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

Abstract

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) has been studied numerically. This flow was modeled by the Navier–Stokes equations coupled with the equation of angular momentum of the cylinder. A simple 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 quantities of interest (such as lift and drag on the cylinder) were computed without taking advantage of the cylindrical geometry of the problem, making the algorithm suitable to study more general geometries. It was found that the cylinder in a channel may rotate in either the clockwise direction or in the opposite direction, depending on the Reynolds number and on the distance from the wall. These solutions could be steady or unsteady, but no unsteady 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 when the cylinder is fixed and when it is released to rotate freely was done in order to understand the mechanisms that cause the cylinder to rotate in one direction or the other, as well as how it is attracted to or repelled from the wall. These simulations may provide improved insight into the physics of the operation of micro-electromechanical systems pumps and turbines in their application to flow control.