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Motion of a rigid sphere penetrating a deep pool

Published online by Cambridge University Press:  28 May 2025

Prasanna Kumar Billa ,
Tejaswi Josyula ,
Cameron Tropea Open the ORCID record for Cameron Tropea [Opens in a new window]  and
Pallab Sinha Mahapatra Open the ORCID record for Pallab Sinha Mahapatra [Opens in a new window]
Prasanna Kumar Billa
Affiliation:
Multiscale Multiphysics Group (MMG), Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
Tejaswi Josyula
Affiliation:
Multiscale Multiphysics Group (MMG), Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India FLOW, Department of Engineering Mechanics, KTH Royal Institute of Technology Stockholm, Stockholm, 11428, Sweden
Cameron Tropea*
Affiliation:
Multiscale Multiphysics Group (MMG), Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India Institute for Fluid Mechanics and Aerodynamics, Technical University of Darmstadt, Darmstadt 64287, Germany
Pallab Sinha Mahapatra*
Affiliation:
Multiscale Multiphysics Group (MMG), Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
*
Corresponding authors: Pallab Sinha Mahapatra, pallab@iitm.ac.in; Cameron Tropea, tropea@sla.tu-darmstadt.de
Corresponding authors: Pallab Sinha Mahapatra, pallab@iitm.ac.in; Cameron Tropea, tropea@sla.tu-darmstadt.de
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Abstract

In this study, we experimentally examine the behaviour of a free-falling rigid sphere penetrating a quiescent liquid pool. Observations of the sphere trajectory in time are made using two orthogonally placed high-speed cameras, yielding the velocity and acceleration vectors through repeated differentiation of the time-resolved trajectories. The novelty of this study is twofold. On the one hand, a methodology is introduced by which the instantaneous forces acting on the sphere can be derived by tracking the sphere trajectory. To do this, we work in a natural coordinate system aligned with the pathline of the sphere. In particular, the instantaneous lift and drag forces can be separately estimated. On the other hand, the results reveal that when decelerating, the sphere experiences a very high drag force compared with steady flow. This is attributed to an upstream shift of the mean boundary-layer separation. The sphere also experiences significant lift force fluctuations, attributed to unsteady and asymmetric wake fluctuations. The trajectories can be reduced to three stages, common in duration for all initial Reynolds numbers and density ratios when expressed in dimensionless time. In addition, the sphere velocity and deceleration magnitude for different initial parameters exhibit a high degree of uniformity when expressed in dimensionless form. This offers prediction capability of how far a sphere penetrates in time and the forces acting on it.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Boundary Layers: Boundary layer separation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1012 , 10 June 2025 , A5
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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