A nonlinear model for aerodynamic configuration of wake behind horizontal-axis wind turbine

doi:10.1007/s10483-019-2536-9

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (9): 1313-1326.doi: https://doi.org/10.1007/s10483-019-2536-9

• Articles • Previous Articles Next Articles

A nonlinear model for aerodynamic configuration of wake behind horizontal-axis wind turbine

Deshun LI^1,2,3, Tao GUO^1,2,3, Rennian LI^1,2,3, Congxin YANG^1,2,3, Zhaoxue CHENG^1,2,3, Ye LI^4,5,6,7, Wenrui HU⁸

1. College of Energy and Power Engineering, Lanzhou University of Technology, Lanzhou 730050, China;
2. Gansu Provincial Technology Centre for Wind Turbines, Lanzhou 730050, China;
3. Gansu Provincial Key Laboratory of Fluid Machinery and Systems, Lanzhou 730050, China;
4. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;
5. State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;
6. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai Jiao Tong University, Shanghai 200240, China;
7. Key Laboratory of Hydrodynamics(Ministry of Education), Shanghai Jiao Tong University, Shanghai 200240, China;
8. Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China

Received:2019-01-31 Revised:2019-06-08 Online:2019-09-01 Published:2019-09-10
Contact: Rennian LI, Ye LI, Zhaoxue CHENG E-mail:lirn@lut.cn;ye.li@sjtu.edu.cn;1040809802@qq.com
Supported by:
Project supported by the National Basic Research Program of China (No. 2014CB046201) and the National Natural Science Foundation of China (Nos. 51766009, 51566011, and 51479114)

Abstract

Abstract: Determination of the aerodynamic configuration of wake is the key to analysis and evaluation of the rotor aerodynamic characteristics of a horizontal-axis wind turbine. According to the aerodynamic configuration, the real magnitude and direction of the onflow velocity at the rotor blade can be determined, and subsequently, the aerodynamic force on the rotor can be determined. The commonly employed wake aerodynamic models are of the cylindrical form instead of the actual expanding one. This is because the influence of the radial component of the induced velocity on the wake configuration is neglected. Therefore, this model should be called a "linear model". Using this model means that the induced velocities at the rotor blades and aerodynamic loads on them would be inexact. An approximately accurate approach is proposed in this paper to determine the so-called "nonlinear" wake aerodynamic configuration by means of the potential theory, where the influence of all three coordinate components of the induced velocity on wake aerodynamic configuration is taken into account to obtain a kind of expanding wake that approximately looks like an actual one. First, the rotor aerodynamic model composed of axial (central), bound, and trailing vortexes is established with the help of the finite aspect wing theory. Then, the Biot-Savart formula for the potential flow theory is used to derive a set of integral equations to evaluate the three components of the induced velocity at any point within the wake. The numerical solution to the integral equations is found, and the loci of all elementary trailing vortex filaments behind the rotor are determined thereafter. Finally, to formulate an actual wind turbine rotor, using the nonlinear wake model, the induced velocity everywhere in the wake, especially that at the rotor blade, is obtained in the case of various tip speed ratios and compared with the wake boundary in a neutral atmospheric boundary layer. Hereby, some useful and referential conclusions are offered for the aerodynamic computation and design of the rotor of the horizontal-axis wind turbine.

Key words: nonlinear wake aerodynamic model, vortex-induced velocity, integral equation of vortex-induced velocity, horizontal-axis wind turbine

2010 MSC Number:

Deshun LI, Tao GUO, Rennian LI, Congxin YANG, Zhaoxue CHENG, Ye LI, Wenrui HU. A nonlinear model for aerodynamic configuration of wake behind horizontal-axis wind turbine. Applied Mathematics and Mechanics (English Edition), 2019, 40(9): 1313-1326.

TrendMD

References

[1] GOURIERES, D. L. Wind power plants. Theory and Design, Pergamon Press, Oxford (1982)
[2] SPERA, S. D. A. Wind Turbine Technology:Fundamental Concepts of Wind Turbine Engineering, ASME Press, New York (1994)
[3] EGGLESTON, D. M. and STODDART, F. S. Wind Turbine Engineering Design, Van Nostrand, New York (1987)
[4] BURTON, T., SHARPE, D., and JENKINS, N. Wind Energy Handbook, John Wiley & Sons, Chichester (2001)
[5] CHENG, Z. X., LI, R. N., YANG, C. X., and HU, W. R. Criterion of aerodynamic performance of large-scale offshore horizontal-axis wind turbines. Applied Mathematics and Mechanics (English Edition), 31(1), 13-20(2010) https://doi.org/10.1007/s10483-010-0102-2
[6] CHENG, Z. X., YE, Z. Q., CHEN, J. Y., and BAI, S. B. Aerodynamic optimization for the rotor of horizontal-axis wind machine. Proceedings of International Conference on New and Renewable Energy, 306-312(1990)
[7] YE, Z. Q., CHENG, Z. X., CHEN, J. Y., and BAI, S. B. Aerodynamic optimum design procedure and program for the rotor of a horizontal-axis wind turbine. Wind Engineering and Industrial Aerodynamics, 39, 179-186(1992)
[8] MADSEN, H. A. and RASMUSSEN, F. A. Near wake model for trailing vorticity compared with the blade element momentum theory. Wind Energy, 7, 325-341(2004)
[9] KERWIN, J. and LEE, C. S. Prediction of a steady and unsteady marine propeller performance by numerical lifting-surface theory. SNAME Transactions, 86, 218-253(1978)
[10] BALTAZAR, J., FALCAO DE CAMPOS, J. A. C., and BOSSCHERS, J. Open-water thrust and torque predictions of a ducted propeller system with a panel method. International Journal of Rotating Machinery, 2012(2), 67-74(2012)
[11] EPPS, B. P. and KIMBALL, R. W. Unified rotor lifting line theory. Journal of Ship Research, 57(4), 181-201(2013)
[12] MENÉNDEZ, A., DAVID, H., and KINNAS, S. A. On fully aligned lifting line model for propellers:an assessment of Betz condition. Journal of Ship Research, 58(3), 130-145(2014)
[13] JOSÉ, A. C. and FALCÃO, D. C. Hydrodynamic power optimization of a horizontal axis marine current turbine with lifting line theory. The Seventeenth International Offshore and Polar Engineering Conference, International Society of Offshore and Polar Engineers, Lisbon (2007)
[14] MELO, D. B., BALTAZAR, J., and FALCAO DE CAMPOS, J. A. C. A numerical wake alignment method for horizontal axis wind turbines with the lifting line theory. Journal of Wind Engineering and Industrial Aerodynamics, 174, 382-390(2018)
[15] MARGERIT, D. and BRANCHER, J. P. Asymptotic expansions of the Biot-Savart law for a slender vortex with core variation. Journal of Engineering Mathematics, 40(3), 279-313(2001)
[16] JOHNSON, W. Recent developments in rotary-wing aerodynamic theory. AIAA Journal, 24(8), 1219-1244(1986)
[17] LI, D. S., GUO, T., LI, Y. R., HU, J. S., ZHENG, Z., LI, Y., DI, Y. J., HU, W. R., and LI, R. N. Interaction between the atmospheric boundary layer and a standalone wind turbine in Gansu-part I:field measurement. Science China Physics, Mechanics and Astronomy, 61, 94711(2018)
[18] ZHENG, Z., GAO, Z. T., LI, D. S., LI, R. N., LI, Y, HU, Q. H., and HU, W. R. Interaction between the atmospheric boundary layer and a stand-alone wind turbine in Gansu-part Ⅱ:numerical analysis. Science China Physics, Mechanics and Astronomy, 61, 94712(2018)

A nonlinear model for aerodynamic configuration of wake behind horizontal-axis wind turbine

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 1

Recommended Articles

Metrics

Comments