Formation Process and 3-D Dynamics of Vortex Rings

小行星9729158 本项目的目标是进行数值研究，以制定一个 更好地理解涡环动力学。 考虑的情况是， 涡流环通过从开口喷射一定量的流体而形成。 上 作为该项目的一部分，重点将放在初步形成过程中， 轴对称环 粘性效应在初始时间间隔内占主导地位 并影响涡的轨迹和总的脱落环量。 粘性效应 通过采用一个成功的高雷诺数的二维Navier Stokes解算器， 将研究轴对称情况下的数流。 无粘效应 还将研究使用涡面模型的流动，以便确定是否 目前的相似性理论预测可以调整，以更好地预测初始 流 该项目的第二部分涉及三维动力学的旋涡 在开口处形成的环。 发展一种数值方法来计算 3-在边缘处的三维涡面分离将使研究 这些流动的稳定性，以及非轴对称开口的影响， 非轴对称强迫 为此，三维涡丝 将开发一种方法，该方法包括在锐缘处的涡流分离 并实现快速求和算法以实现高分辨率计算。 了解涡环的动力学对于了解更多 复杂的流动，如发生在燃烧过程中的流动，或 对飞机构成危险的空中涡流结构。 一个无粘数值 本文建立了一个在圆截面上产生的轴对称涡环模型， 开放后 通过与实验的对比，证明了该模型的有效性 关于真实的流的详细信息。 在目前的工作中，该模型将 扩展到三维流动，并将用于研究的稳定性， 流动，非轴对称开口和非轴对称强迫的影响， 以及目前的理论结果预测流动的潜在适用性。 流动的这些方面中有几个很难通过实验或 分析上，计算承诺给一个更深入的了解流 动力学为了进行这项工作，目前的数字工具，可用于 2-三维流动将扩展到三维。

9729158 Nitsche The goal of the present project is to perform numerical investigations to develop a better understanding of vortex ring dynamics. The case is considered in which a vortex ring is formed by ejecting an amount of fluid from an opening. In the first part of the project, the focus will be on the initial formation process of axisymmetric rings. Viscous effects dominate the flow in an initial time interval and affect the vortex trajectory and total shed circulation. The effects of viscosity by adapting a successful 2-dimensional Navier Stokes solver for high Reynolds number flow to the axisymmetric case will be investigated. Inviscid effects of the flow using a vortex sheet model will also be studied in order to determine whether present similarity theory predictions can be adjusted to better predict the initial flow. The second part of the project concerns 3-dimensional dynamics of vortex rings formed at an opening. The development of a numerical method to compute 3-dimensional vortex sheet separation at an edge will enable the study of the stability of these flows, as well as the effects of nonaxisymmetric openings and nonaxisymmetric forcing. For this purpose, a 3-dimensional vortex filament method will be developed which incorporates vortex separation at a sharp edge and implements a fast summation algorithm to enable high resolution calculations. Understanding the dynamics of vortex rings is essential to understand more complicated flows such as those that occur in combustion processes, or in the airborne vortex structures presenting a hazard to aircraft. An inviscid numerical model has been developed for axisymmetric vortex rings generated at a circular opening. This model was proven by comparison with experiment to recover detailed information about the real flow. In the present work, this model will be extended to 3-dimensional flows, and will be used to study the stability of the flows, the effects of non-axisymme tric openings and nonaxisymmetric forcing, as well as the potential applicability of present theoretical results to predict the flow. Several of these aspects of the flow are difficult to understand experimentally or analytically, and the computations promise to give a deeper insight into the flow dynamics. In order to perform this work, current numerical tools available for 2-dimensional flows will be expanded to 3-dimensions.