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

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=RΩ/U0=0.8−2.4, and the numbers of blades are n=2−5 at the Reynolds number of Re=U0D/ν=80 000, where D(=2R) 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=nc/πD, 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¯PW) 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 λopt=γπ(1−σ), where γ=0.45−0.5. Finally, we show that C¯PW/(σλ3) is a function of λ′.