Improved algorithms for circulation-control airfoils in transonic flow

A zonal model for aerodynamic analysis of two-dimensional transonic circulation control airfoils has been developed. The present approach combines a transonic full potential method for the global flow field and an integral boundary layer method for regions of the airfoil excluding the wall jet with a parabolized Navier-Stokes code for resolving the wall jet region beyond the slot. Existing methods suffer from two deficiencies: the insensitivity of the calculation to small changes in the Coanda surface geometry; and the inability to predict the shock structure of the underexpanded supersonic wall jets. The present wall jet procedure involves a pressure-split approach in the streamwise sense to enable noniterative solution of the coupled continuity and normal momentum equations for increased surface sensitivity and allows for expansion of applications to sonic slot exit conditions. Encouraging results are obtained in comparison with experimental data for two circulation airfoils with subsonic wall jets.