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

A delayed detached eddy simulation of an overexpanded nozzle flow with shock-induced separation is carried out at a Reynolds number of, based on nozzle throat diameter and stagnation chamber properties. In this flow, self-sustained shock oscillations induce local unsteady loads on the nozzle wall as well as global off-axis forces. Despite several studies in the last few decades, a clear physical understanding of the factors driving this unsteadiness is still lacking. The geometry under investigation is a subscale truncated ideal contour nozzle, which was experimentally tested at the University of Texas at Austin at a nozzle pressure ratio of 30. Under these conditions, the nozzle operates in a highly overexpanded state and comprises a conical separation shock that merges to form a Mach disk at the nozzle centre. The delayed detached eddy simulation model agrees well with the experimental results in terms of mean and fluctuating wall-pressure statistics. Wall-pressure spectra reveal a large bump at low frequencies associated with an axisymmetric (piston-like) motion of the shock system, followed by a broad and high-amplitude peak at higher frequencies associated with the Mach waves produced by turbulent eddies convecting through the detached shear layer. Moreover, a distinct peak at an intermediate frequency persists in the wall-pressure spectra downstream of the separation shock. A Fourier-based analysis performed in both time and space (azimuthal wavenumber) reveals that this intermediate-frequency peak is associated with the (non-symmetric) pressure mode and is thus related to the generation of aerodynamic side loads. It is then shown how the unsteady Mach disk motion is characterized by an intense vortex shedding activity that, together with the vortical structures of the annular shear layer, contributes to the sustainment of an aeroacoustic feedback loop occurring within the nozzle.