Abstract
This paper deals with the problem of the flow about a spinning porous sphere moving in an incompressible viscous fluid. The effect of permeability on the flow has been studied analytically at low Reynolds number by the method of matched asymptotic expansions. It turns out that the permeability on the drag force up to 0(R) reduces the effective radius by a factor (2+K′/a 2)−1,K′ being the permeability associated with the porosity of the reduced radius of the sphere. Further, it is found that the permeability affects the lift forceF L , which is orthogonal to its direction of motion. The ratio of the effective angular velocity ω′ and actual angular velocity ω decreases forK>0.25. ForK=0.25 there is no spinning effect on the sphere.
Zusammenfassung
Diese Arbeit behandelt die Strömung um eine rotierende poröse Kugel in einer zähen inkompressiblen Flüssigkeit. Der Einfluss der Durchlässigkeit wurde für kleine Reynolds-Zahlen mit Hilfe von angepassten asymptotischen Entwicklungen bestimmt. Es wurde gefunden, dass die Durchlässigkeit den Widerstand O(R) vermindert, und die Auftriebskraft senkrecht zur Bewegungsrichtung beeinflusst.
References
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S. Swarup, Ph.D. thesis, IIT Delhi (1972).
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Swarup, S., Manocha, P.S. The transverse force on a spinning porous sphere at small Reynolds number. Journal of Applied Mathematics and Physics (ZAMP) 30, 526–530 (1979). https://doi.org/10.1007/BF01588897
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DOI: https://doi.org/10.1007/BF01588897