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Vortex dynamics and vibration modes of a tethered sphere

Published online by Cambridge University Press:  18 December 2019

Methma M. Rajamuni Open the ORCID record for Methma M. Rajamuni [Opens in a new window] ,
Mark C. Thompson  and
Kerry Hourigan
Methma M. Rajamuni*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia
Mark C. Thompson
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia
Kerry Hourigan
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The flow-induced vibration of a tethered sphere was investigated through numerical simulations. A determination of the different modes of sphere vibration was made with simulations conducted at fixed Reynolds numbers (500, 1200 and 2000) with a sphere of mass ratio 0.8 over the reduced velocity range $U^{\ast }\in [3,32]$. The flow was governed by the incompressible Navier–Stokes equations, while the dynamic motion of the sphere was governed by coupled Newtonian mechanics. A new fluid–structure interaction (FSI) solver was implemented to efficiently solve the coupled FSI system. The effect of Reynolds number was found to be significant in the mode I and II regimes. A progressive increase in the response amplitude was observed as the Reynolds number was increased, especially in the mode II regime. The overall sphere response at the highest Reynolds number was relatively close to the observed behaviour of previous higher-$Re$ experimental studies. An aperiodic mode IV response was observed at higher reduced velocities beyond the mode II range in each case, without the intervening mode III regime. However, as the mass ratio increased from 0.8 to 80, the random response of the sphere (mode IV) gradually became more regular, showing a mode III response (characterized by a near-periodic sphere oscillation) at $U^{\ast }=30$. Thus, if the inertia of the system is low, mode IV appears at lower $U^{\ast }$ values, while for high-inertia systems, mode IV appears at high $U^{\ast }$ values beyond a mode III response.

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A10
Copyright
© 2019 Cambridge University Press

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Rajamuni et al. supplementary movie 1

Vortex-induced vibration of the sphere at Re = 500 and U* = 6

Download Rajamuni et al. supplementary movie 1(Video)
Video 8.7 MB

Rajamuni et al. supplementary movie 2

Vortex-induced vibration of the sphere at Re = 500 and U* = 9

Download Rajamuni et al. supplementary movie 2(Video)
Video 9 MB

Rajamuni et al. supplementary movie 3

Vortex-induced vibration of the sphere at Re = 1200 and U* = 9

Download Rajamuni et al. supplementary movie 3(Video)
Video 5.9 MB