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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. 

Direct numerical simulations of turbulent boundary layers with a nominal free-stream Mach number of $6$ and a Reynolds number of $Re_{\unicode[STIX]{x1D70F}}\approx 450$ are conducted at a wall-to-recovery temperature ratio of $T_{w}/T_{r}=0.25$ and compared with a previous database for $T_{w}/T_{r}=0.76$ in order to investigate pressure fluctuations and their dependence on wall temperature. The wall-temperature dependence of widely used velocity and temperature scaling laws for high-speed turbulent boundary layers is consistent with previous studies. The near-wall pressure-fluctuation intensities are dramatically modified by wall-temperature conditions. At different wall temperatures, the variation of pressure-fluctuation intensities as a function of wall-normal distance is dramatically modified in the near-wall region but remains almost intact away from the wall. Wall cooling also has a strong effect on the frequency spectrum of wall-pressure fluctuations, resulting in a higher dominant frequency and a sharper spectrum peak with a faster roll-off at both the high- and low-frequency ends. The effect of wall cooling on the free-stream noise spectrum can be largely accounted for by the associated changes in boundary-layer velocity and length scales. The pressure structures within the boundary layer and in the free stream evolve less rapidly as the wall temperature decreases, resulting in an increase in the decorrelation length of coherent pressure structures for the colder-wall case. The pressure structures propagate with similar speeds for both wall temperatures. Due to wall cooling, the generated pressure disturbances undergo less refraction before they are radiated to the free stream, resulting in a slightly steeper radiation wave front in the free stream. Acoustic sources are largely concentrated in the near-wall region; wall cooling most significantly influences the nonlinear (slow) component of the acoustic source term by enhancing dilatational fluctuations in the viscous sublayer while damping vortical fluctuations in the buffer and log layers.