A method for preliminary rotor design – Part 1:  Radially Independent Actuator Disc model

Loenbaek, Kenneth; Bak, Christian; Madsen, Jens Ingemann; McWilliam, Michael

doi:10.5194/wes-6-903-2021

Cited by 2 publications

(3 citation statements)

References 13 publications

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“…For the special condition that the 1/4 chord line of the blade is straight, the local thrust and power coefficients are the same forms as C LT and C LP derived by Lønbaek et al [5].…”

Section: Total Local Thrust and Power Coefficientsmentioning

confidence: 99%

“…The calculation of the inductions in the BEM method with Prandtl's tip-loss correction with given circulation distribution will require an iteration in the inflow angle φ to solve for the blade axial induction factor a B , which has been described in [5]. The blade axial induction factor a B is calculated from C t,KJ 1 divided by the tip-loss factor F .…”

Section: Same Induction and System Closurementioning

confidence: 99%

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How does the blade element momentum method see swept or prebent blades?

Li,

Gaunaa,

Pirrung

et al. 2024

J. Phys.: Conf. Ser.

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The blade element momentum (BEM) method is among the mostly used engineering aerodynamic models for wind turbine rotors. Even though the BEM method is strictly only applicable to straight blades forming a planar rotor, it is in practice used for load calculation and design optimization of blades with relatively large sweep, prebend or coning. The present work aims to answer the question: How does the BEM method see swept or prebent blades? The blade element part of the method can be adapted for swept or prebent blades by projecting the velocity and loads between the 2-D airfoil section and the 3-D blade geometry under the cross-flow principle. However, momentum theory considers the 3-D wake and the induction of a planar actuator disc with straight blades. There could be significant differences between the results calculated from different implementations of the BEM method, while the details of the implementations are often omitted in the literature. In the present work, a consistent implementation including the definition of airfoil section alignments and the coordinate systems is provided. It is shown that for a given circulation distribution, the BEM method will predict approximately the same local aerodynamic loads for non-straight blades as if the blades were straight and the rotor was planar. This means using the BEM method to perform aerodynamic optimization of modern rotors with curved blades and/or rotors that are not planar can only have little meaningful result. In order to model the impact of the wake geometry on the induction, more advanced models that take into account the wake geometry on the induction are necessary.

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“…For the special condition that the 1/4 chord line of the blade is straight, the local thrust and power coefficients are the same forms as C LT and C LP derived by Lønbaek et al [5].…”

Section: Total Local Thrust and Power Coefficientsmentioning

confidence: 99%

Section: Same Induction and System Closurementioning

confidence: 99%

How does the blade element momentum method see swept or prebent blades?

Li,

Gaunaa,

Pirrung

et al. 2024

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

“…Wind turbine design optimization has been an integral part of wind turbine design since the start of the wind turbine industry. The target for such optimization has varied greatly from pure aerodynamic optimization with the target to maximize the power extraction (see Manwell et al, 2010, Sørensen, 2016and Jamieson, 2018 to a more holistic turbine design where the target is to minimize the cost of the turbine through modeling the physics of the turbine components as well as their associated cost; see, e.g., Fuglsang et al (2002), Hjort et al (2009), Bottasso et al (2012), Meadows (2012), andPerez-Moreno et al (2016). Common to these approaches the connection of a set of simulation tools (e.g., BEM solver, structural solver, controller) through a cost function, leading to a fairly complicated optimization problem with a lot of design variables.…”

Section: Introductionmentioning

confidence: 99%

A method for preliminary rotor design – Part 2: Wind turbine Optimization with Radial Independence

2021

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Abstract. A novel wind turbine rotor optimization methodology is presented. Using an assumption of radial independence it is possible to obtain an optimal relationship between the global power (CP) and load coefficient (CT, CFM) through the use of Karush–Kuhn–Tucker (KKT) multipliers, leaving an optimization problem that can be solved at each radial station independently. It allows solving load constraint power and annual energy production (AEP) optimization problems where the optimization variables are only the KKT multipliers (scalars), one for each of the constraints. For the paper, two constraints, namely the thrust and blade root flap moment, are used, leading to two optimization variables. Applying the optimization methodology to maximize power (P) or annual energy production (AEP) for a given thrust and blade root flap moment, but without a cost function, leads to the same overall result with the global optimum being unbounded in terms of rotor radius (R̃) with a global optimum being at R̃→∞. The increase in power and AEP is in this case ΔP=50 % and ΔAEP=70 %, with a baseline being the Betz optimum rotor. With a simple cost function and with the same setup of the problem, a power-per-cost (PpC) optimization resulted in a power-per-cost increase of ΔPpC=4.2 % with a radius increase of ΔR=7.9 % as well as a power increase of ΔP=9.1 %. This was obtained while keeping the same flap moment and reaching a lower thrust of ΔT=-3.8 %. The equivalent for AEP-per-cost (AEPpC) optimization leads to increased cost efficiency of ΔAEPpC=2.9 % with a radius increase of ΔR=17 % and an AEP increase of ΔAEP=13 %, again with the same, maximum flap moment, while the maximum thrust is −9.0 % lower than the baseline.

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A method for preliminary rotor design – Part 1: Radially Independent Actuator Disc model

Cited by 2 publications

References 13 publications

How does the blade element momentum method see swept or prebent blades?

How does the blade element momentum method see swept or prebent blades?

A method for preliminary rotor design – Part 2: Wind turbine Optimization with Radial Independence

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