Numerical simulation of shock wave/turbulent boundary layer interactions in over-expanded nozzles

The performances of first-stage liquid rocket engines are highly dependent on the fluid dynamic behaviour of the expansion nozzle and for launch-trajectory optimisation purposes, large values of the ratio between the exit and throat areas are desirable. The maximum limit to this ratio is imposed by the need to avoid internal flow separation, since at sea level the flow is highly overexpanded. However, during the start-up phase the chamber pressure is below the design pressure and the flow separates from the nozzle wall. This condition is characterised by complex physical features, including the formation of a shock-wave system that adapts the exhaust flow to the higher ambient pressure, shock-wave/boundary-layer interactions (SWBLI), and a turbulent recirculation zone. As a global effect, the nozzle experiences non-axial forces, known as side-loads, which can be of sufficient strength to cause structural damage to the engine. Despite several studies in the last decades, a clear physical understanding of the driving factors of the unsteadiness is still lacking. The experiments on axi-symmetric nozzles suffer from the lack of flow measurements inside the nozzle itself, due to the challenging flow conditions and absence of optical access. Therefore, numerical simulations represent an important complementary tool to gain a more complete insight into the physics of separated rocket nozzle flows, giving the opportunity to address important open questions. The present thesis investigates shock wave induced flow separation in over-expanded rocket nozzles by means of large-scale high-fidelity numerical computations based on the delayed detached eddy simulation (DDES) methodology, a hybrid RANS/LES method that allows the simulation of high-Reynolds number flows involving massive flow separation. In this approach, attached boundary layers are treated in RANS mode, lowering the computational requirements, while the most energetic turbulent scales of separated shear layers and turbulent recirculating zones are directly treated by the LES mode of the method. The potential of DDES has been first tested on a simple planar nozzle configuration for which experimental and numerical studies are available, with the main aim of highlighting the strengths and weaknesses of the approach. The results indicate that the DDES is able to capture the shock oscillations and that the computed characteristic frequency is close to that reported in literature for the same test case. The study then focuses on the investigation of the unsteadiness in a truncated ideal contoured (TIC) nozzle, a configuration for which experimental data are available. The numerical data agree well with the experimental results 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 an axi-symmetric (piston-like) 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 (f « 1 kHz) is observed in the wall-pressure spectra downstream of the separation shock. A Fourier-based spectral analysis performed in both time and azimuthal wave number space, reveals that this peak is associated with the first (non- symmetrical) pressure mode and is thus related to the generation of the aerodynamic side loads. Furthermore, it is found that the unsteady Mach disk is characterised 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