Interaction of two circular cylinders in inviscid fluid

The unsteady problem of two parallel circular cylinders, moving in an inviscid fluid, is analyzed analytically by exploring a conformal mapping. Exact solutions are obtained for the flow induced and the hydrodynamic forces acting on them, as the two circular cylinders, with any radii and at any locations, expand (contract) and translate arbitrarily at time dependent speeds. As the two bodies are far apart, the solutions of the flow and forces reduce to those for a single circular cylinder moving in an unbounded inviscid flow. The force components along the line of centers are inversely proportional to the distance between them, whereas the force components perpendicular to the line of centers are inversely proportional to the square of the distance between them. Numerical analyses are performed for the two circular cylinders deforming and translating at constant speeds and in various ways, as well as a circular cylinder falling to a wall. It has been noticed that they are attracted to each other, as one of them expands and the other contracts, or as they translate perpendicular to the line of centers; whereas they are repelled from each other, as both of them expand, contract, or as they translate along the line of centers. The force on one of them increases with the size and speed of the other, as well as their proximity. (C) American Institute of Physics.