On the effects of viscoelasticity on two-dimensional vortex dynamics in the cylinder wake

The present paper represents, as far as we are aware, the first linear stability analysis for inertial flows of a viscoelastic fluid around a bluff body. Our particular interest is the effect of polymer additives on the linear stability of two-dimensional viscous flow past a confined cylinder and our investigation involves both direct numerical simulation and the solution of a generalized eigenvalue problem arising from the linearized perturbation equations. For a constant viscosity FENE-type model polymer additive is shown to have a stabilizing effect upon two-dimensional flow past a confined cylinder. In particular, our results reveal that the greater the maximum extensibility of the FENE dumbbells, the larger the value of the critical Reynolds number marking the onset of vortex shedding. Thus the stabilization brought to bear by the presence of the FENE-type dumbbells would appear to depend strongly upon the extensional properties of the polymer solution. This is in agreement with the results of the recent experimental paper of Cressman et al. [J.R. Cressman, Q. Bailey, W.I. Goldburg, Modification of a vortex street by a polymer additive, Phys. Fluids 13 (2001) 867-871] which highlight the importance of the extensional properties of high molecular weight polymers (even at low concentrations) in reducing the kinetic energy contained in the velocity fluctuations behind a cylinder. The impact of elasticity on Strouhal number, time-averaged recirculation length, drag and lift in the vortex-shedding regime are also discussed at some length.