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Parametrizing Wing Surfaces using Partial Differential Equations

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Advanced Course on FAIRSHAPE

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Abstract

A method is presented for generating three-dimensional surface data given two-dimensional section data. The application on which this paper concentrates is that of producing wing surfaces through a set of airfoil sections. It is an extension of a new method for the the efficient parametrization of complex three-dimensional shapes, called the PDE Method. The method views surface generation as a boundary-value problem, and produces surfaces as the solutions to elliptic partial differential equations.

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References

  1. Nicolai, L.M, ‘Fundamentals of Aircraft Design’, University of Dayton, 1975.

    Google Scholar 

  2. Raymer, D. P., Aircraft Design: A Conceptual Approach, AIAA, Washington, 1989.

    Google Scholar 

  3. van der Vooren, J. and van der Wees, A.J., Inviscid Drag Prediction for Transonic Transport Wings using a Full-Potential Method’, Journal of Aircraft, Vol. 28, No. 12, 1991, pp. 869–875.

    Article  Google Scholar 

  4. Agrawal, S., Creasman, S.F. and Lowrie, R.B., ‘Evaluation of Euler Solvers for Transonic Wing-Fuselage Geometries’, Journal of Aircraft, Vol 28, No. 12, 1991, pp. 885–891.

    Article  Google Scholar 

  5. Hutchinson, M.G., Unger, E.R., Mason, W.H., Grossman, B. and Haftka, R.T., ‘Variable-Complexity Aerodynamic Optimization of a High-Speed Civil Transport Wing’, J. Aircraft, Vol 31., No. 1, 1994, pp. 110–116.

    Article  Google Scholar 

  6. Sloof, J. W., “Computational Methods for Subsonic and Transonic Aerodynamic Design”, AGARD, Report 712, Paper 3, 1983.

    Google Scholar 

  7. Lee, K.D. and Eyi, S., ‘Aerodynamic Design via Optimisation’, Journal of Aircraft, Vol 29, No. 6, 1992, pp. 1012–1019.

    Article  Google Scholar 

  8. Barthelemy, J.-F.M., Wrenn, G.A., Dovi, A.R., Coen, P.G. and Hall, L.E., ‘Supersonic Transport Wing Minimum Weight Design Integrating Aerodynamics and Structures’, Journal of Aircraft, Vol. 31, No. 2, 1994, pp. 330–338.

    Article  Google Scholar 

  9. Hager, J.O., Eyi, S. and Lee, K.D., ‘Two-Point Transonic Airfoil Design using Optimization for Improved Off-Design Performance’, Journal of Aircraft, Vol. 31, No. 5, 1994, pp. 1143–1147.

    Article  Google Scholar 

  10. Yiu, K.F.C, ‘Computational Methods for Aerodynamic Shape Design’, Mathematical Computer Modelling, Vol. 20, No. 12, 1994, pp. 3–29.

    Article  MathSciNet  MATH  Google Scholar 

  11. Eyi, S., Hager, J.O. and Lee, K.D., ‘Airfoil Design Optimization using the Navier-Stokes Equations’, J. Optimization Theory and Applications, Vol 83, No. 3, 1994, pp. 447–461.

    Article  MathSciNet  MATH  Google Scholar 

  12. El-banna, H.M. and Carlson, L.A., ‘Aerodynamic Sensitivity Coefficients using the Three-Dimensional Full Potential Equation’, Journal of Aircraft, Vol. 31, No. 5, 1994, pp. 1071–1077.

    Article  Google Scholar 

  13. Bloor, M. I. G. and Wilson, M. J., “The efficient parametrization of generic aircraft geometry”, Journal of Aircraft, Vol. 32, No. 6, pp. 1269–1275, 1995.

    Article  Google Scholar 

  14. Smith, R.E., Bloor, M.I.G., Wilson, M.J. and Thomas, A.M., ‘Rapid Airplane Parametric Input Design’, AIAA Paper 95 1687, 1995.

    Google Scholar 

  15. Seyant, N.M., Bloor, M.I.G., Lowe, T.W. and Wilson, M.J., “The Automatic Design of a Generic Wing/Body Fairing”, eds. Thibault, P.A. and Bergeron, D.M., CFD 95: Third Annual Conference of the CFD Society of Canada, Banff, Canada, Vol. 1, pp. 163–170, 1995.

    Google Scholar 

  16. Requicha, A., A., Voelcker, H.B., “Solid Modelling: Current Status and Research Directions”, IEEE Computer Graphics & Applications, Vol. 3, No. 7, 1983, pp. 25–37.

    Article  Google Scholar 

  17. Dekanski, C., Bloor, M.I.G., and Wilson, M.J., “The Representation of Marine Propeller Blades using the PDE method,’, Journal of Ship Research, Vol 38, No. 2, pp. 108–116, 1995.

    Google Scholar 

  18. Zauderer, E, Partial Differential Equations of Applied Mathematics, Wiley-Interscience, New York, (1983).

    MATH  Google Scholar 

  19. Gerald, C.F. and Wheatley, P.P., Applied Numerical Analysis, 3rd ed., Addision-Wesley, London, 1984.

    MATH  Google Scholar 

  20. Mallat, S.G., “A Theory for Multiresolution Signal Decomposition: The wavelet representation”, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 11, No. 7, pp. 674–693, 1989.

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Applied Mathematical Studies, The University of Leeds, Woodhouse Lane, Leeds, UK

    Prof. Dr. Malcolm I. G. Bloor & Prof. Dr. Michael J. Wilson

Authors
  1. Prof. Dr. Malcolm I. G. Bloor
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  2. Prof. Dr. Michael J. Wilson
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Editor information

Editors and Affiliations

  1. University of Technology Darmstadt, Germany

    Josef Hoschek

  2. National Technical University of Athens, Greece

    Panagiotis D. Kaklis (Project-coordinator) (Project-coordinator)

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© 1996 B. G. Teubner Stuttgart

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Bloor, M.I.G., Wilson, M.J. (1996). Parametrizing Wing Surfaces using Partial Differential Equations. In: Hoschek, J., Kaklis, P.D. (eds) Advanced Course on FAIRSHAPE. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-82969-6_13

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  • DOI: https://doi.org/10.1007/978-3-322-82969-6_13

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-519-02634-1

  • Online ISBN: 978-3-322-82969-6

  • eBook Packages: Springer Book Archive

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