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，尽管其层流抛物线轮廓具有线性稳定性，但圆形横截面的管道中的流动会变成湍流。此外，在低雷诺数下，湍流不会充满管道，而是以空间局部的形式发生。在本世纪初，人们对湍流转变过程和由此产生的湍流状态的理解取得了巨大进展，这一成功首先建立在三维空间的发现之上。相干结构是纳维-斯托克斯方程的（行波）解，并捕获湍流管流的特征。另一个重要方面是观察到烟团是瞬态的，并且它们的衰减统计数据与第一阶段的混沌排斥器的预期一致。在这个项目中，我们描述了相干结构的几个分叉，并确定了混沌运动的路径，我们还确定了与长管道中湍流斑块的空间扩散相关的持续湍流发生的临界点。在该项目的第二阶段，重点将是识别全局分岔、表征临界点附近的行为、开发通过数值和实验稳定行波的方法以及开发简化的管流模型。将继续与埃尔兰根、哥廷根和代尔夫特的实验家密切互动。