Simplified dynamics model of a sphere decelerating freely in a fluid

Abstract

An experimental/theoretical study has been presented on the problem of the dynamic equation of motion of a close to neutral buoyancy sphere (0.04 m in diameter) decelerating freely in water after an impulsive start. It has been verified, via analysis of the acceleration parameter, that, for the range of parameters that have been considered, the motion is governed by unsteady effects. A model has been developed for this specific problem. It contains three forcing terms in the sphere dynamics equation of motion: (a) unsteady drag, (b) added mass, and (c) buoyancy. This departs from the approach following the standard Basset–Boussinesq–Oseen formulation. In this case, the equation of motion would contain four forcing terms: (a) steady drag, (b) added mass, (c) history, and (d) buoyancy. Comparison between the experimental and model results shows reasonable agreement in terms of trajectory, velocity, and acceleration profiles. The model could be used for practical engineering applications that involve this type of unsteady flow situations.