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Research Papers: Multiphase Flows

Study of Pressure Wave Propagation in a Two-Phase Bubbly Mixture

[+] Author and Article Information
Reni Raju1

Dynaflow, Inc., 10621-J Iron Bridge Road, Jessup, MDreni@dynaflow-inc.com

Sowmitra Singh, Chao-Tsung Hsiao, Georges Chahine

Dynaflow, Inc., 10621-J Iron Bridge Road, Jessup, MD

1

Corresponding author.

J. Fluids Eng 133(12), 121302 (Dec 20, 2011) (12 pages) doi:10.1115/1.4005263 History: Received February 18, 2011; Accepted September 30, 2011; Published December 20, 2011; Online December 20, 2011

(1) Background. Bubbly flows are used in a wide variety of applications and require accurate modeling. In this paper, three modeling approaches are investigated using the geometrically simple configuration of a gas bubble strongly oscillating in a bubbly medium. (2) Method of approach. A coupled Eulerian-Lagrangian, a multicomponent compressible, and an analytical approach are compared for different void fractions. (3) Results. While the homogeneous mixture models (analytical and multicomponent) compare well with each other, the Eulerian-Lagrangian model captures additional features and inhomogeneities. The discrete bubbles appear to introduce localized perturbations in the void fraction and the pressure distributions not captured by homogeneous mixture models. (4) Conclusions. The bubbly mixture impedes the growth and collapse of the primary bubble while wavy patterns in the velocity, pressure, and void fraction fields propagate in space and time.

Copyright © 2011 by American Society of Mechanical Engineers
Topics: Pressure , Bubbles , Porosity
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Figures

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Figure 1

Schematic showing representative bubbles used in the computations, the computed void fraction, and its interpolation onto the computational grid

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Figure 2

Schematic showing an oscillating bubble in a bubbly mixture

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Figure 3

Grid used for the viscous Eulerian-Lagrangian 3DYNA FS-VIS calculations

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Figure 4

Grid convergence study for the viscous Eulerian-Lagrangian 3DYNA FS-Vis calculations showing errors in Rmax and bubble period versus the number of grids in the radial direction

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Figure 5

Primary bubble radius versus time for different initial void fractions obtained with the Eulerian-Lagrangian calculations. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 6

Primary bubble radius versus time for different void fractions obtained with the multi-component compressible approach calculations. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb = 1 atm.

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Figure 7

Primary bubble radius versus time for different void fractions calculated using the Gilmore analytical model. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 8

(a) Evolution of the normalized primary bubble radius versus normalized time – Experiments from [29] versus Gilmore analytical model and (b) comparison of void fraction computed from experiments and analytical model [29]

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Figure 9

Comparison of the ratio of maximum radius, Rmax , achieved in the two-phase medium to its value in water only, for the three numerical models. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 10

Comparison of the bubble period achieved in the two-phase medium to its value in water only, for the three numerical models. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 11

Variation of the pressure at r = 7 mm for different void fractions for the Eulerian-Lagrangian approach. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 12

Variation of the pressure at r = 7 mm for different void fractions for the multi-component compressible approach calculations. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 13

Variation of the pressure at r = 7 mm for different void fractions calculated using Gilmore’s model. R0  = 5 mm, Pg0 = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 14

Comparison of the time variation of the pressure at r = 7 mm for α0  = 0% for the three approaches. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 15

Comparison of the time variation of the pressure at r = 7 mm for α0  = 1% for the three approaches. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 16

Variation of pressure and void fraction in the field with α0  = 0.1% for the Eulerian-Lagrangian calculations, at r = 7, 15 and 400 mm. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 17

Variation of pressure and void fraction in the field with α0  = 0.1% for the multi-component compressible approach calculations, at r = 7, 15 and 400 mm

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Figure 18

Variation of pressure and void fraction in the field with α0  = 0.1% calculated using the analytical Gilmore model, at r = 7, 15 and 400 mm. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 19

Comparison of the pressure in the field for the three approaches at different phases of the bubble period (0.25 T, 0.5 T, and 0.75 T) for α0  = 1%. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 20

Comparison of the void fraction in the field for the three approaches at different phases of the bubble period (0.25 T, 0.5 T, and 0.75 T) for α0  = 1%. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 21

Snapshots from a high speed movie of primary bubble growth and collapse in water with bubble injection, reproduced with permission from Ref. [29]

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Figure 22

Comparison of the bubble radius in the field at r = 7, 15 and 400 mm for two-way and one-way coupled approaches. R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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Figure 23

Variation of pressure and void fraction in the field for α0  = 0.1% and r0  = 2 mm, for Eulerian-Lagrangian calculations. R0  = 5 mm, Pg0  = 2 atm, Pamb  = 1 atm.

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Figure 24

Comparison of the time variation of the void fraction at r = 7 mm for three initial field bubble sizes (r0  = 0.5, 1, and 2 mm), calculated using Eulerian-Lagrangian approach. α0  = 0.1%, R0 = 5 mm, Pg0  = 2 atm, Pamb  = 1 atm.

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Figure 25

Comparison of the time variation of the pressure at r = 7 mm for for three initial field bubble sizes (r0  = 0.5, 1, and 2 mm), calculated using Eulerian-Lagrangian approach. α0  = 0.1%, R0  = 5 mm, Pg0  = 2 atm, r0  = 1 mm, Pamb  = 1 atm.

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