An unsteady two-dimensional vortex method for the flow separation over a flapping wing

The flow separation over a very flexible or morphing aircraft, especially during flying or oscillation at a high angle of attack, is stronger than that for conventional aircraft. However, a low-order model for reliably predicting the dynamics of the LEV and its influence on the force is still not found. It is valuable to develop such aerodynamic approaches for optimizing the wing structure and kinematics and for designing a flight control strategy considering the flow separation problem. This paper presents a two-dimensional vortex method in which an artificial boundary is constructed for the velocity adjustment of the vortices near the control panels. This artificial boundary is established in accordance with the thickness of the actual wing. A sub-time step is introduced into the solution process of the vortex method to predict the vortex locations and perform velocity adjustments. Crossing vortices retain only their tangential velocity components relative to the artificial boundary in order to avoid entering the range of the airfoil represented by the artificial boundary. Moreover, the excessive induced velocities on the control panels caused by crossing vortices are decreased, and the nonphysical behaviors and discontinuous pressure are avoided. To demonstrate the advantages of the proposed artificial boundary method in modeling an airfoil during high-angle-of-attack flight, the proposed approach is applied to a flat-plate starting problem and a flapping problem. The simulation results are then compared with the results of several experiments and numerical data for both attached and separated test cases, verifying the capabilities of the proposed method.