INFLUENCE OF VORTEX CORE SIZE ON AERODYNAMIC CALCULATION OF WIND TURBINE IN FREE VORTEX WAKE METHOD1)

doi:10.6052/0459-1879-18-440

Abstract

Abstract:

The vortex core size in the vortex core model is very important for the accurate prediction of aerodynamic characteristics of wind turbines by the free vortex wake (FVW) method. The vortex core size includes the initial radius of the vortex core and the radius variation due to the viscous dissipation effect. In the FVW method, to solve the convection equation of the vortex filaments numerically, the three-step and third-order predictor-corrector scheme was used to approximate the derivatives. The classical Lamb-Oseen model was adopted as the vortex core model in which the effects of viscous diffusion and stretching were taken into account. Firstly, the initial radius of the vortex core was determined through the analysis of the airload and the mean value of the tip vortex vorticity. Secondly, the empirical constant that reflects the increase of the vortex core radius was determined based on the tip vortex dissipation characteristics. Finally, the effect of vortex core size on the shape of tip vortex line was analysed to further verify the influence of the initial radius of the vortex core and the empirical constant that reflects the increase of the vortex core radius on aerodynamic calculation of wind turbine. The results show that when the initial vortex core size is greater than 50% of the chord length, the FVW model can produce a stabler convergent wake system and can accurately predict the blade airload. About 60% to 70% of the chord length is recommended as the initial vortex core size in order to take into account both the airload prediction and the wake dissipation characteristics. Different empirical constants of the viscous dissipation effect correspond to different initial vortex core sizes. The blade airload and the wake geometry are mainly affected by the initial vortex core size, rather than the empirical constant of the viscous dissipation effect. However, the empirical constant mainly affects the vortex disspiation characteristics in the downstream wake field.

Key words: wind turbine, free vortex wake, aerodynamic characteristics, vortex core size, viscous dissipation effect

CLC Number:

O355
TK89

Xu Bofeng, Liu Bingbing, Feng Junheng, Zuo Lu. INFLUENCE OF VORTEX CORE SIZE ON AERODYNAMIC CALCULATION OF WIND TURBINE IN FREE VORTEX WAKE METHOD¹⁾[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1530-1537.

Figures/Tables 15

Fig. 1 Schematic diagram of vortex element solution

Fig. 2 The power coefficient along with the initial vortex core size at different wind speeds

Fig. 3 Development of dimensionless vorticity levels of the blade tip vortex along with the wake age angle

Fig. 4 The vortex core radius along with wake age angle under different values of $a_{1}$

Fig. 5 The variation of low-speed shaft torque along with the wind speed under different values of $a_{1}$

Fig. 6 Development of dimensionless vorticity levels of the blade tip vortex along with the wake age angle under different values of $a_{1}$($r_{0} = 0.6 c$)

Fig. 7 Development of dimensionless vorticity levels of the blade tip vortex along with the wake age angle under different values of $a_{1}$($r_{0} = 0.7 c)$

Fig. 8 Experimental result of streamlines in blade tip region with the wind speed subtracted from the local velocity[32]

Fig. 9 Computational result of streamlines in blade tip region with the wind speed subtracted from the local velocity ($r_{0} = 0.6 c$, $a_{1 } = 0.002$)

Fig. 10 Computational result of streamlines in blade tip region with the wind speed subtracted from the local velocity ($r_{0} = 0.7 c$, $a_{1 } = 0.001$)

Fig. 11 Computational result of streamlines in blade tip region with the wind speed subtracted from the local velocity ($r_{0} = 0.6 c$, $a_{1 } = 0.000,2$)

Fig. 12 Computational result of streamlines in blade tip region with the wind speed subtracted from the local velocity ($r_{0} = 0.4 c$, $a_{1 } = 0.000,2$)

Fig. 13 Vorticity result of tip vortex ($r_{0} = 0.6 c$, $a_{1 } = 0.002$)

Fig. 14 Vorticity result of tip vortex ($r_{0} = 0.6 c$, $a_{1 } = 0.000,2$)

Fig. 15 Vorticity result of tip vortex ($r_{0} = 0.4 c$, $a_{1 } = 0.000,2$)

References 33

[1]	Xu BF, Feng JH, Wang TG , et al. Application of a turbulent vortex core model in the free vortex wake scheme to predict wind turbine aerodynamics. Journal of Renewable and Sustainable Energy, 2018,10(2):023303
[2]	Xu BF, Wang TG, Yuan Y , et al. A simplified free vortex wake model of wind turbines for axial steady conditions. Applied Sciences. 2018,8(6):866
[3]	Su K, Bliss D . A novel hybrid free-wake model for wind turbine performance and wake evolution. Renewable Energy, 2019,131:977-992
[4]	左潞, 唐植懿, 许波峰等. 涡模型对风力机气动特性的影响研究. 可再生能源, 2016,34(10):1491-1496
	( Zuo Lu, Tang Zhiyi, Xu Bofeng , et al. Investigation of effects of vortex models on wind turbine aerodynamic characteristics. Renewable Energy Resources, 2016,34(10):1491-1496 (in Chinese))
[5]	吕品, 廖明夫, 王四季等. 基于升力面和全自由涡尾迹的风力机气动模型及其参数影响. 机械设计与制造, 2017,3:52-55
	( Lü Pin, Liao Mingfu, Wang Siji , et al. Predictions of wind turbine aerodynamics based on lifting surface theory with fully free vortex and the influence of the parameters. Machinery Design and Manufacture, 2017,3:52-55 (in Chinese))
[6]	Vatistas GH, Kozel V, Minh W . A simpler model for concentrated vortices. Experiments in Fluids, 1991,11(1):73-76
[7]	Scully MP . Computation of helicopter rotor wake geometry and its influence on rotor harmonic airloads. [PhD Thesis]. Cambridge: Massachusetts Institute of Technology, 1975
[8]	Lamb H. Hydrodynamics. Cambridge: Cambridge University Press, 1932
[9]	Xu BF, Wang TG, Yuan Y , et al. Unsteady aerodynamic analysis for offshore floating wind turbines under different wind conditions. Philosophical Transactions of the Royal Society A, 2015,373(2035):20140080
[10]	Tang D, Bao SY, Luo LJ , et al. Study on the aeroelastic responses of a wind turbine using a coupled multibody-FVW method. Energy, 2017,141:2300-2313
[11]	张蕴宁, 叶舟, 李春 . 基于改进型升力面自由涡尾迹法的风力机性能研究. 太阳能学报, 2017,38(5):1316-1323
	( Zhang Yunning, Ye Zhou, Li Chun . Wind turbine aerodynamic performance simulation based on improved lifting surface freewake method. Acta Energiae Solaris Sinica, 2017,38(5):1316-1323 (in Chinese))
[12]	Sant T, del Campo V, Micallef D , et al. Evaluation of the lifting line vortex model approximation for estimating the local blade flow fields in horizontal-axis wind turbines. Journal of Renewable and Sustainable Energy, 2016,8(2):023302
[13]	Gupta S, Leishman JG . Validation of a free vortex wake model for wind turbine in yawed flow//Collection of Technical Papers-44th AIAA Aerospace Sciences Meeting, 2006,7:4529-4543
[14]	Yu W , Ferreira CS, van Kuik G, et al. Verifying the blade element momentum method in unsteady,radially varied, axisymmetric loading using a vortex ring model. Wind Energy, 2017,20:269-288
[15]	Basuno B . A prescribed wake model for vertical axis wind turbines. [PhD Thesis]. Glasgow: University of Glasgow, 1992
[16]	Landahl MT . Roll-up model for rotor wake vortices. ASRL-TR-194-4, Massachusetts Institute of Technology, 1981
[17]	Miller RH . Methods for rotor aerodynamic and dynamic analysis. Progress in Aerospace Sciences, 1985,22(2):113-160
[18]	Dobrev I, Maalouf B, Troldborg N , et al. Investigation of the wind turbine vortex structure//14th Int Symp on Applications of the Laser Techniques to Fluid Mechanics, Lisbon, 2008
[19]	Bhagwat MJ, Leishman JG . Correlation of helicopter tip vortex measurements. AIAA Journal, 2000,38(2):301-308
[20]	Bhagwat MJ, Leishman JG . Generalized viscous vortex core models for application to free-vortex wake and aeroacoustic calculations. American Helicopter Society 58th Annual National Forum Proceedings, Montreal,Canada, June 11-13, 2002
[21]	林孟达, 崔桂香, 张兆顺等. 飞机尾涡演变及快速预测的大涡模拟研究. 力学学报, 2017,49(6):1185-1200
	( Lin Mengda, Cui Guixiang, Zhang Zhaoshun , et al. Large eddy simulation and rapid prediction of aircraft tail vortex Evolution. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(6):1185-1200 (in Chinese))
[22]	Gupta S . Development of a time-accutate viscous lagrangian vortex wake model for wind turbine application. [PhD thesis]. Maryland: University of Maryland, 2006
[23]	Chkir S . Unsteady loads evaluation for a wind turbine rotor using free wake method. Energy Procedia, 2011,6:777-785
[24]	Bhagwat M, Leishman JG . Stability, consistency and convergence of time marching free-vortex rotor wake algorithms. Journal of the American Helicopter Society, 2001,46(1):59-71
[25]	Gupta S, Leishman JG . Accuracy of the induced velocity from helicoidal vortices using straight-line segmentation. AIAA Journal, 2005,43(1):29-40
[26]	Elgammi M, Sant T . A new stall delay algorithm for predicting the aerodynamics loads on wind turbine blades for axial and yawed conditions. Wind Energy, 2017,20:1645-1663
[27]	李国强, 张卫国, 陈立等. 风力机叶片翼型动态试验技术研究. 力学学报, 2018,50(4):751-765
	( Li Guoqiang, Zhang Weiguo, Chen Li , et al. Research on dynamic test technology for wind turbine blade airfoil. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(4):751-765(in Chinese))
[28]	Li Y, Calisal SM . A discrete vortex method for simulating a stand-alone tidal current turbine: Modeling and validation. Journal of Offshore Mechanics and Arctic Engineering, 2010,132(3):1102-1110
[29]	Ananthan S, Leishman JG, Ramasamy M . The role of filament stretching in the free-vortex modeling of rotor wakes. Journal of the American Helicopter Society, 2004,49(2):176-191
[30]	Hand MM, Simms DA, Fingersh LJ , et al. Unsteady aerodynamics experiment phase VI: Wind tunnel test configurations and available data campaign. Technical Report NREL/TP-500-29955, National Renewable Energy Laboratory, Golden, 2001
[31]	高天达, 孙姣, 范赢等. 基于PIV技术分析颗粒在湍流边界层中的行为. 力学学报, 2019,51(1):103-110
	( Gao Tianda, Sun Jiao, Fan Ying , et al. Analysis of particle behavior in turbulent boundary layer based on PIV technique. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):103-110(in Chinese))
[32]	Xiao JP, Wu J, Chen L , et al. Particle image velocimetry (PIV) measurements of tip vortex wake structure of wind turbine. Applied Mathematics and Mechanics, 2011,32(6):729-73
[33]	Simms D, Schreck S, Hand M , et al. NREL unsteady aerodynamics experiment in the NASA-Ames wind tunnel: A comparison of predictions to measurements. NREL/TP--500-29494, National Renewable Energy Laboratory, Golden, 2001

INFLUENCE OF VORTEX CORE SIZE ON AERODYNAMIC CALCULATION OF WIND TURBINE IN FREE VORTEX WAKE METHOD¹⁾

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