Gcr. Bodstein et al., THE 3-DIMENSIONAL INTERACTION OF A STREAMWISE VORTEX WITH A LARGE-CHORD LIFTING SURFACE - THEORY AND EXPERIMENT, Journal of Fluid Mechanics, 322, 1996, pp. 51-79
The three-dimensional vortex flow that develops around a close-coupled
canard-wing configuration is characterized by a strong interaction be
tween the vortex generated at the canard and the aircraft wing. In thi
s paper, a theoretical potential flow model is devised to uncover the
basic structure of the pressure and velocity distributions on the wing
surface. The wing is modelled as a semi-infinite lifting-surface set
at zero angle of attack. It is assumed that the vortex is a straight v
ortex filament, with constant strength, and lying in the freestream di
rection. The vortex filament is considered to be orthogonal to the lea
ding-edge, passing a certain height over the surface. An incompressibl
e and steady potential flow formulation is created based on the three-
dimensional Laplace's equation for the velocity potential. The boundar
y-value problem is solved analytically using Fourier transforms and th
e Wiener-Hopf technique. A closed-form solution for the velocity poten
tial is determined, from which the velocity and pressure distributions
on the surface and a vortex path correction are obtained. The model p
redicts an anti-symmetric pressure distribution along the span in regi
on near the leading-edge, and a symmetric pressure distribution downst
ream from it. The theory also predicts no vertical displacement of the
vortex, but a significant lateral displacement. A set of experiments
is carried out to study the main features of the flow and to test the
theoretical model above. The experimental results include helium-soap
bubble and oil-surface flow pattern visualization, as well as pressure
measurements. The comparison shows good agreement only for a weak int
eraction case, whereas for the case where the interaction is strong, s
econdary boundary-layer separation and vortex breakdown are observed t
o occur, mainly owing to the strong vortex-boundary layer interaction.
In such a case the model does not agree well with the experiments.