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.     

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.     

Development of an aeroelastic code based on three‐dimensional viscous–inviscid method for wind turbine computations

Aerodynamic and structural dynamic performance analysis of modern wind turbines are routinely estimated in the wind energy field using computational tools known as aeroelastic codes. Most aeroelastic codes use the blade element momentum (BEM) technique to model the rotor aerodynamics and a modal, multi‐body or the finite‐element approach to model the turbine structural dynamics. The present work describes the development of a novel aeroelastic code that combines a three‐dimensional viscous–inviscid interactive method, method for interactive rotor aerodynamic simulations (MIRAS), with the structural dynamics model used in the aeroelastic code FLEX5. The new code, called MIRAS‐FLEX, is an improvement on standard aeroelastic codes because it uses a more advanced aerodynamic model than BEM. With the new aeroelastic code, more physical aerodynamic predictions than BEM can be obtained as BEM uses empirical relations, such as tip loss corrections, to determine the flow around a rotor. Although more costly than BEM, a small cluster is sufficient to run MIRAS‐FLEX in a fast and easy way. MIRAS‐FLEX is compared against the widely used FLEX5 and FAST, as well as the participant codes from the Offshore Code Comparison Collaboration Project. Simulation tests consist of steady wind inflow conditions with different combinations of yaw error, wind shear, tower shadow and turbine‐elastic modeling. Turbulent inflow created by using a Mann box is also considered. MIRAS‐FLEX results, such as blade tip deflections and root‐bending moments, are generally in good agreement with the other codes. Copyright © 2017 John Wiley & Sons, Ltd.     

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

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

Application and validation of incrementally complex models for wind turbine aerodynamics,isolated wind turbine in uniform inflow conditions

A comparison of several incrementally complex methods for predicting wind turbine performance, aeroelastic behavior, and wakes is provided. Depending on a wind farm's design, wake interference can cause large power losses and increased turbulence levels within the farm. The goal is to employ modeling methods to reach an improved understanding of wake effects and to use this information to better optimize the layout of new wind farms. A critical decision faced by modelers is the fidelity of the model that is selected to perform simulations. The choice of model fidelity can affect the accuracy, but will also greatly impact the computational time and resource requirements for simulations. To help address this critical question, three modeling methods of varying fidelity have been developed side by side and are compared in this article. The models from low to high complexity are as follows: a blade element‐based method with a free‐vortex wake, an actuator disc‐based method, and a full rotor‐based method. Fluid/structure interfaces are developed for the aerodynamic modeling approaches that allow modeling of discrete blades and are then coupled with a multibody structural dynamics solver in order to perform an aeroelastic analysis. Similar methods have individually been tested by researchers, but we suggest that by developing a suite of models, they can be cross‐compared to grasp the subtleties of each method. The modeling methods are applied to the National Renewable Energy Laboratory Phase VI rotor to predict the turbine aerodynamic and structural loads and then also the wind velocities in the wake. The full rotor method provides the most accurate predictions at the turbine and the use of adaptive mesh refinement to capture the wake to 20 radii downstream is proven particularly successful. Though the full rotor method is unmatched by the lower fidelity methods in stalled conditions and detailed prediction of the downstream wake, there are other less complex conditions where these methods perform as accurately as the full rotor method. Copyright © 2014 John Wiley & Sons, Ltd.     

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

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

Flap/lead–lag aeroelastic stability of wind turbine blades

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

Simulating the aerodynamic performance and wake dynamics of a vertical‐axis wind turbine

The accurate prediction of the aerodynamics and performance of vertical‐axis wind turbines is essential if their design is to be improved but poses a significant challenge to numerical simulation tools. The cyclic motion of the blades induces large variations in the angle of attack of the blades that can manifest as dynamic stall. In addition, predicting the interaction between the blades and the wake developed by the rotor requires a high‐fidelity representation of the vortical structures within the flow field in which the turbine operates. The aerodynamic performance and wake dynamics of a Darrieus‐type vertical‐axis wind turbine consisting of two straight blades is simulated using Brown's Vorticity Transport Model. The predicted variation with azimuth of the normal and tangential force on the turbine blades compares well with experimental measurements. The interaction between the blades and the vortices that are shed and trailed in previous revolutions of the turbine is shown to have a significant effect on the distribution of aerodynamic loading on the blades. Furthermore, it is suggested that the disagreement between experimental and numerical data that has been presented in previous studies arises because the blade–vortex interactions on the rotor were not modelled with sufficient fidelity. Copyright © 2010 John Wiley & Sons, Ltd.     

The impact of yaw error on aeroelastic characteristics of a horizontal axis wind turbine blade

Horizontal axis wind turbines operate under yawed conditions for a considerable period of time due to the power control mechanism or sudden changes in the wind direction. This in turn can alter the dynamic characteristics of a turbine blade because the flow over the rotor plane may trigger complicated induced velocity patterns. In this study, an aeroelastic analysis under yawed flow conditions is carried out to investigate the effects of yaw error on the blade behaviors and dynamic stability. A beam model including geometric nonlinearity coupled with unsteady aerodynamics based on a free-vortex wake method with the blade element theory is employed in the present study. The aerodynamic approach for a horizontal axis wind turbine blade under yawed flow conditions is verified through comparison with measurements. It is also shown that the present method gives slightly better results at high yaw angles than does the method previously published in the literature. The dynamic instabilities of a National Renewable Energy Laboratory 5 MW reference wind turbine have subsequently been investigated for various wind speeds and yaw angles. Observations are made that yaw effects induce considerable changes in airloads and blade structural behavior. Also, the aeroelastic damping values for this particular blade under yawed flow conditions can be reduced by up to approximately 33% in the worst case. Therefore, it is concluded that the impacts of yaw misalignments adversely influenced the dynamic aeroelastic stability of the horizontal axis wind turbine blade.     

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.     

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

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

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.     

Predictions of unsteady HAWT aerodynamics in yawing and pitching using the free vortex method

To predict the unsteady aerodynamic loads of horizontal-axis wind turbines (HAWTs) during operations under yawing and pitching conditions, an unsteady numerical simulation method is proposed. This method includes a nonlinear lifting line method to compute the aerodynamic loads on the blades and a time-accurate free-vortex method to simulate the wake. To improve the convergence property in the nonlinear lifting line method, an iterative algorithm based on the Newton–Raphson method is developed. To increase the computational efficiency and the accuracy of the calculation, a new wake vortex model consisting of the vortex core model, the vortex sheet model and the tip vortex model is used. Wind turbines with different diameters, such as NREL Phase VI, the TU Delft model turbine and the Tjæreborg wind turbine, are used to validate the method for rotors operating at given yaw and/or pitch angles and during yawing and/or pitching processes at different wind speeds. The results, including the blade loads, the rotor torque and the locations of the tip vortex cores in the wake, agree well with the measured data and the computed data. It is shown that the proposed method can be used for predictions of unsteady aerodynamic loads and rotor wakes in the operational processes of blade pitching and/or rotor yawing.     

Aeroelastic validation and Bayesian updating of a downwind wind turbine

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

Parked aeroelastic field rotor response for a 20% scaled demonstrator of a 13-MW downwind turbine

Aeroelastic parked testing of a unique downwind two-bladed subscale rotor was completed to characterize the response of an extreme-scale 13-MW turbine in high-wind parked conditions. A 20% geometric scaling was used resulting in scaled 20-m-long blades, whose structural and stiffness properties were designed using aeroelastic scaling to replicate the nondimensional structural aeroelastic deflections and dynamics that would occur for a lightweight, downwind 13-MW rotor. The subscale rotor was mounted and field tested on the two-bladed Controls Advanced Research Turbine (CART2) at the National Renewable Energy Laboratory's Flatiron Campus (NREL FC). The parked testing of these highly flexible blades included both pitch-to-run and pitch-to-feather configurations with the blades in the horizontal braked orientation. The collected experimental data includes the unsteady flapwise root bending moments and tip deflections as a function of inflow wind conditions. The bending moments are based on strain gauges located in the root section, whereas the tip deflections are captured by a video camera on the hub of the turbine pointed toward the tip of the blade. The experimental results are compared against computational predictions generated by FAST, a wind turbine simulation software, for the subscale and full-scale models with consistent unsteady wind fields. FAST reasonably predicted the bending moments and deflections of the experimental data in terms of both the mean and standard deviations. These results demonstrate the efficacy of the first such aeroelastically scaled turbine test and demonstrate that a highly flexible lightweight downwind coned rotor can be designed to withstand extreme loads in parked conditions.     

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.     

A low‐order model for analysing effects of blade fatigue load control

A new low‐order mathematical model is introduced to analyse blade dynamics and blade load‐reducing control strategies for wind turbines. The model consists of a typical wing section model combined with a rotor speed model, leading to four structural degrees of freedom (flapwise, edgewise and torsional blade oscillations and rotor speed). The aerodynamics is described by an unsteady aerodynamic model. The equations of motion are derived in non‐linear and linear form. The linear equations of motion are used for stability analysis and control design. The non‐linear equations of motion are used for time simulations to evaluate control performance. The stability analysis shows that the model is capable of predicting classical flutter and stall‐induced vibrations. The results from the stability analysis are compared with known results, showing good agreement. The model is used to compare the performance of one proportional–integral–derivative controller and two full‐state feedback controllers. Copyright © 2006 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.