Investigation of a Four-Parameter RANS Closure for Low-Prandtl-Number Liquid Metal Heat Transfer in Channels, Pipes, and Wire-Wrapped Rod Bundles

Liquid metals with a low Prandtl number (Pr) show a strong separation between momentum and heat transport, so Reynolds averaged Navier–Stokes (RANS) closures based on a prescribed turbulent Prandtl number may lose accuracy for local temperature and wall heat flux predictions. This work evaluates a four-parameter RANS closure that obtains the turbulent viscosity and turbulent thermal diffusivity from separate mechanical and thermal transport scales. The closure couples the shear stress transport k-ω momentum model with kθ-ϵθ thermal transport equations. The model is tested for forced convection under imposed wall heat flux in periodic channel flow, heated vertical lead–bismuth eutectic pipe flow, and the KALLA 19-rod wire-wrapped bundle. In the channel, direct benchmark comparisons at Reτ=180, 395, and 640 assess mean temperature and turbulent transport, while additional cases examine near-wall scaling and model trends up to Reτ=4400. In the pipe, the model follows the fully developed variation of the Nusselt number with the Péclet number (Pe) over 201≤Pe≤4890 and gives a lower Nusselt number error than the constant Prt calculations considered here. In the bundle, the model predicts local temperatures with mean absolute errors of 2.40, 3.36, and 4.51 K at the three measurement levels (ML1, ML2, and ML3) while also predicting the main pressure drop and thermal nonuniformity trends. The results support the independent thermal scale closure as a useful RANS approach for forced low Pr liquid metal heat transfer.