Unsteady viscous-inviscid interaction procedures for transonic airfoils using Cartesian grids

A viscous-inviscid interaction procedure for transonic airfoils using an Euler/integral boundary layer formulation and Cartesian grids is presented. The approach is based on a time dependent formulation for both the integral boundary layer equations and the Euler equations. Effects of upstream history on the shear stress are modeled by a time dependent rate equation derived from the turbulent kinetic energy equation. Results are presented for two of the test cases reported by Cook et al. (1979) for the RAE 2822 supercritical airfoil and one of the cases reported by Harris (1981) for the NACA 0012 symmetric airfoil. In general, the results are in good agreement with experiment.