Thermal modeling of LN₂-cooled terminals with integrated heat exchangers for superconducting applications

This work presents a comprehensive modeling framework for conduction-cooled terminals with integrated subcooled liquid nitrogen (LN₂)-driven heat exchangers (HXs), developed to support the thermal design of cryogenic power systems. The approach combines analytical, CFD-informed, and semi-empirical models to evaluate terminal performance under varying electrical loads and LN₂ flow conditions. Three analytical models were assessed for estimating cold-end heat loads: the General Model (G.M.), which incorporates temperature-dependent material properties; the Averaged Model (A.M.); and the Wiedemann-Franz Model (W.-F.M.). At 1300 A, the A.M. and W.-F.M. overpredict the cold-end heat load by factors of approximately 12 and 16, respectively, compared to the G.M. (52.5 W and 69 W vs. 4.4 W), emphasizing the importance of resolving axial heat redistribution. Validated high-fidelity CFD simulations for the HX-2-8 configuration captured conjugate heat transfer, resistive heating, and entrance flow effects. The turbulent Prandtl number (Pr_T) was selected through an iterative calibration process based on simulated thermal gradients and solid–liquid interface behavior, where the standard k–ε model with a constant Prandtl number of 0.85 yielded stable and physically consistent results. A tailored semi-empirical model further revealed a counterintuitive phenomenon: under certain conditions, the copper structure locally cools the LN₂, which is driven by strong axial conduction and spatial temperature gradients. The presented framework enables accurate prediction of thermal boundaries and supports geometry-specific optimization. It provides both physical insight and practical utility in the design of next-generation cryogenic terminals for superconducting power systems.