Contributions to the Three-Dimensional Vortex Element Method and Spinning Bluff Body Flows

Citation

Chatelain, Philippe (2005) Contributions to the Three-Dimensional Vortex Element Method and Spinning Bluff Body Flows. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/YEDS-0V89. https://resolver.caltech.edu/CaltechETD:etd-02012005-061553

Abstract

Several contributions to the three-dimensional vortex element method for incompressible flows are presented. We introduce redistribution schemes based on the hexagonal lattice in two dimensions, and the face-centered cubic lattice in three dimensions. Interpolation properties are studied in the frequency domain and are used to build high-order schemes that are more compact and isotropic than equivalent cubic schemes. We investigate the reconnection of vortex rings at small Reynolds numbers for a variety of configurations. In particular, we trace their dissipative nature to the formation of secondary structures.

A method for flows with moving boundaries is implemented. The contributions of rotating or deforming boundaries to the Biot-Savart law are derived in terms of surface integrals. They are implemented for rigid boundaries in a fast multipole algorithm. Near-wall vorticity is discretized with attached panels. The shape function and Biot-Savart contributions of these elements account for the presence of the boundary and its curvature. A conservative strength exchange scheme was designed to compute the viscous flux from these panels to free elements.

The flow past a spinning sphere is studied for a Reynolds number of 300 and a wall velocity that is equal to half the free-stream velocity. Three directions of the angular velocity are considered. Good agreement with previous numerical and experimental measurements of the force coefficients is observed. Topological features such as the separation and critical points are investigated and compared amongst the configurations.

Finally, preliminary results for flapping motions are presented. Simple rigid geometries are used to model a fish swimming in a free-stream and a flapping plate.

Thesis Files