Modeling the Response from a Cascade to an Upstream Acoustic Disturbance

Time-accurate Euler flow field 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 strength, and the initial flow properties prior to the upstream disturbance. The predicted results from the small disturbance model were then compared with the Euler analysis results for a two-dimensional cascade. Agreement between the model and the Euler data indicated that the model was potentially useful as a basis for an outflow boundary condition for time-accurate Euler/Navier-Stokes (ENS) simulations of supersonic mixed compression inlet flows needed to determine the stability margin of an inlet that encounters an atmospheric disturbance. This boundary condition must provide an approximation of the response from the compressor by the inlet flow at the face of the compressor when a disturbance from upstream passes through the inlet and into the compressor. A new characteristic boundary condition based on the small disturbance response model was formulated and demonstrated independently in two one-dimensional Euler codes. The one-dimensional Euler codes with the new boundary condition and with existing boundary condition formulations were used to predict the reflection response for an axial compressor experiment. 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. For a supersonic mixed compression inlet, a one-dimensional Euler code was also used to demonstrate the dependence of the inlet normal-shock response and unstart tolerance on the outflow boundary condition.