Mathematical modelling of the solidification of liquid tin with electromagnetic stirring

It is well known that during alloy solidification, convection currents close to the so-lidification front have an influence on the structure of dendrites, the local solute concentration, the pattern of solid segregation, and eventually the microstructure of the casting and hence its mechanical properties. Controlled stirring of the melt in continuous casting or in ingot solidification is thought to have a beneficial effect. Free convection currents occur naturally due to temperature differences in the melt and for any given configuration, their strength is a function of the degree of superheat present. A more controlled forced convection current can be induced using electro-magnetic stirring. The authors have applied their Control-Volume based MHD method [1, 2] to the problem of tin solidification in an annular crucible with a water-cooled inner wall and a resistance heated outer one, for both free and forced convection situations and for various degrees of superheat. This problem was studied experimentally by Vives and Perry [3] who obtained temperature measurements, front positions and maps of electro-magnetic body force for a range of superheat values. The results of the mathematical model are compared critically against the experimental ones, in order to validate the model and also to demonstrate the usefulness of the coupled solution technique followed, as a predictive tool and a design aid. Figs 6, refs 19.

Magnetic modelling and magneto-hydro-dynamic simulations of an aluminium production electrolytic cell

A simulation of the motion of molten aluminium inside an electrolytic cell is presented. Since the driving term of the aluminium motion is the Lorentz (j × B) body force acting within the fluid,this problem involves the solution of the magneto-hydro-dynamic equations. Different solver modules for the magnetic field computation and for the fluid motion simulation are coupled together. The interactions of all these are presented and discussed.

Determining surface tension using DC magnetic levitation

The values of material physical properties are vital for the successful use of numerical simulations for electromagnetic processing of materials. The surface tension of materials can be determined from the experimental measurement of the surface oscillation frequency of liquid droplets. In order for this technique to be used, a positioning field is required that results in a modification to the oscillation frequency. A number of previous analytical models have been developed that mainly focus on electrically conducting droplets positioned using an A.C. electromagnetic field, but due to the turbulent flow resulting from the high electromagnetic fields required to balance gravity, reliable measurements have largely been limited to microgravity. In this work axisymmetric analytical and numerical models are developed, which allow the surface tension of a diamagnetic droplet positioned in a high DC magnetic field to be determined from the surface oscillations. In the case of D.C. levitation there is no internal electric currents with resulting Joule heating, Marangoni flow and other effects that introduce additional physics that complicates the measurement process. The analytical solution uses the linearised Navier-Stokes equations in the inviscid case. The body force from a DC field is potential, in contrast to the AC case, and it can be derived from Maxwell equations giving a solution for the magnetic field in the form of a series expansion of Legendre polynomials. The first few terms in this expansion represent a constant and gradient magnetic field valid close to the origin, which can be used to position the droplet. Initially the mathematical model is verified in microgravity conditions using a numerical model developed to solve the transient electromagnetics, fluid flow and thermodynamic equations. In the numerical model (as in experiment) the magnetic field is obtained using electrical current carrying coils, which provides the confinement force for a liquid droplet. The model incorporates free surface deformation to accurately model the oscillations that result from the interaction between the droplet and the non-uniform external magnetic field. A comparison is made between the analytical perturbation theory and the numerical pseudo spectral approximation solutions for small amplitude oscillations.

A multilevel algorithm for force-directed graph drawing

We describe a heuristic method for drawing graphs which uses a multilevel technique combined with a force-directed placement algorithm. The multilevel process groups vertices to form clusters, uses the clusters to define a new graph and is repeated until the graph size falls below some threshold. The coarsest graph is then given an initial layout and the layout is successively refined on all the graphs starting with the coarsest and ending with the original. In this way the multilevel algorithm both accelerates and gives a more global quality to the force- directed placement. The algorithm can compute both 2 & 3 dimensional layouts and we demonstrate it on a number of examples ranging from 500 to 225,000 vertices. It is also very fast and can compute a 2D layout of a sparse graph in around 30 seconds for a 10,000 vertex graph to around 10 minutes for the largest graph. This is an order of magnitude faster than recent implementations of force-directed placement algorithms.

A multilevel algorithm for force-directed graph-drawing

We describe a heuristic method for drawing graphs which uses a multilevel framework combined with a force-directed placement algorithm. The multilevel technique matches and coalesces pairs of adjacent vertices to define a new graph and is repeated recursively to create a hierarchy of increasingly coarse graphs, G0, G1, …, GL. The coarsest graph, GL, is then given an initial layout and the layout is refined and extended to all the graphs starting with the coarsest and ending with the original. At each successive change of level, l, the initial layout for Gl is taken from its coarser and smaller child graph, Gl+1, and refined using force-directed placement. In this way the multilevel framework both accelerates and appears to give a more global quality to the drawing. The algorithm can compute both 2 & 3 dimensional layouts and we demonstrate it on examples ranging in size from 10 to 225,000 vertices. It is also very fast and can compute a 2D layout of a sparse graph in around 12 seconds for a 10,000 vertex graph to around 5-7 minutes for the largest graphs. This is an order of magnitude faster than recent implementations of force-directed placement algorithms.

Effect of adding 0.3 wt% Ni into the Sn–0.7 wt%Cu solder: part I: wetting behavior on Cu and Ni substrates

Comparative wetting behavior of Sn-0.7Cu and Sn-0.7Cu-0.3Ni solders on Cu and Ni substrates were assessed through the wetting balance test. No-clean (NC), non-activated (R) and water soluble organic acid (WS) fluxes were used to assess the wetting behavior for three different solder bath temperatures of 255, 275 and 295 °C. Experimental results unveiled that adding of 0.3 wt% Ni into Sn-0.7Cu solder can improve the wetting on Cu substrate when NC and WS fluxes are used. However, such addition of Ni did not improve the wetting of Sn-0.7Cu solder for R-type flux. In the case of Ni substrate, addition of Ni helped to improve the wetting for all three types of fluxes as higher wetting forces were documented for Sn-0.7Cu-0.3Ni solder compared to the Sn-0.7Cu solder. Among the fluxes, worst performance was observed for R-type flux. Very large contact angles were recorded for both solders with this kind of flux. Experimental results also revealed that higher solder bath temperature played an important role to lower the contact angle, to increase the wetting force and to enhance the wetting. Computer modeling of wetting balance test also revealed that both the wetting force and meniscus height are inversely proportional to the contact angles. Besides, solder bath depth and radius do not affect significantly on the wetting behavior.

Magnetic damping of levitated liquid droplets in AC and DC field

The intense AC magnetic field required to produce levitation in terrestrial conditions, along with the buoyancy and thermo-capillary forces, results in turbulent convective flow within the droplet. The use of a homogenous DC magnetic field allows the convective flow to be damped. However the turbulence properties are affected at the same time, leading to a possibility that the effective turbulent damping is considerably reduced. The MHD modified K-Omega turbulence model allows the investigation of the effect of magnetic field on the turbulence. The model incorporates free surface deformation, the temperature dependent surface tension, turbulent momentum transport, electromagnetic and gravity forces. The model is adapted to incorporate a periodic laser heating at the top of the droplet, which have been used to measure the thermal conductivity of the material by calculating the phase lag between the frequency of the laser heating and the temperature response at the bottom. The numerical simulations show that with the gradual increase of the DC field the fluid flow within the droplet is initially increasing in intensity. Only after a certain threshold magnitude of the field the flow intensity starts to decrease. In order to achieve the flow conditions close to the ‘laminar’ a D.C. magnetic field >4 Tesla is required to measure the thermal conductivity accurately. The reduction in the AC field driven flow in the main body of the drop leads to a noticeable thermo-capillary convection at the edge of the droplet. The uniform vertical DC magnetic field does not stop a translational oscillation of the droplet along the field, which is caused by the variation in total levitation force due to the time-dependent surface deformation.

Manufacturing of uniformly-sized silicon particles for solar cell from molten metal jet by electromagnetic pinch force

Spherical silicon solar cells are expected to serve as a technology to reduce silicon usage of photovoltaic (PV) power systems[1, 2, 3]. In order to establish the spherical silicon solar cell, a manufacturing method of uniformly sized silicon particles of 1mm in diameter is required. However, it is difficult to mass-produce the mono-sized silicon particles at low cost by existent processes now. We proposed a new method to generate liquid metal droplets uniformly by applying electromagnetic pinch force to a liquid metal jet[4]. The electromagnetic force was intermittently applied to the liquid metal jet issued from a nozzle in order to fluctuate the surface of the jet. As the fluctuation grew, the liquid jet was broken up into small droplets according to a frequency of the intermittent electromagnetic force. Firstly, a preliminary experiment was carried out. A single pulse current was applied instantaneously to a single turn coil around a molten gallium jet. It was confirmed that the jet could be split up by pinch force generated by the current. And then, electromagnetic pinch force was applied intermittently to the jet. It was found that the jet was broken up into mono-sized droplets in the case of a force frequency was equal to a critical frequency[5], which corresponds to a natural disturbance wave length of the jet. Numerical simulations of the droplet generation from the liquid jet were then carried out, which consisted of an electromagnetic analysis and a fluid flow calculation with a free surface of the jet. The simulation results were compared with the experiments and the agreement between the two was quite good.

DFT calculations of the structures and vibrational spectra of the [Fe(bpy)(3)](2+) and [Ru(bpy)(3)](2+) complexes

Structures of the [M(bpy)(3)](2+) complexes (M = Fe and Ru) have been calculated at the B3-LYP/DZVP level. IR and Raman spectra were calculated using the optimised geometries, employing a scaled quantum chemical force field, and compared with an earlier normal coordinate analysis of [Ru(bpy)(3) ](2+) which was based upon experimental data alone, and the use of a simplified model. The results of the calculations provide a highly satisfactory fit to the experimental data and the normal coordinate analyses, in terms of potential energy distributions, allow a detailed understanding of the vibrational spectra of both complexes. Evidence is presented for Jahn-Teller distortion in the E-1 MLCT excited state. (C) 2008 Elsevier B.V. All rights reserved.