**5. Conclusions**

In this paper, viscous CFD two-phase flow simulations of a novel, vertical, axisymmetric AUH launched into water were carried out based on STAR-CCM+ VOF, UDF, and overlapping grid technologies. Numerical analyses of the axisymmetric impact forces on the disk-type AUH in the vertical plane were implemented with different water entry velocities and immersion angles. The deformable free surface and flow structure, from entry of the inclined AUH structure, were captured in a numerical tank, and the cavity around the AUH was found to form in a highly asymmetric way. The asymmetric degree of the formed cavity is highly correlated with the water entry velocity and immersion angle of the AUH.

In summary, the following conclusions are drawn:


Improvements will be made in future studies, including experiments with the same conditions as the numerical simulation. Based on a fabricated AUH, water entry impact force data on airborne-launched AUH, or on the air-launched AUHs using an improved single-arm suspension, will

be collected in a sea trial to compare with the numerical simulation results. In addition, current and wave effects on launched AUHs will be considered in future work.

**Author Contributions:** Conceptualization, C.-W.C.; Data curation, Y.-F.L.; Formal analysis, Y.-F.L.; Funding acquisition, C.-W.C. and Y.-F.L.; Resources, C.-W.C.; Writing—original draft, C.-W.C. and Y.-F.L.; Writing—review & editing, C.-W.C. and Y.-F.L. The revision was done by C.-W.C. under the direction and supervision by C.-W.C.

**Funding:** This research was funded by the National Key R&D Program of China gran<sup>t</sup> number 2017YFC0306100. And this research was funded by the National Science Foundation of China gran<sup>t</sup> number 51409230. And this research was funded by the Zhejiang Zhoushan Science and Technology Project gran<sup>t</sup> number 2018C81041.

**Acknowledgments:** The authors wish to thank the National Key R&D Program of China (Project Title: Autonomous Underwater Hovering-Vehicle, Project Number: 2017YFC0306100), the National Science Foundation of China (Project Title: Research on Vortex-Based Boundary Integral Method Estimating AUV Maneuverability Based on Euler–Rodriguez Quaternion Method, Project Number: 51409230), and the Zhejiang Zhoushan Science and Technology Project (Project Number: 2018C81041) for financially supporting the research on the hydrodynamic behavior of the AUHs.

**Conflicts of Interest:** The authors declare no conflicts of interest.
