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Research Papers: Fundamental Issues and Canonical Flows

Characteristics of the Flow Past a Wall-Mounted Finite-Length Square Cylinder at Low Reynolds Number With Varying Boundary Layer Thickness

[+] Author and Article Information
Sachidananda Behera

Department of Mechanical Engineering,
Indian Institute of Technology Kanpur,
Kanpur 208016, India
e-mail: sbehera@iitk.ac.in

Arun K. Saha

Department of Mechanical Engineering,
Indian Institute of Technology Kanpur,
Kanpur 208016, India
e-mail: aksaha@iitk.ac.in

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 25, 2018; final manuscript received January 17, 2019; published online March 4, 2019. Assoc. Editor: Elias Balaras.

J. Fluids Eng 141(6), 061204 (Mar 04, 2019) (17 pages) Paper No: FE-18-1289; doi: 10.1115/1.4042751 History: Received April 25, 2018; Revised January 17, 2019

Direct numerical simulation (DNS) is performed to investigate the modes of shedding of the wake of a wall-mounted finite-length square cylinder with an aspect ratio (AR) of 7 for six different boundary layer thicknesses (0.0–0.30) at a Reynolds number of 250. For all the cases of wall boundary layer considered in this study, two modes of shedding, namely, anti-symmetric and symmetric modes of shedding, were found to coexist in the cylinder wake with symmetric one occurring intermittently for smaller time duration. The phase-averaged flow field revealed that the symmetric modes of shedding occur only during instances when the near wake experiences the maximum strength of upwash/downwash flow. The boundary layer thickness seems to have a significant effect on the area of dominance of both downwash and upwash flow in instantaneous and time-averaged flow field. It is observed that the near-wake topology and the total drag force acting on the cylinder are significantly affected by the bottom-wall boundary layer thickness. The overall drag coefficient is found to decrease with thickening of the wall boundary layer thickness.

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Figures

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Fig. 2

Inlet velocity profile for various cases of boundary layer thickness

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Fig. 1

Orthogonal view of computational domain

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Fig. 3

Grid independence and domain independence: variation of the time-averaged streamwise velocity along the centerline at the midspan of the cylinder for δ/h = 0.1. The domain size of 26d ×19d ×16d was considered for grid independent test.

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Fig. 5

Time-history of transverse component of velocity for boundary layer thickness δ/h = 0.1. Velocities measured at locations, (a) x/d =6.0, y/d =4.2, z/d =0.0 and (b) x/d =10.0, y/d =4.2, z/d =0. The circled zone represents periods of low amplitude fluctuations.

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Fig. 12

Instantaneous contours of (left) anti-symmetrically arranged spanwise vorticity and (right) symmetrically arranged spanwise vorticity on the plane, y/d = 4.0, for δ/h = 0.2. The solid lines indicate positive values and the dashed lines indicate negative values.

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Fig. 13

Instantaneous contours of (left) anti-symmetrically arranged spanwise vorticity and (right) symmetrically arranged spanwise vorticity on the plane, y/d = 6.0, for various cases of boundary layer thickness, δ/h, (a) 0.15, (b) 0.20, and (c) 0.30. The solid lines indicate positive values and the dashed lines indicate negative values.

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Fig. 4

Instantaneous contours of anti-symmetrically arranged spanwise vorticity (ωy) ((a)–(d)) and symmetrically arranged spanwise vorticity ((e)–(h)) on the plane y/d = 3.5 for a boundary layer thickness of δ/h = 0.1. ((a)–(d)) and ((e)–(h)), respectively represents the four time instances which are separated by time Δt = 3.0. The solid-lines indicate positive values and the dashed lines indicate negative values.

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Fig. 11

Instantaneous contours of (left) anti-symmetrically arranged spanwise vorticity and (right) symmetrically arranged spanwise vorticity on the plane, y/d = 1.0, for various cases of boundary layer thickness, δ/h, (a) 0.0, (b) 0.1, and (c) 0.2. The solid lines indicate positive values and the dashed lines indicate negative values.

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Fig. 6

Time-history of simultaneously fluctuating transverse component of velocity for boundary layer thickness δ/h =0.1. Velocities measured at locations x/d = 6.0, y/d = 4.2, and z/d = ±1.25. The circled zone represents periods of low amplitude fluctuations.

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Fig. 7

Isosurfaces of vortical structures (λ2 = −0.25) conforming the anti-symmetric nature of the flow ((a)–(d)) and symmetric nature of the flow ((e)–(h)) for a boundary layer thickness of δ/h = 0.1. ((a)–(d)) and ((e)–(h)), repectively represents the four time instances separated by time Δt = 3.0. The vortical structures are colored with the streamwise velocity magnitude.

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Fig. 8

Contours of the phase-averaged spanwise vorticity component (ωy) during HAF (left) and LAF (right), for δ/h = 0.1 at various horizontal plane: (a) y/d = 0.5, (b) y/d = 3.5, and (c) y/d = 6.5

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Fig. 9

Instantaneous contours of vertical velocity (left) for anti-symmetric mode of shedding and (right) symmetric mode of shedding on the plane, z/d = 0.0, for various cases of boundary layer thickness, δ/h, (a) 0.1, (b) 0.2, and (c) 0.3. The solid lines indicate positive values and the dashed lines indicate negative values.

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Fig. 10

Phase averaged contours of vertical velocity (left) for anti-symmetric mode of shedding and (right) symmetric mode of shedding on the plane, z/d = 0.0, for boundary layer thickness, δ/h = 0.1. The solid lines indicate positive values and the dashed lines indicate negative values.

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Fig. 14

Instantaneous contours of vertical velocity on the plane z/d = 0.0, for various cases of boundary layer thickness δ/h = 0.0, 0.10, 0.15, 0.20, 0.25, and 0.30 in alphabetic order. The solid lines indicate positive values and the dashed lines indicate negative values.

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Fig. 15

Time-averaged streamlines on z/d = 0 plane for various cases of boundary layer thickness: (a) δ/h = 0.0, (b) δ/h = 0.1, (c) δ/h = 0.15, (d) δ/h = 0.2, (e) δ/h = 0.25, and (f) δ/h = 0.3

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Fig. 16

Velocity vector and contour of λ2: (a) δ/h = 0.1 and x/d = 7.0, (b) δ/h = 0.1 and x/d = 10.0, and (c) δ/h = 0.3 and x/d = 10.0

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Fig. 17

Spanwise variation of time-averaged (left) streamwise velocity (right) spanwise velocity on z/d = 0 plane at (a) x/d = 3 (b) x/d = 7, for various boundary layer thickness (δ/h)

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Fig. 18

Variation of the time-averaged sectional drag coefficient along the span of the cylinder for various cases of boundary layer thickness

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