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

Ansari, Mohammad Reza; Hadidi, Amin; Nimvari, Majid Eshagh

doi:10.1016/j.jmmm.2012.07.030

Cited by 25 publications

(10 citation statements)

References 12 publications

(16 reference statements)

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“…To eliminate the effects of geometry's walls on the dynamics of bubbles, the distance between the center of the bubble and the vertical walls must be more than three times the bubble radius [25]. In each case investigated in this research, first, the test of independency of the results from wall effects has been conducted and appropriate dimensions of the column determined.…”

Section: Description Of the Problemmentioning

confidence: 99%

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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: Description Of the Problemmentioning

confidence: 99%

“…Boundary condition of the magnetic field equation in all boundaries, except the boundary where the magnetic field was applied, is defined as [25]:…”

Section: Boundary Conditionsmentioning

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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“…where l and g are subscripts denote to liquid and gas phases, respectively; also H() is modified Heaviside function that can be expressed as follows 15 H " ð Þ ¼…”

Section: Governing Equationsmentioning

confidence: 99%

“…The physical properties of fluids, density and viscosity can be expressed according to the level set function as follows 14 where l and g are subscripts denote to liquid and gas phases, respectively; also H(φ) is modified Heaviside function that can be expressed as follows 15 where 2 ɛ is the numerical thickness of the interface, in order to smooth intense changes of fluid and bubble properties along the interface.…”

Section: Mathematical Modeling Of the Problemmentioning

confidence: 99%

A geometric mass control approach in level set method to simulate multiphase flows with complex interface topologies, case study: Oblique coalescence of gas bubbles in a liquid

Hadidi

Nimvari

2019

Proceedings of the Institution of Mechanical Engineers, Part E:

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A geometrical mass control loop is proposed in this research to use in the level set method in order to simulation of multiphase flows with complex topologies of the interface and a case study is investigated using proposed scheme. In this regard oblique interaction and coalescence of bubbles in a liquid is investigated. The level set method is suffering from poor mass conservation in the case of severe changes of interface and complex topologies encountered in a wide range of problems which one of them is oblique coalescence of the bubbles. Despite the use of full re-initialization and reconstruction approach of the level set method as well as application of fine mesh, deviation of mass conservation of the method even becomes 100%. Therefore, simulation of such problems sometimes becomes impossible using this method. So in the geometric mass control loop, mass deviation in each time step is calculated and is compensated in the dispersed phase, which prevents the propagation of mass error entire the simulation. Efficiency of proposed geometrical mass control loop is verified by simulation of oblique interaction and coalescence of gas bubbles in a liquid. The governing equations are continuity and momentum equations which have been discretized using the finite volume method and the SIMPLE algorithm. The results outlined in the present study well agree with the existing experimental and numerical results. Results show that the maximum amount of mass dissipation was less than 4%. Therefore, the level set method with proposed geometric mass control loop could be used properly for the simulation of multiphase flows with sharp and high variations in the interface.

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“…As a result, the scalar potential changes as the interface is moving. Then, the magnetic permeability can be expressed [35]:…”

Section: Magnetic Field Governing Equationsmentioning

confidence: 99%

Simulation of the co-axial ferrofluid droplets interaction under uniform magnetic field

Ghaderi¹,

Kayhani²,

Nazari³

2019

THERM SCI

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In this study, falling and the coalescence of a pair ferrofluid droplets subjected to uniform magnetic field are investigated numerically. For this approach, a 2-D hybrid approach combined of lattice-Boltzmann and finite volume method is used. The lattice Boltzmann equation with the magnetic force term is solved to update the flow field while the magnetic induction equation is solved using finite volume method to calculate the magnetic field. To validate current simulations, three test cases have been considered: Laplace, multiple rising bubbles and deformation of static drop under magnetic field are analyzed. The comparison of results between the present study and previous researches shows a good agreement. The effects of different parameters: magnetic Bond number, magnetic susceptibility, and magnetic field direction are comprehensively studied. The results show that the coalescence of droplets becomes fast with the increasing Bond number and susceptibility in y-direction magnetic field. Also, the coalescence and falling process of droplets takes more time in the horizontal magnetic field in comparison with the vertical magnetic field.

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

Cited by 25 publications

References 12 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

A geometric mass control approach in level set method to simulate multiphase flows with complex interface topologies, case study: Oblique coalescence of gas bubbles in a liquid

Simulation of the co-axial ferrofluid droplets interaction under uniform magnetic field

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