Validation and modification of the Blade Element Momentum theory based on comparisons with actuator disc simulations

Madsen, Helge Aagaard; Bak, Christian; Døssing, Mads; Mikkelsen, Robert Flemming; Øye, Stig

doi:10.1002/we.359

Cited by 98 publications

(96 citation statements)

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“…2). The far-wake component u FW is computed based on the BEM model implementation in HAWC2 that uses a polynomial to relate the local thrust coefficient with the axial induction factor at each annular element (Madsen et al, 2010). Because a part of the total induction is computed by the nearwake model, the BEM implementation used to determine the far-wake induction factor a FW has been modified in two ways compared to the original BEM implementation in HAWC2.…”

Section: Coupling To Far-wake Modelmentioning

confidence: 99%

Comparison of a coupled near- and far-wake model with a free-wake vortex code

et al. 2017

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Abstract. This paper presents the integration of a near-wake model for trailing vorticity, which is based on a prescribed-wake lifting-line model proposed by Beddoes (1987), with a blade element momentum (BEM)-based far-wake model and a 2-D shed vorticity model. The resulting coupled aerodynamics model is validated against lifting-surface computations performed using a free-wake panel code. The focus of the description of the aerodynamics model is on the numerical stability, the computation speed and the accuracy of unsteady simulations. To stabilize the near-wake model, it has to be iterated to convergence, using a relaxation factor that has to be updated during the computation. Further, the effect of simplifying the exponential function approximation of the near-wake model to increase the computation speed is investigated in this work. A modification of the dynamic inflow weighting factors of the far-wake model is presented that ensures good induction modeling at slow timescales. Finally, the unsteady airfoil aerodynamics model is extended to provide the unsteady bound circulation for the near-wake model and to improve the modeling of the unsteady behavior of cambered airfoils. The model comparison with results from a free-wake panel code and a BEM model is centered around the NREL 5 MW reference turbine. The response to pitch steps at different pitching speeds is compared. By means of prescribed vibration cases, the effect of the aerodynamic model on the predictions of the aerodynamic work is investigated. The validation shows that a BEM model can be improved by adding near-wake trailed vorticity computation. For all prescribed vibration cases with high aerodynamic damping, results similar to those obtained by the free-wake model can be achieved in a small fraction of computation time with the proposed model. In the cases with low aerodynamic damping, the addition of trailed vorticity modeling shifts the results closer to those obtained by using the free-wake code, but differences remain.

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Section: Coupling To Far-wake Modelmentioning

confidence: 99%

Comparison of a coupled near- and far-wake model with a free-wake vortex code

et al. 2017

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“…(4) for lower values of a and to empirical results and actuator disc simulations for higher loading (Madsen et al, 2010a). For an annular ring element at radius r, the thrust coefficient is calculated using the formula presented by :…”

Section: Axial Inductionmentioning

confidence: 99%

Free-flow wind speed from a blade-mounted flow sensor

et al. 2018

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Abstract. This paper presents a method for obtaining the free-inflow velocities from a 3-D flow sensor mounted on the blade of a wind turbine.From its position on the rotating blade, e.g. one-third from the tip, a blade-mounted flow sensor (BMFS) is able to provide valuable information about the turbulent sheared inflow in different regions of the rotor. At the rotor, however, the inflow is affected by the wind turbine, and in most cases the wind of interest is the inflow that the wind turbine is exposed to, i.e. the free-inflow velocities.The current method applies a combination of aerodynamic models and procedures to estimate the induced velocities, i.e. the disturbance of the flow field caused by the wind turbine. These velocities are subtracted from the flow velocities measured by the BMFS to obtain the free-inflow velocities. Aeroelastic codes, like HAWC2, typically use a similar approach to calculate the induction, but they use it for the reversed process, i.e. they add the induction to the free inflow to get the flow velocities at the blades, which are required to calculate the resulting aerodynamic forces.The aerodynamic models included in the current method comprise models based on blade element momentum (BEM) for axial and tangential induction, a radial induction model and tip loss correction, and models for skew and dynamic inflow.It is shown that the method is able to calculate the free-inflow velocities with high accuracy when applied to aeroelastic HAWC2 simulations with a stiff structural model while some deviations are seen in simulations with a flexible structure.Furthermore, the method is tested on simulations performed by a flexible structural model coupled with a large-eddy simulation (LES) flow solver. The results of this higher-fidelity verification confirm the HAWC2-based conclusion.

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“…The simulations are performed using HAWC2, which is a nonlinear aeroelastic code intended for computing wind turbine response in the time domain (Aagaard Madsen et al, 2010bKim et al, 2013;Larsen et al, 2015).…”

Section: Numerical Studymentioning

confidence: 99%

“…Over the last 28 years, blade-mounted five-hole pitot tubes have been used in several research projects to characterize the inflow of wind turbines (Aagaard Madsen, 1991;Petersen and Aagaard Madsen, 1997;Aagaard Madsen et al, 2003, 2010bPedersen et al, 2015). Five-hole pitot tubes measure the relative flow velocity as well as the flow angle in two perpendicular planes, and from these quantities threedimensional turbulent wind speeds can be derived.…”

Section: Introductionmentioning

confidence: 99%

Using wind speed from a blade-mounted flow sensor for power and load assessment on modern wind turbines

et al. 2017

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Abstract.In this paper an alternative method to evaluate power performance and loads on wind turbines using a blade-mounted flow sensor is investigated. The hypothesis is that the wind speed measured at the blades has a high correlation with the power and loads such that a power or load assessment can be performed from a few hours or days of measurements.In the present study a blade-mounted five-hole pitot tube is used as the flow sensor as an alternative to the conventional approach, where the reference wind speed is either measured at a nearby met mast or on the nacelle using lidar technology or cup anemometers. From the flow sensor measurements, an accurate estimate of the wind speed at the rotor plane can be obtained. This wind speed is disturbed by the presence of the wind turbine, and it is therefore different from the free-flow wind speed. However, the recorded wind speed has a high correlation with the actual power production as well as the flap-wise loads as it is measured close to the blade where the aerodynamic forces are acting.Conventional power curves are based on at least 180 h of 10 min mean values, but using the blade-mounted flow sensor both the observation average time and the overall assessment time can potentially be shortened. The basis for this hypothesis is that the sensor is able to provide more observations with higher accuracy, as the sensor follows the rotation of the rotor and because of the high correlation between the flow at the blades and the power production. This is the research question addressed in this paper.The method is first tested using aeroelastic simulations where the dependence of the radial position and effect of multiple blade-mounted flow sensors are also investigated. Next the method is evaluated on the basis of fullscale measurements on a pitch-regulated, variable-speed 3.6 MW wind turbine.It is concluded that the wind speed derived from the blade-mounted flow sensor is highly correlated with the power and flap-wise bending moment and that the method has advantages over the traditional approach where the met-mast wind speed is used as reference, e.g. the capability of measuring the shear, veer and turbulence. The aeroelastic simulations show that the assessment time can be reduced, but this reduction cannot be confirmed from the current measurement database due to sensor problems and practical circumstances. Measuring the wind speed at the rotor plane comes with a price as the wind speed is affected by the induction which may be sensitive to the changes you want to evaluate, e.g. different vortex generator configurations. Furthermore it is concluded that a robust instrument and measurement system is required to obtain accurate and reliable wind speed recordings from pitot-tube measurements.Published by Copernicus Publications on behalf of the European Academy of Wind Energy e.V.

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Validation and modification of the Blade Element Momentum theory based on comparisons with actuator disc simulations

Cited by 98 publications

References 10 publications

Comparison of a coupled near- and far-wake model with a free-wake vortex code

Comparison of a coupled near- and far-wake model with a free-wake vortex code

Free-flow wind speed from a blade-mounted flow sensor

Using wind speed from a blade-mounted flow sensor for power and load assessment on modern wind turbines

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