High-fidelity simulation of a supersonic turbulent boundary layer over a pseudo-random roughness pattern

High-speed vehicles for civil and space applications operate in regimes where compressible turbulence interacts strongly with the rough, evolving wall topography. Even though modern manufacturing techniques allow for the realization of nearly smooth external surfaces, aerothermal loading, ablation, localized damage, and environmental or atmospheric hazards can permanently modify the surface and, in turn, the overlying flow. Roughness patterns are, therefore, common on high-speed vehicles and are essentially unavoidable in re-entry configurations employing thermal protection systems (TPSs). The influence of surface roughness in incompressible turbulent flows has been extensively investigated, although several aspects remain under debate. Studies in the compressible regime build on this foundation but introduce additional challenges: the presence of shock and expansion waves, the strong coupling between turbulent and thermodynamic fields, and the dependence on the Mach number. Moreover, the existing database is still limited, with relatively few experimental campaigns and even fewer high-fidelity numerical studies. Additional DNS data are needed to explore different roughness morphologies and to extend current correlations. In this context, the present work performs a high-fidelity simulation of a compressible turbulent boundary layer at M_infty = 2 over a pseudo-random, doubly periodic rough surface generated via the MARS algorithm (Jelly and Busse [18]). The steps and modifications applied to the original algorithm to obtain a numerically admissible rough surface are described, along with a preliminary analysis of the resulting flow field in terms of both mean and instantaneous quantities. The roughness statistics are chosen to be as close as possible to those of cubic roughness used in the recent DNS studies by Modesti et al. [25] and Cogo et al. [7], enabling a comparison between different patterns with comparable element scales. The thesis also includes a concise review of the incompressible and compressible roughness literature to frame the present contribution within the existing knowledge. Overall, this work represents a first step toward the systematic study of this pseudo-random roughness pattern; further analyses will be required to assess thermodynamic behavior, the presence of outer layer similarity for both thermal and velocity statistics, and the performance of compressibility transformations.