Simulation and modeling of compressible and incompressible turbulent channel flows over rough walls

The effects of surface roughness on wall-bounded turbulent flows are important for fundamental turbulence research, and turbulence modeling and control, in both compressible and incompressible regimes. This dissertation studies these effects through statistical and structural analysis of turbulence, and provides practical insights for modeling of turbulence in the presence of roughness for incompressible flows. It also proposes an immersed boundary method to simulate compressible flows over rough walls with complex geometries, and studies the roughness effects on supersonic flows over wavy walls. Turbulence statistics in open channel flows over a smooth wall and three types of wall roughness: sand-grain, cube roughness and a realistic, multi-scale turbine-blade roughness, are examined using direct numerical simulations. Transport of the mean momentum, normal components of the Reynolds stress tensor, and normal components of the dispersive stress tensor are analyzed. The results show higher turbulence isotropy for the rough walls compared to the smooth wall. Wake production, the mechanism through which energy is transported from the wake field to the turbulence field (and vice versa), is strongly influenced by the kind of rough wall. For synthetic rough walls, the wake production has relatively large positive values, while it is negative with a smaller magnitude, for the turbine-blade surface. These results indicate a strong dependence of turbulence processes in the near wall regions on the roughness topography. Turbulent coherent motions in flows over rough walls are also analyzed. Two-point velocity correlations, length scales, inclination angles, and velocity spectra are studied. Results from linear stochastic estimation suggest that, near the wall, the quasi-streamwise vortices observed in smoothwall flow are present in the large-scale recessed regions of multi-scale roughness, whereas they are replaced by a pair of 'head-up, head-down' horseshoe structures in the sandgrain and cube roughnesses, similar to those observed in the previous studies. The configuration of conditional eddies near the wall suggests that the kinematic behavior of vortices differs for each kind of rough surfaces. Vortices over multiscale roughness are conjectured to obey a growth mechanism similar to those over smooth walls, while around the cube roughness the head-down horse-shoe vortices undergo a solid-body rotation on top of the element on account of the strong shear layer. This shortens the longitudinal extent of the near-wall structures and promotes turbulence production. Deep Neural Networks (DNN) and Gaussian Process Regression (GPR) are used to propose a high-fidelity prediction of the Nikuradse equivalent sandgrain height, (ks), which is frequently used in turbulence modeling of flows over rough walls. To provide a good database, 45 widely different surface geometries are generated and simulated at frictional Reynolds number of 1000, which are also accompanied by 15 fully rough experimental data. The designed DNN and GPR models predict ks with errrms < 10% and errmax < 30% which is much more accurate than the models suggested in previous studies. Finally, a new immersed boundary method is proposed to simulate flow over complex geometries in sub- and supersonic regimes. The method uses a level-set field to impose appropriate boundary conditions at the interface of the fluid and solid cells. Different turbulence statistics are then analyzed and compared in supersonic flows over two 2-dimensional and two 3-dimensional surfaces, and the results reveal a strong dependence of the turbulence field on the roughness topographies and the associated shock patterns.