Morphology of the forced oscillatory flow past a finite-span wing at low Reynolds number

Abstract

A study of the morphology of the vortical skeleton behind a flapping NACA0030 wing with a finite aspect ratio of 3, is undertaken. The motivation for this work originates with the proposal that thrust can be efficiently produced by flapping aerofoils. The test condition corresponds to a Strouhal number of 0.35, Reynolds number, based on aerofoil chord, of 600 and an amplitude of flapping, equal to the chord length of the wing. This test condition corresponds to the optimal thrust-producing case in infinite-span flapping wings. This study investigates the effect of wing three-dimensionality on the structure of the wake-flow. This is accomplished here, by quantitatively describing the spatio-temporal variations in the velocity, vorticity and Reynolds stresses for the finite-span-wing case.Preliminary flow visualizations suggest that the presence of wingtip vortices for the three-dimensional-wing case, create a different vortical structure to the two-dimensional-wing case. In the case of a two-dimensional-wing, the flow is characterized by the interaction of leading- and trailing-edge vorticity, resulting in the formation of a clear reverse Kármán vortex street at the selected test condition. In the case of a three-dimensional-wing, the flow exhibits a high degree of complexity and three-dimensionality, particularly in the midspan region. Using phase-averaged particle image velocimetry measurements of the forced oscillatory flow, a quantitative analysis in the plane of symmetry of the flapping aerofoil was undertaken. Using a triple decomposition of the measured velocities, the morphological characteristics of the spanwise vorticity is found to be phase correlated with the aerofoil kinematics. Reynolds stresses in the direction of oscillation are the dominant dissipative mechanism. The mean velocity profiles resemble ajet, indicative of thrust production. Pairs of strong counter-rotating vortices from the leading- and trailing-edge of the aerofoil are shed into the flow at each half-cycle. The large-scale structure of the flow is characterized by constructive merging of spanwise vorticity. The midspan region is populated by cross-sections of interconnected vortex rings.