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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.