航空发动机气动热力系统模型求解方法研究

Research on Methodfor Solving Aero-Engine Thermodynamic System Model

航空发动机气动热力系统模型通过求解部件之间共同工作方程组,来确定发动机相关状态参数。传统的共同工作方程组求解方法是采用定步长Newton迭代方法,每次迭代需要多次调用模型计算雅可比矩阵,为了保证模型的收敛性,通常步长设置比较保守,在一个仿真周期内需要进行多次的迭代计算进行方程组求解,导致航空发动机气动热力系统模型的实时性较差。提出了一种混合变步长Newton-逆Broyden方法求解共同工作方程组。为保证收敛性,在猜值初始偏差较大时采用小步长的Newton迭代法求解方程。为保证收敛速度,在猜值接近真实解的时候采用较大步长的逆Broyden递推法求解方程,并引入松弛因子提高迭代稳定性。应用上述方法求解F404/YJ101变循环发动机的气动热力系统模型,进行了发动机稳态和动态工作仿真。结果表明,混合Newton-逆Broyden方法在航空发动机气动热力系统模型计算中的收敛能力、实时性和计算精度有着明显的优越性。

The aero engine thermodynamic system model is used to get the engine working parameters by solving the components co-working equations. The traditional method for solving co-working equations is the fixed step Newton method,each iteration of which needs to repeatedly call the model to calculate the Jacobian matrix,and the step is conservative to ensure the convergence,resulting in poor real-time. A hybrid variable step Newton-inverse Broyden method was proposed in the paper. To ensure the convergence,the guess value deviation was greater when using Newton method with small step,and the guess value deviation was close to the roots when using inverse Broyden method with large step. To improve the method’s stability,relaxation factor was used in solving process. The method was applied to solve the thermodynamic system model of the F404/YJ101 variable cycle engine,and the steady and dynamic simulation of the engine was realized. Simulation results show the superiority of the proposed method on convergence,real-time performance and accuracy in the solving process of aero-engine thermodynamic model.