Analysis of a tip correction factor for horizontal axis turbines

It is imperative to include three‐dimensional tip flow corrections when using low‐order rotor models that rely on the flow independence principle to compute the blade forces. These corrections aim to account for the effect of pressure equalization at the tips and the accompanying spanwise pressure gradients on the outboard sections, by reducing the computed axial and tangential forces as the blade tips are approached. While Glauert‐type corrections are conventionally employed for actuator disc‐type computations, alternative corrections are required for actuator line computations as they use a finite blade representation. We present actuator line computations of the Model Rotor Experiments in Controlled Conditions (MEXICO) rotor to investigate tip corrections. Using the tip correction factor proposed by Shen et al. (Wind Energy 2005; 8:457–475), the actuator line computations show an improvement in accuracy over similar computations undertaken without a tip correction factor included. Further improvement to the blade loading is achieved by recalibrating the tip correction factor using data extracted from blade resolved computations of the model rotor experiments in controlled conditions rotor. From the rotor resolved computations, the tip loss (reduction in the blade loading on the outboard sections) is found to be more aggressive in the tangential direction than the axial direction. To account for this, we recalibrate the tip correction factor separately in the axial and tangential directions to develop new directionally dependent tip corrections. The resulting actuator line computations show a further improvement in accuracy of the tangential blade loading, resulting in better prediction of the rotor power. Copyright © 2017 John Wiley & Sons, Ltd.     

A new tip correction for actuator line computations

The actuator line method (ALM) is today widely used to represent wind turbine loadings in computational fluid dynamics (CFD). As opposed to resolving the whole blade geometry, the methodology does not require geometry‐fitted meshes, which makes it fast to apply. In ALM, tabulated airfoil data are used to determine the local blade loadings, which subsequently are projected to the CFD grid using a Gaussian smearing function. To achieve accurate blade loadings at the tip regions of the blades, the width of the projection function needs to be narrower than the local chord lengths, requiring CFD grids that are much finer than what is actually needed in order to resolve the energy containing turbulent structures of the atmospheric boundary layer (ABL). On the other hand, employing large widths of the projection function may result in too large tip loadings. Therefore, the number of grid points required to resolve the blade and the width of the projection function have to be restricted to certain minimum values if unphysical corrections are to be avoided. In this paper, we investigate the cause of the overestimated tip loadings when using coarse CFD grids and, based on this, introduce a simple and physical consistent correction technique to rectify the problem. To validate the new correction, it is first applied on a planar wing where results are compared with the lifting‐line technique. Next, the NREL 5‐MW and Phase VI turbines are employed to test the correction on rotors. Here, the resulting blade loadings are compared with results from the blade‐element momentum (BEM) method. In both cases, it is found that the new correction greatly improves the results for both normal and tangential loads and that it is possible to obtain accurate results even when using a very coarse blade resolution.     

A simple improvement of a tip loss model for actuator disc simulations

The loading of a wind turbine decreases towards the blade tip because of the velocities induced by the tip vortex. This tip loss effect has to be taken into account when performing actuator disc simulations, where the single blades of the turbine are not modeled. A widely used method applies a factor on the axial and tangential loading of the turbine. This factor decreases when approaching the blade tip. It has been shown that the factor should be different for the axial and tangential loading of the turbine to model the rotation of the resulting force vector at the airfoil sections caused by the induced velocity. The present article contains the derivation of a simple correction for the tangential load factor that takes this rotation into account. The correction does not need any additional curve fitting but just depends on the local airfoil characteristics and angle of attack. Actuator disc computations with the modified tip loss correction show improved agreement with results from actuator line, free wake lifting line, and blade element momentum simulations.     

Development of an aeroelastic code based on three‐dimensional viscous–inviscid method for wind turbine computations

Aerodynamic and structural dynamic performance analysis of modern wind turbines are routinely estimated in the wind energy field using computational tools known as aeroelastic codes. Most aeroelastic codes use the blade element momentum (BEM) technique to model the rotor aerodynamics and a modal, multi‐body or the finite‐element approach to model the turbine structural dynamics. The present work describes the development of a novel aeroelastic code that combines a three‐dimensional viscous–inviscid interactive method, method for interactive rotor aerodynamic simulations (MIRAS), with the structural dynamics model used in the aeroelastic code FLEX5. The new code, called MIRAS‐FLEX, is an improvement on standard aeroelastic codes because it uses a more advanced aerodynamic model than BEM. With the new aeroelastic code, more physical aerodynamic predictions than BEM can be obtained as BEM uses empirical relations, such as tip loss corrections, to determine the flow around a rotor. Although more costly than BEM, a small cluster is sufficient to run MIRAS‐FLEX in a fast and easy way. MIRAS‐FLEX is compared against the widely used FLEX5 and FAST, as well as the participant codes from the Offshore Code Comparison Collaboration Project. Simulation tests consist of steady wind inflow conditions with different combinations of yaw error, wind shear, tower shadow and turbine‐elastic modeling. Turbulent inflow created by using a Mann box is also considered. MIRAS‐FLEX results, such as blade tip deflections and root‐bending moments, are generally in good agreement with the other codes. Copyright © 2017 John Wiley & Sons, Ltd.     

Prediction of the wind turbine performance by using BEM with airfoil data extracted from CFD

Blade element momentum (BEM) theory with airfoil data is a widely used technique for prediction of wind turbine aerodynamic performance, but the reliability of the airfoil data is an important factor for the prediction accuracy of aerodynamic loads and power. The airfoil characteristics used in BEM codes are mostly based on 2D wind tunnel measurements of airfoils with constant span. Due to 3D effects, a BEM code using airfoil data obtained directly from 2D wind tunnel measurements will not yield the correct loading and power. As a consequence, 2D airfoil characteristics have to be corrected before they can be used in a BEM code. In this article, we consider the MEXICO (Model EXperiments In Controlled cOnditions) rotor where airfoil data are extracted from CFD (Computational Fluid Dynamics) results. The azimuthally averaged velocity is used as the sectional velocity to define the angle of attack and the coefficient of lift and drag is determined by the forces on the blade. The extracted airfoil data are put into a BEM code without further corrections, and the calculated axial and tangential forces are compared to both computations using BEM with Shen's tip loss correction model and experimental data. The comparisons show that the recalculated forces by using airfoil data extracted from CFD have good agreements with the experiment.     

Superposition of vortex cylinders for steady and unsteady simulation of rotors of finite tip‐speed ratio

Joukowski introduced in 1912 a helical vortex model to represent the vorticity of a rotor and its wake. For an infinite number of blades but finite tip‐speed ratio, the model consists of a vortex cylinder of longitudinal and tangential vorticity, a root vortex and a bound vortex disk. A superposition of cylinders is used in this paper to model rotors of radially varying circulation. The relations required to form a consistent system of cylinders are derived. The model contains a term which is not accounted for in the standard blade element momentum (BEM) algorithm. This term is identified as the contribution from the pressure drop due to the wake rotation. The BEM algorithm can be corrected to account for this effect. Unlike previous work on the topic, the contribution is derived for a radially varying circulation. A high‐thrust correction is also presented to extend the model. The optimal power coefficient obtained with this model for the constant circulation rotor is assessed and compared with that of existing solutions. Results from prescribed thrust distributions are compared with that of actuator disk simulations. Steady simulations are performed to compare with the BEM algorithm. The model is also applied to compute the velocity field in the entire domain and perform unsteady simulations. Results for an unsteady simulation corresponding to a pitch change of the rotor is used to compare the model with measurements and a BEM code with a dynamic inflow model. Copyright © 2015 John Wiley & Sons, Ltd.     

Extraction of airfoil data using PIV and pressure measurements

A newly developed technique for determining the angle of attack (AOA) on a rotating blade is used to extract AOAs and airfoil data from measurements obtained during the MEXICO (Model rotor EXperiments in COntrolled conditions) rotor experiment. Detailed surface pressure and Particle Image Velocimetry (PIV) flow fields at different rotor azimuth positions are examined for determining sectional airfoil data. The AOA is derived locally by determining the local circulation on the blade from pressure data and subtracting the induction of the bound circulation from the local velocity. The derived airfoil data are compared to 2D data from wind tunnel experiments and XFOIL computations. The comparison suggests that the rotor is subject to severe 3D effects originating from the geometry of the rotor, and explains why the Blade Element Momentum technique with 2D airfoil data over‐predicts the loading of the rotor. The extraction technique is verified by employing the derived airfoil characteristics as input to computations using the BEM technique and comparing the calculated axial and tangential forces to the measured data. The comparison also demonstrates that the used technique of determining the AOA is a reliable tool to extract airfoil data from experimental data. Copyright © 2010 John Wiley & Sons, Ltd.     

Extracting lift and drag polars from blade‐resolved computational fluid dynamics for use in actuator line modelling of horizontal axis turbines

Low order rotor models such as the actuator line method are desirable as an efficient method of computing the large range of operating and environmental conditions, required to design wind and tidal rotors and arrays. However, the integrated thrust and torque predictions for each rotor are dominated by the blade loading on the outboard sections, where three‐dimensional (3D) effects become increasingly significant, and the accuracy of the reduced order methods remains uncertain. To investigate the accuracy of the spanwise blade loading on an individual rotor, actuator line and blade boundary layer resolved computations of the Model Rotor Experiments in Controlled Conditions (MEXICO) rotor are presented. The high fidelity blade‐resolved simulations give good agreement with measured pressure coefficient and particle image velocimetry data. Alternative lift and drag polars are extracted from the 3D simulated flow fields as a function of radial position. These are then used as replacement inputs for the actuator line method. Significant improvement in the accuracy of the actuator line predictions is found when using these 3D extracted polars, compared with using simulated two‐dimensional lift and drag polars with empirical correction applied to the spanwise loading distribution. Additionally, the 3D flow field data is used to derive different axial and tangential spanwise loading corrections for use with the two‐dimensional blade polars. Copyright © 2016 John Wiley & Sons, Ltd.     

Isogeometric based framework for aeroelastic wind turbine blade analysis

A framework based on isogeometric analysis is presented for parametrizing a wind turbine rotor blade and evaluating its response. The framework consists of a multi‐fidelity approach for wind turbine rotor analysis. The aeroelastic loads are determined using a low‐fidelity model. The model is based on isogeometric approach to model both the structural and aerodynamic properties. The structural deformations are solved using an isogeometric formulation of geometrically exact 3D beam theory. The aerodynamic loads are calculated using a standard Blade Element Momentum(BEM) theory. Moreover, the aerodynamic loads calculated using BEM theory are modified to account for the change in the blade shape due to blade deformation. The aeroelastic loads are applied in finite element solver Nastran, and both the stress response and buckling response are extracted. Furthermore, the capabilities of Nastran are extended such that design dependent loads can be applied, resulting in correct aeroelastic sensitivities of Nastran responses, making this framework suitable for optimization. The framework is verified against results from the commercial codes FAST and GH Bladed, using the NREL 61.5m rotor blade as a baseline for comparison, showing good agreement. Copyright © 2016 John Wiley & Sons, Ltd.     

Quantifying wave and yaw effects on a scale tidal stream turbine

The behaviour of Tidal Stream Turbines (TST) in the dynamic flow field caused by waves and rotor misalignment to the incoming flow (yaw) is currently unclear. The dynamic loading applied to the turbine could drive the structural design of the power capture and support subsystems, device size and its proximity to the water surface and sea bed. In addition, the strongly bi-directional nature of the flow encountered at many tidal energy sites may lead to devices omitting yaw drives; accepting the additional dynamic loading associated with rotor misalignment and reduced power production in return for a reduction in device capital cost. Therefore it is imperative to quantify potential unsteady rotor loads so that the TST device design accommodates the inflow conditions and avoids an unacceptable increase in maintenance action or, more seriously, suffers sudden structural failure.The experiments presented in this paper were conducted using a 1:20th scale 3-bladed horizontal axis TST at a large towing tank facility. The turbine had the capability to measure rotor thrust and torque whilst one blade was instrumented to acquire blade root strain, azimuthal position and rotational speed all at high frequency. The maximum out-of-plane bending moment was found to be as much as 9.5 times the in-plane bending moment. A maximum loading range of 175% of the median out-of-plane bending moment and 100% of the median in-plane bending moment was observed for a turbine test case with zero rotor yaw, scaled wave height of 2 m and intrinsic wave period of 12.8 s.A new tidal turbine-specific Blade-Element Momentum (BEM) numerical model has been developed to account for wave motion and yawed flow effects. This model includes a new dynamic inflow correction which is shown to be in close agreement with the measured experimental loads. The gravitational component was significant to the experimental in-plane blade bending moment and was also included in the BEM model. Steady loading on an individual blade at positive yaw angles was found to be negligible in comparison to wave loading (for the range of experiments conducted), but becomes important for the turbine rotor as a whole, reducing power capture and rotor thrust. The inclusion of steady yaw effects (using the often-applied skewed axial inflow correction) in a BEM model should be neglected when waves are present or will result in poor load prediction reflected by increased loading amplitude in the 1P (once per revolution) phase.     

Shape optimization of wind turbine blades

This paper presents a design tool for optimizing wind turbine blades. The design model is based on an aerodynamic/aero‐elastic code that includes the structural dynamics of the blades and the Blade Element Momentum (BEM) theory. To model the main aero‐elastic behaviour of a real wind turbine, the code employs 11 basic degrees of freedom corresponding to 11 elastic structural equations. In the BEM theory, a refined tip loss correction model is used. The objective of the optimization model is to minimize the cost of energy which is calculated from the annual energy production and the cost of the rotor. The design variables used in the current study are the blade shape parameters, including chord, twist and relative thickness. To validate the implementation of the aerodynamic/aero‐elastic model, the computed aerodynamic results are compared to experimental data for the experimental rotor used in the European Commision‐sponsored project Model Experiments in Controlled Conditions, (MEXICO) and the computed aero‐elastic results are examined against the FLEX code for flow past the Tjæreborg 2 MW rotor. To illustrate the optimization technique, three wind turbine rotors of different sizes (the MEXICO 25 kW experimental rotor, the Tjæreborg 2 MW rotor and the NREL 5 MW virtual rotor) are applied. The results show that the optimization model can reduce the cost of energy of the original rotors, especially for the investigated 2 MW and 5 MW rotors. Copyright © 2009 John Wiley & Sons, Ltd.     

Tip loss corrections for wind turbine computations

As an essential ingredient in the blade element momentum theory, the tip loss effect of rotors plays an important role in the prediction of wind turbine performance. Various tip loss corrections based on the Prandtl tip loss function are analysed in the article. Comparisons with measurements and theoretical analyses show that existing tip loss correction models are inconsistent and fail to predict correctly the physical behaviour in the proximity of the tip. A new tip loss correction model is proposed that remedies the inconsistency. Comparisons between numerical and experimental data show that the new model results in much better predictions of the loading in the tip region. Copyright © 2005 John Wiley & Sons, Ltd.     

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

A comprehensive investigation of the Blade Element Momentum (BEM) model using detailed numerical simulations with an axis symmetric actuator disc (AD) model has been carried out. The present implementation of the BEM model is in a version where exactly the same input in the form of non‐dimensional axial and tangential load coefficients can be used for the BEM model as for the numerical AD model. At a rotor disc loading corresponding to maximum power coefficient, we found close correlation between the AD and BEM model as concerns the integral value of the power coefficient. However, locally along the blade radius, we found considerable deviations with the general tendency, that the BEM model underestimates the power coefficient on the inboard part of the rotor and overestimates the coefficient on the outboard part. A closer investigation of the deviations showed that underestimation of the power coefficient on the inboard part could be ascribed to the pressure variation in the rotating wake not taken into account in the BEM model. We further found that the overestimation of the power coefficient on the outboard part of the rotor is due to the expansion of the flow causing a non‐uniform induction although the loading is uniform. Based on the findings we derived two small engineering sub‐models to be included in the BEM model to account for the physical mechanisms causing the deviations. Finally, the influence of using the corrected BEM model, BEM_cor on two rotor designs is presented. Copyright © 2009 John Wiley & Sons, Ltd.     

Dynamic characteristics and enhanced performance of a novel wind turbine rotor analyzed via experiments and numerical simulation

The enormous demand for large wind turbine rotors has led to a need to develop high‐performance and reliable wind turbine rotors. The flexibility of the huge blade was a challenge in creating a balanced design with regard to dynamic behavior, mass, and power output. To enhance the wind turbine rotor, a newly designed wind turbine system with a supporting rod and damper was proposed and investigated. A scaled blade was experimentally tested, with the results indicating an increase in both frequency and damping of the system. Through the use of a self‐coded numerical model, the correlations between the design constraints and the dynamic behavior, tip displacement, and additional mass of the rotor were demonstrated. This showed that the novel rotor has some preferable characteristics in both static and dynamic aspects. In particular, this blade is stiffer and has a smaller tip displacement compared with a traditional cantilevered blade. These characteristics enabled the effective application of the novel rotor to a 5‐MW wind turbine to achieve a 15.16% power output increase based on the blade element momentum theory with Prandtl correction, as well as 5.1% mass savings. Copyright © 2016 John Wiley & Sons, Ltd.     

Determination of the angle of attack on rotor blades

Two simple methods for determining the angle of attack (AOA) on a section of a rotor blade are proposed. Both techniques consist of employing the Biot–Savart integral to determine the influence of the bound vorticity on the velocity field. In the first technique, the force distribution along the blade and the velocity at a monitor point in the vicinity of the blade are assumed to be known from experiments or CFD computations. The AOA is determined by subtracting the velocity induced by the bound circulation, determined from the loading, from the velocity at the monitor point. In the second method, the full pressure distribution on the blade is assumed to be known and used to determine the local distribution of circulation along the surface contour of the blade. Using the local distribution of circulation to determine the influence of the bound vorticity enables the velocity monitor points to be located closer to the blade, and thus to determine the AOA with higher accuracy. Data from CFD computations for flows past the Tellus 95 kW wind turbine at different wind speeds are used to test both techniques. Comparisons show that the proposed methods are in good agreement with existing techniques. The advantage of the proposed techniques, as compared with existing techniques, is that they can be used to determine the AOA on rotor blades under general flow conditions (e.g. operations in yaw or with dynamic inflow). Copyright © 2008 John Wiley & Sons, Ltd.     

Improved fixed point iterative method for blade element momentum computations

The blade element momentum (BEM) theory is widely used in aerodynamic performance calculations and optimization applications for wind turbines. The fixed point iterative method is the most commonly utilized technique to solve the BEM equations. However, this method sometimes does not converge to the physical solution, especially for the locations near the blade tip and root where the failure rate of the iterative method is high. The stability and accuracy of aerodynamic calculations and optimizations are greatly reduced due to this problem. The intrinsic mechanisms leading to convergence problems are addressed through both theoretical analysis and numerical tests. A term from the BEM equations equals to zero at a critical inflow angle is the source of the convergence problems. When the initial inflow angle is set larger than the critical inflow angle and the relaxation methodology is adopted, the convergence ability of the iterative method will be greatly enhanced. Numerical tests have been performed under different combinations of local tip speed ratio, local solidity, local twist and airfoil aerodynamic data. Results show that the simple iterative methods have a good convergence ability which will improve the aerodynamic or structural design of wind turbines. Copyright © 2017 John Wiley & Sons, Ltd.     

Parametric dependencies of the yawed wind‐turbine wake development

Yaw misalignment is currently being treated as one of the most promising methods for optimizing the power of wind farms. Therefore, detailed knowledge of the impact of yaw on the wake development is necessary for a range of operating conditions. This study numerically investigates the wake development behind a single yawed wind turbine operating at different tip‐speed ratios and yaw angles using the actuator‐line method in the spectral‐element code Nek5000. It is shown that depending on the tip‐speed ratio, the blade loading varies along the azimuth, resulting in a wake that is asymmetric in both the horizontal and vertical directions. Large tip‐speed ratios as well as large yaw angles are shown to decrease the vertical asymmetry of the yaw‐induced counter‐rotating vortex pair. Both parameters have the effect that they increase the spanwise force induced by yaw relative to the wake rotation. However, while the strength of the counter‐rotating vortex pair in the far wake increases with yaw angle, it is shown to decrease with the tip‐speed ratio. The vertical shift in the wake center is found to be highly dependent on the yaw angle and the tip‐speed ratio. These detailed insights into the yawed wake are important when optimizing potential downstream turbines.     

Time‐accurate blade surface static pressure behaviour on a rotating H‐Darrieus wind turbine

Time‐accurate blade pressure distributions on a rotating H‐Darrieus wind turbine at representative tip speed ratios during start‐up are presented here, which allow blade dynamic stall and laminar separation bubbles to be observed clearly and which provide a rare experimental demonstration of the flow curvature effect inherent in H‐Darrieus turbine operation. The convection of a dynamic stall vortex along the blade surface at high reduced frequency has also been clearly identified. This study provides new information of the complex aerodynamics of the vertical axis wind turbines (VAWTs) and provides unique experimental data to validate the transient blade static surface pressure distribution predicted by CFD models. To the best of the authors' knowledge, this is the first time that the instantaneous pressure variation around the blade has been measured and recorded directly for an H‐Darrieus wind turbine.     

An improved BEM model for the power curve prediction of stall‐regulated wind turbines

Blade element momentum (BEM) theory is the standard computational technique for the prediction of power curves of wind turbines; it is based on the two‐dimensional aerodynamic properties of aerofoil blade elements and some corrections accounting for three‐dimensional wing aerodynamics. Although most BEM models yield acceptable results for low‐wind and pitch‐controlled regimes where the local angles of attack are small, no generally accepted model exists up to date that consistently predicts the power curve in the stall regime for a variety of blade properties and operating conditions. In this article we present a modified BEM model which satisfactorily reproduces the power curves of four experimental wind turbines reported in the literature, using no free fit parameters. Since these four experimental cases comprehend a great variety of conditions (wind tunnel vs field experiments, different air densities) and blade parameters (no twist and no taper, no taper but twist, both twist and taper, different aerofoil families), it is believed that our model represents a useful working tool for the aerodynamic design of stall‐regulated wind turbines. Copyright © 2004 John Wiley & Sons, Ltd.