A mesh parameterization method and life reliability-based optimization for turbine blade
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摘要:
涡轮叶片的寿命可靠性优化对保障发动机安全，提高发动机使用寿命具有重要意义。传统的确定性优化由于没有考虑不确定性因素的影响，其结果往往导致结构可靠性低，严重威胁发动机的安全。针对复杂的含气膜孔几何变量的涡轮叶片几何构型，提出局部参数化网格变形方法，在关注的叶片前缘部分采用六面体网格，并利用局部网格变形法实现其参数化变形，其他部分采用四面体网格，以缩短其网格划分时间，提高其网格划分效率。所提方法实现了不确定条件下的含气膜孔几何变量涡轮叶片的寿命可靠性优化，在满足可靠性约束和几何约束的条件下，使得涡轮叶片基于不确定性的寿命均值提高了18.36%。
Abstract:The optimization of the life reliability of turbine blades is of great significance for the safety and service life improvement of aeroengines. The traditional deterministic optimization method does not consider the influence of uncertain factors, which tends to cause low structural reliability, seriously threatening the safety of the aeroengine. Thus, this paper focuses on the life reliability-based optimization of the turbine blade in uncertain environments. A local mesh deformation method is proposed for the turbine blade with geometric variables of the film hole to realize mesh parameterization. Based on the proposed method, the life reliability-based optimization of the turbine blade with film hole geometric variables is achieved under uncertain conditions. With satisfying reliability constraints and geometric constraints, the average lifetime value of turbine blades based on uncertainty is increased by 18.36%.
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图 8 最大工作状态叶身温度分布
Figure 8. Temperature distribution of turbine blade in the maximum working condition
图 10 寿命可靠性设计优化的流程图
Figure 10. Flow chart of life reliability-based design optimization
图 11 完全解耦法建立代理模型的流程图
Figure 11. Flow chart of the surrogate model using full decoupling method
表 1 ANSYS软件网格质量检查结果
Table 1. Results of mesh quality check from ANSYS software
检查指标 网格数量 占比/%
（低质量+畸形）检查总数 低质量 畸形 长宽比 2 283 364 24 0 0 平行偏差 188 393 10 0 0.01 最大角度 2 283 364 201 0 0.01 雅可比 2 283 364 0 0 0 翘曲因子 188 393 0 0 0 合计 2 283 364 235 0 0.01 
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表 2 DZ125合金的材料属性
Table 2. Material properties of DZ125 alloy
温度T/℃ 弹性模量$E/{\text{GPa}} $ 泊松比$\nu $ 剪切模量$ G/{\text{GPa}} $ 线膨胀系数$ \alpha $/℃−1 横向 纵向 横向 纵向 横向 纵向 横向 纵向 20 176.5 127.0 0.26 0.410 70.0 107.0 12.27 12.45 500 161.5 112.5 0.27 0.410 63.5 101.5 13.03 13.26 600 151.5 108.5 0.27 0.415 59.5 97.5 13.39 13.53 700 145.5 104.5 0.29 0.430 56.5 92.5 13.91 14.04 800 139.5 102.0 0.29 0.430 52.5 90.5 14.43 14.55 900 135.0 97.0 0.3 0.435 52.0 89.0 14.96 15.06 1000 123.0 89.0 0.31 0.450 46.5 72.5 15.84 16.02
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温度T/℃ 密度ρ/（kg·m−3） 热导率$\lambda $/(W·(m·℃)−1) 屈服强度$\sigma_{0.2}/{\rm{MPa}} $ 拉伸极限$\sigma_{b}/{\rm{MPa}} $ 横向 纵向 横向 纵向 20 8570 840 985 1090 1320 500 14.99 600 16.79 700 17.96 775 930 975 1220 800 19.63 785 933 933 1130 900 19.51 665 580 808 850 1000 19.43 420 395 560 575 注：下标b表示抗拉强度。
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表 3 发动机典型循环载荷谱
Table 3. Typical cycle load spectrum of the aeroengine
工作循环 工作转速/
(r·min−1)每900 h
循环次数每周运行
时间/min启动-最大-停车 0,21842,0 1014 53.25 慢车-最大-慢车 11125,21842,11125 1190 3.80 巡航-最大-巡航 13357,21842,13357 1053 0.33
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表 4 叶片校核点处的热力耦合分析响应
Table 4. Thermal-mechanical response at the check point of the turbine blade
工作状态 转速/(r·min−1) 温度T/℃ 最大等效应力 $ \sigma {\text{/MPa}} $ 总应变$ \varepsilon $ 最大状态 21 842 817.307 5 796.075 2 0.0111 慢车状态 11 125 659.808 7 352.165 4 0.002 7 巡航状态 13 357 663.506 6 461.846 8 0.003 6
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表 5 叶片校核点处的振动响应
Table 5. Vibration response at the check point of the turbine blade
工作状态 转速/(r·min−1) 激振频率/Hz 最大等效振动应力$ \sigma {\text{/MPa}} $ 最大状态 21 842 5096.466 7 178.324 1 慢车状态 11 125 2595.833 3 15.3682 巡航状态 13 357 3116.633 3 17.1643
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表 6 涡轮叶片寿命可靠性优化结果
Table 6. Life reliability-based optimization results for turbine blade
类型 $r$/mm $d$/mm $ \mu \left( N \right) $ 初值 0.215 0 13081 优化值 0.214 −0.199 15483
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