Mathematical Sciences: Formation Process and 3-D Dynamics of Vortex Rings

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9408697 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-axisymmetric openings a nd 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.