Abstract
We consider a mathematical model of a horizontal-axis wind-energy unit in which Savonius rotors are used instead of classical blades. The Magnus force formed due to the autorotation of Savonius rotors creates a momentum supporting the rotation of the central turbine shaft. The main difference of this study from earlier investigations in this area is as follows: we take into account the variation of the blade width along the radius. In our model, the conical Savonius rotor is replaced by a pair of cylindrical rotors with different diameters, which provides the possibility to use the experimental force-momentum characteristics, taking into account the substantial variations of the velocity field along the blade’s radius. In the model, we consider the possibility to control the value of the external electric resistance in the local circuit of the unit generator. We describe the dependence of the mechanical power on the parameters of the model and construct a control strategy providing the possibility to maintain the power close to the maximum possible value under changes in the wind velocity.
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REFERENCES
X. Sun, Y. Zhuang, Y. Cao, D. Huang, and G. Wu, “A three-dimensional numerical study of the magnus wind turbine with different blade shapes,” J. Renewable Sustainable Energy 4, 063139 (2012).
N. Lopez, B. Mara, B. Mercado, L. Mercado, M. Pascual, and M. A. Promentilla, “Design of modified magnus wind rotors using computational fluid dynamics simulation and multi-response optimization,” J. Renewable Sustainable Energy 7, 063135 (2015).
G. Richmond-Navarro, W. R. Calderon-Munoz, R. LeBoeuf, and P. Castillo, “A Magnus wind turbine power model based on direct solutions using the blade element momentum theory and symbolic regression,” IEEE Trans. Sustainable Energy 8, 425–430 (2017).
R. N. Gustavo, U. S. Noel, and R. Giancarlo, “High correlation models for small scale Magnus wind turbines,” in Proceedings of the 5th 2018 International Conference on Renewable Energy: Generation and Applications (ICREGA) (IEEE, Al Ain, 2018), pp. 11–15.
S. J. Savonius, “Rotor adapted to be driven by wind or flowing water,” U. S. Patent No. 1697574 A (1929).
I. Akira, S. Kawashima, Y. Nishizawa, I. Ushiyama, and N. Komatinovic, “Study on Savonius type Magnus wind turbine,” in Proceedings of the European Wind Energy Conference and Exhibition,2007. www.researchgate.net/publication/240627785_A_Study_on_Savonius_Type_Magnus_Wind_Turbine.
M. V. Ishkhanyan, L. A. Klimina, and O. G. Privalova, “Mathematical modeling of the Magnus-effect-based wind turbine,” Mekhatron. Avtomatiz. Upravl. 19 (8), 523–528 (2018).
M. Dosaev, M. Ishkhanyan, L. Klimina, O. Privalova, and Yu. Selyutskiy, “Wind car driven by the Magnus force,” in ROMANSY 22—Robot Design, Dynamics and Control. Proceedings of the 22nd CISM IFToMM Symposium, June 25–28,2018, Rennes, France, Vol. 584 of CISM International Centre for Mechanical Sciences (Springer, Cham, 2019), pp. 189–195. https://doi.org/10.1007/978-3-319-78963-7_25
M. Z. Dosaev, L. A. Klimina, B. Ya. Lokshin, and Yu. D. Selyutskii, “On wind turbine blade design optimization,” J. Comput. Syst. Sci. Int. 53, 402 (2014).
V. G. Bach, “Untersuchungen über Savonius-Rotoren und verwandte Stromungsmaschinen,” Forsch. Gebiet Ingenieurwes. A 2, 218–231 (1931).
Y. D. Selyutskiy, L. A. Klimina, A. A. Masterova, S. S. Hwang, and C. H. Lin, “Savonius rotor as a part of complex systems,” J. Sound Vibr. 442, 1–10 (2019).
L. D. Akulenko, Ya. S. Zinkevich, D. D. Leshchenko, and A. L. Rachinskaya, “Optimal rotation deceleration of a dynamically symmetric body with movable mass in a resistant medium,” J. Comput. Syst. Sci. Int. 50, 198 (2011).
P. Jaohindy, H. Ennamiri, F. Garde, and A. Bastide, “Numerical investigation of airflow through a savonius rotor,” Wind Energy 17, 853–868 (2014).
S. Roy and A. Ducoin, “Unsteady analysis on the instantaneous forces and moment arms acting on a novel savonius-style wind turbine,” Energy Convers. Manage. 121, 281–296 (2016).
J. Thé and H. Yu, “A critical review on the simulations of wind turbine aerodynamics focusing on hybrid RANS-LES methods,” Energy 138, 257–289 (2017).
M. Z. Dosaev, V. A. Samsonov, Yu. D. Selyutskii, Wen-Lung Lu, and Ching-Huei Lu, “Bifurcation of operation modes of small wind power stations and optimization of their characteristics,” Mech. Solids 44, 214–221 (2009).
M. Z. Dosaev, V. A. Samsonov, and Yu. D. Seliutski, “On the dynamics of a small-scale wind power generator,” Dokl. Phys. 52, 493–495 (2007).
T. Hayashi, Y. Li, and Y. Hara, “Wind tunnel tests on a different phase three-stage Savonius rotor,” JSME Int. J., Ser. B 48, 9–16 (2005).
J. H. Lee, Y. T. Lee, and H. C. Lim, “Effect of twist angle on the performance of Savonius wind turbine,” Renewable Energy 89, 231–244 (2016).
N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations, 2nd ed. (Nauka, Moscow, 1974) [in Russian].
L. A. Klimina and Yu. D. Selyutskiy, “Method to construct periodic solutions of controlled second-order dynamical systems,” J. Comput. Syst. Sci. Int. 58, 503 (2019).
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This work was partially supported by the Russian Foundation for Basic Research, grant no. 18-31-20029.
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Translated by A. Muravnik
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Ishkhanyan, M.V., Klimina, L.A. Wind Turbine of the Savonius–Magnus Type with Conical Blades: Dynamics and Control. J. Comput. Syst. Sci. Int. 59, 630–638 (2020). https://doi.org/10.1134/S1064230720040085
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DOI: https://doi.org/10.1134/S1064230720040085