Airfoil Shape Morphing through a Novel Parameterization and Fitting Optimization Method Based on Uniform Non-Rational B-Spline Functions

Abstract

The aim of this work is to implement an innovative parameterization and fitting procedure for the definition of a mathematical model useful to describe a wide range of airfoils. They are partitioned into three sections: central box, leading edge, and trailing edge. Each section is mathematically represented by two opposed, uniform, non-rational B-spline curves, describing the upper and lower airfoil segments’ perimeter. A novel approach is used to ensure both the desired continuity between two adjacent segments (up to 2nd derivatives) and sufficient model versatility and flexibility while managing a limited number of parameters, defining tangent and curvature vectors as scale factor variables. These parameters allow for a variable separation approach during the geometric fitting procedure that can be carried out considering two nested optimization processes, one based on a genetic algorithm and the other on a numerical gradient evaluation of the objective function. The representation method has been verified against different airfoils, comparing the geometric and aerodynamic properties of the input and model-based generated profile. To show the mathematical model’s capabilities and possible applications, a comparison between existing and proposed airfoil approximation methods has been provided together with examples of “global” and “local” morphing and CFD analyses of the resulting airfoils.