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We study compressible turbulent flow in a circular pipe, at computationallyhigh Reynolds number. Classical related issues are addressed and discussed inlight of the DNS data, including validity of compressibility transformations,velocity/temperature relations, passive scalar statistics, and size ofturbulent eddies.Regarding velocity statistics, we find that Huang'stransformation yields excellent universality of the scaled Reynolds stressesdistributions, whereas the transformation proposed by Trettel and Larsson(2016) yields better representation of the effects of strong variation ofdensity and viscosity occurring in the buffer layer on the mean velocitydistribution. A clear logarithmic layer is recovered in terms of transformedvelocity and wall distance coordinates at the higher Reynolds number underscrutiny ($\Rey_{\tau} \approx 1000$), whereas the core part of the flow isfound to be characterized by a universal parabolic velocity profile. Based onformal similarity between the streamwise velocity and the passive scalartransport equations, we further propose an extension of the abovecompressibility transformations to also achieve universality of passive scalarstatistics. Analysis of the velocity/temperature relationship provides evidencefor quadratic dependence which is very well approximated by the thermal analogyproposed by Zhang et Al.(2014). The azimuthal velocity and scalar spectra showan organization very similar to canonical incompressible flow, with abump-shaped distribution across the flow scales, whose peak increases with thewall distance. We find that the size growth effect is well accounted forthrough an effective length scale accounting for the local friction velocityand for the local mean shear.

Direct numerical simulation of supersonic pipe flow at moderate Reynolds number