International Journal of Fluid Machinery and Systems

Korean Society for Fluid machinery (한국유체기계학회)
권호 표지
DOI QR코드

DOI QR Code

Surrogate Based Optimization Techniques for Aerodynamic Design of Turbomachinery

  • Received : 2009.06.07
  • Accepted : 2009.06.15
  • Published : 2009.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

Recent development of high speed computers and use of optimization techniques have given a big momentum of turbomachinery design replacing expensive experimental cost as well as trial and error approaches. The surrogate based optimization techniques being used for aerodynamic turbomachinery designs coupled with Reynolds-averaged Navier-Stokes equations analysis involve single- and multi-objective optimization methods. The objectives commonly tried to improve were adiabatic efficiency, pressure ratio, weight etc. Presently coupling the fluid flow and structural analysis is being tried to find better design in terms of weight, flutter and vibration, and turbine life. The present article reviews the surrogate based optimization techniques used recently in turbomachinery shape optimizations.

Keywords

References

  1. Japikse, D., 1976, “Review - Progress in Numerical Turbomachinery Analysis,” ASME Transactions, Series I-Journal ofFluids Engineering. Vol. 98, pp. 592-606. https://doi.org/10.1115/1.3448424
  2. Horlock, J.H. and Marsh, H., 1982, “Fluid Mechanics of Turbomachines: A Review,” International Journal of Heat andFluid Flow, Vol. 3, Issue 1, pp. 3-11, doi: 10.1016/0142-727X(82)90036-4.
  3. Mcnally, W.D. and Sockol, P.M., 1985, “Review - Computational Methods for Internal Flows with Emphasis onTurbomachinery,” ASME Transactions, Journal of Fluids Engineering, Vol. 107, no. 1, pp. 6-22. https://doi.org/10.1115/1.3242443
  4. Casey, M.V., 1994, “Computational Methods for Preliminary Design and Geometry Definition in Turbomachinery,” AGARD,Turbomachinery Design Using CFD, (N95-14127 03-34).
  5. Danton, J. and Dawes, W., 1999, “Computational Fluid Dynamics for Turbomachinery Design,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 213, No. 2, pp. 107-124(18). https://doi.org/10.1243/0954411991534843
  6. Horlock, J. H., and Denton, J. D., 2005, “A Review of Some Early Design Practice Using Computational Fluid Dynamicsand a Current Perspective,” Journal of Turbomachinery, Vol. 127, Issue 1, pp. 5-13. https://doi.org/10.1115/1.1650379
  7. Molinari, M. and Dawes, W.N., 2006, “Review of Evolution of Compressor Design Process and Future Perspectives,”Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 220, No. 6, pp.761-771. https://doi.org/10.1243/09544062JMES298
  8. Hirsch, C., 1994, “CFD methodology and validation for Turbomachinery flows,” AGARD, Turbomachinery Design UsingCFD (N95-14127 03-34).
  9. Myers, R.H. and Montgomery, D.C., 1995, “Response Surface Methodology-Process and Product Optimization UsingDesigned Experiments,” John Wiley & Sons, Inc: New York.
  10. Martin, J. D. and Simpson T. W., 2005, “Use of Kriging models to approximate deterministic computer models,” AIAAJournal, Vol. 43, No. 4, pp. 853-863. https://doi.org/10.2514/1.8650
  11. Orr, M.J.L., 1996, “Introduction to Radial Basis Neural Networks” Center for cognitive science, Edinburgh University,Scotland, UK. http://anc.ed.ac.uk/rbf/.
  12. Goel, T., Haftka, R., Shyy, W. and Queipo, N., 2007, “Ensemble of Surrogates,” Structural and MultidisciplinaryOptimization, Vol. 33, No. 3, pp. 199-216(18). https://doi.org/10.1007/s00158-006-0051-9
  13. Eldred, M. S. and Dunlavy, D. M., 2006, “Formulations for Surrogate-Based Optimization with Data Fit, Multifidelity, andReduced-Order Models,” AIAA 2006-7117.
  14. Eldred, M.S., Adams, B.M., Haskell, K., Bohnhoff, W.J., Eddy, J.P., Gay, D.M., Hart, W.E., Hough, P.D., Kolda, T.G.,Swiler, L.P., and Watson, J.P., 2008, "DAKOTA: A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis. Version 4.2 Users Manual," Sandia Technical ReportSAND2006-6337, Updated November 2008.
  15. Li, W. and Padula, S., 2004, “Approximation methods for conceptual design of complex systems,” Eleventh InternationalConference on Approximation Theory (eds. Chui, C., Neaumtu, M., Schumaker, L.).
  16. Queipo, N. V., Haftka, R.T., Shyy, W., Goel, T., Vaidyanathan, R. and Tucker, P.K., 2005, “Surrogate-Based Analysis andOptimization,” Progress in Aerospace Sciences, Vol. 41, pp. 1-28. https://doi.org/10.1016/j.paerosci.2005.02.001
  17. $JMP{\circledR}$ 5.1, 2004, SAS Institute, Inc.
  18. McKay, M.D., Beckman, R.J., Conover, W.J., 1979. “A comparison of three methods for selecting values of input variablesin the analysis of output from a computer code,” Technometrics. 21, pp. 239-245. https://doi.org/10.2307/1268522
  19. Sacks, J., Welch, W.J., Mitchell, T.J. and Wynn, H.P., 1989, “Design and analysis of computer experiments,” StatisticalScience. 4, pp. 409-435. https://doi.org/10.1214/ss/1177012413
  20. Tailor, J.S., and Cristianini, N., 2000, Support Vector Machines and other kernel-based learning methods, CambridgeUniversity Press.
  21. Collette, Y., and Siarry, P., 2003, Multiobjective Optimization: Principles and Case Studies, New York, Springer.
  22. Deb K., 2001, Multi-objective optimization using evolutionary algorithms, 1st ed., John Wiley & Sons Inc.
  23. Gallimore, S. J., Bolger J. J., and Cumpsty, N. A., 2002, “The Use of Sweep and Diahedral in Multistage Axial Flow Compressor Blading, Part 1: University Research and Methods Development,” Proceedings of ASME GT-2002-30328. https://doi.org/10.1115/GT2002-30328
  24. Bliss, D. B., 1976, “Method of and Apparatus for Preventing Leading edge Shock Related Noise in Transonic and Supersonic Blades,” US Patent 3989406.
  25. Hah, C., Puterbaugh, S. L., and Wadia, A. R., 1999, “Control of Shock Structure and Secondary Flow Field Inside TransonicCompressor Rotor Through Aerodynamic Sweep,” Proceedings of ASME 99-GT-561.
  26. Watanabe, H., and Zangeneh, M., 2003, “Design of the Blade Geometry of Swept Transonic Fans by 3D Inverse Design,” Proceedings of ASME Turbo Expo, GT-2003- 38770. https://doi.org/10.1115/GT2003-38770
  27. Denton, J. D., and Xu, L., 2002, “The Effects of Lean and Sweep on Transonic Fan Performance,” Proceedings of ASME Turbo Expo, GT-2002- 30327. https://doi.org/10.1115/GT2002-30327
  28. Cai, N., Xu, J., and Benaissa, A., 2003, “Aerodynamic and Aeroacoustic Performance of a Skewed Rotor,” Proceedings of ASME Turbo Expo, GT-2003-38592. https://doi.org/10.1115/GT2003-38592
  29. Fischer, A., Riess, W., and Seume, J., 2003, “Performance of Strongly Bowed Stators in a 4-Stage High Speed Compressor,” Proceedings of ASME Turbo Expo, GT-2003-38392. https://doi.org/10.1115/GT2003-38392
  30. Kammerer, S., Mayer, J. F., Paffrath, M., Wever, U. and Jung, A. R., 2003, "Three Dimensional Optimization of Turbomachinery Bladings Using Sensitivity Analysis," Proceedings of ASME Turbo expo 2003,Power for Land, Sea and Air, June 16-19, Atlanta Georgia, USA, GT2003-38037. https://doi.org/10.1115/GT2003-38037
  31. Sonoda, T., Yamaguchi, Y., Arima, T., Olhofer, M., Sendhoff, B. and Schreiber, H.A., 2003, "Advanced High Turning Compressor Aerofoils for Low Reynolds Number Condition, Part I: Design and Optimization," Proceedings of ASME Turbo Expo 2003, June 16-19, 2003, Georgia, USA, GT2003-38458. https://doi.org/10.1115/GT2003-38458
  32. Keskin, A., Dutta, A. K., and Bestle, D., 2006, "Modern Compressor Aerodynamic Blading Process using Multi-Objective Optimization," ASME Turbo Expo 2006, Barcelona, Spain, GT2006-90206. https://doi.org/10.1115/GT2006-90206
  33. Vob, C., Aulich, M., Kaplan, B., and Nicke, E., 2006, "Automated Multi-Objective Optimization in Axial Compressor Blade Design," ASME Turbo Expo 2006, Barcelona, Spain, GT2006-90420. https://doi.org/10.1115/GT2006-90420
  34. Buche, D., Guidati,G., and Stoll, P., 2003, "Automated Design Optimization of Compressor Blades for Stationary Large Scale Turbomachinery," ASME Turbo Expo 2003, Georgia, USA, GT2003-38421. https://doi.org/10.1115/GT2003-38421
  35. Jun, L., Guojun, L., Zhenping, F., and Lijun, L., 2005, "Multiobjective Optimization Approach to Turbomachinery Blades Design," ASME Turbo Expo 2005, Reno-Tahoe, Nevada, USA, GT2005-68303. https://doi.org/10.1115/GT2005-68303
  36. Burguburu, S., Toussaint, C., Bonhomme, C., and Leroy, G., 2004, "Numerical Optimization of Turbomachinery Bladings,"Journal of Turbomachinery, January 2004, Vol 126, pp. 91-100. https://doi.org/10.1115/1.1645869
  37. Chung, K. N., Kim, Y. I., Sung, J. H., Sung, I.H., Chung, I.H., and Shin, S. H., 2005, "A Study of Blade Section Shape for aSteam Turbine," ASME Fluid Engineering Division Summer Meeting and Exhibition, 2005, Houston, TX, USA, FEDSM2005-77385.
  38. Pierret, S., Coelho, R. F., and Kato, H., 2007, “Multidisciplinary and Multiple Operating Points Shape Optimization of Three-Dimensional Compressor Blades,” Structural and Multidisciplinary Optimization, Vol. 33, No. 1, pp. 1615-1488. https://doi.org/10.1007/s00158-006-0033-y
  39. Keskin, A. and Bestle, D., 2006, “Application of Multi-Objective Optimization to Axial Compressor Preliminary Design,”Aerospace Science and Technology 10, pp. 581–589. https://doi.org/10.1016/j.ast.2006.03.007
  40. Jang, C.M., Li, P. and Kim, K.Y., 2005, "Optimization of Blade Sweep in a Transonic Axial Compressor Rotor," JSMEInternational Journal-Series B, Vol. 48, No. 4, pp.793-801. https://doi.org/10.1299/jsmeb.48.793
  41. Jang, C.M. and Kim, K.Y., 2005, "Optimization of a Stator Blade Using Response Surface Method in a Single-Stage Transonic Axial Compressor," Proceedings of The Institution of Mechanical Engineers, Part A-Journal of Power and Energy, Vol. 219, No. 8, pp.595-603. https://doi.org/10.1243/095765005X31298
  42. Ahn, C.S. and Kim, K.Y., 2003, "Aerodynamic Design Optimization of A Compressor Rotor with Navier-Stokes Analysis," Proceedings of The Institution of Mechanical Engineers, Part A-Journal of Power and Energy, Vol. 217, No. 2, pp. 179-184. https://doi.org/10.1243/09576500360611209
  43. Lee, S. Y. and Kim, K. Y., 2000, "Design Optimization of Axial Flow Compressor Blades with Three-Dimensional Navier-Stokes Solver," KSME International Journal, Vol. 14, No. 9, pp. 1005-1012.
  44. Choi, J. H., Kim, K. Y. and Chung, D. S., 1997, "Numerical Optimization for Design of an Automotive Cooling Fan,"Journal of Passenger Cars - SAE 1997 Transactions, Vol. 106, Section 6, Part 1, pp. 1485-1489
  45. Cai, N. and Xu, J., 2001, "Aerodynamic-Aeroacoustic Performance of parametric Effects for Skewed-SweptRotor," Proceedings of ASME turbo expo 2001, June 4-7, 2001, New Orleans Louisiana, USA, 2001-GT-0354.
  46. Gummer, V., Wenger, U. and Kau, H. P., 2001, "Using Sweep and Dihedral to Control Three Dimensional Flow in Transonic Stator of Axial Compressor", Transactions of ASME, Vol 123, pp 40-48. https://doi.org/10.1115/1.1330268
  47. Sonoda, T., Yamaguchi, Y., Arima, T., Olhofer, M., Sendhoff, B. and Schreiber, H.A., 2003, "Advanced High Turning Compressor Aerofoils for Low Reynolds Number Condition, Part I: Design and Optimization," Proceedings of ASME Turbo Expo 2003, June 16-19, 2003, Georgia, USA, GT2003-38458. https://doi.org/10.1115/GT2003-38458
  48. Papila. N, Shyy, W., Grif, L., and Dorney, D.J., 2002, "Shape Optimization of Supersonic Turbines Using GlobalApproximation Methods," Journal of Propulsion and Power, Vol. 18, No. 3, pp. 509-518. https://doi.org/10.2514/2.5991
  49. Amano, R.S., and Xu, C., 2003, "Aerodynamic Blade Design of Turbomachinery," Proceedings of the International GasTurbine Congress 2003, Tokyo, Japan, TS-029.
  50. Vob, C., Aulich, M., Kaplan, B., and Nicke, E., 2006, "Automated Multi-Objective Optimization in Axial Compressor Blade Design," ASME Turbo Expo 2006, Barcelona, Spain, GT2006-90420. https://doi.org/10.1115/GT2006-90420
  51. Li, H.D., He, L., Li, Y.S., and Wells, R., 2006, "Blading Aerodynamic Design Optimization with Mechanical and Aeromechanical Constraints", ASME Turbo Expo 2006, Barcelona, Spain, GT2006-90503. https://doi.org/10.1115/GT2006-90503
  52. Buche, D., Guidati,G., and Stoll, P., 2003, "Automated Design Optimization of Compressor Blades for Stationary Large Scale Turbomachinery," ASME Turbo Expo 2003, Georgia, USA, GT2003-38421. https://doi.org/10.1115/GT2003-38421
  53. Benini, E., and Biollo, R., 2006, "On the Aerodynamics of sweep and Leaned Transonic Compressor Rotors," ASME Turbo Expo 2006, Barcelona, Spain, GT2006-90547. https://doi.org/10.1115/GT2006-90547
  54. Kammerer, S., Mayer, J. F., Stetter, H., Paffrath, M., Wever U., and Jung, A. R. 2004, "Development of a Three DimensionalGeometry Optimization Method for Turbomachinery Applications," International Journal of Rotary Machinery, 10(5): 373-385. https://doi.org/10.1155/S1023621X04000387
  55. Lampart, P., and Yershov, S., 2001, "3D Shape Optimization of Turbomachinery Blading," CFD for TurbomachineryApplications, Gdansk, Poland CFD Turbo 2001-C30.
  56. Burguburu, S., Toussaint, C., Bonhomme, C., and Leroy, G., 2004, "Numerical Optimization of Turbomachinery Bladings,"Journal of Turbomachinery, January 2004, Vol 126, pp 91-100. https://doi.org/10.1115/1.1645869
  57. Oyama, A., Liou, M.S., Obayashi, S., 2004, "Transonic Axial-Flow Blade Optimization: Evolutionary Algorithms/Three-Dimensional Navier-Stoke Solver,” Journal of Propulsion and Power, Vol. 20, No. 4, pp. 612-619. https://doi.org/10.2514/1.2290
  58. Lian, Y., and Kim, N. H., 2006, "Reliability Based Design Optimization of a Transonic Compressor", AIAA Journal, Vol. 44,No.2, 2006, pp 368-375. https://doi.org/10.2514/1.16262
  59. Song, L., Feng, Z., and Li, J., 2005, "Shape Optimization of Turbine Stage Using Adaptive Range Differential Evolution and Three-Dimensional Navier-Stokes Solver," ASME Turbo Expo 2005, Nevada, USA, GT2005-68280. https://doi.org/10.1115/GT2005-68280
  60. Yi, W., Huang, H., and Han, W., 2006, "Design Optimization of Transonic Compressor Rotor Using CFD and Genetic Algorithm," ASME Turbo Expo 2006, Barcelona, Spain, GT2006-90155. https://doi.org/10.1115/GT2006-90155
  61. Oksuz, O., and Akmandor, I. S., 2005, "Turbine Blade Shape Aerodynamic Design Using Artificial Intelligence," ASME Turbo Expo 2005, Nevada, USA, GT2005-68094. https://doi.org/10.1115/GT2005-68094
  62. Lampart, P., 2004, "Numerical Shape Optimization of a High Pressure Steam Turbine Stage," Journal of Computational andApplied Mechanics, Vol. 5, No. 2, pp. 311-321.
  63. Oyama, A., Liou, M. S., and Obayashi, S., 2002, "Transonic Axial-Flow Blade Shape Optimization Using Evolutionary Algorithm and Three- Dimensional Navier-Stokes Solver," AIAA 2002-5642.
  64. Papila, N. U., 2001, "Neural Network and Polynomial Based Response Surface Technique for Supersonic Turbine DesignOptimization", PhD Thesis, University of Florida.
  65. Lofti, O., Teixera, J. A., Ivey, P. C., Kinghorn, I.R. and Sheard, A. G., 2006, "Shape Optimization of Axial Fan Blades Using Genetic Algorithms and a 3D Navier-Stokes Solver," ASME Turbo Expo 2006, Spain, GT2006-90659. https://doi.org/10.1115/GT2006-90659
  66. Xing, X. Q. and Damodaran, M., 2003, "Optimal Transonic Aerodynamic Shape Design Using Simultaneous PerturbationStochastic Approximation Method Coupled with Global and Local Optimization Methods," 21st Applied AerodynamicsConference, AIAA2003-3786.
  67. Li, H. D. and He, L., 2005, "Toward Intra-Row Gap Optimization for one and Half Stage Transonic Compressor," Journal ofTurbomachinery, Vol. 127, pp. 589-598. https://doi.org/10.1115/1.1928934
  68. Barankiewicz, W. S. and Hathaway, M. D., 1997, "Effect of Stator Indexing on Performance in a Low Speed MultistageAxial Compressor," NASA TM 113113.
  69. Chen, N.X., Zhang, H. W., Du, H., Xu, Y. J. and Huang, W. G., 2005, "Effect of Maximum Camber Location on Aerodynamics Performance of Transonic Compressor Blades," ASME Turbo Expo 2005, Nevada, USA, GT2005-68541. https://doi.org/10.1115/GT2005-68541
  70. Dennis, B. H., Egorov, I. N., Han, Z. X., Dulikravich, G. S., and Polini, C., 2000, " Multi-Objective Optimization ofTurbomachinery Cascades for Minimum Loss, Maximum Loading, and Maximum Gap-to-Chord Ratio," 8thAIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, California, USA, AIAA2000-4876.
  71. Kelner, V., Grondin, G., Leonard, O. and Moreau, S., 2005, "Multi Objective Optimization of a Fan Blade by Coupling aGenetic Algorithm and a Parametric Flow Solver," Evolution and Deterministic Methods for Design, Optimization and Controlwith Application to Industrial and Societal Problems, EUROGEN 2005, Munich, Germany.
  72. Clarich, A., Mosetti, G., Pediroda, V. and Polini, C., 2005, "Application of Evolutionery Algorithms and Statistical Analysis in the Numerical Optimization of an Axial Compressor," International Journal of Rotating Machinery, Vol. 2, pp. 143-151. https://doi.org/10.1155/IJRM.2005.143
  73. Jang, C.M., and Kim, K.Y., 2007, “Applications of Numerical Optimization Techniques to Design of Axial CompressorBlades,” Journal of Aerospace Power, Vol. 22, No. 4, pp. 29-36.
  74. Yang, L., Ouyang, H., and Hui, D. Z., “Optimization Design and Experimental Study of Low-Pressure Axial Fan withForward-Skewed Blades,” International Journal of Rotary Machinery, Vol. 2007, Article ID 85275, 10 pages,doi:10.1155/2007/85275.
  75. Chen, N., Zhang, H., Xu, Y., and Huang, W., 2007, “Blade Parameterization and Aerodynamic Design Optimization for a3D Transonic Compressor Rotor,” Journal of Thermal Science, Vol. 16, No. 2, pp. 105-114. https://doi.org/10.1007/s11630-007-0105-3
  76. Benini, E., 2004, “Three-Dimensional Multi-Objective Design Optimization of a Transonic Compressor Rotor,” Journal ofPropulsion and Power, Vol. 20, No. 3, pp. 559-565. https://doi.org/10.2514/1.2703
  77. Samad, A., Kim, K.Y., “Shape Optimization of an Axial Compressor Blade by Multiobjective Genetic Algorithm,”Proceedings of The Institution of Mechanical Engineers, Part A-Journal of Power and Energy, Vol. 222, No. 6, Sep. 2008, pp. 599-611. https://doi.org/10.1243/09576509JPE596
  78. Samad, A., Kim, K.Y., Goel, T., Haftka, R.T., and Shyy, W., “Multiple Surrogate Modeling for Axial Compressor BladeShape Optimization,” AIAA Journal of Propulsion and Power, Vol. 24, No. 2, 2008, pp. 302-310. https://doi.org/10.2514/1.28999
  79. Samad, A., Kim, K.Y., “Multi-objective Optimization of an Axial Compressor Blade,” Journal of Mechanical Science andTechnology, 22(2008), pp. 999-1007. https://doi.org/10.1007/s12206-008-0122-5
  80. Lee, K.S., Kim, K.Y. and Samad, A., “Design Optimization of Low-Speed Axial Flow Fan Blade with Three-DimensionalRANS Analysis,” Journal of Mechanical Science and Technology, Vol. 22, No. 10, Oct. 2008, pp. 1864-1869. https://doi.org/10.1007/s12206-008-0724-y
  81. Samad, A., Kim, K.Y., “Application of Surrogate Modeling to Design of a Compressor Blade to Optimize Stacking andThickness,” International Journal of Fluid Machinery and Systems, (Accepted).
  82. Sanger, N. L., 1983, “The Use of Optimization Techniques to Design-Controlled Diffusion Compressor Blading,” Journal ofEngineering for power, Vol. 105, pp. 256-264. https://doi.org/10.1115/1.3227410
  83. Shyy, W., Papila, N., Vaidyanathan, R. and Tucker, K., 2001, “Global Design Optimization for Aerodynamics and RocketPropulsion Components,” Progress in Aerospace Science, Vol. 37, pp. 59-118. https://doi.org/10.1016/S0376-0421(01)00002-1
  84. Zerpa, L., Queipo, N. V., Pintos, S., and Salager, J., 2005, “An Optimization Methodology of Alkaline-Surfactant-PolymerFlooding Processes Using Field Scale Numerical Simulation and Multiple Surrogates,” Journal of Petroleum Science andEngineering, Vol. 47, pp. 197-208. https://doi.org/10.1016/j.petrol.2005.03.002
  85. Goel, T., Zhao, J., Thakur, S., Haftka, R.T. and Shyy, W., 2006, “Surrogate Model-Based Strategy for Cryogenic CavitationModel Validation and Sensitivity Evaluation,” 42nd AIAA/ASME/ SAE/ASEE Joint Propulsion Conference and Exhibit,Sacramento, USA, AIAA-2006-5047.
  86. Samad, A., Shin D. Y., Kim, K. Y., Goel, T. and Haftka, R. T., 2007, “Surrogate Modeling for Optimization of a DimpledChannel to Enhance Heat Transfer Performance. AIAA Journal of Thermophysics and Heat Transfer,” Vol. 21, Number 3, pp.667-670. https://doi.org/10.2514/1.30211
  87. Messac, A., 1996, “Physical Programming: Effective Optimization for Computational Design”, AIAA journal, Vol. 34, No. 1,pp. 149-158. https://doi.org/10.2514/3.13035
  88. Chankong, V., and Haimes, Y. Y., 1983, “Multiobjective Decision Making Theory and Methodology,” New York: ElsevierScience.
  89. Sen, P. and Yang, J.B., 1998, Multiple Criteria Decision Support in Engineering Design, London: Springer Verlag.
  90. Kicinger, R., Arciszewski, T., and Jong, K. D., 2005, “Evolutionary computation and structural design: A survey of the stateof-the-art,” Computers and Structures 83, pp. 1943–1978. https://doi.org/10.1016/j.compstruc.2005.03.002
  91. Marler, R.T., and Arora, J. S., 2004, “Survey of multi-objective optimization methods for engineering,” Structural andMultidisciplinary Optimization, Vol. 26, No. 6, pp. 369–395. https://doi.org/10.1007/s00158-003-0368-6
  92. Yiu, K. F. C., and Zangeneh, M. 2000, “Three-Dimensional Automatic Optimization Method for Turbomachinery BladeDesign,” Journal of Propulsion and Power, Vol. 16, No. 6, pp. 0748-4658, pp. 1174-1181, doi: 10.2514/2.5694.
  93. Ansys-CFX 11.0, 2006, Ansys Inc.

Cited by

  1. Multi-objective optimization of a centrifugal compressor impeller through evolutionary algorithms vol.224, pp.5, 2010, https://doi.org/10.1243/09576509JPE884
  2. Optimization of an inclined elliptic impinging jet with cross flow for enhancing heat transfer vol.47, pp.6, 2011, https://doi.org/10.1007/s00231-011-0763-2
  3. Multi-objective optimization of a rotating cooling channel with staggered pin-fins for heat transfer augmentation vol.68, pp.7, 2011, https://doi.org/10.1002/fld.2590
  4. Multi-objective optimization of a guide vane in the turning region of a rotating U-duct to enhance heat transfer performance vol.48, pp.11, 2012, https://doi.org/10.1007/s00231-012-1041-7
  5. Optimization of zigzag flow channels of a printed circuit heat exchanger for nuclear power plant application vol.49, pp.3, 2012, https://doi.org/10.1080/00223131.2012.660012
  6. Parametric Study and Optimization of Staggered Inclined Impinging Jets on a Concave Surface for Heat Transfer Augmentation vol.61, pp.6, 2012, https://doi.org/10.1080/10407782.2012.654453
  7. Optimization of Duct System with a Cross Flow Fan to Improve the Performance of Ventilation vol.16, pp.1, 2013, https://doi.org/10.5293/kfma.2013.16.1.040
  8. Aerodynamic optimization of a transonic axial compressor with a casing groove combined with tip injection vol.227, pp.8, 2013, https://doi.org/10.1177/0957650913503311
  9. Design Optimization of Manifold Microchannel Heat Sink Through Evolutionary Algorithm Coupled With Surrogate Model vol.3, pp.4, 2013, https://doi.org/10.1109/TCPMT.2013.2245943
  10. Flow Analyses Inside Jet Pumps Used for Oil Wells vol.6, pp.1, 2013, https://doi.org/10.5293/IJFMS.2012.6.1.001
  11. Shape optimization of staggered ribs in a rotating equilateral triangular cooling channel vol.50, pp.4, 2014, https://doi.org/10.1007/s00231-013-1254-4
  12. Aerodynamic and aeroacoustic optimization for design of a forward-curved blades centrifugal fan vol.230, pp.2, 2016, https://doi.org/10.1177/0957650915624611
  13. Three-objective optimization of a centrifugal pump with double volute to minimize radial thrust at off-design conditions vol.230, pp.6, 2016, https://doi.org/10.1177/0957650916656544
  14. Optimization of a regenerative blower to enhance aerodynamic and aeroacoustic performance vol.30, pp.3, 2016, https://doi.org/10.1007/s12206-016-0223-5
  15. High-efficiency design optimization of a centrifugal pump vol.30, pp.9, 2016, https://doi.org/10.1007/s12206-016-0803-4
  16. Aerodynamic Optimization of a Single-Stage Axial Compressor with Stator Shroud Air Injection vol.55, pp.8, 2017, https://doi.org/10.2514/1.J055909
  17. Shape Optimization of a Microchannel Heat Sink with Phase Change vol.284-287, pp.1662-7482, 2013, https://doi.org/10.4028/www.scientific.net/AMM.284-287.919
  18. Computational fluid dynamics based shape optimization of airfoil geometry for an H-rotor using a genetic algorithm vol.50, pp.9, 2018, https://doi.org/10.1080/0305215X.2017.1409350