# Numerical Investigation on the Water Entry of Several Different Bow-Flared Sections
## 1 Introduction  
Ship slamming is an important aspect that needs to be considered in the design of a bow-flared ship. The hydrodynamic impact between the ship hull and the water can cause local damage to the hull and induce global whipping responses [1; 2; 3; 4]. In order to investigate the fundamental mechanisms during slamming, the water entry of two-dimensional (2D) ship sections or three-dimensional (3D) ship structures has been studied extensively. The pioneering work on water entry can be traced back to [PERSON] [5] and [PERSON] [6], which was motivated by seaplane landing problems. [PERSON] et al. presented a fully nonlinear boundary element method for simulating the water entry of an arbitrary section [7]. [PERSON] and [PERSON] [8] studied the 2D water entry of a bow-flared section with a constant roll angle using a boundary element method, and their numerical results were compared with the experiments [9]. [PERSON] and [PERSON] simulated the asymmetric water entry of a bow-flared ship section with a roll angle using the arbitrary Lagrangian-Eulerian solver in LS-DYNA [10]. [PERSON] et al. numerically investigated the water entry of a wedge and a ship section using an incompressible immersed boundary method [11]. [PERSON] and [PERSON] comprehensively studied the effect of geometrical asymmetry and kinematic asymmetry on hydrodynamics during the water entry of a bow-flared ship section [12]. [PERSON] et al. [13] simulated the water entry problem of curved wedges, and the numerical method was validated by comparison with the experimental results reported by [PERSON] et al. [14]. The influence of curvature on the impact force, slamming pressure distribution, and wetted width was numerically investigated. [PERSON] et al. investigated the effect of ice on impact loads during the water entry of a wedge using both computational fluid dynamics (CFD) and a Wagner-type theoretical model [15]. Numerical simulations of slamming loads and whipping responses of a ship in waves can be found in many recent papers. [PERSON] and [PERSON] analyzed bow-flared slamming on a Ro-Ro vessel in regular oblique waves [16]. The motion of the ship and bow-flared slamming loads were solved. Ignoring the influence of slamming loads on the motion of the ship, the relative motion between the ship and the wave was calculated using a nonlinear strip theory. Then, bow-flared slamming loads were calculated using a slamming program that was based on a generalized Wagner formulation and solved by a 2D boundary element method. For the section with a bulbous bow, flow separation may occur at the bulbous bow during the water entry, and the separated fluid may impact the hull surface again. This phenomenon is usually called \"secondary slamming\" [10; 12]. It is difficult to use the boundary element method to reasonably analyze the secondary slamming phenomenon. Therefore, [PERSON] and [PERSON] proposed three simplified sections for the prediction of slamming loads instead of the original bow-flared section [15]. [PERSON] et al. investigated the local structural response due to seakeeping and slamming loads [17]. The seakeeping analysis was conducted using a linear 3D boundary element method. The slamming loads were calculated using the 2D generalized Wagner model, and the original bow-flared section was simplified. [PERSON] et al. also simplified the original bow-flared section in hydroelastic analysis of a container ship [18]. Meanwhile, the CFD method based on Reynolds-averaged Navier-Stokes (RANS) equations has been adopted for the prediction of both slamming pressure and hydroelastic response. [PERSON] et al. predicted the bow-flared slamming pressure and the bottom slamming pressure of an oil tanker under extreme motion conditions using the CFD software StarCCM+ [19]. The predicted pressure was compared with the pressure obtained from harmonized common structural rules (CSR-H), and it was found that the slamming pressures defined by CSR-H were safe and conservative with regard to the structural design. [PERSON] et al.