Unsteady vortex interactions with Joukowski airfoils on elastic supports*

Coherent vortices present in the atmosphere or that are generated by aircraft create a gust field that exerts unsteady aerodynamic forces on the wings and appendages of downstream aircraft. In particular, the unsteady aerodynamic forces resulting from spanwise-oriented gust encounters produce an unsteady vortex wake that is also coupled to the motion of the incident vortex and to the wing shape and position. These coupled interactions between an incident line vortex, a Joukowski airfoil on elastic supports, and its wake are formulated analytically and computed numerically. The vortex motion and the fluid forces on the airfoil are derived from inviscid potential flow, and the continuous shedding of vorticity from the trailing edge is modeled by the emended Brown and Michael equation. Special attention is paid to the limiting cases of flat-plate airfoils that are either stationary or under prescribed motions for which validation data exist. The present effort extends beyond these restrictions to include the geometrical effects of the Joukowski airfoil profile and its aeroelastic influence on the incoming vortex path and the unsteady fluid loading.