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Research Papers: Fundamental Issues and Canonical Flows

Effect of Corner Radius in Stabilizing the Low-Re Flow Past a Cylinder

[+] Author and Article Information
Wei Zhang

Faculty of Mechanical Engineering
and Automation,
Zhejiang Sci-Tech University,
Hangzhou, Zhejiang 310018, China
e-mail: zhangwei@zstu.edu.cn

Ravi Samtaney

Mechanical Engineering,
King Abdullah University of Science
and Technology,
4700 KAUST,
Thuwal 23955-6900, Saudi Arabia
e-mail: ravi.samtaney@kaust.edu.sa

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 5, 2017; final manuscript received July 16, 2017; published online September 1, 2017. Assoc. Editor: Satoshi Watanabe.

J. Fluids Eng 139(12), 121202 (Sep 01, 2017) (11 pages) Paper No: FE-17-1078; doi: 10.1115/1.4037494 History: Received February 05, 2017; Revised July 16, 2017

We perform global linear stability analysis on low-Re flow past an isolated cylinder with rounded corners. The objective of the present work is to investigate the effect of cylinder geometry (corner radius) on the stability characteristics of the flow. Our investigation sheds light on new physics that the flow can be stabilized by partially rounding the cylinder in the critical and weakly supercritical flow regimes. The flow is first stabilized and then gradually destabilized as the cylinder varies from square to circular geometry. The sensitivity analysis reveals that the variation of stability is attributed to the different spatial variation trends of the backflow velocity in the near- and far-wake regions for various cylinder geometries. The results from the stability analysis are also verified with those of the direct simulations, and very good agreement is achieved.

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Figures

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Fig. 1

Left: schematic of physical domain, cylinder geometry, and coordinate system. Right: enlarged view of a typical mesh with every fourth gridline shown in each direction for clarity.

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Fig. 2

Contour of the eigenfunction at Re = 47.0 and R+ = 0.30. Real part of (a) streamwise velocity Re(û) and (b) transverse velocity Re(v̂).

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Fig. 3

Growth rate sensitivity to base flow modification ∇Uσ of the unstable mode at Reynolds number slightly above the critical value: (a) R+ = 0.00, Re = 44.9; (b) R+ = 0.10, Re = 46.2; (c) R+ = 0.20, Re = 46.8; (d) R+ = 0.30, Re = 47.0; (e) R+ = 0.40, Re = 46.9; and (f) R+ = 0.50, Re = 46.6. The magnitude of ∇Uσ is visualized by the contour and its orientation by arrows.

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Fig. 4

Distribution of streamwise velocity of base flow along the wake centerline

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Fig. 5

Fitting of Lr with corner radius as the function Lr/D = kexp(−R+/c) + b. The hollow symbols are the computed results, and the dashed lines are the fitting curves.

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Fig. 6

Dependency of growth rate on Reynolds number and corner radius with respect to that of the square cylinder case Δσ=σ−σR+=0.00, the latter is listed in the figure; the plus symbol marks the minimum value. The Reynolds number increases in the direction of the arrow.

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Fig. 7

Eigenfunction Re(û) at R+ = 0.50

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Fig. 8

Eigenfunction Re(û) at Re = 80

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Fig. 9

Growth rate sensitivity to base flow modification ∇Uσ of the unstable mode at Re = 50: (from (a) to (f)) R+ = 0.00, 0.10, 0.20, 0.26, 0.40, 0.50. The magnitude of ∇Uσ is visualized by the contour and its orientation by arrows.

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Fig. 10

Distribution of streamwise velocity of base flow along the wake centerline

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Fig. 11

Temporal growth of perturbed transverse velocity |v−V|/U0 at Re = 50 for the 2D direct simulation: (a) growth history of perturbation probed at different locations on the wake centerline; the dashed lines approximate the local maxima in each curve and (b) temporal history of local maxima for different corner radii; the dashed lines are the linear fitting curves

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