DESIGN OF A CASCADE OF PROFILES OR A RADIAL CASCADE OF PROFILES BY THE SOLUTION OF THE INVERSE FLOW PROBLEMS

The paper deals with a design problem rebated to a cascade of profiles or a radial cascade of profiles for stator or rotor blades in turbine s or compressors. We design a profile geometry which corresponds to th e preassigned boundary conditions: input/output angles and the tangent ial component of the relative velocity along the profile surface. The solution is based on the well known method which first compares the po tential along the unknown profile with a potential of a model pow arou nd the unit circle and then constructs the corresponding conformal map ping. The problem is usually overdetermined and unsolvable, but if the preassigned velocity is submerged into a suitable broader class of su ch functions, the solution can be found there. The method, developed f or plane potential incompressible flows, has been adapted also to comp ressible subsonic flows.