The near wake of a model horizontal-axis wind turbine at runaway

This paper completes a series which describes measurements within two chord lengths of the blades of a small horizontal-axis wind turbine over a wide range of operating conditions. Prior to the present experiment, the turbine was rebuilt to allow operation at its runaway point, where no power is produced. Runaway can be viewed as the upper limit on wind turbine performance at which thrust and wake expansion are maximised. The measurements, which approximate the mean and fluctuating velocity fields seen by an observer rotating with the blades, were obtained from a stationary X-probe hot-wire anemometer by the technique of phase-locked averaging. It is shown conclusively that there is negative (power-producing) angular momentum extracted from the wake, but a balancing positive angular momentum resides in the tip vortices. The mean velocity through the blades increases significantly with radius, in contrast to the near-constant velocity when the turbine is producing its maximum power. Comparisons with conventional blade calculations suggest that the circulation in the wake is related to the difference between the circumferential components of the lift and drag, rather than the magnitude of the lift as is often assumed. Within the range and accuracy of measurement, the pitch of the tip vortices is constant and proportional to the inverse of the tip speed ratio.     

The starting behaviour of a small horizontal-axis wind turbine

This paper presents selected results taken from an extensive investigation of the starting performance of a small horizontal-axis wind turbine. Starting was observed for blade pitch angles varying between 0 and 35° in 5° increments. At 0°, the angle for maximum power, the turbine’s 5 m diameter blades produce 5 kW at a wind speed of 10 m/s. At this pitch, starting is characterised by a long “idling period” in which the blade’s angular velocity increased only slowly because of the very high angles of attack. As the pitch angle increased, the idling period decreased. At all pitch angles, the measurements of angular velocity are compared with those obtained from a numerical integration of the equation for angular acceleration. The aerodynamic torque was obtained from a quasi-steady blade element analysis and the resistive torque of the drive train and generator was subtracted to determine the net torque accelerating the blades. The agreement between predicted and measured angular velocity was generally good and improved as the pitch angle increased.     

The near wake of a model horizontal-axis wind turbine: Part 3: properties of the tip and hub vortices

This paper concludes a series on the formation and development of the near-wake of a model horizontal-axis wind. The three-dimensional mean velocity and turbulence fields were obtained at six axial locations within two chord lengths of the blades for three operating conditions: stalled flow over the blades, close to optimum performance, and approaching runaway. Here we concentrate on the tip and hub vortices. For the second and third conditions, the hub vortex quickly becomes a sheet of vorticity spread over the cylindrical centrebody. It is suggested that the ‘trailing vorticity’ at the hub is formed by the skewing of the circumferential vorticity in the upstream boundary layer as it encounters the blades, so that the ‘bound’ vorticity of the blades simply passes through the centrebody surface. The tip vortices, which were shown in Part 2 to contain increasing amounts of angular momentum as the tip speed ratio increases, are associated with large variations in all velocity components and high levels of turbulence. The pitch of the helical tip vortices decreases with increasing tip speed ratio.     

相同叶尖速比不同转速的垂直轴风力机气动性能分析

在不考虑连杆、转轴及叶尖损失的简化模型基础上,利用Fluent软件采用雷诺平均Navier-Stokes方程与k-ωSST湍流模型对直叶片垂直轴风力机进行了数值模拟.对比了相同叶尖速比λ=4,叶轮半径r分别为1 m和2 m的垂直轴风力机的气动性能.结果表明,在来流风速V∞和叶尖速比λ相同的情况下,不同半径的垂直轴风力机具有十分相似的翼型表面压力分布,对应位置处的升、阻力系数相差不大.     

Whirl flutter analysis of a horizontal-axis wind turbine with a two-bladed teetering rotor

An investigation to explore the possibility of whirl flutter and to find the effect of pitch-flap coupling (δ₃) on teetering motion of the DOE/NASA Mod-2 wind turbine is presented. The equations of motion are derived for an idealized five-degree-of-freedom mathematical model of a horizontal-axis wind turbine with a two-bladed teetering rotor. The model accounts for the out-of-plane bending motion of each blade, the teetering motion of the rotor, and both the pitching and yawing motions of the rotor support. Results show that the Mod-2 design is free from whirl flutter. Selected results are presented indicating the effect of variations in rotor support damping, rotor support stiffnes, and δ₃ on pitching, yawing, teetering, and blade bending motions.     

风力机叶尖区涡声分析及小翼对其的影响研究

文章对有无V型叶尖小翼的风力机尾迹流场进行了研究,重点对叶尖涡的产生与脱落、叶尖区域声辐射进行了分析。结果表明:风轮尾迹区分为主流区、中心尾迹区及叶尖涡诱导效应区;叶尖涡向下游有序流动,随着轴向距离的增加,叶尖涡向外扩展;声压脉动时均值的最大区域集中在风轮叶尖部位,叶尖区域噪声最大;加装V型小翼可以重整通过叶尖流场的气流,使叶尖涡的产生推迟、脱落提前,总声压级降低;数值模拟无小翼时,所选观测点频谱图中声压级总体处于50~70 dB,加装V型小翼后,频谱图中声压级处于45~65 dB,降低效果较明显。实验得到该点V型小翼风轮总声压级为82 dB,比无小翼风轮减少4 dB;风轮辐射声总声压级随着测点向风轮下游移动逐渐衰减,加装V型小翼后总声压级降低,降幅在1~5 dB。     

An extension of BEM method applied to horizontal-axis wind turbine design

A mathematical model is presented in this work, based on the Blade Element Momentum (BEM) theory for the horizontal-axis wind turbine design, taking into account the influence of the wake on the rotor plane in the general form. This influence is considered when the tip-speed-ratio is small, justifying the development of formulations that predict the effects of the wake on the rotor plane. The proposed mathematical model in this work is an extension of the BEM method, using the Glauert’s model modified for the wind turbine design.     

Stability analysis of the tip vortices of a wind turbine

The aim of the present paper is to obtain a better understanding of the stability properties of wakes generated by wind turbine rotors. To accomplish this, a numerical study on the stability of the tip vortices of the Tjaereborg wind turbine has been carried out. The numerical model is based on large eddy simulations of the Navier–Stokes equations using the actuator line method to generate the wake and the tip vortices. To determine critical frequencies, the flow is disturbed by inserting harmonic perturbations, giving rise to spatially developing instabilities. The results show that the instability is dispersive and that growth arises only for some specific frequencies and type of modes, in agreement with previous instability studies. The result indicates two types of modes; one where oscillations of neighboring vortex spirals are out of phase and one where oscillations in every vortex spiral in phase. The mode with spirals out of phase results in the largest growth with the main extension of the disturbance waves in radial and downstream directions. The out‐of‐phase disturbance leads to vortex pairing once the development leaves the linear stage. The study also provides evidence of a relationship between the turbulence intensity and the length of the near wake. The relationship, however, needs to be calibrated against measurements. Copyright © 2010 John Wiley & Sons, Ltd.     

An analytical expression for the power coefficient of an ideal horizontal-axis wind turbine

The paper shows that an analytical evaluation of the power coefficient C_p for an ideal horizontal-axis wind turbine can be made via an expression giving the direct relationship of C_p and the axial induction factor a. The results obtained agree closely with those obtained numerically from the usual integral expression involving several variables.     

Assessment of optimum tip speed ratio in wind turbines using artificial neural networks

Wind turbine blade design depends on several factors, such as turbine profile used, blade number, power factor, and tip speed ratio. The key to designing a wind turbine is to assess the optimal tip speed ratio (TSR). This will directly affect the power generated and, in turn, the effectiveness of the investment made. TSR is suggested to be taken between 7 and 8 and in practice generally taken as 7 for a 3-blade network-connected wind turbine. However, the optimal TSR is dependent upon the profile type used and the blade number and could fall out of the boundaries suggested. Therefore, it has to be assessed accordingly. In this study, the optimal TSR and the power factor of a wind turbine are predicted using artificial neural networks (ANN) based on the parameters involved for NACA 4415 and LS-1 profile types with 3 and 4 blades. The ANN structure built is found to be more successful than the conventional approach in estimating the TSR and power factor.     

The influence of the wind speed profile on wind turbine performance measurements

To identify the influence of wind shear and turbulence on wind turbine performance, flat terrain wind profiles are analysed up to a height of 160 m. The profiles' shapes are found to extend from no shear to high wind shear, and on many occasions, local maxima within the profiles are also observed. Assuming a certain turbine hub height, the profiles with hub‐height wind speeds between 6 m s^?1 and 8 m s^?1 are normalized at 7 m s^?1 and grouped to a number of mean shear profiles. The energy in the profiles varies considerably for the same hub‐height wind speed. These profiles are then used as input to a Blade Element Momentum model that simulates the Siemens 3.6 MW wind turbine. The analysis is carried out as time series simulations where the electrical power is the primary characterization parameter. The results of the simulations indicate that wind speed measurements at different heights over the swept rotor area would allow the determination of the electrical power as a function of an ‘equivalent wind speed’ where wind shear and turbulence intensity are taken into account. Electrical power is found to correlate significantly better to the equivalent wind speed than to the single point hub‐height wind speed. Copyright © 2008 John Wiley & Sons, Ltd.     

Direct calculation of wind turbine tip loss

The usual method to account for a finite number of blades in blade element calculations of wind turbine performance is through a tip loss factor. Most analyses use the tip loss approximation due to Prandtl which is easily and cheaply calculated but is known to be inaccurate at low tip speed ratio. We develop three methods for the direct calculation of the tip loss. The first is the computationally expensive calculation of the velocities induced by the helicoidal wake which requires the evaluation of infinite sums of products of Bessel functions. The second uses the asymptotic evaluation of those sums by Kawada. The third uses the approximation due to Okulov which avoids the sums altogether. These methods are compared to the tip loss determined independently and exactly for an ideal three-bladed rotor at tip speed ratios between zero and 15. Kawada's asymptotic approximation and Okulov's equations are preferable to the Prandtl factor at all tip speed ratios, with the Okulov equations being generally more accurate. In particular the tip loss factor exceeds unity near the axis of rotation by a large amount at all tip speed ratios, which Prandtl's factor cannot reproduce. Neither the Kawada nor the Okulov equations impose a large computational burden on a blade element program.     

基于额定风速以上的风力机变桨控制研究

变桨控制系统是变速变桨风力发电机组的重要组成部分,它不仅关系到大型MW级风力发电机组的安全运行,而且能控制风力发电机组,使其吸收更多的风能。文章基于2.0 MW变速变桨风力发电系统,采用PI控制策略,提出了增益调度控制算法,计算了PI增益随风速变化而变化的数值。通过调用线性化结果文件,设计了风力发电机组控制器回路,得出了满意的响应结果。最后基于GL规范,在湍流风的情况下对关键零部件是否加控制策略所得到的载荷进行了对比,结果显示关键零部件的载荷有显著降低,满足控制策略设计的要求。     

An experimental study on the effects of winglets on the tip vortex interaction in the near wake of a model wind turbine

An experimental study of the near wake up to four rotor diameters behind a model wind turbine rotor with two different wing tip configurations is performed. A straight‐cut wing tip and a downstream‐facing winglet shape are compared on the same two‐bladed rotor operated at its design tip speed ratio. Phase‐averaged measurements of the velocity vector are synchronized with the rotor position, visualizing the downstream location of tip vortex interaction for the two blade tip configurations. The mean streamwise velocity is found not to be strongly affected by the presence of winglet tip extensions, suggesting an insignificant effect of winglets on the time‐averaged inflow conditions of a possible downstream wind turbine. An analysis of the phase‐averaged vorticity, however, reveals a significantly earlier tip vortex interaction and breakup for the wingletted rotor. In contradistinction, the tip vortices formed behind the reference configuration are assessed to be more stable and start merging into larger turbulent structures significantly further downstream. These results indicate that an optimized winglet design can not only contribute to a higher energy extraction in a rotor's tip region but also can positively affect the wake's mean kinetic energy recovery by stimulating a faster tip vortex interaction.     

A sensorless control for a variable speed wind turbine operating at partial load

This paper presents a sensorless control for a variable speed wind turbine (WT) operating at partial load in order to eliminate the direct measurement of the wind speed. In this proposal, the estimated aerodynamic torque is used to determine the optimal reference of the speed control for maximum energy conversion. The maximization of the efficiency on energy conversion and the minimization of detrimental dynamical loads are control trade-offs considered in the design of an optimal discrete-time feedback LQG/LTR controller for the Wind Energy Conversion System (WECS), which is based on the optimization of a quadratic cost function. The performance of the proposed control when the WT is submitted to a gust or step variation on wind speed is evaluated from computational simulations. It is also presented some proposals for sensorless control of the electrical generator.     

低风速离网型风力发电机的叶片设计

根据内蒙古四子王旗某地2007年逐月平均风速表选取设计风速为6 m/s,根据某型号300 W交流永磁发电机的输出功率特性,利用Matlab编写的叶片优化设计程序,设计了300 W水平轴风力发电机叶片.通过风轮与发电机的匹配,调整叶片参数,使之在小风时具有较高的风能利用系数,提高风力机的效率,在大风时具有较低的风能利用系数,从而达到大风时限速保护的目的.     

Detection of faulty high speed wind turbine bearing using signal intensity estimator technique

Bearings are typically used in wind turbines to support shafts and gears that increase rotational speed from a low speed rotor to a higher speed electrical generator. For various bearing applications, condition monitoring using vibration measurements has remained a subject of intense study to the present day since several decades. Various signal processing techniques are used to analyse vibration signals and extract features related to defects. Statistical indicators such as Crest Factor (CF) and Kurtosis (KU) were reported as very sensitive indicators when the presence of the defects is pronounced, whilst their values may come down to the level of undamaged components when the damage is well advanced. Further, these indicators were applied to an acquired data from proposed diagnostic models, test rigs, and instrumentations that were specifically used for particular research tests, and thus, it is essential to undertake further investigations and analysis to assess the influence of other factors such as the structural noise and other operating conditions on the real‐world applications. With this in mind, the present work proposes Signal Intensity Estimator (SIE) as a new technique to discriminate individual types of early natural damage in real‐world wind turbine bearings. Comparative results between SIE and conventional indicators such as KU and CF are also presented. It was concluded that SIE has an advantage over the other fault indicators if sufficient data are provided.     

切出风速下风力机变桨故障叶片气动特性及准静态结构响应分析

为探究大型水平轴风力机达到切出风速停机后变桨故障叶片的气动特性及准静态结构响应,基于计算流体力学方法对NREL 5 MW风力机变桨故障/成功叶片气动侧状态进行分析,并利用双向弱流固耦合及曲屈分析对典型方位角下变桨故障叶片展开研究。结果显示：切出风速下变桨故障叶片挥舞力矩平均值为变桨成功叶片的13.8倍,且前者的流场尾迹更为明显。此外,180°方位角变桨故障叶片较之0°方位角变桨故障叶片应力及叶尖位移分别减小29.8%和32.7%,一阶屈曲因子增加20.2%。     

变速风力发电机变流器故障诊断方法

大型变距变速风力发电机组状态的监测与故障的诊断是保证机组长期稳定运行和安全发电的关键。文章针对变速风力发电机组中的变流器电路模型非线性强的特点,利用神经网络非线性映射特性,提出了采用基于波形直接分析的BP神经网络故障诊断方法。该方法能动态监视风力发电机变流器并网电路的工作状态,实时在线进行故障诊断和快速分析,确定变流器故障的部位和性质,可缩短风力发电机的故障停机时间。实际运行结果表明,该方法对变速风力发电机组的状态监测与故障诊断是有效的。     

Optimum aerodynamic design for wind turbine blade with a Rankine vortex wake

This paper presents a model to optimize the distribution of chord and twist angle of horizontal axis wind turbine blades, taking into account the influence of the wake, by using a Rankine vortex. This model is applied to both large and small wind turbines, aiming to improve the aerodynamics of the wind rotor, and particularly useful for the case of wind turbines operating at low tip-speed ratios. The proposed optimization is based on maximizing the power coefficient, coupled with the general relationship between the axial induction factor in the rotor plane and in the wake. The results show an increase in the chord and a slightly decrease in the twist angle distributions as compared to other classical optimization methods, resulting in an improved aerodynamic shape of the blade. An evaluation of the efficiency of wind rotors designed with the proposed model is developed and compared other optimization models in the literature, showing an improvement in the power coefficient of the wind turbine.