Three-dimensional global stability analysis of turbulent screeching jets
A three dimensional global stability analysis is performed to investigate the problem of screeching jets under turbulent conditions. The study employs an Unsteady Reynolds-Averaged Navier-Stokes (URANS) framework, in which the compressible flow equations are discretised using the high-fidelity solver dNami, the linearised discrete system is obtained through the automatic differentiation tool Tapenade, and the global stability problem is solved in a time-stepping framework. The fixed-point solutions of the URANS equations are first validated against experimental and numerical data, then a three dimensional global stability analysis is performed around fixed points solutions at different levels of under-expanded regimes. The extracted modes are spatially analysed and examined in terms of acustic radiation and validated against experimental data. Comparison with experimental POD data shows that the linear modes reproduce the main wavenumber content and spatial organisation of the screech resonance loop, even at high levels of under-expansion. The staging behaviour is also recovered from the interaction between the Kelvin--Helmholtz wave and the dominant wavenumbers of the shock-cell structure. Finally, a Helmholtz decomposition is applied to the velocity perturbation in order to separate the vortical and irrotational parts of the modes. An energy budget of the wave components is then used to quantify the repartition of the relative feedback-loop energy perturbation. Notably, the Mach-number effects on energy partition vary depending on the type of staged mode. This insight could prove valuable for interpreting receptivity mechanisms at nozzle lips and shocks in future research.