On the scaling of wind turbine rotors

Abstract. This article formulates laws for scaling wind turbine rotors. Although the analysis is general, the article primarily focuses on subscaling, i.e. on the design of a smaller size model mimicking a full-scale machine. The present study considers both the steady-state and transient response cases, including the effects of aerodynamic, elastic, inertial and gravitational forces. The analysis reveals the changes to physical characteristics induced by a generic change of scale, indicates which characteristics can be matched faithfully by a sub-scaled model, and states the conditions that must be fulfilled for desired matchings to hold. Based on the scaling laws formulated here, two different strategies to design scaled rotors are considered: in the first strategy the scaled model is simply geometrically zoomed from the reference full-scale one, while in the second strategy the scaled rotor is completely redesigned in order to match desired characteristics of the full-scale machine. The two strategies are discussed and compared, highlighting their respective advantages and disadvantages. The comparison considers the scaling of a reference 10-MW wind turbine of about 180 m of diameter down to three different sizes of 54, 27 and 2.8 m. Simulation results indicate that, with the proper choices, several key performance indicators can be accurately matched even by models characterized by significant scaling factors.

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On the scaling of wind turbine rotors

Wind Energy Science ◽

10.5194/wes-6-601-2021 ◽

2021 ◽

Vol 6 (3) ◽

pp. 601-626

Author(s):

Helena Canet ◽

Pietro Bortolotti ◽

Carlo L. Bottasso

Keyword(s):

Wind Turbine ◽

Performance Indicators ◽

Scaling Laws ◽

Full Scale ◽

Exact Match ◽

Matching Problem ◽

Gravitational Forces ◽

Change Of Scale ◽

Turbine Rotors ◽

Generic Change

Abstract. This paper formulates laws for scaling wind turbine rotors. Although the analysis is general, the article primarily focuses on the subscaling problem, i.e., on the design of a smaller-sized model that mimics a full-scale machine. The present study considers both the steady-state and transient response cases, including the effects of aerodynamic, elastic, inertial, and gravitational forces. The analysis reveals the changes to physical characteristics induced by a generic change of scale, indicates which characteristics can be matched faithfully by a subscaled model, and states the conditions that must be fulfilled for desired matchings to hold. Based on the scaling laws formulated here, the article continues by considering the problem of designing scaled rotors that match desired indicators of a full-scale reference. To better illustrate the challenges implicit in scaling and the necessary tradeoffs and approximations, two different approaches are contrasted. The first consists in a straightforward geometric zooming. An analysis of the consequences of zooming reveals that, although apparently simple, this method is often not applicable in practice, because of physical and manufacturing limitations. This motivates the formulation of scaling as a constrained optimal aerodynamic and structural matching problem of wide applicability. Practical illustrations are given considering the scaling of a large reference 10 MW wind turbine of about 180 m in diameter down to three different sizes of 54, 27, and 2.8 m. Results indicate that, with the proper choices, even models characterized by very significant scaling factors can accurately match several key performance indicators. Additionally, when an exact match is not possible, relevant trends can at least be captured.

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3D simulation of wind turbine rotors at full scale. Part I: Geometry modeling and aerodynamics

International Journal for Numerical Methods in Fluids ◽

10.1002/fld.2400 ◽

2010 ◽

Vol 65 (1-3) ◽

pp. 207-235 ◽

Cited By ~ 230

Author(s):

Y. Bazilevs ◽

M.-C. Hsu ◽

I. Akkerman ◽

S. Wright ◽

K. Takizawa ◽

...

Keyword(s):

Wind Turbine ◽

Full Scale ◽

3D Simulation ◽

Geometry Modeling ◽

Turbine Rotors

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Development of a Scaled-Down Floating Wind Turbine for Offshore Basin Testing

Volume 9A: Ocean Renewable Energy ◽

10.1115/omae2014-23441 ◽

2014 ◽

Cited By ~ 9

Author(s):

Erik-Jan de Ridder ◽

William Otto ◽

Gert-Jan Zondervan ◽

Fons Huijs ◽

Guilherme Vaz

Keyword(s):

Wind Turbine ◽

Wind Velocity ◽

Scaling Laws ◽

Scale Effects ◽

Model Testing ◽

Model Tests ◽

Full Scale ◽

Pitch Control ◽

Model Scale ◽

Floating Wind Turbine

In the last years MARIN has been involved in an increasing number of projects for the offshore wind industry. New techniques in model testing and numerical simulations have been developed in this field. In this paper the development of a scaled-down wind turbine operating on a floating offshore platform, similar to the well-known 5MW NREL wind turbine is discussed. To simulate the response of a floating wind turbine correctly it is important that the environmental loads due to wind, waves and current are in line with full scale. For dynamic similarity on model scale, Froude scaling laws are used successfully in the Offshore industry for the underwater loads. To be consistent with the underwater loads, the winds loads have to be scaled according to Froude as well. Previous model tests described by Robertson et al [1] showed that a geometrically-scaled turbine generated a lower thrust and power coefficient with a Froude-scaled wind velocity due to the strong Reynolds scale effects on the flow. To improve future model testing, a new scaling method for the wind turbine blades was developed originally by University of Maine, and here improved and applied. In this methodology, the objective is to obtain power and thrust coefficients which are similar to the full-scale turbine in Froude-scaled wind. This is obtained by changing the geometry of the blades in order to provide thrust equality between model and full scale, and can therefore be considered as a “performance scaling”. This method was then used to design and construct a new MARIN Stock Wind Turbine (MSWT) based on the NREL 5MW wind turbine blade, including an active blade pitch control to simulate different blade pitch control systems. MARIN’s high-quality wind setup in combination with the new model scale stock wind turbine was used for testing the GustoMSC Tri-Floater semi-submersible as presented in Figure 1, including an ECN active blade pitch control algorithm. From the model tests it was concluded that the measured thrust versus wind velocity characteristics of the new MSWT were in line with the full scale prediction and with CFD (Computational Fluid Dynamics) results.

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How realistic are the wakes of scaled wind turbine models?

10.5194/wes-2020-115 ◽

2020 ◽

Author(s):

Chengyu Wang ◽

Filippo Campagnolo ◽

Helena Canet ◽

Daniel J. Barreiro ◽

Carlo L. Bottasso

Keyword(s):

Wind Tunnel ◽

Wind Turbine ◽

Inner Core ◽

Detailed Comparison ◽

Full Scale ◽

Scaling Analysis ◽

Scaled Model ◽

Eddy Simulation ◽

The One ◽

Physical Phenomena

Abstract. The aim of this paper is to analyze to which extent wind tunnel experiments can represent the behavior of full-scale wind turbine wakes. The question is relevant because on the one hand scaled models are extensively used for wake and farm control studies, whereas on the other hand not all wake-relevant physical characteristics of a full-scale turbine can be exactly matched by a scaled model. In particular, a detailed scaling analysis reveals that the scaled model accurately represents the principal physical phenomena taking place in the outer shell of the near wake, whereas differences exist in its inner core. A large eddy simulation actuator line method is first validated with respect to wind tunnel measurements, and then used to perform a detailed comparison of the wake at the two scales. It is concluded that, notwithstanding the existence of some mismatched effects, the scaled wake is remarkably similar to the full-scale one, except in the immediate proximity of the rotor.

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Model Tests for a Floating Wind Turbine on Three Different Floaters

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.4024711 ◽

2014 ◽

Vol 136 (2) ◽

Cited By ~ 54

Author(s):

Bonjun J. Koo ◽

Andrew J. Goupee ◽

Richard W. Kimball ◽

Kostas F. Lambrakos

Keyword(s):

Wind Turbine ◽

Wind Turbines ◽

Wind Farms ◽

Model Tests ◽

Experimental Comparison ◽

Floating Platform ◽

Scaled Model ◽

Advantages And Disadvantages ◽

Floating Wind Turbine ◽

Floating Platforms

Wind energy is a promising alternate energy resource. However, the on-land wind farms are limited by space, noise, and visual pollution and, therefore, many countries build wind farms near the shore. Until now, most offshore wind farms have been built in relatively shallow water (less than 30 m) with fixed tower type wind turbines. Recently, several countries have planned to move wind farms to deep water offshore locations to find stronger and steadier wind fields as compared to near shore locations. For the wind farms in deeper water, floating platforms have been proposed to support the wind turbine. The model tests described in this paper were performed at MARIN (maritime research institute netherlands) with a model setup corresponding to a 1:50 Froude scaling. The wind turbine was a scaled model of the national renewable energy lab (NREL) 5 MW horizontal axis reference wind turbine supported by three different generic floating platforms: a spar, a semisubmersible, and a tension-leg platform (TLP). The wave environment used in the tests is representative of the offshore in the state of Maine. In order to capture coupling between the floating platform and the wind turbine, the 1st bending mode of the turbine tower was also modeled. The main purpose of the model tests was to generate data on coupled motions and loads between the three floating platforms and the same wind turbine for the operational, design, and survival seas states. The data are to be used for the calibration and improvement of the existing design analysis and performance numerical codes. An additional objective of the model tests was to establish the advantages and disadvantages among the three floating platform concepts on the basis of the test data. The paper gives details of the scaled model wind turbine and floating platforms, the setup configurations, and the instrumentation to measure motions, accelerations, and loads along with the wind turbine rpm, torque, and thrust for the three floating wind turbines. The data and data analysis results are discussed in the work of Goupee et al. (2012, “Experimental Comparison of Three Floating Wind Turbine Concepts,” OMAE 2012-83645).

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How realistic are the wakes of scaled wind turbine models?

Wind Energy Science ◽

10.5194/wes-6-961-2021 ◽

2021 ◽

Vol 6 (3) ◽

pp. 961-981

Author(s):

Chengyu Wang ◽

Filippo Campagnolo ◽

Helena Canet ◽

Daniel J. Barreiro ◽

Carlo L. Bottasso

Keyword(s):

Wind Tunnel ◽

Wind Turbine ◽

Inner Core ◽

Full Scale ◽

Scaling Analysis ◽

Scaled Model ◽

Eddy Simulation ◽

The One ◽

Scaled Models ◽

Physical Phenomena

Abstract. The aim of this paper is to analyze to which extent wind tunnel experiments can represent the behavior of full-scale wind turbine wakes. The question is relevant because on the one hand scaled models are extensively used for wake and farm control studies, whereas on the other hand not all wake-relevant physical characteristics of a full-scale turbine can be exactly matched by a scaled model. In particular, a detailed scaling analysis reveals that the scaled model accurately represents the principal physical phenomena taking place in the outer shell of the near wake, whereas differences exist in its inner core. A large-eddy simulation actuator-line method is first validated with respect to wind tunnel measurements and then used to perform a thorough comparison of the wake at the two scales. It is concluded that, notwithstanding the existence of some mismatched effects, the scaled wake is remarkably similar to the full-scale one, except in the immediate proximity of the rotor.

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Similitude analysis of thin-walled composite I-beams for subcomponent testing of wind turbine blades

Wind Engineering ◽

10.1177/0309524x17709924 ◽

2017 ◽

Vol 41 (5) ◽

pp. 297-312 ◽

Cited By ~ 6

Author(s):

Mohamad Eydani Asl ◽

Christopher Niezrecki ◽

James Sherwood ◽

Peter Avitabile

Keyword(s):

Wind Turbine ◽

Scaling Laws ◽

Turbine Blades ◽

Design Criterion ◽

Full Scale ◽

Small Scale ◽

Displacement Fields ◽

Structural Element ◽

Thin Walled ◽

Utility Scale

In this study, the I-beam structure of a utility-scale blade is used as the basis for the design of a small-scale subcomponent emulating the same type of structural element of a utility-scale wind turbine blade. Governing equations for the bending of a shear deformable thin-walled composite I-beam are considered. Similitude theory is applied to derive the corresponding scaling laws. Accuracy of the derived scaling laws in predicting the strain and displacement fields of the full-scale I-beam is considered as a design criterion for small-scale I-beams. Both complete and partial similarity cases are discussed. A novel approach is proposed to design partially similar scaled I-beams with totally different layups from those of the full-scale I-beam. Using the proposed technique, scaled-down composite I-beams are designed that predict the strain and displacement fields of their full-scale parent I-beam with very good accuracy.

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Model Tests for a Floating Windturbine on Three Different Floaters

Volume 7: Ocean Space Utilization; Ocean Renewable Energy ◽

10.1115/omae2012-83642 ◽

2012 ◽

Cited By ~ 1

Author(s):

Bonjun Koo ◽

Andrew J. Goupee ◽

Kostas Lambrakos ◽

Richard W. Kimball

Keyword(s):

Wind Turbine ◽

Wind Turbines ◽

Wind Farms ◽

Model Tests ◽

Floating Platform ◽

Scaled Model ◽

Advantages And Disadvantages ◽

Near Shore ◽

Set Up ◽

Floating Platforms

Wind energy is a promising alternate energy resource. However, the on-land wind farms are limited by space, noise, and visual pollution, and therefore many countries build wind farms near shore. Up to now, most of offshore wind farms have been built in relatively shallow water (less than 30m) with fixed tower type wind turbines. Recently, several countries plan to move wind farms to deep water offshore locations to find stronger and steadier wind fields as compared to near shore locations. For the wind farms in deeper water, floating platforms have been proposed to support the wind turbine. The model tests described in this paper were performed at MARIN (Maritime Research Institute Netherlands) with a model set-up corresponding to a 1:50 Froude scaling. The wind turbine was a scaled model of the National Renewable Energy Lab (NREL) 5MW, horizontal axis reference wind turbine supported by three different generic floating platforms: a spar, a semi-submersible and a tension-leg platform (TLP). The wave environment used in the tests is representative of the offshore in the state of Maine. In order to capture coupling between the floating platform and the wind turbine, the 1st bending mode of the turbine tower was also modeled. The main purpose of the model tests was to generate data on coupled motions and loads between the three floating platforms and the same wind turbine for the operational, design, and survival seas states. The data are to be used for calibration and improvement of existing design analysis and performance numerical codes. An additional objective of the model tests was to establish advantages and disadvantages among the three floating platform concepts on the basis of test data. The paper gives details of the scaled model wind turbine and floating platforms, the set-up configurations, and the instrumentation to measure motions, accelerations and loads as well as wind turbine rpm, torque and thrust for the three floating wind turbines. The data and data analysis results are the subject of another paper in this conference [1].

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Wind/Wave Basin Verification of a Performance-Matched Scale-Model Wind Turbine on a Floating Offshore Wind Turbine Platform

Volume 9B: Ocean Renewable Energy ◽

10.1115/omae2014-24166 ◽

2014 ◽

Cited By ~ 12

Author(s):

Richard Kimball ◽

Andrew J. Goupee ◽

Matthew J. Fowler ◽

Erik-Jan de Ridder ◽

Joop Helder

Keyword(s):

Wind Turbine ◽

Model Test ◽

Reynolds Numbers ◽

Full Scale ◽

Offshore Wind ◽

Scale Model ◽

Scaled Model ◽

Turbine Performance ◽

Wave Basin ◽

The University

In 2011, the DeepCwind Consortium performed 1/50th-scale model tests on three offshore floating wind platforms at the Maritime Research Institute Netherlands (MARIN) using a geometrically scaled model of the National Renewable Energy Laboratory (NREL) 5 MW reference turbine. However, due to the severe mismatch in Reynolds number between full scale and model scale, the strictly Froude-scaled, geometrically-similar (geo-sim) wind turbine underperformed greatly, which required significant modification of test wind speeds to match key wind turbine aerodynamic loads, such as thrust. The conclusion from these prior efforts was to abandon a geometrically similar model turbine and use a performance-matched turbine model in its place, keeping mass and inertia properties properly scaled, but utilizing modified blade geometries to achieve required performance at the lower Reynolds numbers of the Froude scaled model. To this end, the University of Maine and MARIN worked in parallel to develop performance-matched turbines designed to emulate the full scale performance of the NREL 5 MW reference turbine at model scale conditions. An overview of this performance-matched wind turbine design methodology is presented and examples of performance-matched turbines are provided. The DeepCwind semi-submersible platform was retested at MARIN in 2013 using the MARIN Stock Wind Turbine (MSWT), which was designed to closely emulate the performance of the original NREL 5 MW turbine. This work compares the wind turbine performance of the MSWT to the previously used geometrically scaled NREL 5 MW turbine. Additionally, turbine performance testing of the 1/50th-scale MSWT was completed at MARIN and a 1/130th-scale model was tested at the University of Maine under Reynolds numbers corresponding to the Froude-scaled model test conditions. Results from these tests are provided to demonstrate effects on model test fidelity. Comparisons of the performance response of the geometrically matched turbine to the performance-matched turbines are also presented to illustrate the performance-matched turbine methodology. Lastly, examples of the fully dynamic floating system performance using the original geometrically scaled NREL 5 MW turbine and the MSWT are investigated to illustrate the implementation of the model test procedure as well as the effects of turbine performance on floater response. Using the procedures employed for the MARIN tests as a guide, the results of this work support the development of protocols for properly designing scale model wind turbines that emulate the full scale design for Froude-scale wind/wave basin tests of floating offshore wind turbines.

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