Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지

Boundary Method for Shape Design Sensitivity Analysis in Solving Free-Surface Flow Problems

  • Choi Joo Ho (School of Aerospace and Mechanical Engineering, Hankuk Aviation University) ;
  • Kwak H. G. (Department of Aerospace and Mechanical Engineering, Hankuk Aviation University) ;
  • Grandhi R. V. (Department of Mechanical and Materials Engineering, Wright State University)
  • Published : 2005.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

An efficient boundary-based optimization technique is applied in the numerical computation of free surface flow problems, by reformulating them into the equivalent optimal shape design problems. While the sensitivity in the boundary method has mainly been calculated using the boundary element method (BEM) as an analysis means, the finite element method (FEM) is used in this study because of its popularity and easy-to-use features. The advantage of boundary method is that the design velocity vectors are needed only on the boundary, not over the whole domain. As such, a determination of the complicated domain design velocity field, which is necessary in the domain method, is eliminated, thereby making the process easy to implement and efficient. Seepage and supercavitating flow problem are chosen to illustrate the accuracy and effectiveness of the proposed method.

Keywords

References

  1. Burczyski, T. and Adamczyk, T., 1985, 'The Boundary Element Formulation for Multiparameter Structural Shape Optimization,' Applied Mathematical Modeling, Vol. 9, pp. 95-200 https://doi.org/10.1016/0307-904X(85)90007-1
  2. Chang, K. R., Choi, K. K., Tsai, C. S., Chen, C.J., Choi, B. S. and Yu, X., 1995, 'Design Sensitivity Analysis and Optimization Tool (DSO) for Shape Design applications,' Computing Systems in Engineering, Vol. 6, pp. 141-175 https://doi.org/10.1016/0956-0521(95)00006-L
  3. Choi, J. H. and Kwak, B. M., 1988, 'Boundary Integral Equation Method for Shape Optimization of Elastic Structures,' International Journal for Numerical Methods in Engineering, Vol. 26, pp. 1579-1595 https://doi.org/10.1002/nme.1620260709
  4. Choi, J. H., 1987, Shape Optimal Design Using Boundary Integral Equations, Ph.D., Thesis, Korea Advanced Institute of Science and Technology, Seoul, Korea
  5. Choi, J. H., Penmetsa, R. C. and Grandhi, R. V., 2005, 'Shape Optimization of the Cavitator for a Supercavitating Torpedo,' Structural and Multidisciplinary Optimization, Vol. 29, pp. 159-167 https://doi.org/10.1007/s00158-004-0466-0
  6. Choi, K. K. and Haug, E. J., 1983, 'Shape Design Sensitivity Analysis of Elastic Structures,' Journal of Structural Mechanics, Vol. 11, pp. 231-269 https://doi.org/10.1080/03601218308907443
  7. 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, Vol. 57, pp. 1-15 https://doi.org/10.1016/0045-7825(86)90066-6
  8. Dems, K. and Mroz, Z., 1984, 'Variational Approach by Means of Adjoint Systems to Structural Optimization and Sensitivity Analysis - II : Structure Shape Variation,' International Journal of Solids and Structures, Vol. 20, pp. 527-552 https://doi.org/10.1016/0020-7683(84)90026-X
  9. George, Mejak., 1997, 'Finite Element Solution of a Model Free Surface Problem by the Optimal Shape Design Approach,' International Journal for Numerical Methods in Engineering, Vol. 40, pp. 1525-1550 https://doi.org/10.1002/(SICI)1097-0207(19970430)40:8<1525::AID-NME127>3.0.CO;2-S
  10. Haftka, R. T. and Grandhi, R. V., 1986, 'Structural Shape Optimization - A Survey,' Computer Methods in Applied Mechanics and Engineering, Vol. 57, pp. 91-106 https://doi.org/10.1016/0045-7825(86)90072-1
  11. 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, Vol. 30, pp 185-199 https://doi.org/10.1016/S0965-9978(98)00065-9
  12. Karkkainen, Kari T. and Tiihonen, Tirno., 1999, 'Free Surfaces : Shape Sensitivity analysis and Numerical Methods,' International Journal for Numerical Methods in Engineering, Vol. 44, pp. 1079-1098 https://doi.org/10.1002/(SICI)1097-0207(19990320)44:8<1079::AID-NME543>3.0.CO;2-I
  13. 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, Vol. 210, pp. 75-93
  14. Kwak, B. M., 1994, 'A Review on Shape Optimal Design and Sensitivity Analysis,' Journal of Structural Mechanics and Earthquake Engineering, JSCE., Vol. 10, pp. 1595-1745
  15. Leontieva, A. and Huacasi, W., 2001, 'Mathematical Programming Approach for Unconfined Seepage Flow Problem,' Engineering Analysis with Boundary Elements, Vol. 25, pp. 49-56 https://doi.org/10.1016/S0955-7997(00)00067-9
  16. Logvinovich, G. V., 1972, Hydrodynamics of Free- Boundary Flows. Translated From Russian, Israel Program for Scientific Translations : Jerusalem
  17. Meric, R. A., 1995, 'Differential and Integral Sensitivity Formulations and Shape Optimization by BEM,' Engineering Analysis with Boundary Elements, Vol. 15, pp. 181-188 https://doi.org/10.1016/0955-7997(95)00016-H
  18. Park, C. W., Yoo, Y. M. and Kwon, K. H., 1989, 'Shape Design Sensitivity Analysis of an Axisymmetric Turbine Disk Using the Boundary Element Method,' Computers & Structures, Vol. 33, pp. 7-16 https://doi.org/10.1016/0045-7949(89)90123-5
  19. Rousselet, B. and Haug, E. J., 1981, Design Sensitivity Analysis of Shape Variation, in E.J. Haug and J. Cea, (eds.), Optimization of Distributed Parameter Structures, Sijthoff-Noordhoff and Alphen aan den Rijn The Netherlands, pp. 1397-1442
  20. Tsai, W. and Yue, D. K. P., 1996, 'Computation of Nonlinear Free-Surface Flows,' Annual Reviews on Fluid Mechanics, Vol. 28, pp. 249-278 https://doi.org/10.1146/annurev.fl.28.010196.001341
  21. Van Brurnmelen l , E. H. and Segal, A., 2003, 'Numerical Solution of Steady Free-Surface Flows by the Adjoint Optimal Shape Design Method,' International Journal for Numerical Methods in Fluids, Vol. 41, pp. 3-27 https://doi.org/10.1002/fld.375
  22. Yao, T. M. and Choi, K. K., 1989, '3-D Shape Optimal Design and Automatic Finite Element Regridding,' International Journal for Numerical Methods in Engineering, Vol. 28, pp. 369-384 https://doi.org/10.1002/nme.1620280209
  23. Zolesio, J. P., 1981, The Material Derivative (or Speed) Method for Shape Optimization, in E.J. Haug and J. Cea (eds.), Optimization of Distributed Parameters Structures, Sijthoff-Noordhoff and Alphen aan den Rijn, The Netherlands pp. 1152-1194