Solution to Optimize the Airfoils Shapes Placed Into a Supersonic Viscous Flow

To improve the airfoils performances placed in supersonic flow is proposed a method of optimization for their shapes, in order to minimize the effect of the landing vortices. The theoretical modeling starts with the Navier-Stokes equations applied for thin layers, supplemented with additional conditions related to the profile shape. For a proper estimation of efficiency and responses at different flow regime’s conditions, were considered four aerodynamics airfoils, with different shapes and functioning characteristics. Two of them are special shapes of supersonic profiles and the other two deduced by theoretical assessments with an efficient behavior at high Reynolds numbers. The main purpose of this selection was to identify the essential aspects needed to be considered in numerical modeling of the airfoil’s wing shapes, as to assure an optimization of their behavior for different flow conditions. In the supersonic flow, the cross-sections of the wings are thin profiles, mainly symmetric, as to reduce the drag coefficient and to maximize, as possible, the lift coefficient. A supplementary method for the shape calculation of the aerodynamic profiles with small curvature, based on the Fredholm integral equation of the second kind, with a good behavior in the supersonic flow, is presented. Some aspects referring to unsteady flows and air compressibility are considered, as to simulate as much as possible the real, natural conditions. All profiles were tested, firstly, into a subsonic wind tunnel at incidences between 0⁰ – 4⁰ for different values of wind velocity, and secondly, into a supersonic wind tunnel, at the same incidences. The objective was to better understand and analyze the main factors, which influence the aerodynamic of shapes with curvature, and to assure an optimization of their behavior. The purpose of testing these profiles was to estimate a solution to improve the main characteristics, especially into the trailing and leading edges zones. There were also considered the effects of the attack angle, the influence of the wind velocity, air viscosity, and the shape’s curvature, on the vortices development. The obtained results allow a better functioning in supersonic flow regime, by eliminating the adverse pressure gradient and the boundary layer separation, assuring an optimum behavior especially into the leading edge zone.