The aviation sector is increasingly exploring electrified propulsion architecture based on cryogenic liquid hydrogen (LH₂) due to LH₂'s high power density. A major engineering challenge in this transition is designing lightweight, efficient storage tanks that provide adequate thermal insulation to limit boil-off while maintaining competitive gravimetric performance and meeting aircraft integration constraints. As experimental testing with cryogenic fluids is extremely costly, numerical modeling has become a cornerstone for the design and analysis of LH₂ storage systems [1], and certification procedures based on numerical tests are also being considered. Low-order numerical models provide fast and reliable feedback during early design stages, supporting tank pre-sizing, insulation thickness selection, scalability assessments [2], and system-level analyses such as cool-down, filling, and operational phases. However, higher-fidelity simulations are essential for refining these analyses and validating or calibrating reduced-order approaches. In particular, detailed CFD analyses are required to accurately characterize heat transfer phenomena, such as heat fluxes and convective coefficients, associated with internal heat exchangers used for temperature control. Furthermore, three-dimensional parametric simulations are necessary to capture the effects of structural elements, including supports and thermal bridges, which can significantly influence overall thermal performance. This work presents a set of parametric CFD-based methodologies developed using open-source meshing and simulation tools. The proposed approaches are applied to (i) the analysis and optimization of internal tube heat exchangers within LH₂ storage tanks, and (ii) the optimization of support structures and thermal bridge placement to minimize parasitic heat loads. The results highlight the role of high-fidelity parametric simulations in enabling the design of innovative LH₂ storage concepts and in strengthening the reliability of low-order modeling frameworks. The authors would like to acknowledge the financial support of the MISIONES 2024 CDTI (Centro para el Desarrollo Tecnológico y la Innovación) program, through the project VITAL-LH2 (Grant No. MIG-20241172).