Three-dimensional water entry of a solid body: A particle image velocimetry study

Understanding and predicting the hydrodynamic loading experienced by a solid body during water impact is critical for researchers and practitioners in naval engineering. While two-dimensional (2D) water entry problems have been extensively investigated, experimental data on 3D fluid-structure interactions during water impact are rather limited. Here, particle image velocimetry (PIV) is utilized to study the free fall vertical impact of a solid body, modeling a ship hull, on an otherwise quiescent fluid. Planar PIV is used to measure the velocity field on multiple cross-sections along the length and width of the model. These data are combined to infer the 3D velocity field in the entire fluid. The 3D velocity field is then utilized to reconstruct the pressure field by integrating the incompressible 3D Navier-Stokes equations in a time-varying domain, where both the free surface and the fluid-solid interface evolve in time. By evaluating the pressure field on the wetted surface of the model, we estimate the hydrodynamic loading during water entry. Experimental results demonstrate the central role of 3D effects on both the flow physics and the hydrodynamic loading. As the cross-sectional velocity decreases away from the mid-span, we observe a robust increase in the axial velocity component. This translates into a complex spatio-temporal dependence of the hydrodynamic loading, which is initially maximized in the vicinity of the pile-up and later increases toward the keel. Due to the deceleration of the model during the impact and the increase in the wetted surface, the hydrodynamic loading close to the mid-span in the early stage of the impact is considerably larger than the ends. The 3D flow physics is used to study the energy imparted to the fluid during the impact, which we find to be mostly transferred to the risen water, consisting of the pile-up region and the spray jet. Our methodology can be implemented for the analysis of other solid bodies with multiple geometric curvatures, and our experimental results can be utilized for the validation of 3D mathematical models of water entry.