基于现代最优控制理论的轴流涡轮级S_2流面优化设计计算方法探讨

S_2 flow surface optimal design of axial flow turbine stage based on the modern optimal control theory

把数学规划论和现代最优控制论引入了轴流涡轮级的优化设计。采用非线性数学规划条件极值问题的求解方法进行了轴流涡轮级子午面几何通道形状及叶片几何参数的最优化设计 ,再在优化了的子午面几何通道内建立包括涡轮级内所有性能参量的最优流型命题的物理模型及其数学表达式 ,并归化为一个在给定初始状态、自变量终端固定、部分状态变量终端受有约束的条件下使级的输出功率最大的最优控制问题 ,应用“代价函数法”及“共轭梯度法”计算得到符合给定约束条件并使目标函数取极值的最优环量分布 。

The mathematical programming and optimal control theory were introduced into the optimal design of axial flow turbine stages. First, on the basis of conditional extreme value of non linear mathematical programming, the meridian channel shape and vane geometric parameters of axial flow turbine stages were calculated. Then, with the optimized meridian channel of axial flow turbine, the perfect physical model and mathematical expression of the proposition of optimal flow pattern, including all performance in turbine stages, were put forward. This problem was further recasted into a typical control to maximize specific performance index such as that of work of stage with given initial state, fixed terminal condition and constraints of part of state terminal variables. By using cost function method and DFP conjugate direction method, the optimal parameters were calculated.