# Flow dynamics and wall-pressure signature in high-Reynolds number overexpanded nozzle with free shock separation

## TL;DR

This study uses high-fidelity simulations to analyze unsteady shock oscillations and wall-pressure signatures in a high-Reynolds number overexpanded nozzle, revealing key frequencies and mechanisms behind shock-induced unsteadiness.

## Contribution

It provides detailed spectral analysis of wall-pressure fluctuations and identifies the physical mechanisms driving shock oscillations and side loads in overexpanded nozzles.

## Key findings

- Presence of low-frequency shock breathing mode
- High-frequency turbulence-related pressure peaks
- Intermediate frequency peak linked to side loads

## Abstract

A delayed detached eddy simulation (DDES) of an overexpanded nozzle flow with shock-induced separation is carried out at a Reynolds number equal to 1.7 10^7. The flow unsteadiness, characterised by self-sustained shock oscillations, induces local unsteady loads on the nozzle wall as well as global off-axis forces. A clear physical understanding of the driving factors of the unsteadiness is still lacking. Under the current conditions, the nozzle operates in a highly-overexpanded regime and comprises a conical separation shock within the nozzle contour, merging into a Mach disk in the nozzle centre. Our current study focuses on the unsteady pressure signature on the nozzle wall, through the use of Fourier-based spectral analysis performed in time and in the azimuthal wavenumber space. The numerical data well agrees with the experimental measurements in terms of mean and fluctuating wall pressure statistics. The frequency spectra are characterised by the presence of a large bump in the low frequency range associated to a breathing motion of the shock system and a broad and high amplitude peak at high frequencies generated by the turbulent activity of the detached shear layer. Moreover, a distinct peak at an intermediate frequency (of the order 1000 Hz) is observed to persist in the wall-pressure spectra along the nozzle wall. The analysis of the pressure signals in the azimuthal wavenumber space indicates that this peak is clearly associated to the first (non-symmetrical) pressure mode and it is thus connected to the generation of side loads. Furthermore, it is found that the unsteady Mach disk is characterised by an intense vortex shedding activity and the interaction of these vortices with the second shock cell is a key factor in the sustainment of an aeroacoustic feedback loop within the nozzle.