Non-linear singular integral equations analysis for unsteady cascade aeroelasticity applied in turbomachines

Abstract

A two-dimensional unsteady cascade aeroelasticity is introduced for the investigation of flow fields of turbomachines (gas or steam). Especially, the velocity field around a cascade of airfoils is determined, while such a problem is reduced to the solution of a non-linear multidimensional singular integral equation when considering harmonic time dependence between the motions of adjacent blades of the turbine. Consequently, a general non-linear model is investigated by proposing an “innovative” and “groundbreaking” method. An application is finally presented by considering a special description of the velocity field and therefore such a field is determined for arbitrary geometry and arbitrary interblade phase angle.