A numerical model for two-dimensional unsteady flow calculations with a surface panel method

A numerical model for two-dimensional airfoils in unsteady motion with boundary layer separation is described. The airfoil and wake surfaces are represented by a finite set of combined source and vortex panels. The source strengths are prescribed to have the same magnitude as the normal relative velocity on the surface due to the freestream and motion of the airfoil. The vertex strengths on the airfoil surface are determined by applying a kinematic surface tangency condition to a Green's function representation of the potential field, while simultaneously enforcing the Kutta condition. Wake shedding is governed by a dynamic free surface condition and the characteristics of the flow near any boundary layer separation points. Wake deformation is predicted by applying a geometric free surface condition. Calculation results are presented for steady motion, impulsively started rectilinear motion, harmonic pitch oscillations, and constant pitching motions. Experimental data and analytical solutions are also presented for comparison.