Analytical description of the unsteady settling of spherical particles in Stokes and Newton regimes

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• 作者：Hannes Mann ; Peter Mueller ; Thomas Hagemeier ; Christoph Roloff…
• 关键词：Particle sedimentation ; Settling velocity ; Relaxation time ; Laminar flow conditions ; Turbulent flow conditions
• 刊名：Granular Matter
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：17
• 期：5
• 页码：629-644
• 全文大小：1,269 KB
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• 作者单位：Hannes Mann (1)
  Peter Mueller (1)
  Thomas Hagemeier (2)
  Christoph Roloff (3)
  Dominique Th茅venin (3)
  Juergen Tomas (1)
  
  1. Chair of Mechanical Process Engineering, Otto von Guericke University Magdeburg, Universit盲tsplatz 2, 39106, Magdeburg, Germany
  2. NaWiTec, Otto von Guericke University Magdeburg, Universit盲tsplatz 2, 39106, Magdeburg, Germany
  3. Chair of Fluid Dynamics and Technical Flow, Otto von Guericke University Magdeburg, Universit盲tsplatz 2, 39106, Magdeburg, Germany
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Granular Media
  Industrial Chemistry and Chemical Engineering
  Engineering Fluid Dynamics
  Structural Foundations and Hydraulic Engineering
  Engineering Thermodynamics and Transport Phenomena
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1434-7636

文摘

In most solid processes, the separation of particles is important and designed based on the terminal settling velocity as the characteristically distributed particle property. This settling velocity is determined by distributed particle properties like size, density, and shape. Although the settling of particles driven by an external force (gravitation or centrifugal field) is an unsteady process, the temporal changes of the particle settling velocity are relevant for the microscopic process design. These temporal changes correspond to spatial changes along the path-line. Generally, the particle state of motion is described by solving numerically the force balance equations in fluid dynamic simulations which are highly complex. In this work, algebraic solutions are presented instead, suitable for describing the temporal changes of the settling velocity and the displacement at settling for laminar and turbulent flows around the particle. These equations solely depend upon particle properties like size, density, and shape and are valid independently from the initial velocity. Thus, and at the difference to known publications, it is not assumed that the particles are initially at rest. Finally, the relaxation time at which terminal settling velocity is approximately reached can be clearly identified. Keywords Particle sedimentation Settling velocity Relaxation time Laminar flow conditions Turbulent flow conditions