A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow

Fully developed incompressible turbulent pipe flow at bulk-velocity- and pipe-diameter-based Reynolds number Re D =44000 was simulated with second-order finite-difference methods on 630 million grid points. The corresponding Kármán number R +, based on pipe radius R, is 1142, and the computational domain length is 15 R. The computed mean flow statistics agree well with Princeton Superpipe data at Re D =41727 and at Re D =74000. Second-order turbulence statistics show good agreement with experimental data at Re D =38000. Near the wall the gradient of lnuₙ^+ with respect to ln (1− r) + varies with radius except for a narrow region, 70 0. 4. For 5300 0. 4. A rationale based on the curvature of mean velocity gradient profile is proposed to understand the perplexing existence of logarithmic mean velocity profile in very-low-Reynolds-number pipe flows. Beyond Re D =44000, axial turbulence intensity varies linearly with radius within the range of 0. 15 < 1− r < 0. 7. Flow visualizations and two-point correlations reveal large-scale structures with comparable near-wall azimuthal dimensions at Re D =44000 and 5300 when measured in wall units. When normalized in outer units, streamwise coherence and azimuthal dimension of the large-scale structures in the pipe core away from the wall are also comparable at these two Reynolds numbers.