基于自由变形型面的轴流涡轮叶片离散伴随优化

康伟; 王彦清; 徐全勇; 胡仕林

doi:10.13224/j.cnki.jasp.20220943

基于自由变形型面的轴流涡轮叶片离散伴随优化

doi: 10.13224/j.cnki.jasp.20220943

康伟^1,,
王彦清¹,
徐全勇^2,*, ,,
胡仕林¹

1.
西北工业大学航天学院，西安 710072
2.
清华大学航空发动机研究院，北京 100084

基金项目: 国家自然科学基金面上项目（11972307）；基础研究基金（JCKY2021204B141）；国家科技重大专项（J2019-Ⅴ-0001-0092，J2019-Ⅴ-0013-0108）

详细信息

作者简介:
康伟（1983-），男，副教授、硕士生导师，博士，主要从事多物理场耦合的优化与控制研究

通讯作者:
徐全勇（1980-），男，副研究员，博士，研究领域为航空发动机气动热力学。E-mail：xuquanyong@tsinghua.edu.cn

中图分类号: V231.3
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- 被引次数: 0
出版历程
- 收稿日期: 2022-12-09
- 网络出版日期: 2024-10-18

Discrete-adjoint optimization of axial turbine blade using free-form deformation

KANG Wei^1
,,
WANG Yanqing¹,
XU Quanyong^{2,*
, ,},
HU Shilin¹

1.
School of Astronautics，Northwestern Polytechnical University，Xi’an 710072，China
2.
Institute for Aero Engine，Tsinghua University，Beijing 100084，China

摘要

摘要:
针对涡轮机械单级气动优化问题，发展了基于自由变形型面技术的离散伴随CFD优化方法。对二维涡轮静叶与涡轮单级进行了优化分析，给出了叶型在约束条件下的最优形状。静叶优化得到的叶片前缘半径显著减小，厚度减小。在优化前后总压恢复系数减小了12.44%，而流动出口角约束在−74.66°，改变幅度为0.047%。对涡轮单级优化问题，考虑旋转效应后的动叶弯度提高，总效率提高了0.79%。而流动出口角约束在−70°，改变幅度为0.068%。结果表明所提方法在涡轮级气动性能优化问题上的有效性。与传统的有限差分方法，离散伴随方法对单级优化时间仅为有限差分的3%。
- 轴流涡轮 /
- 计算流体力学方法 /
- 离散伴随优化 /
- 自由变形型面 /
- 气动性能
Abstract:
A discrete-adjoint CFD method based on the free-form deformation was developed for aerodynamic performance optimization of the axial turbine stage. Optimization analysis of the two-dimensional turbine stator and single turbine stage was carried out, and the optimal shape of the blade shape under the constraints was given. In the stator blade optimization, the leading edge radius and thickness of the blade obtained were significantly reduced. The total pressure recovery coefficient decreased by 12.44% after optimization, while the flow outlet angle was constrained to −74.66° with the variance of 0.047% during the optimization. For the single-stage turbine optimization problem, the camber of the rotor blade was enhanced, and the total efficiency was improved by 0.79% considering the rotation effect. The constraint condition lied in the flow outlet angle with the variance of 0.068% during the optimization. The results showed the effectiveness of the proposed method on the aerodynamic performance optimization of turbine stage. Compared with the traditional finite difference method, the discrete adjoint method costed only 3% CPU time for single-stage optimization.
- axial turbine /
- CFD method /
- discrete-adjoint optimization /
- free-form deformation /
- aerodynamic performance

HTML

图 1 NASA 35跨声速叶轮叶片的压力分布

Figure 1. Pressure contour on the blade of transonic compressor for NASA 35 stage

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图 2 某涡轮静叶的压力分布

Figure 2. Pressure distribution on the stator airfoil of axial turbine stage

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图 3 涡轮静叶叶片的马赫数与压力分布

Figure 3. Mach number and pressure contour on the stator blade of axial turbine stage

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图 4 涡轮叶片的优化流程

Figure 4. Optimization chart of turbine blade

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图 5 静叶流动混合网格

Figure 5. Hybrid grid of flow past the stator blade

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图 6 优化前后静叶叶片几何比较

Figure 6. Comparison of stator blade shape before and after the optimization

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图 7 优化过程中静叶主要参数的变化过程

Figure 7. Iterative history of performance parameters of the stator blade in the optimization

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图 8 优化前后静叶流场压力与马赫数云图比较

Figure 8. Comparison of pressure and Mach number contour before and after the optimization

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图 9 优化前后静叶表面压力比较

Figure 9. Comparison of pressure distribution on the stator blade before and after the optimization

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图 10 涡轮单级流动混合网格

Figure 10. Hybrid grid of flow past the turbine stage

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图 11 优化前后动叶几何比较

Figure 11. Comparison of rotor blade shape before and after the optimization

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图 12 优化过程中单级涡轮主要参数的变化过程

Figure 12. Iterative history of performance parameters of the turbine stage in the optimization

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图 13 优化前后单级涡轮流场压力与马赫数云图比较

Figure 13. Comparison of pressure and Mach number contour of the turbine stage before and after the optimization

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图 14 优化前后动叶表面压力比较

Figure 14. Comparison of pressure distribution on the rotor blade before and after the optimization

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图 15 离散伴随方法与有限差分方法在涡轮静叶单步优化时40个设计变量的梯度比较

Figure 15. Comparison of gradient for stator blade between discrete-adjoint method and finite difference method at one iterative step

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图 16 离散伴随方法与有限差分方法在涡轮单级单步优化时40个设计变量的梯度比较

Figure 16. Comparison of gradient for stage blade between discrete-adjoint method and finite difference method at one iterative step

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表 1 NASA 35跨声速叶轮单级计算参数

Table 1. Computational parameters of transonic compressor for NASA 35 stage

条件与参数	具体内容	数值
几何参数	动叶叶片数	36
几何参数	静叶叶片数	46
边界条件	总压入口条件/Pa	101 325
	总温入口条件/K	288.15
	静压出口条件/kPa	130
计算参数	ROE格式+MRF	理想气体模型
	转速	17 188.7 r/min（1 800 rad/s）
	准定常	库朗数为5

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表 2 跨声速叶轮性能参数比较

Table 2. Comparison of compressor performance the transonic blade stage

参数	文献[12]数据	计算结果	误差/%
压比	1.82	1.802	−0.989
绝热效率	0.842	0.8134	−3.4
流量/（kg/s）	20.2	19.979	−1.09

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表 3 涡轮静叶的进出口条件与优化目标

Table 3. Inlet and outlet condition of the turbine stator and its optimization objective

参数	数值及说明
入口总压/10⁶ Pa	1.39
入口总温/K	592.3
出口反压/10⁵ Pa	9
叶片表面	无黏绝热
优化目标	熵增最小
约束条件	出口角小于−74°

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表 4 涡轮单级的进出口条件与优化目标

Table 4. Inlet and outlet condition of the turbine stage and its optimization objective

参数	数值及说明
总压/Pa	169623
总温/K	306
背压/Pa	99741
转速/（r/min）	1500
优化目标	熵增最小
约束条件	出气角小于−70°

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表 5 离散伴随和有限差分计算单步优化梯度的CPU时间比较

Table 5. CPU time comparison of optimization gradient between discrete-adjoint method and finite difference method at one iterative step

参数	计算迭代次数	CPU时间/s
参数	计算迭代次数	静叶优化	单级优化
离散伴随	2	89.49	276.11
有限差分	40	1541.13	9510.8

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