Characteristics of cavity dynamics, forces, and trajectories on vertical water entries with two spheres side-by-side

In the present work, a three-dimensional numerical model with six-degrees-of-freedom is adopted to carry out the investigation of twin water entries with two spheres side-by-side. The shear-stress transport k–ω model is used to detail the turbulence structure, and the air–water interface is tracked through the volume of fluid method. The motion of consecutive water entry with spheres is simulated using an independent overset grid technology. Numerical results reveal the variation of different kinds of lateral forces experienced by the trailing sphere following water entry, while simultaneously clarifying the governing law regarding the effects of time interval, lateral distance, and entry velocity on the trajectory behaviors. The repulsive and attractive forces are found upon the trailing sphere (sphere II) entering water, inducing different deviation directions, which are affected by the time interval and lateral distance. In addition, increasing water-entry velocity results in an increase in both attractive and repulsive force acted on sphere II; notwithstanding, the effect of repulsive force on trajectory characteristics is more noticeable.