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

Fully developed incompressible turbulent pipe flow at bulk-velocity- and pipediameter-based Reynolds number ReD=44000 was simulated with second-order finite-difference methods on 630 million grid points. The corresponding KArmAn number R+, based on pipe radius R, is 1142, and the computational domain length is 15R. The computed mean flow statistics agree well with Princeton Superpipe data at ReD=41727 and at ReD=74000. Second-order turbulence statistics show good agreement with experimental data at ReD = 38 000. Near the wall the gradient of Inu+ with respect to In(I - r)+ varies with radius except for a narrow region, Z 70 < (1 - r)+ < 120, within which the gradient is approximately 0. 149. The gradient of u+ with respect to In j(1 - r)+ + a+j at the present relatively low Reynolds number Z of ReD = 44 000 is not consistent with the proposition that the mean axial velocity !i+ is logarithmic with respect to the sum of the wall distance (1 - r)+ and an z additive constant a+ within a mesolayer below 300 wall units. For the standard case of a+ = 0 within the narrow region from (I - r)+ = 50 to 90, the gradient of 7iz+ with respect to In (] - r)+ + a+ is approximately 2.35. Computational results at the lower Reynolds number ReD = 5300 also agree well with existing data. The gradient of uz with respect to 1 - r at ReD = 44 000 is approximately equal to that at ReD = 5300 for the region of I - r > 0.4. For 5300 < ReD < 44 000, bulk-velocity-normalized mean velocity defect profiles from the present DNS and from previous experiments collapse within the same radial range of I - 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 = 44 000, axial turbulence intensity varies linearly with radius within the range of 0. 15 < I - r < 0. 7. Flow visualizations and two-point correlations reveal large-scale structures with comparable near-wall azimuthal dimensions at ReD = 44 000 and 5300 when measured in wall units. When normalized in outer units, strearnwise 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.