A. H. Dilawari

Heat transfer and fluid flow phenomena in electroslag refining

A mathematical formulation has been developed to represent the electromagnetic force field, fluid flow and heat transfer in ESR units. In the formulation, allowance has been made for both electromagnetically driven flows and natural convection; furthermore, in considering heat transfer the effect of the moving droplets has been taken into account. The computed results have shown that the electromagnetic force field appears to be the more important driving force for fluid motion, although natural convection does affect the circulation pattern. The movement of the liquid droplets through the slag plays an important role in transporting thermal energy from the slag to the molten metal pool, although the droplets are unlikely to contribute appreciably to slag-metal mass transfer The for-formulation presented here enables the prediction of thermal and fluid flow phenomena in ESR units and may be used to calculate the electrode melting rates from first principles. While a detailed comparison has not yet been made between the predictions based on the model and actual plant scale measurements, it is thought that the theoretical predictions are consistent with the plant-scale data that are available.

A mathematical model of slag and metal flow in the ESR Process

Through the statement of the turbulent Navier-Stokes equations and Maxwell’s equations a mathematical representation is developed for the electromagnetic force field and the velocity field in the slag phase and the metal pool of cylindrical ESR units. Computed results are presented for both industrial scale (0.5 m electrode diameter) and laboratory scale (0.05 m electrode diameter) units operating with direct currents. It was found that for industrial scale units, the computed slag velocities ranged from 5 to 10 cm/s, while the velocities in the metal pool were substantially lower, except at the slag-metal interface. At a given spatial position, the velocity was found to increase in an almost linear fashion with the current density. The flow was found to be predominately laminar in the laboratory scale units and for comparable current densities the melt velocities were very much smaller. Some 600 to 900 s were required on a CDC 6400 digital computer for the solution of each case involving turbulent flow.

Some perspectives on the modeling of plasma jets

A mathematical representation is developed describing the temperature and the velocity profiles and mixing in a plasma jet discharging into ambient air. In the model, realistic allowance is made for turbulent behavior, the temperature-dependent property values, and also for the boundary conditions, including entrainment. The more precise definition of the boundary conditions, mixing, and entrainment are thought to be important novel features of this work. The theoretical predictions were found to be in good agreement with measurements reported by Vardelle regarding the behavior of a nitrogen plasma, but the agreement was less satisfactory for an argon plasma jet. Possible reasons for the discrepancy are discussed.

The temperature profiles in an argon plasma issuing into an argon atmosphere: A comparison of measurements and predictions

Experimental measurements and computed results are reported on a nontransferred argon plasma discharging into an argon environment in a laminar regime. The experimental data provide information on the temperature profiles, particularly those close to the torch exit. The mathematical representation of the system involves the simultaneous statement of the equations of continuity, motion, and thermal energy balance for an axisymmetric system, but for fully temperature-dependent property values. On the whole, the theoretical predictions are in very good agreement with the measurements, with the maximum discrepancy being of the order of 5–10%. This augurs well for the extension of this work to more complex systems, also including gas mixtures.

A mathematical representation of a modified stagnation flow reactor for MOCVD applications

Abstract Computed results are presented describing the behavior of a modified stagnation point reactor for an MOCVD system, employing a showerhead type gas distributor. The principal findings of the work are the following: (a) By this arrangement, it is possible to obtain a very high spatial uniformity in the deposition rate, in cases better than 0.35% for a five inch diameter wafer. (b) Both the absolute values of the gas velocity and the standoff distance were found to play a critical role in affecting the uniformity of the deposition rate. Indeed a small standoff distance was found to be an essential ingredient in obtaining a good spatial uniformity of the deposit. (c) “An upside down” orientation was found to be helpful in minimizing thermal natural convection and a further refinement was found to be possible by imposing a desired radial distribution on the gas inlet velocity profile.

Fluid flow and heat transfer in plasma reactors—I. Calculation of velocities, temperature profiles and mixing

Abstract A mathematical representation has been developed to describe the velocity field and the associated temperature and concentration fields in a plasma jet system, which involves the injection of additional gas streams. In the statement of the problem, allowance was made for the swirl of the plasma jet, and one important objective of the work was to explore the effect of this swirl on the principal process variables. It was found that swirl plays an important role in providing mixing between the plasma jet and a reactant or diluent gas stream introduced through an annular port. It was shown, furthermore, that the model may be used for representing the quenching of the system by an axi-symmetrically introduced gas stream, having a direction perpendicular to the axis of the jet.

A comparison of experimental measurements and theoretical predictions regarding the behavior of a turbulent argon plasma jet discharging into air

Computed results are presented describing the temperature and concentration fields obtained when an argon plasma jet is being discharged into ambient air. A previously published mathematical model for turbulent plasma plumes is used for the calculations. These predictions are compared with recent), published experimental measurements by Brossa and Pfender, performed with an enthalpy probe. The theoretical predictions appear to agree reasonably well with the measurements of both the temperature and concentration profiles, with a maximum deviation in the 10–20% range.

Electromagnetically and thermally driven flow phenomena in electroslag welding

Through the statement of Maxwells equations, the turbulent Navier-Stokes equations, and the convective heat balance equation, a mathematical model has been proposed for the Electroslag Welding Process. In the formulation, allowance has been made for both electromagnetic and buoyancy forces for driving the slag and the metal flow. The principal finding of the work is that convection in the molten slag region has a marked effect on the heat transfer process. For a rectangular geometry, using plate electrodes, the flow field is driven by buoyancy forces, the circulating flow is less intense, and the thermal efficiency of the process is improved. In contrast, for wire electrodes (approximated by a cylindrical geometry) the flow is driven by electromagnetic forces and a substantial part of the thermal energy is dissipated to the plates.

Computed results for the deposition rates and transport phenomena for an MOCVD system with a conical rotating substrate

Abstract A mathematical representation has been developed for a CVD reactor, involving a rotating substrate, in which gallium arsenide wafers are being produced by the thermal decomposition of arsene and trimethyl gallium. In the model axial symmetry has been assumed, but an allowance has been made for forced and thermal natural convection, for thermal diffusion, homogeneous gas phase kinetics and for a realistically complex geometry. The principal finding of the work is that the uniformity of the deposition in this system can be achieved only by the careful balancing of forced and natural convection and the depletion of the reactant. By a parametric study of the key process parameters, including the reactor geometry, the gas flow rate, the reactant concentration, the reactor pressure and the cooling arrangements for the side walls, directions may be obtained regarding this optimization process.

Fluid flow and heat transfer in plasma reactors—II. A critical comparison of experimentally measured and theoretically predicted temperature profiles in plasma jets in the absence and presence of side-stream injection

Abstract A critical comparison is presented between experimental measurements and theoretical predictions describing the temperature profiles in a nitrogen plasma jet discharging into nitrogen, with a sideways-injected cold gas stream of nitrogen or oxygen. In general, the theoretical predictions, based on the solution of the axi-symmetric Navier-Stokes equations and associated thermal and mass balance relationships are found to be in good agreement with the measurements. A notable feature of the modelling work is that particular care had been taken to specify the temperature and the velocity profiles at the inlet boundary, chosen to be some distance inside the torch, and the thermal boundary conditions at the other bounding surfaces.