Prediction of separated flows around pitching aerofoils using a discrete vortex method
A surface shedding discrete vortex method has been developed for stimulating incompressible flows around pitching aerofoils. The method is able to predict both attached and separated flows, the latter typified by the formation and transport of large vortices. The structures of dynamic stall flow are well captured without the need for other means to predetermine the separation points. In contrast to most other vortex methods, the method presented herein can perform quantitative analysis. Throughout a wide range of incidence, the pressure distributions are smooth and the normal force and pitching moment are in good agreement with experimental data. The method is also able to predict the flow with external constraints for simulating the effects of wind tunnel blockage. In this regard quantitative results and flow structures have been obtained which are consistent with those expected. Following the review of previous work presented in the introduction, the mathematical formulation of the method is expounded. A velocity expression is theoretically derived for flows with both a moving inner boundary (aerofoil) and fixed external constraints (wind tunnel walls). To maintain both no penetration and no slip conditions, it is concluded that an external constraint parallel to the free stream can be modelled by placement of a constant vortex sheet along the boundary, and the introduction of distributed vortices next to the constraint to represent the boundary layer. The vortex sheet strength is equivalent to the free stream velocity while the strength of the vortices can be calculated in the same manner as for the internal boundary. This conclusion avoids the necessity of employing mirror vortices and iteration techniques in traditional models. The aerodynamic loads are computed from the pressure distribution. For the computation of surface pressures, the relationship between the pressure gradient and the rate of vorticity creation on the surface has been developed for a moving boundary.