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Theoretical and Computational Fluid Dynamics

, Volume 32, Issue 6, pp 821–845 | Cite as

The transient development of the flow in an impulsively rotated annular container

  • Sophie A. W. Calabretto
  • James P. Denier
  • Trent W. Mattner
Original Article

Abstract

When a fluid-filled container is spun up from rest to a constant angular velocity the fluid responds in such a way that the fluid–container system is ultimately in a state of rigid-body rotation. The fluid can then be said to have traversed a trajectory in phase space from a simple stable equilibrium state of no motion to another stable equilibrium representing full rigid-body rotation. This simple statement belies the fact that during this process the fluid can undergo a series of transitions, from a laminar through a transient turbulent state, before attaining the stable motion that is rigid-body rotation. Using a combination of analytical and computational methods, we focus on the dynamics resulting from an impulsive change in the rotation rate of a fluid-filled annulus, specifically, the impulsive spin-up of a stationary annulus, or the impulsive spin-down of an annulus already in a state of rigid-body rotation. We explore the initial development of the impulsively generated axisymmetric boundary layer, its subsequent instability, and the larger-scale transient features within this class of flows, allowing us to look at the effect these features have on the time it takes for the system to spin up to a steady state, or spin down to rest.

Keywords

Transient flow Spin-up Transient turbulence Transition to turbulence 

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Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Sophie A. W. Calabretto
    • 1
  • James P. Denier
    • 1
  • Trent W. Mattner
    • 2
  1. 1.Department of Mathematics and StatisticsMacquarie UniversitySydneyAustralia
  2. 2.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

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