Mathematical modeling of a horizontal axis shrouded wind turbine. (February 2020)

• Record Type: Journal Article
• Authors: Keramat Siavash, Nemat; Najafi, G.; Tavakkoli Hashjin, Teymour; Ghobadian, Barat; Mahmoodi, Esmail
• Is Part Of: Renewable energy. Volume 146(2020)
• Page Start: 856
• Page End: 866
• Publication Date: 2020-02
• Subjects: Shrouded wind turbine -- Mathematical modeling -- Power coefficient -- Speed-up ratio -- Augmentation; Renewable energy sources -- Periodicals; Power resources -- Periodicals; Énergies renouvelables -- Périodiques; Ressources énergétiques -- Périodiques; 333.794
• DOI: 10.1016/j.renene.2019.07.022
• Languages: English
• ISSNs: 0960-1481

Abstract

Abstract: In this work, an accurate mathematical modeling of a shrouded wind turbine is presented. This work claims new equations to predict the power coefficient and speed-up ratio effects. In the proposed model, the duct-based pressure drop is considered and the velocity in the far-wake is not suggested to be the same as the bare wind turbines. The mathematical model revealed that any shroud with an optimum design hardly can provide a C P = 1 for a wind turbine. However, using a properly designed duct, C P = 0.93 can be reached practically. This work also reveals that the speed-up ratio should be 0.6 < γ < 1.7 ; in order to exceed Betz limit and work in the optimum condition. The developed model presents a clear relation between the duct efficiency ( η d ), duct exit area ratio ( β ) and its pressure loss coefficient ( K p d ). Finally, a practical limitation for duct parameters is suggested in order to exceed the Betz limit. Further, a physical assumption is applied to approximate the power coefficient, which indicated that the power coefficient growth never can reach the speed-up ratio scale. Highlights: Ducted wind turbine's power coefficient can't reach 1 practically. A non-optimized ducted wind turbine can't exceed CP = 0.8. A well-made ducted wind turbine can reach CP = 0.93. The duct efficiency is more effective than its exit area ratio.