求解航空发动机非线性方程组的变步长牛顿法

Variable Step Newton Method for Solving the Nonlinear Equations of Aero Turbine Engines

详细分析了航空涡轮发动机部件共同工作的非线性方程组的求解收敛性问题,并对计算中常见的迭代不收敛问题的机理进行了研究总结。针对常见的不收敛问题,提出了以传统牛顿迭代法为基础的变步长牛顿法加以解决。采用变步长牛顿法后,对某型定几何单轴涡喷发动机进行了一系列的验证计算,计算结果表明计算收敛性得到较大幅度的改善。变步长牛顿法对改善发动机总体性能计算收敛性具有很好的参考价值。

The convergence problems of solving the nonlinear equations of aero turbine engines were study in detail, the common non- convergence cases were given and the mechanism was analyzed, based on Newton method, an advanced solutions for overcoming the common non- convergence problems was presented：variable step Newton method （VSN）. The improved method was employed in performance computing program, and performance calculation results of some fix geometry turbojet showed that the convergence and convergence rate has been improved greatly. The VSN is of important reference value to solve the convergence problems in the aero engine computation.