Shape Design Sensitivity Analysis of Supercavitating Flow Problem

초공동(超空洞) 유동 문제의 형상 설계민감도 해석

  • 최주호 (한국항공대학교 항공우주 및 기계공학부) ;
  • 곽현구 (한국항공대학교 대학원 항공우주 및 기계공학과) ;
  • Published : 2004.09.01


An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in supercavitating flow problem. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in potential flow problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design in potential flow problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-to-use features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem is chosen to illustrate the efficiency of the proposed methodology. Implementation issues for the sensitivity analysis and optimization procedure are also addressed in this flow problem.


  1. Haftka, R. T. and Grandhi, R. V., 1986, 'Structural Shape Optimization,' Computer Methods in Applied Mechanics and Engineering, 57, pp. 91-106
  2. Kwak, B. M., 1994, 'A Review on Shape Optimal Design and Sensitivity Analysis,' Journal of Structural Mechanics and Earthquake Engineering, JSCE, 10, pp. 1595-1745
  3. Choi, K. K. and Haug, E. J., 1983, 'Shape Design Sensitivity Analysis of Elastic Structures,' Journal of Structural Mechanics, 11, pp. 231-269
  4. Choi, K. K. and Seong, H. G, 1986, 'Domain Method for Shape Design Sensitivity Analysis of Built-up Structures,' Computer Methods in Applied Mechanics and Engineering, 57, pp. 1-15
  5. Hardee, E., Chang, K. H., Tu, J., Choi, K. K., Grindeanu, I., and Yu, X., 1999, 'A CAD-Based Design Parameterization for Shape Optimization of Elastic Solids,' Advances in Engineering Software, 30, pp. 185-199
  6. Dems, K., 1987, 'Sensitivity Analysis in Thermal Problems - II: Structure Shape Variation,' Journal of Thermal Stresses, 10, pp. 1-16
  7. Choi, J. H., 1987, Shape Optimal Design Using Boundary Integral Equations, Ph.D., Thesis, Korea Advanced Institute of Science and Technology, Seoul, Korea
  8. Ansys Inc, 2002, 'ANSYS 6.1 User's Manual,' PA, USA
  9. The MathWorks Inc, 2002, 'MATLAB Release 6.5 User Guides,' MA, USA
  10. VR&D Inc, 2003, 'VisualDOC V3.1 How To Manual,' CO, USA
  11. Meric, R. A., 1995, 'Differential and Integral Sensitivity Formulations and Shape Optimization by BEM,' Engineering Analysis with Boundary Elements, 15, pp. 181-188
  12. Kirschner, I. N., Kring, D. C, Stokes, A. W., Fine, N. E., and Uhlman Jr, J. S., 1995, 'Supercavitating Projectiles in Axisymmetric Subsonic Liquid Flows,' American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED, 210, pp. 75-93
  13. Logvinovich, G V., 1972, Hydrodynamics of Free-Boundary Flows, Translated from Russian, Israel Program for Scientific Translations: Jerusalem
  14. Zolesio, J. P., 1981, 'The Material Derivative (or Speed) Method for Shape Optimization,' in Haug EJ and Cea J (eds.), Optimization of Distributed Parameters Structures, Sijthoff-Noordhoff, Alphen aan den Rijn, The Netherlands, pp. 1152-1194