# Nonlinear dynamics and linear stability analysis of over-expanded nozzle flows

Abstract : Shock wave-boundary layer interactions in over-expanded rocket nozzles are responsible for large detached regions resulting in non-axisymetric forces called side-loads. The mechanism at stake is self-sustained and involves separation, shear layers and Mach disks. In such cases, an hybrid approach for turbulence is required. This thesis aims at investigating the potentially globally unstable nature of this unsteadiness by means of a Delayed Detached Eddy Simulations (DDES) on an over-expanded nozzle and comparing it with a fully-3D linear stability analysis. The geometry considered is a TIC nozzle, experiencing a FSS unsteadiness and operating at 3 different jet Mach number M_j=[1.83, 2.09, 2.27]. Nonlinear calculations confirm the experimental outcomes: energy in PSD spectra for wall perturbations is distributed over 2 peaks at intermediate frequency (St=0.2-0.3) and two humps at low-frequency $left(St<1right)$ and high frequency (St =1), respectively. Particularly, at M_j=1.83 the peak at St=0.2 competes with that at St=0.3, prevails on the latter at M_j=2.09 and finally vanishes as the other at M_j=2.27. A PSD computed for different azimuthal components of wall pressure perturbation show a clear azimuthal separation for all the contribution above mentioned. Particularly, while the peak at St=0.3 has a double contribution m=2-3 at M_j=1.83 and exclusively a m=2 symmetry at M_j=2.09, the peak at St=0.2 has constantly a m=1 symmetry, which behaves has a persistent signature inside the nozzle at M_j=2.09. Consequently, a global stability analysis is performed on the DDES meanflow at M_j=2.09. Such analysis returns an unstable mode at St=0.2 with a m=1 shape, which develops from separation point and is localised at the external shear layer.
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• HAL Id : tel-03169495, version 1

### Citation

Cosimo Tarsia Morisco. Nonlinear dynamics and linear stability analysis of over-expanded nozzle flows. Nuclear Experiment [nucl-ex]. HESAM Université, 2020. English. ⟨NNT : 2020HESAE054⟩. ⟨tel-03169495⟩

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