The blade element momentum (BEM) theory introduced by Lock et al. and formulated in its modern form by Glauert provides a framework to model the aerodynamic interaction between a turbine and a fluid flow. This theory is used either to estimate turbine efficiency or as a design aid. However, a lack of mathematical interpretation limits the understanding of some of its issues. The aim of this paper is to propose an analysis of BEM equations. Our approach is based on a reformulation of Glauert's model which enables us to identify criteria to guarantee the existence of solutions, analyze the convergence of usual and new (and more efficient) solution algorithms, and study turbine design procedures. The mathematical analysis is completed by numerical experiments.
翻译:Lock等人提出并由Glauert以现代形式拟订的刀片元素动力(BEM)理论,为模拟涡轮机与流体之间的空气动力相互作用提供了一个框架,该理论用于估计涡轮机效率或作为一种设计辅助手段,但缺乏数学解释限制了对其中某些问题的理解。本文的目的是提出对BEM方程式的分析。我们的方法基于重新拟订Glauert的模型,该模型使我们能够确定保证解决方案存在的标准,分析常规和新的(和更有效的)溶解算法的趋同,研究涡轮机设计程序。数学分析是通过数字实验完成的。