Flow past rotating cylinders: effect of eccentricity

Abstract

Computational results are presented for flows past a translating and rotating circular cylinder. A stabilized finite element method is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation. To validate the formulation and its implementation certain cases, for which the flow visualization and computational results have been reported by other researchers, are computed. Results are presented for Re=5, 200 and 3800 and rotation rate, (ratio of surface speed of cylinder to the freestream speed of flow), of 5. For all these cases the flow reaches a steady state. The values of lift coefficient observed for these flows exceed the limit on the maximum value of lift coefficient suggested by Goldstein based on intuitive arguments by Prandtl. These observations are in line with measurements reported, earlier, by other researchers via laboratory experiments. To investigate the stability of the computed steady-state solution, receptivity studies involving an eccentrically rotating cylinder are carried out. Computations are presented for flow past a rotating cylinder with wobble; the center of rotation of the cylinder does not match its geometric center. These computations are also important from the point of view that in a real situation it is almost certain that the rotating cylinder will be associated with a certain degree of wobble. In such cases the flow is unsteady and reaches a temporally periodic state. However, the mean values of the aerodynamic coefficients and the basic flow structure are still quite comparable to the case without any wobble. In this sense, it is found that the two-dimensional solution is stable to purely two-dimensional disturbances.