TIME-FREQUENCY CHARACTERISTICS OF UNSTEADY AERODYNAMIC FORCES FOR FEATHERED WIND TURBINE AIRFOIL UNDER TOWER BLADE INTERACTION
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摘要: 由于风力机叶片与塔筒流场相互干涉, 实际气动力与理想情况存在较大差异, 这种干涉作用造成的气动力差异给叶片与塔筒结构可靠性带来不可忽视的影响. 以翼型DU91-W2-250为研究对象, 采用瞬态数值分析与本征正交分解方法, 考虑叶片和塔筒流场相互干涉作用, 分析顺桨工况翼型非稳气动力时频特性及其影响规律, 量化不同雷诺数下塔叶相对位置及几何参数对气动力均值、波动幅度和频率的影响程度, 通过流场模态能量分布形态分析, 揭示流场干涉对气动力的影响机制. 结果表明, 翼型气动中心至塔筒几何中心的垂直距离、水平距离以及塔筒直径相对于翼型弦长的无量纲参数y*, x*和D*对气动力均有不同程度影响, 其中y*对升阻力系数均值影响最大, 对频率无明显影响, y*绝对值越大, Cl均值越接近单翼型Cl值, y*绝对值越小升阻力系数波动幅度越大, y*从−12增大到12, 升力系数均值最小值为−0.48, 最大值为1.16; x*减小和D*增大, 反向阻力均值增大, 波动幅度增大, 波动频率略有下降, 当x*小于临界值5时, 带塔翼型阻力均值反向; 在计算范围内, 带塔翼型升力系数均值相对于单翼型升力系数最大偏差为−221.94%, 其最大波动幅度相对单翼型升力系数为28.0%, 带塔翼型阻力系数均值最大偏差为−1189.3%, 其最大波动幅度为121.1%; 受塔筒前方高压区影响, 翼型流场存在明显对称脉动激励, 造成气动力偏离和波动.Abstract: Due to the interference between the wind turbine blades and the flow field of the tower, the actual value of the aerodynamic force is quite different from the theoretical value. The difference in aerodynamic force caused by this interference has a non-negligible impact on the reliability of the blade and tower structure. Taking the airfoil DU91-W2-250 as the research object, based on the transient numerical analysis and proper orthogonal decomposition method, considering the interaction between the blade and the tower flow field, the time-frequency characteristics and the influence law of unsteady aerodynamic forces for the feathering airfoil are analyzed, the influence degree of the relative position of the tower blade and the geometric parameters on the mean value of aerodynamic force, the fluctuation range and frequency at different Reynolds numbers are quantified, and the influence mechanism of flow field interference on aerodynamic force are revealed through the analysis of flow field modal energy distribution. Results show that, the vertical and horizontal distances from the aerodynamic center of the airfoil to the geometric center of the tower as well the tower diameter relative to the chord length of the airfoil, which are defined as the dimensionless distance parameters y*, x* and D*, have varying degrees of influence on the aerodynamic force. Among which, y* has the greatest influence on the mean value of lift and drag coefficients, but has no obvious influence on the frequency. The greater the absolute value of y* is, the closer the mean value of Cl is to the Cl value of a single airfoil. The smaller the absolute value of y* is, the greater the fluctuation amplitude of lift and drag coefficients is, and y* increases from −12 to 12, the minimum value of average lift coefficient is −0.48, and the maximum value is 1.16. When x* decreases and D* increases, the mean reverse drag force increases, the fluctuation amplitude increases, and the fluctuation frequency decreases slightly. When x* is less than the critical value 5, the average drag force of the airfoil with tower is reversed. Within the calculation range, compared to the single airfoil, the maximum deviation of the mean value of lift coefficient for the airfoil with tower is −221.94% and its maximum fluctuation is 28.0% of the lift coefficient of single airfoil. While the maximum deviation of the mean drag coefficient of for the airfoil with tower is −1189.3% and its maximum fluctuation is 121.1%. Due to the influence of the high pressure area in front of the tower, the airfoil flow field exhibits obvious symmetrical pulsation excitation, resulting in the deviation and fluctuation of the aerodynamic forces.
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图 4 雷诺数为1 × 106时不同x*下升阻力系数的时程曲线和频谱
Figure 4. Time histories and frequency spectra of Cl and Cd under different x* at Re of 1 × 106
图 5 不同x*下翼型升阻力均值和波动幅度曲线
Figure 5. Mean value and amplitude of Cl and Cd of airfoil under different x*
图 6 不同x*下前4阶压力POD模态云图
Figure 6. The first 4 POD mode of pressure contour under different x*
图 7 雷诺数为1 × 106时不同y*下升阻力系数的时程曲线和频谱
Figure 7. Time histories and frequency spectra of Cl and Cd under different y* at Re of 1 × 106
图 8 不同y*下翼型升阻力均值和波动幅度曲线
Figure 8. Mean value and amplitude of Cl and Cd of airfoil under different y*
图 10 雷诺数为1 × 106时不同D*下升阻力系数的时程曲线和频谱
Figure 10. Time histories and frequency spectra of Cl and Cd under different D* at Re of 1 × 106
图 11 不同D*下翼型升阻力均值和波动幅度曲线
Figure 11. Mean value and amplitude of airfoil of Cl and Cd under different D*
图 12 不同D*下前4阶压力POD模态云图
Figure 12. The first 4 POD mode of pressure contour under different D*
表 1 网格无关性验证
Table 1. Mesh independence verification
Total cells Cl mesh 1 4.92 × 104 1.085 mesh 2 7.12 × 104 1.099 mesh 3 9.71 × 104 1.103 mesh 4 1.26 × 105 1.105 mesh 5 1.61 × 105 1.101 
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表 2 低攻角翼型升阻力系数
Table 2. Cl and Cd in small attack angle
Attack angle/(°) This paper Ref. [27] Relative error Cl 0.14 0.389 0.391 −0.5% 2.18 0.606 0.612 −0.9% 4.21 0.838 0.857 −2.2% Cd 0.14 8.90 × 10−3 9.00 × 10−3 −1.3% 2.18 9.90 × 10−3 1.03 × 10−2 −3.5% 4.21 1.15 × 10−2 1.10 × 10−2 4.0%
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表 3 圆柱流场主要模态动能比
Table 3. Kinetic energy ratio of main POD modes
KE of this paper KE of Ref. [30] Absolutely error mode 1 48.65% 50.13% −1.48% mode 2 48.03% 46.89% 1.14% mode 3 1.11% 1.41% −0.31% mode 4 1.11% 1.40% −0.29% mode 5 0.49% 0.78% −0.29%
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表 4 翼型气动力波动主峰St
Table 4. Main St of force fluctuation for airfoil
x* Re = 1.0 × 106 Re = 2.0 × 106 Re = 3.0 × 106 2 St = 0.15 St = 0.14 St = 0.12 3 St = 0.14 St = 0.13 St = 0.11 4 St = 0.13 St = 0.13 St = 0.11 5 St = 0.13 St = 0.12 St = 0.10 $\infty$ — — —
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表 5 不同D*和Re下的翼型主峰St
Table 5. Airfoil main St under different D* and Re
D* Re = 1 × 106 Re = 2 × 106 Re = 3 × 106 1.50 St = 0.19 St = 0.17 St = 0.14 1.75 St = 0.16 St = 0.14 St = 0.12 2.00 St = 0.14 St = 0.13 St = 0.11 2.25 St = 0.12 St = 0.11 St = 0.09 2.50 St = 0.12 St = 0.10 St = 0.08
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