Modeling the Response from a Cascade to an Upstream Acoustic Disturbance

Time-accurate Euler simulations for the flow through a two-dimensional cascade subjected to an upstream acoustic disturbance were used as the basis for a small-disturbance model to predict the reflected response upstream of the cascade. The small-disturbance model results in a linear system of algebraic equations for the properties of the reflected and transmitted disturbances. The model predicts the reflected and transmitted responses as a function of the cascade blade geometry, the disturbance amplitude, and the initial flow properties. A new characteristic outflow boundary condition based on the small-disturbance response model was formulated and demonstrated independently in two one-dimensional Euler codes. The new boundary condition was found to provide a significant improvement in accuracy for the reflection response of an acoustic disturbance from a compressor relative to existing outflow boundary-condition models.