On a General Method of Unsteady Potential Calculation Applied to the Compression Stages of a Turbomachine—Part I: Theoretical Approach

An algorithm using the singularity method was developed. It allows taking into account the interaction between fixed and mobile cascades. Its principle is based on the summation of discrete vortices distributed periodically on the rotor and stator profiles. The overall matrix, obtained by applying the boundary conditions, takes into account the complexity of the studied cascade geometry (presence or not of splitter blades, possibly variable pitch of the profiles, etc…) To illustrate the interest and the impact of the algorithm, two parametric studies on turbomachines cascade are presented: Planes cascade made up of a rotor and a stator (at the mean radius of an axial fan). Circular cascade made up of impeller and a volute (peripheral cascade of a centrifugal pump).