On the Regularistation of Non Reflecting Boundary Conditions Near Acoustic Resonance
In this paper we discuss the phenomenon of acoustic resonance in the context of nonreflecting boundary conditions and its impact on the analysis of turbomachinery blade flutter. Acoustic resonance is observed on the one hand when flutter curves, i.e. the aerodynamic damping as a function of the interblade phase angle, displays singularities at certain angles. On the other hand, the implementation of appropriate inlet and outlet boundary conditions naturally leads to the normal mode analysis of the Euler equations on eiher cylindrical (2D) or annular ducts (3D) To formulate boundary conditions one typically carries out the normal mode analysis and thus decomposes the space of normal modes as a direct sum of incoming and outgoing modes. This decomposition, however, breaks down when the generalised eigenvalue problem no longer produces a complete set of eigenvectors and one obtains non trivial Jordan blocks. Both phenomena are shown to be due to acoustic modes with vanishing normal group velocity. The main goal of this paper is to outline how the numerical boundary conditions can be regularised near acoustic resonance. The impact of this regularisation on the prediction of flutter stability is then demonstrated. Moreover, we interpret the regularisation as an interpolation between the exact non reflecting and the approximative characteristic, one dimensional boundary conditions.