Flow structure on finite-span wings due to pitch-up motion

Abstract

AbstractThe flow structure on low-aspect-ratio wings arising from pitch-up motion is addressed via a technique of particle image velocimetry. The objectives are to: determine the onset and evolution of the three-dimensional leading-edge vortex; provide complementary interpretations of the vortex structure in terms of streamlines, projections of spanwise and surface-normal vorticity, and surfaces of constant values of the second invariant of the velocity gradient tensor (iso-$Q$ surfaces); and to characterize the effect of wing planform (rectangular versus elliptical) on this vortex structure. The pitch-up motion of the wing (plate) is from 0 to $4{5}^{\ensuremath{\circ} } $ over a time span corresponding to four convective time scales, and the Reynolds number based on chord is 10 000. Volumes of constant magnitude of the second invariant of the velocity gradient tensor are interpreted in conjunction with three-dimensional streamline patterns and vorticity projections in orthogonal directions. The wing motion gives rise to ordered vortical structures along its wing surface. In contrast to development of the classical two-dimensional leading-edge vortex, the flow pattern evolves to a strongly three-dimensional form at high angle of attack. The state of the vortex system, after attainment of maximum angle of attack, has a similar form for extreme configurations of wing planform. Near the plane of symmetry, a large-scale region of predominantly spanwise vorticity dominates. Away from the plane of symmetry, the flow is dominated by two extensive regions of surface-normal vorticity, i.e. swirl patterns parallel to the wing surface. This similar state of the vortex structure is, however, preceded by different sequences of events that depend on the magnitude of the spanwise velocity within the developing vortex from the leading edge of the wing. Spanwise velocity of the order of one-half the free stream velocity, which is oriented towards the plane of symmetry of the wing, results in regions of surface-normal vorticity. In contrast, if negligible spanwise velocity occurs within the developing leading-edge vortex, onset of the regions of surface-normal vorticity occurs near the tips of the wing. These extremes of large and insignificant spanwise velocity within the leading-edge vortex are induced respectively on rectangular and elliptical planforms.