Universal parametric geometry representation method

For aerodynamic design optimization, it is very desirable to limit the number of the geometric design variables. In this paper, a "fundamental" parametric airfoil geometry representation method is presented. The method includes the introduction of a geometric "class function/shape function" transformation technique, such that round-nose/ sharp aft-end geometries, as well as other classes of geometries, can be represented exactly by analytic well-behaved and simple mathematical functions having easily observed physical features. The fundamental parametric geometry representation method is shown to describe an essentially limitless design space composed entirely of analytically smooth geometries. The class function/shape function methodology is then extended to more general three-dimensional applications such as wing, body, ducts, and nacelles. It is shown that a general three-dimensional geometry can be represented by a distribution of fundamental shapes, and that the class function/shape function methodology can be used to describe the fundamental shapes as well as the distributions of the fundamental shapes. With this very robust, versatile, and simple method, a three-dimensional geometry is defined in a design space by the distribution of class functions and the shape functions. This design space geometry is then transformed into the physical space in which the actual geometry definition is obtained. A number of applications of the class function/shape function transformation method to nacelles, ducts, wings,, and bodies are presented to illustrate the versatility of this new methodology. It is shown that relatively few numbers of variables are required to represent arbitrary three-dimensional geometries such as an aircraft wing, nacelle, or body.