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Research Papers: Multiphase Flows

Coalescence Prevention Algorithm for Level Set Method

[+] Author and Article Information
Matthew L. Talley

Nuclear Engineering Department,
North Carolina State University,
3140 Burlington Engineering Labs,
2500 Stinson Drive,
Raleigh, NC 27695
e-mail: mltalle2@ncsu.edu

Matthew D. Zimmer

Nuclear Engineering Department,
North Carolina State University,
3140 Burlington Engineering Labs,
2500 Stinson Drive,
Raleigh, NC 27695
e-mail: mdzimmer@ncsu.edu

Igor A. Bolotnov

Nuclear Engineering Department,
North Carolina State University,
3140 Burlington Engineering Labs,
2500 Stinson Drive,
Raleigh, NC 27695
e-mail: Igor_bolotnov@ncsu.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 1, 2016; final manuscript received February 21, 2017; published online May 18, 2017. Assoc. Editor: Alfredo Soldati.

J. Fluids Eng 139(8), 081301 (May 18, 2017) (12 pages) Paper No: FE-16-1489; doi: 10.1115/1.4036246 History: Received August 01, 2016; Revised February 21, 2017

An algorithm to prevent or delay bubble coalescence for the level set (LS) method is presented. This novel algorithm uses the LS method field to detect when bubbles are in close proximity, indicating a potential coalescence event, and applies a repellent force to simulate the unresolved liquid drainage force. The model is introduced by locally modifying the surface tension force near the liquid film drainage area. The algorithm can also simulate the liquid drainage time of the thin film by controlling the length of time the increased surface tension has been applied. Thus, a new method of modeling bubble coalescence has been developed. Several test cases were designed to demonstrate the capabilities of the algorithm. The simulations, including a mesh study, confirmed the abilities to identify and prevent coalescence as well as implement the time tracking portion, with an additional 10–25% computational cost. Ongoing tests aim to verify the algorithm's functionality for simulations with different flow conditions, a ranging number of bubbles, and both structured and unstructured computational mesh types. Specifically, a bubble rising toward a free surface provides a test of performance and demonstrates the ability to consistently prevent coalescence. In addition, a two bubble case and a seven bubble case provide a more complex demonstration of how the algorithm performs for larger simulations. These cases are compared to much more expensive simulations capable of resolving the liquid film drainage (through very high local mesh resolution) to investigate how the algorithm replicates the liquid film drainage process.

Copyright © 2017 by ASME
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References

Figures

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Fig. 1

Schematic of how the coalescence control is implemented and restricts coalescence

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Fig. 2

A later time step after surface tension changed with the coalescence control application volume shown as the white circle and the black circles as the bubble interfaces

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Fig. 3

The distance field of the bubbles shown as the white contour lines with the black circles representing the bubble interface

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Fig. 4

Location of high curvature where coordinates are used to generate average coalescence event coordinates. In this image, the annular shape is shown because only the fifth and sixth distance field contours are intersecting so that only those curvature points are detected.

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Fig. 5

Plot of chosen curvature values plotted against the number of elements across a 5 mm bubble diameter. A linear fit was applied with the resulting equation and square of the correlation coefficient.

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Fig. 6

Summary of process to identify a coalescence event and calculate the average coordinates for the event

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Fig. 7

Summary of process to find the average coordinates for each specific coalescence event during multiple coalescence events

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Fig. 8

Initial setup of the simulation used in the mesh study. The domain contains two 5 mm bubble.

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Fig. 9

Visualization of a (a) structured mesh and a (b) unstructured mesh in Cartesian domain

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Fig. 10

Initial setup to test the algorithm for a single coalescence event identification and prevention

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Fig. 11

Visualization of the simulations for the single coalescence events at iterations: (a) 20, (b) 400, and (c) 870. Left: The simulation performed without the coalescence control algorithm. In iteration 870, the 5 mm bubbles have begun to coalesce (shaded by velocity magnitude). Right: The simulation performed with the coalescence control algorithm. In iteration 870, the coalescence event has been prevented.

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Fig. 12

Initial setup at iteration 7800 of the bubbly flow in turbulent conditions. There are 32 bubbles randomly placed throughout the domain (shaded by velocity magnitude).

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Fig. 13

Visualization of both 32 bubble simulation at multiple iterations. Top: no coalescence control, iterations: (a) 15,600, (b) 23,800, and (c) 27,800. Bottom: coalescence control active, iterations: (a) 15,000, (b) 22600, and (c) 26,800 (shaded by velocity magnitude).

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Fig. 14

Initial setup for the bubble rising toward a free surface. The simulation was used to test the time tracking portion of the algorithm (shaded by X velocity where gravity acts in the Y direction).

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Fig. 15

Visualization of both simulations at iterations (a) 800, (b) 920, and (c) 1150. Top: Simulation run without using the time tracking portion of the algorithm. Bottom: Simulation that uses the time tracking portion of the algorithm (shaded by X velocity where gravity acts in the Y direction).

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Fig. 16

Testing the time tracking capability with multiple coalescence events where (a) is the initial condition, (b) is at 0.1875, (c) is at 0.3375, and (d) is at 0.4375 s where one coalescence has occurred and three bubbles remain (shaded by X velocity)

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Fig. 17

Comparison of a highly refined mesh (top: at times (a) 0.4025, (b) 0.4212, and (c) 0.4365 s) and the algorithm (bottom: at times (a) 0.4025, (b) 0.4212, and (c) 0.4365 s) for a bubble approaching a free surface (shaded by X velocity where gravity acts in the Y direction)

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