Aerodynamic performance and blockage investigation of a cambered multi-bladed windmill

John, Itoje H.; Vaz, Jerson Rogério Pinheiro; Wood, David Murakami

doi:10.1088/1742-6596/1618/4/042003

Cited by 7 publications

(10 citation statements)

References 12 publications

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“…Those experiments used high solidity rotors as a way to ensure fast starting. For λ ≤ 2, John et al (2020) found maximum power coefficients considerably lower than the current values suggesting that an optimization of blade design would be 10.3389/fenrg.2022.971177 beneficial. Sørensen et al (2022) used prescribed loadings to investigate computationally the λ− dependence of the power output of a three-bladed turbine.…”

Section: Wind Turbines At Low Tip Speed Ratiocontrasting

confidence: 53%

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Optimal performance of actuator disc models for horizontal-axis turbines

Wood

Hammam²

2022

Front. Energy Res.

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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.

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Section: Wind Turbines At Low Tip Speed Ratiocontrasting

confidence: 53%

“…Small turbine operation at low λ has been studied by only a few researchers, e.g. John et al (2020) and Bourhis et al (2022), and a thorough understanding of them has not been developed. Those experiments used high solidity rotors as a way to ensure fast starting.…”

Section: Wind Turbines At Low Tip Speed Ratiomentioning

confidence: 99%

Optimal performance of actuator disc models for horizontal-axis turbines

Wood

Hammam²

2022

Front. Energy Res.

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Section: Windmill Model and Experimental Detailsmentioning

confidence: 99%

“…A magnetic particle brake (MPB) was used to load the blades in place of a generator typically used in wind turbines or a cyclic load such as a piston pump for a water pumping windmill. Contrary to the manufacturer's claim, the MPB was found not to provide a torque dependent only on the angular velocity, so a detailed torque and speed calibration was undertaken, see John et al 34 The model was tested in two wind tunnels: the 1 m ñ 1 m open jet tunnel at the University of Calgary and the 2.8 ñ 2.8 m Open Jet Facility (OJF) at TU Delft. Blockage in the former tunnel was significant but negligible in the OJF, so here we concentrate on the results from the OJF.…”

Section: Windmill Model and Experimental Detailsmentioning

confidence: 99%

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

2022

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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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Steady and unsteady characteristics of circular arc airfoils for water pumping windmills

John,

Wood

2023

Journal of Renewable and Sustainable Energy

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Accurate airfoil lift and drag data at low Reynolds number, Re, and high angles of attack, α, are needed to analyze the performance of small wind turbines, particularly their starting. In the current study, the steady and unsteady aerodynamic characteristics of circular arc airfoils (CAAs) with and without spars, as used in water-pumping windmills, were examined in a wind tunnel of 1 m2 cross section at Re<106. The tunnel was configured as an open jet and a closed section. The effects of varying geometrical characteristics on the CAA performance were investigated using a combination of thickness, camber, aspect ratio, and airfoil chord-to-tunnel height ratio. Using force transducers, the aerodynamic forces acting on the airfoils were measured directly for both increasing and decreasing α. The decreasing α measurements produce a higher lift–drag ratio than the increasing measurements, mostly in the post-stall region. In addition, “second stall,” was observed at large α in both the open and closed tunnels depending on the Re and tunnel blockage, but was much more prominent in the closed tunnel due to its wall constraining the wake and preventing the flow from switching from one regime to another. It was shown that the performance of all tested airfoils was sensitive to low Re under steady and unsteady conditions. The latter measurements for an airfoil oscillated at reduced frequencies, k≤0.06, are the first for CAAs. Results from this investigation provide a comprehensive airfoil dataset for the accurate blade element theory modeling of CAAs aerodynamic and starting performances.

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Aerodynamic performance and blockage investigation of a cambered multi-bladed windmill

Cited by 7 publications

References 12 publications

Optimal performance of actuator disc models for horizontal-axis turbines

Optimal performance of actuator disc models for horizontal-axis turbines

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

Steady and unsteady characteristics of circular arc airfoils for water pumping windmills

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