﻿ 大型风电长叶片气动外形的高效低载三维设计
 上海理工大学学报  2023, Vol. 45 Issue (6): 584-590 PDF

High efficiency and low load three-dimensional design of the aerodynamic shape of long blades in large wind turbine blade
YAO Yechen, HUANG Diangui
School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: Large-scale wind power equipment such as offshore wind turbines have long blades, which bear a large aerodynamic load and are prone to deformation, which affects aerodynamic performance and operational stability. In response to this problem, the 5 MW large-scale wind turbine blade of the NREL laboratory in the United States of America was taken as an example. A three-dimensional optimization of high efficiency and low load was carried out with the airfoil profile of each section, the installation angle and the pitch angle at rated power as the design variables. The maximum wind energy utilization rate and the minimum blade root bending moment were taken as the optimization goals. The optimization design based on the blade element momentum theory and the multi-island genetic algorithm, and the aerodynamic performance of the optimized blade under variable pitch and variable wind conditions was compared with the original blade. The optimization results showed that, compared with the original blade, under the design conditions, the optimized blade reduced the root bending moment by 5% while ensuring high aerodynamic efficiency. Under variable wind conditions, the wind energy utilization rate of the optimized blades before the pitch change was increased by an average of 1%, and the root bending moment of the blade was reduced by an average of 5.8%. After the pitching, the blade root bending moment of the optimized blade was reduced by an average of 4%.
Key words: wind turbine blade     airfoil optimization     aerodynamic efficiency     aerodynamic load     genetic algorithm

1 优化方法及验证 1.1 气动性能计算方法

Xfoil气动分析程序采用无黏的线性涡面元法，通过使用以层流线性稳定理论为基础的eN函数控制法来准确识别流动转捩。由Xfoil气动分析计算所得的风力机翼型升阻力数据与实验结果较为符合[8]，具有一定的可靠性，因此，本文以其作为气动参数计算的方法。

 $\left\{ \begin{gathered} {V_a} = {v_0}(1 - a) \\ {V_b} = wr(1 + b) \\ \end{gathered} \right.$ (1)
 ${V_{{\text{rel}}}} = \sqrt {{v_0^2}{{(1 - a)}^2} + {w^2}{r^2}{{(1 + b)}^2}}$ (2)
 $\left\{ \begin{array}{*{20}{l}} \alpha = \phi - \theta \\ \phi = \arctan \left[ {\dfrac{{{v_0}(1 - a)}}{{wr(1 + b)}}} \right] \\ \end{array} \right.$ (3)

 图 1 翼型截面的速度三角形与受力 Fig. 1 Force and velocity triangle of the airfoil section

 $\left\{ {\begin{array}{*{20}{l}} {{{\rm{d}}} T = 4{\text{π}}r\rho {v_0}a(1 - a){{\rm{d}}} r = \dfrac{1}{2}Brc{v_0}^2{C_{\text{n}}}{{\rm{d}}} r} \\ {{{\rm{d}}} M = 4{\text{π}}{r^3}\rho {v_0}w(1 - a)b{{\rm{d}}} r = \dfrac{1}{2}Brc{v_0}^2{C_{\text{t}}}r{{\rm{d}}} r} \end{array}} \right.$ (4)
 $\left\{ {\begin{array}{*{20}{l}} {{C_{\text{n}}} = {C_{\text{l}}}\cos\,\phi + {C_{\text{d}}}\sin \,\phi } \\ {{C_{\text{t}}} = {C_{\text{l}}}\sin \,\phi - {C_{\text{d}}}\cos\, \phi } \end{array}} \right.$ (5)
 $F = {F_{\text{t}}}{F_{\text{h}}}$ (6)
 $\left\{ {\begin{array}{*{20}{l}} {{F_{\text{t}}} = \dfrac{2}{{\text{π}}}\arccos ({{\text{e}}^{ - \frac{B}{2}\frac{{R - r}}{{r\sin \,\phi }}}})} \\ {{F_{\text{h}}} = \dfrac{2}{{\text{π}}}\arccos ({{\text{e}}^{ - \frac{B}{2}\frac{{r - {R_{{\text{hub}}}}}}{{{R_{{\text{hub}}}}\sin\, \phi }}}})} \end{array}} \right.$ (7)

 $\left\{ \begin{gathered} a = \dfrac{1}{{\dfrac{{4F{{\sin }^2}\phi }}{{\sigma {C_{\text{n}}}}} + 1}} \\ b = \dfrac{1}{{\dfrac{{4F\sin\, \phi \cos \,\phi }}{{\sigma {C_{\text{t}}}}} + 1}} \\ \end{gathered} \right.$ (8)
 $\sigma = \frac{{Bc}}{{2{\text{π}}r}}$ (9)

 $\left\{ \begin{array}{*{20}{l}} M = \displaystyle\int_0^R {4{\text{π}}\rho \lambda {v_0}^2{r^3}b} (1 - a){{\rm{d}}} r \\ {C_{\text{p}}} = \dfrac{P}{{\dfrac{1}{2}\rho {v_0}^3S}} = \dfrac{{Mw}}{{\dfrac{1}{2}\rho {v_0}^3{\text{π}}{R^2}}} \end{array} \right.$ (10)

 $\left\{ \begin{array}{*{20}{l}} {M_{{i}}} = \displaystyle\int_{{r_i}}^{{r_{i + 1}}} {\dfrac{1}{2}\rho {v_0}^2c{C_{\rm{n}}}(r - {r_0})} {{\rm{d}}} r \\ {M_{\text{t}}} = \displaystyle\sum\limits_{i = 1}^n {{M_{{i}}}} \end{array} \right.$ (11)

1.2 计算方法验证

 图 2 计算结果对比 Fig. 2 Comparison of calculation results
1.3 优化方法

 $y(x) = {y_0}(x) + \sum\limits_{i = 1}^n {{c_i}{f_i}(x)}$ (12)

 ${f}_{i}(x)=\left\{\begin{array}{*{20}{l}} {{x}^{0.25}(1-x){\text{e}}^{-20x},}&{i=1}\\ {{\mathrm{sin}}^{3}(\text{π}{x}^{e(i)}),}&{1 < i < n}\\ {{x}^{0.5}{(1-x)}^{0.1}{\text{e}}^{-20x},}&{i=n} \end{array} \right.$ (13)
 $e(i) = {\text{ln}}\;0.5/{\text{ln}}\;{x_i},\quad 0 \leqslant {x_i} \leqslant 1$ (14)

 $f(x) = \max ({u_1}P/{s_1} - {u_2}{M_{\rm{t}}}/{s_2})$ (15)

 $\left\{ \begin{array}{*{20}{l}} {c_i} \leqslant 0.02 \\ {\beta _{\min }} \leqslant \cdots \leqslant {\beta _{i - 1}} \leqslant {\beta _i} \leqslant {\beta _{i + 1}} \leqslant \cdots \leqslant {\beta _{\max }} \end{array} \right.$ (16)

 $\left| {{T_{\text{m}}} - {T_{{{\text{m}}_{\text{0}}}}}} \right| \leqslant 0.05$ (17)

 $\left\{ {\begin{array}{*{20}{l}} {P > {P_0}} \\ {{M_{\text{t}}} < {M_{{{\text{t}}_{\text{0}}}}}} \end{array}} \right.$ (18)

 图 3 叶片优化流程图 Fig. 3 Flow chart of the blade optimization
2 优化结果与分析 2.1 叶片几何

 图 4 优化后的翼型形线与原始翼型形线的对比 Fig. 4 Comparison between optimized airfoil profile and original airfoil profile

 图 5 叶片优化前后安装角 Fig. 5 Installation angle before and after the blade optimization

 图 6 叶片优化前后桨距角 Fig. 6 Pitch angle before and after the blade optimization
2.2 优化性能分析

 图 7 叶片优化前后风能利用率 Fig. 7 Wind energy utilization rate before and after the blade optimization

 图 8 叶片优化前后叶根弯矩 Fig. 8 Blade root bending moment before and after the blade optimization
3 结　论

a. 相较于原始叶片，优化后的叶片在设计工况下输出功率基本与原始叶片保持一致，其叶根弯矩降低了5%。优化后的各截面翼型最大厚度位置、弯度及弯度位置改变，叶片扭角呈先增大后减小的趋势，变桨角减小。

b. 对优化叶片变桨前的气动效率与变桨前后的气动载荷进行变风况性能验证。相较于原始叶片，低风速下的优化叶片风能利用率平均提升了1%；低、高风速下的叶片弯矩分别平均降低了5.8%与4.4%。

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