Supersonic turbulent pipe flow at computationally moderate Reynolds numbers

Well-resolved large-eddy simulations (LES) of supersonic turbulent pipe flow at centerline Mach numbers of 1.6 and 1.8 and moderate friction Reynolds numbers of 1000 and 2200 are performed. The present LES of the supersonic pipe flow at friction Reynolds number 2200 is the first in the literature for which no direct numerical simulation (DNS) data are available. The statistics of the lower Reynolds number pipe flow agree quite well with those of the existing DNS by Modesti and Pirozzoli, “Direct numerical simulation of supersonic pipe flow at moderate Reynolds number,” Int. J. Heat Fluid Flow 76, 100–112 (2019), at similar Mach and Reynolds numbers. A distinct low wavenumber k−1 region in the streamwise velocity spectra, appearing due to the presence of large-scale motions (LSM) and very large-scale motions (VLSM), is observed along with a distinct logarithmic region in mean velocity. Other well-known high Reynolds number features such as a bimodal behavior of the premultiplied spectra of streamwise velocity fluctuations and a second outer peak in the Reynolds stresses are seen, which are compared with those found in incompressible pipe flows. A logarithmic variation of azimuthal velocity variance is also observed in a region away from the wall, as predicted by Townsend's attached eddy hypothesis [Townsend, The Structure of Turbulent Shear Flow, 2nd ed. (Cambridge University Press, 1976)].