Design of airfoils in incompressible viscous flows by numerical optimization

A method is outlined for the design of airfoils in incompressible viscous flows by numerical optimization wherein a reduced number of design coordinates are used to define the airfoil shape. The optimization problem is formulated as a nongradient search in a finite constrained parameter space. The approach is to define the airfoil as a linear combination of basic shapes which may be analytically or numerically defined. The design problem is to determine the participation of each of these basic shapes in defining the optimum airfoil. The aerodynamic analysis program is specially developed to fit the requirements of the optimization program and is based on the vortex singularity method for inviscid flow analysis and the momentum integral method for boundary layer analysis. Four examples have been worked out to illustrate the proposed design method. In these, modifications to four different airfoil geometries are made to achieve either a minimum drag coefficient or a minimum pitching moment coefficient under prescribed constraints. The results show that significant drag or pitching moment reduction is possible through shape manipulation alone.