典型涡轮气冷叶片参数化建模及优化设计

董少静; 杨傲然; 苑旺; 张立章; 方宇凡; 申秀丽

doi:10.13224/j.cnki.jasp.20230316

典型涡轮气冷叶片参数化建模及优化设计

doi: 10.13224/j.cnki.jasp.20230316

董少静^{1, 2,},
杨傲然^{1, 2},
苑旺³,
张立章⁴,
方宇凡^{1, 2},
申秀丽^{1, 2}

1.
北京航空航天大学能源与动力工程学院，北京 100191
2.
北京航空航天大学航空发动机结构强度北京市重点实验室，北京 100191
3.
中国航空工业集团有限公司沈阳飞机设计研究所，沈阳 110035
4.
中国航发湖南动力机械研究所，湖南株洲 412002

详细信息

作者简介:
董少静（1986—），女，副研究员，博士，主要从事航空发动机热端部件结构、材料及工艺方面的研究。E-mail：dongshaojing@buaa.edu.cn

中图分类号: V232.4
计量
- 文章访问数: 15
- HTML浏览量: 9
- PDF量: 6
- 被引次数: 0
出版历程
- 收稿日期: 2023-05-13
- 网络出版日期: 2024-06-07

Parametric modeling and optimization design of typical turbine air-cooled blade

DONG Shaojing^{1, 2
,},
YANG Aoran^{1, 2},
YUAN Wang³,
ZHANG Lizhang⁴,
FANG Yufan^{1, 2},
SHEN Xiuli^{1, 2}

1.
School of Energy and Power Engineering，Beihang University，Beijing 100191，China
2.
Beijing Key Laboratory of Aero-Engine Structure and Strength，Beihang University，Beijing 100191，China
3.
Shenyang Aircraft Design and Research Institute，Aviation Industry Corporation of China，Shenyang 110035，China
4.
Hunan Aviation Powerplant Research Institute，Aero Engine Corporation of China，Zhuzhou Hunan 412002，China

摘要

摘要:
为更好保证涡轮气冷叶片结构强度设计阶段的气动综合性能，在二维叶栅传统四线造型方法的基础上，引入了喉道宽度和尾缘弯折角两个参数以保证相关气动指标，同时，提出了一种基于自由曲线的异形冷气入口建模方法以改善冷气入口处的应力集中问题并通过优化算例证明了其潜在价值。在此基础上，对涡轮气冷叶片内部典型冷却结构进行参数化建模。最后，以涡轮叶片质量和叶身最大拉伸应力为优化目标，选取参数对涡轮气冷叶片进行优化，优化后涡轮叶片质量和优化前相比下降0.99%，最大拉伸应力下降6.55%。优化结果表明，相关参数化方法可以满足具有复杂内冷结构的涡轮叶片的设计需求，可以有效提高涡轮设计效率。
- 涡轮气冷叶片 /
- 参数化建模 /
- 二维叶栅 /
- 冷却结构 /
- 优化设计
Abstract:
In order to better ensure the comprehensive aerodynamic performance of turbine air-cooled blades in the structural strength design stage, based on the traditional four-line modeling method of two-dimensional cascade, two parameters, i.e. throat width and trailing edge bending angle, were introduced to ensure the aerodynamic performance. A modeling method based on free curve for irregular cooling air inlet was proposed to alleviate the stress concentration problem at the cold air inlet and its potential value was demonstrated by optimization calculation. On this basis, the typical cooling structure inside the turbine air-cooled blade was modeled parametrically. The mass of blade and the maximal tensile stress of blade body were taken as the optimization objectives, and parameters were selected to optimize turbine air-cooled blades. After optimization, the mass of blade decreased by 0.99% and maximum tensile stress decreased by 6.55%. The optimization results showed that the relevant parameterization method can meet the design requirements of turbine blades with complex internal cooling structure, and can effectively improve turbine design efficiency.
- air-cooled blade /
- parametric modeling /
- two-dimensional aerofoil /
- cooling structure /
- optimization design

HTML

图 1 涡轮叶片叶型造型参数

Figure 1. Turbine two-dimensional cascade parameter

下载: 全尺寸图片幻灯片

图 2 叶栅造型曲线类型

Figure 2. Curve types of aerofoil

下载: 全尺寸图片幻灯片

图 3 造型曲线控制多边形

Figure 3. Aerofoil and control polygon

下载: 全尺寸图片幻灯片

图 4 原始模型及重构模型对比

Figure 4. Comparison of reconstruction model and original model

下载: 全尺寸图片幻灯片

图 5 变壁厚内腔

Figure 5. Variable thickness of inner cavity

下载: 全尺寸图片幻灯片

图 6 内腔前缘曲线造型

Figure 6. Leading edge curve modeling of inner cavity

下载: 全尺寸图片幻灯片

图 7 伸根段内腔面

Figure 7. Inner cavity surface of root extending segment

下载: 全尺寸图片幻灯片

图 8 伸根段内腔面造型

Figure 8. Modeling of root extending segment inner cavity surface

下载: 全尺寸图片幻灯片

图 9 冷却通道造型

Figure 9. Cooling channal modeling

下载: 全尺寸图片幻灯片

图 10 冷气入口参数化曲线

Figure 10. Paramtric curves of cooling air inlet

下载: 全尺寸图片幻灯片

图 11 冷气入口模型

Figure 11. Cooling air inlet model

下载: 全尺寸图片幻灯片

图 12 带扰流肋的冷气通道模型

Figure 12. Cooling channal model with ribs

下载: 全尺寸图片幻灯片

图 13 尾缘孔模型

Figure 13. Tail edge holes model

下载: 全尺寸图片幻灯片

图 14 参数化造型流程图

Figure 14. Work flow of parametric modeling

下载: 全尺寸图片幻灯片

图 15 叶片温度分布

Figure 15. Temperature distribution of blade

下载: 全尺寸图片幻灯片

图 16 原始模型叶身拉伸应力及弯曲应力合力

Figure 16. Resultant force of tensile stress and bending stress of blade

下载: 全尺寸图片幻灯片

图 17 原始模型叶身拉伸应力

Figure 17. Tensile stress of blade

下载: 全尺寸图片幻灯片

图 18 优化流程

Figure 18. Work flow of optimization

下载: 全尺寸图片幻灯片

图 19 优化前后叶片叶型对比

Figure 19. Comparison of blade before and after optimization

下载: 全尺寸图片幻灯片

图 20 优化前后叶片尾缘圆角对比

Figure 20. Comparison of blade before and after optimization

下载: 全尺寸图片幻灯片

图 21 优化后叶身拉伸应力及弯曲应力合力大小

Figure 21. Resultant stress of tensile stress and bending stress of blade

下载: 全尺寸图片幻灯片

图 22 优化后叶身拉伸应力

Figure 22. Tensile stress of blade

下载: 全尺寸图片幻灯片

图 23 冷气入口处结构强度分析结果

Figure 23. Strength of structure analysis result in cooling inlet

下载: 全尺寸图片幻灯片

图 24 冷气入口面积控制流程

Figure 24. Work flow of cooling inlet aera control

下载: 全尺寸图片幻灯片

图 25 冷气入口面积控制

Figure 25. Cooling inlet aera control

下载: 全尺寸图片幻灯片

图 26 优化前后冷气入口形状对比

Figure 26. Comparison of cooling inlet before and after optimization

下载: 全尺寸图片幻灯片

图 27 优化后冷气入口最大应力

Figure 27. Maximum stress of optimized cooling inlet

下载: 全尺寸图片幻灯片

叶尖高度	h_t/mm	几何出气角	α_out/（°）
叶根高度	h_r/mm	进气角	β₁/（°）
弦长中心	（x_cc, y_cc）/mm	出气角	β₂/（°）
前缘半径	r_l/mm	攻角	i/（°）
尾缘半径	r_t/mm	喉部宽度	w_th/mm
轴向弦长	L/mm	尾缘弯折角	α_tur/（°）
安装角	α_ins/（°）	前楔角	α_wf/（°）
几何进气角	α_in/（°）	后楔角	α_wb/（°）

下载: 导出CSV

表 1 重构误差

Table 1. Reconstruction error

比较项目	最大值	平均值	标准差
整体误差/mm	0.173	0.032	0.075
弯曲度/mm	0.2341	0.2509	0.0168
扭曲度/（°）	17.6304	17.5290	0.1014

下载: 导出CSV

表 2 边界条件设置表

Table 2. Boundary conditions table

参数	设置
旋转周期对称	设置于涡轮盘的一对周期对称面上
转速/（r/min）	根据实际工况给定（优化算例中为 35 000 r/min）
接触	榫头榫槽对应榫齿面施加bonded约束
涡轮盘温度/℃	见式（2）
叶片温度/℃	由CFX固体域温度导入
叶片表面压力/MPa	CFX固体域表面压力

下载: 导出CSV

表 3 优化变量

Table 3. Optimization variable

截面位置		参数
叶尖	叶型参数	B_ep2
叶尖	壁厚参数	h_b2、h_b3
叶中	叶型参数
叶中	壁厚参数	h_b1
叶根	叶型参数	B_eb1、B_ep2、B_ep1
叶根	壁厚参数	h_b3

下载: 导出CSV

表 4 设计变量前后对比

Table 4. Comparison of design variable

截面位置	变量	优化前	优化后
叶根	B_eb1	0.531	0.889
	B_ep2	0.574	0.417
	B_ep1	0.351	0.889
	h_b3	1.336	1.292
叶中	h_b1	0.781	0.753
叶尖	h_b2	1.164	1.079
	h_b3	0.738	0.656
	B_ep2	0.881	0.764

下载: 导出CSV

表 5 叶身最大拉伸应力及质量优化结果

Table 5. Optimized result of blade maximum stress and mass

模型	最大拉伸应力/MPa	质量/g
原始设计	590.04	28.32
优化设计	551.37	28.04
变化幅度/%	6.55	0.99

下载: 导出CSV

表 6 优化结果

Table 6. Optimized result

模型	最大等效应力/MPa
原始设计	663.97
优化设计	637.59
变化幅度/%	3.97

下载: 导出CSV

参考文献(27)

[1]	尹泽勇,米栋,吴立强,等. 航空发动机多学科设计优化技术研究[J]. 中国工程科学,2007,9(6): 1-10. YIN Zeyong,MI Dong,WU Liqiang,et al. Study on multidisciplinary design optimization of aero-engine[J]. Engineering Science,2007,9(6): 1-10. (in Chinese YIN Zeyong, MI Dong, WU Liqiang, et al. Study on multidisciplinary design optimization of aero-engine[J]. Engineering Science, 2007, 9(6): 1-10. (in Chinese)
[2]	王婧超. 航空发动机三维单晶涡轮叶片的多学科设计优化[D]. 西安: 西北工业大学,2007. WANG Jingchao. Multidisciplinary design optimization for 3D single-crystal turbine blade[D]. Xi’an: Northwestern Polytechnical University,2007. (in Chinese WANG Jingchao. Multidisciplinary design optimization for 3D single-crystal turbine blade[D]. Xi’an: Northwestern Polytechnical University, 2007. (in Chinese)
[3]	虞跨海,李立州,王婧超,等. 涡轮叶片三维气动优化设计[J]. 机械设计,2005,22(11): 31-32,35. YU Kuahai,LI Lizhou,WANG Jingchao,et al. Aerodynamic 3D optimization design for turbine blade[J]. Journal of Machine Design,2005,22(11): 31-32,35. (in Chinese YU Kuahai, LI Lizhou, WANG Jingchao, et al. Aerodynamic 3D optimization design for turbine blade[J]. Journal of Machine Design, 2005, 22(11): 31-32, 35. (in Chinese)
[4]	ALEXEEV R A,TISHCHENKO V A,GRIBIN V G,et al. Turbine blade profile design method based on Bezier curves[J]. Journal of Physics: Conference Series,2017,891: 012254. doi: 10.1088/1742-6596/891/1/012254
[5]	NANTHINI R,PRASAD B V S S S,SANYASIRAJU Y V S S. Effect of Bezier control points on blade pressure distribution[J]. AIP Conference Proceedings,2021,2316(1): 030035.
[6]	张立章,尹泽勇,米栋,等. 基于自适应本征正交分解的涡轮级多学科设计优化[J]. 推进技术,2017,38(6): 1249-1258. ZHANG Lizhang,YIN Zeyong,MI Dong,et al. Multidisciplinary design optimization for turbine stage based on self-adaptive proper orthogonal decomposition[J]. Journal of Propulsion Technology,2017,38(6): 1249-1258. (in Chinese ZHANG Lizhang, YIN Zeyong, MI Dong, et al. Multidisciplinary design optimization for turbine stage based on self-adaptive proper orthogonal decomposition[J]. Journal of Propulsion Technology, 2017, 38(6): 1249-1258. (in Chinese)
[7]	GRA¨SEL J,KESKIN A,SWOBODA M,et al. A full parametric model for turbomachinery blade design and optimisation[C]//Proceedings of ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Salt Lake City,Utah,US: ASME,2008: 907-914.
[8]	AGROMAYOR R,ANAND N,MÜLLER J D,et al. A unified geometry parametrization method for turbomachinery blades[J]. Computer-Aided Design,2021,133: 102987. doi: 10.1016/j.cad.2020.102987
[9]	余锐. 涡轮叶栅的优化设计和气动分析[D]. 上海: 上海交通大学,2014. YU Rui. Optimization design and aerodynamic analysis of turbine cascade[D]. Shanghai: Shanghai Jiao Tong University,2014. (in Chinese YU Rui. Optimization design and aerodynamic analysis of turbine cascade[D]. Shanghai: Shanghai Jiao Tong University, 2014. (in Chinese)
[10]	朱谦,宁涛,席平. 基于引导线的涡轮气冷叶片伸根建模方法[J]. 北京航空航天大学学报,2012,38(8): 1085-1089. ZHU Qian,NING Tao,XI Ping. Root extending section of turbine blade modeling method based on guide curves[J]. Journal of Beijing University of Aeronautics and Astronautics,2012,38(8): 1085-1089. (in Chinese ZHU Qian, NING Tao, XI Ping. Root extending section of turbine blade modeling method based on guide curves[J]. Journal of Beijing University of Aeronautics and Astronautics, 2012, 38(8): 1085-1089. (in Chinese)
[11]	余伟巍,宋玉旺,席平. 基于离散数据点的变壁厚叶身参数化设计[J]. 北京航空航天大学学报,2008,34(11): 1319-1322. YU Weiwei,SONG Yuwang,XI Ping. Parametric design of variational-wall-thickness blade body based on discrete data[J]. Journal of Beijing University of Aeronautics and Astronautics,2008,34(11): 1319-1322. (in Chinese YU Weiwei, SONG Yuwang, XI Ping. Parametric design of variational-wall-thickness blade body based on discrete data[J]. Journal of Beijing University of Aeronautics and Astronautics, 2008, 34(11): 1319-1322. (in Chinese)
[12]	WANG Jie,ZHAO Miaodong,MAO Jianxing. Parametric modeling system for cooling turbine blade based on feature design[J]. Transactions of Nanjing University of Aeronautics and Astronautics,2020,37(5): 758-767.
[13]	杨炯,席平,胡毕富,等. 适应弯扭隔肋的涡轮叶片多种扰流肋造型方法[J]. 北京航空航天大学学报,2014,40(6): 775-781. YANG Jiong,XI Ping,HU Bifu,et al. Multi-type ribs of turbine blade modeling method fitting bowed-twist wall[J]. Journal of Beijing University of Aeronautics and Astronautics,2014,40(6): 775-781. (in Chinese YANG Jiong, XI Ping, HU Bifu, et al. Multi-type ribs of turbine blade modeling method fitting bowed-twist wall[J]. Journal of Beijing University of Aeronautics and Astronautics, 2014, 40(6): 775-781. (in Chinese)
[14]	虞跨海,杨茜,罗昌金,等. 涡轮叶片二维冷却结构参数化设计技术研究[J]. 燃气涡轮试验与研究,2013,26(1): 12-15,29. YU Kuahai,YANG Xi,LUO Changjin,et al. Parametric design method of 2D turbine blade cooling structure[J]. Gas Turbine Experiment and Research,2013,26(1): 12-15,29. (in Chinese doi: 10.3969/j.issn.1672-2620.2013.01.006 YU Kuahai, YANG Xi, LUO Changjin, et al. Parametric design method of 2D turbine blade cooling structure[J]. Gas Turbine Experiment and Research, 2013, 26(1): 12-15, 29. (in Chinese) doi: 10.3969/j.issn.1672-2620.2013.01.006
[15]	方堪羡,李维,张绍文,等. 尾缘弯折角对宽攻角范围涡轮叶片气动性能影响的数值研究[J]. 装备制造技术,2018(12): 38-42,50. FANG Kanxian,LI Wei,ZHANG Shaowen,et al. Influence of uncovered turning on aerodynamic performance of turbine cascade in wide incidence[J]. Equipment Manufacturing Technology,2018(12): 38-42,50. (in Chinese FANG Kanxian, LI Wei, ZHANG Shaowen, et al. Influence of uncovered turning on aerodynamic performance of turbine cascade in wide incidence[J]. Equipment Manufacturing Technology, 2018(12): 38-42, 50. (in Chinese)
[16]	张宸. 涡轮气冷叶片多学科优化关键技术研究[D]. 北京: 北京航空航天大学,2022. ZHANG Chen. Essential technologies for multidisciplinary optimization of turbine air-cooled Blade[D]. Beijing: Beihang University,2022. (in Chinese ZHANG Chen. Essential technologies for multidisciplinary optimization of turbine air-cooled Blade[D]. Beijing: Beihang University, 2022. (in Chinese)
[17]	苑旺. 涡轮冷却叶片解析法参数化建模及设计优化研究[D]. 北京: 北京航空航天大学,2019. YUAN Wang. Analytical parametric modeling and design optimization of turbine cooling blade[D]. Beijing: Beihang University,2019. (in Chinese YUAN Wang. Analytical parametric modeling and design optimization of turbine cooling blade[D]. Beijing: Beihang University, 2019. (in Chinese)
[18]	白涛,邹正平,张伟昊,等. 前缘形状对涡轮叶栅损失影响的机理[J]. 航空动力学报,2014,29(6): 1482-1489. BAI Tao,ZOU Zhengping,ZHANG Weihao,et al. Mechanism of effect of leading-edge geometry on the turbine blade cascade loss[J]. Journal of Aerospace Power,2014,29(6): 1482-1489. (in Chinese BAI Tao, ZOU Zhengping, ZHANG Weihao, et al. Mechanism of effect of leading-edge geometry on the turbine blade cascade loss[J]. Journal of Aerospace Power, 2014, 29(6): 1482-1489. (in Chinese)
[19]	彭茂林,杨自春,曹跃云,等. 基于贝赛尔曲线和粒子群算法的涡轮叶片型线参数化建模[J]. 中国电机工程学报,2012,32(32): 101-108,17. PENG Maolin,YANG Zichun,CAO Yueyun,et al. Parameter modeling of turbine blade model line construction based on bezier curve and particle swarm optimization algorithm[J]. Proceedings of the CSEE,2012,32(32): 101-108,17. (in Chinese PENG Maolin, YANG Zichun, CAO Yueyun, et al. Parameter modeling of turbine blade model line construction based on bezier curve and particle swarm optimization algorithm[J]. Proceedings of the CSEE, 2012, 32(32): 101-108, 17. (in Chinese)
[20]	席平,孙肖霞. 基于CAD模型的涡轮叶片误差检测系统[J]. 北京航空航天大学学报,2008,34(10): 1159-1162. XI Ping,SUN Xiaoxia. Error analysis system of turbine blade based on CAD model[J]. Journal of Beijing University of Aeronautics and Astronautics,2008,34(10): 1159-1162. (in Chinese XI Ping, SUN Xiaoxia. Error analysis system of turbine blade based on CAD model[J]. Journal of Beijing University of Aeronautics and Astronautics, 2008, 34(10): 1159-1162. (in Chinese)
[21]	李毅,金隼,殷金祥,等. UG中桥接曲线参数的自动寻优方法研究[J]. 机械,2004,31(3): 45-48. LI Yi,JIN Sun,YIN Jinxiang,et al. An algorithm for the calculation of bridge curve in UG[J]. Machinery,2004,31(3): 45-48. (in Chinese LI Yi, JIN Sun, YIN Jinxiang, et al. An algorithm for the calculation of bridge curve in UG[J]. Machinery, 2004, 31(3): 45-48. (in Chinese)
[22]	TERZOPOULOS D,PLATT J,BARR A,et al. Elastically deformable models[J]. ACM SIGGRAPH Computer Graphics,1987,21(4): 205-214. doi: 10.1145/37402.37427
[23]	张玲,史梦颖,原峥,等. 涡轮叶片尾缘凹坑/凸起结构气膜冷却特性研究[J]. 推进技术,2020,41(2): 372-381. ZHANG Ling,SHI Mengying,YUAN Zheng,et al. Film cooling characteristic on trailing edge cutback of gas turbine airfoils with dimple/protrusion structure[J]. Journal of Propulsion Technology,2020,41(2): 372-381. (in Chinese ZHANG Ling, SHI Mengying, YUAN Zheng, et al. Film cooling characteristic on trailing edge cutback of gas turbine airfoils with dimple/protrusion structure[J]. Journal of Propulsion Technology, 2020, 41(2): 372-381. (in Chinese)
[24]	郑杰,张雅荣,窦益华,等. 涡轮叶片尾缘端部冲击流动与换热特性研究[J]. 热能动力工程,2017,32(11): 48-54,131. ZHENG Jie,ZHANG Yarong,DOU Yihua,et al. Investigation on flow performances and heat transfer characteristics of turbine blade trailing edge endwall impingement[J]. Journal of Engineering for Thermal Energy and Power,2017,32(11): 48-54,131. (in Chinese ZHENG Jie, ZHANG Yarong, DOU Yihua, et al. Investigation on flow performances and heat transfer characteristics of turbine blade trailing edge endwall impingement[J]. Journal of Engineering for Thermal Energy and Power, 2017, 32(11): 48-54, 131. (in Chinese)
[25]	薛圆圆. 基于核心机的高压涡轮叶尖径向间隙分析技术研究[D]. 北京: 北京航空航天大学,2017. XUE Yuanyuan. Turbine radial tip clearance analysis based on core-engine model[D]. Beijing: Beihang University,2017. (in Chinese XUE Yuanyuan. Turbine radial tip clearance analysis based on core-engine model[D]. Beijing: Beihang University, 2017. (in Chinese)
[26]	罗尔斯-罗伊斯公司. EGD-3斯贝MK202发动机应力标准[S]. 丁爱祥,吴君,译. 北京: 国际航空编辑部,1979.
[27]	中国航空材料手册编委会. 中国航空材料手册: 第2卷[M]. 北京: 中国标准出版社,2002.