Drag enhancement and drag reduction in viscoelastic fluid flow around a cylinder

We here use direct numerical simulations to describe the flow of a viscoelastic fluid, modeled using the so-called Oldroyd B model, around a cylinder in two dimensions. A wide range of flow parameters is covered in these simulations allowing to draw definitive conclusions as to the effect of viscoelasticity on such a flow situation. Both drag enhancement and drag reduction are observed and a phase diagram is proposed in the parameter space Reynolds number vs. Weissenberg number. While only drag enhancement is observed below a Reynolds number of 40, both drag enhancement and drag reduction are observed for higher Reynolds numbers indicating that drag reduction is a feature associated with the shedding of vortices behind the cylinder. An interesting observation accompanies the onset of drag enhancement in the vortex-shedding regime: the shedding is suppressed.