Hub ratio of horizontal axis wind turbine rotors for optimal performance

Abstract

Manufacturers of large horizontal axis wind turbines (HAWTs) have produced wind turbines with hub ratios ranging mostly from 1.5% to 3.5%, but some exceed 9% and prototypes have been tested with hub ratios over 18%. The hub ratios of wind turbines below 100 kW range from 1% to 12%. This study investigates the effect of hub ratio on the peak performance of ideal HAWT rotors. The performance of two sets of rotors (standard design vs. adapted design) with varying hub ratios (10%, 15%, 20% and 25%) were compared against the performance of a 5% hub ratio rotor of standard design. Computational fluid dynamics (CFD) simulation and physical testing produced performance data. Size of models (280 mm rotor) necessitated physical testing and simulation within a laminar flow regime. Testing utilised vertical relative velocity of rotors into a stationary body of water. A similar CFD simulation case study of a 30 m diameter HAWT rotor in air provides further results - applicable to a fully turbulent flow regime. The Blade Element Momentum Method (BEMM) in its standard form, as well as with an adaption, was used to predict performance of the rotors and to generate blade chord and pitch angles for creation of virtual models for CFD simulation and 3D-printed models for physical testing of the 280 mm rotors. A large hub in a HAWT rotor accelerates the air close to the hub. If this effect is included in the rotor design then performance is enhanced. The classical BEMM does not take this effect into account and an adaption to the BEMM was created so that the performance benefit of a larger hub could be included in the ‘adapted’ rotor designs. The adaption uses potential flow theory to predict an axial velocity gradient along the span of the blade in the rotor plane. This axial velocity gradient replaces the uniform axial velocity that is assumed across the entire rotor plane in the classical BEMM. The adaption also takes rotor ‘spillage’ losses into account. The adapted BEMM was found to be a better performance predictor than the standard BEMM for the 280 mm 10% and 15% hub ratio rotors and for all of the 30 m rotors. Results show that when blade designs were customised to the size of the hub, peak rotor power occurred at a hub ratio close to 10%, with power improvements of 0.35% (CFD, 280 mm), 0.44% (testing, 280 mm) and 0.27% (CFD, 30 m case study) compared to the 5% hub ratio baseline rotors. In contrast, if the standard BEMM is used in the design and performance prediction, no benefit is predicted for hub ratios greater than the 5% rotor. The 280 mm 10% hub ratio rotor, designed using the adapted BEMM, produced power improvement of 0.29% (CFD) and 0.90% (testing), compared to the equivalent rotor designed with the standard BEMM. The CFD simulations, of both the 280 mm and the 30 m rotors show that a custom-designed rotor up to a hub ratio of 15% produces at least as much power as a 5% hub ratio rotor.