Interaction between Rotating Elliptic Cylinder and Fixed Circular Cylinder

Abstract

The general planar motion of an elliptic cylinder through an inviscid and incompressible fluid in the vicinity of a fixed circular cylinder is investigated analytically. The velocity potential is derived by using the successive-image method and the perturbation method, and it is used to determine the hydrodynamic interactions between them. In a relative coordinate system moving with the uniform flow, the kinetic energy of the fluid is expressed as a function of 15 generalized added masses due to the motion of these two cylinders. The generalized added masses are then employed to determine the translational and rotational motion of the elliptic cylinder based on the dynamic equations of motion that are obtained from Lagrange's equations of motion. Numerical results show that the initial configuration of the elliptic cylinder greatly affects its subsequent motions.