Flap/lead–lag aeroelastic stability of wind turbine blade sections

The scope of this article is to investigate the aeroelastic stability of wind turbine blade sections subjected to combined flap/lead–lag motion. The work is motivated by recent concern about destructive ‘edgewise' vibrations of modern, half‐megawatt‐scale, blades. The aeroelastic governing equations derive from the combination of a spring–mass–damper equivalent of the structure and a ‘non‐stationary' aerodynamic model. The aerodynamic model used in the present context is the differential dynamic stall model developed at ONERA. The resulting equations of motion are linearized and their stability characteristics are investigated in terms of the system entries, expressed through suitable, non‐dimensional, structural and aerodynamic parameters. Copyright © 1999 John Wiley & Sons, Ltd.     

Flap/lead–lag aeroelastic stability of wind turbine blades

A numerical tool for investigating the aeroelastic stability of a single wind turbine blade subjected to combined flap/lead–lag motion is presented. Its development is motivated by recent concern about destructive edgewise vibrations of modern stall‐controlled blades. The stability tool employs a finite element formulation to discretize in space the structural and aerodynamic governing equations. Unsteady aerodynamics is considered by means of the extended ONERA lift and drag models. The mathematical form of these models allows for a combined treatment of dynamics and aerodynamics through the introduction of a so‐called ‘aeroelastic beam element’. This is an extended two‐node beam element having both deformation and aerodynamic degrees of freedom. Several linear and non‐linear versions of the stability tool are available, differing in the way that instantaneous lift and/or drag is treated. In the linear case, stability is investigated through eigenvalue analysis. Time domain integration is employed for non‐linear stability analysis. Results are presented and discussed for a 17 m stall‐controlled blade. Copyright © 2001 John Wiley & Sons, Ltd.     

Aeroelastic instability problems for wind turbines

This paper deals with the aeroelastic instabilities that have occurred and may still occur for modern commercial wind turbines: stall‐induced vibrations for stall‐turbines, and classical flutter for pitch‐regulated turbines. A review of previous works is combined with derivations of analytical stability limits for typical blade sections that show the fundamental mechanisms of these instabilities. The risk of stall‐induced vibrations is mainly related to blade airfoil characteristics, effective direction of blade vibrations and structural damping; whereas the blade tip speed, torsional blade stiffness and chordwise position of the center of gravity along the blades are the main parameters for flutter. These instability characteristics are exemplified by aeroelastic stability analyses of different wind turbines. The review of each aeroelastic instability ends with a list of current research issues that represent unsolved aeroelastic instability problems for wind turbines. Copyright © 2007 John Wiley & Sons, Ltd.     

Assessment of passive instability suppression means on pitch‐regulated wind turbines

The significance of three types of design modifications in view of defining passive means to extend the stability bounds of modern wind turbines is assessed in this paper. The first concerns the use of optimized airfoil shapes on a fixed blade planform while the other two concern the increase of structural flexibility by either bringing closer the flap and lead‐lag mode frequencies or introducing a soft yaw connection. Such an exploration of the stability envelope aims at providing the necessary understanding of the mechanisms that control aeroelastic damping and therefore at identifying means for improving the stability behaviour of the lowest damped system modes. Stability calculations are performed in the context of linear eigenvalue analysis using a state‐of‐the‐art stability tool. The model accounts for the full wind turbine configuration and the eigenvalue problem is formulated with reference to the non‐rotating (ground‐fixed) frame of reference through the multi‐blade transformation of all the rotating degrees of freedom. Results are presented in reference to a commercial multi‐MW, pitch‐regulated, variable‐speed wind turbine. They indicate that the soft yaw concept offers more significant margins of improvement compared with the flap‐lag coincidence, while aerodynamic optimization could be a basis for improvement. Copyright © 2007 John Wiley & Sons, Ltd.     

Viscous and Aeroelastic Effects on Wind Turbine Blades. The VISCEL project. Part I: 3D Navier–Stokes Rotor simulations

Aerodynamic modelling of HAWT rotors by means of “engineering methods” has reached a saddle point, where no further development can be expected without a breakthrough in understanding the physics of unsteady, rotating three‐dimensional flows. However, such a breakthrough becomes ever more necessary, as the size of the wind turbines increases. With the experimental work in that direction being mostly limited to observing the phenomena and interpreting the associated mechanisms, and its increased cost, alternatives are being sought. The use of CFD techniques and state‐of‐the‐art Navier–Stokes solvers is considered a very serious contender, a belief shared by the members of the present consortium, which has worked on the VISCEL JOR3‐CT98‐0208 Joule III project. This project's goal was to determine the aerodynamic characteristics as well as the aeroelastic behaviour of wind turbine blades across their broad range of operational conditions, from attached to highly separated flow regimes. The work programme included specific tasks for the validation and assessment of existing 3D solvers, for the parametric study of 3D flow around realistic blades and for the investigation of aeroelastic stability, at the blade section level. Copyright © 2003 John Wiley & Sons, Ltd.     

Aeroelastic validation and Bayesian updating of a downwind wind turbine

Downwind wind turbine blades are subjected to tower wake forcing at every rotation, which can lead to structural fatigue. Accurate characterisation of the unsteady aeroelastic forces in the blade design phase requires detailed representation of the aerodynamics, leading to computationally expensive simulation codes, which lead to intractable uncertainty analysis and Bayesian updating. In this paper, a framework is developed to tackle this problem. Full, detailed aeroelastic model of an experimental wind turbine system based on 3‐D Reynolds‐averaged Navier‐Stokes is developed, considering all structural components including nacelle and tower. This model is validated against experimental measurements of rotating blades, and a detailed aeroelastic characterisation is presented. Aerodynamic forces from prescribed forced‐motion simulations are used to train a time‐domain autoregressive with exogenous input (ARX) model with a localised forcing term, which provides accurate and cheap aeroelastic forces. Employing ARX, prior uncertainties in the structural and rotational parameters of the wind turbine are introduced and propagated to obtain probabilistic estimates of the aeroelastic characteristics. Finally, the experimental validation data are used in a Bayesian framework to update the structural and rotational parameters of the system and thereby reduce uncertainty in the aeroelastic characteristics.     

Aeroelastic stability predictions for a MW‐sized blade

Classical aeroelastic flutter instability historically has not been a driving issue in wind turbine design. In fact, rarely has this issue even been addressed in the past. Commensurately, among the wind turbines that have been built, rarely has classical flutter ever been observed. However, with the advent of larger turbines fitted with relatively softer blades, classical flutter may become a more important design consideration. In addition, innovative blade designs involving the use of aeroelastic tailoring, wherein the blade twists as it bends under the action of aerodynamic loads to shed load resulting from wind turbulence, may increase the blade's proclivity for flutter. With these considerations in mind it is prudent to revisit aeroelastic stability issues for a MW‐sized blade with and without aeroelastic tailoring. Focusing on aeroelastic stability associated with the shed wake from an individual blade turning in still air, the frequency domain technique developed by Theodorsen for predicting classical flutter in fixed wing aircraft has been adapted for use with a rotor blade. Results indicate that the predicted flutter speed of a MW‐sized blade is slightly greater than twice the operational speed of the rotor. When a moderate amount of aeroelastic tailoring is added to the blade, a modest decrease (12%) in the flutter speed is predicted. By comparison, for a smaller rotor with relatively stiff blades the predicted flutter speed is approximately six times the operating speed. When frequently used approximations to Theodorsen's method are implemented, drastic underpredictions result, which, while conservative, may adversely impact blade design. These underpredictions are also evident when this MW‐sized blade is analysed using time domain methods. Published in 2004 by John Wiley & Sons, Ltd.     

基于升力线理论的大型风力机气弹响应研究

针对风力机不断向大型化发展的趋势,导致结构柔度增加,气弹耦合特性和振动增强,研究了大型风力机高效精确的气弹响应分析方法。为了更准确模拟大型风力机气流沿叶片展向的三维流动现象,采用螺旋尾涡升力线模型代替传统叶素动量理论,建立了叶片气动载荷分析模型,进而结合风力机多体系统动力学模型,构建了机组的气弹耦合动力学方程和数值求解方法。以某10 MW风力机叶片为例,研究了稳态风况下不同风速的叶片气动性能,以及有效攻角、切向力等沿叶展方向的分布特点,并与采用修正叶素动量理论的气弹分析程序（HAWC）对比,结果表明,升力线理论无需引入经验修正模型即能获得叶素动量理论经修正后的分析精度。最后,通过非稳态风况下风力机的气弹响应分析,证明本文方法对大型风力机气弹耦合分析的有效性和准确性。     

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.     

Aeroelastic design of large wind turbine blades considering damage tolerance

Modern offshore turbine blades can be designed for high fatigue life and damage tolerance to avoid excessive maintenance and therefore significantly reduce the overall cost of offshore wind power. An aeroelastic design strategy for large wind turbine blades is presented and demonstrated for a 100 m blade. High fidelity analysis techniques like 3D finite element modeling are used alongside beam models of wind turbine blades to characterize the resulting designs in terms of their aeroelastic performance as well as their ability to resist damage growth. This study considers a common damage type for wind turbine blades, the bond line failure, and explores the damage tolerance of the designs to gain insight into how to improve bond line failure through aeroelastic design. Flat‐back airfoils are also explored to improve the damage tolerance performance of trailing‐edge bond line failures. Copyright © 2016 John Wiley & Sons, Ltd.     

Stability analysis of pitch‐regulated,variable‐speed wind turbines in closed loop operation using a linear eigenvalue approach

A multi‐body aeroelastic design code based on the implementation of the combined aeroelastic beam element is extended to cover closed loop operation conditions of wind turbines. The equations of a controller for variable generator speed and pitch‐controlled operation in high wind speeds are combined with the aeroelastic equations of motion for the complete wind turbine, in order to provide a compound aeroservoelastic system of equations. The control equations comprise linear differential equations for the pitch and generator torque actuators, the control feedback elements (proportional–integral control) and the various filters acting on the feedback signals. In its non‐linear form, the dynamic equations are integrated in time to provide the reference state, while upon linearization of the system and transformation in the non‐rotating frame, the linear stability equations are derived. Stability results for a multi‐MW wind turbine show that the coupling of the controller dynamics with the aeroelastic dynamics of the machine is important and must be taken into account in view of defining the controller parameters. Copyright © 2008 John Wiley & Sons, Ltd.     

Aeroelastic analysis of a floating offshore wind turbine in platform‐induced surge motion using a fully coupled CFD‐MBD method

Modern offshore wind turbines are susceptible to blade deformation because of their increased size and the recent trend of installing these turbines on floating platforms in deep sea. In this paper, an aeroelastic analysis tool for floating offshore wind turbines is presented by coupling a high‐fidelity computational fluid dynamics (CFD) solver with a general purpose multibody dynamics code, which is capable of modelling flexible bodies based on the nonlinear beam theory. With the tool developed, we demonstrated its applications to the NREL 5 MW offshore wind turbine with aeroelastic blades. The impacts of blade flexibility and platform‐induced surge motion on wind turbine aerodynamics and structural responses are studied and illustrated by the CFD results of the flow field, force, and wake structure. Results are compared with data obtained from the engineering tool FAST v8.     

风力机叶片气动降载与流动分离控制技术综述

风力机大型化已成为风电技术发展的主要趋势。但随之而来的叶片尺寸增大、气弹特性增强、多尺度流动等问题将导致叶片处于更加复杂严峻的风况及载荷环境。为提高叶片应对复杂风况及载荷的能力,提高叶片气动效率,有必要采用先进有效的流动控制技术以满足叶片气动降载与流动分离控制的需求。针对当前主流的流动控制技术进行了介绍,并对较具发展潜力的尾缘襟翼与自适应襟翼研究现状进行了重点介绍。现阶段流动控制技术并未在风力机叶片中得到广泛应用,一方面在于流动控制技术尚难与叶片现有主体控制技术相结合,以达到相辅相成的控制效果;另一方面在于对于部分控制技术,如自适应襟翼等,其控制特点尤其是其在风力机实际运行中的控制特点尚不明确。后续研究中,对于叶片气动降载,应结合更为先进的控制方法与更可靠的研究手段开展尾缘襟翼控制与叶片主体控制的协同控制研究;对于流动分离控制技术,应侧重于改善被动控制技术在非适用工况下的不良影响,同时开展流动控制技术在整机中的实验与数值研究,加快流动分离控制技术的实际应用。     

Wind turbine blade vibration at standstill conditions—the effect of imposing lag on the aerodynamic response of an elastically mounted airfoil

The present study investigated physical phenomena related to stall‐induced vibrations potentially existing on wind turbine blades at standstill conditions. The study considered two‐dimensional airfoil sections while it omitted three‐dimensional effects. In the study, a new engineering‐type computational model for the aeroelastic response of an elastically mounted airfoil was used to investigate the influence of temporal lag in the aerodynamic response on the aeroelastic stability in deep stall. The study indicated that even a relatively low lag significantly increases the damping of the model. A comparison between the results from a model with lag imposed on all force components with the results from a model with lag imposed exclusively on the lift showed only marginal difference between the damping in the two cases. A parameter study involving positions of the elastic hinge point and the center of gravity indicated that the stability is relatively independent of these parameters. Another parameter study involving spring constants showed that the stability of each mode is dependent only on the spring constant acting in the direction of the leading motion of the mode. An investigation of the influence of the added mass terms showed that only the pitch‐rate and flapwise‐acceleration terms have any influence on the stability. An investigation of three different profiles showed that the stability is heavily dependent on the aerodynamic characteristics of the profiles—mainly on the lift. It was also shown that only the edgewise mode is unstable in deep stall. Moreover, independent of the amount of temporal lag in the aerodynamic response of the model, the inflow‐angle region in the vicinity of 180° remains unstable in the edgewise mode. Therefore, this inflow‐angle region may create stability problems in real life. The other type of vibrations potentially present at standstill conditions is vortex‐induced, being outside the scope of the present study. Copyright © 2014 John Wiley & Sons, Ltd.     

Indicial lift response function: an empirical relation for finite‐thickness airfoils,and effects on aeroelastic simulations

The aeroelastic response of wind turbines is often simulated in the time domain by using indicial response techniques. Unsteady aerodynamics in attached flow are usually based on Jones's approximation of the flat plate indicial response, although the response for finite‐thickness airfoils differs from the flat plate one. The indicial lift response of finite‐thickness airfoils is simulated with a panel code, and an empirical relation is outlined connecting the airfoil indicial response to its geometric characteristics. The effects of different indicial approximations are evaluated on a 2D profile undergoing harmonic pitching motion in the attached flow region; the resulting lift forces are compared with computational fluid dynamics (CFD) simulations. The relevance for aeroelastic simulations of a wind turbine is also evaluated, and the effects are quantified in terms of variations of equivalent fatigue loads, ultimate loads, and stability limits. The agreement with CFD computations of a 2D profile in harmonic motion is improved by the indicial function accounting for the finite‐thickness of the airfoil. Concerning the full wind turbine aeroelastic behavior, the differences between simulations on the basis of Jones's and finite‐thickness indicial response functions are rather small; Jones's flat‐plate approximation results in only slightly larger fatigue and ultimate loads, and lower stability limits. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

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.     

High‐fidelity linear time‐invariant model of a smart rotor with adaptive trailing edge flaps

A high‐fidelity linear time‐invariant model of the aero‐servo‐elastic response of a wind turbine with trailing‐edge flaps is presented and used for systematic tuning of an individual flap controller. The model includes the quasi‐steady aerodynamic effects of trailing‐edge flaps on wind turbine blades and is integrated in the linear aeroelastic code HAWCStab2. The dynamic response predicted by the linear model is validated against non‐linear simulations, and the quasi‐steady assumption does not cause any significant response bias for flap deflection with frequencies up to 2–3 Hz. The linear aero‐servo‐elastic model support the design, systematic tuning and model synthesis of smart rotor control systems. As an example application, the gains of an individual flap controller are tuned using the Ziegler–Nichols method for the full‐order poles. The flap controller is based on feedback of inverse Coleman transformed and low‐pass filtered flapwise blade root moments to the cyclic flap angles through two proportional‐integral controllers. The load alleviation potential of the active flap control, anticipated by the frequency response of the linear closed‐loop model, is also confirmed by non‐linear time simulations. The simulations report reductions of lifetime fatigue damage up to 17% at the blade root and up to 4% at the tower bottom. Copyright © 2016 John Wiley & Sons, Ltd.     

Passive load alleviation on wind turbine blades from aeroelastically driven selectively compliant morphing

Load alleviation control is highly desirable to reduce penalties associated with the added structural mass required to withstand rare load scenarios. This is particularly true for wind turbine designs incorporating long‐span blades. Implementation of compliance‐based morphing structures to modify the lift distribution passively has the potential to mitigate the impact of rare, but integrally threatening, loads on wind turbine blades while limiting the addition of actuation and sensing systems. We present a novel passive load alleviation concept based on a morphing flap exhibiting selective compliance from an embedded bistable element. A multifidelity, aeroelastic tool is used to study the shape adaptability of a morphing flap indicating that passive changes from high lift generation to load alleviation configurations can be achieved by exploiting the energy of the flow. This mechanism offers a method to reduce catastrophic peak loads potentially, thus offering the possibility to lower the overall structural weight of wind turbine blades.