Influence of wind turbine flexibility on loads and power production

Most aeroelastic codes used today assume small blade deflections and application of loads on the undeflected structure. However, with the design of lighter and more flexible wind turbines, this assumption is not obvious. By scaling the system mass and stiffness properties equally, it is possible to compare wind turbines of different degrees of slenderness and at the same time keep system frequencies the same in an undeformed state. The developed model uses the commercial finite element system MSC. Marc, focused on non‐linear design and analysis, to predict the structural response. The aerodynamic model AERFORCE, used to transform the wind to loads on the blades, is a blade element momentum model. A comparison is made between different slenderness ratios in three wind conditions below rated wind speed. The results show that large blade deflections have a major influence on power production and the resulting structural loads and must be considered in the design of very slender turbines. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical validation of a finite element thin‐walled beam model of a composite wind turbine blade

This paper presents a numerical validation of a thin‐walled beam (TWB) finite element (FE) model of a realistic wind turbine rotor blade. Based on the theory originally developed by Librescu et al. and later extended to suit FE modelling by Phuong, Lee and others, this computationally efficient yet accurate numerical model is capable of capturing most of the features found in large blades including thin‐walled hollow cross section with variable thickness along the section's contour, inner reinforcements, arbitrary material layup and non‐linear anisotropic fibre‐reinforced composites; the present application is, for the time being, restricted to linearity. This one‐dimensional (1D) FE model allows retaining information of different regions of the blade's shell and therefore approximates the behaviour of more complex three‐dimensional (3D) shell or solid FE models more accurately than typical 1D FE beam models. A 9.2 m rotor blade, previously reported in specialized literature, was chosen as a case study to validate the static and dynamic behaviour predicted by a TWB model against an industry‐standard 3D shell model built in a commercial software tool. Given the geometric and material complexities involved, an excellent agreement was found for static deformation curves, as well as a good prediction of the lowest frequency modes in terms of resonance frequencies, mode shapes and frequency response functions; the highest (sixth) frequency mode shows only a fair agreement as expected for an FE model. It is concluded that despite its simplicity, a TWB FE model is sufficiently accurate to serve as a design tool for the recursive analyses required during design and optimization stages of wind turbines using only readily available computational tools. Copyright © 2011 John Wiley & Sons, Ltd.     

Representation of wind turbine blade responses in power production load cases by linear mode shapes

The wind turbine industry is designing large MW size turbines with very long blades, which exhibit large deflections during their operational life. These large deflections decrease the accuracy of linear models such as linear finite element and modal‐based models, in which the structure is represented by linear mode shapes. The aim of this study is to investigate the competence of the mode shapes to represent the large blade responses in normal operation load cases. For this purpose, blade deflections are projected onto the linear modal space, swept by mode shape vectors. The projection shows the contribution of each mode and the projection error. The blade deflections are calculated by a nonlinear aero‐servo‐elastic solver for power production fatigue load cases with normal turbulence. The mode shapes are calculated at the steady‐state deflected blade position computed at different wind speeds. Three reference turbine blades are used in the study to evaluate the effects of various blade design parameters such as length, stiffness, mass, and prebend. The results show that although the linear mode shapes can represent the flapwise and edgewise deflections accurately, axial and torsional deflections cannot be captured with good accuracy. The geometric nonlinear effects are more apparent in the latter directions. The results indicate that the blade deflections occur beyond the linear assumptions.     

A vortex model for Darrieus turbine using finite element techniques

Since 1970 several aerodynamic prediction models have been formulated for the Darrieus turbine. We can identify two families of models: stream-tube and vortex. The former needs much less computation time but the latter is more accurate. The purpose of this paper is to show a new option for modelling the aerodynamic behaviour of Darrieus turbines. The idea is to combine a classic free vortex model with a finite element analysis of the flow in the surroundings of the blades. This avoids some of the remaining deficiencies in classic vortex models. The agreement between analysis and experiment when predicting instantaneous blade forces and near wake flow behind the rotor is better than the one obtained in previous models.     

Fatigue load computation of wind turbine gearboxes by coupled finite element,multi‐body system and aerodynamic analysis

The main concern of the present publication is the computation of dynamic loads of wind turbine power trains, with particular emphasis on planetary gearbox loads. The applied mathematical approach relies on a non‐linear finite element method, which is extended by multi‐body system functionalities, and aerodynamics based on the blade element momentum theory. Copyright © 2007 John Wiley & Sons, Ltd.     

Aeroelastic analysis of a wind turbine blade using the harmonic balance method

An aeroelastic model for wind turbine blades derived from the unsteady Navier‐Stokes equations and a mode shape–based structural dynamics model are presented. For turbulent flows, the system is closed with the Spalart‐Allmaras turbulence model. The computation times for the aerodynamic solution are significantly reduced using the harmonic balance method compared to a time‐accurate solution. This model is significantly more robust than standard aeroelastic codes that rely on blade element momentum theory to determine the aerodynamic forces. Comparisons with published results for the Caradonna‐Tung rotor in hover and the classical AGARD 445.6 flutter case are provided to validate the aerodynamic model and aeroelastic model, respectively. For wind turbines, flutter of the 1.5 MW WindPACT blade is considered. The results predict that the first flapwise and edgewise modes dominate flutter at the rotor speeds considered.     

BeamDyn: a high‐fidelity wind turbine blade solver in the FAST modular framework

This paper presents a numerical implementation of the geometrically exact beam theory based on the Legendre‐spectral‐finite‐element (LSFE) method. The displacement‐based geometrically exact beam theory is presented, and the special treatment of three‐dimensional rotation parameters is reviewed. An LSFE is a high‐order finite element with nodes located at the Gauss–Legendre–Lobatto points. These elements can be an order of magnitude more computationally efficient than low‐order finite elements for a given accuracy level. The new module, BeamDyn, is implemented in the FAST modularization framework for dynamic simulation of highly flexible composite‐material wind turbine blades within the FAST aeroelastic engineering model. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples are provided to validate BeamDyn and examine the LSFE performance as well as the coupling algorithm in the FAST modularization framework. BeamDyn can also be used as a stand‐alone high‐fidelity beam tool. Copyright © 2017 John Wiley & Sons, Ltd.     

Wind turbine rotor imbalance detection using nacelle and blade measurements

Wind power is the world's fastest growing renewable energy source, but operations and maintenance costs are still a major obstacle toward reliability and widescale adoption of wind power, accounting for a large part of the cost of energy for offshore installations. Structural health monitoring systems have been proposed for implementing condition‐based maintenance. The wind energy industry currently uses condition monitoring systems that are mostly adapted from roating machinery in other power generation industries. However, these systems have had limited effectiveness on wind turbines because of their atypical operating conditions, which are characterized by low and variable rotational speed, rapidly varying torque, extremely large rotors and stochastic loading from the wind. Although existing systems primarily take measurements from the nacelle, valuable information can be extracted from the structural dynamic response of the rotor blades to mitigate potentially damaging loading conditions. One such condition is rotor imbalance, which not only reduces the aerodynamic efficiency of the turbine and therefore its power output but can also lead to very large increases in loading on the drivetrain, blades and tower. The National Renewable Energy Laboratory's fast software was used to model both mass and aerodynamic imbalance in a 5 MW offshore wind turbine. It is shown that a combination of blade and nacelle measurements, most of which can be obtained from standard instrumentation already found on utility‐scale wind turbines, can be formulated into an algorithm used to detect and locate imbalance. The method described herein allows for imbalance detection that is potentially more sensitive than existing on‐line systems, while taking advantage of sensors that are already in place on many utility‐scale wind turbines. Copyright © 2014 John Wiley & Sons, Ltd.     

A finite element model for pre‐stressed or post‐tensioned concrete wind turbine towers

Wind turbine support towers have been traditionally formed of structural steel tubular sections, being fabricated in large sections under factory conditions before being transported to site for erection. Given the trend towards developing turbines with hub heights in excess of 90 m, it is now necessary to develop towers of concrete and other materials that can provide improved dynamic properties and ease transportation difficulties over the structural steel solutions. Concrete towers of this height require pre‐stressing to overcome high vertical stresses induced in bending, which would otherwise lead to cracking in the concrete, with a resulting reduction in the tower's natural frequency. In order to properly understand the behaviour of concrete towers, it is necessary to take account of both material and geometric non‐linearity. Material non‐linearity of concrete is well understood, and geometric non‐linearity arises because of the imposition of an initial stress into the concrete by way of the application of pre‐stress. In this paper, a finite element model is proposed, which will describe the concrete as a continuum of four‐noded, two‐dimensional Reisser–Mindlin shell elements. The pre‐stressing tendons are to be represented by one‐dimensional bar elements, with an imposed pre‐stress. For the numerical examples considered in the paper, tendons are modelled to be post‐tensioned and debonded. The effect of varying the design parameter of magnitude of pre‐stress and the time dependence of pre‐stress force has been investigated using the model described. The impact that concrete compressive strength had on overall tower stiffness was also investigated. Copyright © 2014 John Wiley & Sons, Ltd.     

基于有限元法的漂浮式风力机Spar平台动态响应分析

以美国可再生能源实验室(NREL)的5 MW漂浮式风力机和Spar平台为参考模型,采用有限元分析法分析了Spar平台的波浪载荷频域特性,包括对振幅响应算子、绕射力和F-K力频域动态响应分析,并对比了三种波浪谱(P-M谱、JONSWAP谱和Wen’s谱)海况下的时域响应.结果表明:Spar平台载荷峰值出现在低频波浪作用下,且响应明显,而随着频率的增大,其值逐渐减小;在P-M谱和Wen’s谱作用下的平台动态响应无明显差异,且两者的振幅和周期大致相同,而在JONSWAP谱作用下的平台动态响应最小,但其往复周期小,频率大,使得系泊系统承受较大的周期性张力.     

具有温度场的冷却叶片振动特性计算方法研究

根据稳态热传导的相关理论,建立了透平冷却叶片温度场和热应力场的四面体三维有限元分析模型和方法,并在此基础上建立了透平冷却叶片振动特性三维有限元分析方法,开发了相关计算软件。对某航空发动机透平高压第1级冷却叶片在不同工作条件下的振动特性进行了计算分析,同时研究了热应力、温度场、转速等对叶片振动特性的影响,表明本文中所建立模型和方法是科学、合理和精确的,为开展透平冷却叶片的设计和振动安全性评价奠定了基础。     

Open‐loop frequency response analysis of a wind turbine using a high‐order linear aeroelastic model

Wind turbine controllers are commonly designed on the basis of low‐order linear models to capture the aeroelastic wind turbine response due to control actions and disturbances. This paper characterizes the aeroelastic wind turbine dynamics that influence the open‐loop frequency response from generator torque and collective pitch control actions of a modern non‐floating wind turbine based on a high‐order linear model. The model is a linearization of a geometrically non‐linear finite beam element model coupled with an unsteady blade element momentum model of aerodynamic forces including effects of shed vorticity and dynamic stall. The main findings are that the lowest collective flap modes have limited influence on the response from generator torque to generator speed, due to large aerodynamic damping. The transfer function from collective pitch to generator speed is affected by two non‐minimum phase zeros below the frequency of the first drivetrain mode. To correctly predict the non‐minimum phase zeros, it is essential to include lateral tower and blade flap degrees of freedom. Copyright © 2013 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.     

Aerodynamic optimization of wind turbine rotors using a blade element momentum method with corrections for wake rotation and expansion

The blade element momentum (BEM) method is widely used for calculating the quasi‐steady aerodynamics of horizontal axis wind turbines. Recently, the BEM method has been expanded to include corrections for wake expansion and the pressure due to wake rotation (), and more accurate solutions can now be obtained in the blade root and tip sections. It is expected that this will lead to small changes in optimum blade designs. In this work, has been implemented, and the spanwise load distribution has been optimized to find the highest possible power production. For comparison, optimizations have been carried out using BEM as well. Validation of shows good agreement with the flow calculated using an advanced actuator disk method. The maximum power was found at a tip speed ratio of 7 using , and this is lower than the optimum tip speed ratio of 8 found for BEM. The difference is primarily caused by the positive effect of wake rotation, which locally causes the efficiency to exceed the Betz limit. Wake expansion has a negative effect, which is most important at high tip speed ratios. It was further found that by using , it is possible to obtain a 5% reduction in flap bending moment when compared with BEM. In short, allows fast aerodynamic calculations and optimizations with a much higher degree of accuracy than the traditional BEM model. Copyright © 2011 John Wiley & Sons, Ltd.     

钝尾缘叶片有限元模态与实验模态的对比研究

风力机叶片的模态分析是保障风力机整机稳定性及其可靠性分析的重要基础。对中国科学院工程热物理研究所研发的100kW钝尾缘实验叶片进行了有限元模态及实验模态研究,得出了叶片前几阶模态的振型及频率,探讨了对叶片稳定性影响比较显著的模态特性,通过对有限元模态及实验模态结果对比,分析了产生误差的原因及产生共振的可能性,为风力机叶片的稳定运行提供了理论依据。     

5MW风力发电机复合材料叶片结构力学特性分析

大型风力发电机复合材料叶片的强度、刚度和抵抗屈曲等结构力学特性对风机的性能及寿命有重要的影响。文章结合MATLAB和ANSYS有限元建模方法,建立了含有铺层信息的复合材料叶片三维有限元模型,对5MW风力发电机叶片进行了静态结构力学特性分析;定义了两种极端运行工况,分析和计算了极端工况载荷作用下的叶尖位移及力学特性,得到了应力最大的关键区域及屈曲特征。将仿真分析结果与FAST软件计算结果进行对比,验证了该方法的有效性,为进一步地分析和铺层厚度优化提供了可行的方法和参考依据。     

Load control on a dynamically pitching finite span wind turbine blade using synthetic jets

The feasibility of active flow control, via arrays of synthetic jet actuators, to mitigate hysteresis was investigated experimentally on a dynamically pitching finite span S809 blade. In the present work, a six‐component load cell was used to measure the unsteady lift, drag and pitching moment. Stereoscopic Particle Image Velocimetry (SPIV) measurements were also performed to understand the effects of synthetic jets on flow separation during dynamic pitch and to correlate these effects with the forces and moment measurements. It was shown that active flow control could significantly reduce the hysteresis in lift, drag and pitching moment coefficients during dynamic pitching conditions. This effect was further enhanced when the synthetic jets were pulsed modulated. Furthermore, additional reduction in the unsteady load oscillations can be observed in post‐stall conditions during dynamic motions. This reduction in the unsteady aerodynamic loading can potentially lead to prolonged life of wind turbine blades. Copyright © 2014 John Wiley & Sons, Ltd.     

Wind plant power optimization through yaw control using a parametric model for wake effects—a CFD simulation study

This article presents a wind plant control strategy that optimizes the yaw settings of wind turbines for improved energy production of the whole wind plant by taking into account wake effects. The optimization controller is based on a novel internal parametric model for wake effects called the FLOw Redirection and Induction in Steady‐state (FLORIS) model. The FLORIS model predicts the steady‐state wake locations and the effective flow velocities at each turbine, and the resulting turbine electrical energy production levels, as a function of the axial induction and the yaw angle of the different rotors. The FLORIS model has a limited number of parameters that are estimated based on turbine electrical power production data. In high‐fidelity computational fluid dynamics simulations of a small wind plant, we demonstrate that the optimization control based on the FLORIS model increases the energy production of the wind plant, with a reduction of loads on the turbines as an additional effect. Copyright © 2014 John Wiley & Sons, Ltd.     

A new correlation on the MEXICO experiment using a 3D enhanced blade element momentum technique

The blade element momentum (BEM) theory is based on the actuator disc (AD) model, which is probably the oldest analytical tool for analysing rotor performance. The BEM codes have very short processing times and high reliability. The problems of the analytical codes are well known to the researchers: the impossibility of describing inside the one-dimensional code the three-dimensional (3D) radial flows along the span-wise direction. In this work, the authors show how the 3D centrifugal pumping affects the BEM calculations of a wind turbine rotor. Actually to ascertain the accuracy of the analytical codes, the results are compared with rotor performance, blade loads and particle image velocimetry measurements of the model experiment in controlled conditions. A reliable agreement with the measurement is obtained. A good improvement is gained when the blade stall state modified aerofoil data instead of the original aerofoil data are used in the calculations.     

Experimental investigation of bearing slip in a wind turbine gearbox during a transient grid loss event

This work investigates the behaviour of the high‐speed stage of a wind turbine gearbox during a transient grid loss event. Dynamometer testing on a full‐scale wind turbine nacelle is used. A combination of external and internal gearbox measurements are analysed. Particular focus is on the characterization of the high‐speed shaft tapered roller bearing slip behaviour. This slipping behaviour is linked to dynamic events by many researchers and described as a potential bearing failure initiator; however, only limited full‐scale dynamic testing is documented. Strain gauge bridges in grooves along the circumference of the outer ring are used to characterize the bearing behaviour in detail. It is shown that during the transient event the high‐speed shaft experiences a combined torsional and bending deformation. These unfavourable loading conditions induce roller slip in the bearings during the torque reversals, indicating the potential of the applied load case to go beyond the preload of the tapered roller bearing. Copyright © 2016 John Wiley & Sons, Ltd.