid metals via Reynolds–Averaged Navier–Stokes (RANS) remains challenging because the very low Prandtl number weakens the similarity between momentum and thermal transport. In this work, several thermal turbulence closures for forced convection in liquid metals are assessed using the finite-volume code OpenFOAM v2212. The investigated model combinations include the 𝑘 – 𝜔 SST model with the Kays correlation for the turbulent Prandtl number, the four-equation 𝑘 – ɛ – 𝑘 𝜃 – ɛ 𝜃 model, the logarithmic 𝑘 – 𝛺 – 𝑘 𝜃 – 𝛺 𝜃 model, and two algebraic heat-flux formulations coupled with either a low-Reynolds 𝑘 – ɛ model or an elliptic blending Reynolds-stress model (EBRSM). The models are evaluated in turbulent channel flow, pipe flow, and heated backward-facing step flow against direct numerical simulation data and reference results reported in the original model publications, with particular attention to reproducibility, numerical robustness, and predictive accuracy. The results show that only a limited subset of models can be considered reliable for low-Prandtl-number flows. The 𝑘 – 𝜔 SST combined with the Kays correlation provides the most robust overall performance and accurate temperature predictions in all cases. The 𝑘 – ɛ – 𝑘 𝜃 – ɛ 𝜃 model also shows good reproducibility and satisfactory agreement with reference data, remaining the most consistent multi-equation alternative. In contrast, the logarithmic four-equation model exhibits reduced numerical robustness, while the algebraic heat-flux model coupled with the 𝑘 – ɛ momentum 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 by reconciling discrepancies and correcting inconsistencies in their published formulations, and systematically verifies their reproducibility and robustness in low-Prandtl-number forced convection.