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 $\left(\overline{C_d}\right)$, root mean square of lift coefficient (C_lrms) 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 C_lrms 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.

本研究对雷诺数为 100 的二维粘弹性流在圆柱体上的涡旋脱落进行数值分析。选择 Giesekus 模型来描述粘弹性本构关系并研究剪切稀化和弹性的组合效应。对数构象重构被用来稳定我们的数值模拟。这里考虑的 Giesekus 模型参数包括范围从 0 到 80的魏森伯格数 ( Wi )，范围从 0 到 0.5的迁移因子 ( α )，以及固定在 0.1 和 0.9的粘度比 ( β )。剪切稀化和弹性对流动特性和时均阻力系数等宏观参数的综合影响$\left(\overline{C_d}\right)$,系统讨论了升力系数 ( C _lrms ) 和 Strouhal 数 ( St ) 的均方根。剪切稀化通过降低圆柱壁附近的表观粘度引发惯性不稳定性。弹性在尾流场中引入拉伸粘度以抑制流动不稳定性。这两种效应的结合导致循环尾流的延长和C _lrms和St的降低，这与仅由剪切稀化引起的相反。此外，模拟结果表明，强弹性还可能引发弹性不稳定，其特征是圆柱前缘处的流动波动非常大，这与剪切稀化引起的惯性不稳定不同。此外，强弹性或强剪切稀化会增加阻力。但是弱弹性可以增加剪切稀化溶液的减阻效果。与 Giesekus 模型相关的当前数值方法可以捕获之前实验结果揭示的粘弹性流体流过圆柱体的所有典型流动行为。