Level set method for two-phase incompressible flows under magnetic fields

Ki, Hyungson

doi:10.1016/j.cpc.2010.02.002

Cited by 51 publications

(25 citation statements)

References 6 publications

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“…Effects of uniform magnetic field on the dielectric two-phase flows were shown by Ki [24]. There are various and numerous studies conducted on the effects of non-uniform magnetic field on the behavior of bubbles or effects of uniform magnetic on the dynamics of two-phase flows of electrically conducting fluids.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of dielectric bubbles coalescence under the effects of uniform magnetic field

Hadidi

Jalali-Vahid

2015

Theor. Comput. Fluid Dyn.

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In this research, the co-axial coalescence of a pair of gas bubbles rising in a viscous liquid column under the effects of an external uniform magnetic field is simulated numerically. Considered fluids are dielectric, and applied magnetic field is uniform. Effects of different strengths of magnetic field on the interaction of inline rising bubbles and coalescence between them were investigated. For numerical modeling of the problem, a computer code was developed to solve the governing equations which are continuity, Navier-Stokes equation, magnetic field equation and level set and reinitialization of level set equations. The finite volume method is used for the discretization of the continuity and momentum equations using SIMPLE scheme where the finite difference method is used to discretization of the magnetic field equations. Also a level set method is used to capture the interface of two phases. The results are compared with available numerical and experimental results in the case of no-magnetic field effect which show a good agreement. It is found that uniform magnetic field accelerates the coalescence of the bubbles in dielectric fluids and enhances the rise velocity of the coalesced bubble.Keywords Magnetic field · Coalescence · Bubble pairs · Two-phase flow List of symbols B, bMagnetic field in flow field-magnetic flux density (T) D Rate of strain tensor (1/s) Eo Eotvos number F Surface tension force (N/m 3 ) g Gravity acceleration (m/s 2 ) H External magnetic field (A/m) J c Electric current (A) M Morton number Communicated by S. Balachandar. Electronic supplementary material The online version of this article (

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Section: Introductionmentioning

confidence: 99%

Numerical simulation of dielectric bubbles coalescence under the effects of uniform magnetic field

Hadidi

Jalali-Vahid

2015

Theor. Comput. Fluid Dyn.

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“…(9) and (10) and using the potential vector defined in Eq. (12), the magnetic field equation governing the problem can be stated as [1] 1 ZðfÞ…”

Section: The Governing Equationsmentioning

confidence: 99%

“…In the absence of an electric field, the Maxwell equations are simplified to the two following equations [1]:…”

Section: The Governing Equationsmentioning

confidence: 99%

“…Therefore, the concept was that no force acts in dielectric fluids under a uniform magnetic field. Later, Ki [1] showed that a force acts on the interface of two-phase flow with dielectric fluids under a uniform magnetic field. Ki derived and presented the related governing equations under the mentioned conditions.…”

Section: Introductionmentioning

confidence: 99%

“…This force, which results from the coupling of matter and the magnetic field, acts as an additional driving force for the flow. For this reason, the magnetic field is used in many thermo-fluid applications, such as controlling flow or increasing the heat transfer rate [1]. In metallurgy processes, gas bubbles are injected into the molten metal to accelerate movement, homogenize chemical and physical properties of the molten metal flow or refine it.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effect of a uniform magnetic field on dielectric two-phase bubbly flows using the level set method

Ansari

Hadidi

Nimvari

2012

Journal of Magnetism and Magnetic Materials

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Optimization of unsteady incompressible Navier–Stokes flows using variational level set method

Deng

Zhang

Liu

et al. 2012

Numerical Methods in Fluids

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SUMMARYThis paper presents the optimization of unsteady Navier–Stokes flows using the variational level set method. The solid–liquid interface is expressed by the level set function implicitly, and the fluid velocity is constrained to be zero in the solid domain. An optimization problem, which is constrained by the Navier–Stokes equations and a fluid volume constraint, is analyzed by the Lagrangian multiplier based adjoint approach. The corresponding continuous adjoint equations and the shape sensitivity are derived. The level set function is evolved by solving the Hamilton–Jacobian equation with the upwind finite difference method. The optimization method can be used to design channels for flows with or without body forces. The numerical examples demonstrate the feasibility and robustness of this optimization method for unsteady Navier–Stokes flows.Copyright © 2012 John Wiley & Sons, Ltd.

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Level set method for two-phase incompressible flows under magnetic fields

Cited by 51 publications

References 6 publications

Numerical simulation of dielectric bubbles coalescence under the effects of uniform magnetic field

Numerical simulation of dielectric bubbles coalescence under the effects of uniform magnetic field

Effect of a uniform magnetic field on dielectric two-phase bubbly flows using the level set method

Optimization of unsteady incompressible Navier–Stokes flows using variational level set method

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