  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.

Fluid Dynamics