Numerical correlations for thermal-hydraulic performance of He-Xe and He-Kr binary mixtures in pebble-bed geometries

A comprehensive CFD study was conducted to analyze the thermal and hydraulic behavior of He-Xe and He-Kr binary mixtures in pebble-bed geometries with varying Reynolds numbers (10 3 -5×10 4 ) and helium molar fractions (0.2-0.8). The simulations included both transitional and fully developed turbulent regimes, allowing for a systematic assessment of the effect of mixture composition on convective heat transfer and pressure drop. The results showed that the Nusselt number grows monotonically with Reynolds number, with helium-rich mixtures (≥60% He) showing improved heat transfer due to helium's strong thermal conductivity, while heavier gas mixtures provide lower Nusselt numbers. Pressure drop trends show how gas density and velocity interact, with He-Kr combinations providing more hydraulic resistance than He-Xe at equal compositions. Both accurately predict Nusselt numbers and pressure drops across the studied parameter space, showing good agreement with well-established correlations in the literature. Two correlation models were developed: one that provides mixture-specific power-law relationships and another that generalizes the findings into a composition-dependent framework. Both accurately predict Nusselt numbers and pressure drops across the studied parameter space. The findings highlight the trade-off between thermal performance and hydraulic resistance, and they provide practical guidance for optimizing helium-heavy gas combinations in pebble-bed reactor cooling systems.