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A delayed detached eddy simulation (DDES) of an overexpanded nozzle flow withshock-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-axisforces. A clear physical understanding of the driving factors of theunsteadiness is still lacking. Under the current conditions, the nozzleoperates in a highly-overexpanded regime and comprises a conical separationshock within the nozzle contour, merging into a Mach disk in the nozzle centre.Our current study focuses on the unsteady pressure signature on the nozzlewall, through the use of Fourier-based spectral analysis performed in time andin the azimuthal wavenumber space. The numerical data well agrees with theexperimental measurements in terms of mean and fluctuating wall pressurestatistics. The frequency spectra are characterised by the presence of a largebump in the low frequency range associated to a breathing motion of the shocksystem and a broad and high amplitude peak at high frequencies generated by theturbulent activity of the detached shear layer. Moreover, a distinct peak at anintermediate frequency (of the order 1000 Hz) is observed to persist in thewall-pressure spectra along the nozzle wall. The analysis of the pressuresignals in the azimuthal wavenumber space indicates that this peak is clearlyassociated to the first (non-symmetrical) pressure mode and it is thusconnected to the generation of side loads. Furthermore, it is found that theunsteady Mach disk is characterised by an intense vortex shedding activity andthe interaction of these vortices with the second shock cell is a key factor inthe sustainment of an aeroacoustic feedback loop within the nozzle.

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