Effect of Hydrodynamic Interaction on the Motion of a Rotating Body

The hydrodynamic interaction between two bodies with rotational motion through an inviscid and incompressible fluid is investigated theoretically. The dynamical behavior of an elliptic cylinder moving around a fixed circular cylinder is described first based on the dynamical equations of motion in the plane of motion. In a relative coordinate system moving with the stream, the kinetic energy of the fluid is expressed as a function of fifteen generalized added masses due to the planar motion of the two cylinders. By means of the generalized added masses, the planar motion of an elliptic cylinder around a fixed circular cylinder can be computed without considering the flow field. The trajectories of an elliptic cylinder around a fixed circular cylinder in planar motion are obtained and the effects of non-circularity, initial position and initial velocity on the interaction between two cylinders are discussed. Similarly, the planar motion of a prolate spheroid around a sphere is investigated. The numerical results show explicitly that the dynamical behaviors of the moving bodies with rotational motion appear nonlinear. Their moving properties exhibit significant difference from those in the particle dynamics.