Vortex-induced vibration in a cylinder with an azimuthal degree of freedom

We present a numerical study on the motion of a rigid cylinder promoted by its interaction with an incoming flow when the cylinder is restricted to move along the arc of a circle and thus has only one degree of freedom. The analysis also includes the description of the flow around the cylinder, which is influenced by the motion of the cylinder. The Reynolds number, based on the diameter of the cylinder and the far-away incoming flow velocity, is 180. It is considered that the diameter of the circle is three times the diameter of the cylinder and that the ratio of the cylinder to fluid densities is 1.6. The mass and momentum conservation equations in two dimensions are solved in a Cartesian grid, and the presence and motion of the cylinder are resolved using the immersed boundary method. The motion of the cylinder and the flow are two-way coupled in the sense that the aerodynamic forces that drive the displacement of the cylinder result from the fluid-solid interaction, and in turn, the flow around the cylinder is modified by its motion. We analyze the initial transient dynamics and long-time behavior for two different cases. The present results illustrate that the motion of the cylinder and the torque are quasiperiodic with cycles composed of three oscillations with different amplitudes. The stagnation point and the boundary layers are displaced periodically around the rim of the cylinder according to the incoming direction of its relative velocity with respect to the fluid. The upper and lower separation points undergo similar periodic angular displacements. This effect is superposed to the alternating vortex shedding mechanism that occurs in fixed cylinders. Two rows of alternating vortices similar to von Karman vortex street are formed downstream of the cylinder, but their centers are farther apart from the symmetry line than those generated in the wake of a fixed cylinder; this effect is closely related to the coupling between the oscillatory motion of the cylinder and the vortex shedding process. The pressure field and the instantaneous streamlines are also presented and related to the dynamical features of the cylinder motion. It is found that the pressure is the dominant effect on the dynamics of the cylinder and its magnitude and the direction of the total force on the cylinder is related to the motion of the cylinder and the genesis and emission of vortices.