Hydrodynamic Interaction In Fuild Among Many-Bodies

In this paper, the hydrodynamic interaction among three circular cylinders with interacting potential and between two circular cylinders with periodic variations in the body radii, translating in an inviscid, incompressible unbounded fluid were theoretically investigated. At first, the complex potential of the corresponding flow field was derived using the method of successive offset functions. And then the instantaneous added-mass coefficients obtained using a method extended from one given by Landweber & Yih. Finally, the Lagrange equations of motion were employed to acquire a dynamical equation of motion in vector form for describing trajectories of these translational bodies.From this thesis, we could find out some interesting and important phenomena of moving circular cylinders in fluid and describe their dynamic behaviors. First, it had been noticed that the two circular cylinders with periodic variations in the body radii in an inviscid, incompressible unbounded fluid were attracted to each other, as one of them expanded and the other contracted, or as they translated perpendicular to the line of centers; whereas they were repelled from each other, as both of them expanded, contracted, or as they translated along the line of centers. Secondly, the trajectories of the two moving circular cylinders with periodic expansion and contraction could form a circular orbit only under the hydrodynamic interaction. Thirdly, the trajectories of the three moving circular cylinders with interacting potential could form a circular orbit under the hydrodynamic interaction. Fourthly, under the influence of interacting potential, the hydrodynamic interaction made the trajectories of two of the three circular cylinders form a circular orbit. Furthermore, we could found out there was a tendency for the two circularly moving cylinders to spread when the third cylinder approached to them.