Trajectory prediction of a freely rising cylinder

Abstract

In the present study, we present a model that can predict the trajectory of a freely rising cylinder. For this purpose, the motion of the cylinder is recorded using a high-speed camera in the range of 0.15 < ρ* < 1.0 and 275 < Ga < 13000, where ρ* is the ratio of the cylinder density to the fluid density and Ga is the Galileo number. The rising motion of the cylinder is modeled based on the two-dimensional wave equation as the two-dimensional cylinder rises in the form of a sine wave. For the modeling, dimensional analysis is conducted by using physical variables, and the two main parameters, 1-ρ* and Ga, are obtained. A newly defined Galileo number, Ga*, is defined by the relationship between 1-ρ* and Ga, which can be expressed in the form of a power function. In addition, empirical formulae are derived based on the Ga*, to predict the amplitude, wavelength, and period of the wave. The proposed model is shown to accurately predict the motion of the freely rising cylinder, and the time at which the rising cylinder arrives at a specific position. Some more details about the trajectory prediction will be discussed in the presentation.