Karman Vortices in the Flow of Drag-reducing Polymer Solutions

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

“…Consistent with the findings of Kalashnikov and Kudin [27], Usui et al [55] demonstrated that an increase of polymer concentration or a decrease of cylinder diameter further reduced the Strouhal number at a given Reynolds number. The authors were able to establish a strong correlation between the Strouhal number and a Weissenber number We and equally with the square root of the reciprocal of the elasticity number E = Re/We.…”

“…9a) of a stabilization effect of elasticity on the vortex shedding, Re vs being slightly larger than that for a Newtonian fluid. What may explain the observation of the opposite tendency in papers such as that of Kalashnikov and Kudin [27], for example, is the presence of shear-thinning and possibly threedimensional effects. Certainly, in some very recent vortex shedding experiments [41] performed in our own laboratory with Boger fluids consisting of very dilute aqueous solutions of polyethylene oxide for Reynolds numbers in the range 50-150, elasticity was found to have a stabilizing effect on the flow past an isolated cylinder.…”

“…Thus, some of the results of Gadd [20] were extended and made more precise. It is also of interest to note from the paper of Kalashnikov and Kudin [27] that the addition of polymer seemed to destabilize the flow in that the Reynolds number Re vs at which the first vortices appeared were less than for the water for all cylinder diameters, the reduction being greatest for the wires having the smallest diameter. Here, however, it is not possible to claim viscoelasticity as the sole explanation since the same phenomenon was seen with the solutions of inelastic polymer.…”

“…Sarpkaya et al [47] worked with solutions of the same PEO as Gadd [20] and Kalashnikov and Kudin [27], although at different concentrations. Reynolds numbers for the experiments were selected in the range 5 × 10 4 to 3 × 10 5 and the general conclusion was that polymer additives precipitated the occurrence of flow characteristics normally seen at higher Reynolds numbers in a Newtonian fluid.…”

“…Working with water and a PEO solution at a concentration of 100 wppm past wires of varying diameters and at Reynolds numbers up to almost 400, Kalashnikov and Kudin [27] demonstrated that the vortex shedding frequency was much lower for the polymer solution than for water. The authors were able to attribute the reduction in shedding frequency for any given wire to viscoelasticity since when the same concentration of an inelastic solution of PEO was used in the flow around a wire the frequency of the Kármán vortex street was higher than for the Newtonian fluid.…”