Nagy El-Kaddah

The effect of coil design on materials synthesis in an inductively coupled plasma torch

A mathematical model for the analysis and design of inductively coupled plasma torches is presented. The model is based upon a solution of the electromagnetic vector potential equation and is capable of predicting the two‐dimensional velocity, temperature, and electromagnetic fields as well as the reaction kinetics inside the torch for any axisymmetric coil configuration. The model is used to study the effect of coil design on the thermal decomposition of silicon tetrachloride to silicon. The coil design is found to affect both the temperature field and the flow field and to have a significant effect on the reaction kinetics in the torch. It is demonstrated that through fundamental changes in the coil design it is possible to control the location of the reaction zone and to reduce silicon deposition on the wall of the reactor.

A comprehensive study of the induced current, the electromagnetic force field, and the velocity field in a complex electromagnetically driven flow system

A mathematical formulation is developed to describe the electromagnetic parameters and the velocity fields in an inductively stirred melt, both in the presence and the absence of shields. The theoretically predicted results are compred with experimental measurements pertaining to the induced current, the components of the magnetic flux, and the phase angle between the current and the magnetic flux. In addition, the melt velocity was also determined, using a Vives probe. The excellent agreement obtained between measurements and predictions regarding both the individual input parameters and secondary quantities, such as the electromagnetic force field and the velocity field, shows a full validation of the technique employed. It has also been demonstrated that the use of magnetic shields may be a useful way of modifying the flow patterns in these systems.

Finite element analysis of electromagnetic and fluid flow phenomena in rotary electromagnetic stirring of steel

Abstract This paper describes a fixed-grid methodology for the numerical simulation of electromagnetically driven flow in three-dimensional inductively stirred systems. It is based on a hybrid differential–integral formulation of the electromagnetic field to limit the finite difference/element solution of the electromagnetic field problem to the fluid flow domain. The electromagnetic field in the system was described using current vector potential ( T ) and reduced magnetic scalar potential ( ψ ) formulation of the field. The fluid flow problem was represented by turbulent Navier–Stokes equation. The governing equations were discretized using Galerkin method of weighted residual, and the discretized electromagnetic and fluid flow equations were solved simultaneously using an efficient finite element segregated algorithm. This new method was used to simulate sub-mold rotary electromagnetic stirring in continuous casting of steel. The computed results have shown that the electromagnetic force field generates a strong rotational flow within the vertical section covered by the stirrer, and a relatively strong secondary flow beyond the stirrer. It has also been shown that the rotational and secondary flows were driven primarily by the vorticity of the force field at the billet corners. The induced flow in the molten pool was found to be turbulent and the effective mixing region in the molten pool was about three times the length of the stirrer. The principal conclusion emerging form this work is that the secondary flow promotes mixing beyond the region confined by the stirrer, and the extent of mixing depends on the frequency of the applied rotating magnetic field.

The electromagnetic filtration of molten aluminum using an induced-current separator

The production of clean metal, free from oxides and other types of nonmetallic inclusions, is central to product quality and performance. Toward this end, electromagnetic filtration is an emerging technology for the purification of molten metals. This paper reviews the theory and the mechanism of the electromagnetic separation of inclusions from molten metal and describes the induced-current electromagnetic separator developed at the University of Alabama. The results of laboratory and large-scale experiments on the purification of molten aluminum demonstrate the capability of the system for producing super clean metals.

Electromagnetic and fluid flow phenomena in a mercury model system of the electromagnetic casting of aluminum

A mathematical formulation has been developed to represent the electromagnetic force field and the velocity field in the melt for the electromagnetic casting of aluminum. The theoretical predictions based on fundamental considerations are compared with experimental measurements obtained on a physical model system. The measurements and predictions were found to be in good agreement, regarding both the velocity fields and the electromagnetic force fields. The principal conclusion emerging from this work is of critical importance in achieving the dual objective, that is providing a restraining force, while minimizing the melt velocity perpendicular to the free surface. The mathematical formulation presented in the paper provides the theoretical framework for quantitatively defining these conditions in terms of the coil and the shield parameters.

Turbulent recirculating flow in induction furnaces: a comparison of measurements with predictions over a range of operating conditions

Experimental measurements and theoretical predictions are presented concerning the velocity fields, the maps of the turbulent kinetic energy, and the turbulent kinetic energy dissipation in an inductively stirred mercury pool. A single coil arrangement was used, and the frequencies examined ranged from 50 to 5000 Hz. A hot film anemometer and a direction probe were employed for characterizing the velocity fields. The theoretical predictions were based on the numerical solution of the turbulent Navier-Stokes equations. The technique of mutual inductances was employed to compute the magnetic field, while thek-ε model was used for calculating the turbulent viscosity. Overall, the theoretical predictions were in reasonable agreement with the measurements both regarding the velocities and the turbulence parameters. By presenting the results in a normalized, dimensionless form these findings were given a rather broader applicability than the actual numerical range explored.

Modeling of materials synthesis in hybrid plasma reactors: Production of silicon by thermal decomposition of SiCI4

A mathematical model for the analysis and design of a combined direct current (DC) and radio frequency (RF) plasma reactor for advanced materials synthesis has been developed. The RF electromagnetic field is calculated by solving Maxwell’s equations expressed in terms of the vector potential, which permits great flexibility in the specification of the RF coil design. The velocity and temperature fields in the plasma are calculated by solving the turbulent Navier-Stokes equations and the thermal energy balance equation. The model is used to study the thermal decomposition of silicon tetrachloride through the solution of the mass diffusion equation arid the associated reaction kinetics. It is found that the coupling between the flow and temperature fields generated by the RF and DC components significantly improves the silicon production and recovery in the reactor as compared with either DC or RF systems alone. In addition, the conversion efficiency of the hybrid system is found to depend on both the design and the operating parameters of the RF coil.

On the dispersion of SiCAl slurries in rotating flows

Abstract An experimental study was conducted to determine the role of fluid flow on dispersion of SiC particles in molten aluminum. In this work, slurries containing up to 18 vol.% SiC were dispersed in rotational Couette flow at high shear rates ranging from 50 to 500 s −1 . The relative viscosity of SiCAl metal matrix composite slurries was also measured. It was found that the particles were uniformly dispersed in the radial direction. No particle agglomeration was observed. Axial dispersion was found to occur under certain stirring conditions. A particulate dispersion number PD based on stirring parameters and particle-settling velocity was developed to describe the dispersion behavior of particles in rotating fluids. The measured viscosities of the SICAl slurries investigatedwere found to be in good agreement with Einsteins equation.

An Improved Model for the Flow in an Electromagnetically Stirred Melt during Solidification

A mathematical model for simulating the electromagnetic field and the evolution of the temperature and velocity fields during solidification of a molten metal subjected to a time-varying magnetic field is described. The model is based on the dual suspended particle and fixed particle region representation of the mushy zone. The key feature of the model is that it accounts for turbulent interactions with the solidified crystallites in the suspended particle region. An expression is presented for describing the turbulent damping force in terms of the turbulent kinetic energy, solid fraction, and final grain size. Calculations were performed for solidification of an electromagnetically stirred melt in a bottom chill mold. It was found that the damping force plays an important role in attenuating the intensity of both the flow and turbulent fields at the beginning of solidification, and strongly depends on the final grain size. It was also found that turbulence drops significantly near the solidification front, and the flow becomes laminarized for solid fraction around 0.3.

Experimental measurement and numerical computation of velocity and turbulence parameters in a heated liquid metal system

Experimental measurements are reported describing the velocity field and the turbulence parameters in molten Woods metal due to the passage of a DC current between two electrodes immersed into the melt. The measurements were made using a hot film anemometer. A mathematical model has been developed to represent these measurements; in essence, this relied on the solution of Maxwell’s equations to represent the electromagnetic force field and turbulent Navier-Stokes equations to represent the fluid flow field. Three different turbulence models were examined; two were variants of thek-ε model, while the third was mixing length model type. In general, the velocities were well predicted by all three of these models, but there were significant discrepancies as far as the turbulence parameters were concerned. In the paper, a new criterion was suggested to predict the onset of turbulence in systems of this type.