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Research Papers: Multiphase Flows

Liquid Turbulence Kinetic Energy Budget of Co-Current Bubbly Flow in a Large Diameter Vertical Pipe

[+] Author and Article Information
M. E. Shawkat

Fuel and Fuel Channel Safety Analysis, AMEC Nuclear Safety Solutions Ltd., 700 University Ave., Toronto, Ontario M5G1X6, Canada

C. Y. Ching1

Dept. of Mechanical Engineering,  McMaster University, 1280 Main St. West, Hamilton, Ontario L8S4L7, Canadachingcy@mcmaster.ca

1

Corresponding author.

J. Fluids Eng 133(9), 091303 (Sep 15, 2011) (14 pages) doi:10.1115/1.4003855 History: Received October 14, 2010; Revised March 14, 2011; Published September 15, 2011; Online September 15, 2011

The liquid turbulence kinetic energy transfer between the liquid and gas phases was investigated for upward air-water bubbly flow in a 200 mm diameter pipe. The liquid and gas axial momentum equations were analyzed to estimate the interfacial drag from experimental measurements, and hence the liquid turbulence production due to the relative velocity of the bubbles. The liquid turbulence production due to the bubbles was significantly higher than that due to the liquid shear. The liquid turbulence kinetic energy budget indicates that the turbulence production due to the bubbles is approximately balanced by the viscous dissipation, estimated assuming an isotropic turbulence structure, with negligible dissipation due to the bubbles. The liquid turbulence kinetic energy spectra showed an addition of energy at length scales in the range corresponding to the bubble diameter. A model for the turbulence energy production spectra due to the bubbles is proposed and used to investigate the spectral turbulence energy budget. The model indicates that when there is a liquid turbulence augmentation, most of the production occurs in the low wave number range with only a small overlap with the viscous dissipation region. In the case of a turbulence suppression, most of the bubble production occurs in the same wave number range as the viscous dissipation.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of experimental test facility

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Figure 2

Radial distribution of the void fraction and the bubble diameter at Jf (a and c) 0.2 m/s and (b and d) 0.68 m/s for Jg of (*, 0.005 m/s; +, 0.015 m/s; ⋆, 0.03 m/s; ×, 0.05 m/s; ▿ 0.065 m/s; □ 0.085 m/s; ▵ 0.1 m/s; and ⋄ 0.18 m/s)

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Figure 3

Radial distribution of (a and b) axial turbulent velocity, (c and d) radial turbulent velocity, and (e and f) Reynolds stress at Jf of 0.2 and 0.68 m/s for Jg of (◯, 0.0 m/s; *, 0.005 m/s; +, 0.015 m/s; ⋆, 0.03 m/s; ×, 0.05 m/s; ▿ 0.065 m/s; □ 0.085 m/s; ▵ 0.1 m/s; and ⋄ 0.18 m/s)

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Figure 4

The induced axial turbulent velocity versus the void fraction at different r/R from Eq. (5) and Jf of (*, 0.2 m/s; +, 0.26 m/s; ×, 0.35 m/s; □ 0.45 m/s; ▵ 0.58 m/s; and ⋄ 0.68 m/s)

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Figure 5

Radial distribution of the liquid turbulence production by the shear stress, -(1-α)u'v'¯dU/dr, at Jf (a) 0.2 m/s and (b) 0.68 m/s for Jg of (◯, 0.0 m/s; *, 0.005 m/s; +, 0.015 m/s; ×, 0.05 m/s; □ 0.085 m/s; ▵, 0.1 m/s; and ⋄ 0.18 m/s)

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Figure 6

Radial distribution of the liquid turbulence production due to the bubbles at Jf (a) 0.2 m/s and (b) 0.68 m/s for Jg of (*, 0.005 m/s; +, 0.015 m/s; ×, 0.05 m/s; □ 0.085 m/s; ▵ 0.1 m/s; and ⋄ 0.18 m/s)

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Figure 7

Radial distribution of the components of the turbulence energy budget at different flow conditions, where (*,-ɛL,×PrL ; ▵ diffusion terms; ⋄ Prb ; and ◯, -ɛb)

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Figure 8

Axial turbulence energy spectra at r/R = 0 and 0.95 at different Jf on a semi-log scale for Jg of (◯, 0.0 m/s; *, 0.005 m/s; +, 0.015 m/s; ▵ 0.1 m/s; and ⋄ 0.18 m/s)

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Figure 9

Radial turbulence energy spectra at r/R= 0 and 0.95 at different Jf on a semi-log scale for Jg of (◯, 0.0 m/s; *, 0.005 m/s; +, 0.015 m/s; ▵ 0.1 m/s; and ⋄ 0.18 m/s)

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Figure 10

The normalized axial turbulence kinetic energy spectra for data of (a) Michiyoshi and Serizawa [9] (Dpipe = 60 mm) at r/R of (+, 0.0 and □ 0.9) and (b) Wang [19] (Dpipe = 57.15 mm) at Jg of (◯, 0.0 m/s; *, 0.1 m/s; ▵ 0.4 m/s) on a semi-log scale

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Figure 11

A schematic of the proposed interaction between the bubbles and liquid turbulence eddies of comparable size

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Figure 12

Spectral distribution of ◯ stretching term and □ displacement term of ⋄ Prb(k1) as given by Eq. (29) for different flow conditions at (a and c) r/R= 0.0 and (b and d) r/R= 0.95

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Figure 13

Spectral energy budget as the pipe wall is approached for (a and b) Jf= 0.68 m/s -Jg= 0.18 m/s and (c and d) Jf= 0.68 m/s - Jg= 0.015 m/s, where (⋄, Prb(k1); ◯, ɛL(k1); and *, Tb(k1))

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