Influence of the nutation angle in gravitational settling of particles near vortices and in turbulence |
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| Affiliation: | 1. Institute of Cardiology, Medical University of Lodz, Lodz, Poland;2. Heart Research Follow-Up Program, Cardiology Unit, University of Rochester, Rochester, New York, USA;1. CNRS, UMR MIP 5640, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex, France;2. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain;1. Institut de recherche sur les phenomenes hors equilibre (IRPHE), technopole de Chateau-Gombert, 49, rue Joliot Curie, BP 146, 13384 Marseille cedex 13, France;2. Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, 46 Uljanov Street, Nizhny Novgorod, 603950 Russia;1. Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA;2. The Boeing Company, P.O. Box 516, St. Louis, MO 63166-0516, USA;3. Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA;1. UPR 15 du CNRS, Interfaces et Systèmcs Electrochimiques, University P. et M. Curie, T22, 4 place Jussieu, 75252 Paris Cedex 05, France;2. Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Rozvojova 135, 16502 Prague, Czech Republic |
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| Abstract: | The knowledge of the conditions in which particles denser than fluid settle is important in many areas of engineering, environmental sciences, meteorology, etc.For particle flows influenced by vortices, research mainly related to steady horizontal vortices has been undertaken. In this paper we determine the influence of the inclination of the vortex axis in the gravitational settling of particles.The results obtained, in relation to the trajectories, are qualitatively similar to previous ones for horizontal vortices. The main difference is this: in a horizontal vortex particles always remain in a plane perpendicular to the vortex axis and in an inclined vortex (angle θ) particles do not remain on that plane because there is a component vtcosθ that takes them out.The average fall velocity 〈vz〉 has an asymptote to the dimensionless terminal velocity vt; this tendency is faster as the Stokes Number St increases and as vt decreases. A fundamental result is the following: as θ decreases, vt is reached faster because the component of the velocity u of the Rankine vortex over the Oz direction is small and because the vt component that tries to keep the particles in a plane perpendicular to the vortex axis is small, so the vortex takes action over the particles for a small period of time. |
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