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 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.     

Predicting wind turbine blade loads and aeroelastic response using a coupled CFD–CSD method

The aeroelastic response and the airloads of horizontal-axis wind turbine rotor blades were numerically investigated using a coupled CFD–CSD method. The blade aerodynamic loads were obtained from a Navier–Stokes CFD flow solver based on unstructured meshes. The blade elastic deformation was calculated using a FEM-based CSD solver which employs a nonlinear coupled flap-lag-torsion beam theory. The coupling of the CFD and CSD solvers was accomplished in a loosely coupled manner by exchanging the information between the two solvers at infrequent intervals. At first, the present coupled CFD–CSD method was applied to the NREL 5MW reference wind turbine rotor under steady axial flow conditions, and the mean rotor loads and the static blade deformation were compared with other predicted results. Then, the unsteady blade aerodynamic loads and the dynamic blade response due to rotor shaft tilt and tower interference were investigated, along with the influence of the gravitational force. It was found that due to the aeroelastic blade deformation, the blade aerodynamic loads are significantly reduced, and the unsteady dynamic load behaviors are also changed, particularly by the torsional deformation. From the observation of the tower interference, it was also found that the aerodynamic loads are abruptly reduced as the blades pass by the tower, resulting in oscillatory blade deformation and vibratory loads, particularly in the flapwise direction.     

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.     

Full‐scale test of trailing edge flaps on a Vestas V27 wind turbine: active load reduction and system identification

A full‐scale test was performed on a Vestas V27 wind turbine equipped with one active 70 cm long trailing edge flap on one of its 13 m long blades. Active load reduction could be observed in spite of the limited spanwise coverage of the single active trailing edge flap. A frequency‐weighted model predictive control was tested successfully on this demonstrator turbine. An average flapwise blade root load reduction of 14% was achieved during a 38 minute test, and a reduction of 20% of the amplitude of the 1P loads was measured. A system identification test was also performed, and an identified linear model, from trailing edge flap angle to flapwise blade root moment, was derived and compared with the linear analytical model used in the model predictive control design model. Flex5 simulations run with the same model predictive control showed a good correlation between the simulations and the measurements in terms of flapwise blade root moment spectral densities, in spite of significant differences between the identified linear model and the model predictive control design model. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Analytic analysis of load alignment for coning extreme‐scale rotors

Extreme‐scale wind turbines (rated powers greater than 10 MW) with large rotor diameters and conventional upwind designs must resist extreme downwind and gravity loads. This can lead to significant structural design challenges and high blade masses that can impede the reduction of levelized cost of wind energy. Herein, the theoretical basis for downwind load alignment is developed. This alignment can be addressed with active downwind coning to reduce/eliminate flapwise bending loads by balancing the transverse components of thrust, centrifugal, and gravitational force. Equations are developed herein that estimates the optimal coning angle that reduces flapwise loads by a specified amount. This analysis is then applied to a 13.2‐MW scale with 100‐m‐level wind turbine blades, where it is found that a load alignment coning schedule can substantially reduce the root flapwise bending moments. This moment reduction in this example can allow the rotor mass to be decreased significantly when compared with a conventional upwind three‐bladed rotor while maintaining structural performance and annual energy output.     

Load response of a two-rotor floating wind turbine undergoing blade-pitch system faults

Multi-rotor floating wind turbines are among the innovative technologies proposed in the last decade in the effort to reduce the cost of wind energy. These systems are able to offer advantages in terms of smaller blades deployed offshore, cheaper operations, fewer installations, and sharing of the floating platform. As the blade-pitch actuation system is prone to failures, the assessment of the associated load scenarios is commonly required. Load assessment of blade-pitch fault scenarios has only been performed for single-rotor solutions. In this work, we address the effect of blade-pitch system faults and emergency shutdown on the dynamics and loads of a two-rotor floating wind turbine. The concept considered employs two NREL 5-MW baseline wind turbines and the OO-Star semi-submersible platform. The blade-pitch faults investigated are blade blockage and runaway, that is, the seizure at a given pitch angle and the uncontrolled actuation of one of the blades, respectively. Blade-pitch faults lead to a significant increase in the structural loads of the system, especially for runaway fault conditions. Emergency shutdown significantly excites the platform pitch motion, the tower-bottom bending moment, and tower torsional loads, while suppressing the faulty blade flapwise bending moment after a short peak. Shutdown delay between rotors increases significantly the maxima of the torsional loads acting on the tower. Comparison of blade loads with data from single-rotor spar-type study show great similarity, highlighting that the faulty blade loads are not affected by (1) the type of platform used and (2) the multi-rotor deployment.     

Modelling the aerodynamics of vertical‐axis wind turbines in unsteady wind conditions

Most numerical and experimental studies of the performance of vertical‐axis wind turbines have been conducted with the rotors in steady, and thus somewhat artificial, wind conditions—with the result that turbine aerodynamics, under varying wind conditions, are still poorly understood. The vorticity transport model has been used to investigate the aerodynamic performance and wake dynamics, both in steady and unsteady wind conditions, of three different vertical‐axis wind turbines: one with a straight‐bladed configuration, another with a curved‐bladed configuration and another with a helically twisted configuration. The turbines with non‐twisted blades are shown to be somewhat less efficient than the turbine with helically twisted blades when the rotors are operated at constant rotational speed in unsteady wind conditions. In steady wind conditions, the power coefficients that are produced by both the straight‐bladed and curved‐bladed turbines vary considerably within one rotor revolution because of the continuously varying angle of attack on the blades and, thus, the inherent unsteadiness in the blade aerodynamic loading. These variations are much larger, and thus far more significant, than those that are induced by the unsteadiness in the wind conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Aeroelastic multidisciplinary design optimization of a swept wind turbine blade

Mitigating loads on a wind turbine rotor can reduce the cost of energy. Sweeping blades produces a structural coupling between flapwise bending and torsion, which can be used for load alleviation purposes. A multidisciplinary design optimization (MDO) problem is formulated including the blade sweep as a design variable. A multifidelity approach is used to confront the crucial effects of structural coupling on the estimation of the loads. During the MDO, ultimate and damage equivalent loads are estimated using steady‐state and frequency‐domain–based models, respectively. The final designs are verified against time‐domain full design load basis aeroelastic simulations to ensure that they comply with the constraints. A 10‐MW wind turbine blade is optimized by minimizing a cost function that includes mass and blade root flapwise fatigue loading. The design space is subjected to constraints that represent all the necessary requirements for standard design of wind turbines. Simultaneous aerodynamic and structural optimization is performed with and without sweep as a design variable. When sweep is included in the MDO process, further minimization of the cost function can be obtained. To show this achievement, a set of optimized straight blade designs is compared to a set of optimized swept blade designs. Relative to the respective optimized straight designs, the blade mass of the swept blades is reduced of an extra 2% to 3% and the blade root flapwise fatigue damage equivalent load by a further 8%.     

Effect of steady deflections on the aeroelastic stability of a turbine blade

This paper deals with effects of geometric non‐linearities on the aeroelastic stability of a steady‐state deflected blade. Today, wind turbine blades are long and slender structures that can have a considerable steady‐state deflection which affects the dynamic behaviour of the blade. The flapwise blade deflection causes the edgewise blade motion to couple to torsional blade motion and thereby to the aerodynamics through the angle of attack. The analysis shows that in the worst case for this particular blade, the edgewise damping can be decreased by half. Copyright © 2010 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.     

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.     

Bend‐bend‐twist vibrations of a wind turbine blade

Dynamics of a wind turbine blade under bend‐bend‐twist coupled vibrations is investigated. The potential and kinetic energy expressions for a straight nonuniform blade are written in terms of beam parameters. Then, the energies are expressed in terms of modal coordinates by using the assumed mode method, and the equations of motion are found by applying Lagrange's formula. The bend‐bend‐twist equations are coupled with each other and have stiffness variations due to centrifugal effects and gravitational parametric terms, which vary cyclicly with the hub angle. To determine the natural frequencies and mode shapes of the system, a modal analysis is applied on the linearized coupled equations of constant angle snapshots of a blade with effects of constant speed rotation. Lower modes of the coupled bend‐bend‐twist model are dominantly in‐plane or out‐of‐plane modes. To investigate the parametric effects, several blade models are analyzed at different angular positions. The stiffness terms involving centrifugal and gravitational effects can be significant for long blades. To further see the effect of blade length on relative parametric stiffness change, the blade models are scaled in size and analyzed at constant rotational speeds, at horizontal and vertical orientations. These studies show that the parametric stiffness effects should be taken into account when designing long blades.     

Rapid optimization of stall‐regulated wind turbine blades using a frequency‐domain method: Part 2, cost function selection and results

A fast and effective frequency‐domain optimization method was developed for stall‐regulated blades. It was found that when using linearized dynamics, typical cost functions employing damage‐equivalent root bending moments are not suitable for stall‐regulated wind turbines: when the cost function is minimized, the edgewise damping can be low, and the flapwise damping can approach zero during an extreme operating gust. A new cost function is proposed that leads to nicely balanced stall behavior and damping over the entire operating windspeed range. The method was used to design the blades of two multi‐MW, stall‐regulated, offshore wind turbines, comparable with the NREL 5 MW and NTNU 10 MW pitch‐regulated turbines. It is shown that the optimal stall‐regulated blade has a unique aerodynamic profile that gives high flapwise and edgewise damping and a uniform mean power output above the rated windspeed. The blades are described in sufficient detail that they can be used in further aeroelastic analyses, to compare large stall‐regulated and pitch‐regulated turbines. Copyright © 2014 John Wiley & Sons, Ltd.     

Comparison of the near‐wake between actuator‐line simulations and a simplified vortex model of a horizontal‐axis wind turbine

The flow around an isolated horizontal‐axis wind turbine is estimated by means of a new vortex code based on the Biot–Savart law with constant circulation along the blades. The results have been compared with numerical simulations where the wind turbine blades are replaced with actuator lines. Two different wind turbines have been simulated: one with constant circulation along the blades, to replicate the vortex method approximations, and the other with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind‐turbine conditions (Tjæreborg wind turbine). The vortex model matched the numerical simulation of the turbine with constant blade circulation in terms of the near‐wake structure and local forces along the blade. The results from the Tjæreborg turbine case showed some discrepancies between the two approaches, but overall, the agreement is qualitatively good, validating the analytical method for more general conditions. The present results show that a simple vortex code is able to provide an estimation of the flow around the wind turbine similar to the actuator‐line approach but with a negligible computational effort. Copyright © 2015 John Wiley & Sons, Ltd.     

预弯外形对风力机叶片气弹稳定性的影响

为了研究预弯外形对风力机气弹稳定性的影响,以某2 MW低风速风电叶片为研究对象,采用外形参数化表达方法构造叶尖预弯量分别为3、4和5 m的叶片.基于SIMPACK软件建立并验证气-弹-控耦合的风力机整机模型,对配装不同预弯叶片的风力机进行仿真分析.结果显示,在湍流风况下,随着叶尖预弯量的增大,叶根载荷、叶尖附近截面的气...     

Optimization‐based study of bend–twist coupled rotor blades for passive and integrated passive/active load alleviation

This work is concerned with the design of wind turbine blades with bend‐twist‐to‐feather coupling that self‐react to wind fluctuations by reducing the angle of attack, thereby inducing a load mitigation effect. This behavior is obtained here by exploiting the orthotropic properties of composite materials by rotating the fibers away from the pitch axis. The first part of this study investigates the possible configurations for achieving bend‐twist coupling. At first, fully coupled blades are designed by rotating the fibers for the whole blade span, and a best compromise solution is found to limit weight increase by rotations both in the spar caps and in the skin. Next, partially coupled blades are designed where fibers are rotated only on the outboard part of the blade, this way achieving good load mitigation capabilities together with weight savings. All blades are designed with a multilevel constrained optimization procedure, on the basis of combined cross‐sectional, multibody aero‐servo‐elastic and three‐dimensional finite element models. Finally, the best configuration of the passive coupled blade is combined with an active individual pitch controller. The synergistic use of passive and active load mitigation technologies is shown to allow for significant load reductions while limiting the increase in actuator duty cycle, thanks to the opposite effects on this performance metric of the passive and active control solutions. 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.     

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

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