NUMERICAL AND EXPERIMENTAL INVESTIGATION OF THE TRANSIENT MOTION OF A SETTLING SPHERE

Abstract

This work aims to experimentally and numerically study the transient motion of a sphere falling in liquids. The different force models that represent different contributions to the total force are described. These “point mass” force models are introduced into the equations of motion of a moving sphere/spherical particle which can be solved numerically. A MATLAB^® code is developed for this purpose and is validated with published experimental data and showed a very good agreement at a wide range of Reynolds’ numbers and density rations. The experimental part is intended to be performed using available technologies that we use in our daily lives. Digital videos are recorded at a known framerate and are analyzed using an open-source video analysis software “Tracker”. The experiments were performed at two different outer cylinder diameters to examine the effect of the confinement on the steady-state condition (namely the terminal velocity). Different spheres with different properties were tested along with two different fluids (oil and water). Results from the current experiment are validated with the developed code results and reasonably good agreement was obtained. Different wall correction formulas were testes and the formula of Landenburg was found to give better agreement with most of the current results. The effect of the experimental uncertainty on both the transient and steady-state results were examined and found to be insignificant for the steady-state condition and insignificant for the transient behavior.