A Study of the CST Parameterization Characteristics

This paper presents a study of the recently introduced Class-Shape function Transformation (CST). The study assesses some of the main characteristics that parameterization exhibits, such as the sensitivity to parameter perturbations, the uniqueness of a geometric representation, its filtering capability and parameter inter-dependence. In a gradient-based shape optimization process, the solutions of intermediate design cycles are naturally subject to numerical inaccuracy. Under such circumstances, those characteristics of the CST may affect the path and, eventually, compromise the performance of the optimization process depending on the gradient calculation method and minimum-search algorithm. A comparison of two different gradient calculation methods is presented in the context of inverse aerodynamic design along with some validation test cases.

[1]  Patrice Castonguay,et al.  SURVEY OF SHAPE PARAMETERIZATION TECHNIQUES AND ITS EFFECT ON THREE-DIMENSIONAL AERODYNAMIC SHAPE OPTIMIZATION , 2007 .

[2]  Luis Santos,et al.  Inverse aerodynamic design applications using the MGM hybrid formulation , 2009 .

[3]  S. Obayashi,et al.  Aerodynamic Optimization of Supersonic Transport Wing Using Unstructured Adjoint Method , 2001 .

[4]  Raymond M. Hicks,et al.  Wing design by numerical optimization , 1977 .

[5]  Antony Jameson,et al.  Reduction of the Adjoint Gradient Formula in the Continuous Limit , 2003 .

[6]  Antony Jameson,et al.  Reduction of the Adjoint Gradient Formula for Aerodynamic Shape Optimization Problems , 2003 .

[7]  John E. Bussoletti,et al.  "Fundamental" Parameteric Geometry Representations for Aircraft Component Shapes , 2006 .

[8]  Kazuhiro Nakahashi,et al.  Unstructured adjoint method for Navier-Stokes equations , 2005 .

[9]  João Luiz F. Azevedo,et al.  A Framework for Aerodynamic Optimization Based On Genetic Algorithms , 2009 .

[10]  B. Kulfan.  Universal Parametric Geometry Representation Method , 2008 .

[11]  B. Kulfan.  A Universal Parametric Geometry Representation Method - "CST" , 2007 .

[12]  Patrice Castonguay,et al.  Effect of Shape Parameterization on Aerodynamic Shape Optimization , 2007 .

[13]  Brenda Kulfan.  Recent Extensions and Applications of the "CST" Universal Parametric Geometry Representation Method , 2007 .

[14]  Rida T. Farouki,et al.  Legendre-Bernstein basis transformations , 2000 .