Investigation on the Influences of Parallel Walls on the Immersed Spherical Pendulum Motion and Its Collision
Date Issued
2011
Date
2011
Author(s)
Hsing Chen, Hung
Abstract
This work investigated the influence of parallel lateral walls on the motion of an immersed spherical pendulum midway between them. In addition, a downstream target pendulum of identical size was introduced to study the interaction between the dual pendulums and how their interaction changed with the wall spacing. The pendulum motion was recorded by a high-speed camera and the image sequence was analyzed using the circular Hough transform procedure to locate the sphere. Its position time sequence was then employed to compute the velocity and the maximal particle Reynolds number, Rem. By changing the pendulum release angle, θo (11, 15,and 20 degrees), and the liquid viscosity, μ(from 385.5 to 34.62cP), a wide range of Rem, from 3.45 to 295.39, had been achieved under five to eight wall spacings represented by the spacing-to-diameter ratios W/D =1.2, 1.4, 1.7, 2.0, 2.4, 3.0, 4.0, and 5.0.
In the single-pendulum case, it was observed that as W/D was decreased from 5 to 4, the reduction in maximum velocity was negligible. However, as W/D kept decreasing down to 1.2, much greater deduction in the maximum velocity occurred at an even prior location. This phenomenon persisted as the liquid viscosity was lowered but the discrepancy between different W/D cases was also diminished. Hence, the wall effect was less pronounced for the pendulum motions in a liquid of lower viscosity.
In the dual-pendulum case, the target sphere was set in motion prior to physical contact with the impact pendulum and this phenomenon was observed for all the examined viscosities specified above. Therefore, a coupling distance, xtic, was defined as the horizontal distance between two vertical planes with one tangent to the impact pendulum frontal face and the other to the target sphere rear surface. The coupling distance was found to increase as W/D decreased but the value at each W/D decreased as liquid viscosity was lowered.
On the other hand, collisions between the dual pendulums occurred when the viscosity was low enough (μ<= 128.4cP [θo = 20 degrees]). The resulting coefficient of restitution, e, was calculated as the ratio between the relative pendulum velocity after and before the collisions. A lower e was found when W/D was decreased but the degree of deduction was lessened when in less viscous liquid. And for each W/D, the value of coefficient increased as the liquid viscosity decreased.
Subjects
wall effect
wall influence
immersed pendulum motion
Hough transform
coupling distance
collision
coefficient of restitution
Type
thesis
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