Exploiting Patterns in the Kulfan Transformations of Supercritical Airfoils

For a parametric airfoil to be genuinely useful in preliminary design opti-mization it has to satisfy a number of requirements. Perhaps most importantly the number of design variables has to be small and the design space defined by them has to exclude geometrically unrealistic shapes. Ideally, the design variables should also have intuitive significance, that is, they should be directly linked to geometrical or aerodynamic features. Furthermore, it is advantageous to have a multi-level parameterisation built into the same mathematical form, to allow design searches with increasing level of detail. Here we propose two general methods for generating airfoils that satisfy these criteria by exploit-ing certain patterns in the Kulfan (or class-shape function) transformations of families of existing airfoils. We illustrate the two methods by constructing concise parametric airfoils based on the NASA SC(2) family of supercritical sections. I. Parametric Airfoils in Preliminary Design THE cost of exploring a design space increases exponentially with the number of design vari-ables. This curse of dimensionality is particularly pressing in the context of preliminary design