Using invariant material manifolds and flow topology, the flow behavior and structure of flow around a two-dimensional Eppler 387 airfoil is examined with an emphasis on vortex shedding and the time-dependent reattachment profile. The examination focuses on low Reynolds number (Re = 60 000) flow at several angles of attack. Using specialized software, we identify invariant manifolds in the flow and use these structures to illuminate the process of vortex formation and the periodic behavior of the reattachment profile. Our analysis concludes with a topological view of the flow, including fixed points and a discussion of phase plots and the frequency spectrum of several key points in the flow. The behavior of invariant manifolds directly relates to the flow topology and illuminates some aspects seen in phase space during vortex shedding. Furthermore, it highlights the reattachment behavior in ways not seen before.
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Utilizing ideas from dynamical system theory to find invariant material manifolds, the structure of mixing behavior in vortex formation and shedding in two dimensional low Reynolds number flow is investigated. The test case is a low Reynolds number flow over an Eppler 387 airfoil at 6 • angle of attack. A software was developed, tested and validated for calculating material manifolds on unstructured grid. It is shown that the stable manifolds are an excellent method of visualizing the reattachment profile, and that the manifold associated with reattachment behaves in a periodic shedding type manner. Structural elements of the flow, not found in traditional flow maps, are discovered and found to have important interactions in the vortex roll up process. Structures are formed ahead of the airfoil and transported above and below the airfoil before they interact at the trailing edge of the airfoil to form the wake vortices. It is expected that these structures could play a role in flow control of the shedding process. Finally, it is shown that the combination of stable and unstable manifolds allow for a time dependent definition of the separation bubble.
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