# Numerical Investigation on the Water Entry of Several Different Bow-Flared Sections
## 3 Computational Overview, Convergence, and Validation Studies
### Validation Studies  
Considering that the secondary slamming phenomenon may appear during the water entry impact of a bow-flared section, the two previous drop tests were simulated using the present method, which corresponded to the water entry without and with the secondary slamming phenomenon, respectively.  
The shape of the bow-flared section in the drop test by [PERSON] [9] is shown in Figure 7. The section was symmetrical, so only half of the section is shown. P4-P7 are the positions where the pressure sensors were installed. The total weight of the falling rig was 261 kg. The total length of the ship bow section was 1.0 m. The initial impact velocity was 2.43 m/s, corresponding to the time when the section touched the still water surface. Figure 8 shows a comparison between the experimental results of [PERSON] [9] and numerical results. Because [PERSON]'s section had no obvious bulbous bow structure, the second slamming phenomenon did not appear in the process of water entry. [PERSON] and [PERSON] [8] validated the nonlinear boundary element method by comparison with [PERSON]'s drop tests, and the results of the boundary element method are also shown in Figure 8. As can be seen in the figure, the numerical results obtained by the present method are in good agreement with the experimental results reported by [PERSON] [9] and the numerical results reported by [PERSON] and [PERSON] [8]. Because the three-dimensional effect in the drop tests was not taken into account in the present numerical simulation and in the study by [PERSON] and [PERSON] [8], the numerical results obtained by the present method are closer to those reported by [PERSON] and [PERSON] [8], especially for the impact pressure of P5, P6, and P7.  
In the Wave Induced Loads on Ships (WILS) Joint Industry Project [28], a drop test of a symmetrical bow-flared section was performed. The profile of half section is shown in Figure 9. Unlike the bow-flared section of Aarsnes [9], the profile in Figure 9 has an obvious bulbous bow structure. P8 and P9 are the positions where the pressure sensors were installed. The initial impact velocity was 2.43 m/s. Figure 10 shows the free surface elevations obtained by the present numerical study and the drop test. It can be seen that the present numerical method could reasonably predict the free surface elevation near the dropping section, and the second slamming phenomenon caused by the bulbous bow structure was also well simulated. Figure 11 shows the contrastive results for the water entry of MOERI's bow-flared section. The results of the immersed boundary method in the work of [PERSON] et al. [11] are also shown in Figure 11. It can be seen that even if the second slamming phenomena appeared, the present numerical method could reasonably predict the impact pressure on the dropping section.  
Figure 6: Impact forces and impact pressures of “S2” with different mesh densities: (**a**) impact force; (**b**) P1; (**c**) P2; (**d**) P3.  
Figure 8: _Cont._  
Figure 7: Shape of the bow-flared section in the drop test by [PERSON] (1996).  
Figure 8: Comparison between experimental results of [PERSON] (1996) and numerical results: **(a)** force; **(b)** velocity; **(c)** acceleration; **(d)** P4; **(e)** P5; **(f)** P6; **(g)** P7.  
Figure 9: Shape of the bow-flared section in MOERI (2013).  
Figure 11: Contrastive results for the water entry of MOERI’s bow-flared section: (**a**) P8; (**b**) P9.  
Figure 10: Free surface elevations obtained by the present numerical method and the drop test in MOERI (2013): (**a**) the drop test (0.24 s); (**b**) the present method (0.24 s); (**c**) the drop test (0.26 s); (**d**) the present method (0.26 s).