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Research Papers: Flows in Complex Systems

Smoothed Particle Hydrodynamics for the Rising Pattern of Oil Droplets

[+] Author and Article Information
Mehdi Rostami Hosseinkhani

Department of Physical Oceanography,
Faculty of Science and Research Branch,
Islamic Azad University,
Tehran 1651153311, Iran

Pourya Omidvar

Department of Mechanical Engineering,
Faculty of Engineering,
Yasouj University,
Yasouj 7591874934, Iran
e-mail: omidvar@yu.ac.ir

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 12, 2017; final manuscript received February 25, 2018; published online April 10, 2018. Assoc. Editor: Shizhi Qian.

J. Fluids Eng 140(8), 081105 (Apr 10, 2018) (16 pages) Paper No: FE-17-1340; doi: 10.1115/1.4039517 History: Received June 12, 2017; Revised February 25, 2018

The problem of rising droplets in liquids is important in physics and has had many applications in industries. In the present study, the rising pattern of oil droplets has been examined using the smoothed particle hydrodynamics (SPH), which is a fully Lagrangian meshless method. The open-source SPHysics2D code is developed to two phase by adding the effects of surface tension and an added pressure term to the momentum equation. Several problems of droplet dynamics were simulated, and the performance of the developed code is evaluated. First, the still water–oil tank problem was solved to examine the hydrostatic pressure, especially at the interface, for different density ratios. Then, the rising patterns of an oil droplet of different densities are simulated and the time evolutions of the rising velocity and center of mass are shown. It is shown that the shape and behavior of the droplet rising depend on the balance between viscous, surface tension, and dynamic forces. Afterward, the flow morphologies of multiple droplet rising are shown where the density ratio causes negligible effects on the droplet shape, but it has large effects on the dynamics behavior of rising process.

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Figures

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Fig. 1

Particles arrangement for still water–fluid tank, where ρ1/ρ2 = 0.1 and Δx=0.01 at (a) t = 0 s and (b) t = 5 s

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Fig. 2

A comparison between analytical and SPH hydrostatic pressure of the still water–fluid tank (density ratio of 0.1) for Δx=0.02,Δx=0.01 after 5 s

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Fig. 3

A comparison between analytical and SPH hydrostatic pressure of the still water–fluid tank (density ratio of 0.8) for Δx=0.02,Δx=0.01 after 5 s

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Fig. 4

Initial geometry of the problem of an oil droplet rising in a still water tank

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Fig. 5

The rising pattern of an oil droplet in a still water tank (density ratio of 0.1) for different times

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Fig. 6

The rising pattern of an oil droplet in a still water tank (density ratio of 0.8) for different times

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Fig. 7

The time evolutions of the rising velocity and center of mass with density ratio of 0.1 in a still water tank

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Fig. 8

The time evolutions of the center of mass and rising velocity with density ratio of 0.8 in a still water tank

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Fig. 9

Morton and Ohnesorge numbers versus Reynolds number for the density ratio of 0.1

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Fig. 10

Morton and Ohnesorge numbers versus Reynolds number for the density ratio of 0.8

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Fig. 11

The initial geometry of droplets rising

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Fig. 12

The integration of two droplets (density ratio of 0.1 and Bo = ∞); Navier–Stokes solution and the SPH solution at the left and right of each panel, respectively

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Fig. 21

The time evolutions of the center of mass with density ratio of 0.8 in a still water tank for two droplet sticking

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Fig. 20

The rising of two oil droplets (density ratio of 0.8) at different times

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Fig. 19

The rising of two oil droplets (density ratio of 0.8) at different times

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Fig. 18

The time evolutions of the center of mass with density ratio of 0.1 in a still water tank for two droplet (a) sticking and (b) separated

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Fig. 17

The rising of two droplets (density ratio of 0.1) at different times

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Fig. 16

The rising of two droplets (density ratio of 0.1) at different times

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Fig. 15

The initial geometry of droplets rising

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Fig. 14

The rising of two oil droplets in a water tank at different dimensionless times with Bo=122.6

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Fig. 13

The integration of two droplets (density ratio of 0.1 and Bo = 80); Navier–Stokes solution and the SPH solution at the left and right of each panel, respectively

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