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Research Papers: Fundamental Issues and Canonical Flows

Linear Shear Flow Past a Rotating Elliptic Cylinder

[+] Author and Article Information
Sandeep N. Naik

Fluid Mechanics Laboratory,
Department of Applied Mechanics,
Indian Institute of Technology Madras,
Chennai 600036, Tamil Nadu, India

S. Vengadesan

Professor
Department of Applied Mechanics,
Indian Institute of Technology Madras,
Chennai 600036, Tamil Nadu, India
e-mail: vengades@iitm.ac.in

K. Arul Prakash

Department of Applied Mechanics,
Indian Institute of Technology Madras,
Chennai 600036, Tamil Nadu, India

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 3, 2017; final manuscript received May 18, 2018; published online June 26, 2018. Assoc. Editor: Samuel Paolucci.

J. Fluids Eng 140(12), 121202 (Jun 26, 2018) (10 pages) Paper No: FE-17-1634; doi: 10.1115/1.4040365 History: Received October 03, 2017; Revised May 18, 2018

Simulations are carried out for linear shear flow past a rotating elliptic cylinder to investigate the effect of shear flow on hovering vortex. An in-house fluid solver that is based on immersed boundary method (IBM) is used to study the flow features and variation in aerodynamic forces. The simulations are carried out for various nondimensional rotation rates, axis ratio (AR) of the cylinder, and shear parameter. In shear flow past rotating elliptic cylinder, the negative vortices are sustained for longer distances in the downstream of the cylinder, and due to the velocity gradient, the sequence of the vortex street changes. It also has significant effect on the formation and composition of hovering vortex. To capture these features, each vortex is tracked as they form, detach, and move in the wake of the cylinder. Hovering vortex, formed due to coalescing of multiple vortices near the cylinder, is subdued for smaller rotation rates at moderate shear. It is also observed that lift forces increase linearly with shear, while the frequency of shedding shows no dependency on shear parameter.

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References

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Figures

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Fig. 1

Computational domain with boundary conditions

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Fig. 2

Vorticity contours corresponding to the instant of maximum ((a) and (b)) and minimum ((c) and (d)) lift force for one cycle at Re = 100, α = 0, and G = 0.1. ((a) and (c)) are from Kang [5] and ((b) and (d)) are from present simulations.

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Fig. 3

Instantaneous vorticity contours for different ARs at G = 0.1 and 0.15

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Fig. 4

Phase plot for G = 0.1 and different ARs

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Fig. 5

Nomenclature associated with the elliptic cylinder. LE: Leading edge (rotates into the flow), TE (rotates away from the flow), LEV, TEV, a—major axis, b—minor axis.

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Fig. 6

Instantaneous λ2 contours for one rotation of the elliptic cylinder for AR = 0.1, α = 1.0 at G = 0 and 0.1. Encircled region shows LEV (–ve) and TEV (+ve) as they form and detach from LE and TE, respectively.

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Fig. 7

Formation of hovering vortex as LE rotates from β ≈ 60 deg to 140 deg. AR = 0.1 and α = 1.5 at G = 0. (a)–(e) denotes the first half rotation and (f)–(j) denotes the second half rotation. Legend is same as in Fig. 6.

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Fig. 8

Trajectories of vortices shed during one cycle for different rotation rates at AR = 0.1 and G = 0. (a) α = 0.5, (b) α = 1.0, and (c) α = 1.5. Zoomed-in view of trajectories in the rectangular region is shown as insets for selective cases. The circles denote the path traced by the tips of the elliptic cylinder as it rotates.

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Fig. 9

Trajectories of vortices shed during one cycle for α = 0.5 and 1.0 at AR = 0.1 and G = 0.1. (a) α = 0.5 and (b) α = 1.0. Magnified view of LEV trajectories in the rectangular region is shown as insets for clarity purpose. The circles denote the path traced by the tips of the elliptic cylinder as it rotates.

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Fig. 10

Trajectories of vortices shed during one cycle for AR = 0.5 and α = 1.0 for different G. (a) G = 0 and (b) G = 0.1. Magnified view of LEV trajectories in the rectangular region is shown as insets for clarity purpose. The circles denote the path traced by the tips of the elliptic cylinder as it rotates.

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Fig. 11

Variation of lift coefficient for AR = 0.1, α = 1.0 for G = 0 (red) and 0.1 (blue). Encircled region shows the difference in maximum lift force for the two cases.

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Fig. 12

Fast Fourier transform (FFT) of CL for different ARs, α and G. Red: α = 0.5; Green: α = 1.0 and Blue: α = 1.5: AR = 0.1: (a)–(c), AR = 0.5: (d)–(f) and AR = 1.0: (g)–(i).

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