Numerical simulation of two-dimensional unsteady Giesekus flow over a circular cylinder

Abstract

This study numerically examines vortex shedding of two-dimensional viscoelastic flow over a circular cylinder at a Reynolds number of 100. The Giesekus model is selected to describe the viscoelastic constitutive relationship and investigate the combined effects of shear-thinning and elasticity. Log-conformation reformulation is employed to stabilize our numerical simulations. The parameters of the Giesekus model considered herein include the Weissenberg number (Wi) ranged from 0 to 80, the mobility factor (α) ranged from 0 to 0.5, and the viscosity ratio (β) fixed at 0.1 and 0.9. The combined effects of shear-thinning and elasticity on flow characteristics and macro parameters such as time-averaged drag coefficient (Cd¯), root mean square of lift coefficient (Clrms) and Strouhal number (St) are systematically discussed. Shear-thinning triggers an inertial instability by decreasing the apparent viscosity near the cylindrical wall. Elasticity introduces the extensional viscosity in the wake field to suppress flow instability. The combination of these two effects results in an elongation in the recirculating wake and a decrease in both Clrms and St, which are opposite to those solely induced by shear-thinning. Moreover, the simulation results indicate that strong elasticity may also trigger an elastic instability characterised with very high flow fluctuation at the leading edge of the cylinder, which is unlike the inertial instability caused by shear-thinning. Additionally, strong elasticity or strong shear-thinning increases the drag. But weak elasticity can increase the drag-reduction effect of shear-thinning solutions. The present numerical method associated with the Giesekus model can capture all the typical flow behaviors of a viscoelastic fluid flow past a cylinder revealed by previous experimental results.