A Boundary Integral Method for the Planar External Potential Flow Around Airfoils

This paper presents a boundary integral equation for the external potential flow problem around airfoils without cusped trailing edge angle. The derivation of the integral equation is based upon reducing the external potential flow problem to an exterior Riemann problem. The solution technique is different from the known techniques in the literature since it involves an application of the Riemann problem, instead of the usual Dirichlet or Neumann problems. The solution of the integral equation contains an arbitrary real constant, which may be determined by imposing the Kutta-Joukowski condition. The integral equation is solved numerically using the Nyström method with Kress quadrature rule. Comparisons between the calculated and analytical values of the pressure coefficient for the van de Vooren airfoil and the Karman-Trefftz airfoil with 15% thickness ratio and different angles of attack show very good agreement. Numerical results of the pressure coefficient for NACA0012 airfoil with different angles of attack are also presented.