Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

Abstract

Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two-and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parametrizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.

Robust optimisation of computationally expensive models using adaptive multi-fidelity emulation

“…The aerofoil test case involved obtaining a set of aerofoil solutions that maximise lift-to-drag ratio whilst minimising maximum blade thickness of a turbine blade in the face of potential perturbation of input values caused by uncertainty. A prospective aerofoil geometry was defined using the Class-Shape Transformation (CST) method [37] . In particular the Au and Al parameters are the weighting coefficients that help prescribe the thickness/shape at various locations along the upper and lower surfaces respectively.…”

Three-Dimensional CST Parameterization Method Applied in Aircraft Aeroelastic Analysis

“…There are some comparisons with other shape parameterization methods [11,12], showing that the CST method has advantages in smoothness, mathematical efficiency, fitting performances, and Intuitiveness. CST has been widely used to parameterize and optimize two-dimensional airfoil [13,14] and simple 3D aircraft [15,16]. Liu [17,18] presents a multiblock CST method to model the hypersonic aircraft with complex shape, which can join adjacent surfaces smoothly and retain the good properties of the CST method.…”