Numerical modeling of bubble-driven liquid metal flows with external static magnetic field

Abstract Three-dimensional numerical simulations are presented considering the impact of a steady magnetic field on a bubble-driven liquid metal flow inside a cylinder. The injection of moderate gas flow rates through a single orifice at the bottom of the fluid vessel results in the formation of a bubble plume. The magnetic field is applied in either vertical or horizontal direction. The calculations were performed by means of the commercial software package CFX using the Euler–Euler multiphase model and the RANS–SST turbulence model. The non-isotropic nature of MHD turbulence was taken into account by specific modifications of the turbulence model. The numerical models are validated with recent experimental results. (Zhang, C., Eckert, S., Gerbeth, G., 2007. The flow structure of a bubble-driven liquid–metal jet in a horizontal magnetic field, J. Fluid Mech. 575, 57–82.) The comparison between the numerical simulations and the experimental findings shows a good agreement. The calculations are able to reproduce a striking feature of a horizontal magnetic field found in the range of moderate Hartmann numbers revealing that such a steady transverse magnetic field may destabilize the flow and cause distinct oscillations of the liquid velocity.

[1]  R. Clift,et al.  Bubbles, Drops, and Particles , 1978 .

[2]  Akio Tomiyama,et al.  On the role of the lateral lift force in poly-dispersed bubbly flows , 2011 .

[3]  P. Moresco,et al.  Experimental study of the instability of the Hartmann layer , 2004, Journal of Fluid Mechanics.

[4]  I. Zun,et al.  The transverse migration of bubbles influenced by walls in vertical bubbly flow , 1980 .

[5]  Manabu Iguchi,et al.  Water model study of the frequency of bubble formation under reduced and elevated pressures , 1998 .

[6]  J. Converti,et al.  A model for turbulent polydisperse two-phase flow in vertical channels , 2003 .

[7]  B. Smith,et al.  On the modelling of bubble plumes in a liquid pool , 1998 .

[8]  Effects of magnetic field on the shape of a bubble in a uniaxial straining flow , 2002 .

[9]  Sven Eckert,et al.  Experimental study of single bubble motion in a liquid metal column exposed to a DC magnetic field , 2005 .

[10]  Peter Davidson,et al.  Magnetic damping of jets and vortices , 1995, Journal of Fluid Mechanics.

[11]  Gretar Tryggvason,et al.  The rise of bubbles in a vertical shear flow , 1997 .

[12]  G. Gerbeth,et al.  MHD turbulence measurements in a sodium channel flow exposed to a transverse magnetic field , 2001 .

[13]  Hallvard F. Svendsen,et al.  Modeling of Vertical Bubble-Driven Flows , 1997 .

[14]  Chidambaram Narayanan,et al.  A numerically convergent Lagrangian–Eulerian simulation method for dispersed two-phase flows , 2009 .

[15]  Michio Sadatomi,et al.  Momentum and heat transfer in two-phase bubble flow—I. Theory , 1981 .

[16]  Gordon A. Irons,et al.  Measurement and modeling of turbulence in the gas/liquid two-phase zone during gas injection , 1993 .

[17]  Annalisa Manera,et al.  Influence of the lift force on the stability of a bubble column , 2005 .

[18]  K. Mukai,et al.  Influence of Wettability on the Behavior of Argon Bubbles and Fluid Flow inside the Nozzle and Mold , 1999 .

[19]  Hiromichi Kobayashi,et al.  Large eddy simulation of magnetohydrodynamic turbulent duct flows , 2008 .

[20]  F. Menter.  Two-equation eddy-viscosity turbulence models for engineering applications , 1994 .

[21]  Roderick I. L. Guthrie,et al.  A Comparison of three mathematical modeling procedures for simulating fluid flow phenomena in bubble-stirred ladles , 1994 .

[22]  Kunio Hijikata,et al.  Experimental study of bubble motion in mercury with and without a magnetic field , 1977 .

[23]  Minoru Takahashi,et al.  Characteristics of flow and heat transfer in air-mercury two-phase stratified flow under a vertical magnetic field , 1993 .

[24]  Hua Bai,et al.  Bubble formation during horizontal gas injection into downward-flowing liquid , 2001 .

[25]  Said Zahrai,et al.  Development of a Reynolds stress closure for modeling of homogeneous MHD turbulence , 1998 .

[26]  P. Lykoudis,et al.  Magneto‐Fluid‐Mechanic Channel Flow. I. Experiment , 1967 .

[27]  Sven Eckert,et al.  The flow structure of a bubble-driven liquid-metal jet in a horizontal magnetic field , 2007, Journal of Fluid Mechanics.

[28]  V. Roig,et al.  Eulerian–Eulerian two-fluid model for turbulent gas–liquid bubbly flows , 2003 .

[29]  M. Milelli.  A numerical analysis of confined turbulent bubble plumes , 2002 .

[30]  Sven Eckert,et al.  Experimental Investigation of the Flow in a Continuous-Casting Mold under the Influence of a Transverse, Direct Current Magnetic Field , 2011 .

[31]  Thomas Boeck,et al.  Numerical study of the instability of the Hartmann layer , 2004, Journal of Fluid Mechanics.

[32]  Rene Moreau,et al.  Why, how, and when, MHD turbulence becomes two-dimensional , 1982, Journal of Fluid Mechanics.

[33]  Kouji Takatani,et al.  Mathematical Modeling of Incompressible MHD Flows with Free Surface , 2007 .

[34]  Eckhard Krepper,et al.  Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows , 2007 .

[35]  Jyeshtharaj B. Joshi,et al.  Design of a gas distributor: three-dimensional CFD simulation of a coupled system consisting of a gas chamber and a bubble column , 2007 .

[36]  M. Hirata,et al.  TURBULENT HEAT AND MOMENTUM TRANSFER FOR ELECTRICALLY CONDUCTING FLUID FLOWING IN TWO-DIMENSIONAL CHANNEL UNDER TRANSVERSE MAGNETIC FIELD , 1978 .

[37]  G. Gerbeth,et al.  The behaviour of gas bubbles in a turbulent liquid metal magnetohydrodynamic flow: Part I: Dispersion in quasi-two-dimensional magnetohydrodynamic turbulence , 2000 .

[38]  Tron Solberg,et al.  Large eddy simulation of the Gas-Liquid flow in a square cross-sectioned bubble column , 2001 .

[39]  G. Gerbeth,et al.  Marginal turbulent magnetohydrodynamic flow in a square duct , 2010 .

[40]  I. Zun,et al.  Effects of Eötvös Number and Dimensionless Liquid Volumetric Flux on Lateral Motion of a Bubble in a Laminar Duct Flow , 1995 .

[41]  P. Davidson.  An Introduction to Magnetohydrodynamics , 2001 .

[42]  Manabu Iguchi,et al.  Measurement of bubble characteristics in a molten iron bath at 1600 °C using an electroresistivity probe , 1995 .

[43]  Th. Frank,et al.  VALIDATION OF CFD MODELS FOR MONO- AND POLYDISPERSE AIR-WATER TWO-PHASE FLOWS IN PIPES , 2008 .

[44]  Sven Eckert,et al.  Modification of Bubble-driven Liquid Metal Flows under the Influence of a DC Magnetic Field , 2007 .

[45]  Donald A. Drew,et al.  Averaged Field Equations for Two‐Phase Media , 1971 .

[46]  N. Zuber,et al.  Drag coefficient and relative velocity in bubbly, droplet or particulate flows , 1979 .

[47]  Y. Sato,et al.  Liquid velocity distribution in two-phase bubble flow , 1975 .

[48]  L. van Wijngaarden.  On Pseudo Turbulence , 1998 .

[49]  Computation of a Rising Bubble in an Enclosure Filled with Liquid Metal under Vertical Magnetic Fields , 2010 .

[50]  Eckhard Krepper,et al.  Experimental and numerical studies of void fraction distribution in rectangular bubble columns , 2007 .

[51]  M. Iguchi,et al.  Bubble and liquid flow characteristics in a wood’s metal bath stirred by bottom helium gas injection , 1997 .

[52]  Paul Gherson,et al.  Local measurements in two-phase liquid-metal magneto-fluid-mechanic flow , 1984, Journal of Fluid Mechanics.

[53]  H.-C Ji,et al.  Numerical analysis of turbulent pipe flow in a transverse magnetic field , 1997 .

[54]  J. W. Haverkort,et al.  Magnetohydrodynamic Effects on Insulating Bubbles and Inclusions in the Continuous Casting of Steel , 2010 .