Flow about a circular cylinder between parallel walls

Abstract

The flow about a body placed inside a channel differs from its unbounded counterpart because of the effects of wall confinement, shear in the incoming velocity profile, and separation of vorticity from the channel walls. The case of a circular cylinder placed between two parallel walls is here studied numerically with a finite element method based on the vorticity–streamfunction formulation for values of the Reynolds number consistent with a two-dimensional assumption.

The transition from steady flow to a periodic vortex shedding regime has been analysed: transition is delayed as the body approaches one wall because the interaction between the cylinder wake and the wall boundary layer vorticity constrains the separating shear layer, reducing its oscillations. The results confirm previous observations of the inhibition of vortex shedding for a body placed near one wall. The unsteady vortex shedding regime changes, from a pattern similar to the von Kármán street (with some differences) when the body is in about the centre of the channel, to a single row of same-sign vortices as the body approaches one wall. The separated vortex dynamics leading to this topological modification is presented.

The mean drag coefficients, once they have been normalized properly, are comparable when the cylinder is placed at different distances from one wall, down to gaps less than one cylinder diameter. At smaller gaps the body behaves similarly to a surface-mounted obstacle. The lift force is given by a repulsive component plus an attractive one. The former, well known from literature, is given by the deviation of the wake behind the body. Evidence of the latter, which is a consequence of the shear in front of the body, is given.