## 4 Conclusions  
This article numerically simulates static evaporation and sloshing dynamics in LCO\({}_{2}\) storage tanks, providing a comprehensive analysis of thermodynamic and hydrodynamic behaviors under varying pressures and sloshing conditions. Key findings, with implications for engineering design and operation, include the following:  
1. Static evaporation initiates vortex formation near tank walls, driven by buoyancy and phase-change effects, resulting in gas-phase temperature rises up to 2.5 K due to the unique physical properties of CO\({}_{2}\). Sloshing effectively reduces thermal stratification in the vapor phase by enhancing interfacial heat and mass transfer, particularly near bulkheads, thus lowering peak temperatures;
2. Increased storage pressure significantly suppresses natural convection, leading to a narrower range of vortex formation and a deceleration of fluid. Operation near resonance sloshing periods (e.g., 8.6 s at 80% filling) amplifies interfacial disturbances, minimizing vapor temperature gradients (\(\Delta\)T \(\approx\) 0.1 K) through intense mixing, while off-resonance periods result in considerably larger gradients (\(\Delta\)T \(\approx\) 0.3 K);
3. Boil-off gas (BOG) generation exhibits a clear inverse relationship with storage pressure, plateauing above 1.5 MPa. Conversely, low filling rates (30%) can exacerbate gas-phase thermal gradients due to enhanced interfacial instabilities, potentially leading to increased BOG. Quantitatively, average BOG generation rates varied significantly with the filling ratio;
4. Liquid-phase flow inertia dominates under sloshing conditions, effectively suppressing surface rupture at high filling rates. In contrast, low filling rates prioritize gas-liquid interfacial interactions, intensifying splashing and thermal stratification in the gas phase. The insights gained from this study offer valuable guidance for optimizing LCO\({}_{2}\) storage tank design and operational strategies. By carefully selecting operating pressures and avoiding resonance sloshing frequencies, BOG losses can be minimized, and thermal management enhanced. Higher filling rates, while potentially increasing BOG in static conditions, can offer advantages during sloshing by promoting mixing and reducing thermal stratification. However, the current study has limitations, including simplifications in the sloshing model. Future research should focus on exploring more complex sloshing scenarios, investigating a wider range of tank geometries and sizes, and importantly, conducting experimental studies to validate numerical predictions. Furthermore, exploring the economic implications of different design and operational choices based on these findings would be beneficial. This research contributes to a deeper understanding of the complex interplay between thermodynamic and hydrodynamic phenomena in LCO\({}_{2}\) storage tanks, providing a foundation for improved design and operational practices aimed at enhancing efficiency and safety. **Author Contributions:** Conceptualization, M.S. and Z.Z. ; methodology, M.S. ; software, M.S. and J.G. ; validation, M.S. and J.G. ; formal analysis, M.S. and Z.Z. ; writing--original draft preparation, M.S. ; writing--review and editing, Z.Z. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by the authors on request. **Acknowledgments:** The authors sincerely thank the editors and anonymous reviewers for their constructive comments, which significantly improved the quality of this paper. Use DeepSeek V3 and Chat GPT 3.5 for language polishing during the article writing process. **Conflicts of Interest:** The authors declare no conflicts of interest.