Vortex method for DNS of flows about arbitrarily ...

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Vortex method for DNS of flows about arbitrarily moving, multiple bodies. Goeric Daeninck*, Guy Dumas**, Gregoire Winckelmans*. * Universite Catholique de ...
Paper 10193 presented to the 57th Annual Meeting of the Division of Fluid Dynamics (DFD) of the American Physical Society (APS), November 21–23, 2004, Seattle, WA, USA

Vortex method for DNS of flows about arbitrarily moving, multiple bodies Goeric Daeninck*, Guy Dumas**, Gregoire Winckelmans* * Universite Catholique de Louvain (UCL), Belgium ** Universite Laval, Quebec, Canada

Abstract The vortex element method (VEM) combined with the boundary element method (BEM) was extended for the aerodynamics of arbitrarily moving multiple bodies. This was done by augmenting our previous method for DNS of flows about bodies of general geometry (see J. Comput. Phys. 165: 354-406, 2000). This approach uses the fast multipole method (to efficiently evaluate the Biot-Savart velocity), the particle redistribution schemes (to maintain good uniformity in the distribution of the vortex particles, and thus second-order accuracy) with arbitrary crossing between the redistribution lattice and the bodies’ boundaries, an accurate viscous scheme (PSE), the proper vorticity flux at the wall to satisfy no slip (using a BEM with vortex panels) and its accurate diffusion on the nearby particles. We added the displacement (translation and rotation) of the bodies, the BiotSavart velocity induced by the rotational rate of each body (with same methodology as in “contour dynamics”, reducing the integral over each body area to an integral over its contour), and the vorticity flux correction due to the moving walls. Results of DNS at moderate Reynolds numbers will be presented, including cases of multiple oscillating airfoils. Because of the “grid-free” behavior of the method, cases where the bodies have complex, large amplitude movements (including close relative approaches) are handled conveniently.

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