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Research Papers: Fundamental Issues and Canonical Flows

Effects of System Rotation on Vortical Structure in Wall Turbulence

[+] Author and Article Information
Oaki Iida

Department of Mechanical Engineering,
Nagoya Institute of Technology,
Gokiso-cho, Showa-ku,
Nagoya 466-8555, Japan
e-mail: iida.oaki@nitech.ac.jp

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 24, 2014; final manuscript received June 23, 2014; published online September 10, 2014. Assoc. Editor: Sharath S. Girimaji.

J. Fluids Eng 137(2), 021201 (Sep 10, 2014) (10 pages) Paper No: FE-14-1147; doi: 10.1115/1.4027953 History: Received March 24, 2014; Revised June 23, 2014

Direct numerical simulations (DNSs) of rotating turbulent Poiseuille flows are performed to study the effects of both cyclonic and anticyclonic system rotation on the kinematics of the quasi-streamwise vortices. By using the second invariant of the deformation tensor, a number of streamwise vortices are detected and averaged in the wall vicinity where the intense sweep motion, i.e., the inrush motion of high-speed fluid toward the wall, is related to the quasi-streamwise vortices. The effects of the system rotation on the angle of vortex axis are clearly observed as studied in longitudinal vortices of the homogeneous shear flow. Moreover, by calculating the probability of the emergence of the counterclockwise vortices (CCVs) around a clockwise vortex (CV), we find that with increase in the anticyclonic system rotation, the probability increases and decreases in the ejection and sweep sides of a CV, respectively. In contrast, cyclonic system rotation attenuates CCVs in both sides of a CV, though it increases at the top of the CV. This distribution of CCVs is found to affect sweep motion related to the quasi-streamwise vortices.

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Figures

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Fig. 1

Flow geometry and coordinate system

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Fig. 2

Grid resolution of a part of computational region with 16 × 65 × 9 grids points in the x-, y- and z-directions, respectively: Sides of the box, nondimensionalized by ν ad uτ* are 129.6, 120, and 58.5, respectively.

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Fig. 3

Statistical turbulent structure: (a) mean velocity profiles for all cases and (b) distributions of Reynolds shear stress and total stress for all cases. In Fig. (a), slope of tangent line to mean velocity profile is set to 2Ω.

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Fig. 4

Streamwise energy spectra E11 and E22 for case re70ro025: (a) energy spectra at y = 10 on suction side and (b) energy spectra at y = 10 on pressure side. Both E11 and E22 are functions of streamwise wavenumber kx, and their summations over all kx result in the Reynolds stresses u2¯ and v2¯, respectively.

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Fig. 5

Instantaneous distribution of longitudinal vortical structures represented by isosurfaces of II colored by red and blue, and low-speed streaks colored by green for Figs. 5(a)5(d), while in Fig. 5(e) detected vortex cores are visualized. All figures are viewed from the channel center, and hence the coordinate system is different between pressure and suction sides. Red and blue colors on vortical structures represent the positive and negative streamwise vorticity of the isosurfaces, respectively; (a) case re60ro025, II = 0.01, u = −3, (b) case re60ro15, II = 0.01, u = −3, (c) case re70ro025, II = 0.002, u = −3, (d) case re70ro05, II = 0.002, u = −3, and (e) detected vortex cores in case re60ro025.

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Fig. 6

Pdfs of streamwise length of longitudinal vortical structures: (a) cases re60ro025, re60ro15 and re60ro30 and (b) cases re70ro025 and re70ro05. Pdfs are plotted every 30ν/ur.

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Fig. 7

Pdfs of tilting angle: (a) case re60ro0, (b) case re60ro025, (c) case re60ro15, (d) case re60ro30, (e) case re70ro025, and (f) case re70ro05

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Fig. 8

Averaged velocity vectors u2˜×u3˜ and streamwise vorticity ω1˜ in cross streamwise plane: (a) case re60ro0, (b) case re60ro025, (c) case re60ro15, and (d) case re70ro05. Contour interval of streamwise vorticity is 0.05 for (a), (b), and (c), while it is 0.025 for (d). In all cases, red and blue colors of the contour represent positive and negative values, respectively, while green represents zero.

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Fig. 9

Pdfs of Y-Z location of CCVs around a detected CV: (a) case re60ro0, (b) case re60ro025, (c) case re60ro15, and (d) case re60ro30. Both colored shading and height represent the pdfs of CCVs, while contour lines, representing the streamwise vorticity, are same as those in Fig. 8.

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Fig. 10

Isosurfaces of averaged streamwise vorticity ω1˜ in X-Y plane: (a) case re60ro0, (b) case re60ro025, (c) case re60ro15, and (d) case re70ro05. Isosurface of ω1˜ is 0.15 for (a)–(c), while it is 0.08 for (d).

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Fig. 11

Isosurfaces of averaged streamwise vorticity ω1˜, contours of the Reynolds shear stress -u1u2˜ at Y = 10 in X-Z plane (contours begin from 0.4 and their interval is also 0.4; red contours are sweep, while blue contours are ejection). Shading contour represents vertical velocity: (a) case re60ro0, (b) case re60ro025, (c) case re60ro15, and (d) case re70ro05. Isosurface of ω1˜ is 0.15 for (a)–(c), while it is 0.08 for (d).

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Fig. 12

Segment for detecting the sweep related to the CV

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Fig. 13

Isosurfaces of averaged streamwise vorticity ω1˜ = 0.15 and contours of the averaged Reynolds shear stress -u1u2˜ at Y = 10 in case re60ro025 (contour begins from 0.4 and its interval is also 0.4; red contours are sweep, while blue contours are ejection). Shading contour represents the vertical velocity: (a) vortical structure accompanied by smaller sweep than its averaged value at Y = 10 and (b) vortical structure accompanied by larger sweep than its averaged value at Y = 10.

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Fig. 14

Averaged velocity vectors u2˜×u3˜ and contours of averaged streamwise vorticity ω1˜ in cross streamwise plane of case re60ro025; (a) and (b) are the same cases with those of Fig.13. Contour interval of streamwise vorticity is 0.05. In all cases, red and blue colors represent positive and negative values, respectively, while green represents zero.

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