Elucidation and control of near-wall turbulence-A new approach by saddle solutions

近壁湍流的阐明和控制——鞍解的新方法

基本信息

批准号：
16360090
负责人：
KAWAHARA Genta
金额：
$ 9.09万
依托单位：
Osaka University (2005-2006)Kyoto University (2004)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

项目摘要

In this research project, recently found appealing saddle solutions (unstable equilibrium or periodic solutions) were recomputed in plane Couette, plane Poiseuille, and autonomous wall systems to compare their properties. It has been shown that in spite of diffrernce in the way of driving the systems, there exist universal saddle solutions in wall-bounded shear flow. These solutions have been shown to be classified into two families, one of which is an upper-branch solution characterized by dominant streamwise vortical motion and the other of which is a lower-branch solution characterized by dominant streaky structures. The former represents well structures and statistics for near-wall turbulence, while the latter exhibits wall shear rate much less than that for a turbulent state. In numerical experiments of plane Couette flow, the lower-branch solution (unstable periodic solution) with much less wall shear rate has been stabilized by the use of a chaos control theory to accomplish a s … More ignificant reduction of skin friction drag in turbulent flow. The linear stability analysis of the lower-branch solution for the plane Couette system has been performed to demonstrate that the solution has only one unstable eigenvalue. At subcritical Reynolds numbers the lower-branch solution and its stable manifold form the basin boundary between laminar and turbulent attractors. It has been shown that turbulent flow can be laminarized if a small-amplitude control input is imposed on the flow during its transient approach to the lower solution and so to the basin boundary. The properties of the upper-branch solution (unstable periodic solution) representing near-wall turbulence was examined in plane Couette flow to show that the solution reproduces the universal statistical law of near-wall turbulence, i.e., the Prandtl wall law. Furthermore, the same kind of an upper-branch solution has been discovered in periodic-box turbulence with the high-symmetry to confirm that the statistics of the solution is in good agreement with that in a turbulent state. It has been found that the upper-branch solution also reproduces the universal statistical law of isotropic turbulence, i.e., the Kolmogorov similarity law. Less

在该研究项目中，最近发现的鞍溶液（不稳定的平衡或周期性解决方案）在平面的couette，Plan Poiseuille和自主壁系统中被认识到，以比较其性质。已经表明，尽管驱动系统的方式有所不同，但在壁挂剪切流中仍存在通用的鞍溶液。这些溶液已被证明分为两个家族，其中一个是一种以巨大的流向涡流运动为特征的高分支溶液，另一种是以优势性条纹结构为特征的下支流溶液。前者代表了近壁湍流的井结构和统计数据，而后者的剪切速率远低于湍流状态。在平面couette流的数值实验中，通过使用混乱控制理论来实现S的较小壁剪切速率的下支流溶液（不稳定的周期溶液）已稳定了……更明显地减少了湍流中皮肤摩擦的拖动。已经对平面couette系统的下支流解决方案进行了线性稳定性分析，以证明该溶液只有一个不稳定的特征值。在亚临界雷诺数上，下支流溶液及其稳定的歧管形成了层层和湍流吸引子之间的盆地边界。已经表明，如果在其瞬态接近较低溶液的瞬时接近流量，以及盆地边界的瞬时流量，则可以将湍流流动层流。在平面cOUTETS流中检查了代表近壁湍流的上支流溶液（不稳定的周期性解决方案）的性质，以表明该解决方案重现了近壁湍流的通用统计定律，即PrintTL Wall Law。此外，已经在高对称性的周期性盒湍流中发现了同样的上支流解决方案，以确认该溶液的统计数据与在湍流状态下的统计数据非常吻合。已经发现，大支分支的解决方案还重现了各向同性湍流的普遍统计法，即Kolmogorov相似性法。较少的