| Jet engines are tested in testing facilities, inside so-called test cells, where the desired sea-level or altitude environmental conditions are controlled. The jet plume is exhausted out of the test cell, usually through a diffuser. Under certain testing conditions, high-intensity pressure fluctuations can be observed in such facilities. The intensity of these fluctuations reaches in some cases nearly 170dB in the exhaust system, which is beyond the acceptable limit for the testing installations. In general, the frequency of the fluctuations is close to that of an acoustic normal mode of the facility, typically that of the exhaust-diffuser. There is to date no means to predict whether or not this high-amplitude resonance will occur for a given set of testing conditions. So far these resonances have been suppressed by trial-and-error procedures. A complete understanding of this phenomenon is still sought.;The aim of the present work is to study the high-amplitude resonance phenomenon observed in test cell facilities from a fundamental point of view. To this end, a simple, two-dimensional model of a jet thorough a duct is simulated numerically for different jet regimes. The use of numerical simulations allows us to visualize in detail the flow variables as they go through a resonance cycle. This allows for identification of the features involved in the acoustic loop and characterize the acoustic-jet coupling better. The numerical method that is used to solve the Navier-Stokes equations, a high-order finite difference compressible flow solver on a staggered mesh, is presented. The method features shock capturing capabilities. A study on boundary closures allowed for the selection of high-order boundary schemes and the implementation of characteristics-based boundary closures on the staggered mesh.;The results of selected test cases are presented and the main features of resonant and non-resonant regimes for this model problem are discussed. A high-amplitude resonance, qualitatively similar to experiments in more complex geometries, was observed for a symmetric overexpanded M jet 1.2. It is seen that the resonance depends upon acoustic fluctuations reaching the nozzle lip and exciting the shear layers of the jet, the growth of the shear layer perturbations until vortices are rolled up and convected downstream, the interaction of the vortices with the shock-cell structure releasing another pressure pulse from the jet, and the reflection of this pulse in the duct walls closing the cycle. Results for a ducted non-resonant jet at Mjet = 1.5, and for a free jet at Mjet = 1.2 are also presented, to provide for comparisons with the resonant jet. The hydrodynamic mechanism is studied using linear stability analysis of the jet, where good qualitative agreement with the data from the DNS is obtained, especially near the inflow. For the acoustic part, the Fourier analysis of the data reveals the presence of excited normal modes of the duct. The hydrodynamic perturbation pattern near the inflow is consistent with the excited modes present in the duct. Furthermore, a numerical experiment is carried out where the normal mode of the duct of highest amplitude is damped, with the result that the resonance behavior is suppressed after a few cycles. The implications of the results obtained in the model problem on the resonance phenomena in test tell facilities are also discussed. |
