Hydrodynamic interaction between two cylinders with rotation

The hydrodynamic interaction between two cylinders with rotational motion t hrough an inviscid and incompressible fluid is investigated theoretically. The dynamical behaviors of an elliptic cylinder moving around a fixed circu lar cylinder are described based on the dynamical equations of motion in th e plane of motion. In a relative coordinate syst;em moving with the stream, the kinetic energy of the fluid is expressed as a function of fifteen gene ralized added masses due to the planar motion of the two cylinders. By mean s of the generalized added masses, the planar motion of an elliptic cylinde r around a fixed circular cylinder can be computed without considering the flow field. In order to proceed the problem analytically, a set of transfor mations of harmonics between two corresponding spaces are obtained. These t ransformations are applied to derive the complete complex potentials by usi ng the successive potential procedure, which is an extension of the circle theorem in two dimensions. These results are utilized to predict trajectori es of an elliptic cylinder around a fixed circular cylinder in planar motio n and to estimate the effects of non-circularity, initial position and init ial velocity on the interaction between two cylinders. The numerical result s show explicitly that the dynamical behaviors of the moving bodies with ro tational motion appear nonlinear. Their moving properties exhibit significa nt difference from those in the particle dynamics.