A new fixed-point algorithm to solve the blade element momentum equations with high robustness

Abstract

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.