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A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. (English) Zbl 1145.76393
Summary: 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 \(15R\). 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 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 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 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 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 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.

MSC:
76F65 Direct numerical and large eddy simulation of turbulence
76M20 Finite difference methods applied to problems in fluid mechanics
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[1] DOI: 10.1017/S0022112098002419 · Zbl 0941.76510 · doi:10.1017/S0022112098002419
[2] DOI: 10.1017/S0022112000002408 · Zbl 1007.76067 · doi:10.1017/S0022112000002408
[3] DOI: 10.1017/S0022112005008116 · Zbl 1222.76062 · doi:10.1017/S0022112005008116
[4] DOI: 10.1017/S0022112000001385 · Zbl 1004.76037 · doi:10.1017/S0022112000001385
[5] DOI: 10.1017/S0022112004001958 · Zbl 1065.76106 · doi:10.1017/S0022112004001958
[6] DOI: 10.1016/S0045-7930(01)00007-X · Zbl 1008.76034 · doi:10.1016/S0045-7930(01)00007-X
[7] DOI: 10.1017/S0022112004008985 · Zbl 1060.76508 · doi:10.1017/S0022112004008985
[8] DOI: 10.1017/S0022112082001116 · Zbl 0491.76058 · doi:10.1017/S0022112082001116
[9] DOI: 10.1017/S0022112004009796 · Zbl 1061.76503 · doi:10.1017/S0022112004009796
[10] DOI: 10.1017/S0022112003007304 · Zbl 1067.76513 · doi:10.1017/S0022112003007304
[11] DOI: 10.1017/S0022112006008871 · Zbl 1156.76316 · doi:10.1017/S0022112006008871
[12] DOI: 10.1017/S002211207100171X · doi:10.1017/S002211207100171X
[13] DOI: 10.1006/jcph.2002.7138 · Zbl 1178.76260 · doi:10.1006/jcph.2002.7138
[14] DOI: 10.1063/1.869889 · Zbl 1147.76430 · doi:10.1063/1.869889
[15] DOI: 10.1017/S002211209400131X · doi:10.1017/S002211209400131X
[16] DOI: 10.1016/0021-9991(85)90148-2 · Zbl 0582.76038 · doi:10.1016/0021-9991(85)90148-2
[17] DOI: 10.1017/S0022112095001984 · doi:10.1017/S0022112095001984
[18] DOI: 10.1063/1.2162185 · doi:10.1063/1.2162185
[19] Barenblatt, Appl. Mech. Rev. 50 pp 413– (1997)
[20] Hinze, Turbulence. (1975)
[21] DOI: 10.1063/1.869788 · Zbl 1185.76655 · doi:10.1063/1.869788
[22] Bailey, Bull. Am. Phys. Soc. 52 pp 24– (2007)
[23] DOI: 10.1006/jcph.1996.0107 · Zbl 0847.76043 · doi:10.1006/jcph.1996.0107
[24] DOI: 10.1017/S0022112096002479 · Zbl 0875.76444 · doi:10.1017/S0022112096002479
[25] DOI: 10.1063/1.869451 · doi:10.1063/1.869451
[26] DOI: 10.1063/1.869625 · Zbl 1185.76673 · doi:10.1063/1.869625
[27] Satake, In Lecture Notes in Computer Science pp 514– (2000)
[28] DOI: 10.1017/S0022112004008213 · Zbl 1116.76374 · doi:10.1017/S0022112004008213
[29] DOI: 10.1017/S002211208600304X · Zbl 0597.76052 · doi:10.1017/S002211208600304X
[30] DOI: 10.1017/S0022112001004840 · doi:10.1017/S0022112001004840
[31] DOI: 10.1017/S0022112097005715 · Zbl 0901.76047 · doi:10.1017/S0022112097005715
[32] DOI: 10.1063/1.869328 · Zbl 1185.76675 · doi:10.1063/1.869328
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