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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

罗杰, 何旭, 李彬. 考虑大变形的涡轮叶片热应力有限元算法研究[J]. 航空动力学报, 2024, 39(9):20220915 doi: 10.13224/j.cnki.jasp.20220915
引用本文: 罗杰, 何旭, 李彬. 考虑大变形的涡轮叶片热应力有限元算法研究[J]. 航空动力学报, 2024, 39(9):20220915 doi: 10.13224/j.cnki.jasp.20220915
LUO Jie, HE Xu, LI Bin. Study on finite element method of thermal stress of turbine blade under large deformation[J]. Journal of Aerospace Power, 2024, 39(9):20220915 doi: 10.13224/j.cnki.jasp.20220915
Citation: LUO Jie, HE Xu, LI Bin. Study on finite element method of thermal stress of turbine blade under large deformation[J]. Journal of Aerospace Power, 2024, 39(9):20220915 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
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

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

  • 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。

     

  • 图 1  八节点六面体单元示意图

    Figure 1.  Eight-node hexahedron element

    图 2  连续体变形过程

    Figure 2.  Diagram of continuum deformation

    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

    图 4  混合单元

    Figure 4.  Mixed elements

    图 5  不同网格悬臂梁模型

    Figure 5.  Cantilever beam model with different grid

    图 6  不同网格相对误差

    Figure 6.  Relative error with different grids

    图 7  相对误差

    Figure 7.  Relative error

    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)

    图 9  缺口平板热应力云图

    Figure 9.  Thermal stress contour of notched plate

    图 10  立方体算例(1mm×1mm×1mm)

    Figure 10.  Cube model (1mm×1mm×1mm)

    图 11  立方体热应力云图

    Figure 11.  Stress contour of cube

    图 12  悬臂梁算例(40 mm×50 mm×500 mm)

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

    图 13  悬臂梁x向位移云图

    Figure 13.  x-direction displacement contour of cantilever beam

    图 14  Line1 x向位移

    Figure 14.  x-direction displacement of Line1

    图 15  圆环算例(10 mm×110 mm×120 mm)

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

    图 16  圆环z向位移云图

    Figure 16.  z-direction displacement contour of ring model

    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)

    图 18  涡轮叶片温度场

    Figure 18.  Temperature field of turbine blade

    图 19  涡轮叶片位移场

    Figure 19.  Displacement field of turbine blade

    图 20  涡轮叶片应力场

    Figure 20.  Stress field of turbine blade

    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

    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xyz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
    下载: 导出CSV

    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9140.1146778.26
    六面体6400.1237860.97
    混合33990.1251310.10
    下载: 导出CSV

    表  3  悬臂梁挠度

    Table  3.   Cantilever beam deflection

    泊松比 ABAQUS
    B-bar
    相对
    误差/%

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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/%
    120200
    220200
    320200
    465.665865.33370.51
    565.645165.32590.49
    680.396980.120.35
    780.376780.11380.33
    879.419179.20160.27
    975.073574.79320.37
    1074.051773.72780.44
    1192.737192.37350.39
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    泊松比 0.3
    边界条件 固支约束(左端面,z轴向)/mm 0
    集中载荷(右端面,z轴向)/N 6×105
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    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
    环境温度/℃ 800
    离心力 Wx/(rad/s) 1256
    下载: 导出CSV
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  • 收稿日期:  2022-11-29
  • 网络出版日期:  2024-04-22

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