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Helical coil once-through tube steam generators (HCOTSGs) represent a promising heat exchanger solution for future applications in small-scale Lead-Bismuth Eutectic (LBE) fast reactors. Due to their complex geometry and thermal-hydraulic behavior, full-scale 3D simulation tools are essential for design optimization and safety assessment. In this work, a thermal-hydraulic model of an LBE HCOTSG is developed using the GeN-Foam multi-physics platform. It is employed to investigate flow and heat transfer characteristics under representative operating conditions. The model employs a porous-medium approach and is first validated against separate-effect tests for the two-phase water-steam flow on the tube side and the LBE flow on the shell side. Additionally, the coupled heat transfer process is compared with detailed high-fidelity simulations, demonstrating good agreement while significantly reducing computational cost. Following validation, the HCOTSG behavior is analyzed under both normal and off-normal conditions. Temperature changes and temperature differences at different radial locations were obtained. The study examines the influence of flow fluctuations and inlet non-uniformities on phase distribution and thermal performance. Overall, this study provides a comprehensive analysis of the thermal-hydraulic behavior of LBE HCOTSGs and demonstrates the capability of the developed tool to efficiently support design and safety evaluations.