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

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

HAWT dynamic stall response asymmetries under yawed flow conditions

Horizontal axis wind turbines can experience significant time‐varying aerodynamic loads, potentially causing adverse effects on structures, mechanical components and power production. As designers attempt lighter and more flexible wind energy machines, greater accuracy and robustness will become even more critical in future aerodynamics models. Aerodynamics modelling advances, in turn, will rely on more thorough comprehension of the three‐dimensional, unsteady, vortical flows that dominate wind turbine blade aerodynamics under high‐load conditions. To experimentally characterize these flows, turbine blade surface pressures were acquired at multiple span locations via the NREL Phase IV Unsteady Aerodynamics Experiment. Surface pressures and associated normal force histories were used to characterize dynamic stall vortex kinematics and normal force amplification. Dynamic stall vortices and normal force amplification were confirmed to occur in response to angle‐of‐attack excursions above the static stall threshold. Stall vortices occupied approximately one‐half of the blade span and persisted for nearly one‐fourth of the blade rotation cycle. Stall vortex convection varied along the blade, resulting in dramatic deformation of the vortex. Presence and deformation of the dynamic stall vortex produced corresponding amplification of normal forces. Analyses revealed consistent alterations to vortex kinematics in response to changes in reduced frequency, span location and yaw error. Finally, vortex structures and kinematics not previously documented for wind turbine blades were isolated. Published in 2000 by 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.     

A solution‐based stall delay model for horizontal‐axis wind turbines

This work proposes a new solution‐based stall delay model to predict rotational effects on horizontal‐axis wind turbines. In contrast to conventional stall delay models that correct sectional airfoil data prior to the solution to account for three‐dimensional and rotational effects, a novel approach is proposed that corrects sectional airfoil data during a blade element momentum solution algorithm by investigating solution‐dependent parameters such as the spanwise circulation distribution and the local flow velocity acting at a section of blade. An iterative process is employed that successively modifies sectional lift and drag data until the blade circulation distribution is converged. Results obtained with the solution‐based stall delay model show consistent good agreement with measured data along the National Renewable Energy Laboratory Phase VI and Model Experiments in Controlled Conditions rotor blades at low and high wind speeds. Copyright © 2014 John Wiley & Sons, Ltd.     

Computational fluid dynamics simulation of the aerodynamics of a high solidity,small‐scale vertical axis wind turbine

A computational fluid dynamics simulation was performed for a small‐scale, high solidity (σ = 0.48) H‐type Darrieus vertical axis wind turbine. Two‐dimensional unsteady Reynolds‐averaged Navier–Stokes equations were solved for the turbine numerical model, which has a large stationary domain and smaller rotating subdomain connected by a sliding mesh interface. The simulation results were first validated against steady‐state airfoil data. The model was then used to solve for three rotating blades with constant ambient flow velocity (Re = 360,000) over numerous blade speed ratios. The high solidity and the associated low blade speed ratio and rotational speed of the turbine result in complex flow–blade interaction mechanisms. These include dynamic stall resulting in vortex shedding, vortex impingement on the source blade and significant flow momentum extraction causing reduced power production from the downstream blade pass. Copyright © 2011 John Wiley & Sons, Ltd.     

A new stall delay algorithm for predicting the aerodynamics loads on wind turbine blades for axial and yawed conditions

Stall delay is a complicated phenomenon that has gained for many years the attention of industry and academics in the fields of helicopter and wind turbine aerodynamics. Since most of the potential flow theories still rely on the use of 2D aerofoil data for simulating loads on a rotating blade, less degree of accuracy is expected because of 3D rotational effects. In this work, a new model for correcting the 2D steady aerodynamic data for 3D effects is presented. The model can reduce the uncertainty in the blade design process and, subsequently, make wind turbines more cost‐effective. This model combines the stall delay model of Corrigan and Schillings, a modified version of an inviscid stall delay model, a new modification factor to account for the effect of the angle of attack changes and a new tip loss factor. Furthermore, the model applies the use of the separation factor of Du and Selig to evaluate the area on the rotor disc where stall delay is most prominent. The new stall delay model was embedded in a free‐wake vortex model to estimate the aerodynamic loads on the National Renewable Energy Laboratory Phase VI rotor blades consisting of the S809 aerofoil sections. The results in this study confirm the validity of the 3D corrections by the proposed new model under both axial and yawed flow conditions. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

分形尾缘叶片气动性能及流场数值模拟

针对风力机存在尾流效应问题,通过在垂直轴风力机叶片尾缘布置分形孔的方法,建立分形叶片三维实体造型,进行了分形叶片和原始叶片三维非定常不可压流动的分析,得出叶片绕流流场数值模拟结果,重点研究具有分形特征的尾缘对叶片尾流流场及叶片气动特性的影响。结果表明:分形叶片对改善叶片尾流流场有较显著作用。在8°~18°攻角范围内,分形叶片升、阻力系数随攻角变化波动性小于原始叶片;当攻角大于原始叶片失速攻角时,这种波动性差距更大。分形孔的存在使叶片周围流场结构及气动参数对攻角变化敏感性降低:在攻角大于原始叶片失速攻角时,分形叶片阻力系数随攻角变化标准差仅为原始叶片的0.6倍,升力系数标准差仅为原始叶片0.4倍。研究结果将改善垂直轴风力机叶片尾流互相干扰及水平轴风力机叶尖脱落涡情况。     

Time‐accurate blade surface static pressure behaviour on a rotating H‐Darrieus wind turbine

Time‐accurate blade pressure distributions on a rotating H‐Darrieus wind turbine at representative tip speed ratios during start‐up are presented here, which allow blade dynamic stall and laminar separation bubbles to be observed clearly and which provide a rare experimental demonstration of the flow curvature effect inherent in H‐Darrieus turbine operation. The convection of a dynamic stall vortex along the blade surface at high reduced frequency has also been clearly identified. This study provides new information of the complex aerodynamics of the vertical axis wind turbines (VAWTs) and provides unique experimental data to validate the transient blade static surface pressure distribution predicted by CFD models. To the best of the authors' knowledge, this is the first time that the instantaneous pressure variation around the blade has been measured and recorded directly for an H‐Darrieus wind turbine.     

Validation of the Beddoes–Leishman dynamic stall model for horizontal axis wind turbines using MEXICO data

The aim of this study is to assess the load predicting capability of a classical Beddoes–Leishman dynamic stall model in a horizontal axis wind turbine environment, in the presence of yaw misalignment. The dynamic stall model was tailored to the horizontal axis wind turbine environment and validated against unsteady thick airfoil data. Subsequently, the dynamic stall model was implemented in a blade element‐momentum code for yawed flow, and the results were compared with aerodynamic measurements obtained in the MEXICO (Model Rotor Experiments under Controlled Conditions) project on a wind turbine rotor placed in a large scale wind tunnel. In general, reasonable to good agreement was found between the blade element‐momentum model and MEXICO data. When large yaw misalignments were imposed, poor agreement was found in the downstroke of the movement between the model and the experiment. Still, over a revolution, the maximum normal force coefficient predicted was always within 8% of experimental data at the inboard stations, which is encouraging especially when blade fatigue calculations are being considered. Copyright © 2012 John Wiley & Sons, Ltd.     

Self‐induced vibrations of a DU96‐W‐180 airfoil in stall

This work presents an analysis of two‐dimensional (2D) and three‐dimensional (3D) non‐moving, prescribed motion and elastically mounted airfoil computational fluid dynamics (CFD) computations. The elastically mounted airfoil computations were performed by means of a 2D structural model with two degrees of freedom. The computations aimed at investigating the mechanisms of both vortex‐induced and stall‐induced vibrations related to a wind turbine blade at standstill conditions. In this work, a DU96‐W‐180 airfoil was used in the angle‐of‐attack region potentially corresponding to stall‐induced vibrations. The analysis showed significant differences between the aerodynamic stability limits predicted by 2D and 3D CFD computations. A general agreement was reached between the prescribed motion and elastically mounted airfoil computations. 3D computations indicated that vortex‐induced vibrations are likely to occur at modern wind turbine blades at standstill. In contrast, the predicted cut‐in wind speed necessary for the onset of stall‐induced vibrations appeared high enough for such vibrations to be unlikely. Copyright © 2013 John Wiley & Sons, Ltd.     

Three‐dimensional viscous‐inviscid coupling method for wind turbine computations

In this paper, a computational model for predicting the aerodynamic behavior of wind turbine wakes and blades subjected to unsteady motions and viscous effects is presented. The model is based on a three‐dimensional panel method using a surface distribution of quadrilateral sources and doublets, which is coupled to a viscous boundary layer solver. Unlike Navier‐Stokes codes that need to solve the entire flow domain, the panel method solves the flow around a complex geometry by distributing singularity elements on the body surface, obtaining a faster solution and making this type of codes suitable for the design of wind turbines. A free‐wake model has been employed to simulate the wake behind a wind turbine by using vortex filaments that carry the vorticity shed by the trailing edge of the blades. Viscous and rotational effects inside the boundary layer are taken into account via the transpiration velocity concept, applied using strip theory with the cross sectional angle of attack as coupling parameter. The transpiration velocity is obtained from the solution of the integral boundary layer equations with extension for rotational effects. It is found that viscosity plays a very important role in the predictions of blade aerodynamics and wake dynamics, especially at high angles of attack just before and after boundary layer separation takes place. The present code is validated in detail against the well‐known MEXICO experiment and a set of non‐rotating cases. Copyright © 2014 John Wiley & Sons, Ltd.     

定常吸气对垂直轴风力机性能影响研究

定常吸气装置可有效提高垂直轴风力机气动性能,改善风轮流场结构及翼型动态失速特性.基于CFD方法对垂直轴风力机进行数值模拟,研究不同叶尖速比(TSR)下定常吸气对风力机气动及流场特性的影响,对比分析原始风力机及定常吸气作用下的风能利用率、整机转矩系数及涡量分布.结果表明:不同尖速比下定常吸气均可显著提高风力机气动性能,减...     

海上浮式水平轴风力机气动特性研究

以NREL-5 MW风力机为研究对象,基于叶素动量理论,考虑动态失速、风剪切及塔影效应等气动修正模型,开发Matlab非定常气动载荷计算程序,研究浮式水平轴风力机气动特性。结果表明:为保证风力机气动载荷模拟的正确性,气动修正模型必不可少;基础运动对风力机气动性能有显著影响,基础运动使风力机输出功率增大,但同时存在较大的振荡幅度,导致功率输出不稳定;叶片变桨失效导致功率输出更加不稳定。     

基于BEDDOES-LEISHMAN动态失速模型的水平轴风力机动态气动载荷计算方法

从对附着流和分离流的建模两方面阐述了Beddoes-Leishman动态失速模型.基于Beddoes-Leishman模型开发了动态失速数值计算程序,并将其集成到了现有的风力机气动载荷分析软件中.利用所开发的程序,计算了NACA 63-418翼型的动态失速特性,分析了平均攻角、衰减频率和马赫数的变化对动态失速特性的影响.仿真了一台1.5MW变速恒频风电机组的发电工况,结果表明,动态失速对风力机的动态气动载荷有极大影响,在进行动态载荷仿真时必须予以充分考虑.     

Methods to control dynamic stall for wind turbine applications

Dynamic stall (DS) on a wind turbine is encountered when the sectional angles of attack of the blade rapidly exceeds the steady-state stall angle of attack due to in-flow turbulence, gusts and yaw-misalignment. The process is considered as a primary source of unsteady loads on wind turbine blades and negatively influences the performance and fatigue life of a turbine. In the present article, the control requirements for DS have been outlined for wind turbines based on an in-depth analysis of the process. Three passive control methodologies have been investigated for dynamic stall control: (1) streamwise vortices generated using vortex generators (VGs), (2) spanwise vortices generated using a novel concept of an elevated wire (EW), and (3) a cavity to act as a reservoir for the reverse flow accumulation. The methods were observed to delay the onset of DS by several degrees as well as reduce the increased lift and drag forces that are associated with the DSV. However, only the VG and the EW were observed to improve the post-stall characteristics of the airfoil.     

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.     

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.     

Load control on a dynamically pitching finite span wind turbine blade using synthetic jets

The feasibility of active flow control, via arrays of synthetic jet actuators, to mitigate hysteresis was investigated experimentally on a dynamically pitching finite span S809 blade. In the present work, a six‐component load cell was used to measure the unsteady lift, drag and pitching moment. Stereoscopic Particle Image Velocimetry (SPIV) measurements were also performed to understand the effects of synthetic jets on flow separation during dynamic pitch and to correlate these effects with the forces and moment measurements. It was shown that active flow control could significantly reduce the hysteresis in lift, drag and pitching moment coefficients during dynamic pitching conditions. This effect was further enhanced when the synthetic jets were pulsed modulated. Furthermore, additional reduction in the unsteady load oscillations can be observed in post‐stall conditions during dynamic motions. This reduction in the unsteady aerodynamic loading can potentially lead to prolonged life of wind turbine blades. Copyright © 2014 John Wiley & Sons, Ltd.     

A simple frequency‐domain method for stress analysis of stall‐regulated wind turbines

A simple method, based in the frequency domain, was developed for calculating the dynamic response of a stall‐regulated wind turbine. Emphasis is placed on two aspects of the method, which are necessary in order to obtain a reasonable linearization of behavior when the blades are stalled. First, the tangential (in‐plane) component of turbulence is included, in addition to the axial component. Second, the linearized relationship between lift coefficient and angle‐of‐attack is adjusted to account for the effects of dynamic stall: separate linearizations are used for excitation and damping of vibration. A thorough comparison is made between linear and non‐linear dynamic‐stall methods, with the conclusion that the accuracy of the linear method depends upon the frequency and amplitude of oscillation. The linear dynamic‐stall method is accurate at blade vibrational frequencies, but it can be inaccurate at frequencies in the vicinity of 1P or below, when the angle‐of‐attack oscillates with an amplitude of 3° or more. Load spectra of a Nordtank 500 turbine, calculated using the frequency‐domain method, are compared with measurements. The frequency‐domain method provides estimates of load spectra and aerodynamic damping (stability) that are useful for preliminary design and optimization, but the method lacks sufficient accuracy and generality to be used for certification. Copyright © 2011 John Wiley & Sons, Ltd.