# Numerical Investigation on the Water Entry of Several Different Bow-Flared Sections
## 5 Conclusions  
The original bow-flared section needs to be simplified when BEM based on the potential flow theory is adopted in studies about slamming loads and whipping responses of ships ([16; 17; 18]). In the present study, water entry of several different bow-flared sections, including the original section and the simplified sections, was numerically investigated using the CFD method based on RANS equations. The objective of the present study was to evaluate the difference between the simplified sections and the original section on the slamming loads using the validated CFD method. The simplified sections corresponded to three different alternatives. The motion of the sections was specified according to a previous ship model test [16]. Reasonable grid size and time step were determined through a convergence study. The numerical method was validated by comparison with published free-fall drop tests ([9; 28]). Due to the influence of the bulbous bow, the secondary slamming phenomenon may appear during the water entry of the original bow-flared section. For the water entry of simplified sections, the free surface was gradually raised along the section, and secondary slamming did not appear. Compared with the other two simplified sections, the pile-up coefficient of section S2 was closer to that of the original section. In the secondary slamming process, the free surface separated from the bulbous bow may form a small angle with the surface of the bow-flared section, thereby arousing greater slamming pressure and slamming force. However, the slamming loads caused by secondary slamming cannot be  
Figure 21: History of the impact force for different sections. reasonably reflected when simplified bow-flared sections are adopted. After secondary slamming, the pressure distributions of different simplified sections were close to that of the original section. For the position away from the bulbous bow, the slamming pressure was less affected by the secondary slamming phenomenon. The secondary slamming phenomenon caused two peaks in the slamming force of the original section, while all the simplified profiles could not give a reasonable prediction of the first peak value. For the second peak, the simplified sections could give a relatively reasonable prediction. Compared with the other two simplified sections, the slamming force of section S3 was closer to that of the original section, especially to the impact force at the initial stage and the second peak value of the impact force. In general, by considering different impact forces of different simplified sections, the simplified section S3 would be the best choice when it is necessary to simplify the original bow-flared section. Although simplified sections cannot reflect the secondary slamming phenomenon of the original bow-flared section, the slamming force of the simplified section S3 was very close to that of the original section, except for the first peak caused by the second slamming phenomenon. Therefore, in studying global nonlinear motions and whipping responses of ships, the simplified section can give good predictions. However, the secondary slamming phenomenon can generate large slamming pressure near the bulbous bow, which could cause damage of the local structure. Therefore, it may be unsafe to use the slamming pressure provided by the simplified section for designing the local structure of a ship bow. In subsequent research, a prediction formula of slamming pressure considering the influence of secondary slamming will be given by regressing the CFD results of a series of bow-flared sections with bulbous bow, which could be useful for designing the local structure of a ship bow. In the present study, two fluids (water and air) were assumed to be immiscible and incompressible by referring to previous studies on the water entry of ship sections [11; 12]. Further research is needed to examine the effect of air compressibility on hydrodynamics during the water entry of a ship section. Conceptualization, Q.W., P.Y., B.Z. and Z.Y. ; investigation, Q.W., B.Z.