Numerical modelling of liquid droplet dynamics in microgravity

Microgravity provides ideal experimental conditions for studying highly reactive and under-cooled materials where there is no contact between the sample and the other experimental apparatus. The non-contact conditions allow material properties to be measured from the oscillating liquid droplet response to perturbations. This work investigates the impact of a strong magnetic field on these measurement processes for weakly viscous, electrically conducting droplets. We present numerical results using an axisymmetric model that employs the pseudo-spectral collocation method and a recently developed 3D model. Both numerical models have been developed to solve the equations describing the coupled electromagnetic and fluid flow processes. The models represent the changing surface shape that results from the interaction between forces inside the droplet and the surface tension imposed boundary conditions. The models are used to examine the liquid droplet dynamics in a strong DC magnetic field. In each case the surface shape is decomposed into a superposition of spherical harmonic modes. The oscillation of the individual mode coefficients is then analysed to determine the oscillation frequencies and damping rates that are then compared to the low amplitude solutions predicted by the published analytical asymptotic theory

Thermoelectric Magnetohydrodynamic effects on the crystal growth rate of undercooled Ni dendrites

In the undercooled solidification of pure metals, the dendrite tip velocity has been shown experimentally to have a strong dependence on the intensity of an external magnetic field, exhibiting several maxima and minima. In the experiments conducted in China, the undercooled solidification dynamics of pure Ni was studied using the glass fluxing method. Visual recordings of the progress of solidification are compared at different static fields up to 6 T. The introduction of microscopic convective transport through thermoelectric magnetohydrodynamics is a promising explanation for the observed changes of tip velocities. To address this problem, a purpose-built numerical code was used to solve the coupled equations representing the magnetohydrodynamic, thermal and solidification mechanisms. The underlying phenomena can be attributed to two competing flow fields, which were generated by orthogonal components of the magnetic field, parallel and transverse to the direction of growth. Their effects are either intensified or damped out with increasing magnetic field intensity, leading to the observed behaviour of the tip velocity. The results obtained reflect well the experimental findings. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’

Liquid Droplet Dynamics in Gravity Compensating High Magnetic Field

Numerical models are used to investigate behavior of liquid droplets suspended in high DC magnetic fields of various configurations providing microgravity-like conditions. Using a DC field it is possible to create conditions with laminar viscosity and heat transfer to measure viscosity, surface tension, electrical and thermal conductivities, and heat capacity of a liquid sample. The oscillations in a high DC magnetic field are quite different for an electrically conducting droplet, like liquid silicon or metal. The droplet behavior in a high magnetic field is the subject of investigation in this paper. At the high values of magnetic field some oscillation modes are damped quickly, while others are modified with a considerable shift of the oscillating droplet frequencies and the damping constants from the non-magnetic case

Dynamic modelling and validation of the metal/flux interface in continuous casting

This paper concerns the development and validation (using an oil/water system) of a finite volume computer model of the continuous casting process for steel flat products. The emphasis is on hydrodynamic aspects and in particular the dynamic behaviour of the metal/slag interface due to the momentum imparted by the submerged entry nozzle (SEN) jets that bring the metal into the mould. Instability and wave action encourage the entrainment of inclusions into the melt affecting product quality. To track the interface between oil and water a new implicit algorithm was developed, called the Counter Diffusion Method. To prevent numerical damping of low frequency waves, a time-filtered version of the k- model was incorporated in the model. The physics of the interface dynamics are affected by density stratification and surface interfacial tension, with additional source terms introduced in the turbulence model to account for the former effect. Gas bubbles were modelled using a Lagrangian tracking method. The model was validated against experimental measurements obtained in a water model apparatus at Arcelor Research. Silicon oil was used to represent the lighter layer whilst air was pumped through the SEN to represent the argon

Numerical modelling of silicon melt purification in induction directional solidification system

Solar grade silicon production is an energy intensive and harmful to the environment process. Yet 40% of this valuable product material is lost into sawdust (kerf loss) during wafering. The kerf waste from Fixed Abrasive Sawing of PV silicon wafers is pelletized and then remelted in an induction furnace. The furnace has a square cross-section quartz crucible, surrounded by graphite susceptors and heated by an induction coil that enables directional solidification of the new ingot. Top and bottom 'pancake' coils provide additional temperature control. Once melted, silicon becomes electrically conductive and subject to stirring by induction. To recycle the silicon, particulate impurities (due to the sawing, condensed silicon oxides or carbides) need to be removed. Flow control and the electromagnetic Leenov-Kolin force are used to expel particulates, through a novel dual frequency induction scheme. Three-dimensional, multi-physics numerical modelling captures the electromagnetic, fluid-flow and heat-transfer effects in this process. The presented results show it is possible to retain the impurity particles on the sides of the solidified ingot where they can be sliced off and removed

Study of thermoelectric magnetohydrodynamic convection on solute redistribution during laser additive manufacturing

Melt pools formed in laser additive manufacturing (AM) are subject to large thermal gradients, resulting in the formation of thermoelectric currents due to the Seebeck effect. When in the presence of an external magnetic field, a Lorentz force is formed which drives fluid flow in the melt pool. This Thermoelectric Magnetohydrodynamics (TEMHD) phenomenon, can have a significant impact on the melt pool morphology and can alter the microstructural evolution of the solidification process. By coupling steady-state mesoscopic melt pool calculations to a microscopic solidification model, predictions of the resulting microstructure for multiple deposited layers have been obtained. The results indicate that the magnetic field can have a transformative effect on the microstructure and solute redistribution. This study highlights the theoretical potential for using magnetic fields as an additional control system to tailor AM microstructures

The effects of Thermoelectric Magnetohydrodynamics in directional solidification under a transverse magnetic field

The mechanism of macrosegregation and modification to dendrite size and spacing from a transverse magnetic field has been modelled through direct numerical simulation. The primary driver for this mechanism was identified as a strong Lorentz force formed in the interdendritic region, which leads to a large scale flow circulation. The microstructure evolution is modified by convective transport of solute and the predicted morphological features compare favourably to experimental data in the literature. The numerical results also give an insight into the magnitude of flow velocities within the interdendritic region.</p

Droplet Formation with Electromagnetic Pulse Force

Abstract Methods for serial generation of droplets from a liquid jet are shortly reviewed. A method of liquid metal droplet generation based on AC high frequency magnetic field is considered in detail. Numerical model for direct simulation of the time dependent droplet generation process is presented. Computed examples demonstrate the liquid silicon droplet formation for the cases of 500-1500 µm diameter

Thermoelectric magnetohydrodynamic control of melt pool dynamics and microstructure evolution in additive manufacturing

Large thermal gradients in the melt pool from rapid heating followed by rapid cooling in metal additive manufacturing generate large thermoelectric currents. Applying an external magnetic field to the process introduces fluid flow through thermoelectric magnetohydrodynamics. Convective transport of heat and mass can then modify the melt pool dynamics and alter microstructural evolution. As a novel technique, this shows great promise in controlling the process to improve quality and mitigate defect formation. However, there is very little knowledge within the scientific community on the fundamental principles of this physical phenomenon to support practical implementation. To address this multiphysics problem that couples the key phenomena of melting/solidification, electromagnetism, hydrodynamics, heat and mass transport, the lattice Boltzmann method for fluid dynamics was combined with a purpose-built code addressing solidification modelling and electromagnetics. The theoretical study presented here investigates the hydrodynamic mechanisms introduced by the magnetic field. The resulting steady-state solutions of modified melt pool shapes and thermal fields are then used to predict the microstructure evolution using a cellular automata based grain growth model. The results clearly demonstrate that the hydrodynamic mechanisms and, therefore, microstructure characteristics are strongly dependent on magnetic field orientation

Magnetic Effects on Microstructure and Solute Plume Dynamics of Directionally Solidifying Ga-In Alloy

The effects of applying a 0.2-T transverse magnetic field on a solidifying Ga-25 wt%In alloy have been investigated through a joint experimental and numerical study. The magnetic field introduced significant changes to both the microstructure and the dynamics of escaping high-concentration Ga plumes. Plume migration across the interface was quantified and correlated to simulations to demonstrate that thermoelectric magnetohydrodynamics (TEMHD) is the underlying mechanism. TEMHD introduced macrosegregation within the dendritic structure, leading to the formation of a stable “chimney” channel by increasing the solutal buoyancy in the flow direction. The resulting pressure difference across the solidification front introduced a secondary hydrodynamic phenomenon that subsequently caused solute plume migration