On the Three-dimensional Impeller with Loxodromic Curved Blade

抄録

This paper deals with a method of theoretical analysis on the flow in a three-dimensional impeller or turbomachine. By considering the stream surface of revolution as Riemann's space (Einstein's space) and by introducing the stream surface with a constant Gaussian curvature, a conformal and projective transformation is used, in which a flow on Riemann's plane corresponds to one on the spherical or pseudo-spherical surface under a hydrodynamical condition of isometric transformation. In this paper the numerical examples in the case that the aerofoil profile on Riemann's plane is logarithmic spiral, are reported. They give the basic slip factors for the arbitrary three-dimensional pumps and compressors and by using the geometrical representation of aerofoil profile and theoretical analysis show in this paper, the potential flow may be nearly realized when the viscosity of fluid is relatively low.