Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Inverse Design Method of Supersonic wings Using Intergral Equations

적분방정식을 이용한 초음속 날개의 역설계법

  • Published : 2003.05.01
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Abstract

A practical design method for supersonic wings has been developed. The method is based on Takanashi's method that uses integral equations and iterative "residual-correction" concept. The geometry correction is calculated by solving linearized small perturbation equation (LSP) with the difference between garget and objective surface pressure distributions as a boundary condition. In the present method, LSP equation is analytically transformed to integral equations by using the Green's theorem. Design results of an isolated wing and wing-nacelle configurations are presented here.

본 연구는 적분 방정식과 반복 "오차-수정" 개념을 이용하는 Takanashi의 이론에 기초한 초음속 실용적인 설계방법의 개발 결과로서, 형상의 수정량은 목표 압력분포와 설계대상의 압력분포와의 차를 경계조건으로 이용해 LSP 방정식을 풀므로써 계산되어진다. 이 연구에서는 Green의 정리를 이용하여 편미방정식 형태의 LSP 방정식을 적분방정식으로 변환하여 계산하는 방법을 이용하고 있다. 여기서는 Isolated wing과 wign-nacelles 두가지 경우의 설계를 예로 들었다.

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References

  1. L. A. Carlson, "Transonic Airfoil Design Using Cartesian Coordinates," NASA CR-2578, 1976.
  2. T. L. Tranen, "A Rapid Computer Aided Transonic Airfoil Design Methods," AIAA Paper 74-501, 1974.
  3. P. A. Henne, "Inverse Transonic Wing Design Method," Journal of Aircraft, Vol. 18, No. 2, pp. 121-127, February 1981. https://doi.org/10.2514/3.57472
  4. V.Shankar, "A Full Potential Inverse Method Based on a Density Linearization scheme for Wing Design," AIAA Paper 81-1234, 1981.
  5. W. H. Davis, Jr., "Technique for Developing Design Tools from the Analysis Methods of Computational Aerodynamics," AIAA Journal, Vol. 18, No. 9, pp.1080-1087, September, 1980. https://doi.org/10.2514/3.50857
  6. J. B Malone, J. Vadyak and L. N. Shanker, "A Technique for the Inverse Aerodynamic Design of Nacelles and Wing Configurations," AIAA Paper 85-4096, 1985.
  7. L. C. Santos and L. N. Sankar, "A Hybrid Inverse Optimization Method for the Aerodynamic Design of Lifting Surfaces," AIAA Paper 94-1895, 1994.
  8. S. Takanashi, "Iterative Three-Dimensional Transonic Wing Design Using Integral Equations," Journal of Aircraft, Vol.22, No.8, pp.655-660, August 1985. https://doi.org/10.2514/3.45182
  9. J. Hahamard, "Lectures of Cauchy's Problem in Linear Partial Differential Equations," Yale University Press, 1928
  10. H. Lomax, M. A. Heaslet and B. F. Franklyn, "Integral and integral Equation in Linearized Wing Theory," NACA Rep. 1054, 1951.
  11. M. A. Heaslet, H. Lomax and A. L. Jones, "Voterra's Solution of the Wave Equation as Applied to Three-Dimensional Supersonic airfoil Problem," NACA Rep. 889, 1947.(Formerly NACA TN 1412.)
  12. Y. Shimbo, K. Yoshida, T. Iwamiya, R. Takaki and K. Matsushima, "Aerodynamic Design of the Scaled Supersonic Experimental Airplane," Proceeding of 1st International Workshop on CFD for SST, 1998.
  13. K. Sakata, "Suppersonic Experimental Airplane Program in NAL(NEXST) and its CFD-Design Research Demand," Proceeding of 2nd International Workshop on CFD for SST, pp. 53-56, 2000.
  14. S. Obayashi and G. P. Guruswamy, "Convergence Acceleration of Navier-Stokes Solver for Efficient Static Aeroelastic Computations," AIAA Journal, vol.33, No. 6, pp.1134-1141, June, 1995. https://doi.org/10.2514/3.12533
  15. V. Venkatakrishnan, "A perspective on Unstructured Grid Flow Solves," AIAA Paper 95-0667, 1995.
  16. K. Nakahashi and D. sharov, "Direct Surface Triangultion Using the Advencing Front Method," AIAA Paper 95-1686, 1995.
  17. D. Sharov and K. Nakahashi, "A Boundary Recovery Algorithm for Delaunay Tetrahedral Meshing," 5th International Confrence on Numerical Grid Generation in Computational Filed Simulation, pp. 229-238, 1996
  18. A. Jameson and S. Yoon, "Lower-Upper Implicit Schemes with Multiple Grids for the Euler Equations," AIAA Journalm Vol. 25, No. 7, pp. 929-935, 1987
  19. Obayashi, S., Jeong, S. K. and Matsuo, Y., "Inverse Optimization Method for Blunt-Trailing-Edge Airfoils," Journal of Aircraft, Vol. 34, No. 2, pp. 255-257, March-April, 1997. https://doi.org/10.2514/2.7571
  20. Kim, K. H., Jeong, S. K. and Obayashi, S., "New Blunt-Trailing-Edge Airfoil Design by Inverse Optimization," Journal of The Korean Society for Aeronautical and Space Science, vol. 27, No.2, pp. 1-6, 1999