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Research Papers: Fundamental Issues and Canonical Flows

Vortex Dynamics in the Turbulent Wake of a Single Step Cylinder

[+] Author and Article Information
C. Morton

Department of Mechanical
and Mechatronics Engineering,
University of Waterloo,
200 University Avenue West,
Waterloo, ON, N2L 3G1, Canada
e-mail: cmorton@uwaterloo.ca

S. Yarusevych

Department of Mechanical
and Mechatronics Engineering,
University of Waterloo,
200 University Avenue West,
Waterloo, ON, N2L 3G1, Canada

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 19, 2013; final manuscript received December 2, 2013; published online January 27, 2014. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 136(3), 031204 (Jan 27, 2014) (11 pages) Paper No: FE-13-1174; doi: 10.1115/1.4026196 History: Received March 19, 2013; Revised December 02, 2013

The turbulent wake development of a circular cylinder with a single stepwise discontinuity in diameter was investigated experimentally using flow visualization and two-component Laser Doppler Velocimetry (LDV). A single step cylinder is comprised of two cylinders of different diameters (D and d). Experiments were performed at a Reynolds number (ReD) of 1050 and a diameter ratio (D/d) of two. A combination of hydrogen bubble and laser induced fluorescence techniques allowed visualization of complex vortex dynamics in the near wake. The results show that turbulent vortex shedding from a single step cylinder occurs in three distinct cells of constant shedding frequency. The differences in frequency and strengths between vortices in the cells lead to complex vortex interactions at the cell boundaries. The results demonstrate that vortex splitting, half-loop vortex connections, and direct cross-boundary vortex connections occur near the cell boundaries. A comparative analysis of flow visualizations and velocity measurements is used to characterize the main vortex cells and the attendant vortex interactions, producing a simplified model of vortex dynamics in the step cylinder wake for ReD = 1050 and D/d = 2.

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Figures

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Fig. 1

Single step cylinder geometry

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Fig. 2

Water flume test section setup for wake visualizations in different planes: (a) x–z plane visualization, (b) x–y plane visualization. The dashed white line in each figure marks the location of the hydrogen bubble wire.

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Fig. 3

Hydrogen bubble flow visualization in the wakes of cylindrical geometries: (a) uniform cylinder, (b) single step cylinder. Curled braces are used to identify the approximate extent of the vortex shedding cells.

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Fig. 4

A sequence of hydrogen bubble flow visualization images depicting N-cell development. t* is the number of small cylinder vortex shedding periods. Dashed circles identify some vortex interactions occurring in the wake.

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Fig. 5

Changes in planar vortex shedding patterns along the span of a single step cylinder

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Fig. 6

Hydrogen bubble visualization of a half-loop vortex connection in the S-cell. t* is the number of S-cell shedding periods.

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Fig. 7

Planar visualization of S-cell vortices near the N-S cell boundary at z/D = −0.5. t* is the number of S-cell shedding periods.

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Fig. 8

Planar visualization of N-cell vortex splitting near the N-S cell boundary at z/D = −3. t* is the number of S-cell shedding periods.

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Fig. 9

Hydrogen bubble visualization of vortex splitting in the N-cell. t* is the number of S-cell shedding periods.

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Fig. 10

Planar visualization of N-cell vortex splitting near the N-L cell boundary at z/D = −5.5. t* is the number of S-cell shedding periods.

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Fig. 11

Streamwise velocity spectra in the wake of a single step. Arrows indicate the peaks in the spectra corresponding to the S-cell, N-cell, and L-cell shedding frequencies. All velocity measurements were acquired at x/D = 5 and y/D = 0.75.

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Fig. 12

Velocity spectra at four spanwise: (a) z/D = 4, (b) z/D = −1.0, (c) z/D = −3, (d) z/D = −5, and (e) z/D = −10. All velocity measurements were acquired at x/D = 5 and y/D = 0.75.

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Fig. 13

Variation of the dominant shedding frequency along the span of a single step cylinder. Note, the uncertainty in the dimensionless frequency estimates is accommodated by the size of the data symbols.

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Fig. 14

Reynolds number effect on the ratio of N-cell and L-cell frequencies for a single step cylinder with D/d ≈ 2 [14,15,22]

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Fig. 15

Downwash over the step discontinuity: (a) and (b) LIF visualizations downstream of the step, (c) spanwise velocity signal at x/D = 1.0, y/D = 0, z/D = −1.5, and (d) spectrum of the spanwise velocity fluctuations. t* is the number of S-cell shedding periods. The dashed line in (c) depicts the mean spanwise velocity.

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Fig. 16

Histogram for the duration of the N-cell cycle. The solid line represents a Gaussian fit to the histogram data. t* is the number of small cylinder shedding periods.

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Fig. 17

Spectrograms illustrating temporal variations in the dominant frequency and energy content in the wake of a single step cylinder: (a) z/D = 4, (b) z/D = −1, (c) z/D = −3, (d) z/D = −5, and (e) z/D = −10. Spectrograms are normalized by the variance of the corresponding velocity signal. t* is the number of S-cell shedding periods.

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Fig. 18

A simplified sketch of vortex interactions occurring in the wake of a single step cylinder for ReD = 1050, and D/d = 2. Dashed lines show vortex connections occurring between main vortex filaments.

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