Windmills for water pumping typically operate at low speed and high torque owing to their multi-bladed nature. This, however, complicates the rotor aerodynamic behavior due to the mutual interaction between adjacent blades and low Reynolds number, Re, operation. While studies on their aerodynamic performance indicate that increasing blade number, N, and airfoil type are critical analysis and design parameters, its low Re behavior with cambered airfoils appears complicated and is still poorly understood. Accordingly, the performance of a windmill model of diameter 0.68 m with 3 ≤ N ≤ 24 identical blades was investigated in two open jet wind tunnels, with different test section sizes: one with high blockage of 36.3 % and the other with a negligible blockage of 4.5 %, for comparison with Blade Element Theory (BET) predictions of thrust, torque, and power. It was found that BET is accurate except at low tip speed ratios, λ where it under-predicts the torque primarily because of the high solidity at high N. Furthermore, the study reveals that high blockage impacts significantly on rotor performance and is a function of N. Overall, the experiment gave a better performance, highlighting the importance of accounting for solidity in aerodynamic performance prediction.

Multi-bladed windmills usually pump water for agriculture and domestic consumption, often in remote locations. Although they have been around for over 150 years, their aerodynamic performance is still poorly understood. This paper describes the use of helical vortex theory (HVT) and blade element momentum (BEM) analysis to predict windmill thrust, torque, and extracted power. We emphasize the unusual features of windmills: low Reynolds numbers and tip speed ratios and high solidity, all related to the generation of high torque at low wind speeds. Wind tunnel tests on a model rotor with 3, 6, 12, and 24 circular-arc, constant-chord blades determined the thrust, torque, and extracted power over a range of tip speed ratio that extended to runaway. For comparison, BEM was implemented with a correction for finite blade number derived from HVT, as well as the classical Prandtl tip loss factor. The HVT correction predicted the rotor power coefficient to within 3% of the test data on the average. At low tip speed ratios and smaller blade numbers, HVT was consistently more accurate than the Prandtl factor. At all blade numbers, the measured rotor torque exceeded the BEM predictions at the lowest tip speed ratios indicating stall delay which became more important (and more beneficial for windmill performance) as the blade number increased. The Prandtl formulation predicted the thrust to within a mean accuracy of 13% and was more accurate than the HVT method.

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