Acoustic Energy Exchange Between Frequencies During Non-Linear Propagation of Shock Waves

In a previous paper dedicated to the validation of a numerical methodology to predict shock wave generation and propagation from the ACAT1 fan stage, unexpected variations of the power levels associated with the blade passing frequencies were observed inside the duct. Such variations are theoretically possible due to the non-linearity of the propagation of shock waves, but their amplitude and their localization close to the duct exit were uncommon. This phenomenon is further investigated in this paper using two different computational aeroacoustic solvers. The effects of duct geometry, non-linearity of the equations, and injection data are investigated. The results show that these power level variations are due to non-linear effects combined with the heterogeneity of the mean flow. When the input signal is prescribed frequency by frequency, these variations become minor. An interesting observation is that the complete result obtained when injecting all frequencies together is recovered when injecting only the dominant frequency due to the diffusion over its harmonics by non-linear effects.