Modeling and numerical simulation of the forces acting on a sphere during early-water entry

• Forces exerted on devices that pass from air into water are determined.
• The numerically predicted results are compared with literature and are in agreement.
• Drag coefficients are extracted from the results which can be used to improve trajectory of devices.

Mathematical modeling, absent simplifying assumptions and coupled with numerical simulation, has been implemented to determine the motions and forces experienced by a sphere penetrating a water surface from an air space above the surface. The model and simulation are validated by comparisons with extensive experimental data and with trends from approximate analyses. Although the present work adds to the understanding and quantification of the sphere as an entry object, its major contribution is model development and validation to enable investigation of water entry of objects of practical utility such as the expendable bathythermograph (XBT). The XBT device is widely used in the determination of temperature distributions in large water bodies such as oceans. The measured temperature distributions are, in turn, used to determine the thermal energy content of oceans. During the course of the numerical simulations, parametric variations were made of the sphere velocity, surface tension, flow regime (laminar or turbulent), and Reynolds number. The drag-coefficient results were found to be independent of these quantities. This outcome indicates that momentum transfer from the sphere to the adjacent liquid is responsible for the drag force and that friction is a secondary issue.