The aerodynamics of water pumping windmills

John, Itoje H.; Wood, David

doi:10.1049/pbpo169e_ch6

Cited by 2 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The literature on windmills and circular arc airfoils that are normally used in their construction, is reviewed extensively by John and Wood 8 . Only a summary is given here.…”

Section: Introductionmentioning

confidence: 99%

“…The literature on windmills and circular arc airfoils that are normally used in their construction, is reviewed extensively by John and Wood. 8 Only a summary is given here. Pinilla et al 9 showed that the maximum efficiency of water pumping occurred below the cut-in wind speed: the minimum wind speed at which power is extracted as determined by the turbine's power curve.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Helical vortex theory and blade element analysis of multi‐bladed windmills

2022

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…The literature on windmills and circular arc airfoils that are normally used in their construction, is reviewed extensively by John and Wood 8 . Only a summary is given here.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Helical vortex theory and blade element analysis of multi‐bladed windmills

2022

Self Cite

View full text Add to dashboard Cite

show abstract

Optimal performance of actuator disc models for horizontal-axis turbines

Wood

Hammam²

2022

Front. Energy Res.

View full text Add to dashboard Cite

This study analyzes actuator disc (AD) models of horizontal-axis turbines to determine optimal performance, defined as the maximum power extracted at any tip speed ratio. We use the calculus of variations to maximize rotor torque relative to the thrust without making any assumptions about the rotor loading. The torque was obtained from the angular momentum equation and the thrust from the Kutta-Joukowsky equation which depends on the circumferential velocity and tip speed ratio. The optimality requirement is that the pitch of the vorticity exiting the rotor must be constant across the wake and equal to the ratio of torque to thrust. This result generalizes the classical finding of Betz and Goldstein that optimal lightly-loaded ADs have constant pitch. Optimizing the torque in the far-wake, well downstream of the rotor, leads to the same requirement of constant pitch. This implies that the pitch of an optimal rotor is constant everywhere in the wake at all tip speed ratios. We show that it is not possible for the pitch to reach its optimal value because of the vorticity distribution in the wake, and propose modifications to the pitch at the rotor and in the far-wake. The axial and circumferential velocities in the far-wake, which are easily determined, were used to find those at the rotor from the “disc loading equation” for the angular momentum which is also the normalized bound circulation at the rotor. For the simplest case of a lightly-loaded rotor at zero tip speed ratio, the induced circumferential velocity is linear in radius and the axial component is quadratic, As the tip speed ratio increases, the optimal power and thrust asymptote to the familiar Betz-Joukowsky values, and the induced axial velocity and rotor bound circulation become constant. At low tip speed ratios, the optimal wakes are constrained by the need to avoid breakdown of the flow at high swirl, and the conventional thrust equation, involving the axial velocity only, is inaccurate. As found in previous studies, the power coefficient increases monotonically with tip speed ratio, but the thrust coefficient reaches a maximum value slightly above the Betz-Joukowsky limit at a tip speed ratio of two, before decreasing towards the limit.

show abstract

The aerodynamics of water pumping windmills

Cited by 2 publications

References 0 publications

Helical vortex theory and blade element analysis of multi‐bladed windmills

Helical vortex theory and blade element analysis of multi‐bladed windmills

Optimal performance of actuator disc models for horizontal-axis turbines

Contact Info

Product

Resources

About