用流函数方法求解叶轮机械三维气动设计问题

 将三维流动中定义于任意曲线坐标系上的两个流函数φ(x~1,x~2,x~3)和ψ(x~1,x~2,x~3)反演为x~1=x~1(φ,x~2,x~3)及ψ=ψ(φ,x~2,x~3)形式。在反演后的坐标系(φ,x~2,x~3)上导出三维流体动力学主控方程(坐标流函数方程)。该方程对于给定叶片厚度和叶片表面某气动参数(压强、速度等)分布,计算叶型坐标的问题(半反问题)易于求解。在求解差分方程时采用对x~1和ψ联立求解可得到较好的收敛性。通过算例计算表明该方法可给出满意的三维叶型坐标。

A METHOD FOR THREE-DIMENSIONAL INVERSE PROBLEM INTURBOMACHINERY BY MEANS OF STREAMFUNCTION FORMULATION

In arbitrary nonorthogonal curvilinear coordinates, the 3D two stream functions, Φ(x1 , x2 ,x3 ) and Ψ(x1 , x2 , x3 ) are inversed to x1 (Φ, x2 , x3 ) and Ψ(Φ, x2 , x3 ). In the inversed coordinates (Φ, .x2 ,x3 )the principal equations of 3D flow, the coordinate-stream function equations, are derived. There equaitons can be solved directly and easily according to the given distributions of the thickness of blade and any aerodynamic parameter of blade surface, such as pressure or velocity, etc.. To guarantee the good convergence of the computation, the difference equations of the CSF equations are solved as the simultaneous equations for solving x1 and Ψ. The computation shows that the method can give the correct coordinates of a 3D blade.