透平机械内部三维可压缩Navier-Stokes方程的流面方法和维数分裂算法

The Stream Surface Method and Dimension Split Method for 3D Viscous Compressible Flow in Turbomachinery

在这篇文章中,运用经典的张量分析方法,把流动区域用一个二维流形序列分割成一系列流层之并,推得在流层内半测地坐标之下的Navier-Stokes方程,在流形的法线方向应用向后Euler差分,推导了两维流形上的可压缩Navier-Stokes方程,和流函数满足的方程.在这个基础上,提出了一种维数分裂法的新算法.这种方法不同于区域分解法.对于三维问题,在区域分解法中我们必须在每个子区域上仍解三维问题,但是在这种新方法中,只需要在每个子区域上求解二维问题,不过是几个二维流形上的NS方程.文中还给出了一个透平机械内部流动的数值计算实例.

In this paper, 3D-flow domain is decomposed into a series of thin stream flow layers by a series of 2D-manifolds（surface） using calssical tensor anslysis method. Applied Euler backward difference scheme along normal direction to manifold, the compressible Navier-Stokes equations on the 2D-manifold are derived. Accoding to this idea, a dimension split method is proposed.this method is different from the classical domain decomposition method, in which one must solve a 3D problem into each subdomain, but in our method we only solve a 2D-subproblem on 2D manifold, which is a quasi-Navier-Stokes equations on 2D manifold. In addition, the paper provide several numerical examples for turbomachinary flow.