透平机械内部三元流动的有限元解

本文运用张量分析,建立了透平机械内部流动任意流面流函数之偏微分方程,给出了有限元解的误差估计,研制了通用程序.在跨音速流情形,证明了相应的变分问题等价于一个线性分布参数的最优控制问题.应用有限元离散化,可用共轭梯度法求解.

FINITE ELEMENT APPROXIMATION OF THREE DIMENSIONAL FLOW IN TURBOMACHINES

In this paper, by applying the tensor analysis and semigeodesio coordinate system, we have established a partial differential equation and conditions satisfied by the stream function on any stream surface of three dimensional flow in turbomachines. We have also provided computational examples by use of finite element method, and the error estimate of Galerkin's finite element approximation solution which depends on Mach number.In addition, we have drawn the conclusion that the transonic equation for three dimensional compressible flow in the turbomachines is equivalent to an optimal control problem of a linearly distributed parameter system. This problem can be disoretized by the finite element method and solved by a conjugate gradient algorithm. A new class of method for solving the transonic equation is particularly well adapted to problems with complicated three dimensional geometries and shocks, and at the same time it can be used to improve the precision of approximation solution.