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Coupled Systems Mechanics Volume 7, Number 4, August 2018 , pages 407-420 DOI: https://doi.org/10.12989/csm.2018.7.4.407 |
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Hydrodynamic coupling distance between a falling sphere and downstream wall |
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Cheng-Chuan Lin, Hung-Tien Huang and Fu-Ling Yang
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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 Sc-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 Sc-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 Sc-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. | ||
| Key Words | ||
| hydrodynamic coupling; Stokes number; wall effect; added mass force; history force | ||
| Address | ||
| Cheng-Chuan Lin, Hung-Tien Huang and Fu-Ling Yang: Department of Mechanical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan (R.O.C.) | ||
