考虑大变形的涡轮叶片热应力有限元算法研究

罗杰; 何旭; 李彬

doi:10.13224/j.cnki.jasp.20220915

考虑大变形的涡轮叶片热应力有限元算法研究

doi: 10.13224/j.cnki.jasp.20220915

中国空气动力研究与发展中心计算空气动力研究所，绵阳 621000

详细信息

作者简介:
罗杰（1992-），男，工程师，硕士，主要从事航空发动机结构强度研究。E-mail：luojie_nor_email@163.com

通讯作者:
何旭（1990-），男，助理研究员，博士，主要从事金属和复合材料延性断裂和有限元算法研究。E-mail：hexu713@163.com

中图分类号: V231.91
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- 文章访问数: 34
- HTML浏览量: 12
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- 被引次数: 0
出版历程
- 收稿日期: 2022-11-29
- 网络出版日期: 2024-04-22

Study on finite element method of thermal stress of turbine blade under large deformation

LUO Jie,
HE Xu^{*
, ,},
LI Bin

Computational Aerodynamic Institute，China Aerodynamics Research and Development Center，Mianyang 621000，China

摘要

摘要:
以航空发动机涡轮叶片为研究对象，基于有限单元法，采用六面体八节点单元，提出考虑几何非线性影响的热应力计算方法；使用B-bar和混合网格技术提高了复杂网格的求解精度；采用更新拉格朗日格式考虑了大变形条件下的几何非线性问题，使用Newton-Raphson迭代方法进行涡轮叶片热应力数值求解。通过缺口平板、立方体、悬臂梁、圆环算例，与ABAQUS对比，热应力、大变形模型的相对精度达到99%；最后讨论了考虑大变形对热应力的影响，在温度、气动、离心力载荷工况下，考虑大变形后，涡轮叶片变形量减小，热应力降低，相对计算精度提高4.67%。提出的考虑大变形的热应力数值算法，可用于涡轮叶片径向间隙设计和服役寿命评估，为航空发动机零部件精细化设计提供理论和计算工具支撑。
- 涡轮叶片 /
- 大变形 /
- 热应力 /
- 几何非线性 /
- 有限元算法
Abstract:
Focusing on the finite element method for simulating the large deformation of turbine blade under varied loads, a method for calculating the thermal stress coupled with geometric nonlinearity was proposed based on the eight-node hexahedron element. B-bar and hybrid element technologies were used to improve the precision of results; the Updated-Lagrangian (U.L.) incremental approach was presented for the simulation of large deformation, and the Newton-Raphson iterative method was utilized to numerically calculate the thermal stress of turbine blade. Compared with ABAQUS, the relative accuracy of thermal stress and large deformation models reached 99% through examples of notched plate, cube, cantilever beam, and ring; finally, the influence of considering large deformation on thermal stress was discussed. Under temperature, aerodynamic, and centrifugal load conditions, the radial deformation of turbine blades and thermal stress decreased, and relative calculation accuracy improved by 4.67%. This research is of great benefit to the design of radial clearance and assessment of low cycle fatigue life of turbine blade, and furthermore it can provide theoretical and computational support for exquisite design of aeroengine components.
- turbine blade /
- large deformation /
- thermal stress /
- geometrically nonlinear /
- finite element algorithm

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图 1 八节点六面体单元示意图

Figure 1. Eight-node hexahedron element

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图 2 连续体变形过程

Figure 2. Diagram of continuum deformation

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图 3 考虑几何非线性的热应力计算流程

Figure 3. Solution procedure of thermal stress coupled with geometric nonlinearity

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图 4 混合单元

Figure 4. Mixed elements

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图 5 不同网格悬臂梁模型

Figure 5. Cantilever beam model with different grid

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图 6 不同网格相对误差

Figure 6. Relative error with different grids

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图 7 相对误差

Figure 7. Relative error

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图 8 缺口平板算例（4 mm×4 mm×1 mm）

Figure 8. Notched plate model （4 mm×4 mm×1 mm）

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图 9 缺口平板热应力云图

Figure 9. Thermal stress contour of notched plate

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图 10 立方体算例（1mm×1mm×1mm）

Figure 10. Cube model （1mm×1mm×1mm）

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图 11 立方体热应力云图

Figure 11. Stress contour of cube

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图 12 悬臂梁算例（40 mm×50 mm×500 mm）

Figure 12. Cantilever beam model （40 mm×50 mm×500 mm）

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图 13 悬臂梁x向位移云图

Figure 13. x-direction displacement contour of cantilever beam

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图 14 Line1 x向位移

Figure 14. x-direction displacement of Line1

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图 15 圆环算例（10 mm×110 mm×120 mm）

Figure 15. Ring model （10 mm×110 mm×120 mm）

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图 16 圆环z向位移云图

Figure 16. z-direction displacement contour of ring model

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图 17 涡轮叶片算例（14 mm×12 mm×37 mm）

Figure 17. Turbine blade model （14 mm×12 mm×37 mm）

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图 18 涡轮叶片温度场

Figure 18. Temperature field of turbine blade

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图 19 涡轮叶片位移场

Figure 19. Displacement field of turbine blade

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图 20 涡轮叶片应力场

Figure 20. Stress field of turbine blade

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图 21 不同载荷下考虑和不考虑大变形对比

Figure 21. Comparison with geometric nonlinearity on/off under different loads

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表 1 传热参数

Table 1. Heat transfer parameters

参数	说明
$ \rho $/（kg/m³）	材料密度
$ {\text{c}} $/（J/（kg·℃））	材料比热容
$ t $/s	时间
$ {k_x},{k_y},{k_{\textit{z}}} $/（W/（m·℃））	材料沿x、y、z三个方向导热系数
$ Q $/（W/kg）	物体内部热源密度
$ {n_x},{n_y},{n_{\textit{z}}} $	边界外法向方向余弦
$ \overline \phi $/℃	第一类边界上的给定温度
$ q $/（W/m²）	第二类边界上的给定热流密度
$ h $/（W/m²·℃）	表面传热系数
$ {\phi _{\mathrm{a}}} $/ ℃	第三类边界条件的外界环境温度

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表 2 不同网格悬臂梁挠度

Table 2. Cantilever beam deflection with different grids

网格模型	网格数量	挠度	相对误差/%
四面体	914	0.114677	8.26
六面体	640	0.123786	0.97
混合	3399	0.125131	0.10

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表 3 悬臂梁挠度

Table 3. Cantilever beam deflection

泊松比	ABAQUS	无 B-bar	相对误差/%	有 B-bar	相对误差/%
0.3	0.1254	0.1237	1.31	0.1253	0.09
0.35	0.1252	0.1229	1.83	0.1251	0.10
0.4	0.1249	0.1213	2.91	0.1248	0.12
0.45	0.1245	0.1176	5.56	0.1244	0.13
0.46	0.1245	0.1162	6.66	0.1243	0.09
0.465	0.1244	0.1151	7.44	0.1243	0.12

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表 4 缺口平板材料参数和边界条件

Table 4. Material parameters and boundary conditions of notched plate

	名称	数值
材料参数	参考温度/℃	0
	导热系数/（W/（mm/℃））	16
	弹性模量/GPa	100
	泊松比	0.4
	线膨胀系数	1.36×10⁻⁵
边界条件	给定温度（圆弧面）/℃	20
	固支位移（圆弧面）/ mm	0
	给定热流密度（对称面）/（W/mm²）	50
	表面传热系数（其余面）/（W/mm²·℃）	4
	环境温度（其余面）/℃	100

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表 6 缺口平板特征点合位移

Table 6. Notched plate total displacement of chosen points

特征点	本文/mm	ABAQUS/mm	相对误差/%
1	0	0
2	0	0
3	0	0
4	0.001308	0.001302	0.46
5	0.001308	0.001302	0.47
6	0.002548	0.002539	0.38
7	0.002548	0.002538	0.39
8	0.001662	0.001656	0.33
9	0.001512	0.001506	0.39
10	0.00153	0.001524	0.42
11	0.003982	0.003968	0.34

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表 5 缺口平板特征点温度

Table 5. Notched plate temperature of chosen points

特征点	本文/℃	ABAQUS/℃	相对误差/%
1	20	20	0
2	20	20	0
3	20	20	0
4	65.6658	65.3337	0.51
5	65.6451	65.3259	0.49
6	80.3969	80.12	0.35
7	80.3767	80.1138	0.33
8	79.4191	79.2016	0.27
9	75.0735	74.7932	0.37
10	74.0517	73.7278	0.44
11	92.7371	92.3735	0.39

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表 7 缺口平板特征点von Mises应力

Table 7. Notched plate von Mises stress of chosen points

特征点	本文/MPa	ABAQUS/MPa	相对误差/%
1	66.7524	66.5184	0.35
2	95.0655	94.6352	0.45
3	95.0753	94.6301	0.47
4	16.56	16.5222	0.23
5	16.5627	16.5191	0.26
6	3.14614	3.15748	0.36
7	3.14128	3.14837	0.23
8	10.5039	10.4971	0.06
9	11.255	11.2304	0.22
10	9.3826	9.37852	0.04
11	1.13527	1.13303	0.20

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表 8 立方体特征点温度

Table 8. Cube temperature of chosen points

特征点	本文/℃	ABAQUS/℃	相对误差/%
1	100	100	0
2	100	100	0
3	100	100	0
4	100	100	0
5	100	100	0
6	59.109	59.522	0.69
7	59.1089	59.522	0.69
8	44.8767	45.2803	0.89
9	44.8766	45.2803	0.89
10	50.5658	51.0097	0.87

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表 9 立方体特征点von Mises应力

Table 9. Cube von Mises stress of chosen points

特征点	本文/MPa	ABAQUS/MPa	相对误差/%
1	325.944	326.111	0.05
2	353.258	353.152	0.03
3	325.949	326.111	0.05
4	353.255	353.152	0.03
5	325.939	326.111	0.05
6	62.0222	62.1076	0.14
7	62.0176	62.1076	0.14
8	16.7717	16.7197	0.31
9	16.7725	16.7197	0.32
10	11.1343	11.1527	0.16

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表 10 悬臂梁材料参数&边界条件

Table 10. Material parameters and boundary conditions of cantilever beam

	名称	数值
材料参数	弹性模量/GPa	100
材料参数	泊松比	0.3
边界条件	固支约束（左端面，z轴向）/mm	0
边界条件	集中载荷（右端面，z轴向）/N	6×10⁵

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表 11 圆环特征点位移

Table 11. Ring displacement of chosen points

特征点	本文/mm	ABAQUS/mm	相对误差/%
1	17.441	17.3	0.81
2	14.9961	14.8821	0.76
3	10.6651	10.5635	0.95
4	8.61171	8.5362	0.88
5	6.55719	6.5072	0.76
6	2.2499	2.2143	1.58
7	−0.0667	−0.0651	2.41
8	2.24991	2.2143	1.58
9	6.5572	6.5072	0.76
10	8.61172	8.5362	0.88
11	10.6652	10.5635	0.95
12	14.9961	14.8821	0.76

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表 12 涡轮叶片材料参数和边界条件

Table 12. Material parameters and boundary conditions of turbine blade

	名称		数值
材料参数	参考温度/℃		0
	导热系数/（ W/mm/℃）		0.0167
	弹性模量/GPa		121
	泊松比		0.42
	密度/（kg/m³）		8849
	线膨胀系数/10⁻⁵		1.36
边界条件	左端面，z 轴向	给定温度/℃	400
	左端面，z 轴向	固支位移/ mm	0
	压力面	p/MPa	0.7
	除左端面的其余面	表面传热系数/ （ W/mm²·℃）	0.004
	除左端面的其余面	环境温度/℃	800
	离心力	W_x/（rad/s）	1256

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