Transport and pattern formation in pipe flow: theory / simulation

管流中的传输和模式形成：理论/模拟

• 批准号: 154133604
• 负责人: Professor Dr. Marc Avila Canellas
• 金额: --
• 依托单位: Zentrum für angewandte Raumfahrttechnologie und Mikrogravitation (ZARM)
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/154133604?language=en
• 关键词: Transport; pattern; formation; pipe; flow

In contrast to many other flows, the flow down a pipe of circular cross-section becomes turbulent despite linear stability of its laminar parabolic profile. In addition, at low Reynolds numbers turbulence does not fill the pipe but it occurs in the form of spatially localized patches, called puffs, surrounded by laminar flow. During the start of this century there has been great progress in the understanding of the turbulent transition process and the resulting turbulent state. This success has built first on the discovery of three-dimensional coherent structures that are (traveling wave) solutions of the Navier-Stokes equation and capture features of turbulent pipe flow. Another important aspect has been the observation that puffs are transient and that their decay statistics are as expected from chaotic repellers. In the first phase of this project we have described several bifurcations of coherent structures and identified the routes to chaotic motions. We have also identified the critical point for the onset of sustained turbulence that is connected with the spatial proliferation of turbulent patches in long pipes. In the second phase of the project the focus will be on identifying the global bifurcations, on characterizing the behaviour near the critical point, on developing methods to stabilize travelling waves numerically and experimentally and on developing reduced models of pipe flow. Throughout the second phase we will continue to closely interacting with experimentalists in Erlangen, Göttingen and Delft.

与许多其他流动相反，沿圆形横截面管道向下的流动变得湍流，尽管其层流抛物线剖面是线性稳定的。此外，在低雷诺数下，湍流不会充满管道，而是以被层流包围的空间局部斑块的形式发生，称为喷流。在本世纪开始的时候，人们对湍流过渡过程和由此产生的湍流状态的理解有了很大的进展。这一成功首先建立在三维相干结构的发现上，这些相干结构是Navier-Stokes方程的（行波）解，并捕获湍流管流的特征。另一个重要的方面是观察到喷流是短暂的，并且它们的衰减统计数据与混沌排斥子的预期一致。在这个项目的第一阶段，我们已经描述了几个分叉的相干结构，并确定了路线的混沌运动。我们还确定了临界点的持续湍流，这是与空间扩散的湍流补丁长管道的发病。在该项目的第二阶段，重点将是确定全局分叉，描述临界点附近的行为特征，制定在数值上和实验上稳定行波的方法，以及开发简化的管流模型。在整个第二阶段，我们将继续密切互动与实验学家在埃尔兰根，哥廷根和德尔夫特。