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A new fixed-point algorithm to solve the blade element momentum equations with high robustness
Energy Science & Engineering ( IF 3.5 ) Pub Date : 2021-07-17 , DOI: 10.1002/ese3.945 Meng Jin 1 , Xiaogang Yang 1
Energy Science & Engineering ( IF 3.5 ) Pub Date : 2021-07-17 , DOI: 10.1002/ese3.945 Meng Jin 1 , Xiaogang Yang 1
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The most common approach to solving blade element momentum (BEM) equations is through fixed point method. The fixed point method can provide reliable solutions with high precision, yet the robustness of the method has been challenged when infrequent failures of converging to a physical solution are found for some design space. Though the lack of robustness is alleviated by applying two improved algorithms, their shortcomings should not be of an understatement. Ning's method can result in a converged yet nonphysical solution, and Sun's method decreases the computational efficiency remarkably. To overcome these setbacks, a new algorithm has been proposed in this paper. A clear classification of a wind turbine operating states has been given first to correct the thrust relation for a > 1, followed by discussions of three failure cases encountered during solving BEM equations. Then, the new algorithm with three major modifications has been introduced and explained. The test of Section 4 reveals that the decreasing rf technique has a positive effect on improving the robustness. Besides, the first two tests in Section 5 prove that the new thrust equation can greatly enhance the robustness, and Aitken's squared process can significantly strengthen the efficiency. The results show that all three modifications contribute to offering a new FPA with high robustness and satisfactory computing efficiency, which serves as the best option for solving the BEM equations.
中文翻译：
一种新的定点算法求解具有高鲁棒性的叶片单元动量方程
求解叶片单元动量 (BEM) 方程的最常用方法是通过定点法。定点方法可以提供高精度的可靠解决方案，但是当发现某些设计空间不经常出现收敛到物理解决方案的失败时，该方法的鲁棒性受到了挑战。虽然通过应用两种改进的算法可以缓解鲁棒性的不足，但它们的缺点也不应轻描淡写。Ning 的方法可以得到收敛但非物理的解，而 Sun 的方法显着降低了计算效率。为了克服这些挫折，本文提出了一种新算法。风力涡轮机的运行状态的明确分类已经给出了第一次修正推力关系一 > 1，然后讨论求解 BEM 方程时遇到的三个失败案例。然后，介绍和解释了具有三个主要修改的新算法。第 4 节的测试表明，降低rf技术对提高鲁棒性有积极的影响。此外，第 5 节的前两个测试证明新的推力方程可以大大增强鲁棒性，而 Aitken 的平方过程可以显着增强效率。结果表明，所有三种修改都有助于提供具有高鲁棒性和令人满意的计算效率的新 FPA，这是求解 BEM 方程的最佳选择。
更新日期：2021-07-17
中文翻译：
一种新的定点算法求解具有高鲁棒性的叶片单元动量方程
求解叶片单元动量 (BEM) 方程的最常用方法是通过定点法。定点方法可以提供高精度的可靠解决方案，但是当发现某些设计空间不经常出现收敛到物理解决方案的失败时，该方法的鲁棒性受到了挑战。虽然通过应用两种改进的算法可以缓解鲁棒性的不足，但它们的缺点也不应轻描淡写。Ning 的方法可以得到收敛但非物理的解，而 Sun 的方法显着降低了计算效率。为了克服这些挫折，本文提出了一种新算法。风力涡轮机的运行状态的明确分类已经给出了第一次修正推力关系一 > 1，然后讨论求解 BEM 方程时遇到的三个失败案例。然后，介绍和解释了具有三个主要修改的新算法。第 4 节的测试表明，降低rf技术对提高鲁棒性有积极的影响。此外，第 5 节的前两个测试证明新的推力方程可以大大增强鲁棒性，而 Aitken 的平方过程可以显着增强效率。结果表明，所有三种修改都有助于提供具有高鲁棒性和令人满意的计算效率的新 FPA，这是求解 BEM 方程的最佳选择。
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