﻿ Savonius风机叶轮双侧外形优化设计
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 哈尔滨工程大学学报  2019, Vol. 40 Issue (2): 254-259, 272  DOI: 10.11990/jheu.201705082 0

引用本文

WANG Wei, SONG Baowei, MAO Zhaoyong, et al. Optimization of Savonius wind turbine impeller with bilateral contour[J]. Journal of Harbin Engineering University, 2019, 40(2), 254-259, 272. DOI: 10.11990/jheu.201705082.

文章历史

Savonius风机叶轮双侧外形优化设计

Optimization of Savonius wind turbine impeller with bilateral contour
WANG Wei , SONG Baowei , MAO Zhaoyong , TIAN Wenlong
School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China
Abstract: To improve the utilization rate of wind energy on Savonius wind turbines, this study proposes an impeller scheme with different bilateral contour and optimizes bilateral shape parameters. Based on the Reynolds averaged N-S equations and SST k-ω turbulence model, the computational fluid dynamics (CFD) model of numerical calculation is established using the sliding mesh technique. Then, the kriging-PSO optimization model of the wind turbine impeller with bilateral contour is developed. Finally, the CFD and kriging-PSO optimization models are used to optimize the bilateral shape of the Savonius wind turbine impeller. Results show that the impeller with shape parameter of (0.626 8, 0.541 3) has the highest efficiency (0.284), which is 7.17% more than that of the conventional Savonius impeller (0.265).
Keywords: Savonius wind turbine impeller    utilization rate of wind energy    bilateral contour    computational fluid dynamics    optimization    efficiency

Savonius风机与其他水平轴风机和升力型垂直轴风力机相比，其气动性能较差、风能转化率低，普通Savonius风机的最高发电效率仅为25%。因此，国内外学者通过实验方法和数值模拟方法从风机基本结构参数、叶轮几何参数和风机辅助结构等各方面来研究改善Savonius风机的气动性能，从而提高其风能转化率[2]。文献[3]通过风洞实验得出高径比为5的风机的风能利用率为0.25。文献[4]通过实验得出两叶片的Savonius风机性能高于三叶片和四叶片的Savonius风机。文献[5]利用风洞实验得出风机孔隙比在0.2左右时，风能转化率最高。文献[6]利用CFD方法对非定常流中的Savonius风机进行数值模拟，研究表明：在CFD中，2D/k-ω模型可以获得较好的仿真效果。文献[7]通过风洞实验发现通过叠加风机的数量(风机在垂直方向上进行安装叠加，旋转轴相同)也可以提高风机输出功率。

1 Savonius风机叶轮

 ${\delta _1} = \frac{{{R_1}}}{R}$ (1)
 ${\delta _2} = \frac{{{R_2}}}{R}$ (2)

 $\lambda = \frac{{\omega D}}{{2U}}$ (3)

 ${C_m} = \frac{M}{{0.25\rho S{U^2}D}}$ (4)

 ${C_p} = \frac{P}{{0.5\rho S{U^3}}} = \lambda {C_m}$ (5)

2 计算数学模型 2.1 数值模型设置

2.2 网格无关性验证

2.3 数值模型实验验证

2.4 叶轮优化模型

Kriging模型是一种方差最小无偏估计模型。利用叶轮形状参数(δ1δ2)来建立Kriging代理模型，该模型可以描述优化目标Cp和叶轮形状参数之间的关系。设欲近似的的函数为y(x)，并假设Kriging模型的响应值和自变量之间的关系为:

 $y\left( x \right) = \beta + Z\left( x \right)$

 $\left\{ \begin{gathered} {\text{E}}\left[{Z\left( x \right)} \right] = 0 \hfill \\ {\text{Var}}\left[{\left( {Z\left( x \right)} \right.} \right] = {\sigma ^2} \hfill \\ {\text{F}}\left[{Z\left( x \right)Z\left( {{x_i}} \right)} \right] = {\sigma ^2}R\left( {x, {x_i}} \right) \hfill \\ \end{gathered} \right.$

 $R\left( {x, {x_i}} \right) = \exp \left[{-\sum\limits_{i = 1}^n {{\theta _k}{{\left( {{x_{ki}}-{x_k}} \right)}^2}} } \right]$

 $\mathit{\boldsymbol{R}} = \left[{\begin{array}{*{20}{c}} {R\left( {{x_1}, {x_1}} \right)}& \cdots &{R\left( {{x_1}, {x_N}} \right)} \\ \vdots&\vdots&\vdots \\ {R\left( {{x_N}, {x_1}} \right)}& \cdots &{R\left( {{x_N}, {x_N}} \right)} \end{array}} \right]$

 $\mathit{\boldsymbol{r}} = \left[{\begin{array}{*{20}{c}} {R\left( {x, {x_1}} \right)} \\ \vdots \\ {R\left( {x, {x_N}} \right)} \end{array}} \right]$

 $\hat y\left( x \right) = \hat \beta + {\mathit{\boldsymbol{r}}^{\text{T}}}\left( x \right){\mathit{\boldsymbol{R}}^{-1}}\left( {\mathit{\boldsymbol{Y}}-\mathit{\boldsymbol{X}}\hat \beta } \right)$

 $\hat \beta = {\left( {{\mathit{\boldsymbol{X}}^{\text{T}}}{\mathit{\boldsymbol{R}}^{-1}}\mathit{\boldsymbol{X}}} \right)^{-1}}{\mathit{\boldsymbol{X}}^{\text{T}}}{\mathit{\boldsymbol{R}}^{-1}}\mathit{\boldsymbol{Y}}$

1) 初始化粒子(初始化速度和位置)；

2) 计算适应度函数值；

3) 如果当前粒子适应度函数值大于历史最优值，那么历史最优值将被当前值替代；

4) 计算粒子群的最优解。如果粒子群的历史最优比全局最优要好，那么粒子群的全局最优被历史最优替代；

5) 对每个粒子的速度和位置进行更新；

6) 进化代数增加1，没有达到终止条件，转至2)；否则，结束算法并输出最优值。

PSO算法流程图如图 6所示。

PSO算法可通过MATLAB编程语言来实现，将Kriging代理模型中的响应值函数作为PSO优化算法的目标函数，最终建立Kriging-PSO优化模型。

3 计算结果分析 3.1 优化结果

Kriging-PSO优化模型对Savonius风力机叶轮双侧外形优化的结果为：双侧最优形状为(0.626 8, 0.541 3)，对应的最优发电功率系数为0.284。Kriging模型的响应面如图 7所示，寻得最优点如图 8所示。

 Download: 图 7 Kriging模型的响应面 Fig. 7 The response surface of Kriging model

3.2 叶轮力矩特性分析

 Download: 图 9 优化前后叶轮力矩系数的变化曲线(λ=1.0) Fig. 9 Moment coefficients curves before and after optimization(λ=1.0)
 Download: 图 10 δ1变化时的力矩系数曲线(λ=1.0) Fig. 10 Moment coefficient curves when δ1 changes(λ=1.0)
 Download: 图 11 δ2变化时的力矩系数曲线(λ=1.0) Fig. 11 Moment coefficient curves when δ2 changes(λ=1.0)
3.3 双侧外形参数对叶轮特性影响的原因

 Download: 图 12 叶轮优化前后的压力云图(正力矩区域，λ=1.0) Fig. 12 Pressure nephogram before and after impeller optimization(positive torque region, λ=1.0)

 Download: 图 13 叶轮优化前后的压力云图(负力矩区域，λ=1.0) Fig. 13 Pressure nephogram before and after impeller optimization(negative torque region, λ=1.0)
4 结论

1) 优化叶轮相比于常规叶轮，最大力矩系数提高，最小力矩系数减小；

2) 叶片力矩系数在一个旋转周期内，呈现一次正负交替的变化；

3) 基于Kriging-PSO优化模型找到最优形状的Savonius风机叶轮, 叶轮最优形状为(0.626 8，0.541 3)，最优发电效率系数为0.284，相比于常规叶轮(0.265)提高了7.17%。

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