Parametric Study on the Free-Fall Water Entry of a Sphere by Using the RANS Method

Motivated by the application of water-entry problems in the air-drop deployment of a spherical oceanographic measuring device, the free-fall water entry of a sphere was numerically investigated by using the transient Reynolds-averaged Navier–Stokes (RANS) method. A convergence study was carried out, which accounts for the mesh density and time-step independence. The present model was validated by the comparison of non-dimensional impact force with previous experimental and numerical results. Effects of parameters, such as impact velocity, radius, and mass of the sphere on the impact force and the acceleration of the sphere, are discussed. It is found that the peak value of the non-dimensional impact force is independent of the impact velocity and the radius of the sphere, while it depends on the mass of the sphere. By fitting the relationship between the peak value of the non-dimensional impact force and the non-dimensional mass, simplified formulas for the prediction of peak values of the impact force and the acceleration were achieved, which will be useful in the design of the spherical oceanographic measuring device.