Evolution of water column pulled by partially submerged spheres with different velocities and submergence depths

Abstract

Abstract The evolution of a water column pulled by a partially submerged sphere, known as the water exit problem, is evaluated by numerical simulation. The lattice Boltzmann method was combined with a mass-tracking algorithm. The accuracy of the numerical method was demonstrated by comparisons with previous experimental results. Moreover, the evolution processes of the water column with different Froude and Weber numbers (0.4134 ≤ Fr ≤ 8.2479, 5.15 × 102 ≤ We ≤ 2.06 × 105), as well as different initial submergence depths (Hs/D = 1/2, 1/4, 1/8), were discussed. Spontaneous breakup of water column was observed for higher Weber numbers. Moreover, vertical stretching of the water column approximately followed a power law in which the power exponent depended on the initial setup of the sphere and its time scales. However, the horizontal evolution of the water column followed an approximately linear rule. Variation in the water column diameter appeared to be irregular at different physical times or in non-dimensional time. Furthermore, the initial submergence depth of the sphere was also a significant factor in the pinch-off dynamics and water column evolution. This study of water exit is of a great importance in designing marine vehicles that take off from a free water surface.