Fluid structure interaction of a subaqueous pendulum: Analyzing the effect of wake correction via large eddy simulations

Abstract

The dynamic behavior of a subaqueous cylindrical pendulum and corresponding flow dynamics are investigated. The objectives were twofold: (i) to examine whether the two-dimensional model equations sufficiently capture the three-dimensional dynamics and (ii) to investigate the emerging three-dimensional vortical flow structures. Large eddy simulations with two-way coupling fluid structure interaction were carried out using the immersed boundary method to simulate the motion of the pendulum and its interactions with the initially stagnant water. The resulting pendulum motion is compared against measured data obtained in a series of experimental tests to validate the simulation results and the model equations with and without wake corrections. An analysis of the flow vorticity revealed the development of a vortex ring during the first swing and the formation of tip vortices. The evolution of the vortex rings emerging from the motion of the subaqueous cylindrical pendulum was visualized using Q-criteria showing a reasonable agreement with vortical structures observed in the experiment using particle imaging velocimetry. The hydrodynamic moments acting on the simulated pendulum and the moments calculated from the model equations are analyzed. Using the insights from these numerical simulations, a modification of the wake correction is proposed to enhance the accuracy of the rate of decay and period. The transient effect of coherent flow on pendulum dynamics, especially the added mass effect, is discussed.

Lagrangian particle tracking velocimetry investigation of vortex shedding topology for oscillating heavy spherical pendulums underwater

“…While propagating, the vortex ring remains remarkably stable until reaching its terminal velocity and eventually dissipating. This behaviour is similar to the aforementioned case of the cylinder pendulum investigated experimentally by Mathai et al (2019) and numerically by Worf et al (2022). Based on their findings, Worf et al (2022) described the development and downward shedding of the vortex ring in the wake of a cylinder during the first swing.…”

“…This behaviour is similar to the aforementioned case of the cylinder pendulum investigated experimentally by Mathai et al (2019) and numerically by Worf et al (2022). Based on their findings, Worf et al (2022) described the development and downward shedding of the vortex ring in the wake of a cylinder during the first swing. Later on, the vortex stretches out and dissipates near the side walls of the glass tank.…”

“…The first known study of pendulum motion was carried out by Galileo Galilei in 1605 as he discovered that the period of the swings remained constant. Since then, pendulums have been subject to much research and utilised in many technical applications, such as, among others, the pendulum clock, ballistic pendulums, seismometers, metronomes, viscosimeters and mass dampers in high-rise buildings (Mongelli & Battista 2020;Worf et al 2022). Also, the pendulum is an 'educational classic' and a standard device to study the concept of oscillating motions, starting with the undamped case and simple harmonic motion (Mongelli & Battista 2020).…”

“…Since the cylinder length was relatively short, Mathai et al (2019) found the added mass coefficient to be significantly lower (0.53) than the potential flow value (1). Worf et al (2022) re-investigated the case with m * = 4.98 from Mathai et al (2019) by conducting large-eddy simulations. Their simulation results suggested that the added mass deviation is caused by the predominance of a 3-D flow field featuring tip vortices during the first downward swing.…”

“…They suggested that for large amplitudes, vortex streets are induced by the shedding of vortices at the turning points, which in turn causes additional drag forces on the spherical bob. With the exception of Mongelli & Battista (2020) and Worf et al (2022), all the aforementioned studies are based on experimental observations. The present work contributes to a better understanding of the vortex dynamics of heavy objects oscillating in a dense fluid.…”