中国科学院力学研究所机构知识库

鉴于风能的能量密度相对较低，通常需要将多台风力机布置成风电场，以充分利用环境中的风资源。而上游风力机的尾迹会导致下游风力机发电功率的下降和结构载荷的增加。近年来，随着风力机尺寸和轮毂高度的不断增加，风力机尾迹与大气边界层(Atmospheric Boundary Layer, ABL) 中复杂流动的相互作用变得更加显著。此外，风力机远尾迹整体的低频大尺度振荡，即尾迹蜿蜒，会进一步增加下游风力机的结构载荷，且尾迹蜿蜒也会与ABL 中的复杂流动相互作用，导致更复杂的尾迹现象。目前关于尾迹蜿蜒的机制有两种主流观点：一种观点认为来流中的大涡是远尾迹蜿蜒的主要因素，另一种观点认为叶片带来的剪切层失稳也可诱导尾迹蜿蜒。由于具有不同载荷分布的叶片设计会产生不同的剪切层效应，因此，对于不同设计风力机尾迹机理的研究具有重要意义。结合了叶片参数化模型的大涡模拟(Large Eddy Simulation, LES) 方法是目前实尺寸风力机尾迹机理数值研究中最常用的方法。常用的叶片参数化模型包括致动盘(Actuator Disk, AD)、致动线(Actuator Line, AL) 和致动面(Actuator Surface, AS) 模型。其中，AD 模型计算快，常用于风电场模拟；而AL 和AS 模型计算慢，但对尾迹的预测更好，常用于尾迹机理研究。

然而，目前的叶片气动设计多以提高其自身性能为目标，并未考虑叶片设计对于尾迹的影响。因此，本文结合了叶素动量理论(Blade Element Momentum, BEM) 和多维牛顿迭代法，发展了基于给定载荷分布的风力机叶片逆向设计方法；并采用LES+AS 的方法，研究了不同叶片设计对尾迹的影响机理；随后，系统评估了AD 模型对不同叶片设计尾迹的预测能力，为风电场的模拟提供理论支撑；最后，采用LES+AD 的方法，研究了风电场尾迹。

本文的主要创新性工作包括以下四个部分：

(一) 发展了给定载荷分布的风力机叶片逆向设计方法
该部分工作结合了BEM 方法和多维牛顿迭代法，发展了基于指定载荷分布的风力机叶片逆向设计方法。并基于NREL 5 MW 风力机，逆向设计了四种具有不同载荷分布的新叶片设计，即：(i) Root-CP、(ii) Tip-CP、(iii) Root-CT 和(iv) Tip-CT 设计，分别为靠近叶根和叶尖区域具有较高载荷的叶片设计。且如名字的右半部分所示，不同叶片设计具有相同的功率系数(𝐶𝑃 ) 或推力系数(𝐶𝑇 )。最后，在不同叶尖速比(Tip Speed Ratio, TSR) 下，研究了不同设计的空气动力学特性，发现了Root-CP 和Root-CT 设计具有更好的抗载荷效应，且在TSR 大于9时具有更高的功率系数。

(二) 研究了叶片设计对风力机尾迹的影响机理
该部分内容采用LES+AS 的方法，在三种不同地面粗糙度(𝑘0 = 0.001 米、𝑘0 = 0.01 米和𝑘0 = 0.1 米) 湍流来流下，研究了三种叶片设计对尾迹的影响机理。这三种设计为：(i) NREL-Ori 设计(美国NREL 实验室设计的海上5 MW 风 力机)、(ii) NREL-Root 设计和(iii) NREL-Tip 设计，其中，后两者设计是采用上述逆向设计方法新设计的，它们相较于NREL-Ori 设计分别在靠近叶根和叶尖处具有较高的载荷，且这三种设计的推力系数相同。研究结果表明，在近尾迹处NREL-Root 设计的中心涡最强，向外扩展最大，而其叶尖涡最弱。在近尾迹处，NREL-Tip 设计的速度亏损最小，湍动能最大，表明其近尾迹恢

复最快；虽然在近尾迹处NREL-Root 设计的速度亏损最大，但在远尾迹处(12𝐷)，其速度亏损最小，表明其远尾迹恢复最快。随后的平均动能(Mean Kinetic Energy, MKE) 预算方程分析表明，NREL-Tip/NREL-Root 设计近/远尾迹恢复快的主要原因是其近/远尾迹处的湍动能输运(Turbulent Convection, TC) 项更大。接着，对于瞬时尾迹中心位置的统计学分析显示，NREL-Root 设计尾迹的展向扩展最大，且尾迹蜿蜒幅度最大，这表明NREL-Root 设计的尾迹蜿蜒更剧烈。最后，我们将不同设计尾迹蜿蜒的频率进行分解和重构并结合预乘谱的结果，揭示了在叶根处具有更高载荷的NREL-Root 设计的剪切层不稳定性更强，进而诱导其尾迹蜿蜒出现的更早且更剧烈。

(三) 评估了致动盘模型对不同叶片设计尾迹的预测能力
该部分内容基于LES+AS 的结果，系统评估了有无旋转力的两种AD 模型(AD-R 和AD-NR 模型分别对应有无旋转力的两种AD 模型)，对三种叶片设计尾迹的预测能力。这三种设计为：EOLOS (EOLOS 2.5 MW 风力机)、NREL (NREL 5 MW 风力机) 和NREL-V 设计(采用逆向设计方法基于NREL 5 MW 风力机的一个新设计)。这三种设计具有两类不同的载荷分布，即NREL 设计的轴向力系数沿着径向分布较为均匀，而另外两种设计的轴向力系数在叶根处较大，叶尖处较小。结果表明，对于不同的设计，两种AD 模型均能很好的预测速度亏损，但AD-R 模型对于湍动能的预测效果更好；且两种AD 模型对于载荷分布较均匀的NREL 设计的尾迹预测结果较另外两种设计更好。进一步的本征正交分解(Proper Orthogonal Decomposition, POD) 研究表明，由于不同设计的尾迹具有不同的失稳机理，AD 模型对不同设计具有不同预测能力。具体而言，NREL 设计的叶尖涡出现的更早，尾迹动力学特性主要受叶尖剪切层不稳定性的影响；而另外两种设计的中心涡更强，尾迹动力学特性受中心涡的影响更大。

(四) 研究了风电场尾迹的发展和恢复
该部分研究基于LES+AD 的数值结果，对由40 台实尺寸风力机组成的风电场(4 排×10 列) 的尾迹进行了研究。结果表明，由于风电场内部尾迹的相互作用，风电场尾迹在展向存在明显的不均匀性；直到风电场最末排风力机下游55𝐷(5.5 千米) 处，速度才恢复至未受扰动来流风速的95%；且风电场尾迹的影响在下游持续存在，甚至在最末排风力机下游165𝐷 (16.5 千米) 处，速度亏损仍清晰可见，这表明风电场尾迹持续时间长，影响范围广。

Considering the relatively low energy density of wind energy, it is typically necessary to arrange multiple turbines in a wind farm to fully utilize the wind energy resources in the environment. However, the presence of turbine wakes leads to a reduction in the power generation capacity of downstream turbines while increasing structural loads on the downstream turbines. Recently as turbine scales continue to increase, the interaction between wind turbine wakes and the complex flow within the ABL becomes increasingly significant. In addition, The low-frequency, large-scale meandering motion of turbine wakes, known as wake meandering, further significantly increase the fatigue loads on downstream turbines.

Currently, there are two main viewpoints regarding the mechanisms of wake meandering. One perspective suggests that large eddies in the inflow are the primary cause of far wake meandering, while another viewpoint argues that the instability introduced by the shear layer instability from the turbine blades can also induce wake meandering. Therefore, conducting an in-depth investigation into the wake meandering mechanisms of different blade designs is of significant theoretical and practical importance.

Currently, large eddy simulation (LES) combined with blade parameterization models is the most commonly used approach in the study of utility-scale wind turbine wake dynamics. The actuator disk (AD), actuator line (AL), and actuator surface (AS) model are the most common blade parameterization models. Among them, the AD model is computationally efficient and is the most commonly used in wind farm simulations; the AL and AS models are computationally more expensive but offer better predictive capabilities for wind turbine wakes, making them suitable for the study of wake dynamics in single or multiple turbine simulations.

However, current aerodynamic blade design methods primarily focus on improving their individual performance without considering the impact of blade design on the wake. Therefore, to investigate the influence of blade design on the wake, an inverse design method is developed in the present work by combining the blade element momentum (BEM) theory and the multi-dimensional Newton method. Subsequently, utilizing the LES+AS approach, the wake mechanisms of three different utility-scale blade designs are investigated. Furthermore, based on the results of LES+AS, the predictive capability of two AD models are systematically evaluated. Finally, employing the LES+AD method, the recovery and development of the wind farm wakes are investigated.

This paper’s primary innovative contributions are comprised of four main aspects:

1. Development of a wind turbine blade inverse design method In this part, a wind turbine blade inverse design method based on a specified load distribution is developed by combining the BEM method and a multi-dimensional Newton iteration method. Based on the NREL 5 MW wind turbine, four utility-scale wind turbines with different load distributions are inversely designed, namely: (i) Root-CP, (ii) Tip-CP, (iii) Root-CT, and (iv) Tip-CT turbine designs, representing blade designs with higher loads near the blade root and tip regions as indicated by the left part in the name, respectively. Besides, these different design turbines have the same power coefficient (𝐶𝑃 ) or thrust coefficient (𝐶𝑇 ) as indicated by the right part in the name. Subsequently, under different tip-speed ratios (TSR), the aerodynamic performance are compared.

2. Investigation of the impact of blade design on wind turbine wake mechanisms In this part, the LES+AS model is employed to study the wake mechanisms of three different blade designs under three different turbulent inflow (𝑘0 = 0.001 m, 𝑘0 = 0.01 m, and 𝑘0 = 0.1 m). The three blade designs studied are: (i) NREL-Ori design (the 5 MW offshore baseline wind turbine designed by the U.S. National Renewable Energy Laboratory), (ii) NREL-Root design, and (iii) NREL-Tip design. The latter two designs are newly designed by using the inverse design method, and they exhibit higher loads near the blade root and blade tip, respectively, compared to the NREL-Ori design. It’s worth noting that these three blade designs have the same thrust coefficient. In the near-wake region, the hub vortex of the NREL-Root design is the strongest and extends the farthest outward, while its tip vortex is the weakest; The NREL-Tip design exhibits less velocity deficit and higher turbulence kinetic energy, indicating faster recovery of the wake in this region. Although the NREL-Root design has the largest velocity deficit in the near-wake, it has the smallest velocity deficit at the far downstream distance, suggesting faster wake recovery for the NREL-Root design in the far-wake region. Subsequent analysis of the mean kinetic energy (MKE) budget equation indicates that the primary reason for the fast recovery of the NREL-Tip / NREL-Root design in the near-wake / far-wake region is the larger turbulent convection term. Moreover, statistical analysis of the instantaneous wake center positions reveals the stronger wake meandering for the NREL-Root design. Lastly, by decomposing and reconstructing the wake meandering frequencies for different designs and combining the results of the pre-multiplied spectrum analysis, it is revealed that shear layer instability is stronger for the NRELRoot design, which has higher loads near the blade root, leading to earlier onset of and stronger wake meandering.

3. Systematic evaluation of two actuator disk models for predicting wakes of different blade designs In this part, a systematic evaluation of two AD models (AD-R and AD-NR models) for predicting the wake dynamics of wind turbines with three different blade designs is conducted based on results from LES + AS. These three blade designs are the EOLOS 2.5 MW design (EOLOS 2.5 MW turbine), the NREL design (NREL 2.5 MW turbine), and the NREL-V design (a new design of the NREL 5 MW wind turbine) with the axial force coefficient of the NREL 5 MW blade design being relatively uniform along its radial direction, while the other two design have higher values at the blade root and lower values at the blade tip, respectively. The study reveals that both AD models can effectively predict the time-averaged velocity deficit profiles, with the AD-R model showing better predictive performance for turbulence kinetic energy. Furthermore, both AD models provide better predictions for the wake of the NREL 5 MW design, which has a more uniform load distribution, compared to the other two designs. Further analysis using proper orthogonal decomposition (POD) suggests that the tip vortices of the NREL 5 MW design appear earlier, and the wake dynamics are primarily influenced by instability in the tip shear layer. In contrast, the other two designs exhibit stronger hub vortex, with the wake dynamics being more influenced by this hub vortex. These differences in instability mechanisms are the primary reasons for the varying predictive capabilities of the AD models for different blade designs.

4. Investigation of wind farm wake development and recovery In this part, the LES+AD model is used to study the wake dynamics of a wind farm consisting of 40 utility-scale wind turbines (4 rows × 10 columns). The results reveals that the interaction of wakes within the wind farm resulting the significant nonuniform distribution