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

Abstract

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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