Nonlinear Modeling of Shock Wave Trains in Ducts with Wall Discontinuities

Abstract

Analytical approaches were developed for modeling shock wave train propagation in a one dimensional duct with wall discontinuities. This modeling approach was developed primarily for the design and analysis of non-uniformities on inlet liners of high bypass ratio turbofan engines to mitigate the radiated buzz-saw noise. The presence of non-uniformities on the surface of acoustic liners always leads to reflection of acoustic energy back towards the fan which makes the problem more complex than that of progressive shock propagation. Two analytical techniques were investigated for modeling the compound shock wave propagation to include the resulting wave interaction, namely the perturbation expansion techniques referred to as the method of strained coordinates and the method of multiple scales. The technique based on the method of strained coordinates has been more fully developed into a robust method of predicting shock propagation in a duct with wall discontinuities. A shock wave train propagation test bed was also fabricated and operated in order to validate the shock propagation model. This test bed produced shocked sound wave trains between 3 and 4 meters downstream of the acoustic compression drivers with fundamental harmonic sound pressure levels of up to 152 dB at a distance of 4 meters downstream of the sources. The model based on strained coordinates predicted shock waves that were transmitted beyond the duct discontinuities accurate to within 1.5 dB SPL at the fundamental frequency as compared to experimental measurements.