On non-viscous flows in cascades of blades

A study of a model is given, describing nonviscous flows in blade machines whose walls can differ from cylindrical surfaces. The model overcomes a disadvantage of the well known Martensen method for plane, irrotational, incompressible flows in cascades of profiles, a model which can be applied with success if the walls of a channel, into which the blades are inserted, do not differ too much from concentric cylindrical surfaces. The three-dimensional character of the stream fields is taken into consideration by introducing the so-called axial velocity ratio. A new stream function formulation of (generally incompressible) stream fields in cascades of blades is introduced, and a short survey is given on the mathematical and numerical study of this problem.