Dynamics of corotating vortex pairs in the wakes of flapped airfoils.
A. L. Chen, J. D. Jacob, and Ö. Savas
Journal of Fluid Mechanics, Vol. 382, 155-193, 1999.
The behavior of a pair of corotating vortices in the wake of a flapped airfoil is experimentally studied in a water towing tank. Three rectangular airfoils with an aspect ratio of 6 and flap spans of 0%, 30%, and 67% are used in the experiments. Reynolds numbers based on total circulation of the vortices range from 1.0 x 10^4 to 6.4 x 10^4. An underwater camera is used to capture a time sequence of PIV images. Planar velocity vector fields and their gradients are derived from these images using an adaptive Lagrangian parcel tracking algorithm. Isovorticity surfaces are extracted from time series of planar vorticity data. The behavior of the vortices are tracked by using various moments of both the probability density distribution and the spatial distribution of their streamwise vorticity. Several observations are noted in the vortex wake. All vortices show a Lamb-Oseen circulation distribution when they are clearly identifiable. Further, vortices from the flapless wing exhibit Lamb-Oseen velocity and vorticity distributions with slow growth. Merger of the corotating vortex pair is observed at all circulation Reynolds numbers in these experiments. A key observation is that the merger occurs at around 0.8 orbit period of a corotating vortex pair. The merger process appears to be inviscid and three-dimensional. 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 center of vorticity remains unaffected by the merger process. Kinetic energy and angular momentum of the flow are conserved during the merger. 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 somewhere in between. Mechanisms contributing to the merger dynamics are discussed.