The inner and outer solutions to the inertial flow over a rolling circular cylinder

Abstract

This paper proposes a new approach for evaluating numerically the forces and moments applied to a circular cylinder that is immersed in a fluid and which translates and rotates near a plane wall. Under the proposed approach, the flow is decomposed into inner and outer flows. The inner flow represents the flow in the thin interstice between the cylinder and the wall, and is obtained as an analytic expression using lubrication theory. The outer flow represents the flow far from the interstice, which does not depend on the magnitude of the gap between the cylinder and the wall, when the gap is small. The outer flow is obtained using numerical simulation as a function of both the Reynolds number and the slip coefficient. The force and moment coefficients are then obtained, as functions of the Reynolds number, slip coefficient and gap-to-diameter ratio, by combining the inner and outer solutions. Importantly, since the outer flow does not depend on the gap-to-diameter ratio, the parameter space to be explored by numerical simulations is greatly reduced compared to using finite gap ratio simulations. Moreover, the numerical difficulties associated with resolving the interstitial flow are avoided. The proposed approach can be extended to a wide range of rolling bodies, including spherical particles and wheels, and should significantly reduce the computational expense required to model the hydrodynamic forces and predict the subsequent motion of such bodies.