A method for solving numerically the fully time-dependent two-dimensional Euler equations, applied to unsteady subsonic flow through vibrating turbomachine cascades with thin blades, is developed. The blades are assumed to vibrate at a constant interblade phase angle and the computed region is reduced to one blade passage, with the implementation of the interblade phase angle as a periodicity condition. The reliability of the method is validated by comparing it with an analytical flat plate theory, and the importance of radiative inlet and outlet boundary conditions for unsteady flow calculations is shown in an example.

The method can be used to compute the aerodynamic force and damping coefficients acting on the blades and to investigate the propagation of unsteady disturbances through a cascade in flutter conditions.