Steady approach of unsteady low-Reynolds-number flow past two rotating circular cylinders

Abstract

The long-time viscous flow about two identical rotating circular cylinders in a sideby-side arrangement is investigated using an adaptive numerical scheme based on the vortex method. The Stokes solution of the steady flow about the two-cylinder cluster produces a uniform stream in the far field, which is the so-called Jeffery's paradox. The present work first addresses the validation of the vortex method for a low-Reynolds-number computation. The unsteady flow past an abruptly started purely rotating circular cylinder is therefore computed and compared with an exact solution to the Navier-Stokes equations. The steady state is then found to be obtained for t 1 with Re ω r 2 t, where the characteristic length and velocity are respectively normalized with the radius a 1 of the circular cylinder and the circumferential velocity Ω 1 a 1 . Then, the influence of the Reynolds number Re ω = a 2 1 Ω 1 /ν about the twocylinder cluster is investigated in the range 0.125 Re ω 40. The convection influence forms a pair of circulations (called self-induced closed streamlines) ahead of the cylinders to alter the symmetry of the streamline whereas the low-Reynoldsnumber computation (Re ω = 0.125) reaches the steady regime in a proper inner domain. The self-induced closed streamline is formed at far field due to the boundary condition being zero at infinity. When the two-cylinder cluster is immersed in a uniform flow, which is equivalent to Jeffery's solution, the streamline behaves like excellent Jeffery's flow at Re ω = 1.25 (although the drag force is almost zero). On the other hand, the influence of the gap spacing between the cylinders is also investigated and it is shown that there are two kinds of flow regimes including Jeffery's flow. At a proper distance from the cylinders, the self-induced far-field velocity, which is almost equivalent to Jeffery's solution, is successfully observed in a two-cylinder arrangement.

Codimension three bifurcation of streamline patterns close to a no-slip wall: A topological description of boundary layer eruption

“…The vortex-generated flow studied in the present paper is only an example; In addition to the cases mentioned in the Introduction another fundamental problem where the method we present would be applicable is the recently studied impulsively started rotation of two cylinders [48]. Here topological changes occur in a flow quite different from the one considered here, and, in particular, at much lower Reynolds numbers.…”

Flow Kinematics in Variable-Height Rotating Cylinder Arrays

“…In recent years, it has been shown that for specific regimes of geometric spacing, rotational orientation, Reynolds number, and rotation rate, paired rotating cylinders can suppress bluff-body vortex shedding and can exhibit increased lift coefficients and decreased drag coefficients (see Refs. [1][2][3][4][5][6], among others). Motivated by the potential implications that such positive interactions between rotating elements could have for VAWT arrays (see Refs.…”

A Kinematic Description of the Key Flow Characteristics in an Array of Finite-Height Rotating Cylinders

“…[1,2]), in recent years the dynamics of paired rotating cylinders have also become of interest (see, e.g., Refs. [3][4][5][6][7][8]). It has been shown that for specific regimes of geometric configuration, rotational configuration, Reynolds number, and rotation rate, suppression of bluff-body vortex shedding is observed.…”