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The Treatment of Convected Vortices in Compressible Potential Flow,

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A method is described for incorporating line vortices into the three dimensional compressible Potential Flow equation. A method Biot-Savart law is used to compute a vortical velocity field, which is added to the gradient of the potential to form a total velocity. A rapidly converging Approximate Factorization AFZ scheme is then used to compute a potential such that the modified Potential Flow equation as well as the appropriate boundary conditions, based on total velocity, are satisfied. As part of a coupled iteration procedure, the positions of the line vortices are computed so that they convect with the total flow. The method is used to compute the field due to a single line vortex convecting past a wing. This represents an approximation of the effect of a canard or other lifting surface ahead of the wing, which sheds a tip vortex. It can be seen that the flow field is substantially modified by the passage of the vortex. Unlike Euler equation schemes, which could also be used to compute these flows, our solutions exhibit no numerical diffusion The convected vortices retain their initial upstream width. Euler solutions, on the other hand, involve a vorticity which is numerically convected in an Eulerian frame and, unless extensive adaptive grid refinement is used they results in vortices which spread as they convect. Also, the Potential Flow method requires approximately two orders of magnitude less computing time and much less computer storage than the Euler methods. Author

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This article is from 'Aerodynamics of Vortical Type Flows in Three Dimensions: Conference Proceedings Held at Rotterdam, Netherlands on 25-28 April 1983,' AD-A135 157, p22-1-22-12.



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