Unsteady computational fluid dynamics analysis and statistical performance characterisation of a three-bladed NACA 0015 H-Darrieus vertical-axis wind turbine

The optimum tip-speed ratio of a Darrieus rotor is usually reported as a sampled maximum: without uncertainty, without a transferable physical criterion, and without economic interpretation. This study addresses all three for a three-bladed NACA 0015 H-Darrieus rotor (D = 2.5 m, c = 0.4 m, σ = 0.48). All computations are transient two-dimensional URANS simulations using the SST k–ω closure with a sliding-mesh treatment of rotor rotation. The free stream is fixed at 10 m s−1 (Re ≈ 2 × 106) and five operating points spanning λ = 1.5–3.5 are generated by varying rotor speed from 12 to 28 rad s−1. Grid independence is established over three meshes; validation at λ = 2.5 gives a power coefficient (0.341 against 0.319, +6.90%) and mean torque (26.12 against 24.27 N m, +7.62%); the positive sign of both deviations is the documented signature of two-dimensional modelling, which omits tip, strut and spanwise losses. The power coefficient peaks at 0.341 at λ = 2.5, falling to 0.256 at λ = 1.5 and 0.093 at λ = 3.5, while mean torque falls monotonically from 32.62 to 5.09 N m: the power maximum arises from the product Tω, not from a torque maximum. Bayesian model selection (ΔBIC = 12.5) supports a quadratic response (R2 = 0.968), locating the optimum at λ* = 2.21 ± 0.32 with a 90%-power bandwidth of Δλ90 = 0.95. The novelty is a kinematic stall-excess ratio Λ = αmax/αss: peak power occurs at Λ ≈ 1.69, establishing the optimum as controlled exploitation of dynamic stall, not stall avoidance; inverted, it predicts λopt ≈ 2.5 from static aerofoil data alone. Rayleigh-weighted calculations show fixed-speed operation sacrifices 34% of the yield achievable with maximum-power-point tracking at a 5.5 m s−1 site but only 7% at 7.0 m s−1.