Three-Dimensional Instabilities and Transition to Vortex Breakdown in Swirling Flows

申请号：CTS 9804745项目负责人：Rusak这是一笔用于继续研究旋涡流动中观察到的流动结构的突变，即旋涡分解的基金。研究的主要目的是建立一个物理理解和一致的数学描述的方式，其中小和大振幅的三维扰动在流动中演变。目的是确定引起不稳定的机制和导致各种类型崩溃的关键条件。希望这项研究可以为机械和航空工程技术的各种应用带来控制这些现象的技术。该项目将建立在一个理论研究过程中开发的方法上，该理论研究是在以前的NSF支持下完成的，该理论研究是通过管道和旋转射流的旋转流动的三维动力学。在此过程中，研究轴对称涡旋流动的框架将扩展到三维不稳定的一般情况。提出的理论方法将结合经典的渐近分析技术与现代数学工具从泛函和全局分析，动力系统理论。以及非线性偏微分方程理论。这项研究还将以目前在以色列理工学院进行的实验调查为指导，作为首席研究员和J. Cohen博士之间的合作努力，由美国-以色列两国科学基金会资助。采用激光多普勒风速法（LDA）和粒子成像测速法（PIV）测量速度场和流动可视化技术研究流动动力学。理论和数值研究将模拟实验条件，分析预测将与测量数据相关联，并作为实验的指导。2 1

Abstract Proposal Number: CTS 9804745 Principal Investigator: Rusak This is a grant to continue the study of abrupt changes in the flow structure observed in swirling flows, known as vortex breakdown. The main objective of the research is to construct a physical understanding and consistent mathematical description of the manner in which small and large-amplitude three-dimensional disturbances evolve in the flow. It is intended that the mechanisms that provoke instabilities and the critical conditions leading to the various types of breakdown will be determined. It is hoped that the study may lead to techniques to control these phenomena for variety of applications in mechanical and aeronautical engineering technologies. The program will build on the methodology developed during a theoretical study of the three-dimensional dynamics of swirling flows through pipes and in swirling jets that was completed under previous NSF support. During this effort, the framework of research for the study of axisymmetric vortex flows will be extended to the general case of three-dimensional instabilities. The proposed theoretical approach will combine classical techniques of asymptotic analysis with modern mathematical tools from functional and global analysis, theory of dynamical systems. and theory of nonlinear partial differential equations. The study will also be guided by experimental investigations that are currently being carried out at the Technion, as a collaborative effort between the principal investigator and Dr. J. Cohen, supported by a grant from the U.S.-Israel Binational Science Foundation. Laser Doppler Anemometry (LDA) and Particle Imaging Velocimetry (PIV) measurements of the velocity fields and flow visualization techniques are used to study the flow dynamics. The theoretical and numerical studies will model the experimental conditions and the analytical predictions will be correlated with the measured data as well as acting as a guide for the experiments. 2 1