A Universal Parametric Geometry Representation Method - "CST"

Abstract

For aerodynamic design optimization, it is very desirable to limit the number of the geometric design variables. In reference 1, a “fundamental parametric airfoil geometry representation method was presented. The method included the introduction of a geometric function / class function” transformation technique such that round nose / sharp aft end geometries as well as other classes of geometries could be represented exactly by analytic well behaved and simple mathematical functions having easily observed physical features. The fundamental parametric geometry representation method was shown to describe an essentially limitless design space composed entirely of analytically smooth geometries. In this paper, the “shape function / class function” methodology is extended to more general three dimensional applications such as wing, body, ducts and nacelles. It is shown that any general 3D geometry can be represented by a distribution of fundamental shapes, and that the “shape function / class function” methodology can be used to describe the fundamental shapes as well as the distributions of the fundamental shapes. The “CST” method of representing 3D geometries is introduced. With this very robust, versatile and simple method, a 3D 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 is defined. A number of applications of the “CST” 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 3D geometries such as an aircraft wing, nacelle or body.