<p dir="ltr">The high-order, block spectral numerics of the Navier-Stokes solver H³AMR are presented. H³AMR operates on unstructured meshes where each unstructured hexahedral element can be considered its own block-spectral domain exchanging fluxes with other elements on faces between element boundaries. The solver features two forms of adaptive mesh refinement (AMR): through increasing or decreasing the polynomial order within each element (P-refinement); or by subdividing each hexahedral element in half in each computational direction yielding 8 sub-elements that can then be further refined hierarchically (H-refinement). Fluxes between elements and along domain boundaries are exchanged and re-interpolated within the mesh using Flux Reconstruction (FR) numerical methods. H³AMR allows for arbitrarily high-order solution reconstructions, allowing for the simulation of strong gradients in hypersonic boundary layers and capturing the wave-like nature of waves such as second modes.</p><p dir="ltr">H³AMR was validated in two canonical cases: a flat plate at near zero angle of attack and a 3-degree half angle cone at zero-degrees angle of attack. Both cases only considered the low enthalpy conditions achievable in the BAM6QT and the AFRL Mach 6 Ludwieg Tube at Wright-Patterson AFB, spanning Freestream Reynolds numbers from 4-22 million/meter. The solver was validated against experimental data measuring the development of the second-mode instability along the surface of each geometry. The computations and experimental data were both verified against Linear Stability Theory (LST) and agreement was found across all three measurement and analysis techniques. Best practices were developed for the the external, non-reacting hypersonic flows with spectral numerics, including the determination of a minimum resolution is required for stable simulations.</p><p dir="ltr">The effects of high-porosity Silicon-Carbide (SiC) as a surrogate for porous aeroshell material was investigated with LST using the Impedance Boundary Condition (IBC) to computationally model the acoustic absorptivity of the material using the Johnson-Champoux-Allard (JCA) model to relate pressure and second mode frequency to absorption. The material was applied to the aforementioned geometries at specific locations to attenuate second mode growth. Due to the low angle of attack and memory effects at the tip of the flat geometry, H³AMR was required to generate a basic state for LST from the laminar solution of the Navier-Stokes equations. The sharp cone geometry was allowed to use a rescaled compressible Blasius' solution as the basic state. While the SiC foams showed significant second mode suppression, an ''over shoot'' in second mode amplitude was observed before breakdown when the SiC foam was applied in comparison to the solid wall experiments. While the SiC foams were effective at attenuating the high-frequency modes, LST was used to predict the exacerbation of low-frequency growth modes that result from the application of the SiC foam and may cause the overshoot in second mode amplitude before transition.</p><p dir="ltr">With the validation and verification of H³AMR for external flows completed, the code was used in transitional simulations of the High-Speed Army Reference Vehicle (HARV) geometries to investigate the effects of pressure gradients on second mode wave growth. These geometries feature a 20 inch long blunted cone-cylinder geometry with the conical frustum taking up one half of the overall length. Two variants of the geometry exist on the frustum section with different streamwise pressure profiles: a straight cone version and a Von Karman ogive. The nose tip bluntness is 2.54mm on both geometries. The geometries are first simulated at freestream conditions matching those found at in the Boeing and Air Force Mach 6 Quiet Tunnel (BAM6QT) at Purdue University at a freestream Reynolds number of 10-20 million/meter with a wall temperature ratio of 0.84 (310K). These conditions on both geometries were found to be overwhelmingly stable in both numerical studies and wind tunnel experiments, with no transition being seen at any of the Reynolds numbers or frustum variants. To further destabilize the boundary layer, the Reynolds number was doubled twice to 40 and 80 million/meter and the wall temperature ratio was decreased by half twice from 0.84 to 0.42 to 0.21 (155K and 75K respectively). While the onset of transition at these conditions seemed plausible, transition was deemed unlikely by the axisymmetric stability analysis, Unsteady DNS fed by a finite time of wall-normal suction and blowing with a pink-noise profile showed the possible existence of non-modal mechanisms that may lead to break down for extreme wall cooling. The ogive geometry was deemed marginally more unstable than the straight cone geometry, despite the adverse pressure gradient environment. This effect may be in competition with the stabilizing effect extended entropy layer on the straight cone geometry.</p><p dir="ltr">Finally, 3D time accurate simulations over both geometries were ran over an 8-degree arc sector of the cone to open up the ability for oblique wave modes to exist and determine if any three-dimensional effects might lead to the onset of transition. No breakdown to turbulence was observed in the conditions tested. While these simulations did not contain the comprehensive list of conditions as the axisymmetric simulations did, the Reynolds number and wall temperature tested showed itself to be exceedingly stable, and did not show any signs of break down to turbulence.</p>

V této diplomové práci je provedena optimalizace profilu křídla vybaveného elastickou klapkou umístěnou na horní straně profilu. Optimalizační proces je proveden s vyžitím CFD prostředků, konkrétně URANS metody. V prvních kapitolách je popsána historie vývoje křídla vybaveného pohyblivými klapkami. Práce pokračuje popisem a zdůvodněním volby numerické metody. Vytvoření geometrie a výpočetní sítě je krátce popsáno. V práci je také prezentována validace a verifikace dané výpočetní metody. Případová studie je zaměřena na profil LS(1)-0417mod vybavený 20%, 30% a 40% dlouhou, pevnou kalpkou na různých úhlech náběhu. Aerodynamická účinnost společně s proudovým polem je analyzována. Je provedena nelineární pevnostní analýza s využitím MKP programu za účelem vyhodnocení ohybové tuhosti a deformovaného tvaru elastické klapky tak, aby byly splněný podmínky nutné pro automatické vychýlení.