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

旋流中的三维不稳定性和涡流破坏的过渡

• 批准号: 9804745
• 负责人: Zvi Rusak
• 金额: $ 22.5万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-09-01 至 2002-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9804745&HistoricalAwards=false
• 关键词: Three; Dimensional; Instabilities; Transition; Vortex

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

摘要 提案编号：CTS 9804745 首席研究员：Rusak 这是一项拨款，旨在继续研究在旋流中观察到的流动结构的突然变化，即涡流破坏。 该研究的主要目标是对流动中小幅度和大幅度三维扰动演化的方式建立物理理解和一致的数学描述。其目的是确定引起不稳定的机制和导致各种类型故障的关键条件。 希望这项研究能够带来控制这些现象的技术，用于机械和航空工程技术的各种应用。 该项目将建立在对通过管道和旋流射流的旋流的三维动力学的理论研究中开发的方法的基础上，该理论研究是在美国国家科学基金会之前的支持下完成的。 在此过程中，轴对称涡流的研究框架将扩展到三维不稳定性的一般情况。 所提出的理论方法将结合渐近分析的经典技术与来自泛函和全局分析、动力系统理论的现代数学工具。和非线性偏微分方程理论。 该研究还将以以色列理工学院目前正在进行的实验研究为指导，这是首席研究员和 J. Cohen 博士之间的合作努力，并得到了美国-以色列两国科学基金会的资助。 使用激光多普勒风速测量 (LDA) 和粒子成像测速 (PIV) 测量速度场和流动可视化技术来研究流动动力学。 理论和数值研究将对实验条件进行建模，分析预测将与测量数据相关联并作为实验指南。 2 1