مجله ی مهندسی مکانیک شریف

مجله ی مهندسی مکانیک شریف

بررسی روش‌های پارامتری‌سازی پره در کمپرسورهای محوری

نوع مقاله : مقاله پژوهشی

نویسندگان
دانشکده‌ی مهندسی هوافضا، دانشگاه صنعتی شریف، تهران، ایران.
10.24200/j40.2026.68965.1774
چکیده
پارامتری‌سازی هندسه‌ی پره، نقشی تعیین‌کننده در فرآیند طراحی و تحلیل عملکرد کمپرسورهای محوری ایفا می‌کند و در ارزیابی اثر خطاهای ساختی در عملکرد آئرودینامیکی پره‌ها، جایگاهی کلیدی دارد. دستیابی به تعادل میان تعداد پارامترهای هندسی و حفظ دقت بازتولید سطوح، چالشی اساسی محسوب می‌شود. روش‌های مختلفی برای پارامتری‌سازی هندسی در آئرودینامیک وجود دارد. با توجه به بررسی‌های صورت‌گرفته، تاکنون مقایسه‌ای جامع از کارایی روش‌های پارامتری‌سازی مذکور در پره‌های کمپرسور محوری ضمن درنظرگرفتن عدم‌قطعیت‌های ساختی صورت نگرفته است. در پژوهش حاضر، روش‌های مطرح، شامل: برازش منحنی، تابع انتقال کلاس و پیکره، مقاطع پارامتری، هیکس- هن، تجزیه‌ی مقادیر منفرد ،و روش لانگ، تشریح و پیاده‌سازی شده‌اند. به‌منظور ارزیابی دقیق، دو نوع ایرفویل متداول در پره‌ی‌ کمپرسورهای محوری با استفاده از روش‌های اخیر پارامتری‌سازی شده‌اند. نتایج نشان داده‌اند اگرچه روش‌های مبتنی بر برازش منحنی، دقت بازتولید بسیار بالایی ارائه می‌دهند؛ اما روش لانگ با استفاده از پارامترهای فیزیکی صریح و پیاده‌سازی آسان، عملکرد قابل‌قبولی در پارامتری‌سازی پره‌ی کمپرسورهای محوری داشته است. به‌منظور انتخاب بهترین روش پارامتری‌سازی، عملکرد روش‌های مذکور با معیارهای مختلفی، مانند: دقت بازتولید هندسه، تعداد و نوع پارامترها، قابلیت تولید انحراف‌های هندسی بررسی و مقایسه شده‌اند. پژوهش حاضر، امکان شناسایی روش مناسب در کاربردهای مختلف را فراهم ساخته است.
کلیدواژه‌ها
موضوعات

عنوان مقاله English

Investigation of Blade Parameterization Methods for Axial Compressors

نویسندگان English

Mohammad Farahani
Mehrab Kalabi
Arman Mohammadi Joozdani
Sajjad Ghadiri
Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iran
چکیده English

Geometry parameterization is essential for turbomachinery design, optimization, and modeling of geometric deviations. A key challenge is achieving high geometric accuracy with a minimal set of variables. While various parameterization techniques exist, a comprehensive comparison of their efficacy for axial compressor blades remains limited. This study implements and compares prominent aerodynamic parameterization methods: curve-fitting, Class/Shape Function Transformation (CST), Hicks-Henne, Singular Value Decomposition (SVD), and the Lange method, which are commonly used for turbomachinery blades. To evaluate performance, two transonic compressor airfoils were parameterized using parameter sets of 10 and 12. Results indicate that while curve-fitting methods provide superior geometric accuracy, the Lange method offers highly competitive performance owing to its explicit physical parameters and ease of implementation. No single method is globally optimal, as the best choice depends on the parameter count, specific geometry, and problem type. To facilitate decision-making, the methods were ranked based on key criteria.

کلیدواژه‌ها English

Geometry parameterization
turbomachinery
axial compressor
compressor blades
manufacturing variability
parametrization methods
Lange method
CST
 
1. Masters, D.A., Taylor, N.J., Rendall, T., Allen, C.B. and Poole, D.J., 2015. Review of aerofoil parameterisation methods for aerodynamic shape optimisation. In 53rd AIAA Aerospace Sciences Meeting, p. 0761. https://doi.org/10.2514/6.2016-0558
2. Masters, D.A., Taylor, N.J., Rendall, T.C.S., Allen, C.B. and Poole, D.J., 2017. Geometric comparison of aerofoil shape parameterization methods. AIAA journal, 55(5), pp.1575-1589. https://doi.org/10.2514/1.J054943
3 . Lauer, M.G. and Ansell, P.J., 2025. A review of parameterization methods for airfoil design. Progress in Aerospace Sciences, 158, p.101140.  https://doi.org/10.1016/j.paerosci.2025.101140
4. Zhang, T.T., Wang, Z.G., Huang, W. and Yan, L., 2018. A review of parametric approaches specific to aerodynamic design process. Acta Astronautica, 145, pp.319-331. https://doi.org/10.1016/j.actaastro.2018.02.011
5. Sripawadkul, V., Padulo, M. and Guenov, M., 2010, September. A comparison of airfoil shape parameterization techniques for early design optimization. In 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, p. 9050. https://doi.org/10.2514/6.2010-9050
6. Wang, J., Yang, H., Zhou, K., Wei, J., Wen, M. and Zheng, X., 2022. Performance dispersion control of a multistage compressor based on precise identification of critical features. Aerospace Science and Technology, 129, p.107845. https://doi.org/10.1016/j.ast.2022.107845
7. Junying, W.A.N.G., Baotong, W.A.N.G., Heli, Y.A.N.G., Zhenzhong, S.U.N. and Kai, Z.H.O.U., 2023. Compressor geometric uncertainty quantification under conditions from near choke to near stall. Chinese Journal of Aeronautics, 36(3), pp.16-29. https://doi.org/10.1016/j.cja.2022.10.012
8. Prots, A., Schlüter, L., Voigt, M., Meyer, M. and Mailach, R., 2023, June. Sensitivity analysis of performance parameters of a compressor blade with correlated profile parameters. In Turbo Expo: Power for Land, Sea, and Air, 87110, p. V13DT34A014). American Society of Mechanical Engineers. https://doi.org/10.1115/GT2023-102442
9. Wang, H., Gao, L., Yang, G. and Wu, B., 2023. A data-driven robust design optimization method and its application in compressor blade. Physics of Fluids, 35(6).multi-storey reinforced concrete frame”, Struct. Design Tall Spec. Build. 21, 405–415, 2012. https://doi.org/10.1063/5.0150040
10. Zhang, Q., Shenren, X.U., Xianjun, Y.U., Jiaxin, L.I.U., Dingxi, W.A.N.G. and Huang, X., 2022. Nonlinear uncertainty quantification of the impact of geometric variability on compressor performance using an adjoint method. Chinese Journal of Aeronautics, 35(2), pp.17-21. https://doi.org/10.1016/j.cja.2021.06.007
11. Altafi, D., Mojaddam, M. and Ghadimi, B., 2022. Investigation of the effect of the geometric deviations on the performance of a radial flow compressor employing uncertainty quantification (UQ) and sensitivity analysis. The Journal of Engine Research, 67(67), pp.51-63. [In Persian]. 10.22034/er.2022.697920
12. Aligoodarz, M., Mehrpanahi, A. and Karrabi, H., 2017. Investigation of blade tolerances effect on efficiency, using 1D modeling of an axial flow turbine [In Persian]. https://www.sid.ir/paper/245524/en
13. Sadeghi Malek-Abadi, M. and Davari, A. (2024) ‘An experimental study of the acoustics of small horizontal-axis wind turbines based on computational fluid dynamics and neural network approaches’, Sharif Journal of Mechanical Engineering(SJME), 40(2), pp. 52–63. doi: 10.24200/j40.2024.64121.1704. [in Persian].     https://doi.org/10.24200/j40.2024.64121.1704
14. Abraham, S., Tsirikoglou, P., Lacor, C., Ghorbaniasl, G., Wunsch, D., Hirsch, C. and Contino, F., 2018. Uncertainty quantification in industrial turbo-machinery design using sparse polynomial chaos expansions. In 2018 Multidisciplinary Analysis and Optimization Conference, p. 3103. https://doi.org/10.2514/6.2018-3103
  15. Li, J., Liu, B., Yang, X. and Lu, X., 2015, June. Study on coupling optimization design of aspirated compressor airfoil based on two different parameterization methods. In Turbo Expo: Power for Land, Sea, and Air, 56659, p. V02CT45A001). American Society of Mechanical Engineers. https://doi.org/10.1115/GT2015-42009
16. Ivanov, T.D., Simonović, A.M., Svorcan, J.S. and Peković, O.M., 2017. VAWT optimization using genetic algorithm and CST airfoil parameterization. FME Transactions, 45(1). doi:10.5937/fmet1701026I
17. Xiang, H. and Chen, J., 2021. Aerothermodynamics optimal design of a multistage axial compressor in a gas turbine using directly manipulated free-form deformation. Case Studies in Thermal Engineering, 26, p.101142. https://doi.org/10.1016/j.csite.2021.101142
18. Bestle, D. and Flassig, P., 2010, July. Optimal aerodynamic compressor blade design considering manufacturing noise. In Proceedings of the 8th ASMO UK/ISSMO Conference. https://www.researchgate.net/publication/259150461
19. Ji, T., Chu, W., Liang, C. and Meng, D., 2023. Uncertainty quantification on the influence of blade thickness deviation at different rotational speeds based on flow dissipation analysis. Physics of Fluids, 35(6). https://doi.org/10.1063/5.0155693
20. Ji, T. and Chu, W., 2024. Uncertainty quantification of compressor performance affected by data-driven blade geometric deviations. Journal of Engineering for Gas Turbines and Power, 146(12), p.121016. https://doi.org/10.1115/1.4066231
21. Büche, D., Klostermann, S., Rogé, G. and Loyatho, X., 2018. Uncertainties in compressor and aircraft design. In Uncertainty Management for Robust Industrial Design in Aeronautics: Findings and Best Practice Collected During UMRIDA, a Collaborative Research Project (2013–2016) Funded by the European Union, pp. 35-51. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-77767-2_3
22. Dunham, J., 1998. CFD validation for propulsion system components (la validation CFD des organes des propulseurs) (No. AGARDAR355).
23. Moore, R.D., 1980. Performance of single-stage axial-flow transonic compressor with rotor and stator aspect ratios of 1.19 and 1.26 respectively, and with design pressure ratio of 2.05. National Aeronautics and Space Administration.
24. Dahlquist, G. and Björck, Å., 2008. Numerical methods in scientific computing, volume I. Society for Industrial and Applied Mathematics.
25. McClarren, R., 2017. Computational nuclear engineering and radiological science using python. Academic Press.
26. Marino, E., Hosseini, S.F., Hashemian, A. and Reali, A., 2020. Effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear-deformable beams with varying curvature and torsion. Computers & Mathematics with Applications, 80(11), pp.2563-2585. https://doi.org/10.1016/j.camwa.2020.06.006
27. Kulfan, B.M., 2010. Recent extensions and applications of the ‘CST’universal parametric geometry representation method. The Aeronautical Journal, 114(1153), pp.157-176. https://doi.org/10.2514/6.2007-62
28. Kulfan, B.M., 2008. Universal parametric geometry representation method. Journal of Aircraft, 45(1), pp.142-158. https://doi.org/10.2514/1.29958
29. Kulfan, B. and Bussoletti, J., 2006, September. " Fundamental" parameteric geometry representations for aircraft component shapes. In 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (p. 6948). https://doi.org/10.2514/6.2006-6948
30. Sobieczky, H., 1999. Parametric airfoils and wings. In Recent Development of Aerodynamic Design Methodologies: Inverse Design and Optimization (pp. 71-87).
31. Sobieczky, H., 2000, January. Aerodynamic design and optimization tools accelerated by parametric geometry preprocessing. In European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS, 2000.
32. Hicks, R.M. and Henne, P.A., 1978. Wing design by numerical optimization. Journal of Aircraft, 15(7), pp.407-412. https://doi.org/10.2514/3.58379
33. Wu, H.Y., Yang, S., Liu, F. and Tsai, H.M., 2003, June. Comparisons of three geometric representations of airfoils for aerodynamic optimization. In 16th AIAA Computational Fluid Dynamics Conference (p. 4095). https://doi.org/10.2514/6.2003-4095
34. Toal, D.J., Bressloff, N.W., Keane, A.J. and Holden, C.M., 2010. Geometric filtration using proper orthogonal decomposition for aerodynamic design optimization. AIAA journal, 48(5), pp.916-928. https://doi.org/10.2514/1.41420
35. Ghoman, S., Wang, Z., Chen, P. and Kapania, R., 2012. A POD-based reduced order design scheme for shape optimization of air vehicles. In 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA (p. 1808). https://doi.org/10.2514/6.2012-1808
36. Poole, D.J., Allen, C.B. and Rendall, T.C., 2015. Metric-based mathematical derivation of efficient airfoil design variables. AIAA Journal, 53(5), pp.1349-1361. https://doi.org/10.2514/1.J053427
37. Lange, A., Vogeler, K., Gu Mmer, V., Schrapp, H. and Clemen, C., 2009, January. Introduction of a parameter based compressor blade model for considering measured geometry uncertainties in numerical simulation. In Turbo Expo: Power for Land, Sea, and Air, 48876, pp. 1113-1123). https://doi.org/10.1115/GT2009-59937
38. Lange, A., Voigt, M., Vogeler, K., Schrapp, H., Johann, E. and Gu Mmer, V., 2010, October. Probabilistic CFD simulation of a high-pressure compressor stage taking manufacturing variability into account. In Turbo expo: power for land, sea, and air, 44014, pp. 617-628). https://doi.org/10.1115/GT2010-22484
39. Hajilou Banisi, A. and Khajeh Kolki, M. R. (2025) ‘Design and replacement of a three-stage axial compressor with a centrifugal compressor in a gas turbine to enhance performance’, Sharif Journal of Mechanical Engineering(SJME), 41(1), pp. 29–42 [in Persian]. https://doi.org/10.24200/j40.2025.65087.1719