Coupled systems mechanics

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Hydrodynamic coupling distance between a falling sphere and downstream wall

  • Lin, Cheng-Chuan (Department of Mechanical Engineering, National Taiwan University) ;
  • Huang, Hung-Tien (Department of Mechanical Engineering, National Taiwan University) ;
  • Yang, Fu-Ling (Department of Mechanical Engineering, National Taiwan University)
  • Received : 2018.01.29
  • Accepted : 2018.01.31
  • Published : 2018.08.25
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Abstract

In solid-liquid two phase flow, the knowledge of how descending solid particles affected by the presence of downstream wall is important. This work studies at what interstitial distance the velocity of a vertically descending sphere is affected by a downstream wall as a consequence of wall-modified hydrodynamic forces through a validated dynamic model. This interstitial distance-the hydrodynamic coupling distance ${\delta}_c-is$ found to decay monotonically with the approach Stokes number St which compares the particle inertia to viscous drag characterized by the quasi-steady Stokes' drag. The scaling relation ${\delta}_c-St-1$ decays monotonically as literature below the value of St equal to 10. However, the faster diminishing rate is found above the threshold value from St=10-40. Furthermore, an empirical relation of ${\delta}_c-St$ shows dependence on the drop height which clearly indicates the non-negligible effect of unsteady hydrodynamic force components, namely the added mass force and the history force. Finally, we attempt a fitting relation which embedded the particle acceleration effect in the dependence of fitting constants on the diameter-scaled drop height.

Keywords

Acknowledgement

Supported by : Ministry of Science and Technology of Taiwan

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