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Research Papers: Multiphase Flows

A Level Set Method Coupled With a Volume of Fluid Method for Modeling of Gas-Liquid Interface in Bubbly Flow

[+] Author and Article Information
Bogdan A. Nichita

 EPFL STI IGM LTCM, ME G1 464, Station 9, CH-1015 Lausanne, Switzerlandbogdan.nichita@epfl.ch

Iztok Zun

LFDT, Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, 1000 Ljubljana, Sloveniaiztok.zun@fs.uni-lj.si

John R. Thome1

 EPFL STI IGM LTCM, ME G1 464, Station 9, CH-1015 Lausanne, Switzerlandjohn.thome@epfl.ch

1

Corresponding author.

J. Fluids Eng 132(8), 081302 (Aug 26, 2010) (15 pages) doi:10.1115/1.4002166 History: Received November 03, 2009; Revised July 09, 2010; Published August 26, 2010; Online August 26, 2010

This paper describes the implementation of a 3D parallel and Cartesian level set (LS) method coupled with a volume of fluid (VOF) method into the commercial CFD code FLUENT for modeling the gas-liquid interface in bubbly flow. Both level set and volume of fluid methods belong to the so called “one” fluid methods, where a single set of conservation equations is solved and the interface is captured via a scalar function. Since both LS and VOF have advantages and disadvantages, our aim is to couple these two methods to obtain a method, which is superior to both standalone LS and VOF and verify it versus a selection of test cases. VOF is already available in FLUENT , so we implemented an LS method into FLUENT via user defined functions. The level set function is used to compute the surface tension contribution to the momentum equations, via curvature and its normal to the interface, using the Brackbill method while the volume of fluid function is used to capture the interface itself. A re-initialization equation is implemented and solved at every time step using a fifth-order weighted essentially nonoscillatory scheme for the spatial derivative, and a first-order Euler method for time integration. The coupling effect is introduced by solving at the end of each time step an equation, which connects the volume fractions with the level set function. The verification of parasitic currents and interfacial deformation due to numerical error is assessed in comparison to original VOF scheme. Validation is presented for free rising bubbles of different diameters for Morton numbers ranging from 102 to 1011.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A typical nonorthogonal control volume from Ref. 30

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Figure 2

LS-VOF comparison. Dashed contour-LS function. Continuous contour-VOF function.

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Figure 3

Static bubble parasitic currents for 2D CLSVOF and VOF

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Figure 4

Interface location for a 2D droplet deformed by a vortex with T=6 s and a grid of 128×128

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Figure 5

Interface location for a 2D droplet deformed by a vortex with T=6 s and a grid of 256×256

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Figure 6

Interface location for a 2D droplet deformed by a vortex with T=6 s and a grid of 512×512

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Figure 7

Interface position for an inviscid, axisymmetric gas bubble rising in liquid; 128×256 grid

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Figure 8

Interface position for an inviscid, axisymmetric gas bubble rising in liquid from Sussman (22)

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Figure 9

Bubble rise velocity as a function of time with CLSVOF and VOF

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Figure 10

Interface position at different time with CLSVOF and VOF for different Morton numbers

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Figure 11

Dimensionless height and width of the bubbles

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Figure 12

Drag coefficient versus Reynolds number

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Figure 13

Predicted bubble shape by CLSVOF for air bubbles rising in clear mineral oil

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Figure 14

Characteristic bubble path with 3D CLSVOF and VOF

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Figure 15

Pressure contours for 5 mm bubble with CLSVOF, time=0.35 s and 0.39 s

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Figure 16

Pressure contours for 5 mm bubble with VOF, time=0.35 s and 0.39 s

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Figure 17

Pressure contours for 5 mm bubble with CLSVOF, time=0.455 s and 0.5 s

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Figure 18

Pressure contours for 5 mm bubble with VOF, time=0.455 s and 0.5 s

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Figure 19

Interface position and velocity field with 3D CLSVOF and VOF for 5 mm bubble

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Figure 20

A comparison between bubble rise velocity obtained experimentally by Zun and Groselj (37) and bubble rise velocity obtained with CLSVOF and VOF

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Figure 21

A comparison between bubble rise velocity obtained with CLSVOF, VOF, and bubble rise velocity predicted by Wallis (41)

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