Application of wall-modeled LES for compressible turbulent boundary layers over rough walls

Turbulent flows arise in most aerodynamic systems and even today remain one of the most challenging problems in fluid dynamics. Understanding and predicting their chaotic motion is crucial for engineering applications, and great effort has been put into the numerical simulation of such flows. In recent decades, interest in high-speed compressible flow has increased signifi- cantly; even though supersonic boundary layers exhibit a more complex behavior with respect to their incompressible counterparts, due to velocity and thermal fields coupling, density fluc- tuations, and the presence of shock waves, proper modeling of these flows is crucial for effective system design and analysis. Moreover, since every surface, even those that seem perfectly smooth, has a certain degree of roughness, it is necessary to determine whether the surface topography affects the evolution of the flow. From these considerations, it is evident that accurately predicting drag and heat trans- fer in boundary layers is a challenging task, in particular for supersonic turbulent flows over rough walls. The purpose of this thesis is to demonstrate the ability of a Wall-Modeled Large Eddy Simula- tion (WMLES) to resolve velocity and temperature profiles with a much lower computational cost than a Direct Numerical Simulation (DNS). In particular, the study focuses on analyzing different coupling strategies between the wall model and the LES, i.e. the way in which wall shear stress and heat transfer are enforced as boundary conditions to the simulation. The main case of interest is a supersonic, zero-pressure-gradient turbulent boundary layer at a freestream Mach number of 2 over cubical shaped roughness elements. The first chapters of the thesis are dedicated to the theoretical background of compressible and turbulent flows, focusing in particular on boundary layer flows. Subsequently, the WMLES simulation method is introduced as a low-cost computational cost approach for modeling wall- bounded flows. The model developed by Yang et al. (2016) is used here in its adaptation to su- personic flows. Density variations are taken into account using Van Driest (1951) compressible transformation and the temperature profile is derived using Walz (1966) relation for the Reynolds analogy in compressible turbulent boundary layers. Then, different coupling strategies between the wall model and the simulation are proposed and analyzed. Finally, the obtained results are presented, showing good agreement with DNS data provided by Cogo et al. (2025); these results are used to discuss the performance and effectiveness of the employed coupling strategies.