Dynamics of corotating vortex pairs in the wakes of flapped airfoils

Abstract

The behaviour of a pair of corotating vortices in the wake of a flapped airfoil is experimentally studied in a water towing tank. Reynolds numbers based on total circulation of the vortices range from 1.0×104 to 6.4×104. Planar velocity vector fields and their gradients are derived from PIV images using an adaptive Lagrangian parcel tracking algorithm. Isovorticity surfaces are extracted from time series of planar vorticity data. The behaviour of the vortices is tracked by using various moments of both the probability density distribution and the spatial distribution of their streamwise vorticity. All vortices show a Lamb–Oseen circulation distribution when they are clearly identifiable. Further, vortices from the apless wing exhibit Lamb–Oseen velocity and vorticity distributions with slow growth. All corotating vortex pairs are observed to merge at about 0.8 orbit periods. First-order statistics of the flow field remain invariant during the merger. The higher-order moments of the vorticity distribution show strong time dependence, which implies three-dimensionality of the flow resulting from vortex stretching. The strengths of the individual vortices before merger are constant, and the total circulation before and after merger remains constant within the range of observations. The trajectory of the centre of vorticity remains unaffected by the merger process. The merger is preceded by a splitting of the weaker vortex into filaments which, depending on the relative strengths of the vortices, can occur in the radial direction, the axial direction, or a combination of the two. Mechanisms contributing to the merger dynamics are discussed.