Efficient Aerodynamic Optimization Method for Turbine Blades Based on Multi-degree-of-freedom Parameterized Dimensionality Reduction

doi:10.3969/j.issn.1004-132X.2026.02.001

Abstract

Abstract:

In view of the high design dimension and difficulty in constructing surrogate models in the aerodynamic optimization of three-dimensional turbine blades， a multi-degree-of-freedom parameterized dimensionality reduction method was proposed to construct an efficient optimization framework， that integrated DFFD and PCA， and combined the pre-screened surrogate model assisted differential evolution （Pre-SADE） algorithm. Taking a small gas turbine as the object， a snapshot set was generated through experimental design， and the 36-dimensional DFFD design space was mapped to the 10-dimensional basis modal coefficient space. A concise and effective surrogate model was established in the dimensionality reduction space and rapid optimization was completed. The results show that the proposed method significantly reduces the shock wave intensity and aerodynamic loss while improving the design point flow （+0.46%） and isentropic efficiency （+3.191%）， and the optimization time is reduced by 24.58%. The study verifies the intuitiveness， effectiveness and optimization efficiency improvement advantages of this dimensionality reduction method in high-dimensional design problems， providing a more efficient and low-cost solution for blade aerodynamic optimization.

Key words: principal component analysis（PCA）, direct manipulation free-form deformation （DFFD）method, parameterized dimensionality reduction, turbine blade aerodynamic optimization

摘要：

针对涡轮三维叶片气动优化中设计维度高、代理模型构建困难等问题，提出一种融合直接操纵自由变形（DFFD）与主成分分析（PCA）的多自由度参数化降维方法，并结合预筛选代理模型辅助差分进化（Pre-SADE）算法构建高效优化框架。以某小型燃气轮机为对象，通过实验设计生成快照集合，将36维DFFD设计空间映射至10维基模态系数空间，在降维空间内建立简洁有效的代理模型并完成快速优化。结果表明，所提方法在提高设计点流量（+0.46%）与等熵效率（+3.191%）的同时，显著减弱激波强度与气动损失，优化耗时缩短24.58%。研究结果验证了该降维方法在高维设计问题中的直观性、有效性与优化效率提升优势，为叶片气动优化提供了更高效、低成本的解决方案。

关键词: 主成分分析, 直接操纵自由变形方法, 参数化降维, 涡轮叶片气动优化

CLC Number:

V231.3

HUANG Pengfei, CHEN Jiang, CHENG Jinxin, LI Bin, XIANG Hang. Efficient Aerodynamic Optimization Method for Turbine Blades Based on Multi-degree-of-freedom Parameterized Dimensionality Reduction[J]. China Mechanical Engineering, 2026, 37(2): 255-263.

黄鹏飞, 陈江, 成金鑫, 李斌, 向航. 基于多自由度参数化降维方法的涡轮叶片高效气动优化[J]. 中国机械工程, 2026, 37(2): 255-263.

Figures/Tables 21

Fig.1 DFFD control points， frame points and deformation

Fig.2 DFFD parameterization process

Fig.3 PCA dimensionality reduction and reconstruction flow chart

Fig.4 Some of the geometries generated in the experimental design

Fig.5 Pre-SADE flow chart

Fig.6 Turbine geometric model

Tab.1 Turbine design parameters

设计参数	S₁	R₁
内径/mm	72.7	68.4
外径/mm	85.7	85.7
进口相对气流角/（°）	0	34.3
出口相对气流角/（°）	61.3	58.0
叶片数	38	58
转速/（r·min $- 1$ ）	0	54 000
流量/（kg·s $- 1$ ）	1.9632±0.0038

Tab.1 Turbine design parameters

设计参数	S₁	R₁
内径/mm	72.7	68.4
外径/mm	85.7	85.7
进口相对气流角/（°）	0	34.3
出口相对气流角/（°）	61.3	58.0
叶片数	38	58
转速/（r·min $- 1$ ）	0	54 000
流量/（kg·s $- 1$ ）	1.9632±0.0038

Fig.7 Grid topology

Tab.2 Grid independence verification

网格数量/10⁴	落压比	流量/（kg·s $- 1$ ）	等熵效率/%
137.1212	2.8837	1.9646	84.710
167.8328	2.8866	1.9636	84.808
209.5852	2.8743	1.9644	85.190
238.2220	2.8713	1.9665	85.192
270.6436	2.8711	1.9665	85.190

Tab.2 Grid independence verification

网格数量/10⁴	落压比	流量/（kg·s $- 1$ ）	等熵效率/%
137.1212	2.8837	1.9646	84.710
167.8328	2.8866	1.9636	84.808
209.5852	2.8743	1.9644	85.190
238.2220	2.8713	1.9665	85.192
270.6436	2.8711	1.9665	85.190

Fig.8 Aerodynamic optimization framework

Fig.9 Displacement direction of blade control point

Fig.10 Fundamental modes of each order

Tab.3 Decision variable boundaries

决策变量	下边界	上边界
$α 1$	0.03	0.04
$α 2$	$-$ 0.08	0.10
$α 3$	$-$ 0.10	0.10
$α 4$	$-$ 0.08	0.09
$α 5$	$-$ 0.10	0.14
$α 6$	0.02	0.04
$α 7$	$-$ 0.09	0.10
$α 8$	$-$ 0.10	0.10
$α 9$	$-$ 0.08	0.09
$α 10$	$-$ 0.10	0.10

Tab.3 Decision variable boundaries

决策变量	下边界	上边界
$α 1$	0.03	0.04
$α 2$	$-$ 0.08	0.10
$α 3$	$-$ 0.10	0.10
$α 4$	$-$ 0.08	0.09
$α 5$	$-$ 0.10	0.14
$α 6$	0.02	0.04
$α 7$	$-$ 0.09	0.10
$α 8$	$-$ 0.10	0.10
$α 9$	$-$ 0.08	0.09
$α 10$	$-$ 0.10	0.10

Fig.11 Comparison of optimization results using different parameterization methods

Tab.4 Performance comparison of turbine before and after aerodynamic optimization

	流量/（kg·s $- 1$ ）	落压比	等熵效率/%
设计原型	1.9644	2.8743	85.190
单一参数化优化	1.9859	2.9931	87.765
参数化降维优化	1.9734	2.8289	88.381

Tab.4 Performance comparison of turbine before and after aerodynamic optimization

	流量/（kg·s $- 1$ ）	落压比	等熵效率/%
设计原型	1.9644	2.8743	85.190
单一参数化优化	1.9859	2.9931	87.765
参数化降维优化	1.9734	2.8289	88.381

Fig.12 Turbine design speed full operating condition characteristic line

Fig.13 Optimized front and rear blade geometry

Fig.14 Turbine blade tip， blade center and blade root profiles before and after optimization

Fig.15 Relative Mach number distribution cloud diagram of each S1 flow surface of the turbine before and after optimization

Fig.16 Extreme streamline distribution of turbine suction surface before and after optimization

Fig.17 Entropy distribution cloud diagram of turbine guide vane and moving blade outlet before and after optimization

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