Computational modeling of the aerodynamics of windmill blades at high solidity

• The high solidity of the blades of water pumping windmills has a major effect on the lift and drag.
• Solidity effects have not been analyzed previously.
• Calculations of low Reynolds number circular arc airfoils were used to adjust the transition model constants.
• Increasing solidity reduces lift and drag but increases the ratio of lift:drag and the angle at which it occurs.
• Solidity effects should be included in performance analysis of water pumping windmills.

Water pumping is one of the oldest uses of wind energy with the multi-bladed, high-solidity windmill still in widespread use. In contrast to the low-solidity, high-speed blades of modern wind turbines which use airfoil profiles, windmills typically employ thin, circular-arc blades at high solidity and low speed. While there is considerable data on the aerodynamic behavior of circular arc airfoils (of zero solidity) there is very little data on cascades of circular arc blades. This paper investigates computationally the effects of solidity on the lift and drag of thin, circular arc blades in preparation for a detailed blade element analysis of windmill performance. Typical Reynolds numbers, Re, for windmills are around 105, so modeling of laminar separation and transition was expected to be as important as modeling the subsequent turbulent flow. The SST-transition model was, therefore, used. The “constants” in the transition equations were adjusted to match surface pressure measurements on circular arc airfoils at Re = 62,000, and then compared to separate measurements of the lift and drag at Re = 105. Excellent agreement was found in the former but the agreement for the latter was poorer. Computational modeling of solidity showed significant variation in the lift and drag which should be included in a blade element calculation.