Numerical study of chemically reacting hypersonic boundary layers by means of non-linear parabolized stability equations

The future of space exploration and commercial space travels relies on the development of high-performance, efficient and reliable hypersonic vehicles, for the access to and return from Earth orbits, satellites and other planets. The primary concern in designing such spacecrafts is to manage and reduce the thermal loads they are subjected to, particularly during the atmospheric re-entry phase. In this regard, laminar-to-turbulent boundary-layer transition is a key aspect to consider, since severe heat-flux increments are observed on the body surfaces, when the flow transit to the turbulent regime. This has a direct impact on the thermal protection system sizing, thus compromising not only the vehicle performances, but its whole integrity and the final mission success. Accurate predictions of transition locations are of paramount importance in order to reduce the design margins and eventually implement control strategies. In hypersonic flows, the analysis increases in complexity since high-temperature gas effects need to be properly considered, and much is still unknown about their influence on the flow stability and transition phenomenon.The widely used linear stability theory (LST) is based on the simplifying parallel-flow assumption, thus not being suitable to investigate complex geometries. Moreover, it has to rely on correlations, through for example the e method, in order to provided transition-location estimations.The objective of this thesis is to investigate non-local and non-linear effects on the stability and transition of hypersonic boundary layers, in presence of high-temperature gas effects, including chemical reactions. To this end, a parabolized stability equations (PSE) solver is developed within the VESTA toolkit suite. PSE can take into account non-parallel effects and most importantly they can model and describe the transition weakly non-linear stages, thus being a valid alternative to semi-empirical methods and direct numerical simulations (DNS), thanks to their more affordable computational cost. The developed algorithm is used to investigate the linear and non-linear characteristics of different instability types, for a variety of flow assumptions, up to include thermo-chemical non-equilibrium conditions.The conducted analyses reveal that non-parallel effects modify the perturbation growth rate in different ways depending on the flow assumption considered, however their influence changes in a consistent manner with respect to Mach-number and wall-temperature variations. In terms of $Nrm$-factor predictions, the effect of non-parallelism is not affected by the aerothermodynamic model choice. Moreover, the stability study of a second-Mack's mode over a wedge, during an atmospheric re-entry trajectory, shows that non-parallel effects destabilize the velocity, temperature and kinetic-energy perturbations at the highest re-entry locations. The effect is weakened as lower altitudes are reached, until switching to being stabilizing at the lowest atmospheric locations. On the contrary, the mass-flux perturbation quantity is always found stabilized by non-parallel effects.The investigation of curvature effects on a crossflow and second-Mack's-mode instability reveals respectively a significant and weak stabilizing contribution on both linear and non-linear disturbance evolutions, thus leading to a delayed transi-tion-onset prediction. Within the PSE framework, the destabilizing effect of flow non-parallelism is found to compete with the stabilizing one of curvature. The net result is problem dependent and it highlights the importance of simultaneously taking into account both aspects in the analysis.The PSE study of supersonic modes shows that the method is able to retrieve the same qualitative results obtained by direct numerical simulations. In particular, the oscillations in the disturbance growth rate, highlighted in previous literature studies, have to be attributed to the presence of multiple LST eigenmodes in the solution. Some of these modes are found to have supersonic characteristics, but they do not have to be necessarily the ones associated to the main instability. The investigation of the non-linear transition stages in presence of chemical reactions represents a novelty in the framework of PSE transition studies, while very rare are the works based on DNS computations. The error analysis on the order of non-linearities to consider in the PSE derivation reveals the importance to include cubic-order disturbance non-linear interactions, while for the description of the perturbation thermo-transport properties, quadratic non-linear terms must be included for chemically reacting flows, while a linear approximation is sufficient in frozen conditions. Chemical reactions do not direct modify the non-linear transition mechanisms, but they do it as a consequence of the modified linear stability properties of the primary instability mode. In particular, they lead to an anticipated boundary-layer distortion and predicted transition-onset location. Similarly to incompressible and low supersonic regimes, a tendency to switch from a subharmonic to a fundamental secondary-mechanism type is found, even if a clear establishment of the latter is not observed. On the contrary, preliminary investigations shows that the chemistry effect on the sole perturbation field does alter the occurring breakdown type.Doctorat en Sciences de l'ingénieur et technologie