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Research Papers: Fundamental Issues and Canonical Flows

Swirling Flow in a Fixed Container: Generation and Attenuation of a Vortex Column

[+] Author and Article Information
A. Nahas, A. Calvo

Grupo de Medios Porosos, Facultad de Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, 1063 Buenos Aires, Argentina

M. Piva1

Grupo de Medios Porosos, Facultad de Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, 1063 Buenos Aires, Argentinampiva@fi.uba.ar

1

Corresponding author.

J. Fluids Eng 132(11), 111204 (Nov 12, 2010) (9 pages) doi:10.1115/1.4002773 History: Received July 29, 2009; Revised October 12, 2010; Published November 12, 2010; Online November 12, 2010

The development of a columnar vortex and its attenuation using radial rods at the bottom boundary of a stationary container are experimentally studied. The fluid motion is achieved combining two independent flows: a global circulation around the cylinder axis and a meridian flow generated by recirculating fluid through a central nozzle located at the vessel bottom. The resulting velocity field is analyzed under two conditions: with and without the meridian or suction flow. It is shown that in the second condition a columnar vortex merges and that its intensity increases when the suction flow rate is increased. The key role played by the bottom boundary layer in the vortex formation is demonstrated. In the last part of the work, the attenuation of the vortex intensity produced by a set of rods located at the vessel bottom is investigated. It is found that obstacles with heights of the order of the boundary layer thickness are enough to produce the total annihilation of the vortex column.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic plan views of the experimental setup

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Figure 2

Mean tangential velocity at the top of the circulation distributor as a function of the circulation flow rate

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Figure 3

The mean tangential velocity vθ is plotted as a function of the radial coordinate, r, for equatorial planes at different heights: squares, z=3 cm; circles, 5 cm; and triangles, 7 cm. The total height of the liquid column is H=10 cm and Q1 increases from (a) to (f).

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Figure 7

Effects on the circulation flow for Q1=1.8 l/mn and H=10 cm due to a low suction flow, Q2. White markers Q2=0, black markers Q2=0.25 l/mn, and triangles and squares correspond to measurements at z=3 and 7 cm, respectively. The dotted line represents a rigid rotation profile.

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Figure 8

Tangential velocity profiles for z=5 cm, H=10 cm, Q1=1 l/mn, and several values of Q2. Markers are ◻: Q2=0.25 l/mn; ○: 0.3 l/mn; △: 0.35 l/mn; ▽: 0.4 l/mn; ◇: 0.45 l/mn; +: 0.5 l/mn; ×: 0.5 l/mn; and ∗: 0.7 l/mn. Dotted line: rigid rotation profile with Ωp=0.271/s.

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Figure 16

Flow circulation intensity, Γ as a function of the effective flow rate, Q2∗; (a) N=6 and (b) N=12 rods. Markers are ○: hr=1.5 mm; △: hr=2.5 mm; ▽: hr=3 mm; and ◇: hr=4.5 mm. The straight line corresponds to hr=0.

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Figure 12

Flow circulation intensity Γ obtained by fitting the experimental profiles of vθ with Eq. 1 as a function of the effective suction flow rate, Q2∗

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Figure 11

Tangential velocity profiles for z=5 cm, H=10 cm, Q1=1 l/mn, and several values of Q2. Markers are ◻: Q2=0.4 l/mn; ◇: 0.45 l/mn; +: 0.5 l/mn; ×: 0.55 l/mn; and ∗: 0.6 l/mn. Solid lines: data fittings with Eq. 1.

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Figure 10

Snapshots of equatorial planes visualized by laser-sheet illumination of fluorescent dye. Parameters are H=10 cm, Q1=1 l/mn, and Q2=0.55 l/mn. (a) z=5 cm and (b) z=0.1 cm.

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Figure 9

Snapshot of a meridian plane for Q1=1 l/mn and Q2=1 l/mn. The columnar vortex appears as a thin column of dyed fluid at the center of the image. The imposed strong suction produces a pronounced deflection of the free surface clearly visible at the top of the figure. The arrows show the direction of the meridian flow in different zones. Close to the bottom wall the flow is radially inward and confined to the boundary layer. As it approaches the vortex location, the radial flow is deflected upward and then enters the vortex core. The localized axial downward flow inside the vortex drives the fluid outside the vessel.

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Figure 6

Maximum mean value of the tangential velocity as a function of the circulation imposed to the system for different heights of the liquid column: squares, H=20 cm; circles, H=15 cm; and triangles, H=10 cm. Straight lines correspond to the variation predicted by Eq. 7.

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Figure 5

Tangential velocity normalized with its maximum mean value as a function of the radial position. Dashed line: first term of Eq. 1 (rigid rotation contribution). Solid line: data fitting with Eqs. 1,2. (a) H/R1>1, Rp=0.9R1, a=0.09 cm−1, b=0, and c=−0.002 cm−3 and (b) H/R1<1, Rp=R1, a=0.13 cm−1, b=0, and c=−0.002 cm−3. The radius Rp is defined in Sec. 3.

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Figure 4

Snapshots of meridian planes using fluorescent dye for Q1=1 l/mn and Q2=0. The sequence shows the evolution of a pulse of dye entering the test volume with tangential velocity through the bottom of the container in the zone R1<R<R2: (a) t=5 s, (b) t=7 s, (c) t=9 s, and (d) t=11 s after dye injection.

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Figure 13

Sketch of the rod configuration at the bottom boundary

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Figure 14

Tangential velocity profiles with six radial rods at the bottom plate for z=5 cm, Q1=1 l/mn, Q2=0.5 l/mn, and H=10 cm. Continuous line: unperturbed flow (hr=0); ◻: hr=0.5 mm; ○: hr=1.5 mm; △: hr=2.5 mm; ▽: hr=3 mm; and ◇: hr=4.5 mm.

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Figure 15

Tangential velocity profiles with 12 radial rods at the bottom plate for z=5 cm; Q1=1 l/mn, Q2=0.5 l/mn, and H=10 cm. Continuous line: unperturbed flow (hr=0); ◻: hr=0.5 mm; ○: hr=1.5 mm; △: hr=2.5 mm; ▽: hr=3 mm; and ◇: hr=4.5 mm.

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