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Research Papers: Fundamental Issues and Canonical Flows

Relaxation of Spatially Advancing Coherent Structures in a Turbulent Curved Channel Flow

[+] Author and Article Information
Koji Matsubara

e-mail: matsu@eng.niigata-u.ac.jp

Tomoya Ohishi

Department of Mechanical and Production
Engineering,
Niigata University,
Ikarashi 2-nocho 8050,
Nishi-ku, Niigata 950-2181, Japan

Keisuke Shida

Sorimachi Giken Co., Ltd.,
Misono 2-2-34, Nagaoka,
Niigata 940-0866, Japan

Takahiro Miura

Tonetsu Corporation,
Kakemama 2-28-25, Ichikawa,
Chiba 272-0142, Japan

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the Journal of Fluids Engineering. Manuscript received September 6, 2012; final manuscript received May 12, 2013; published online July 22, 2013. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 135(9), 091202 (Jul 22, 2013) (9 pages) Paper No: FE-12-1433; doi: 10.1115/1.4024591 History: Received September 06, 2012; Revised May 12, 2013

A direct numerical simulation is made for the incompressible turbulent flow in the 180 deg curved channel with a long straight portion connected to its exit port. An examination is made for how the organized coherent vortex grows and decays in the curved channel: the radius ratio of 0.92, the aspect ratio of 7.2, and the succeeding straight section length of 75 times the channel half width. The 1552 × 91 × 128 ( = 18,427,136) grids are allocated to the computational domain. The frictional-velocity-based Reynolds number is kept at 150 to resolve the long domain including curved and straight regions. In contrast to that the coherent vortex grows along the concave wall, the vortex remains strong in the convex-wall side after the curvature accompanying a tail of the small-scale turbulence near the convex wall. The dissimilarity between the onset and disappearing of the coherent vortex essentially comes from the mean pressure gradient, which aids or averts the near-wall fluid oppositely between the curvature inlet and the exit. The mean flow is decelerated near the inlet of the convex wall to destabilize the flow and to trigger the onset of the coherent vortex. Contrary, the mean flow is accelerated near the exit of the convex wall to weaken the coherent vortex, and is decelerated near the exit of the concave wall to enhance the turbulence. Therefore, the turbulence enhancement and attenuation occurs oppositely between the inlet and exit of the curvature, and the coherent vortex draws a wake in the convex-side rather than the concave-side where it starts.

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Figures

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Fig. 1

Computational domain (case 1). (a) Computational domain and coordinate system, and (b) grid mesh (grid number reduced to 1/8 in each direction for presentation).

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Fig. 2

Mean velocity distribution (case 1). (a) Straight part, (b) ϕ = 45 deg, and (c) ϕ = 135 deg.

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Fig. 3

Friction coefficient (case 1)

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Fig. 4

Contour of mean streamwise velocity, U¯/Um (case 1)

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Fig. 5

Contour of mean pressure, (P¯-Pref)/ρUm2 (case 1)

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Fig. 6

Contour of streamwise velocity fluctuation intensity, urms/Um (case 1)

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Fig. 7

Contour of radial velocity fluctuation intensity, υrms/Um (case 1)

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Fig. 8

Contour of spanwise velocity fluctuation intensity, wrms/Um (case 1)

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Fig. 9

Vectors of time-mean velocity on cross-sectional plane and contour of temperature, (⟨T⟩-TC)/(TH-TC) (case 1). (a) Straight, (b) ϕ = 15 deg, (c) ϕ = 75 deg, (d) ϕ = 135 deg, (e) ϕ = 180 deg, (f) (x−πrm)/δ = 5, (g) (x−πrm)/δ = 15, (h) (x−πrm)/δ = 35, (i) (x−πrm)/δ = 55, and (j) (x−πrm)/δ = 75.

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Fig. 10

Contour of preintensified power spectrum for radial velocity, kzEvvz/Um2 (case 1). (a) Straight, (b) ϕ = 15 deg, (c) ϕ = 75 deg, (d) ϕ = 135 deg, (e) ϕ = 180 deg, (f) (x−πrm)/δ = 5, (g) (x−πrm)/δ = 15, (h) (x−πrm)/δ = 35, (i) (x−πrm)/δ = 55, and (j) (x−πrm)/δ = 75.

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Fig. 11

Isosurface of preintensified power spectrum for radial velocity, kzEvvz/Um2 (case 1). (a) The bird-eye view, (b) the view from the concave-wall side, and (c) the view from the wave-length axis.

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Fig. 12

Isosurface of second invariant for deformation tensor and radial velocity (case 1). (a) x/δ = –4 to ϕ = 30 deg, (b) ϕ = 60 deg to 120 deg, and (c) ϕ = 150 deg to (xπrm)/δ = 12.

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