Aerodynamic Optimization of Radial Turbines Based on Surrogate Model of Pre-screened Strategies and DFFD Parameterization

doi:10.3969/j.issn.1004-132X.2025.10.002

Abstract

Abstract:

There were some problems such as difficult geometric control， many control variables and low optimization efficiency in aerodynamic optimization of three-dimensional complex blade surfaces of radial turbines. To solve these problems， multi-degree-of-freedom parameterization of radial turbine runner and blade multidimensional geometry were implemented based on DFFD method. Then an differential evolution algorithm assisted by surrogate models of pre-screened strategies（Pre-SADE） was introduced. Finally， a data-driven three-dimensional aerodynamic optimization platform for centripetal turbines was constructed by combining python and batch script of process automation. The platform was used to carry out the joint optimization design of flow channel-static/rotating blades for the radial turbines. The results show that after optimization， the adiabatic efficiency and mass-flow of the design point of the centripetal turbines are increased by 1.66% and 1.7% respectively， which effectively reduces the shock intensity in the guide vane channel and the shock loss on the suction surfaces of the guide vane， and the efficiency characteristics of the design rotational speed are improved in all working conditions. Finally， the method and platform may ensure the aerodynamic optimization efficiency， and effectively reduce the optimization variables and sample real evaluation times， significantly improve the optimization efficiency， and meet the rapid and elaborate optimization design requirements of radial turbines.

Key words: radial turbine, aerodynamic optimization, directly manipulated free-form deformation（DFFD）, surrogate model of pre-screened strategy, differential evolution algorithm

摘要：

针对向心涡轮三维复杂叶片曲面气动优化过程中存在的几何调控难、控制变量多、寻优效率低等问题，基于直接操纵自由变形方法对向心涡轮流道和叶片多维度几何实施多自由度参数化，并引入预筛选代理模型辅助差分进化算法（Pre-SADE），结合python和流程自动化批处理脚本构建了数据驱动的向心涡轮全三维气动优化平台。对某向心涡轮开展流道-静/转叶片联合优化设计，结果表明，优化后向心涡轮导叶通道内马赫数明显降低，动静叶吸力面激波损失和分离损失减小，向心涡轮设计点绝热效率和流量分别提高了1.66%和1.7%，设计转速全工况效率特性均有所提升。该方法和平台在保证气动优化效果的同时，可有效减少优化变量和样本真实评估次数，显著改善寻优效率，满足向心涡轮快速、精细化优化设计需求。

关键词: 向心涡轮, 气动优化, 直接操纵自由变形, 预筛选代理模型, 差分进化算法

CLC Number:

V231.3

Tianqi WANG, Jiang CHEN, Hang XIANG, Xiaofei SONG. Aerodynamic Optimization of Radial Turbines Based on Surrogate Model of Pre-screened Strategies and DFFD Parameterization[J]. China Mechanical Engineering, 2025, 36(10): 2171-2178.

王天奇, 陈江, 向航, 宋晓飞. 基于预筛选代理模型和直接操纵自由变形参数化的向心涡轮气动优化[J]. 中国机械工程, 2025, 36(10): 2171-2178.

Figures/Tables 18

Fig.1 Flow chart of the DFFD parameterization process

Fig.2 Parametric method for DFFD of a centrifugal turbine

Fig.3 Basic framework of RBNN

Fig.4 Diagram of Pre-SADE

Fig.5 Flow chart of the design optimization platform

Fig.6 Diagram of the meridional flow path of turbine

Fig.7 3D model diagram of radial turbine

Fig.8 Diagram of grid of turbine

Tab.1 Grid independence verification

网格数目/10⁴	流量/（kg·s^-1）	绝热效率
67	0.5027	0.8941
97	0.5055	0.9007
136	0.5054	0.9030
179	0.5054	0.9038
254	0.5054	0.9044

Fig.9 Diagram of flow path and blade control frame and frame control point

Tab.2 Performance comparison at design point

	压比	绝热效率	流量
原始几何	3.6140	90.30%	0.5054 kg·s
优化后几何	3.6088	91.80%	0.5142 kg·s
相对差值	$-$ 0.14%	+1.66%	+1.7%

Tab.2 Performance comparison at design point

	压比	绝热效率	流量
原始几何	3.6140	90.30%	0.5054 kg·s
优化后几何	3.6088	91.80%	0.5142 kg·s
相对差值	$-$ 0.14%	+1.66%	+1.7%

Fig.10 Comparison of turbine aerodynamic performance

Fig.11 Geometric comparison of meridian flow path and stator and rotor

Fig.12 Comparison of stator and rotor profile with different spanwise height before and after optimization

Fig.13 Comparison of relative Mach of S1 surface

Fig.14 Comparison of limited streamline at the stator and the rotor suction surface

Fig.15 Comparison of entropy contour at the stator and rotor outlet

Fig.16 Pre- and post-optimization radial distribution of circumferentially mass-averaged entropy rise at the stator vane and rotor blade exit plane

References 21

[1]	WALSH P P， FLETCHER P. Gas Turbine Performance［M］. Malden， MA： Blackwell Science， 2004.
[2]	陈明升，陈江，成金鑫，等.基于全叶片曲面参数化方法的涡轮气动优化［J］.工程热物理学报，2023，44（3）：641-653.
	CHEN Mingsheng， CHEN Jiang， CHENG Jinxin， et al. Turbine Aerodvnamic Optimization Based on Total-blade Surface Parameterization Methoo［J］. Journal of Engineering Thermophysics， 2023， 44（3）：641-653.
[3]	LI Yan， XUE Songli， REN Xiaodong. Aerodynamic Optimization of a High-expansion Ratio Organic Radial-in-flow Turbine［J］. Journal of Mechanical Science and Technology，2016，30（12）：5485-5490.
[4]	杨伟平，欧阳玉清，房兴龙，等.基于iSIGHT的大膨胀比5.0级向心涡轮多目标优化与分析［J］.推进技术，2022，43（9）：79-89.
	YANG Weiping， OUYANG Yuing， FANG Xinglong， et al. Multi-object Optimization and Analysis of 5.0 Expansion Ratio Radial Turbine Based on Isight［J］. Journal of Propulsion Technology， 2022， 43（9）：79-89.
[5]	LASSE M， ZUHEYR A， TOM V. Multidisciplinary Optimization of a Turbocharger Radial Turbine［J］. Journal of Turbomachinery， 2013，135（2）：021022.
[6]	SONG P， SUN J， WANG K， et al. Development of an Optimization Design Method for Turbomachinery by Incorporating the Cooperative Coevolution Genetic Algorithm and Adaptive Approximate Model［C］∥Turbo Expo：Power for Land， Sea， and Air. Vancouver， British Columbia， Canada， 2011， 54679：1139-1153.
[7]	SEDERBERG T W， PARRY S R. Free-form Deformation of Solid Geometric Models［J］. ACM SIGGRAPH Computer Graphics， 1986， 20：151-160.
[8]	COQUILLART S. Extended Free-form Deformation：a Sculpturing Tool for 3D Geometric Modeling［J］. Proceedings of the 17th Annual Conference on Computer Graphics and Interactive Techniques， 1990， 20（4）：187-196.
[9]	PREM K， ANGELO M， MAGNENAT T N， et al. Simulation of Facial Muscle Actions Based on Rational Free Form Deformations［J］. Computer Graphics Forum， 1992， 11（3）：59-69.
[10]	LAMOUSIN H J， WAGGENSPACK W N. NURBS-based Free-form Deformations［J］. Computer Graphics&Applications IEEE， 1994， 14（6）：59-65.
[11]	XIANG H， CHEN J. Aerothermodynamics Optimal Design of a Multistage Axial Compressor in a Gas Turbine Using Directly Manipulated Free-form Deformation［J］. Case Studies in Thermal Engineering， 2021， 26：101142.
[12]	郭艺璇，陈江，刘熠，等. 数据驱动的两级轴流涡轮多自由度气动优化设计［J］.推进技术， 2024， 45（6）：100-109.
	GUO Yixuan， CHEN Jiang， LIU Yi， et al. Aerodvnamic Optimization Desian with Multiple Dearees of Freedom for a Two-stace Axial Turbine Based on Cata-driven［J］. Journal of Propulsion Technology， 2024， 45（6）：100-109.
[13]	LIU Y， CHEN J， CHENG J， et al. Aerodynamic Optimization of Transonic Rotor Using Radial Basis Function Based Deformation and Data-driven Differential Evolution Optimizer［J］. Aerospace， 2022， 9（9）：508.
[14]	HU H， YU J， SONG Y， et al. The Application of Support Vector Regression and Mesh Deformation Technique in the Optimization of Transonic Compressor Design［J］. Aerospace Science and Technology， 2021， 112：106589
[15]	向航. 高负荷压气机气动设计与多型面整体优化探究［D］. 北京：北京航空航天大学， 2021.
	XIANG Hang. Exploring Aerodynamic Design and Multi-surface Overall Optimization of Highly Loaded Compressor［D］. Beijing：Beihang University， 2021.
[16]	池元成，方杰，饶大林，等. 自适应中心变异差分进化算法及其在涡轮叶型优化设计中的应用［J］. 航空动力学报， 2010， 25（8）：1849-1854.
	CHI Yuancheng， FANG Jie， RAO Dalin， et al. Self-adaptive Center-mutation Differential Evolution and Its Application to Shape Optimization Design of a Turbine Blade［J］. Journal of Aerospace Power， 2010， 25（8）：1849-1854.
[17]	KRIGE D G. A Statistical Approach to Some Basic Mine Valuation Problems on the Witwatersrand［J］. Journal of the Southern African Institute of Mining and Metallurgy， 1951， 52（6）：119-139.
[18]	MATHERON G. Principles of Geostatistics［J］. Economic Geology， 1963， 58（8）：1246-1266.
[19]	BUHMANN M D. Radial Basis Fimctions［J］. Acta numerica， 2000， 9：1-38
[20]	刘熠. 轴流压气机人工智能气动设计优化探索［D］. 北京：北京航空航天大学， 2023.
	LIU Yi. Exploring Artificial Intelligence Assisted Aerodynamic Design and Optimization of Axial Compressor［D］. Beijing：Beihang University， 2023.
[21]	CHENG J， YANG C， ZHAO S. A Phased Aerodynamic Optimization Method for Compressors Based on Multi-degrees-of-freedom Surface Parameterization［J］. Journal of Thermal Science， 2021， 30（6）：2071-2086.