Inviscid Nonlinear Modeling of Vibration-Induced Acoustic Resonance of a Linear Cascade

A nonlinear model is developed to investigate the blade vibration-induced acoustic resonance in a linear cascade. The Euler equations are solved by using high-order computational aeroacoustics techniques. To satisfy no-penetration wall boundary conditions for vibrating blades, a semi-implicit time-accurate body force model is developed. Leading-edge singularity at resonance is remarkably strong, and so the balance of globally high-order quality (less dissipation) and numerical stability is significant. The adaptive discontinuity-capturing filtering is introduced as a local operation to achieve the good balance. To validate our model, the benchmark case of the Parker beta acoustic resonance induced by the vibrating cascade of flat plates is revisited. Compared to the linearized theory and viscous flow solution, our inviscid model economically achieves a good prediction both for the unsteady loading and the near-field sound pressure for the small blade vibration amplitude of Ym/c=0.4%. When it comes to a larger vibration amplitude of Ym/c=2.0%, nonlinearity on the unsteady lift and sound pressure appears in our results, and it cannot be considered in the linearized theory. The results, to some extent, are also consistent with the viscous flow solution. The study well verifies the capability of our nonlinear model in predicting this category of linear and nonlinear sound-vortex/structure interaction problems.