Giraldo, S., Garcia, M. and Boulanger, P.(2008). CFD Based Wing Shape
Optimization Through Gradient-Based Method. *Engineering Optimization
(EngOpt2008)*, 95-102, Rio de Janeiro, Brasil.

This paper deals with the optimization of shape of aerodynamic profiles. The objective is to reduce the drag coeffcient on a given airfoil while preserving the lift coefficient within acceptable ranges. A set of control points defining the geometry are passed and parameterized as a B-Spline curve. These points are modied automatically by means of CFD analysis. A given shape is dened by an user and a valid volumetric CFD domain is constructed from this planar data and a set of user-dened parameters. The construction process involves the usage of 2D and 3D meshing algorithms that were coupled into owncode.The volume of air surrounding the airfoil and mesh quality are also parametrically dened. Some standard NACA proles were used by obtaining rst its control points in order to test the algorithm. Navier-Stokes equations were solved for turbulent, steady-state ow of compressible uids using the k-epsilon model and SIMPLE algorithm. In order to obtain data for the optimization process an utility to extract drag and lift data from the CFD simulation was added. After a simulation is run drag and lift data are passed to the optimization process. A gradient-based method using the steepest descent was implemented in order to de ne the magnitude and direction of the displacement of each control point. The control points and other parameters dened as the design variables are iteratively modied in order to achieve an optimum. Preliminary results on conceptual examples show a decrease in drag and a change in geometry that obeys to aerodynamic behavior principles.

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