Towards optimal aerodynamic design of vertical axis wind turbines: Impact of solidity and number of blades

The current study systematically analyzes the impact of solidity (σ) and number of blades (n) on the aerodynamic performance of 2-, 3- and 4-bladed Darrieus H-type vertical axis wind turbines (VAWTs). Solidity varies within the wide range of 0.09–0.36. A large number of operational parameters, i.e., tip speed ratio (λ), Reynolds number (Re), turbulence intensity and reduced frequency (K) are investigated to provide a deeper insight into the impact of σ and n on the dynamic loads on blades, the turbine performance and the wake. High-fidelity unsteady Reynolds-averaged Navier-Stokes (URANS) simulations, extensively validated with experiments, are employed. The results show that the turbine optimal tip speed ratio (λ_opt) is invariant to a newly-introduced parameter ‘σλ³’ regardless of the turbine geometrical and operational characteristics. In addition, a new correlation is derived to estimate λ_opt as a function of σ which can also be employed to predict the optimal σ for a turbine with a given λ. It is also found that: (i) for constant-speed urban VAWTs, which due to the low mean wind speed in the urban environment, frequently operate at moderate to high λ a relatively-low σ is optimal; (ii) an optimal VAWT is a moderately-high-solidity variable-speed rotor maintaining a relatively-low λ where due to the large blade chord length the resulting Re and K are favorably high; (iii) within the turbine optimal operational range, turbine power coefficient (C_P) is almost independent of n. The present findings support the optimal aerodynamic design of small-to large-scale VAWTs.