Search

Browse

• Communities
• Authors
• Year
• Titles
• Subjects

My Space

• Login

On the optimal design of airfoils

Leloudas Stavros

Full record

---

Summary

During recent years, computer graphics techniques such as Free-Form Deformation (FFD), have become extremely useful and widely employed in the field of Aerodynamic Shape Optimization and particular throughout the design of airfoil sections. Although FFD is a powerful parameterization and deformation technique of any given arbitrary two- or three-dimensional shape, there is no guarantee that provides the preservation of the shape’s enclosed area or volume respectively, after its application. Given the importance of the structural integrity required by aerodynamic shapes, such as aircraft wings and wind turbine blades, the necessity of including a cross-sectional area preservation constraint (among several other geometrical and aerodynamic ones) arises during the optimization process of the airfoil sections forming the aforementioned applications. Even though previous works exist, where a cross-sectional area constraint is utilized, the implementation is done by either non-linear time consuming expressions or by penalty function approaches, which are not always sufficient and do not guarantee the exact satisfaction of a strict equality constraint throughout the design process. In this work an airfoil optimization scheme is presented, based on Area-Preserving Free-Form Deformation technique, which serves as an alternative approach for the handling and satisfaction of a strict cross-sectional area equality constraint, while a parallel Differential Evolutionary (DE) algorithm is utilized for the optimization procedure. The DE algorithm is combined with two Artificial Neural Networks (ANNs), a multilayer perceptron (MLP) feed-forward ANN and a Radial Basis Functions (RBF) network, which serve as surrogate models, to decrease the computational cost of the optimization procedure. In each iteration of the DE algorithm, before the evaluation of the fitness function for each candidate solution, an area preservation step is applied to that solution in order to meet the cross-sectional area constraint. The area preservation step is achieved by solving an area correction sub problem, which consists of computing and applying the minimum possible offset to each free-to-move control point of the FFD lattice, subject to the area conservation. Due to the linearity of the area constraint in each axis, the extraction of an inexpensive closed-form solution to the sub problem is possible by using Lagrange Multipliers method. The proposed technique overcomes the disability of Evolutionary Algorithms (EAs) to effectively treat strict equality constraints such as exact area preservation one. Throughout the optimization process both structural and aerodynamic requirements can be taken into account, as constraints while the objective function is focused on the improvement of aerodynamic efficiency. Additionally, the use of multiple surrogate models, in conjunction with the inexpensive solution to the area correction sub problem, render the optimization process time saving. This thesis demonstrates the applicability and effectiveness of the proposed methodology.

Available Files

Services