| The nonlinear Euler equations in rotating coordinates are used as the basic governing equations. A linearization is carried out about a nominal mean flow, which is obtained by solving the nonlinear Euler equations. Time and frequency-domain approaches to solving the linearized Euler equations are presented. The linearization of the flux vector is based on a high-resolution flux formulation. The linearized equations are maintained in conservation-law form permitting the use of shock-capturing methods. The nonlinear and linearized equations are used to compute the aerodynamic response of two and three dimensional geometries to prescribed blade vibrations. Numerical solutions are compared to theoretical results (where available), to other linearized solutions and to numerical solutions of the nonlinear Euler equations. The overall agreement between the various solutions is good. The frequency domain approach is at least an order of magnitude faster than the corresponding time domain approaches. |
