Improved aerofoil parameterisation based on class/shape function transformation

Abstract

A new aerofoil parameterisation method is put forward to represent an aerofoil by combining the leading edge modification class/shape function transformation (LEM CST) method and improved Hicks–Henne bump function’s method. The new class/shape function transformation (NEW CST) method has two additional basis functions comparing the original CST method. In order to confirm these two basis functions, the radial basis functions neural network (RBF) model is trained by some samples which are generated by the Latin hypercube design (LHD) method and Genetic Algorithm (GA) is proposed to achieve the basis functions of the NEW CST method. The NEW CST method has been evaluated in fitting precision of 1,545 aerofoils by comparison with the LEM CST method and the original CST method. And the improved ability of the NEW CST at the leading edge and trailing edge is verified by a series of complex aerofoil case studies within 1,545 aerofoils. The results indicate that the NEW CST method can represent the whole aerofoils and possesses the intuitive property as well as the original CST. Moreover, the number of control parameters (NCP) to parameterise aerofoils is the fewest among these three methods. Furthermore, when the NCP of the NEW CST and LEM CST is the same, the NEW CST method has the higher accuracy and smaller root mean square errors (RMSE) especially at the leading edge and trailing edge.

Aerodynamic Optimization Framework for a Three-Dimensional Nacelle Based on Deep Manifold Learning-Assisted Geometric Multiple Dimensionality Reduction

“…Choosing a geometric dimensionality reduction method with enough flexibility, simplicity, and smoothness to describe the complex 3D geometry of a cylindrical-like nacelle is crucial for developing a nacelle aerodynamic design method. The most common and traditional nacelle design method simplifies the optimization of 3D nacelle geometry into individual optimizations of one or more two-dimensional (2D) cross-sections, which are described by a proper parametric method (e.g., Hicks-Henne [10], CST [11] and B-Spline [12]). As shown in Figure 1, these 2D cross-sections are usually chosen as typical circumferential profiles, e.g., at the angle of 0, 90, and 180 [13].…”

“…Aerospace 2023, 10, x FOR PEER REVIEW 2 of 25 are described by a proper parametric method (e.g., Hicks-Henne [10], CST [11] and B-Spline [12]). As shown in Figure 1, these 2D cross-sections are usually chosen as typical circumferential profiles, e.g., at the angle of 0, 90, and 180 [13].…”

Modifications of class-shape transformation driven by aerodynamic concerns over leading-edge region

“…12 An additional composite is applied to the accumulation of Bernstein polynomials as new basis function for airfoil description so that the leading-edge region can be expressed by linear terms in mathematical formulation, which enhances geometric accuracy. 13,14 Simple trigonometric function has also been used as cutoff filter on the Bernstein basis as local refinement 15,16 ; however, in the stage of design where the ‘big picture’ of the problem has not been shown yet (e.g., by sensitivity analysis), the application of this approach requires conjectures. Data manipulation is also proposed based on airfoil database initiated by CST so that dimension can be reduced with proper orthogonal decomposition 17 ; the disadvantage is that the problem of economically selecting relevant parameters is just another problem of selecting good airfoils that constitute database.…”