Polar coordinate transformation representation of symmetric airfoil curves

In this thesis, a new parameterization method is studied to define symmetrical airfoils or airfoil thickness curves. The method is named as Polar Coordinate Transformation (PCT) method and basically performed as transforming airfoil cartesian coordinates to polar coordinates by means of changing the starting point of airfoil coordinates. After polar transformation is performed, two third degree Bezier curves are used to be able to fit transformed airfoil coordinates. Control points of Bezier approximation curves used in PCT method can be calculated as PARSEC and Bezier-PARSEC similar parameters in the form of simple equations. To evaluate the performance capability of presented technique, PCT method has been compared with the BP3333 method for a number of conventional NACA type symmetric airfoils with respect to convergence performance and capabilty of obtaining optimum geometries that provide certian flow conditions. Results show that for corvergence performance most of airfoils which are tested in this study, Polar Coordinate Transformation (PCT) technique is superior to BP3333 method in computational time, ease of implementation and deviation values. Performance of obtaining optimum geometry in certain flow conditions, PCT method provides higher fitness value than BP3333 but also consumes higher CPU time.