Numerical study of consecutive water entries in flowing water with twin spheres side-by-side

A three-dimensional numerical model with six-degree-of-freedom is developed to simulate the side-by-side entry of twin spheres into flowing water. With the explicit volume of fluid (VOF) approach, the shear-stress transport (SST) k-ω model is adopted to delineate the turbulence structures within the flow, while the independent movements of the two spheres are tracked using advanced multi-overset mesh technology. The numerical findings elucidate the effects of water flow on cavity dynamics, flow field evolution, forces, and trajectories during consecutive sphere entries. Distinct flow field characteristics emerge depending on whether the trailing sphere enters the upstream side or downstream side. The flow-induced tilting of the first cavity results in a different scale of expansion of the trailing cavity with respect to that in quiescent water, diminishing the attractive force on the upstream-side sphere and enhancing it for the downstream-side sphere. As the lateral distance between the spheres increases, the forces of attraction and repulsion generated by the leading cavity become marginal in their effect on the trailing sphere's trajectory, particularly when compared with the impact force of the water flow.