Shape Parametrization Using Freeform Deformation

  • Arno Ronzheimer
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM) book series (NNFM, volume 89)


Shape parametrization has been identified as an import issue in aerodynamic design optimisation based on high-fidelity CFD-methods. For given shapes, which are available as CAD-models, post-parameterization method, based on freeform deformation, has been established to simplify and to automate the generation of geometrical variants to be used for CFD analyses. To create the necessary deformation lattices, structured grid generation techniques of a grid generation system, developed at DLR, are utilized. As this grid generation system has the salient feature to store and to replay a sequence of processes with different parameter settings, modifications of shapes, given by polygonal curves and surfaces, can be performed instantly.

The present freeform deformation method has reached a state, where it can be integrated into design loops to handle a variety of shape optimisation tasks. In two examples the applicability of the method for aerodynamic wing design and detailed design of a wing tip is demonstrated.


Deformation Lattice Grid Generation Adjoint Method Surface Grid Aerodynamic Shape 
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  1. 1.
    O. Brodersen, A. Ronzheimer, R. Ziegler, T. Kunert, J. Wild, M. Hepperle: “Aerodynamic Applications using MegaCads”, 6th Intern. Conf. on Numerical Grid Generation, Ed.: M. Cross, London, 1998, pp. 793–802.Google Scholar
  2. 2.
    CentaurSoft: Scholar
  3. 3.
    S. Coquillart: “Extended Free-Form Deformation: A Sculpting Tool for 3D Geometric Modeling”, Proceedings of SIGGRAPH’ 90, Dallas, Texas, Aug. 6–10, 1990.Google Scholar
  4. 4.
    O. Frommann: “Conflicting Criteria Handling in Multiobjective Optimization Using the Principles of Fuzzy-Logic”, AIAA-98-2370, 1998.Google Scholar
  5. 5.
    N. Gauger, J. Brezillon: “Aerodynamic Shape Optimization Using Adjoint Method”, Journal of Aero. Soc. of India, Vol. 54, No. 3, 2002.Google Scholar
  6. 6.
    T. Gerhold, J. Evans: “Efficient computation of 3D-flows for complex configurations with the DLR-TAU code using automatic adaption”, New Results in Numerical and Experimental Fluid Mechanics II, Vieweg Notes on Numerical Fluid Mechanics, Vol. 72, 1998, pp. 178–185.Google Scholar
  7. 7.
    J. Griessmair, W. Purgathofer: “Deformation of Solids with Trivariate B-Splines”, EUROGRAPHICS’ 89, Elsevier Science Publishers (North Holland), 1989, pp. 137–148.Google Scholar
  8. 8.
    N. Kroll, C.-C. Rossow, K. Becker, F. Thiele: “MEGAFLOW — A Numerical Flow Simulation System”, 21st ICAS Congress, Melbourne, paper 98-2.7.4, 1998.Google Scholar
  9. 9.
    C.-C. Rossow, A. Ronzheimer: “Investigations of Interference Phenomena of Modern Wing-Mounted High-Bypass-Ratio Engines by the Solution of the Euler-Equations”, AGARD Conference Proceedings 498, Aerodynamic Engine/Airframe Integration for High Performance Aircraft and Missiles.Google Scholar
  10. 10.
    J. A. Samareh: “A Novel Shape P Approach”, NASA TM-1999-209116, NASA Langley Research Center, Hampton, VA 23681.Google Scholar
  11. 11.
    V. Schmitt, F. Charpin: “Pressure Distributions on the ONERA-M6-Wing at transonic Mach Numbers”, AGARD Advisory Report No. 138, May 1979.Google Scholar
  12. 12.
    T. W. Sederberg, S. R. Parry: “Freeform Deformation of Solid Geometric Models”, Proceedings of SIGGRAPH’ 86, Dallas, Texas, Aug. 18–22, 1986.Google Scholar
  13. 13.
    J. Wild: “Numerische Optimierung von zweidimensionalen Hochauftriebskon-figurationen durch Lösung der Navier-Stokes-Gleichungen”, DLR Forschungsbericht 2001-11, ISSN 1434-8454.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Arno Ronzheimer
    • 1
  1. 1.DLR BraunschweigInstitute of Aerodynamics and Flow Technology, Transport AircraftBraunschweigGermany

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