论文标题
粘弹性流在圆形圆柱上的亚临界稳定性：数值研究
Subcritical insability of viscoelastic flow over a circular cylinder: A numerical study
论文作者
论文摘要
在本文中，我们讨论了圆形圆柱体周围粘弹性流的不稳定性是通过数值模拟的亚临界还是超临界的。选择OldRoyd-B模型来描述粘弹性本构的关系。对数结构重新构造用于稳定数值模拟。所研究的参数范围是雷诺数（$ re $）从5到100，魏森伯格数字（$ Wi $）从0到10，固定粘度比为$β= 0.9 $。模拟是在两条路径下进行的，即1）增加$ re $（或$ wi $）和2）逐渐减少$ re $（或$ wi $），并从一个州逐渐逐渐从一个州到下一个状态。结果表明，沿这两个路径获得的时间平均速度等统计解决方案在某些参数范围内与从稳定到不稳定流量的过渡点范围内并不相同。这种加载路径依赖性行为表明流动不稳定性是亚临界的。
In this paper, we discuss whether the instability of viscoelastic flow around a circular cylinder is subcritical or supercritical by numerical simulation. The Oldroyd-B model is selected to describe the viscoelastic constitutive relationship. The Log-conformation reformulation is employed to stabilize numerical simulation. The parameter ranges investigated are the Reynolds numbers ($Re$) spanning from 5 to 100 and the Weissenberg number ($Wi$) spanning from 0 to 10, with a fixed viscosity ratio of $β= 0.9$. Simulations are performed under two paths, i.e., 1) increasing $Re$ (or $Wi$) and 2) decreasing $Re$ (or $Wi$) slowly and gradually from one state to the next. The results show that the statistical solutions such as the time-averaged velocity obtained along the two paths are not identical over certain parameter range, which is around the transition point from the steady to unsteady flow. This loading path dependence behaviour indicates that the flow instability is subcritical.
