Direct simulation of freely rotating cylinders in viscous flows by high-order finite element methods

Flow past a freely rotating cylinder with a fixed axis of rotation, placed asymmetrically in a two-dimensional channel (closer to one of the walls) ha s been studied numerically. This flow was modeled by the Navier-Stokes equa tions coupled with the equation of angular momentum of the cylinder. A simp le explicit algorithm to simulate the cylinder-fluid interaction was used, and a semi-implicit scheme in combination with a high-order Lagrange finite element method was employed to solve the Navier-Stokes equations. All quan tities of interest (such as lift and drag on the cylinder) were computed wi thout taking advantage of the cylindrical geometry of the problem, making t he algorithm suitable to study more general geometries, It was found that t he cylinder in a channel may rotate in either the clockwise direction or in the opposite direction, depending on the Reynolds number and on the distan ce from the wall. These solutions could be steady or unsteady, but no unste ady solutions were found when the cylinder rotates in the counterclockwise direction. Also, it was found that the cylinder may experience a repulsive or attractive force to the wall. A detailed comparison of the solutions whe n the cylinder is fixed and when it is released to rotate freely was done i n order to understand the mechanisms that cause the cylinder to rotate in o ne direction or the other, as well as how it is attracted to or repelled fr om the wall. These simulations may provide improved insight into the physic s of the operation of micro-electromechanical systems pumps and turbines in their application to flow control. (C) 2000 Elsevier Science Ltd. All righ ts reserved.