基于Broyden改进算法的航空发动机性能模拟研究  

Research of a Corrected Broyden's Method on the Aero-engine Performance Simulation

作　　者：黄旭[1] 王占学[1] 张晓博[1] 

机构地区：[1]西北工业大学动力与能源学院,西安710072

出　　处：《科学技术与工程》2012年第21期5231-5234,5252,共5页Science Technology and Engineering

摘　　要：航空发动机特性计算的核心问题之一就是求解描述发动机部件共同工作的非线性方程组。目前,最常用的求解非线性方程组的方法是Newton-Raphson方法,但是Newton-Raphson方法,在迭代次数很多的情况下需要大量发动机气动热力过程计算,计算速度明显下降。同时Newton-Raphson方法还存在不收敛的问题。为了克服Newton-Raphson方法的缺陷,详细分析了航空发动机部件共同工作的非线性方程组的求解收敛性问题。分析了不收敛的机理,并发展了基于Broyden方法求解发动机非线性方程组的改进算法。利用基于Broyden方法的改进算法对某型发动机进行一系列验证计算。通过分析计算结果,证明了采用Broyden方法可以提高发动机特性计算的计算速度,并且改善发动机特性计算的收敛性。One of the substantial problems of aircraft engine performance simulation is the solution to nonlinear equations depicting the engine components cooperation. Presently, Newton-Raphson method is frequently applied to solving the nonlinear equations. However, tremendous amount of calculation is needed when the number of iteration is extremely large. Besides, there also exist non-convergence problems in aircraft engine performance simulation usingNewton-Raphson method. To overcome the shortcomings of Newton-Raphson method, the non-convergence problems of solving the nonlinear equations of aircraft engine were combated via utilizing the corrected algorithm based on Broyden＇ s method. Moreover, the non-convergence cases were specialized and the mechanism of nonconvergence was analyzed. By analyzing results obtained by applying the corrected Broyden＇ s method and contrasting the two methods, it is proved that Broyden＇ s method is a more beneficial way for engine performance simulation due to its high calculation speed and the promotion of the convetgence.

关 键 词：航空发动机性能模拟 非线性方程组 收敛性 BROYDEN方法 

分 类 号：V373[航空宇航科学与技术—航空宇航推进理论与工程]