Nonlinear Dynamics of "Triggering Controllers"

研究了一类典型流体系统的非线性动力学和控制问题：绕后向台阶流动，钝体两个尖锐凸角的流动分离，以及一个或多个翼型的高频颤振。在这里，“控制”不应被解释为传统意义上的。最近的“控制”工作集中在触发流体剪切层中的不稳定性；通过创建某些涡旋动态相互作用，系统性能通常会显著提高。所提出的研究旨在了解系统的非线性动态过程和分叉结构，以便有可能系统地综合这样的触发控制器，而不是依赖于特别的试错。该方法包括建立低阶涡旋模型来捕捉系统的本质特征，然后进行规范形和分叉分析。相信从本文将要研究的三个正则问题中得到的经验教训将适用于更广泛的流体流动问题，其表现为剪切层内的敏感的非线性涡动。该项目将支持PI和联合技术研究中心之间的密切合作，联合技术研究中心的工程师/科学家正在寻找将触发控制器集成到几种产品中的实用方法。此外，拟议的项目将形成一个焦点范围，以产生几个本科生研究项目。国际学生联合会观察到，这样的经历，本科生做出了重大贡献，往往会激发他们攻读更高学位的动力和愿望。

The investigator proposes to study the nonlinear dynamics and controlof a class of canonical fluid systems: flow over a backward facingstep, flow separation from two sharp convex corners of a bluff body,and high frequency flutter of one or multiple airfoils. Here,"Control" should not be interpreted in the traditional sense. Recent"control" efforts have focused on triggering instabilities in thefluid shear layers; by creating certain vortex dynamic interactions,system performance often improves dramatically. The proposed researchseeks to gain an understanding of the nonlinear dynamic processes andthe bifurcation structure of the systems, so that it may be possibleto synthesize such triggering controllers systematically, rather thanrelying on ad hoc trial and error. The approach consists ofconstructing low order vortex models that capture essential featuresof the systems, and then performing normal form and bifurcationanalyses. It is believed that lessons learned from the threecanonical problems to be studied here will be applicable to a broadclass of fluid flow problems whose performance is sensitive tononlinear vortex dynamics within shear layers. The project willsupport close collaboration between the PI and United TechnologiesResearch Center, whose engineers/scientists are searching forpractical ways of incorporating triggering controllers into severalproducts. Furthermore, the proposed project will form a focal pointaround which to generate several undergraduate research projects. ThePI has observed that such experiences, in which undergraduates makemeaningful contributions, often buoy their motivation and desire forpursuing advanced degrees.