Inception and evolution of coherent structures in under-expanded supersonic jets

The purpose of this paper is to examine the generation and nature of the large coherent structures observed experimentally in an under-expanded supersonic impinging jet. More specifically, the questions to answer are: What mechanisms govern the receptivity process at the nozzle lip?, how does the underlying flow field affect the evolution of the large-scale coherent structure generated from the initial instability? and what are the interactions between the large-scale (forced) coherent structures and the developing turbulence in the jet shear layer? In order to answer some of these questions both alternatives, that these structures come from global modal flow instabilities or from convective instabilities, the latter, are considered in this work. The stability analysis considered in the former case is performed in this work near the nozzle around the temporal average of the flow obtained by using an in-house LES (Large Eddy Simulation) code. The flow in this region is considered laminar, steady and without non-linear effects. The well known feedback loop in the impinging jet, according to which acoustic waves propagate upstream and excite the jet shear-layer (see Figure 2), advises against some of the hypothesis considered previously in the global stability analysis (ie. non-linear approximation). However the acoustic waves are orders of magnitude smaller than the hydrodynamic waves and should be smoothed out in the temporal average used in the calculation of the mean flow. The results show that both, axisymmetrical (m = 0) and azimuthal modes (m ≥ 1) are stable to global modal analysis and only convective instability could justify the instabilities observed in experiments in the shear layer. A study on the receptivity problem confirms that external disturbances may enter and excite the shear layer, being responsible of the instabilities observed in both experiments and direct numerical simulations.