resulting in high computational costs. An optimization method based on surrogate model was proposed to replace CFD calculations
thereby conducting optimization of dynamic stall characteristics of airfoils. The surrogate model was constructed using the Gaussian process regression model
and the accuracy of the model was continuously improved by adopting the point addition criterion. The surrogate model was verified using the normalized root mean square error
and the feasibility of the optimization framework was verified using the S809 airfoil as the research object. Results show that compared with the baseline airfoil
the average drag coefficient and moment coefficient of the optimized airfoil are reduced by 32.87% and 23.74%
respectively
the aerodynamic performence was significantly improved. And the change in the aerodynamic shape accelerates the velocity recovery of the suction surface near the wall and reduces the boundary layer thickness.
LEE J, ZHAO Feng. Global wind report 2022[R]. Brussels, Belgium: Global Wind Energy Council, 2022.
LI Li, LIN Jian, WU Nianyuan, et al. Review and outlook on the international renewable energy development[J]. Energy and Built Environment, 2022, 3(2): 139-157.
YAO Shulong, CHETAN M, GRIFFITH D T, et al. Aero-structural design and optimization of 50 MW wind turbine with over 250-m blades[J]. Wind Engineering, 2022, 46(1): 273-295.
CHEN Jincheng, WANG Feng, STELSON K A. A mathematical approach to minimizing the cost of energy for large utility wind turbines[J]. Applied Energy, 2018, 228: 1413-1422.
李羽, 柳灿, 连波, 等. 基于强迫振动和自由振动的风力机翼型涡激振动数值研究[J]. 动力工程学报, 2024, 44(2): 270-276.LI Yu, LIU Can, LIAN Bo, et al. Numerical study on vortex-induced vibration of wind turbine airfoil via prescribed vibration and free vibration[J]. Journal of Chinese Society of Power Engineering, 2024, 44(2): 270-276.
ZHU Chengyong, FENG Yi, SHEN Xiang, et al. Effects of the height and chordwise installation of the vane-type vortex generators on the unsteady aerodynamics of a wind turbine airfoil undergoing dynamic stall[J]. Energy, 2023, 266: 126418.
李根, 缪维跑, 李春, 等. 尾缘主动式凹槽-襟翼垂直轴风力机气动性能研究[J]. 动力工程学报, 2021, 41(6): 511-518.LI Gen, MIAO Weipao, LI Chun, et al. Aerodynamic performance of a vertical axis wind turbine with active dimple-flaps at the trailing edge[J]. Journal of Chinese Society of Power Engineering, 2021, 41(6): 511-518.
WANG Haipeng, JIANG Xiao, CHAO Yun, et al. Effects of leading edge slat on flow separation and aerodynamic performance of wind turbine[J]. Energy, 2019, 182: 988-998.
LIU Jiaqi, CHEN Rongqian, QIU Ruofan, et al. Study on dynamic stall control of rotor airfoil based on coflow jet[J]. International Journal of Aerospace Engineering, 2020, 2020(1): 8845924.
季康, 李春, 阳君, 等. 尾缘襟翼动态气动特性与控制策略研究[J]. 太阳能学报, 2017, 38(7): 1912-1920.JI Kang, LI Chun, YANG Jun, et al. Research on dynamic aerodynamic performance and flow control of airfoil with flap[J]. Acta Energiae Solaris Sinica, 2017, 38(7): 1912-1920.
邬晓敬, 张伟伟, 肖华, 等. 一种基于响应面的翼型鲁棒优化设计方法[J]. 工程力学, 2015, 32(2): 250-256.WU Xiaojing, ZHANG Weiwei, XIAO Hua, et al. A robust aerodynamic design for airfoil based on response surface method[J]. Engineering Mechanics, 2015, 32(2): 250-256.
HAN Zhonghua, XU Chenzhou, ZHANG Liang, et al. Efficient aerodynamic shape optimization using variable-fidelity surrogate models and multilevel computational grids[J]. Chinese Journal of Aeronautics, 2020, 33(1): 31-47.
陈晨铭, 郭雪岩, 常林森. 基于BP神经网络代理模型的翼型优化及领域自适应研究[J]. 动力工程学报, 2022, 42(7): 657-663.CHEN Chenming, GUO Xueyan, CHANG Linsen. Research on airfoil optimization and domain adaptation based on BP neural network surrogate model[J]. Journal of Chinese Society of Power Engineering, 2022, 42(7): 657-663.
喻伯平, 李高华, 谢亮, 等. 基于代理模型的旋翼翼型动态失速优化设计[J]. 浙江大学学报(工学版), 2020, 54(4): 833-842.YU Boping, LI Gaohua, XIE Liang, et al. Dynamic stall optimization design of rotor airfoil based on surrogate model[J]. Journal of Zhejiang University (Engineering Science), 2020, 54(4): 833-842.
LIU Pengyin, YU Guohua, ZHU Xiaocheng, et al. Unsteady aerodynamic prediction for dynamic stall of wind turbine airfoils with the reduced order modeling[J]. Renewable Energy, 2014, 69: 402-409.
JING Simeng, ZHAO Qijun, ZHAO Guoqing, et al. Multi-objective airfoil optimization under unsteady-freestream dynamic stall conditions[J]. Journal of Aircraft, 2023, 60(2): 293-309.
GHARALI K, JOHNSON D A. Numerical modeling of an S809 airfoil under dynamic stall, erosion and high reduced frequencies[J]. Applied Energy, 2012, 93: 45-52.
BUTTERFIELD C P, SIMMS D, HUYER S. Recent results from data analysis of dynamic stall on wind turbine blades[R]. Golden, CO, USA: National Renewable Energy Laboratory, 1992.
RAMSAY R F, HOFFMANN M J, GREGOREK G M. Effects of grit roughness and pitch oscillations on the S809 airfoil[R]. Golden, CO, USA: National Renewable Energy Laboratory, 1995.
KULFAN B M. Universal parametric geometry representation method[J]. Journal of Aircraft, 2008, 45(1): 142-158.
SHI Lei, YANG R J, ZHU Ping. A method for selecting surrogate models in crashworthiness optimization[J]. Structural and Multidisciplinary Optimization, 2012, 46(2): 159-170.
LIO W H, LI Ang, MENG Fanzhong. Real-time rotor effective wind speed estimation using Gaussian process regression and Kalman filtering[J]. Renewable Energy, 2021, 169: 670-686.
RASMUSSEN C E, WILLIAMS C K I. Gaussian processes for machine learning[M]. Cambridge, MA, USA: MIT Press, 2006.
JONES D R, SCHONLAU M, WELCH W J. Efficient global optimization of expensive black-box functions[J]. Journal of Global Optimization, 1998, 13(4): 455-492.
BELAMADI R, DJEMILI A, ILINCA A, et al. Aerodynamic performance analysis of slotted airfoils for application to wind turbine blades[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2016, 151: 79-99.
CORKE T C, THOMAS F O. Dynamic stall in pitching airfoils: aerodynamic damping and compressibility effects[J]. Annual Review of Fluid Mechanics, 2015, 47: 479-505.
ZHONG Junwei, LI Jingyin, GUO Penghua, et al. Dynamic stall control on a vertical axis wind turbine aerofoil using leading-edge rod[J]. Energy, 2019, 174: 246-260.