A nonlinear wake model of a wind turbine considering the yaw wake steering

Duo to fluctuations in atmospheric turbulence and yaw control strategies,wind turbines are often in a yaw state.To predict the far wake velocity field of wind turbines quickly and accurately,a wake velocity model was derived based on the method of momentum conservation considering the wake steering of the wind turbine under yaw conditions.To consider the shear effect of the vertical incoming wind direction,a two-dimensional Gaussian distribution function was introduced to model the velocity loss at different axial positions in the far wake region based on the assumption of nonlinear wake expansion.This work also developed a“prediction-correction”method to solve the wake velocity field,and the accuracy of the model results was verified in wake experiments on the Garrad Hassan wind turbine.Moreover,a 33-kW two-blade horizontal axis wind turbine was simulated using this method,and the results were compared with the classical wake model under the same parameters and the computational fluid dynamics(CFD)simulation results.The results show that the nonlinear wake model well reflected the influence of incoming flow shear and yaw wake steering in the wake velocity field.Finally,computation of the wake flow for the Horns Rev offshore wind farm with 80 wind turbines showed an error within 8%compared to the experimental values.The established wake model is less computationally intensive than other methods,has a faster calculation speed,and can be used for engineering calculations of the wake velocity in the far wakefield of wind turbines.

A modified wake model in bubble-induced three-phase inverse fluidized bed(BIFB)

A modified wake model was proposed for the newly developed bubble-induced three-phase inverse fluidized bed(BIFB),by combining the generalized wake model and the gas-perturbed liquid model.On the basis of the modified wake model,the solids and liquid holdups and the complete fluidization gas velocity in BIFB system have been successfully predicted with two established correlations.The predictions achieved very good agreements with the experimental data.

A Novel Wake Oscillator Model for Vortex-Induced Vibrations Prediction of A Cylinder Considering the Influence of Reynolds Number

It is well known that the Reynolds number has a significant effect on the vortex-induced vibrations(VIV) of cylinders. In this paper, a novel in-line(IL) and cross-flow(CF) coupling VIV prediction model for circular cylinders has been proposed, in which the influence of the Reynolds number was comprehensively considered. The Strouhal number linked with the vortex shedding frequency was calculated through a function of the Reynolds number. The coefficient of the mean drag force was fitted as a new piecewise function of the Reynolds number, and its amplification resulted from the CF VIV was also taken into account. The oscillating drag and lift forces were modelled with classical van der Pol wake oscillators and their empirical parameters were determined based on the lock-in boundaries and the peak-amplitude formulas. A new peak-amplitude formula for the IL VIV was developed under the resonance condition with respect to the mass-damping ratio and the Reynolds number. When compared with the results from the experiments and some other prediction models, the present model could give good estimations on the vibration amplitudes and frequencies of the VIV both for elastically-mounted rigid and long flexible cylinders. The present model considering the influence of the Reynolds number could generally provide better results than that neglecting the effect of the Reynolds number.

A nonlinear model for aerodynamic configuration of wake behind horizontal-axis wind turbine

Determination of the aerodynamic configuration of wake is the key to analysis and evaluation of the rotor aerodynamic characteristics of a horizontal-axis wind turbine. According to the aerodynamic configuration, the real magnitude and direction of the onflow velocity at the rotor blade can be determined, and subsequently, the aerodynamic force on the rotor can be determined. The commonly employed wake aerodynamic models are of the cylindrical form instead of the actual expanding one. This is because the influence of the radial component of the induced velocity on the wake configuration is neglected. Therefore, this model should be called a "linear model". Using this model means that the induced velocities at the rotor blades and aerodynamic loads on them would be inexact. An approximately accurate approach is proposed in this paper to determine the so-called "nonlinear" wake aerodynamic configuration by means of the potential theory, where the influence of all three coordinate components of the induced velocity on wake aerodynamic configuration is taken into account to obtain a kind of expanding wake that approximately looks like an actual one. First, the rotor aerodynamic model composed of axial (central), bound, and trailing vortexes is established with the help of the finite aspect wing theory. Then, the Biot-Savart formula for the potential flow theory is used to derive a set of integral equations to evaluate the three components of the induced velocity at any point within the wake. The numerical solution to the integral equations is found, and the loci of all elementary trailing vortex filaments behind the rotor are determined thereafter. Finally, to formulate an actual wind turbine rotor, using the nonlinear wake model, the induced velocity everywhere in the wake, especially that at the rotor blade, is obtained in the case of various tip speed ratios and compared with the wake boundary in a neutral atmospheric boundary layer. Hereby, some useful and referential conclusions are offered for the aerodynamic computation and design of the rotor of the horizontal-axis wind turbine.

Wake Numerical Simulation of Wind Field Based on Two Modified Wind Engineering Models

With the assumption of the Park model that the wake region is in linear expansion and the cross-wind is in multinomial and Gaussian distribution in wake region,one develops the Park-polynomial model and the ParkGaussian model to numerically simulate the wake flow field for a single wind turbine.Compared with the measured data of wind farm and the wind tunnel test,it shows that the prediction precision of wake field has been improved obviously under the modified initial wake radius.Moreover,both of the newly modified two models could well simulate the wind velocity in wake region,because the predicted results is approximately consistent with the test result,and the cross-wind distribution conforms to that of the real flow field.The two models have still inherited many advantages of engineering models,such as simple form,easy-to-code,and high computational efficiency.Particularly,the Park-Gaussian model is the best in overall performance among them.

Nonlinear tight formation control of multiple UAVs based on model predictive control

A tight formation of unmanned aerial vehicles(UAVs) has many advantages, such as fuel saving and deceiving enemy radar during battlefield entry. As a result, research on UAVs in close formation has received much attention, and the controller design for formation holding has become a popular research topic in the control field. However, there are many unknown disturbances in tight formation, and the tail aircraft is disturbed by the wake. This paper establishes a mathematical model of wake vortices for tail aircraft that considers uncertainty and strong interference. Two UAVs are simulated by Computational Fluid Dynamics software, followed by the design of a semiphysical simulation model predictive control(MPC) scheme that suppresses uncertainty and interference sufficiently to enable the tail aircraft to accurately track the lead aircraft and maintain a stable, tight formation. The tight formation controller is verified by numerical simulation and semiphysical simulation. The results show that the designed controller has an excellent control effect in the case of disturbance caused by the wake vortex.

On the Wake Flow Interaction between Model Turbines with Varying Streamwise Distance

Wind tunnel measurements using particle image velocimetry have been performed around two perforated discs, with varying streamwise distance, in order to simulate the wake interaction between wind turbines. The static pressure footprint (p-f) on ground level associated with the wake behind the disc and wake velocity data for both the streamwise and wall-normal velocity components with the corresponding turbulence intensities are reported. The p-f method shows that the size of the wake regions, behind the wind turbine models, initially drop when a second disc is placed just downstream of the first one. From a mutual distance (Δ χ) of about five disc diameters (5D), both wake footprints increase as the mutual distance is increased, and for very large mutual distances, approximately Δ χ/ D > 15, the footprint of the downstream disc has recovered and is about the same as for a single disc. At last we conclude that despite very different inlet conditions to the discs, with about 50% of reduced velocity on the centre line upstream of the second disc and an increase of the maximum streamwise fluctuations by 90%, the mean velocities in the wake are proven to scale with the hub height velocity.

A Non-geometrically Similar Model for Predicting the Wake Field of Full-scale Ships

规模效果导致在模型规模和实际轮船的 wake 地之间的大差异，并且在在预言实际轮船的表演的成穴性能和令人激动的力量测试引起差别。因此，从轮船模型的测试数据是什么时候，直接使用了预言实际轮船的表演，测试结果必须受到实验修正。这研究为壳模型的反向的设计建议一个方法。比作一个几何上类似的壳模型，修改模型产生的 wake 地接近一艘实际轮船的。一非 -- 轮船和海洋工程(KRISO ) s 容器轮船(KCS ) 的一个朝鲜研究院的几何上类似的模型被设计。数字模拟用这个模型被执行，并且它的结果与照原尺寸的计算结果相比。由非几何上类似的模型得到照原尺寸的轮船的 wake 领域的变丑方法成功地被用于 KCS。

基于尾流振子模型的柔性悬挂立管涡激振动分析

为了分析深海采矿柔性立管涡激振动响应特性,提出了一种高效的针对特殊边界的处理方法.基于欧拉梁模型和尾流振子模型,结合有限差分方法,系统研究不同边界条件、中间仓质量和海流剪切参数对深海采矿立管涡激振动的影响规律.结果表明:悬挂立管底部会产生较大位移,与传统两端铰接立管相比,相同激励下悬挂立管会激发出更高阶的振动模态,从原本5阶模态升至6阶;随着中间仓质量增加,立管振动的主导模态会随之降低,在同一模态下,悬挂立管底部位移逐渐减小,从0.460降至0.405,当模态转换时,底部位移均方根会迅速增大,由0.405升至0.413;底部位移随着均匀流速的增加呈现出波动趋势,在一定流速范围内,位移随流速线性变化;随着剪切参数增大,在同一模态下,立管底部的位移逐渐减小,当模态转换时,底部位移会增加.

基于POD和DMD的60°交叉管绕流分析

本文利用本征正交分解(Proper Orthogonal Decomposition,POD)和动力学模态分解(Dynamic Mode Decom⁃position,DMD)分析雷诺数Re=200时三维60°交叉管在间隙比G=4下的涡量数据,并探究尾涡的演变规律。分析结果表明:尾流场中的涡流尺度及重要程度随频率增加而减小,少数低频模态便可主导大尺度流动现象,而高频模态主要丰富尾流场中的小尺度湍流细节;上下游圆柱的涡结构以0.19 Hz的频率从两圆柱脱落,并在相同的频率下以平行形态向下游演变;上游圆柱脱落涡与下游圆柱的相互作用导致下游圆柱涡激振动明显,并产生多个高频升力频谱峰值。

考虑迟延的风电场模型预测尾流优化控制

降低风电场出力波动性有利于促进电网友好运行,而尾流优化控制是降低整场出力波动的重要措施。现有尾流优化控制大都基于稳态模型,却忽略尾流动态迟延特性。但尾流迟延在风速不确定性基础上会进一步增加风电场出力的波动性。为此,该文基于稳态尾流模型辅以迟延计算,构建风电场准稳态尾流模型以同时兼顾尾流干涉作用与动态迟延特性。在此基础上,提出一种考虑迟延的模型预测平稳控制方法(predictive control considering delay,MPC-D),以指令跟踪与功率波动最小为目标协调各机组出力。最后,在WFSim上构建含33台机组的风电场仿真模型,并基于此分析尾流迟延对风电机组以及整场运行性能影响。结果表明,所建准稳态尾流模型能同时模拟尾流速度损失、机组功率迟延和整场功率阶梯变化等特性。并且由MPC-D所得整场出力较基于稳态模型的控制方法平均相对误差、均方根误差以及滑动均方根误差均得到改善,同时能防止机组桨距角频繁动作。

基于鲸鱼优化算法的串列风力机主动尾流控制策略

主动尾流控制技术通过协调风电场中每台风力机的运行状态,降低上游机组尾流对下游机组的负面影响,进而提高整场发电功率。为探究尾流控制的规律,以10台串列排布的风力机为研究对象,采用Jensen尾流模型与平方和叠加模型计算尾流速度分布,通过鲸鱼优化算法(whale optimization algorithm,WOA)优化风力机的轴向诱导因子分布,并与粒子群优化算法(particle swarm optimization algorithm,PSO)对比。研究结果显示:WOA优化效果更好,收敛速度更快,使风电场输出功率提高了5.63%~42.76%;轴向诱导因子的分布规律和风电场输出功率的优化效果受入流风速影响较小,受风力机的数量及流向间距影响较大。

基于三次修正Jensen尾流模型的海上风电场布局优化

目前修正的Jensen尾流模型均没有同时修正尾流初始半径和尾流初始风速,无法准确预测海上风电场的实际尾流风速。基于二次修正Jensen尾流模型基础上,提出三次修正Jensen尾流模型,并通过海上风电场风洞实验数据验证该修正尾流模型的正确性。其次,考虑全尾流及部分尾流面积,将该三次修正Jensen尾流模型应用到海上风电场的布局优化中,以风力机的坐标及数量为优化变量,以度电成本为优化目标函数,并利用樽海鞘算法对海上风电场的风力机布局进行优化设计。优化结果表明:对比采用改进Jensen模型指导风电场布局,采用三次修正Jensen模型时,风电场的布局更加均匀;对比考虑全尾流的布局,当考虑部分尾流布局时,度电成本降低了2.16%。

浅海高压立管涡激振动及疲劳特性分析工艺

随着东海油气资源的不断开发,开发成本较低的自升式平台将得到广泛应用。立管所在海洋环境复杂多变,其结构长度与直径比值较大,在海流作用下会发生涡激振动。采用尾流振子模型对高压立管涡激振动响应进行预报,并基于DNV规范,根据S-N曲线法对结构疲劳进行计算。模型通过有限差分法进行离散求解。研究重点关注顶张力对立管的涡激振动及疲劳特性影响。结果表明,顶张力会影响立管的涡激振动响应,并进一步改变结构的疲劳寿命,影响结构安全性。

基于OrcaFlex的钢悬链立管疲劳损伤预报

涡激振动是钢悬链立管疲劳损伤的重要诱导因素之一,因此涡激振动分析在钢悬链立管设计中占据重要地位。OrcaFlex在海洋工程领域功能强大、应用广泛,能够提供两种涡激振动疲劳损伤预报方法,分别是基于模态叠加法的频域预报方法和基于Iwan-Blevins尾流振子模型的时域预报方法。OrcaFlex的涡激振动时域预报模型只考虑了横流向涡激振动造成的疲劳损伤,基于OrcaFlex的时域预报方法开发了双自由度涡激振动尾流振子模型的接口,考虑了浮式平台运动对钢悬链立管的涡激振动激励作用,实现了钢悬链立管双自由度涡激振动疲劳损伤预报。

基于二维代理模型的风力机尾流计算和风电场布局优化

针对现有风力机尾流采用计算流体力学方法(CFD)进行数值模拟遇到的网格数量多、计算资源需求大的问题,提出采用二维代理模型的风力机尾流数值模拟方法,并将此代理模型运用于风电场的布局优化中。首先对单台风力机的尾流进行数值模拟研究,并根据现场实测数据对模拟结果进行检验;其次将代理模型运用于多台风力机的风电场模拟中,分析风力机在不同来流风向角下尾流效应情况。最后结合风速风向玫瑰图计算多台等距矩形布置的风电场的年发电量,分析风电场与N(北)方向的夹角与风电场年发电量的关系。仿真表明:现场实测数据和模拟数据相关程度高且误差较小,验证了二维代理模型的可行性和计算结果的准确性。风电场与N(北)方向的夹角在0°~40°范围内时,夹角大于0°时的风电场年发电量均大于夹角等于0°时的年发电量;风电场布局优化时选择合适的风电场与N(北)方向的夹角有利于提高风电场的年发电量,提高经济效益。

考虑大气稳定度的风电场等效粗糙度模型研究

目前模型未充分考虑大气稳定度的影响,针对该问题,在不同大气稳定度下,通过建立风电场边界层的动量平衡关系和揭示风电场的流动不均匀性,提出一种适用于不同大气稳定度的风电场等效粗糙度模型。采用大涡模拟方法对所提模型进行验证,结果显示该方法能有效评估大气稳定度对风电场流动不均匀性以及等效粗糙度的影响,所得等效粗糙度平均误差约10%。

风力机组尾流模型适用性评价

[目的]风力机组的尾流效应是风电场能量损失的重要因素,研究机组尾流有利于优化机组排布,提升风电场的经济性。[方法]分别对8种常见尾流模型的尾流风速衰减、湍流强度预测情况进行对比研究。为确保评估的合理性,基于风场测量数据及风洞实验数据进行定量分析,对比数据范围限定于风机下游距离3倍到10倍风轮直径。[结果]分析结果表明:对于尾流风速预估,二维模型较一维模型与实际尾流风速分布结构更契合,其中Jensen-Guass有着更好的尾流宽度预测,而2D-k-Jensen尾流中心风速预测精度更高且多工况适应性更强,最大平均偏差及偏差标准差分别为8.7%、5.5%,均适用于机组尾流风速预估。一维模型中的Jensen模型尾流中心风速预估能力虽最好,部分工况平均偏差低于10%,但Park模型在尾流风速水平分布预测上表现更佳,案例2中预测性能与二维模型相当,各工况平均偏差均低于10%,较前者更适合尾流速度预测。对于湍流强度的预测,Ishihara模型在湍流结构的预测展现出明显优势,平均偏差均低于10%,但尾流中心处湍流强度预测结果较差,不利于下游机组位置处湍流强度的预测,其余模型中Frandsen、Jensen-Guass在低环境湍流强度工况的预测相对较好,但高环境湍流强度下两者存在相反趋势,Frandsen模型预测精度更高,适合机组湍流强度预估,而Jensen-Guass的预估结果远大于实验值,预测结果较不稳定。高上游风速下各模型尾流风速预估精度均有较大的提升,环境湍流强度的提高对模型尾流风速和湍流强度预估精度有一定的促进作用,Jensen-Guass模型除外。[结论]Jensen-Guass和2D-k-Jensen模型尾流风速预测值与实测数据吻合较好,Frandsen模型湍流强度预测性能更佳,可作为海上风场机位排布优化及尾流控制分析的参考尾流模型。