| Augmenting the flow around an airfoil by stabilizing a vortex on the surface can provide lift enhancement. By using potential flow theory, this flow condition can be modeled with a vortex and sink located at the same spatial location. Therefore, through application of the Blasius theorem and enforcing various Kutta conditions, the instantaneous induced circulation of the flat plate can be computed (and thus the lift and pressure drag coefficients). Using this flow model, a parametric study is performed on several flow parameters in order to determine the neighborhoods of vortex-sink positions that provide maximum lift enhancement and lift to pressure drag ratios. Solutions are presented for a range of vortex-sink positions, vortex-sink strengths, flat-plate angle of attacks, and constant lift contours. It is observed that the largest lift enhancement occurs when the vortex-sink pair is located near the trailing edge of the at plate, however this induces a stall condition. In order to maximize the lift to pressure drag ratio while avoiding the stall condition, the vortex-sink pair should be located near the leading edge. With these results, a limiting process is taken in order to compute the velocity of the vortex-sink combination in the flow and natural stability locations of the vortex-sink combination are computed. By linearization of this model about various equilibrium points the system is shown to be hyperbolic with unstable equilibria. Using two span-wise, variable position, variable strength jets, the flow model is augmented and control laws developed to show that the vortex-sink combination near the leading edge can be stabilized on the surface of a at plate by simple flow augmentation and feedback control. |
