Frederik Verhaeghe

Lattice Boltzmann modeling of microchannel flow in slip flow regime

We present the lattice Boltzmann equation (LBE) with multiple relaxation times (MRT) to simulate pressure-driven gaseous flow in a long microchannel. We obtain analytic solutions of the MRT-LBE with various boundary conditions for the incompressible Poiseuille flow with its walls aligned with a lattice axis. The analytical solutions are used to realize the Dirichlet boundary conditions in the LBE. We use the first-order slip boundary conditions at the walls and consistent pressure boundary conditions at both ends of the long microchannel. We validate the LBE results using the compressible Navier-Stokes (NS) equations with a first-order slip velocity, the information-preservation direct simulation Monte Carlo (IP-DSMC) and DSMC methods. As expected, the LBE results agree very well with IP-DSMC and DSMC results in the slip velocity regime, but deviate significantly from IP-DSMC and DSMC results in the transition-flow regime in part due to the inadequacy of the slip velocity model, while still agreeing very well with the slip NS results. Possible extensions of the LBE for transition flows are discussed.

Water-cooled probe technique for the study of freeze lining formation

Furnace protection by water-cooled freeze linings becomes increasingly important as the metal producing industry attempts to achieve higher process intensities. Systematic investigations of the growth and the resulting microstructure and compositional profile of freeze linings are necessary to understand the behavior of freeze linings, their relation with the industrial process, and their interaction with the wall cooling system. We have developed a technique based on the submergence of a water-cooled probe into a liquid slag bath. Freeze linings of two industrial nonferrous slags have been produced using this technique and their growth, microstructural, and compositional profiles as a function of submergence time were determined. Thermodynamic equilibrium for the investigated slag systems was calculated and compared with the observed microstructures. The freeze linings form in approximately 15 minutes. Close to the water cooling, the freeze linings are predominantly amorphous in structure. With increasing distance from the water cooling, the proportion of crystalline phases increases and bath material is entrapped in the microstructure. Cellular crystals are observed close to the bath. The freeze linings exhibit an approximate homogeneous composition. The results demonstrate that the technique is a successful tool in obtaining information on the growth, microstructure, and composition of freeze linings in industrial water-cooled furnaces.

Dissolution and diffusion behavior of Al2O3 in a CaO-Al2O3-SiO2 liquid : An experimental-numerical approach

A technique to study the dissolution and diffusion behavior of Al2O3 in CaO–Al2O3–SiO2 liquids is presented. The dissolution of spherical Al2O3 particles at elevated temperatures is observed using confocal scanning laser microscopy and interpreted by means of numerical simulations with a lattice Boltzmann dissolution model. The dissolution mechanism is identified as diffusion-controlled and an estimate of the effective binary diffusion coefficient and its activation energy is obtained. The technique is readily applicable to other systems.

Effect of the strong magnetic field on the magnetic interaction between two non-magnetic particles migrating in a conductive fluid

This paper presents a theoretical analysis of the interaction between two non-magnetic particles migrating in a conductive fluid due to an imposed strong magnetic field. A repulsive force induced by the conductive fluid flow around the particles is first derived and calculated for a concrete example. From the numerical results, a counteracting behavior with the interparticle magnetic dipole-dipole attractive force is found to exist at a critical particle size which makes the particles controllable under strong magnetic fields (e.g., B> 10 T). This renders a better understanding of recent experimental results and provides a basis to control the particle size distribution using strong magnetic fields for materials processing. Copyright c EPLA, 2009

Magnetic Interaction Between Two Non-Magnetic Particles Migrating in a Conductive Fluid Induced by a Strong Magnetic Field-an Analytical Approach

An analytical approach is developed in the present paper to investigate the interaction between two non-magnetic particles migrating in a conductive ∞uid due to an imposed strong magnetic fleld (e.g., 10 Tesla). The interaction between the conductive ∞uid and a single particle migrating along the magnetic lines is in∞uenced by the magnetic fleld and can be represented by an additional ∞uid viscosity. Thus the efiective ∞uid viscosity is discussed and the magnetic fleld efiect on the particle migrating velocity is examined. For two particles, two kinds of magnetic forces are induced: namely, the attractive force due to the magnetisation and the repulsive force caused by the conductive ∞uid ∞ow around the non-magnetic particles. The forces are then evaluated with the consideration of the magnetic fleld efiect on the particle migration and become signiflcant with the increase of the magnetic ∞ux density. The counteracting behavior with a critical particle size of the interparticle magnetic forces is discussed and compared with difierent magnetic fleld densities and gradient values.

Experimental and numerical study of buoyancy-driven single bubble dynamics in a vertical Hele-Shaw cell

Buoyancy-driven single bubble behaviour in a vertical Hele-Shaw cell with various gap Reynolds numbers Re(h/d)2 has been studied. Two gap thicknesses, h = 0.5 mm (Re(h/d)2 = 1.0–8.5) and 1 mm (Re(h/d)2 = 6.0–50) were used to represent low and high gap Reynolds number flow. Periodic shape oscillation and path vibration were observed once the gap Reynolds number exceeds the critical value of 8.5. The bubble behaviour was also numerically simulated by taking a two-dimensional volume of fluid method coupled with a continuum surface force model and a wall friction model in the commercial computational fluid dynamics package Fluent. By adjusting the viscous resistance values, the bubble dynamics in the two gap thicknesses can be simulated. For the main flow properties including shape, path, terminal velocity, horizontal vibration, and shape oscillation, good agreement is obtained between experiment and simulation. The estimated terminal velocity is 10%–50% higher than the observed one when the bubble diameter d...

Theoretical evaluation of influence of convective heat transfer and original sample size on shell melting time during Ti dissolution in secondary steelmaking

Abstract The dissolution of Ti additions in liquid steel during secondary steelmaking occurs in a two step process. In the first step, a steel shell solidifies around the initial cold addition, whereas in the second step, after this shell has remelted, the Ti dissolves directly in the steel bath. The initial presence of this steel shell modifies the position of dissolution and influences the local concentration and thus the inclusion formation. Further complications arise from the fact that part of the Ti will dissolve while enclosed by the steel shell, altering the alloy composition first released in the ladle and effectively shortening the subsequent free dissolution period. The duration of the steel shell period and the fraction of predissolved Ti have been investigated using a conservative one-dimensional sharp interface model solving the coupled heat and mass transfer in a cylindrical shell/addition composite. The influence of the convection conditions and the original Ti radius was evaluated in a parametric study. A pronounced effect of the convective heat transfer on the shell melting time was found. It is thus concluded that the dissolution behaviour is strongly dependent on the local flow conditions, which is determined by factors such as stirring conditions and addition characteristics.

Determination of the dissolution mechanism of Al2O3 in CaO-Al2O3-SiO2 liquids using a combined experimental-numerical approach

Experimental results obtained from the in situ observation of the dissolution of spherical Al2O3 particles in CaO-Al2O3-SiO2-containing melts at elevated temperatures are analyzed using a lattice Boltzmann dissolution model. Through a comparison of the experimental dissolution curve with analytical predictions and numerical simulations, the rate-limiting step is identified as diffusion control. Estimations of the effective binary diffusion coefficient are obtained, together with an estimate of the activation energy for the diffusion process.

Lattice Boltzmann model for diffusion-controlled indirect dissolution

Indirect dissolution is modelled using a two-component lattice Boltzmann model. A boundary condition is developed to impose equilibrium concentrations on the interfaces. The interfaces are captured using a volume-tracking scheme. The model is applied to a one-dimensional diffusion couple and the expected behaviour is observed. A two-dimensional situation with and without convection is also simulated, and the behaviour under grid refinement is studied.

Volume-of-fluid simulations of bubble dynamics in a vertical Hele-Shaw cell

Bubbles in confined geometries serve an important role for industrial operations involving bubble-liquid interactions. However, high Reynolds number bubble dynamics in confined flows are still not well understood due to experimental challenges. In the present paper, combined experimental and numerical methods are used to provide a comprehensive insight into these dynamics. The bubble behaviour in a vertical Hele-Shaw cell is investigated experimentally with a fully wetting liquid for a variety of gap thicknesses. A numerical model is developed using the volume of fluid method coupled with a continuum surface force model and a wall friction model. The developed model successfully simulates the dynamics of a bubble under the present experimental conditions and shows good agreement between experimental and simulation results. It is found that with an increased spacing between the cell walls, the bubble shape changes from oblate ellipsoid and spherical-cap to more complicated shapes, while the bubble path changes from only rectilinear to a combination of oscillating and rectilinear; the bubble drag coefficient decreases and this results in a higher bubble velocity caused by a lower pressure exerted on the bubble; the wake boundary and wake length evolve gradually accompanied by vortex formation and shedding.