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

9706961 Lopez and Shen本项目将通过分析、计算和实验相结合的方法，研究水动力系统的动态控制和参数激励，并研究参数共振与过渡/分岔的稳定/不稳定之间的相互作用。选择了两种基本流集，即Taylor-Couette流和涡击穿流，以便对复杂的流体动力学和控制策略有一个大致的了解。这些通用流之所以具有吸引力，是因为它们的复杂程度可以通过流动状态或边界条件的相对简单的变化来精确控制，同时它们具有丰富的动力学，这些动力学代表了广泛的一般流体动力系统，这些系统可能以复杂的方式响应动态控制。特别是，这类流可能对应用控制的参数激励产生共振响应。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随时间变化的水动力系统。动态控制机制和参数共振之间的相互作用将使用（线性）Floquet理论作为理解过渡点或分岔点动力学的第一步进行研究。本文将使用三种不同的非线性计算方法来研究超出Floquet分析有效性的流，每种方法都有其独特的优点和局限性。它们的组合实现能够解决广泛的问题，并在每个问题中处理不同的问题。实验结果将用于改进分析和控制实施。本研究不仅将使人们对水动力系统复杂的时空动力学有更深入的认识，而且将产生重大的实际影响。例如，在空气动力学行业，控制策略将有助于减少阻力和减少由气动声学结构共振引起的疲劳；事实上，德克萨斯大学和其他研究人员最近在实验中证明了以边界跨向振荡形式的参数激励可以减少湍流边界层中的阻力。在材料和化学加工工业中，许多制造过程依赖于对过渡和不稳定性的有效控制。这项研究预计将为复杂系统控制动力学提供新的基础和实用见解，为美国工业提供竞争优势。

9706961 Lopez and Shen This project is 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. Two basic flow sets, namely the Taylor-Couette flow and vortex breakdown flow, have been chosen in order to develop a general understanding of the complex hydrodynamics and control strategies. 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 (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 refine the analysis and control implementation. This research will not only result in a deeper understanding of the complex spatio-temporal dynamics of hydrodynamic systems, but will also make a significant practical impact. For example, in the aerodynamics industry, the control strategies will aid in drag reduction a nd reduced fatigue due to aero-acoustic structural resonances; in fact, parametric excitation in the form of span-wise oscillations of the boundary has recently been demonstrated experimentally to reduce drag in turbulent boundary layers by researchers at the University of Texas and others. In the materials and chemical processing industries, many of the manufacturing processes rely on an effective control of transitions and instabilities. The new fundamental and practical insights on control dynamics of complex systems anticipated from this research can provide U.S. industry with a competitive edge.