论文标题
基于简化院长模型的弯曲导管流中的分叉
Bifurcations in curved duct flow based on a simplified Dean model
论文作者
论文摘要
我们提出了经过轻微弯曲的正方形导管中不可压缩流的最小模型。使用庞加莱般的部分，我们根据问题的唯一控制参数（DEAN NUMBER（DE））确定静止，周期性，周期性，上的和混乱的制度。除了代表一个简单而丰富的动力学系统外，当前的简化模型还代表了整个问题，可以准确地重现文献中观察到的分叉点。我们分析了从de = 0（无曲率）到de = 500的分叉图，观察到一个周期性段，然后观察两个单独的混乱区域。周期性状态下流动的相图显示了两个对称稳态，该系统在异斜周期后围绕这些溶液振荡。在附录中，为验证目的提供了一些定量结果，以及用于Navier-Stokes方程的数值解决方案的Python代码。
We present a minimal model of an incompressible flow in square duct subject to a slight curvature. Using a Poincaré-like section we identify stationary, periodic, aperiodic and chaotic regimes, depending on the unique control parameter of the problem: the Dean number (De). Aside from representing a simple, yet rich, dynamical system the present simplified model is also representative of the full problem, reproducing quite accurately the bifurcation points observed in the literature. We analyse the bifurcation diagram from De = 0 (no curvature) to De = 500, observing a periodic segment followed by two separate chaotic regions. The phase diagram of the flow in the periodic regime shows the presence of two symmetric steady states, the system oscillates around these solutions following a heteroclinic cycle. In the appendix some quantitative results are provided for validation purposes, as well as the python code used for the numerical solution of the Navier-Stokes equations.
