Damping of edgewise vibration in wind turbine blades by means of circular liquid dampers

This paper proposes a new type of passive vibration control damper for controlling edgewise vibrations of wind turbine blades. The damper is a variant of the liquid column damper and is termed as a circular liquid column damper (CLCD). Rotating wind turbine blades generally experience a large centrifugal acceleration. This centrifugal acceleration makes the use of this kind of oscillatory liquid damper feasible with a small mass ratio to effectively suppress edgewise vibrations. A reduced 2‐DOF non‐linear model is used for tuning the CLCD attached to a rotating wind turbine blade, ignoring the coupling between the blade and the tower. The performance of the damper is evaluated under various rotational speeds of the rotor. A special case in which the rotational speed is so small that the gravity dominates the motion of the liquid is also investigated. Further, the legitimacy of the decoupled optimization is verified by incorporating the optimized damper into a more sophisticated 13‐DOF aeroelastic wind turbine model with due consideration to the coupled blade‐tower‐drivetrain vibrations of the wind turbine as well as a pitch controller. The numerical results from the illustrations on a 5 and a 10MW wind turbine machine indicate that the CLCD at an optimal tuning can effectively suppress the dynamic response of wind turbine blades. Copyright © 2015 John Wiley & Sons, Ltd.     

Accuracy of an efficient framework for structural analysis of wind turbine blades

This paper presents a novel framework for the structural design and analysis of wind turbine blades and establishes its accuracy. The framework is based on a beam model composed of two parts—a 2D finite element‐based cross‐section analysis tool and a 3D beam finite element model. The cross‐section analysis tool is able to capture the effects stemming from material anisotropy and inhomogeneity for sections of arbitrary geometry. The proposed framework is very efficient and therefore ideally suited for integration within wind turbine aeroelastic design and analysis tools. A number of benchmark examples are presented comparing the results from the proposed beam model to 3D shell and solid finite element models. The examples considered include a square prismatic beam, an entire wind turbine rotor blade and a detailed wind turbine blade cross section. Phenomena at both the blade length scale—deformation and eigenfrequencies—and cross section scale—3D material strain and stress fields—are analyzed. Furthermore, the effect of the different assumptions regarding the boundary conditions is discussed in detail. The benchmark examples show excellent agreement suggesting that the proposed framework is a highly efficient alternative to 3D finite element models for structural analysis of wind turbine blades. Copyright © 2015 John Wiley & Sons, Ltd.     

Classical flutter analysis of composite wind turbine blades including compressibility

For wind turbine blades with the increased slenderness ratio, flutter instability may occur at lower wind and rotational speeds. For long blades, at the flutter condition, relative velocities at blade sections away from the hub center are usually in the subsonic compressible range. In this study, for the first time for composite wind turbine blades, a frequency domain classical flutter analysis methodology has been presented including the compressibility effect only for the outboard blade sections, which are in the compressible flow regime exceeding Mach 0.3. Flutter analyses have been performed for the baseline blade designed for the 5‐MW wind turbine of NREL. Beam‐blade model has been generated by making analogy with the structural model of the prewisted rotating thin‐walled beam (TWB) and variational asymptotic beam section (VABS) method has been utilized for the calculation of the sectional properties of the blade. To investigate the compressibility effect on the flutter characteristics of the blade, frequency and time domain aeroelastic analyses have been conducted by utilizing unsteady aerodynamics via incompressible and compressible indicial functions. This study shows that with use of compressible indicial functions, the effect of compressibility can be taken into account effectively in the frequency domain aeroelastic stability analysis of long blades whose outboard sections are inevitably in the compressible flow regime at the onset of flutter.     

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.     

Viscous and Aeroelastic Effects on Wind Turbine Blades. The VISCEL Project. Part II: Aeroelastic Stability Investigations

The recent introduction of ever larger wind turbines poses new challenges with regard to understanding the mechanisms of unsteady flow–structure interaction. An important aspect of the problem is the aeroelastic stability of the wind turbine blades, especially in the case of combined flap/lead–lag vibrations in the stall regime. Given the limited experimental information available in this field, the use of CFD techniques and state‐of‐the‐art viscous flow solvers provides an invaluable alternative towards the identification of the underlying physics and the development and validation of sound engineering‐type aeroelastic models. Navier–Stokes‐based aeroelastic stability analysis of individual blade sections subjected to combined pitch/flap or flap/lead–lag motion has been attempted by the present consortium in the framework of the concluded VISCEL JOR3‐CT98‐0208 Joule III project. Copyright © 2003 John Wiley & Sons, Ltd.     

Assessment of a comprehensive aeroelastic tool for horizontal‐axis wind turbine rotor analysis

This paper presents the development of a computational aeroelastic tool for the analysis of performance, response and stability of horizontal‐axis wind turbines. A nonlinear beam model for blades structural dynamics is coupled with a state‐space model for unsteady sectional aerodynamic loads, including dynamic stall effects. Several computational fluid dynamics structural dynamics coupling approaches are investigated to take into account rotor wake inflow influence on downwash, all based on a Boundary Element Method for the solution of incompressible, potential, attached flows. Sectional steady aerodynamic coefficients are extended to high angles of attack in order to characterize wind turbine operations in deep stall regimes. The Galerkin method is applied to the resulting aeroelastic differential system. In this context, a novel approach for the spatial integration of additional aerodynamic states, related to wake vorticity and dynamic stall, is introduced and assessed. Steady‐periodic blade responses are evaluated by a harmonic balance approach, whilst a standard eigenproblem is solved for aeroelastic stability analyses. Drawbacks and potentialities of the proposed model are investigated through numerical and experimental comparisons, with particular attention to rotor blades unsteady aerodynamic modelling issues. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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.     

Stochastic dynamic response analysis of a tension leg spar‐type offshore wind turbine

This paper presents a stochastic dynamic response analysis of a tension leg spar‐type wind turbine subjected to wind and wave actions. The dynamic motions, structural responses, power production and tension leg responses are analyzed. The model is implemented using the HAWC2 code. Several issues such as negative damping, rotor configuration (upwind or downwind rotor) and tower shadow effects are discussed to study the power performance and structural integrity of the system. The operational and survival load cases considering the stochastic wave and wind loading are analyzed to investigate the functionality of the tension leg spar‐type wind turbine. Amelioration of the negative damping applied for this concept reduces the structural dynamic responses, which are important for fatigue life. It is found that the responses induced by wave and wind actions at the wave frequencies are not affected much by the aerodynamic excitation or damping forces. Because of the nonlinear effects of the tension leg, all of the motion responses are strongly coupled. The global responses of upwind and downwind versions of the turbine are found to be close because the tower shadow has a limited effect on the global responses. However, the structural dynamic responses of the blades are more affected by the tower shadow. In this study, the extrapolation methods are applied to efficiently estimate the maximum responses. The maximum response is found to occur in the survival cases as a result of the wave actions and the increased aerodynamic drag forces on the tower. The results show that the maximum responses corresponding to the up‐crossing rate of 0.0001 (corresponding to the maximum response within a 3 hour period) can be expressed by the mean plus 3 to 5 standard deviations. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonlinear model predictive control of wind turbines using LIDAR

LIDAR systems are able to provide preview information of wind disturbances at various distances in front of wind turbines. This technology paves the way for new control concepts in wind energy such as feedforward control and model predictive control. This paper compares a nonlinear model predictive controller with a baseline controller, showing the advantages of using the wind predictions in the optimization problem to reduce wind turbine extreme and fatigue loads on tower and blades as well as to limit the pitch rates. The wind information is obtained by a detailed simulation of a LIDAR system. The controller design is evaluated and tested in a simulation environment with coherent gusts and a set of turbulent wind fields using a detailed aeroelastic model of the wind turbine over the full operation region. Results show promising load reduction up to 50% for extreme gusts and 30% for lifetime fatigue loads without negative impact on overall energy production. This controller can be considered as an upper bound for other LIDAR assisted controllers that are more suited for real time applications. Copyright © 2012 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.     

Wind turbine load reduction by rejecting the periodic load disturbances

For the cost per kilowatt hour to be decreased, the trend in offshore wind turbines is to increase the rotor diameter as much as possible. The increasing dimensions have led to a relative increase of the loads on the wind turbine structure; thus, it is necessary to react to disturbances in a more detailed way, e.g. each blade separately. The disturbances acting on an individual wind turbine blade are to a large extent deterministic; for instance, tower shadow, wind shear, yawed error and gravity are depending on the rotational speed and azimuth angle and will change slowly over time. This paper aims to contribute to the development of individually pitch‐controlled blades by proposing a lifted repetitive controller that can reject these periodic load disturbances for modern fixed‐speed wind turbines and modern variable‐speed wind turbines operating above‐rated. The performance of the repetitive control method is evaluated on the UPWIND 5 MW wind turbine model and compared with typical individual pitch control. Simulation results indicate that for relatively slow changing periodic wind disturbances, this lifted repetitive control method can significantly reduce the vibrations in the wind turbine structure with considerably less high‐frequent control action. Copyright © 2012 John Wiley & Sons, Ltd.     

New vortex‐lift and tangential‐force models for HAWT aerodynamic load prediction

Horizontal axis wind turbines (HAWTs) experience three‐dimensional rotational and unsteady aerodynamic phenomena at the rotor blades sections. These highly unsteady three‐dimensional effects have a dramatic impact on the aerodynamic load distributions on the blades, in particular, when they occur at high angles of attack due to stall delay and dynamic stall. Unfortunately, there is no complete understanding of the flow physics yet at these unsteady 3D flow conditions, and hence, the existing published theoretical models are often incapable of modelling the impact on the turbine response realistically. The purpose of this paper is to provide an insight on the combined influence of the stall delay and dynamic stall on the blade load history of wind turbines in controlled and uncontrolled conditions. New dynamic stall vortex and nonlinear tangential force coefficient modules, which integrally take into account the three dimensional rotational effect, are also proposed in this paper. This module along with the unsteady influence of turbulent wind speed and tower shadow is implemented in a blade element momentum (BEM) model to estimate the aerodynamic loads on a rotating blade more accurately. This work presents an important step to help modelling the combined influence of the stall delay and dynamic stall on the load history of the rotating wind turbine blades which is vital to have lighter turbine blades and improved wind turbine design systems.     

Modeling dynamic stall on wind turbine blades under rotationally augmented flow fields

This paper presents an investigation of two well‐known aerodynamic phenomena, rotational augmentation and dynamic stall, together in the inboard parts of wind turbine blades. This analysis is carried out using the following: (1) the National Renewable Energy Laboratory's Unsteady Aerodynamics Experiment Phase VI experimental data, including constant as well as continuously pitching blade conditions during axial operation; (2) data from unsteady delayed detached eddy simulations (DDES) carried out using the Technical University of Denmark's in‐house flow solver Ellipsys3D; and (3) data from a reduced order dynamic stall model that uses rotationally augmented steady‐state polars obtained from steady Phase VI experimental sequences, instead of the traditional two‐dimensional, non‐rotating data. The aim of this work is twofold. First, the blade loads estimated by the DDES simulations are compared with three select cases of the N‐sequence experimental data, which serves as a validation of the DDES method. Results show reasonable agreement between the two data in two out of three cases studied. Second, the dynamic time series of the lift and the moment polars obtained from the experiments are compared with those from the dynamic stall model. This allowed the differences between the stall phenomenon on the inboard parts of harmonically pitching blades on a rotating wind turbine and the classic dynamic stall representation in two‐dimensional flow to be investigated. Results indicated a good qualitative agreement between the model and the experimental data in many cases, which suggests that the current two‐dimensional dynamic stall model as used in blade element momentum‐based aeroelastic codes may provide a reasonably accurate representation of three‐dimensional rotor aerodynamics when used in combination with a robust rotational augmentation model. Copyright © 2015 John Wiley & Sons, Ltd.     

基于气动弹性理论的风力机叶片耦合分析

针对风力机叶片,建立其结构动力学方程,推导分析了叶片旋转所产生的振动速度及其对来流的影响。基于BEM(Blade Element Momentum)理论,在风力机空气动力学基础上,建立了风力机的气动耦合分析模型。应用该模型,对某2MW风力机进行了计算分析,得到了叶片在额定工作风速下的振动变形、速度、加速度以及叶片沿展向的变形和载荷分布。充分考虑叶片的结构振动特性与来流风速的耦合效应,使得风力机空气动力学特性模型更加准确,对于风力机的设计和分析具有重要意义。