Suppression and augmentation in vortex shedding frequency due to fluid elasticity

Abstract

Several previous experimental and numerical studies have demonstrated the suppression of vortex shedding frequency from bluff bodies, such as circular cylinders, due to fluid elasticity induced by adding solid polymer additives to a solvent like water, even in parts per million (ppm) quantities. However, this study reveals a more complex relationship between the two using extensive two-dimensional (2D) direct numerical simulations (DNS) of flows past a circular cylinder at a fixed Reynolds number of 100. Our findings show that the vortex shedding frequency initially decreases with increasing Weissenberg number (a measure of fluid elasticity), reaches a minimum at a critical Weissenberg number, and then increases with further increments in the Weissenberg number. The same non-monotonic trend is also observed in the temporal variation of the spanwise velocity component fluctuation within the flow domain. This study aims to elucidate the reasons behind these non-monotonic trends in vortex shedding frequency and velocity component fluctuations as functions of the Weissenberg number. Our detailed analysis attributes these trends to significant alterations in the vortex-shedding mechanism as fluid elasticity increases due to the appearance of inertio-elastic instability at higher Weissenberg numbers. Our findings also align with limited experimental observations of similar unexpected behaviors in viscoelastic fluids, providing new insights into the underlying mechanisms. Moreover, the study highlights that shear-thinning behavior in viscoelastic fluids counteracts these non-monotonic trends, instead promoting a monotonic increase in vortex shedding frequency with the Weissenberg number. Finally, the 2D simulation results show both qualitative and quantitative agreement with limited three-dimensional (3D) simulations conducted at higher Weissenberg numbers where the flow may transit from 2D to 3D due to the appearance of inertio-elastic instability.