针对风力机叶片流固耦合计算复杂，耗时量大的局限性，建立了一种风力机叶片的弱耦合计算降阶模型。采用本征正交分解（proper orthogonal decomposition,POD）方法建立流固耦合计算中空气流体方程的降阶模型，利用POD方法将流体控制方程的速度和压力等未知量进行基模态分解并用一小部分空间模态表示，对流体方程进行时间离散，在既有缩减空间上采用Galerkin投影方法获得流体控制方程的最小残差投影，构造流体方程的最小残差降阶模型。再将流体降阶模型与风力机叶片进行流固耦合计算。将该降阶模型应用于经典NREL V风力机叶片的流固耦合计算中，对比了该降阶模型和经典Galerkin法的时间离散系数；计算得到了风力机叶片的受力和变形变化特征，并与CFD结果进行了对比，结果表明了该降阶模型的正确性和有效性。最后对比了该降阶模型和全阶模型的计算效率，结果表明降阶模型的计算效率有较大幅度提高，节约了大量机时。提出的降阶模型是正确有效的，达到了准确高效进行风力机叶片流固耦合计算的目的。
Abstract
Aiming at the limitation of complex and time-consuming wind turbine blade fluid-structure coupled calculation, a reduced order model of wind turbine blade weak coupling calculation was proposed. The reduced order model of air-fluid equation in fluid-structure interaction calculation was established by using the proper orthogonal decomposition (POD) method. Base mode decomposition was done for unknown variables, such as, velocity and pressure of fluid control equation using POD method and they were represented by a small part of space modes. The fluid equation was discretized in time domain. The minimum residual projection of fluid control equation was obtained by using Galerkin projection method in the existing reduced space to construct the minimum residual reduced order model of fluid equation. Then, the fluid-structure coupled calculation was performed for the fluid reduced model and wind turbine blades. The reduced order model was applied in the fluid-structure coupled calculation of the classical NREL-V wind turbine blades, temporal discretization factors of the reduced order model and the classical Galerkin method were compared, and force and deformation varying characteristics of wind turbine blade were obtained and compared with those obtained with CFD. The results showed that the reduced order model is correct and effective; compared with the computational efficiency of the full order model, the reduced order model’s is greatly improved to save much time; the reduced order model can be used to accurately and effectively perform fluid-structure coupled calculation of wind turbine blades.
关键词
风力机叶片 /
流固耦合计算 /
本征正交分解 /
降阶模型
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Key words
wind turbine blade /
fluid-structure coupled calculation /
proper orthogonal decomposition /
reduced order model
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参考文献
［1］HEINZ J C, SRENSEN N N, ZAHLE F, et al. Vortex-induced vibrations on a modern wind turbine blade［J］. Wind Energy, 2016, 19(11): 2041-2051.
［2］SAEED E A, STEFANO M. Investigation of computational and accuracy issues in POD-based reduced order modeling of dynamic structural systems［J］. Engineering Structures, 2013, 54: 150-167.
［3］陈刚, 李跃明. 非定常流场降阶模型及其应用研究进展与展望［J］. 力学进展, 2011, 41(6)：686-701.
CHEN Gang, LI Yueming. Research progress and prospect of unsteady flow field reduction model and its application［J］. Advances in Mechanics, 2011, 41(6): 686-701.
［4］KRACK M, VON SCHEIDT L P, WALLASCHEK J, et al. Reduced order modeling based on complex nonlinear modal analysis and its application to bladed disks with shroud contact［J］. J. Eng. Gas Turbines Power, 2013, 135(10): 102-502.
［5］BENNER P, GUGERCIN S, WILLCOX K. A survey of projection-based model reduction methods for parametric dynamical systems［J］. SIAM Rev, 2015, 57(4): 483-531.
［6］胡金秀，郑保敬，高效伟. 基于特征正交分解降阶模型的瞬态热传导分析［J］. 中国科学(物理学 力学 天文学), 2015,45(1)：73-84.
HU Jinxiu, ZHENG Baojing, GAO Xiaowei. Transient heat conduction analysis based on feature orthogonal decomposition reduced order model［J］. Scientia Sinica(Physics Mechanics Astronomy), 2015,45(1): 73-84.［7］SIROVICH L. Turbulence and the dynamics of coherent structures［J］. Part I: coherent structures. Quarterly of Applied Mathematics, 1987, 45: 561-571.
［8］俞国华, 水平轴风力机叶片失速问题研究［D］. 上海:上海交通大学,2013.
［9］康伟，张家忠，李凯伦. 利用本征正交分解的非线性Galerkin降维方法［J］. 西安交通大学学报, 2011, 45(11): 58-67.
KANG Wei, ZHANG Jiazhong, LI Kailun. Nonlinear galerkin method for dimension reduction using proper orthogonal decomposition［J］. Xi’an Jiaotong University Xuebao, 2011, 45(11): 58-67.
［10］赵玲, 冉景洪, 吕计男, 等.风力机叶片非定常气动力降阶模型方法［J］. 南京航空航天大学学报, 2011, 43(5): 682-687.
ZHAO Ling, RAN Jinghong, L Jinan, et al. Reduced order model for unsteady aerodynamic of wind turbine blade［J］.Journal of Nanjing University of Aeronautics & Astronautics, 2011, 43(5): 682-687.
［11］WANG Q, WANG Z X, SONG J J, et al. Study on a new aerodynamic model of HAWT based on panel method and Reduced Order Model using Proper Orthogonal Decomposition［J］. Renewable Energy, 2012, 48: 436-447.
［12］GABRIEL D, RZVAN
瘙 塁 , NAVON I M. Comparative numerical analysis using reduced-order modeling strategies for nonlinear large-scale systems［J］. Journal of Computational and Applied Mathematics, 2017, 3(10): 32-43.
［13］GIOVANNI S, GIANLUIGI R. Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations［J］. Computers & Fluids, 2018, 173(15): 273-284.
［14］JONKMAN J, BUTTERFIELD S, MUSIAL W, et al. Definition of a 5 MW reference wind turbine for offshore system development［C］. Technical Report, 2009.
［15］SHEN W, JUN W, SOENSEN J N. Shape optimization of wind turbine blades ［J］. Wind Energy, 2009, 12: 781-803.
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