# Effect of Waves on the Behavior of Emergent Buoyantly Rising Submarines Using CFD
## 5 Summary and Conclusions  
In this study, the effect of waves on the behavior of an emergent buoyantly rising submarine was analyzed. The behavior of a submarine rising in different sea situations was predicted using the CFD method. The varying sea situations included static water, head wave, 30\({}^{\circ}\) and 60\({}^{\circ}\) bow waves, 30\({}^{\circ}\) and 60\({}^{\circ}\) quartering waves, and beam sea. The motion of the submarine was expressed by solid-body EOM. The hydrodynamic force was calculated using the RANS equations. The wave was generated by the fifth-order Stokes wave method. The submarine had four stern appendages and a sail with planes. There were three casings on the submarine, each of which flooding holes and vents to let air and water flow out into the casing; thus, the CFD could predict behavior of the submarine when it emerged through the water and oscillated on the water surface. Three different meshes were used to predict the behavior of the submarine when it rose in static water. The result of the medium mesh was approximately the same as that of the refined mesh; therefore, the medium mesh was used for all the simulations.  
During the rising procedure underwater in the head and following waves, when the water surface above the submarine sail transitioned from wave valley to peak, the pitching angle velocity was larger than that when the submarine rose in static water. When the water surface transitioned from wave peak to valley, the pitching angle velocity was smaller than that when the submarine rose in static water. When the submarine rose in the head and following waves, a large pitching oscillation occurred after the submarine submerged into the water from the highest position; the submarine maintained its nose up most of the time when it rose in the head wave and down when it rose in the following wave. When the submarine rose in beam sea, the pitch angle before the submarine rose to the water surface was approximately the same as that when the submarine rose in static water; however, the pitch oscillated between \(-5.5^{\circ}\) and \(5.5^{\circ}\) after falling on the water from the highest position. When the submarine rose in the head and following waves, the sail was under the water surface after the submarine submerged into the water from the highest position. When the submarine rose in beam sea, the water line was approximately the same as that when the submarine rose in static water. The rule of longitudinal motion for a submarine rising in the bow (quartering) wave is the same as that for the submarine rising in the head (following) wave; however, the effect of the bow (quartering) wave decays with the increase in the initial angle between the submarine centerline and the wave direction.  
When the submarine rose in beam sea, the maximum roll angle was 4.43 times that of the submarine rising in static water, and the submarine rolling oscillated sinusoidally with an amplitude of \(13^{\circ}\). The difference in the maximum roll angle between the submarine rising in the oblique wave and beam sea was below \(6.3^{\circ}\). Here, for the submarine rising in the head and following waves, the roll and yaw before the submarine rose to the water surface was approximately the same as that when the submarine rose in static water; however, they rapidly increased after the submarine submerged into the water from the highest position, and the maximum roll angle was several times that when the submarine rose in static water.  
[PERSON] and [PERSON] designed the research, [PERSON] wrote the paper, [PERSON] directed the design of the research, [PERSON] performed the research, [PERSON] and [PERSON] analyzed the data. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (No. 51779057, 51709061).  
The authors declare no conflict of interest.