Extension to the Class-Shape-Transformation Method Based on B-Splines

Abstract

A new parameterization method to enhance shape optimization for aircraft design was developed based on the class-shape-transformation method. This method was implemented in a tool that combined all aspects of the aerodynamic design process: parameterization, aerodynamic analysis, and optimization. The parameterization method used a combination of Bernstein polynomials and B-splines to allow for both local and global control of a shape. Additionally, the use of B-splines made it possible to efficiently handle volume constraints, which are very common in aircraft design. The parameterization method was coupled to two different aerodynamic analysis tools: the commercial panel method code VSAERO and an in-house Euler code. As a first test case, a wing was optimized for maximum lift-to-drag ratio in subsonic conditions using VSAERO and various optimization algorithms. It was shown that the optimizer was capable of arriving at wing shapes that demonstrated laminar flow up to 80%, without violating the implemented volume constraints. As a second test case, an airfoil was optimized for lift-to-drag ratio in transonic conditions using the in-house Euler solver and a gradient-based optimizer. Refining the shape using B-splines proved to be an efficient way of increasing the design freedom, resulting in additional improvements in the drag divergence Mach number in the order of 0.02.