A theoretical and experimental study of the interaction of a streamwise vortex with a surface

The interaction of a streamwise vortex with a surface is studied theoretically and experimentally. This type of vortex flow is of relevance to an aircraft possessing a close-coupled canard-wing configuration.; A physical model is developed based on the assumption that the wing has a large surface, with a large chord. The wing is represented by a semi-infinite surface set at zero angle of attack. It is assumed that the vortex, generated upstream, is a straight vortex filament, with constant strength, and lying in the direction of the freestream. The vortex filament is orthogonal to the leading-edge and it passes a certain distance over the surface. The three-dimensional flow obtained is assumed to be incompressible, steady, inviscid and irrotational. A mathematical formulation for this model is devised based on Laplace's equation for the velocity potential. The boundary value problem is solved analytically using Fourier transforms and the Wiener-Hopf technique. A closed form solution for the velocity potential is determined, from which the velocity and pressure distributions and a vortex path correction are calculated.; Experimental results are obtained for the pressure distribution on the surface and the velocity field around the vortex. Helium-soap bubble flow visualization studies are performed to trace the vortex, and oil-surface flow pattern visualization results are also obtained to assess the occurrence of boundary-layer separation.; The main conclusions are: both the theoretical and the experimental results indicate that the pressure distribution is anti-symmetric along the surface's span, in regions near the leading-edge, and symmetric downstream from it; the agreement between experimental and theoretical results is good for weak interactions; when the interaction becomes strong, the model overestimates the suction peak and does not predict the occurrence of a secondary vortex due to secondary boundary layer separation; vortex core/boundary layer interaction and vortex breakdown are also observed to occur in the strong interaction cases; the vertical displacement of the vortex is observed to be small and is predicted well by the theory, whereas the lateral displacement is non-negligible and is predicted well only for weak interactions.