Table of Contents Author Guidelines Submit a Manuscript
International Journal of Aerospace Engineering
Volume 2017, Article ID 5263897, 15 pages
https://doi.org/10.1155/2017/5263897
Review Article

Wind Turbine Aeroelastic Modeling: Basics and Cutting Edge Trends

1School of Mechanical and Electrical Engineering, Wuhan University of Technology, P.O. Box No. 205, Luoshi Road, Wuhan, China
2Department of Mechanical Engineering, Woldia University, Woldia, Ethiopia

Correspondence should be addressed to Mesfin Belayneh Ageze; moc.oohay@laemzle

Received 21 September 2016; Accepted 6 December 2016; Published 14 March 2017

Academic Editor: Roger L. Davis

Copyright © 2017 Mesfin Belayneh Ageze et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The interaction of fluid flow and the structure dynamic of the system is a vital subject for machines operating under their coupling. It is not different for wind turbine either, especially as the coupling enhanced for multi-MW turbine with larger and flexible blades and complex control methods, and other nonlinearity, more comprehensive aeroelastic tools will be required to investigate the realistic phenomena. The present paper will overview the aeroelastic tool for wind turbine, the efforts done, gaps, and future directions indicated. One starts with background of the subject, presenting a case study to demonstrate the effect of fluid-structure interaction considering NREL 5MW blade and a brief comparison of several aeroelastic codes. Cutting edge efforts done in the area such as complex inflow, effect of geometric nonlinearity, and other stability and smart control issues are addressed and concluded by elaborating the gaps and future direction of aeroelasticity of wind turbine.

1. Background

Wind energy is emerging towards a mainstreaming competitive and reliable power technology, and significant forecasting (such as [13]) revealed that the progress will continue strongly. So far design trends of wind turbine are towards longer (refer to Figure 1) and more flexible blades, smart rotor and control, and offshore application. Early design loads on wind turbine were evaluated on the quasi-static aerodynamic calculation base, with structural dynamic either ignored or included through the use of estimate dynamic magnification factor. This upscaling trend demands a more comprehensive tool to investigate the complex coupling between aerodynamic and structural dynamic of megascale wind turbines, that is, aeroelasticity. The present paper will review the trend of aeroelastic study of wind turbine and available aeroelastic codes and tools, and current and future research direction and gaps will be addressed.

Figure 1: Wind turbine upscaling trend [3].

The review considered a number of original research articles, review papers, summary of reports, project completion reports, manual, and others, thoroughly analyzed during the preparation of this report. In the following section, the basis of aeroelastic modeling of wind turbine will be discussed, including aerodynamic, structural dynamic, and their coupling.

2. Aeroelasticity

Though the idea of aeroelasticity goes back to 1947 as introduced by A. R. Collar, its application for wind turbine design and analysis begins as late as 1976 by Friedmann [4] who derived a set of coupled flap-lag-torsional equation of motion for a single blade. In later years significant evolution has been achieved [58]. Aeroelasticity studies the coupling effects between the inertia, elastic, and aerodynamic forces, which occur as an elastic body exposed to a fluid flow. As the scope of the study is enhanced to include other relevant phenomena such as hydrodynamic for offshore wind turbines, thermal effects, or control action, one will have to extend the subject as hydroaeroelasticity, aerothermoelasticity, or aeroservoelasticity, respectively. Refer to Figure 2, collar’s triangle.

Figure 2: Collar’s triangle: interaction of different forces.

To model and simulate the aeroelasticity of wind turbine, several aeroelastic tools and methods are available, which roughly include aerodynamic component to determine the wind loads and structural part to calculate the dynamic response of structure, with time history and spatial distribution of wind as input, Figure 3.

Figure 3: Typical aeroelastic tool principle.

In the following sections, both aerodynamic and structural dynamic component of wind turbine aeroelasticity will be elaborated, including methods to model the corresponding phenomena.

2.1. Aerodynamic

Aerodynamic part of aeroelastic analysis entitled to determine the aerodynamic loads developed due to the flow pattern of wind against the wind turbine blade orientation. Different models and methods have been developed, such as the very common and popular Blade Element Momentum method, lifting line, panel and vortex models, generalized actuator disc models, and Navier Stokes based solvers; each theory possesses pros and cons. In this section, a brief discussion will be included about the common aerodynamic methods.

2.1.1. Blade Element Momentum (BEM) Method

BEM also called strip theory was originally introduced by Glauert [9]; it is computationally fast and cheap, and provided that reliable aerofoil data is available, it will give satisfactory results. It is a combination of the simple momentum theory and blade element theory [10] and assumes that there is no aerodynamic interaction between all sections along the rotor and can be treated separately, which imply there is no radial flow. Refer to Figures 4 and 5.

Figure 4: Schematic of finite number of elements of the blade (blade element theory).
Figure 5: Schematic of momentum theory.

The forces on the blades are determined solely by the lift and drag characteristics of the airfoil shape of the blades, and it is assumed the flow is incompressible steady state. Subsequently, combining the two expressions for thrust/normal forces and torque from momentum theory and blade element theory, the BEM will be derived. After some algebraic manipulation, the resulting relations will be ((1)-(2))And considering turbulent flow, the thrust coefficient can be expressed with Glauert correction aswhere is the lift coefficient, is Prandtl’s Tip Loss Correction Factor, is the relative wind angle, is the local speed ratio, is the local blade solidity, are the radial and axial induction factor, respectively, is the thrust coefficient, and is Glauert correction factor.

Perhaps at this point we can see that the classical BEM theory is assumed a quasi-static/steady flow condition, but to investigate the unsteady aerodynamic effects of wind turbine, additional models have to be included such as dynamic wake/inflow, yaw/tilt model, and dynamic stall.

Dynamic Inflow. There is a time delay for the wake behind the rotor to maintain a steady state condition after a disturbance such as sudden change in pitch angle, rotor, and/or wind speed, and this phenomenon is called dynamic inflow. As the velocity field is the vectorial sum of the free stream velocity and the induced velocity, the dynamic inflow represents the later one. Typical example can be evident from Tjaerborge machine result presented at Figure 6 (reproduced from [7]). For sudden change in pitch angle from 0 to 3.7 degrees at = 2 s, the rotor shaft torque drops from 250 to 150 kNm, and it takes around 10 s to settle to the new equilibrium state. Therefore dynamic inflow model is required to predicate such a delay.

Figure 6: Comparison between measured and computed time series of the rotor shaft torque for the Tjaereborg machine during a step input of the pitch for a wind speed of 8.7 m/s [7].

Under Joule 1 program, several investigations have been done on the effect of dynamic inflow and implementation into engineering methods [1116]. The most accurate model to represent dynamic wake is unsteady vortex wake model but it has computational drawback that makes it less favorable for engineering application, following Snel and Schepers [11] who formulated six different engineering models to determine the effect of dynamic inflow phenomenon. One of these methods proposed by Sige Øye is a filter for the induced velocity consisting of two first-order differential equations (refer to Hansen et. al [7] for details). To alleviate the numerical demand of the existing models, [17] proposed a simplified model which is an approximate modeling of dynamic inflow. The method is placing a lead-lag filter after rotor torque and thrust calculated from static tables of the power and thrust coefficients. The filter constants will then vary with the average wind speed.

Dynamic Stall. It is a rapid aerodynamic change that may bring about or delay stall behavior. Due to tower shadow, yaw or tilt, wind shear, and/or turbulent wind condition, the boundary begins to separate at the trailing edge and gradually moves upstream with increasing angles of attack, that is, dynamic stall. Dynamic stall effects occur on time delay proportional to chord divided with the relative velocity seen at the blade section. This phenomenon results in highly transient forces, and results from [1820] revealed also the significant effect of dynamic stall, more specifically for instability problems. Variety of dynamic stall models have been developed such as Gormont and Beddoes–Leishman model [7, 10, 20]. Considering unsteady loads on wind blade and the negative influences on the performance and fatigue life of a turbine, introducing a dynamic stall control method is necessary. The control methods can be active control [21] or passive control (such as streamwise vortex generators, spanwise vortices generated using an elevated wire, and a cavity to act as a reservoir for the reverse flow accumulation). And these control methods showed significant delay of the onset of dynamic stall by several degrees and reduce the increased lift and drag forces as well [22].

Yaw/Tilt Model. During misalignment between rotor normal vector and the incoming wind, yaw/tilt model will redistribute the induced velocity so that the induced velocities are higher when a blade is positioned deep in the wake than when it is pointing more upstream. Glauert proposed the yaw/tilt model and more detailed discussions are included in [14, 15]. Hansen et al. [7] also discussed a yaw/tilt model adapted from helicopter literatures. The typical feature of yaw/title model is to include the effect of misalignment by increasing and decreasing the induced velocities on the downstream and upstream part of the rotor disc, respectively.

2.1.2. 3D Inviscid Aerodynamic Models

These models developed to obtain more detailed description of the three-dimensional flow that develops around a wind turbine, with viscous effects neglected. Besides maturity to apply as engineering tools, these models contribute a better understanding of dynamic inflow effect and overall flow development [7, 1416]. To include the viscous effect several attempts had been made in time, using viscous-inviscid interaction techniques [7]. Detailed discussion about the 3D inviscid models such as lifting line, panel, and vortex models can be found in [7] and potential applications and challenges are included.

2.1.3. CFD Based Models

CFD application developed from aerospace industry which employs potential flow solvers, to alleviate their limitation, and the use of unsteady Euler solvers emerged. As the computing power grows, the application of full Reynolds Averaged Navier Stokes equations including viscous effects applied for helicopter rotor computations, later on the full Navier Stokes computations of wind turbine rotor aerodynamics, was reported [7].

NS solver originally developed from an aerospace code solving compressible NS equations, intended for high speed aerodynamic in subsonic and transonic regime; apparently this nature of the code is not compatible for wind turbine application, because of low Mach numbers around the roots of the blades. As the flow approaches the incompressible limit, it is very difficult to solve the compressible flow equation. Two remedies have been suggested [7]: the first one is preconditioning that changes the eigenvalues of the system of the compressible flow equations by premultiplying the time derivative by a matrix. The other method is artificial compressibility method in which an artificial sound speed is introduced to allow standard compressible solution methods and schemes to be applied for incompressible flows. This method has many merits such as ease of implementation of overlapping grids as the compressible codes, and the main limitation is problem to enforce incompressibility in transient computations without the need for a huge amount of subiterations and the problem of determining the optimum artificial compressibility parameter. The method is well suited for solving nearly incompressible problems often experienced in connection with wind energy. In connection with steady state problems, the method can be accelerated using local time stepping, while the method using global time stepping still is well suited for transient computations.

2.2. Structural Dynamics

Structural component of aeroelastic model will determine the dynamic response of the system for aerodynamic load and exchange results with aerodynamic component simultaneously. The earliest work on dynamic modeling of wind turbine was by [4], which is the equation of motion of a single blade, assumed as an elastic beam with the root being fixed at the hub and the tip being free. With application of Hamilton’s principle and Newtonian method, equations of motions which are valid to second order, for long, slender, straight, homogeneous, and isotropic beams undergoing moderate displacements have been developed by [23]. These equations are also validated for several beam properties, and the final equations include different nonlinear structural and inertial terms which influence the aeroelastic stability and response of hingeless helicopter rotor blades. In extension to the previous work, [24] provides a new set of partial differential equations of motion for a wind turbine blade rotating in a gravity field with variable rotor speed and pitch action. Hansen et al. [7] employed the two frequently used approaches (principle of virtual work with modal shape function and nonlinear beam theory with FEM) to formulate the dynamic structural model of wind turbine. As the flexibility and length of wind turbine are increasing, the capability of the classical beam theory to model the structural dynamic will not be enough, in contrary to the fact that the utilization of more nonlinear beam theory with less assumption is demanded.

Besides the beam theory (linear or nonlinear) and elements (shell or beam elements) to be employed, there are three frequent discretization methods to model the structural dynamic in relation to wind turbine, that is, modal reduction approach, multibody dynamics (MBD), and finite elements methods (FEM).

FEM Approach. It discretizes the wind turbine system to finite elements as flexural beam, lumped masses, springs, and joints. The methods have the advantage of fewer restrictions regarding the type of configuration to consider such as geometrical and material nonlinearity; apparently this will result in a high degree of freedom which will lead to high computational effort by extension cost.

Modal Approach. In this method the deflection of components such blade, tower, and support structure is superimposed from linear combination of some physically realistic models, typically the lowest eigenmodes such as 1st and 2nd flapwise and edgewise modes. The deflection of blades and tower is coupled with a low number of prescribed discrete degrees of freedom. In contrary to its computational efficiency this approach has various limitations such as a fixed number and type of degree of freedom, the assumption of linearity, and inadequacy to handle a certain type of structures.

MBD Approach. In this method the structure is approximated by a finite number of elements consisting of rigid and flexible bodies coupled by elastic joints. This discretized system is described with a finite number of ordinary differential equations. This approach combines the merits of both above methods, since it needs relatively less set of equations of motion and nonlinearity is considered. In addition, this model treats nonlinear kinematics efficiently compared to FEM and allows modeling of mechanical system with both large deflection and large rotation.

2.3. Fluid-Structure Coupling

The final stage of aeroelastic modeling is fluid-structure coupling so that the responses at each model (aerodynamic force and structural deformation) mapped to one another. In classical aeroelastic methods, the fluid and structure interaction is treated separately and uncoupled, ignoring the interaction [5]. As the computing power improved, several integrated approaches developed including inherent fluid-structure coupling. As the fidelity requirement of the analysis increases to include explicit details such as turbulence [25], nonlinear composite layered blades and large deformation [26], application of strong fluid-structure coupling is necessary. However, on the contrary, computational efficiency with small compromises on accuracy is also another route of coupling demands, such as introducing reduced order model as [27]. As the choice of aeroelastic tool is dependent on the application focus area or operational conditions to be studied, accuracy demanded, cost, time, and computational resource available, understanding the limitations and merits of each tool over the other is vital. A few comparisons have been made in this regard, as presented [26, 28, 29]; in the following section a simple case study will be presented to compare one- and two-way fluid-structure coupling.

Case Study: FSI for NREL 5MW Baseline Wind Turbine Blade. In the following few paragraphs, to demonstrate the effect of coupling choice, a simple case study will be discussed considering uni- and bidirectional fluid-structure coupling for half cycle of operation of a blade, that is, 2.5 seconds. The target wind turbine blade is NREL 5MW baseline wind turbine blade with 61.5 length and 1.5 hub radius; the aerofoil and chord distribution is based on [30, 31] with some minor modification at the tip and root sections, Figure 7. The material distribution for leading edge, root, trailing edge, tip, and spar caps is set as EP-LT-5500/EP-3 composite; for the spar webs it is Saertex/EP-3 composite. The simulation is carried out on ANSYS, that is, the fluid flow on ANSYS Fluent and the structural model on ANSYS Mechanical; other simulation parameters are included in Table 1. For unidirectional coupling, the ANSYS system coupling feature is employed.

Table 1: Simulation parameters.
Figure 7: NREL 5MW blade 3D model.

The computation domain is limited to be as 1/3rd of the rotor to reduce the computational effort; periodic boundary with 120-degree spacing will be introduced, as shown in Figure 8, comprising elements for flow solver and elements for structural solver.

Figure 8: Computational domain.

Based on the unidirectional and bidirectional coupling, the simulation of the blade done and the velocity, pressure, and tip deflection were examined, as shown in Figures 911.

Figure 9: Velocity distribution at 2.5 seconds. Unidirection coupling (a) and bidirectional coupling (b).
Figure 10: Pressure distribution at 2.5 seconds. Unidirection coupling (a) and bidirectional coupling (b).
Figure 11: Blade tip deflection (a) and maximum equivalent stress (b) for half cycle of operation.

Comparing the results, one can evidence the significant difference between the two couplings; specifically bidirectionally coupled simulation produced maximum tip deflection of 12.662 m while it is 11.174 m for unidirectional coupling; moreover, the deflection and equivalent stress in unidirectional coupling remain constant after some variations, as compared with its counterpart which is still changing significantly, implying damping difference. To finalize, although there is enormous amount of computation effort required for strong coupling between fluid and structure, to simulate the full aeroelasticity characteristics of wind turbine with a proper degree of fidelity application of stronger coupling is uncanny.

3. Aeroelastic Codes for Wind Turbine

Variety of codes are available to model, design, and simulate the aeroelastic characteristic of wind turbine; refer to Table 2. Several aeroelastic modeling codes verifications and literatures including [3241] are reviewed. For offshore wind turbine interested readers Passon and Kühn [39] reviewed codes which are suitable for such application.

Table 2: Comparison of aeroelastic codes for wind turbine.

In addition to the codes shown in Table 2, several commercial and academic institutes developed variety of aeroelastic codes, such as FOCUS at Stork Product Engineering, the Stevin Laboratory, GAROS at aerodyn-Energiesysteme GmbH, Cp-Lambda at Politecnico di Milano [42], and BHawC at Siemens Wind Power [43], and some general purpose programs such as ANSYS, ABAQUS, and SOLVIA with add-on packages, cosimulation, or subroutine programs can be employed to work with the aeroelasticity of wind turbine.

4. Cutting Edge Trends and Gaps

The current energy market demands efficient, cost effective, reliable sources, as the development of wind turbines with larger, more flexible design (especially torsionally), with complex control, is inherent. Coupling of different phenomena and their nonlinear characteristics are escalating the challenge; to alleviate such challenges several researches have been done and tools are formulated. In this section effort done to improve and study the aeroelastic characteristic of wind turbine system will be reviewed. The review is categorized into four major areas as complex inflow, geometric nonlinearity and large blade deflection, aeroelastic stability, and smart control.

4.1. Complex Inflow

Complex terrain will result in extreme wind shear and high turbulence intensity, and interactions with large blades and tower will cause variation of the induced wind flow as function of blades azimuthal position. Hence, it is obvious that reliable tools are needed to map the energy production and loads expected to improve cost of repair and fatigue life of components. Thereafter it has been one area of interest of the industry.

4.1.1. Wind Shear

The European UpWind [44, 45] project performed 3D CFD rotor computation using EllipSys3D Navier Stokes solver to provide new insight about rotor operation in shear with the aim of improving engineering models. The results include the azimuthal variation of rotor loads and inflow velocity, the wake behavior downstream, and the disturbance of the upstream flow due to the rotor loading.

4.1.2. Tower Shadow Effect

As the blades pass the tower the pressure driving them will be weakened so as the instant power production and the aerodynamic loads, creating cyclic impulsive load on the rotor. In general term, tower interference can be modeled as anemometer reading [46], CFD simulation [47, 48], or using potential flow method [49]. Gómez and Seume [47] evaluated the cyclic load variation due to tower interference and the results adopted to correct the prediction of BEM. Several investigations had been made to evaluate their fidelity and [50] simulate wind turbine rotor and tower interaction with wind shear, using CFD model, and the result showed this model underpredicted the effect compared to BEM; [46] also extended the effort for various wind turbine concepts. Zhang et al. [49, 51] also proposed a 3D potential flow model of tower interference for BEM. As the effect of both wind shear and tower shadow is significant on the power production as well as the loading of the rotor, improvement of the current models and new methods are expected.

4.1.3. Wake Operation

Wind turbines in farm will be exposed to upwind wake operation, which needs better modeling tool to develop better control algorithm adapted for load reduction in wake. Variety of wake models are available depending on the fidelity and application required and the effort and computational resource available. The traditional way to model wake operation is an Equivalent Turbulent Method [52]; that is, it takes into account the wake by increasing the effective turbulence intensity. It is based on the assumption that all load generating mechanisms causing increased loads in wake operation can be merged into an equivalent value of increased turbulence intensity and is included in IEC6400-1 standard for wind turbine safety [53]. For extreme response during operation the success of this approach depends significantly on the physical mechanism causing the extremes; that is, if the physical mechanism creating increased loads in wake operation differs from increased turbulence intensity, the resulting extremes might be erroneous [54]. Other wake models (from lower to higher fidelity, resp.) are empirical models (e.g., Park model [55, 56]), linearized RANS models (e.g., Eddy viscosity model [57] and Fuga model [58, 59]), probabilistic and conjugative methods (e.g., dynamic wake meandering [60, 61] and stochastic model), nonlinear RANS models (e.g., closure with actuator disk, line, and fully resolved), large eddy simulation models (e.g., dynamic Smagorinsky with actuator disk, line), and vortex method [62]. Power prediction and annual energy production tool requires steady and time-averaged wake models, whereas load calculation requires unsteady and time accurate, and for control strategies both steady and unsteady will be applied. The dynamic wake meandering model is more detailed model considering the transversal and vertical dynamics of the wake (i.e., wake meandering). Thomsen et al. [54] compared the load response for a wind turbine in wake operation using equivalent turbulent and wake meandering methods and revealed the wake model considered has significant influence, for extreme load under normal operation. Ott et al. [58] considered three closures as the “simple closure” using an unperturbed eddy viscosity, the mixing length closure, and the E-ɛ closure. As comparison with wind farm data, the “simple closure” showed satisfactory agreement, while mixing length closure and E-ɛ closure are under- and overestimated, respectively; and for near wake case all models fail. Bastankhah and Porté-Agel [63] proposed a new analytic model for wind turbine wakes. This model only requires one parameter to determine the velocity distribution in the wake. And the comparison of the high-resolution wind tunnel measurements and the LES results shows that the velocity profiles obtained with the proposed model are in acceptable agreement with both.

There have been different benchmarking and validation research for wake models such as [54, 61, 6467]. Though these wake models are developed, there are still gaps in the subject including modeling wake-wake interaction, wake-terrain interaction, and understanding influence of atmospheric stability and nonuniform terrain, further more evaluating these models using yaw control [68] and integrating with full 3D CFD models.

4.2. Geometric Nonlinearity and Large Blade Deflection

Longer and more flexible blades with mechanical properties of high strength and relatively low Young’s modulus (i.e., lower stiffness) will deform significantly. Therefore, it is clear to include its effect in wind turbine analysis as it has an impact on the overall efficiency of the structure, including aeroelastic stability [6972]. Most of the existing commercial codes use simple linear structural model, which might not be enough to consider large deformation. Thus it is necessary to understand the various nonlinear interactions thoroughly and develop a geometrical nonlinear analysis method for such wind turbine blades. Different approaches have been used to deal with large deflection problems, such as elliptic integral formulation, numerical integration with iterative shooting techniques, incremental finite element method, incremental finite differences method, method of weighted residual (MWR), and perturbation method [7377].

Larsen et al. [72] incorporate three nonlinear approaches to evaluate the effect of including large deflection. The results showed including the influence of large deflection will reduce the effective rotor area causing a reduction in power output at low wind speeds and a change in pitch angle setting at high wind speeds which lead to a higher flapwise mean load level. On the contrary no main differences regarding fatigue load levels could be obtained from the load simulations. For structural behavior, an increment in flap frequency is seen as a function of deflection whereas edgewise frequency seems to remain constant. Kallesøe [70] investigated the effect of blade deformation on flutter boundaries, by comparing natural modes of aeroelastic motions of an undeformed blade to that of a predeformed blade. The theoretical analysis showed “the flutter instability known from the undeformed blade is delayed to a higher rotational speed, on the other hand a new rout to flutter instability appears, which has a lower stability boundary then the original flutter boundary for the undeformed blade” which imply the significant effect of large blade deflection. The effect of edgewise bending-torsion coupling on flutter limits of wind turbines is investigated by [69, 71] using the aeroelastic mode suggested by [78] and indicated slightly decreased flutter limit on the rotor speed due to the blade deflection.

Yuan and Chen [76] proposed a Variable Step Deformation Difference Method (VSDDM) to analyze the nonlinear blade structure. According to [76], an approximated deflection equation for moderate large deflection problems developed from the differential equation of large deflection cantilever beams (3) using Newton binomial theorem. This method possesses the merits of distinct concept, ease of understanding, rapid convergence speed, and simplicity to program. Analysis based on this method is carried out for 200 kW wind turbine blade subjected to extreme wind. The results revealed that VSDDM provides an accurate prediction of the blade tip deflection and is effective to solve such nonprismatic cantilever beams with variable stiffness and large deflection and subjected to complicated loads. Besides geometric nonlinearity, effect of material nonlinearity is worth considering [79]. Nonlinear effect of large deflection has a significant effect on power production, loading, and also stability; more comprehensive study of the subject and including these nonlinear effects into aeroelastic codes are expected.

4.3. Aeroelastic Stability

In wind turbine, instability can be pitch-flap flutter, stall induced instability, rotor shaft whirl, aeromechanical instability, and/or hydrodynamic interaction brought on by the ocean currents and surface waves from offshore wind turbines. Stability is one of the vita designs constrained of wind turbine, as Bir and Jonkman [80] pointed out that future would likely be stability-driven in contrast to loads-driven designs during that time.

4.3.1. Edgewise Instability

Though the shift from stall regulation to pitch control will significantly avoid stall related instability during operation, due to the inherent low aerodynamic damping for edgewise model, the edgewise instability is still a critical problem. The experimental evidence of edgewise instability has been seen in the mid nineties on stall regulated rotors with a diameter of 35–40 m. Hansen et al. [7] illustrated the subject matter in detail and explained the early efforts done; typical examples on stability analysis with linear stability tool HAWCStab are included to elaborate the edgewise instability of wind turbine.

Lindenburg and Snel [81] pointed out the reason for edgewise blade vibration instability, as less structural damping due to application of carbon fibers, more UD (unidirectional) layers, vacuum production techniques, and a smoother transition from the airfoil-sections to the blade root, relatively small chord and a decreasing slope of the torque-speed relation of the generator at full-load.

Part of EC Joule III project [82] with objective of improving the prediction capability with respect to dynamic loads in stall and stall induced vibration and establishing guidelines to achieve safety margin against stall induced vibration were one of the early efforts done between 1995 and 1998. In contrary to the violent effects of edgewise blade vibration, Thomsen et al. [83] formulated an experimental method to determine the effective damping for the edgewise blade mode shape for wind turbines. Rasmussen et al. [84] used dynamic stall model to analyze and reproduce open air blade section measurements as well as wind tunnel measurements. The results from wind tunnel experiment revealed that aerodynamic damping characteristics sensitivity to stall induced vibrations depends highly on the relative motion of the airfoil in flapwise and edgewise direction and on a possibly coupled pitch variation, which is determined by the structural characteristics of the blade. Chaviaropoulos [85] also used differential dynamic stall model and linearized equation of motion to investigate the combined flap/lead-lag motion characteristic. In extension [86] also analyzed and pointed out that these models provided important knowledge at the qualitative level but also significant uncertainty at the quantitative level.

The European project VISCEL (2003, 2004) considered the stability characteristic of the typical section using an unsteady Navier Stokes treatment of the aerodynamics [81, 87]; another European project DAMPBLADE (2003) made a step to full section of a blade. Subsequently, several researches on wind turbine aeroelastic instability had been conducted including STABCON [81, 88], in which experimental data are used to cross-validate different methods. In later years, several inventions have been recorded such as [89, 90], which developed an active stall control method for damping edgewise oscillations in one or more blades of a wind turbine. This method works as first detecting if one or more of said blades oscillates edgewise during operation of said wind turbine and substantially cyclically generating a pitch angle difference between at least two of said blades.

4.3.2. Pitch-Flap Flutter Instability

It is a dynamic instability caused by a positive feedback between the body’s deflection and aerodynamic force. Although this type of aeroelastic instability is an infant in commercial wind turbines so far, however as the size of the blades is increasing, the flutter speed decreases due to increasing structural flexibility of the blades and not least the torsional frequency decreases. It is a smart way to include a flutter speed calculation in the design verification. Flutter involves two DOF of the blade: torsion and translation. The flutter speed decreases when the frequency of these two DOF approaches each other. The other design parameter for flutter instability is the center of mass in the blade sections relative to the center of the elastic axis. As the center of mass moves away from the elastic axis in the direction of the trailing edge, the flutter speed decreases [7].

In [91] the frequency domain techniques developed by Theodorsen adapted to investigate aeroelastic stability of a MW-size blade with and without aeroelastic tailoring. 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 observed.

4.4. Smart Rotor and Control
4.4.1. Active Load Control Devices

Due to complex inflow and turbulence and its dynamic characteristic wind turbine blades are exposed to fatigue loading. Several load control methods can be employed to modify these aerodynamic characteristics of the blades and flow condition, by extension to the aerodynamic forces. There are three major categories of active load control techniques, (i) surface blowing/suction, (ii) VG’s, surface heating, plasma, and so forth, or (iii) changes in section shape (aileron, smart materials, and microtabs), Figure 12.

Figure 12: Active flow control devices, (a) Microtab [99], (b) flow pattern after application of Microtab [100], (c) vortex generators [101], and (d) air jet vortex generator [102].

The early progress of the subject matter is reviewed thoroughly in [9294]. Comparison among aerodynamic load control methods (i.e., deformable flap, microtabs, camber control or morphed trailing edge, active twist, boundary layer suction/blowing, synthetic jets, active vortex generator, and plasma actuator) in terms of lift controllability is done by [94], and the result showed that trailing edge flaps, camber control, and microtabs have very good average and maximum lift control capability. Trailing edge flap control is demonstrated as the most efficient control method. The change in lift and drag characteristics as well as the linearity, the bandwidth, and the simplicity of these concepts makes it attractive from the control point of view. The other methods have also some unique merits; microtabs simplicity, bandwidth, and small actuating power needed make it attractive, except that its on-off characteristic makes them less efficient for detailed load control; further investigation is needed for advance uses. Active twist control is rotating the whole span of the blade about the blade axis. This method in general is feasible but it is expensive, results in heavier rotor, and consumes more power, which will make it inefficient method to reduce fatigue loading.

Two researches at Sandia National Laboratories [95] using Microtab concept reported 20–32% reduction blade root flap bending moments; and [96] for another procedure, that is, increasing the blade and other components size for the same blade root flap fatigue damage as the baseline rotor by enrolling morphed trailing edge, reported 11% increment in energy capture. A smart rotor configuration employing linear quadratic to control adaptive trialing edge flap was proposed by [97], and its performance was evaluated based on aeroelastic simulation of a baseline NREL5MW wind turbine with the flaps extending along 20% of span using HAWC2 code. Control algorithm includes frequency weighting to discourage flap activity at frequencies higher than 0.5 Hz and also uses periodic disturbance signals described by simple functions of the blade azimuthal position to determine period component of the load.

The effects of the adaptive trailing edge flap control are quantified in terms of lifetime fatigue damage equivalent load reduction, and it is recorded 10% blade root flapwise moment reduction, including the periodic load anticipation, will improve the result as 13.8% with the d Sin-Cos configuration and 4.5% with Wsp, Figure 13. Zhang et al. [98] also investigate the impact of smart load control using trialing edge flap on NREL 5MW and the results showed significant reduction on flapwise blade root bending moment. Furthermore, the smart load control altered the nature of the flow-blade interactions and changed the in-phased fluid-structure synchronization into much weaker couplings, as a result of fluid-structure damping enhanced.

Figure 13: Fatigue damage equivalent loads D L at the blade root flapwise bending moment. The DEL refers to a 25-year lifetime and 10 million equivalent cycles [97].
4.4.2. Smart Material Actuators

Smart materials are materials which possess the capability to sense and actuate in a controlled way in response to variable ambient stimuli. Actuators for smart load control comprise a vital role. In a general sense, there are two classes of actuators as embedded and discrete. The conventional load control actuators (i.e., hydraulic, pneumatic, and electrical actuators) are mostly used in existing wind turbine blade pitch and yaw control applications. However, their inherent demerits, including leakage problems and contamination, delay in actuation, regular maintenance requirement, reduced frequency range, and exhibiting certain instability, weight, space, and power requirement, limit them from active smart load control application.

The common criteria for active control include less weight contribution, achieving the required deflection, being dynamically responsive at the frequency range of interest, linear actuation behavior, high resistance to fatigue loads, insensitivity to oxidation and lightning strikes, and limited degradation or reduced performance. Smart material includes ferroelectric materials (piezoelectric, electrostrictive, and magnetostrictive), variable rheology materials (electrorheological, magnetorheological), and shape memory alloys. Though these materials are not yet commercialized, several researches indicated their feasibility; thorough discussion and comparison are presented by [94].

5. Concluding Remarks

The present article reviewed the science of wind turbine aeroelasticity and its trend through time. Considering market competitiveness and related constraints, the design trends are driven towards multimegawatt, large, and flexible turbine, utilization of smart rotor control devices, more geometric and material nonlinear structure, and offshore and complex terrain applications. On the contrary this will alter the aeroelastic characteristic and raise numerous system stability issues, which will demand detailed methods to model and simulate the system for further optimal outputs. In the previous few sections several remedies done have been discussed, and the gaps to be addressed can be categorized into the need for comprehensive aeroelastic tools, coupled or hybrid solver, and multidisciplinary optimizations.

(1) Comprehensive Aeroelastic Tool. As the complexity of the wind turbine system is enhancing and number of coupling systems is increasing, the requirement of comprehensive aeroelastic tool to handle realistic model of the system is mandatory. Such requirements include(i)complex inflow, including wind shear;(ii)hydrodynamic effects in offshore application;(iii)nonlinearity due to large deflection, geometric and material distribution, and manufacturing methods;(iv)application of smart rotor and control methods and their coupling to the system.

(2) Coupled/Hybrid Solver. Computational efficiency and high fidelity output are the two main compromises in computational studies. As single model only allows achieving either of the two and due to inherent limitations they possess, application of hybrid model is canny. In fluid flow study, hybrid LES/RANS model is a common approach, as RANS will be applied near the wall and LES to the far field domain of the flow. Its application in wind turbine aeroelastic modeling will advance the accuracy because of LES and reduce computation effort because of RANS. Similarly, in structural modeling hybrid model can be applied such as FEM and modal reduction approach.

(3) Multidisciplinary Optimization. Most of aeroelastic codes in wind turbine industry are used as a standalone design tool, and their application in multidisciplinary optimization of wind turbine system is not common and at infant stage. Multidisciplinary wind turbine system optimization framework will identify the possible aerodynamic, structural, control, and other subsystem configurations, to produce minimum cost of energy. Such integration will avoid common suboptimal design trend and enhance the competitiveness of wind energy conversion.

Conflicts of Interest

The authors declare that there is no conflict of interests.

Acknowledgments

This work was financially supported by the China Government Scholarship Program. The first author also would like to acknowledge Wuhan University of Technology for providing holistic assistance in the course of the study.

References

  1. International Energy Agency-IEA, Long Term Research and Development Needs for Wind Energy for the Time Frame 2000 to 2020, International Energy Agency-IEA, 2001.
  2. IEA, Long-Term Research and Development Needs for Wind Energy for the Time Frame 2012 to 2030, International Energy Agency-IEA, 2013.
  3. EWEA, Upwind—Design Limits and Solutions for Very Large Wind Turbines, EWEA (European Wind Energy Association), Brussels, Belgium, 2011.
  4. P. P. Friedmann, “Aeroelastic modeling of large wind turbines,” Journal of the American Helicopter Society, vol. 21, no. 4, pp. 17–27, 1976. View at Publisher · View at Google Scholar · View at Scopus
  5. J. G. Marshall and M. Imregun, “A review of aeroelasticity methods with emphasis on turbomachinery applications,” Journal of Fluids and Structures, vol. 10, no. 3, pp. 237–267, 1996. View at Publisher · View at Google Scholar · View at Scopus
  6. A. D. Garrad, “Dynamics of wind turbines,” IEE Proceedings A: Physical Science. Measurement and Instrumentation. Management and Education. Reviews, vol. 130, no. 9, pp. 523–530, 1983. View at Publisher · View at Google Scholar · View at Scopus
  7. M. O. L. Hansen, J. N. Sørensen, S. Voutsinas, N. Sørensen, and H. A. Madsen, “State of the art in wind turbine aerodynamics and aeroelasticity,” Progress in Aerospace Sciences, vol. 42, no. 4, pp. 285–330, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. P. Zhang and S. Huang, “Review of aeroelasticity for wind turbine: current status, research focus and future perspectives,” Frontiers in Energy, vol. 5, no. 4, pp. 419–434, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. H. Glauert, “Airplane propellers,” in Aerodynamic Theory, W. F. Durand, Ed., Dover Publications, New York, NY, USA, 1963. View at Google Scholar
  10. J. F. Manwell, J. G. McGowan, and A. L. Rogers, Wind Energy Explained: Theory, Design and Application, John Wiley & Sons, 2nd edition, 2009.
  11. H. Snel and J. G. Schepers, “Engineering moles for dynamic inflow phenomena,” in Proceedings of the European Wind Energy Conference, Amsterdam, The Netherlands, October 1991.
  12. S. Øye, “Tjæreborg wind turbine (Esbjerg): first dynamic inflow measurement,” AFM Notat no. VK-189, AFM, Lyngby, Denmark, 1991, http://orbit.dtu.dk/files/3524739/VK189.pdf. View at Google Scholar
  13. S. Øye, “Tjæreborg wind turbine: 4. Dynamic inflow measurement,” AFM Notat no. VK-204, AFM, Lyngby, Denmark, 1991, http://orbit.dtu.dk/files/3524469/VK204.pdf. View at Google Scholar
  14. H. Snel and J. G. Schepers, “JOULE1: joint investigation of dynamic inflow effects and implementation of an engineering method,” Tech. Rep. ECN-C-94-107, 1994. View at Google Scholar
  15. J. G. Schepers, H. Snel, and G. J. W. Bussel, “JOULE2: Dynamic Inflow: Yawed Conditions and Partial Span Pitch,” 1995.
  16. J. G. Schepers and H. Snel, Final Results of the EU Joule Projects “Dynamic Inflow”, Netherlands Energy Research Foundation ECN, Petten, The Netherlands, 1996.
  17. T. Knudsen and T. Bak, “Simple model for describing and estimating wind turbine dynamic inflow,” in Proceedings of the 1st American Control Conference (ACC '13), June 2013. View at Scopus
  18. S. Øye, “Dynamic stall-simulated as time lag of separation,” in Proceedings of the 4th IEA Symposium on the Aerodynamics of Wind Turbines, Rome, Italy, 1991.
  19. J. W. Larsen, S. R. K. Nielsen, and S. Krenk, “Dynamic stall model for wind turbine airfoils,” Journal of Fluids and Structures, vol. 23, no. 7, pp. 959–982, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. J. G. Leishman and T. S. Bcddoes, “A semi-empirical model for dynamic stall,” Journal of the American Helicopter Society, vol. 34, no. 3, pp. 3–17, 1989. View at Publisher · View at Google Scholar · View at Scopus
  21. A. Hani, Active Control of Dynamic Stall, University of California, Los Angeles, Calif, USA, 1998.
  22. A. Choudhry, M. Arjomandi, and R. Kelso, “Methods to control dynamic stall for wind turbine applications,” Renewable Energy, vol. 86, pp. 26–37, 2016. View at Publisher · View at Google Scholar · View at Scopus
  23. D. H. Hodges and E. H. Dowell, “Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades,” Tech. Rep., NASA, Washington, DC, USA, 1974. View at Google Scholar
  24. B. S. Kallesøe, “Equations of motion for a rotor blade, including gravity, pitch action and rotor speed variations,” Wind Energy, vol. 10, no. 3, pp. 209–230, 2007. View at Publisher · View at Google Scholar · View at Scopus
  25. Y. Li, A. M. Castro, T. Sinokrot, W. Prescott, and P. M. Carrica, “Coupled multi-body dynamics and CFD for wind turbine simulation including explicit wind turbulence,” Renewable Energy, vol. 76, pp. 338–361, 2015. View at Publisher · View at Google Scholar · View at Scopus
  26. J. Kumar and F.-H. Wurm, “Bi-directional fluid-structure interaction for large deformation of layered composite propeller blades,” Journal of Fluids and Structures, vol. 57, pp. 32–48, 2015. View at Publisher · View at Google Scholar · View at Scopus
  27. F. Debrabandere, B. Tartinville, C. Hirsch, and G. Coussement, “Fluid-structure interaction using a modal approach,” Journal of Turbomachinery, vol. 134, no. 5, Article ID 051043, 6 pages, 2012. View at Publisher · View at Google Scholar
  28. F.-K. Benra, H. J. Dohmen, J. Pei, S. Schuster, and B. Wan, “A comparison of one-way and two-way coupling methods for numerical analysis of fluid-structure interactions,” Journal of Applied Mathematics, vol. 2011, Article ID 853560, 16 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. Y.-B. Chen, Z.-K. Wang, and G.-C. Tsai, “Two-way fluid-structure interaction simulation of a micro horizontal axis wind turbine,” International Journal of Engineering and Technology Innovation, vol. 5, no. 1, pp. 33–44, 2015. View at Google Scholar · View at Scopus
  30. J. Jonkman, S. Butterfield, W. Musial, and G. Scott, “Definition of a 5-Mw reference wind turbine for offshore system development,” Tech. Rep. NREL/TP-500-38060, National Renewable Energy Laboratory-NREL, 2009. View at Google Scholar
  31. H. J. T. Kooijman, C. Lindenburg, D. Winkelaar, and E. L. van der Hooft, DOWEC 6 MW Pre-Design: Aero-Elastic Modelling of the DOWEC 6 MW Pre-Design in PHATAS, ECN: Wind Energy, Petten, The Netherlands, 2003.
  32. A. Ahlstrom, Aeroelastic Simulation of Wind Turbine Dynamics, KTH-Royal Institute of Technology, Stockholm, Sweden, 2005.
  33. T. Buhl, Research in Aeroelasticity EFP-2007-II, Risø National Laboratory, Roskilde, Denmark, 2009.
  34. C. Lindenburg, Comparison of Phatas Versions and the Wind Turbine Module, Energy Research Center of the Netherlands, ECN, 2011.
  35. J. G. Schepers, J. Heijdra, D. Foussekis et al., VerIfication of European Wind Turbine Design Codes, VEWTDC, Energy Research Center of the Netherlands, ECN, 2002.
  36. J. G. Schepers, J. Heijdra, K. Thomsen et al., “Verification of European wind turbine design codes,” in Proceedings of the European Wind Energy Conference (EWEC '01), Copenhagen, Denmark, 2001.
  37. J. M. Jonkman and M. L. Buhl Jr., FAST User's Guide, NREL, Golden, Colo, USA, 2005.
  38. T. J. Larsen and A. M. Hansen, How 2 HAWC2, The User's Manual, Risø National Laboratory, Roskilde, Denmark, 2007.
  39. P. Passon and M. Kühn, State-of-the-Art and Development Needs of Simulation Codes for Offshore Wind Turbines, Copenhagen Offshore Wind, 2005.
  40. F. S. J. Peeringa, Aero-Elastic Simulation of Offshore Wind Turbines in the Frequency Domain TURBU@Sea, Energy Research Center of the Netherlands, ECN, 2009.
  41. T. G. Van Engelen, “Control design based on aero-hydro-servo-elastic linear models from TURBU (ECN),” in Proceedings of the European Wind Energy Conference and Exhibition (EWEC '07), pp. 114–140, Milan, Italy, May 2007. View at Scopus
  42. P. T. D. M. Lano, 2015, http://www.aero.polimi.it/~bottasso/POLI-Wind.htm.
  43. R. Rubak and J. T. Petersen, “Monopile as part of aeroelastic wind turbine simulation code,” in Proceedings of the Conference Copenhagen Offshore Wind, Copenhagen, Denmark, October 2005.
  44. N. N. Sørensen and J. Johansen, “UpWind, aerodynamics and aero-elasticity, rotor aerodynamics in atmospheric shear flow,” in Proceedings of the European Wind Energy Conference & Exhibition, Milan, Italy, May 2007.
  45. R. Flemming, “UpWind: aerodynamics and aeroelastics,” in Proceedings of the European Wind Energy Conference & Exhibition, Brussels, Belgium, 2007.
  46. F. Zahle, H. Aagaard Madsen, and N. Sørensen, Evaluation of Tower Shadow Effects on Various Wind Turbine Concepts, Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi, Roskilde, Denmark, 2009.
  47. A. Gómez and J. R. Seume, “Load pulses on wind turbine structures caused by tower interference,” Wind Engineering, vol. 33, no. 6, pp. 555–570, 2009. View at Publisher · View at Google Scholar · View at Scopus
  48. S.-Y. Lin and T.-H. Shieh, “Study of aerodynamical interference for a wind turbine,” International Communications in Heat and Mass Transfer, vol. 37, no. 8, pp. 1044–1047, 2010. View at Publisher · View at Google Scholar · View at Scopus
  49. P. Zhang, S. Huang, T. Yang, and J. Li, “3D potential flow model of tower interference for upwind wind turbine,” Advances in Mechanical Engineering, vol. 2014, Article ID 612453, 10 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  50. F. Zahle, N. N. Sørensen, and H. A. Madsen, The Influence of Wind Shear and Tower Presence on Rotor and Wake Aerodynamics Using CFD, Risø National Laboratory, Roskilde, Denmark, 2008.
  51. P. Zhang, S. Huang, T. Yang, and J. Li, “Research on the aeroelastic response of tower effects for great grade wind turbine,” Journal of Applied Sciences, vol. 13, no. 15, pp. 3042–3048, 2013. View at Publisher · View at Google Scholar · View at Scopus
  52. S. T. Frandsen, “Turbulence and turbulence-generated structural loading in wind turbine clusters,” Risoe-R no. 1188(EN), Forskningscenter Risoe, Roskilde, Denmark, 2007. View at Google Scholar
  53. “IEC 6400-1-International Standard. Wind turbines—Part 1: Design requirements,” International Electrotechnical Commission (IEC), 2005.
  54. K. Thomsen, H. A. Madsen, G. C. Larsen, and T. J. Larsen, “Comparison of methods for load simulation for wind turbines operating in wake,” Journal of Physics: Conference Series, vol. 75, no. 75, 2007. View at Publisher · View at Google Scholar · View at Scopus
  55. N. Jensen, A Note on Wind Generator Interaction, Risø National Laboratory, Roskilde, Denmark, 1983.
  56. I. Katíc, J. Højstrup, and N. O. Jensen, “A simple model for cluster efficiency,” in Proceedings of the European Wind Energy Association Conference and Exhibition (EWEC '86), Rome, Italy, 1987.
  57. J. F. Ainslie, “Calculating the flowfield in the wake of wind turbines,” Journal of Wind Engineering and Industrial Aerodynamics, vol. 27, no. 1–3, pp. 213–224, 1988. View at Publisher · View at Google Scholar · View at Scopus
  58. S. Ott, J. Berg, and M. Nielsen, “Linearised CFD Models for Wakes, Risø-R-1772(EN),” Risø National Laboratory, Roskilde, Denmark, 2011.
  59. S. Ott, M. Nielsen, and K. S. Hansen, “Fuga—validating a wake model for offshore wind farms,” in Proceedings of the European Wind Energy Association Meeting, Dublin, Ireland, 2013.
  60. G. C. Larsen, H. A. Madsen, F. Bingöl et al., Dynamic Wake Meandering Modeling, Risø National Laboratory-Risø-R-1607(EN), Roskilde, Denmark, 2007.
  61. T. J. Larsen, H. A. Madsen, G. C. Larsen, and K. S. Hansen, “Validation of the dynamic wake meander model for loads and power production in the Egmond aan Zee wind farm,” Wind Energy, vol. 16, no. 4, pp. 605–624, 2012. View at Publisher · View at Google Scholar · View at Scopus
  62. L. J. Vermeer, J. N. Sørensen, and A. Crespo, “Wind turbine wake aerodynamics,” Progress in Aerospace Sciences, vol. 39, no. 6-7, pp. 467–510, 2003. View at Publisher · View at Google Scholar · View at Scopus
  63. M. Bastankhah and F. Porté-Agel, “A new analytical model for wind-turbine wakes,” Renewable Energy, vol. 70, pp. 116–123, 2014. View at Google Scholar
  64. M. Gaumond, P.-E. Réthoré, A. Bechmann et al., Benchmarking of Wind Turbine Wake Models in Large Offshore Wind Farms, The Science of Making Torque from Wind, Oldenburg, Germany, 2012.
  65. B. Schmidt, U. Smolka, S. Hartmann, and P. W. Cheng, “Validation of the dynamic wake meander model with AREVA M5000 load measurements at alpha ventus,” in Proceedings of the EWEA Offshore, Frankfurt, Germany, November 2013.
  66. T. J. Larsen, G. Larsen, H. A. Madsen, and K. Thomsen, Comparison of Design Methods for Turbines in Wake, EWEC, Brussels, Belgium, 2008.
  67. J. Annoni, P. Seiler, K. Johnson, P. Fleming, and P. Gebraad, “Evaluating wake models for wind farm control,” in Proceedings of the American Control Conference (ACC '14), pp. 2517–2523, IEEE, Portland, Ore, USA, June 2014. View at Publisher · View at Google Scholar · View at Scopus
  68. M. J. Churchfield, “A review of wind turbine wake models and future directions,” in Proceedings of the North American Wind Energy Academy Symposium (NAWEA '13), Boulder, Colo, USA, 2013.
  69. B. S. Kallesøe and M. H. Hansen, “Some effects of large blade deflections on aeroelastic stability,” in Proceedings of the 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Fla, USA, January 2009. View at Scopus
  70. B. S. Kallesøe, “Large blade deformations effect on flutter boundaries,” in Research in Aeroelasticity EFP-2006, pp. 83–89, Risø National Laboratory, Roskilde, Denmark, 2007. View at Google Scholar
  71. M. H. Hansen and B. S. Kallesøe, “Some nonlinear effects on the flutter speed and blade stability,” in Research in Aeroelasticity EFP-2007, vol. Risø-R-1649(EN), pp. 93–105, Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi, Roskilde, Denmark, 2008. View at Google Scholar
  72. T. J. Larsen, A. M. Hansen, and T. Buhl, Aeroelastic Effects of Large Blade Deflections for Wind Turbines, The Science of Making Torque from Wind, Copenhagen, Denmark, 2004.
  73. M. Dado and S. Al-Sadder, “A new technique for large deflection analysis of non-prismatic cantilever beams,” Mechanics Research Communications, vol. 32, no. 6, pp. 692–703, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  74. J. W. Larsen and S. R. K. Nielsen, “Non-linear dynamics of wind turbine wings,” International Journal of Non-Linear Mechanics, vol. 41, no. 5, pp. 629–643, 2006. View at Publisher · View at Google Scholar · View at Scopus
  75. A. Banerjee, B. Bhattacharya, and A. K. Mallik, “Large deflection of cantilever beams with geometric non-linearity: analytical and numerical approaches,” International Journal of Non-Linear Mechanics, vol. 43, no. 5, pp. 366–376, 2008. View at Publisher · View at Google Scholar · View at Scopus
  76. G. Yuan and Y. Chen, “Geometrical nonlinearity analysis of wind turbine blade subjected to extreme wind loads,” in Proceedings of the International Symposium on Computational Structural Engineering, Shanghai, China, June 2009.
  77. L. Chen, “An integral approach for large deflection cantilever beams,” International Journal of Non-Linear Mechanics, vol. 45, no. 3, pp. 301–305, 2010. View at Publisher · View at Google Scholar · View at Scopus
  78. B. S. Kallesøe, J. J. Thomsen, and M. H. Hansen, Aeroservoelasticity of Wind Turbines, Technical University of Denmark, Copenhagen, Denmark, 2007.
  79. C. Athisakul, B. Phungpaingam, G. Juntarakong, and S. Chucheepsakul, “Effect of material nonlinearity on large deflection of variable-arc-length beams subjected to uniform self-weight,” Mathematical Problems in Engineering, vol. 2012, Article ID 345461, 9 pages, 2012. View at Google Scholar · View at MathSciNet
  80. G. Bir and J. Jonkman, “Aeroelastic instabilities of large offshore and onshore wind turbines,” Journal of Physics: Conference Series, vol. 75, Article ID 012069, 2007. View at Publisher · View at Google Scholar
  81. C. Lindenburg and H. Snel, “Aero-elastic stability analysis tools for large wind turbine rotor blades,” in Proceedings of the European Wind Energy Conference, Madrid, Spain, 2003.
  82. J. Thirstrup Petersen, H. Aagaard Madsen, A. Björck et al., “Prediction of dynamic loads and induced vibrations in stall,” Risoe-R no. 1045(EN), Forskningscenter Risoe, Roskilde, Denmark, 1998. View at Google Scholar
  83. K. Thomsen, J. T. Petersen, E. Nim, S. Øye, and B. Petersen, “A method for determination of damping for edgewise blade vibrations,” Wind Energy, vol. 3, no. 4, pp. 233–246, 2000. View at Publisher · View at Google Scholar
  84. F. Rasmussen, J. T. Petersen, and H. A. Madsen, “Dynamic stall and aerodynamic damping,” in Proceedings of the AIAA/ASME Wind Energy Symposium, pp. 44–51, January 1998. View at Scopus
  85. P. K. Chaviaropoulos, “Flap/lead-lag aeroelastic stability of wind turbine blades,” Wind Energy, vol. 4, no. 4, pp. 183–200, 2001. View at Publisher · View at Google Scholar
  86. V. A. Riziotis, S. G. Voutsinas, E. S. Politis, and P. K. Chaviaropoulos, “Aeroelastic stability of wind turbines: the problem, the methods and the issues,” Wind Energy, vol. 7, no. 4, pp. 373–392, 2004. View at Publisher · View at Google Scholar · View at Scopus
  87. P. K. Chaviaropoulos, N. N. Soerensen, M. O. L. Hansen et al., “Viscous and aeroelastic effects on wind turbine blades. The VISCEL project. Part II: aeroelastic stability investigations,” Wind Energy, vol. 6, no. 4, pp. 387–403, 2003. View at Publisher · View at Google Scholar · View at Scopus
  88. M. H. Hansen, “Aeroelastic stability analysis of wind turbines using an eigenvalue approach,” Wind Energy, vol. 7, no. 2, pp. 133–143, 2004. View at Publisher · View at Google Scholar · View at Scopus
  89. T. S. B. Nielsen and C. J. Spruce, “Wind Turbine, A Method For Damping Edgewise Oscillations In One Or More Blades Of A Wind Turbine By Changing The Blade Pitch And Use Hereof,” Patent US20090185901 A1, 23 July 2009.
  90. T. S. B. Nielsen, B. J. Pedersen, and C. J. Spruce, “Method for damping edgewise oscillations in one or more blades of a wind turbine, an active stall controlled wind turbine and use hereof,” Patent US8070437 B2, 6 December 2011.
  91. D. W. Lobitz, “Aeroelastic stability predictions for a MW-sized blade,” Wind Energy, vol. 7, no. 3, pp. 211–224, 2004. View at Publisher · View at Google Scholar · View at Scopus
  92. C. P. van Dam, D. E. Berg, and S. J. Johnson, “Active load control techniques for wind turbines,” Tech. Rep. SAND2008-4809 TRN: US200902%%565, Sandia National Laboratories, Albuquerque, NM, USA, 2008. View at Google Scholar
  93. T. K. Barlas and G. A. M. van Kuik, “State of the art and prospectives of smart rotor control for wind turbines,” Journal of Physics: Conference Series, vol. 75, Article ID 012080, 2007. View at Publisher · View at Google Scholar
  94. T. K. Barlas and G. A. M. van Kuik, “Review of state of the art in smart rotor control research for wind turbines,” Progress in Aerospace Sciences, vol. 46, no. 1, pp. 1–27, 2010. View at Publisher · View at Google Scholar · View at Scopus
  95. D. G. Wilson, D. E. Berg, M. F. Barone, J. C. Berg, B. R. Resor, and D. W. Lobitz, “Active aerodynamic blade control design for load reduction on large wind turbines,” in Proceedings of the in European Wind Energy Conference & Exhibition, Parc Chanot, France, March 2009.
  96. D. E. Berg, D. G. Wilson, M. F. Barone et al., “The impact of active aerodynamic load control on fatigue and energy capture at low wind speed sites,” in Proceedings of the European Wind Energy Conference and Exhibition (EWEC '09), pp. 2670–2679, Marseille, France, March 2009. View at Scopus
  97. L. Bergami and N. K. Poulsen, “A smart rotor configuration with linear quadratic control of adaptive trailing edge flaps for active load alleviation,” Wind Energy, vol. 18, no. 4, pp. 625–641, 2015. View at Publisher · View at Google Scholar · View at Scopus
  98. M. Zhang, W. Yu, and J. Xu, “Aerodynamic physics of smart load control for wind turbine due to extreme wind shear,” Renewable Energy, vol. 70, pp. 204–210, 2014. View at Publisher · View at Google Scholar · View at Scopus
  99. K.-C. Tsai, C.-T. Pan, A. M. Cooperman, S. J. Johnson, and C. P. van Dam, “An innovative design of a microtab deployment mechanism for active aerodynamic load control,” Energies, vol. 8, no. 6, pp. 5885–5897, 2015. View at Publisher · View at Google Scholar · View at Scopus
  100. C. P. Van Dam, R. Chow, J. R. Zayas, and D. E. Berg, “Computational investigations of small deploying tabs and flaps for aerodynamic load control,” Journal of Physics: Conference Series, vol. 75, 2007. View at Publisher · View at Google Scholar · View at Scopus
  101. J. C. Lin, “Review of research on low-profile vortex generators to control boundary-layer,” Progress in Aerospace Sciences, vol. 38, no. 4-5, pp. 389–420, 2012. View at Google Scholar
  102. S. Shun and N. A. Ahmed, “Wind turbine performance improvements using active flow control techniques,” Procedia Engineering, vol. 49, pp. 83–91, 2012. View at Google Scholar