Direct numerical simulation of turbulent pipe flow up to Re_τ=5200

Well-resolved direct numerical simulations (DNSs) of a turbulent pipe flow were conducted at several friction Reynold numbers up to Re_τ=5200. The axial domain has a length  of 10πR, with 12288×1024×5120 grid points in axial, radial, and azimuthal directions, respectively, following standard DNS resolution. We employ the open-source code “OPENPIPE”,  using a Fourier-Galerkin method  in the axial and azimuthal directions, and a central finite difference scheme with a 9-point stencil  in the wall-normal direction. Turbulence statistics have been obtained, and  a clear Reynolds number dependency is documented and  compared with other DNS data  in pipes as well as channels. In particular, the mean pressure is the quantity that found to differ  notably between pipes and channels – linked to the different geometry in the outer wake region.  In addition, the pressure fluctuations in the pipe are higher than that in the channel, but  the difference progressively decreases as Re increases. The inner peak of the axial velocity fluctuation  and the wall-shear stress rms for  the pipe, which is slightly lower than for the channel, continuously increase  with Re_τ as in all other wall flows. Confidence intervals for the the various statistical quantities are also provided to assess  the fidelity of the current data.