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TECHNICAL PAPERS

New Physically Based Approach of Mass Conservation Correction in Level Set Formulation for Incompressible Two-Phase Flows

[+] Author and Article Information
Snehamoy Majumder

Department of Mechanical Engineering, Jadavpur University, Calcutta-700032, India

Suman Chakraborty

Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur-721302, India Member, ASMEsuman@mech.iitkgp.ernet.in

J. Fluids Eng 127(3), 554-563 (Mar 07, 2005) (10 pages) doi:10.1115/1.1899172 History: Received April 08, 2004; Revised March 07, 2005

A novel physically based mass conservation model is developed in the framework of a level set method, as an alternative to the Heaviside function based formulation classically employed in the literature. In the proposed “volume fraction based level set approach,” expressions for volume fraction function for each interfacial computational cell are developed, and are subsequently correlated with the corresponding level set functions. The volume fraction function, derived from a physical basis, is found to be mathematically analogous to the Heaviside function, except for a one-dimensional case. The results obtained are compared with the benchmark experimental and numerical results reported in the literature. Finally, transient evolution of a circular bubble in a developing shear flow and rising bubbles in a static fluid, are critically examined. The Cox angle and the deformation parameter characterizing the bubble evolution are critically examined. An excellent satisfaction of the mass conservation requirements is observed in all case studies undertaken.

Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

One-dimensional control volume with fluid interface at I

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Figure 2

Orientation of an interface cutting the adjacent sides of the control volume, A1A2≻A2A3 and A1A2≺ΔX∕2, A2A3≺ΔY∕2

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Figure 3

Orientation of an interface cutting the adjacent sides of the control volume, A1A2≻A2A3 and A1A2≺ΔX∕2, A2A3≺ΔY∕2

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Figure 4

Orientation of an interface cutting the adjacent sides of the control volume, A1A2≻A2A3 and A1A2≻ΔX∕2, A2A3≺ΔY∕2

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Figure 5

Orientation of an interface cutting the adjacent sides of the control volume, A1A2≻A2A3 and A1A2≺ΔX∕2, A2A3≻ΔY∕2

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Figure 6

Orientation of an interface cutting the adjacent sides of the control volume, A1A2≻A2A3 and A1A2≻ΔX∕2, A2A3≻ΔY∕2

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Figure 7

Orientation of an interface cutting the adjacent sides of the control volume, A1A2≻A2A3 and A1A2≻ΔX∕2, A2A3≻ΔY∕2

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Figure 8

Interface cutting opposite horizontal sides

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Figure 9

Interface cutting vertical opposite sides

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Figure 10

(a) Change of interface within control volume. (b) Change of interface to the next control volume. (c) Change of interface adjacent control volumes

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Figure 11

(a) Distribution of Heaviside function and volume fraction function for one-dimensional case. Interface width is taken as 2.5h for Heaviside function and h for volume fraction function. (b) Distribution of Heaviside function and volume fraction function for one-dimensional case. Interface width is taken as h for both Heaviside function and volume fraction function.

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Figure 12

(a) Distribution of Heaviside function and volume fraction function for two-dimensional case with θ=30°. Interface width is taken as 2.5h for Heaviside function and h for volume fraction function. (b) Distribution of Heaviside function and volume fraction function for two-dimensional case with θ=30°. Interface width is taken as h for both Heaviside function and volume fraction function.

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Figure 13

(a) Distribution of Heaviside function and volume fraction function for two-dimensional case with θ=45°. Interface width is taken as 2.5h for Heaviside function and h for volume fraction function. (b) Distribution of Heaviside function and volume fraction function for two-dimensional case with θ=45°. Interface width is taken as h for both Heaviside function and volume fraction function.

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Figure 14

(a) Distribution of Heaviside function and volume fraction function for two-dimensional case with θ=60°. Interface width is taken as 2.5h for Heaviside function and h for volume fraction function. (b) Distribution of Heaviside function and volume fraction function for two-dimensional case with θ=60°. Interface width is taken as h for both Heaviside function and volume fraction function.

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Figure 15

Experimental arrangement for studying collapsing of water column

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Figure 16

Height of the collapsing water column, h=instantaneous height, initial height=2a

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Figure 17

Position of leading edge of the collapsing water column, z=instantaneous leading edge position

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Figure 18

Effects of density ratio on the collapsing water column height

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Figure 19

Two bubbles of same density rising up. Density ratio between the bubbles and the background is 1:10, grid size is 256×256, viscosity of the bubbles is 0.000 25 units and that of the background is 0.0005 units, t1=0s, t2=0.1s, t3=0.18s, t4=0.24s, t5=0.28s, t6=0.32s.

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Figure 20

Position versus time curve corresponding problem data reported in Sussman (5). The continuous and dotted lines correspond to results obtained using the present method, by employing a 72×72 and 36×36 square grid, respectively, while the square marks represent numerical results reported in Sussman (5).

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Figure 21

Transient evolution of a circular bubble in a developing flow field with inlet shear flow. The different snapshots are computed at the following instances of time: t1=0s, t2=0.0027s, t3=0.0054s, t4=0.0081s, t5=0.0108s, t6=0.0135s

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