Leading-edge vortex and aerodynamic performance scaling in a simplified vertical-axis wind turbine

Abstract

Numerical analysis is conducted to investigate the aerodynamic performance and characteristics of flow around a simplified vertical-axis wind turbine (VAWT) by varying the tip-speed ratio and number of blades. The tip-speed ratios considered are λ = R Ω / U 0 = 0.8 − 2.4 , and the numbers of blades are n = 2 − 5 at the Reynolds number of R e = U 0 D / ν = 80 000 , where D ( = 2 R ) and Ω are the turbine diameter and rotation rate, respectively, U0 is the free-stream velocity, and ν is the kinematic viscosity. The primary flow feature observed around the VAWT is the formation and evolution of leading-edge vortices (LEVs) at lower tip-speed ratios of λ = 0.8 − 1.2 , which have a notable impact on the power coefficient in the upwind region. At high tip-speed ratios ( λ > 1.2 ), the LEV is not generated due to fast blade rotating speeds. Depending on the tip-speed ratio and solidity ( σ = n c / π D , where c represents the blade chord length), these LEVs are generated at different azimuthal angles and exhibit varying strengths. A modified tip-speed ratio, λ ′ = λ / π ( 1 − σ ) , proposed in the present study allows the flow structures with different λ's and n's to exhibit similarity when they are represented with λ ′ . Thus, the time-averaged power coefficient (i.e., aerodynamic performance; C ¯ P W ) is a function of λ ′ (rather than λ and n) in the range of σ = 0.2 − 0.5 considered, and its maximum occurs at λ ′ = 0.45 − 0.5 regardless of the number of blades, providing the optimal tip-speed ratio of λ opt = γ π ( 1 − σ ) , where γ = 0.45 − 0.5 . Finally, we show that C ¯ P W / ( σ λ 3 ) is a function of λ ′ .