Numerical Studies of Supersonic Turbulent Boundary Layers

<p dir="ltr">This dissertation is divided into two studies. Each study utilized high performing supercomputing clusters to perform direct numerical simulations of supersonic turbulent boundary layers.</p><p dir="ltr">The first study investigated the effect of a wavy-wall surface on a boundary layer with a freestream Mach number of M = 2. Turbulent boundary layers have near-wall coherent structures which are mechanisms of momentum transfer. Multiple surface geometries were investigated including: a smooth wall case (Case SW); a wavy wall case where the spanwise wavelength was much greater than the spanwise spacing of the near-wall streaks (Case W1); and a wavy wall case where the spanwise wavelength was set on the order of the spanwise spacing of the near-wall streaks (Case W2). Case W2 was used to intentionally perturb the near wall structures and analyze the effect the perturbation has across the boundary layer. A breakdown of wall-similarity was observed in only Case W2, highlighting the significance of the spanwise spacing of surface perturbations. Additionally, drag reduction was observed in the same case. The mechanism of drag reduction in the riblet-like surface was found to be a lack of turbulent mixing in the valleys, keeping low-speed fluid near the surface and reducing skin friction drag substantially to cause a net total drag reduction. </p><p dir="ltr">The second study investigated the efficacy of standard turbulent heat flux formulations. Both smooth wall and wavy wall test cases were conducted with adiabatic and cold wall temperatures. Standard scalar turbulent diffusivity models were shown to perform well in predicting wall-normal turbulent heat flux in the smooth wall cases of either temperature condition. Standard models did not perform well in capturing the divergence of the turbulent heat flux in the presence of wavy surface geometry. A tensor diffusivity model for incompressible flow was tested and showed promising results, but with the need for compressibility adjustments. Mach waves, which are a result of the surface geometry, had significant impact on gradients present in the flow, which the model struggled to capture accurately. Modeling coefficients were also investigated for the simulated cases and adjustments are needed for compressible flows.</p>