Abstract
Fully developed incompressible turbulent pipe flow at bulk-velocity- and pipe-diameter-based Reynolds number ReD=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 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=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 ReD=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 ReD=5300 also agree well with existing data. The gradient of $\overline{u}_{z}$ with respect to 1−r at ReD=44000 is approximately equal to that at ReD=5300 for the region of 1−r > 0.4. For 5300 < ReD < 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 ReD=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 ReD=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.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
320 articles.
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