Abstract
In this paper, an optimization approach of a small horizontal axis wind turbine based on BEM theory including De Vries and Shen et al. tip loss corrections is proposed. The optimal blade geometry was obtained by maximizing the power coefficient along the blade using the optimal angle of attack and the optimal tip speed ratio. The Newton’s iterative method applied to axial induction factor was used to solve the problem. This study was conducted for a NACA4418 small wind turbine, at low wind velocity. Among the two used tip loss corrections, the De Vries correction was found to be the most suitable for this blade optimization method. The optimal design was obtained for a tip speed ratio of 5 and has recorded a power coefficient equal to 0.463.
Highlights
Introduced by Glauert in 1935 [1], blade element momentum theory (BEM) was and still is the most used mathematical model for blade optimization
The BEM theory is a combination of two theories: The first one is the axial momentum theory and the second one is the blade element theory
Glauert established an approximation to Prandtl’s tip loss correction that can be used in BEM theory calculations, and he assumed that this correction only corrects the induced velocities not the mass flux
Summary
Introduced by Glauert in 1935 [1], blade element momentum theory (BEM) was and still is the most used mathematical model for blade optimization. Glauert established an approximation to Prandtl’s tip loss correction that can be used in BEM theory calculations, and he assumed that this correction only corrects the induced velocities not the mass flux. Shen et al [6] adopted the same correction of De Vries, but he proposed a new tip loss correction that predicts better the loadings in the tip region. Another limitation of the BEM theory is that when the induction factor exceeds ac =0.5, the theory is no longer valid. An optimization of small wind turbine blade based on BEM theory combined with De Vries and Shen et al tip loss corrections is presented. The final optimal design of the blade is obtained by calculating the maximum power coefficient at different tip speed ratio
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