Dynamic Control and Parametric Resonance in Hydrodynamic Systems: A Theoretical, Computational and Experimental Investigation

这笔赠款和数字管理系统(DMS-9706951)的一项配套拨款将支持一个来自数学和工程界的跨学科小组，研究流体动力系统中的动态控制和参数激励，并通过一个综合的分析、计算和实验计划，研究参数共振与转变/分叉的稳定/失稳之间的相互作用。研究人员专业知识的多样化组合提供了一个难得的机会，可以开发一个基础广泛的创新研究计划，研究动力学和流体动力学控制。为了对复杂的流体力学和控制策略有一个总体的了解，我们选择了两个基本的流动集合。这两种流动是Taylor-Couette流和旋涡破裂流的变种。这些一般流动之所以具有吸引力，是因为它们的复杂程度可以通过相对简单的流动状态或边界条件的变化来精确控制，同时它们具有丰富的动力学，这些动力学代表了一大类可能以复杂方式响应动态控制的一般流体动力系统。具体地说，这些类别的流可以对所应用的控制的参数激励作出共振响应。对这些一般流动行为的研究将有助于更好地理解更一般的含时流体动力系统。动态控制机构和参数共振之间的相互作用将使用(线性)Floquet理论进行研究，作为理解转折点或分叉点的动力学的第一步。我们将使用三种不同的非线性计算方法来研究超出弗洛奎特分析有效性的流动，每种方法都有不同的优点和局限性。它们的结合实施能够解决广泛的问题，并解决每个问题中的不同问题。实验结果将用于指导分析和控制实施。这项研究的影响不仅具有基础性，从而加深了对流体动力系统复杂时空动力学的理解，而且还将对几个具有实际意义的问题产生重大影响，如航空领域的气动声学结构共振减阻和减少疲劳，以及材料和化学加工行业中的过渡和不稳定性的有效控制。从这项研究中期待着对复杂系统控制动力学的新的基本和实用的见解，可以为美国工业提供竞争优势。

This grant and a companion grant in DMS (DMS-9706951) will support an interdisciplinary group drawn from the mathematics and engineering communities to study dynamic control and parametric excitations in hydrodynamic systems and to examine the interplay between parametric resonance and stabilization/destabilization of transitions/bifurcations, through an integrated program of analysis, computation and experiment. The diverse combination of the investigators' expertise offers an exceptional opportunity to develop a broadly based and innovative research program of research in dynamics and control in hydrodynamics. Two basic flow sets have been chosen in order to develop a general understanding of the complex hydrodynamics and control strategies. The two flows are variations on Taylor-Couette flow and on vortex breakdown flow. These generic flows are attractive because the degree of complexity can be precisely controlled by relatively simple changes in the flow state or boundary conditions, and at the same time they possess rich dynamics which are representative of a wide class of general hydrodynamic systems that may respond to dynamic control in a complex manner. In particular, these classes of flows may respond resonantly to the parametric excitation of the applied control. An investigation of the behavior of these generic flows will help to form a better understanding of more general time-dependent hydrodynamic systems. The interplay between dynamic control mechanisms and parametric resonance will be investigated using the (linear) Floquet theory as a first step in understanding the dynamics at the point of transition or bifurcation. Flows beyond the validity of the Floquet analysis will be studied using three different nonlinear computational approaches, each with distinct advantages and limitations. Their combined implementation is capable of resolving a wide range of problems and addressing distinct issues within each problem. The results from the experiment will be used to ref ine the analysis and control implementation. The impact of this research will not only be of a fundamental nature, resulting in a deeper understanding of the complex spatio-temporal dynamics of hydrodynamic systems, but it will also make a significant impact on several problems of practical importance, such as drag reduction and reduced fatigue due to aeroacoustic structural resonances in aeronautics, and effective control of transitions and instabilities in the materials and chemical processing industries. The new fundamental and practical insights on control dynamics of complex systems anticipated from this research can provide US industry with a competitive edge.