Recent extensions and applications of the ‘CST’ universal parametric geometry representation method

For aerodynamic design optimisation as well as for multidisciplinary design optimisation studies, it is very desirable to limit the number of the geometric design variables. In Ref. 1, a ‘fundamental’ parametric aerofoil geometry representation method was presented. The method included the introduction of a geometric ‘class function/shape function’ transformation technique, CST, 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 CST method was shown to describe an essentially limitless design space composed entirely of analytically smooth geometries. In Ref. 2, the CST methodology was extended to more general three dimensional applications such as wing, body, ducts and nacelles. It was 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. A number of applications of the ‘CST’ method to nacelles, ducts, wings and bodies were presented to illustrate the versatility of this new methodology. In this paper, the CST method is extended to include geometric warping such as variable camber, simple flap, aeroelastic and flutter deflections. The use of the CST method for geometric morphing of one geometric shape into another is also shown. The use of CST analytic wings in design optimisation will also be discussed.