On the fluid entry of light solid spheres

The effects of sphere impact energy on the entry of solid objects in water and non-Newtonian ambient were studied experimentally. The impact energy varied by changing the density of solid spheres and their release heights, and the ambient fluid mixture was characterized by the relative viscosity. A series of controlled experiments was conducted using spheres with varying densities while released into different fluid mixtures with different viscosities and from three release heights. High-speed imaging combined with in-house image-processing algorithms was used to quantify cavity evolution, pinch-off dynamics, splash characteristics, and post-impact trajectories. The measured length and time scales were correlated with impact Froude, densimetric Froude, and Reynolds numbers. New length and time scales were identified and measured to determine the trajectory and motion of light spheres in water and viscous ambient, such as the stationary period, balance depth, and time. The correlations between normalized splash height and diameter in water were found to be nonlinear with Reynolds number but independent of sphere density. The correlation between densimetric Froude number and pinching ratio showed a threshold at which, for Frd < 4, the correlation was direct while the pinching ratio was constant for Frd ≥ 4. Another threshold was found between variations in the normalized density ratio with non-dimensional balance depth, with a threshold value of ρs/ρw = 0.70. Many practical models were introduced with the utilization of multi-variable regression analysis to predict the trajectory and motion of light spheres in water and non-Newtonian fluid mixtures, which can be used for engineering design and validation of numerical models.