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

Abstract

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 $\mbox{ln}\overline{u}_{z}^{+}$ with respect to ln(1− r ) + varies with radius except for a narrow region, 70 < (1− r ) + < 120, within which the gradient is approximately 0.149. The gradient of $\overline{u}_{z}^{+}$ with respect to ln{(1− r ) + + a + } at the present relatively low Reynolds number of Re D =44000 is not consistent with the proposition that the mean axial velocity $\overline{u}_{z}^{+}$ is logarithmic with respect to the sum of the wall distance (1− r ) + and an additive constant a + within a mesolayer below 300 wall units. For the standard case of a + =0 within the narrow region from (1− r ) + =50 to 90, the gradient of $\overline{u}_{z}^{+}$ with respect to ln{(1− r ) + + a + } is approximately 2.35. Computational results at the lower Reynolds number Re D =5300 also agree well with existing data. The gradient of $\overline{u}_{z}$ with respect to 1− r at Re D =44000 is approximately equal to that at Re D =5300 for the region of 1− r > 0.4. For 5300 < Re D < 44000, bulk-velocity-normalized mean velocity defect profiles from the present DNS and from previous experiments collapse within the same radial range of 1− r > 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.