Hydrodynamic forces on a rotating sphere |
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| Institution: | 1. Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia;2. Air Vehicles Division, Defence Science & Technology, Organisation, 506 Lorimer St., Fishermans Bend, VIC 3207, Australia;3. CSIRO Mathematics, Informatics & Statistics, Clayton, VIC 3168, Australia;1. Université de Lorraine, Laboratoire Réactions et Génie des Procédés, UMR 7274 CNRS, Nancy F-54000, France;2. CNRS, Laboratoire Réactions et Génie des Procédés, UMR 7274 CNRS, Nancy F-54000, France;3. Chimie ParisTech, Institut de Recherche de Chimie Paris, UMR 8247 CNRS, 11 rue Pierre et Marie Curie, 75005 Paris, France;4. UPMC-Université Paris 06, Institut de Recherche de Chimie Paris, UMR 8247 CNRS, 11 rue Pierre et Marie Curie, 75005 Paris, France;1. Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117576, Singapore;2. Mathematics Application Consortium for Science and Industry (MACSI), Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland;1. Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Chongqing University, Ministry of Education, Chongqing 400030, China;2. Institute of Engineering Thermophysics, Chongqing University, Chongqing 400030, China;1. School of Chemical Engineering, the University of Adelaide, SA 5005, Australia;2. School of Chemical Engineering and Advanced Materials, Newcastle University, Merz Court, Newcastle-upon-Tyne NE1 7RU, UK;3. School of Science, Loughborough University, Loughborough LE11 3TU, UK;1. Université de Lorraine, Laboratoire Réactions et Génie des Procédés, UMR 7274, Nancy F-54001, France;2. CNRS, Laboratoire Réactions et Génie des Procédés, UMR 7274, Nancy F-54001, France;3. CNRS/Saint-Gobain, Laboratoire de Synthèse et Fonctionnalisation des Céramiques, UMR 3080, Cavaillon F-84306, France |
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| Abstract: | The wake dynamics of a rotating sphere with prescribed rotation axis angles are quantitatively analysed by carrying out numerical simulations at Reynolds numbers of Re = 100, 250 and 300, non-dimensional rotational rates Ω1 = 0–1 and rotation axis angles α = 0, π/6, π/3 and π/2 measured from the free stream axis. These parameters are the same as those in an earlier study (Poon et al., 2010, Int. J. Heat Fluid Flow) where the instantaneous flow structures were discussed qualitatively. This study extends the findings of the earlier study by employing phase diagrams (CLx, CLy) and (CD, CL) to provide a quantitative analysis of the time-dependent behaviour of the flow structures. At Re = 300 and Ω1 = 0.05, the phase diagrams (CLx, CLy) show ‘saw tooth’ patterns for both α = 0 and π/6. The ‘saw tooth’ pattern indicates that the flow structures comprise a higher frequency oscillation component at a Reynolds number of 300 which is not observed until Re ≈ 800 for a stationary sphere. This ‘saw tooth’ pattern disappears as Ω1 increases. The employment of the phase diagrams also reveals that different flow structures induce different oscillation amplitudes on both lateral force coefficients. With the exception of the vortices formed from a shear layer instability, all other flow regimes show larger fluctuations in CL than CD. |
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