A Parametrization Method of Blade Section Based on Topological Transformation of Ellipse

doi:10.3901/JME.2023.07.081

Abstract

Abstract: The parametrization method of the blade section serves the whole life cycle of the blade, including design, manufacturing and remanufacturing. However, it is difficult for the current parametric methods to take into account the intuitive geometric meaning of modeling parameters and the continuities of the curvature and the slope of curvature. To solve the problem, a parameterization method based on the ellipse topology transformation is proposed. The method is based on the consistency of the curvature distribution and that of the topological structure between the ellipse and the blade section and the ellipse is transformed into the blade section by applying several designed topological transformations. Meanwhile, one-to-one correspondences between the blade key geometry parameters and the modeling parameters are established and the high-order continuity of the ellipse is maintained. To verify the effectiveness of the proposed method, the inversions of several blade sections with different geometrical characteristics are carried out respectively. The results show that compared with the existing method, the proposed method achieves higher fitting accuracy with fewer modeling parameters; the curvature and the curvature derivative of the inversion sections are both continuous; the aerodynamic performance of the inversion sections is consistent well with that of the original ones; modifying a single modeling parameter can intuitively change the corresponding blade geometry. Therefore, the proposed method facilitates the design of lower-loss higher-loading blade sections and the transmitted design intentions are easier to be understood and used in the manufacturing and remanufacturing process, which are both conducive to guarantee the final service performance of the blade.

Key words: parametrization method, topological transformation of ellipse, blade section, whole life cycle of blade

CLC Number:

V231

SI Chuanrui, CHENG Jinxin, CHEN Zhitong, ZHANG Yun, ZHU Zhengqing, CHEN Mingsheng. A Parametrization Method of Blade Section Based on Topological Transformation of Ellipse[J]. Journal of Mechanical Engineering, 2023, 59(7): 81-91.

References

[1] 张云. 叶轮叶片几何自适应加工技术研究[D]. 北京:北京航空航天大学,2016. ZHANG Yun. Study on the geometry-based adaptive machining of impeller and blade[D]. Beijing:Beihang University,2016.
[2] LI Z,ZHENG X. Review of design optimization methods for turbomachinery aerodynamics[J]. Progress in Aerospace Sciences,2017,93:1-23.
[3] MOHAGHEGH K,SADEGHI M H,ABDULLAH A. Reverse engineering of turbine blades based on design intent[J]. The International Journal of Advanced Manufacturing Technology,2007,32(9-10):1009-1020.
[4] ZHANG Y,CHEN Z,NING T. Reverse modeling strategy of aero-engine blade based on design intent[J]. The International Journal of Advanced Manufacturing Technology,2015,81(9-12):1781-1796.
[5] KULFAN B,BUSSOLETTI J. "Fundamental" parametric geometry representations for aircraft component shapes[C]//11th AIAA/ISSMO multidisciplinary analysis and optimization conference,September 6-8,2006,Renaissance Portsmouth Hotel,Portsmouth,Virginia. New York:AIAA,2006:1-45.
[6] MASTERS D A,TAYLOR N J,RENDALL T,et al. Review of aerofoil parameterization methods for aerodynamic shape optimization[C]//53rd AIAA Aerospace Sciences Meeting,January 5-9,2015,Kissimmee,Florida. New York:AIAA,2015:1-20.
[7] ZHU F,QIN N. Intuitive Class/Shape function parameterization for airfoils[J]. AIAA Journal,2014,52(1):17-25.
[8] AGROMAYOR R,ANAND N,MULLER J,et al. A unified geometry parametrization method for turbomachinery blades[J]. Computer-Aided Design,2021,133:102987.
[9] KORAKIANITIS T,Papagiannidis P. Surface- curvature-distribution effects on turbine-cascade performance[J]. Journal of Turbomachinery,1992,115(2):334-341.
[10] Persico G,Rodriguez-Fernandez P,Romei A. High-fidelity shape optimization of non-conventional turbomachinery by surrogate evolutionary strategies[J]. Journal of Turbomachinery,2019,141(8):081010.1- 081010.11.
[11] Mazaheri K,Khatibirad S. Using a shock control bump to improve the performance of an axial compressor blade section[J]. Shock Waves,2017,27(2):299-312.
[12] XIANG H,CHEN J. Aerothermodynamics optimal design of a multistage axial compressor in a gas turbine using directly manipulated free-form deformation[J]. Case Studies in Thermal Engineering,2021,26:101142.
[13] Pritchard L J. An eleven-parameter axial turbine airfoil geometry model[C]//American Society of Mechanical Engineers. Gas Turbine Conference and Exhibit,March 18-21,1985,Houston,Texas. New York:ASME,1985:1-12.
[14] Dunham J. A parametric method of turbine blade profile design[C]//American Society of Mechanical Engineers. Gas Turbine Conference and Products Show,March 30-April 4,1974,Zurich,Switzerland. New York:ASME,1974:1-10.
[15] Pierret S,Braembussche R. Turbomachinery blade design using a Navier-Stokes solver and artificial neural network[J]. Journal of Turbomachinery,1999,121(2):326-342.
[16] 彭铖,李强,杨金广,等. 一种新的轴流压气机叶片参数化方法[J]. 燃气涡轮试验与研究,2020,33(02):34-38. PENG Cheng,LI Qiang,YANG Jinguang,et al. A novel parameterization method of axial compressor blade[J]. Gas Turbine Experiment and Research,2020,33(02):34-38.
[17] 张书义,杨波,任兰学,等. 三维低雷诺数叶片参数化方法研究[J]. 热能动力工程,2021,36(10):113-118. ZHANG Shuyi,YANG Bo,REN Lanxue,et al. The study of the parameterization method applied to three-dimensional low Reynolds number blade[J]. Journal of Engineering for Thermal Energy and Power,2021,36(10):113-118.
[18] Korakianitis T,Hamakhan I A,Rezaienia M A,et al. Design of high-efficiency turbomachinery blades for energy conversion devices with the three-dimensional prescribed surface curvature distribution blade design (CIRCLE) method[J]. Applied Energy,2012,89(1):215-227.
[19] Mahmood S M H,Turner M G,Siddappaji K. Flow characteristics of an optimized axial compressor rotor using smooth design parameters[C]//American Society of Mechanical Engineers. ASME Turbo Expo 2016:Turbomachinery Technical Conference and Exposition,June 13-17,2016,Seoul,South,Korea. New York:ASME,2016:1-12.
[20] 江辉有. 拓扑学[M]. 北京:机械工业出版社,2013. JIANG Huiyou. Topology[M]. Beijing:China Machine Press,2013.
[21] 姜言峰,刘文兵,崔建明. 指纹特征点拓扑变换的非对称加解密研究[J]. 计算机工程,2011,37(8):137-139. JIANG Yanfeng,LIU Wenbing,CUI Jianming. Study of asymmetric encryption and decryption by fingerprint feature point topological transformation[J]. Computer Engineering,2011,37(8):137-139.
[22] 张力宁,张定华,陈志强. 基于等距线的叶片截面中弧线计算方法[J]. 机械设计,2006,23(5):39-41. ZHANG Lining,ZHANG Dinghua,CHEN Zhiqiang. Calculation method on central arced curve of blade section based on equidistance line[J]. Journal of Machine Design,2006,23(5):39-41.