基于高斯过程回归的垂直轴风力机翼型气动设计

Aerodynamic design of vertical axis wind turbine airfoils based on Gaussian process regression

  • 摘要: 针对垂直轴风力机(vertical-axis wind turbine, VAWT)翼型气动优化中高保真数值计算成本较高的问题,以NACA 0021翼型为研究对象,构建融合XFOIL、高斯过程回归(Gaussian process regression, GPR)和遗传算法(genetic algorithm, GA)的气动优化方法。以前缘半径比、最大相对厚度、最大弯度和后缘襟翼偏角为设计变量,生成480组参数化翼型,并在Ma = 0.03、Re = 1.2×105α = 8°工况下利用XFOIL建立升阻比数据库,其中380组用于训练,100组用于测试。分别构建SE、RQ、Matérn 3/2和Matérn 5/2核GPR模型,并采用GA优化核函数的超参数。结果表明,RQ核综合预测性能最优,优化后RMSE由3.046降至2.571,R2由0.944提高至0.956。进一步以升阻比最大化为目标,通过GA搜索最优几何参数组合,获得最优翼型。CFD验证表明,α = 8°时优化翼型升阻比较基准翼型提高6.4%,GA-GPR预测结果与CFD计算结果的相对误差为4.4%;在0°~20°攻角范围内,最大升力系数和最大升阻比分别提高14.6%和12.3%。本文方法能够兼顾预测精度与计算效率,可为VAWT翼型气动优化提供参考。

     

    Abstract: To address the high computational cost of high-fidelity numerical simulations used in the aerodynamic optimization of vertical-axis wind turbine (VAWT) airfoils, an optimization framework integrating XFOIL, Gaussian process regression (GPR), and a genetic algorithm (GA) was developed using the NACA 0021 airfoil as the baseline. The leading-edge radius ratio, maximum thickness ratio, maximum camber, and trailing-edge flap deflection angle were selected as design variables. A total of 480 parametric airfoils were generated, and their aerodynamic performance was evaluated using XFOIL at Ma = 0.03, Re = 1.2 × 105, and α = 8° to establish a lift-to-drag ratio dataset. Of these samples, 380 were used for training and 100 for testing. Four GPR models employing squared exponential (SE), rational quadratic (RQ), Matérn 3/2, and Matérn 5/2 kernels were constructed, and their kernel hyperparameters were optimized using GA. The results showed that the RQ kernel achieved the best overall predictive performance. Following optimization, the root mean square error (RMSE) decreased from 3.046 to 2.571, while the coefficient of determination (R2) increased from 0.944 to 0.956. The Optimized 0021 airfoil was subsequently obtained by applying GA to identify the geometric parameter combination that maximized the lift-to-drag ratio. CFD validation showed that, at α = 8°, the lift-to-drag ratio of the optimized airfoil was 6.4% higher than that of the baseline airfoil, and the relative error between the GA-GPR prediction and the CFD result was 4.4%. Over the angle-of-attack range of 0°–20°, the maximum lift coefficient and maximum lift-to-drag ratio increased by 14.6% and 12.3%, respectively. The proposed method achieves a favorable balance between predictive accuracy and computational efficiency and provides a reference for the aerodynamic optimization of VAWT airfoils.

     

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