Theoretical Study of the Behaviour of a Few Spheres Moving in Low Reynolds Number Oscillatory Flows.
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概要
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Theoretical study is made of the behaviour of a few spheres moving in low Reynolds number oscillatory flows under the assumptions that sphere Reynolds number is small and the distance between any two spheres is large compared with their radii. The method of reflection is applied once so that the effects of interaction between any spheres are incorporated. The resulting equations of motion is shown to be a nonlinear integro-differential equation since the velocity fields will be affected by the positions of spheres and the viscous term of Navier-Stokes equation represent a historical effect of spheres.<BR>Two equal spheres oscillate obliquely relative to the flow direction and their orbit describes an ellipse when their center line has an angle of inclination to the flow. It must be emphasized that in case of the two spheres with a little different masses, their center of gravity moves with uniform average velocity. Furthermore, the numerical simulations of the simplified equations of motion of three spheres, which are obtained under the assumption that two equal larger spheres have no influences from a smaller sphere, will be presented. It will be remarked that a smaller sphere approaches to a larger one and then collides with it when the amplitude of a smaller sphere is small compared with the diameter of a larger one. Finally, it will be shown analytically that three equal spheres arranged with a cross-stream direction approach each other under oscillatory flows.
- 社団法人 日本流体力学会の論文