Abstract: 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.

Key words: stream function, three-dimensional flow, turbo-machines, blades