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  1. Direct numerical simulations (DNS) are performed to investigate the spatial evolution of flat-plate zero-pressure-gradient turbulent boundary layers over long streamwise domains ( ${>}300\delta _i$ , with $\delta _i$ the inflow boundary-layer thickness) at three different Mach numbers, $2.5$ , $4.9$ and $10.9$ , with the surface temperatures ranging from quasiadiabatic to highly cooled conditions. The settlement of turbulence statistics into a fully developed equilibrium state of the turbulent boundary layer has been carefully monitored, either based on the satisfaction of the von Kármán integral equation or by comparing runs with different inflow turbulence generation techniques. The generated DNS database is used to characterize the streamwise evolution of multiple important variables in the high-Mach-number, cold-wall regime, including the skin friction, the Reynolds analogy factor, the shape factor, the Reynolds stresses, and the fluctuating wall quantities. The data confirm the validity of many classic and newer compressibility transformations at moderately high Reynolds numbers (up to friction Reynolds number $Re_\tau \approx 1200$ ) and show that, with proper scaling, the sizes of the near-wall streaks and superstructures are insensitive to the Mach number and wall cooling conditions. The strong wall cooling in the hypersonic cold-wall case is found to cause a significant increase in the size of the near-wall turbulence eddies (relative to the boundary-layer thickness), which leads to a reduced-scale separation between the large and small turbulence scales, and in turn to a lack of an outer peak in the spanwise spectra of the streamwise velocity in the logarithmic region. 
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  2. Direct numerical simulations (DNS) of the full-scale axisymmetric nozzle of a Mach 8 wind tunnel are conducted with an emphasis on characterizing the properties of the pressure fluctua- tions induced by the turbulent boundary layer (TBL) along the nozzle wall. The axisymmetric nozzle geometry and the flow conditions of the DNS match those of the Sandia Hypersonic Wind Tunnel at Mach 8. The mean and turbulence statistics of the nozzle-wall boundary layer show good agreement with those predicted by Pate’s correlation and Reynolds Averaged Navier-Stokes (RANS) computations. The wall-pressure intensity, power spectral density, and coherence predicted by DNS show good comparisons with those measured in the same tunnel. The Corcos model is found to deliver good prediction of wall pressure coherence over inter- mediate and high frequencies. The streamwise and spanwise decay constants at Mach 8 are similar to those predicted by DNS and experiments at lower supersonic Mach numbers. 
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