Karman vortex behind a circular cylinder in dilute polymer solutions.

Abstract

In a previous paper3\ it was shown that the numerical solution of the cross flow around a circular cylinder submerged in viscoelastic fluids agreed with the experimental results obtained by James and Acosta1^The analysis was restricted to the moderate Reynolds number range (l<ite<20), because of vortex formation at higher Reynolds numbers. In the higher Reynolds number range, an individual fluid particle undergoes a more rapid change in deformation, and this rapid straining is expected to vary the flow field more significantly if the test fluid has viscoelasticity. James and Gupta2) reported that the drag coefficient of a circular cylinder submerged in viscoelastic fluid flow showed a drastic increase in this Reynolds number range. For example, they observed that the drag coefficient in a 160-ppm polymer solution of Polyox Coagulant was almost 5 times the Newtonian drag coefficient at Re=100. This information should be combined with the stability and vortex formation problems in viscoelastic cross flow. The present work was thus planned to observe Karmanvortex formation in polymer solutions by a flow visualization technique. The results of Strouhal number measurements will be compared with the previous experimental results to discuss what kind of non-dimensional parameter should be suitable to correlate the observed phenomenon.

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

“…The results presented for the polyacrylamide solution showed that for the lowest Reynolds numbers (≈10 4 ) the Strouhal numbers were slightly lower than for water, in qualitative agreement with Usui et al [55] (who nevertheless operated at much lower Reynolds numbers). Overall, however, the authors concluded that polymer additives had no effect on the frequency of vortex shedding.…”

“…Increasing elasticity was found to attenuate the shedding frequence, the rate of decrease of the Strouhal number closely matching that of Usui et al [55]. The reduction in the time-averaged rms value of the lateral velocity component observed by Cressman et al [15] were corroborated by Oliveira.…”

“…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.…”

“…Moreover, crude dumbbell models of the FENE-type have already been shown [37] to capture much of the essential physics of the viscoelastic wake dynamics for inertial flows. (2) Despite the encouraging agreement in the laminar vortex shedding regime between numerical and experimental results with the MCR model and solutions of PEO, respectively, for quantities such as shedding frequency, rms lateral velocity magnitude and formation length [9,10,15,37,55], the numerical prediction (see Fig.9a of [37]) of an increase in Re vs with viscoelasticity is at variance with most experimental evidence, even for constant viscosity fluids. However, the observation was made via direct numerical simulations for only one value of the Deborah number (De = 80) and polymer extensibility.…”

“…In the experiments of Usui et al [55], a striking suppression of vortex formation for flow of solutions of PEO at various concentrations (c = 100, 200 and 400 wppm) was observed in the flow regime Re ≤ 300. 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.…”