论文标题
粘弹性上游不稳定性的数值研究
Numerical Study of Viscoelastic Upstream Instability
论文作者
论文摘要
在这项工作中，我们报告了有关狭窄通道中密闭气缸上游区域中粘弹性流体的流动不稳定性和分叉的数值结果。使用数值稳定技术进行了基于FENE-P模型（具有有限扩展的非线性弹性模型）的二维直接数值模拟。我们的结果表明，宏观粘弹性构成关系可以捕获先前针对低雷诺德流量的实验中报道的粘弹性上游不稳定性。数值模拟表明，非二维再循环长度（$ L_D $）受气缸阻滞率（$ BR $），Weissenberg数字（$ WI $），粘度比（$β$）和最大聚合物扩展（$ L $）的影响。接近上游再循环的开始，具体取决于$ l $和$β$的值，分叉可能是超临界或亚临界的。 $β$对上游再循环长度有非线性影响。这项工作有助于我们对粘弹性尾流的这种新不稳定机制的理论理解。
In this work, we report numerical results on the flow instability and bifurcation of a viscoelastic fluid in the upstream region of a confined cylinder in a narrow channel. Two-dimensional direct numerical simulations based on the FENE-P model (the finite-extensible nonlinear elastic model with the Peterlin closure) are conducted with numerical stabilization techniques. Our results show that the macroscopic viscoelastic constitutive relation can capture the viscoelastic upstream instability reported in previous experiments for low-Reynolds-number flows. The numerical simulations reveal that the non-dimensional recirculation length ($L_D$) is affected by the cylinder blocking rate ($BR$), the Weissenberg number ($Wi$), the viscosity ratio ($β$), and the maximum polymer extension ($L$). Close to the onset of upstream recirculation, depending on the values of $L$ and $β$, the bifurcation can be supercritical or subcritical. $β$ has a nonlinear influence on the upstream recirculation length. This work contributes to our theoretical understanding of this new instability mechanism in viscoelastic wake flows.
