Symmetry based scaling of the multi-point statistics of a turbulent Couette flow extended by wall-transpiration

由壁蒸腾扩展的湍流库埃特流的多点统计的基于对称的缩放

• 批准号: 267513790
• 负责人: Professor Dr.-Ing. Martin Oberlack
• 金额: --
• 依托单位: Fachgebiet Strömungsdynamik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/267513790?language=en
• 关键词: Symmetry; based; scaling; multi; point

The ultimate goal of the present proposal is to deepen our knowledge on turbulent shear flows based on Lie symmetries, and to extend our knowledge of the multi-point correlation equations (MPCE) to the companion more fundamental probability density function (PDF) Ludgren-Monin-Novikov equations.Our understanding of the fact that certain symmetries of canonical shear flow are active or broken has to be completely revised as physical mechanisms such as wall transpiration appears to break certain symmetries for the mean velocity, however, at the same time gives rise to new symmetries for higher order correlations.The present proposal aims in closing this gap by revising parts of the symmetry based turbulence theory by analysing the turbulent Couette flow with and without transpiration supplemented by related large Reynolds number DNS particularly focussing on the PDF approach. The latter flow is ideal in the sense that certain symmetries may be freely switched on and off.For this we need to comprehend that turbulent scaling laws are Lie symmetry group based solutions. Based on this theory the present applicant generated various scaling laws for the mean velocity of plane shear flows (2000,2001), all of which, except the plane Couette case, have since then been undoubtedly validated.A substantial progress was gained in 2010 where the present applicant derived an extended set of Lie symmetries of the MPCE. This significantly revised our understanding of turbulence statistics and, most important, also delivered the missing link to compute higher correlations, which was nicely validated including the classical near-wall log-region.In the precursor proposal even a new logarithmic centre region scaling law was forecasted for a turbulent Poiseuille flow with constant wall transpiration and convincingly validated including all related stresses against large scale DNS data.Still, various issues of the theory are unresolved: (i) recent large-scale DNS for the turbulent Couette flow nicely validated additional new statistical symmetries though for the mean velocity the latter only appear active for the Couette flow the reason being unknown. (ii) the higher correlations selectively rely on these new statistical symmetries, e.g. for fully parallel shear flows this symmetry is only switched on for the 11-component while for non-parallel flows, i.e due to wall transpiration, these symmetry is pivotal for all second moments.Finally, and most important, all symmetries have their counterparts both in the MPCE and in the more central PDF equations. Symmetry-invariant solutions for the PDF have to obey the non-negativity restriction of PDFs, which poses a significant constraint onto the solution and hence on the values of the group parameters. In turn, this inflicts constraints onto the scaling law parameter such as log-law parameter $\kappa$ with the eventual goal to obtain first principle constraints for them.

本提案的最终目标是使我们对基于谎言对称性的湍流剪切流的知识加深我们对多点相关方程（MPCE）的了解更加基本的概率密度函数（PDF）ludgren-nomon-novikov方程。 wall transpiration appears to break certain symmetries for the mean velocity, however, at the same time gives rise to new symmetries for higher order correlations.The present proposal aims in closing this gap by revising parts of the symmetry based turbulence theory by analysing the turbulent Couette flow with and without transpiration supplemented by related large Reynolds number DNS particularly focussing on the PDF approach.从某种意义上说，后一个流是理想的，可以自由地打开和关闭某些对称性。为此，我们需要理解湍流缩放定律是基于对称的解决方案。基于这一理论，目前的申请人为平面剪切流的平均速度（2000,2001）生成了各种缩放定律（2000,2001），此后，除了平面couette案例外，所有这些都无疑已得到验证。2010年，在2010年获得了实质性进展，目前的申请人得出了MPCE的扩展级别的Symmetries。这显着修改了我们对湍流统计数据的理解，最重要的是，还提供了与较高相关性的缺失链接，该链接经过了很好的验证，包括经典的近壁log区域。尚未解决的：（i）湍流cOUETTE流的最新大规模DNS验证了其他新的统计对称性，尽管对于平均速度，后者仅对COUETTE流动而显得活跃，原因是未知的原因。 （ii）较高的相关性选择性地依赖于这些新的统计对称性，例如对于完全平行的剪切流，此对称性仅针对11组分打开，而对于非平行流，即由于壁蒸腾引起的，这些对称性对于所有第二瞬间都是关键的。在本文中，最重要的是，所有对称性在MPCE中均具有同步性，并且在MPCE和更多的中央PDF方程中。 PDF的对称不变解决方案必须遵守PDF的非阴性限制，这对溶液构​​成了重要的约束，因此对组参数的值构成了重要的约束。反过来，这对缩放定律参数构成了约束，例如log-law参数$ \ kappa $，最终目标是为其获得第一原理约束。