Critical assessment of RANS Models for Turbulent Heat Transfer in Low-Prandtl-Number Forced Convection

Abstract

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.