Heat transfer and fluid flow in plasma spraying

A mathematical model is developed to describe the plasma spray process in which particular attention is paid to the fluid flow and temperature fields in the plasma jet, the plasma/particle interaction, and the heat transfer phenomena associated with the deposition process. On the basis of the heat transfer analysis it was possible to define the limiting conditions for satisfactory operation of the deposition process in terms of basic process variables. For high deposition rates, high levels of superheat, and low thermal conductivity of the deposit, the limiting condition is set by the rate at which heat may be removed by the substrate. For large particle sizes and materials with high melting points the limiting condition is determined by the need to transfer sufficient thermal energy to the particles so that they arrive at the substrate in a fully molten state. Wherever possible, the model predictions were compared with experimental measurements and good agreement was obtained.     

Heat-transfer enhancement using weakly ionized, atmospheric pressure plasma in metallurgical applications

Experimental measurements and computational analysis of heat transfer in atmospheric pressure, midtemperature range (1200 to 1600 K) plasma flow over an aluminum cylinder have been carried out. A comparison of transient temperature measurements for the aluminum cylinder under convective unionized air flow and those with convective plasma flow shows significantly higher heat transfer from plasma flow compared to air flow under identical temperature and flow conditions. A heattransfer problem is computationally modeled by using available experimental measurements of temperature rise in the cylinder to determine the degree of ionization in the plasma flow. The continuity, momentum, and energy conservation equations, as well as conservation equations for electrons and ions, and the Poisson’s equation for self-consistent electric field are solved in the plasma by a finite volume method. The conjugated transient heat transfer in the cylinder and in the plasma is obtained by simultaneous solution of the transient energy conservation equations. It is shown that the enhancement of heat transfer in plasma flow is due to the energy deposited by charged species during recombination reaction at the solid surface. An important finding is that even a small degree of ionization (<1 pct) provides significant enhancement in heat transfer. This enhancement in heat transfer can lead to a productivity increase in metallurgical applications.     

Physical modeling studies of electrolyte flow due to gas evolution and some aspects of bubble behavior in advanced hall cells: Part II. Flow and interpolar resistance in cells with a grooved anode

This article illustrates the role of anode design in increasing the energy efficiency of advanced Hall-Héroult cells. In this study, a “novel” anode that promotes the removal of gas bubbles, generated by the anodic reaction, from the interelectrode gap has been simulated. The efficacy of this anode has been judged with the help of electrolyte flow and interpolar resistance measurements in the horizontal, near-horizontal, and near-vertical electrode configurations. The experimental arrangement was similar to that used in Part I, the companion article. Velocities were measured with a laser-Doppler velocimeter (LDV). Both velocity and interpolar resistance measurements indicate the superiority of this novel anode over a flat anode. Use of this novel anode (vis-à-vis the flat anode) should lead to a reduction (approximately 40 Pct) in interpolar resistance at current density levels used in the industry. Furthermore, electrolyte flow in the anode-to-cathode gap (ACG) is uniform, thereby minimizing the possible problem of reoxidation of aluminum which might be present in cells operated with flat anodes. This study also highlights the major drawbacks of advanced Hall cells operated in the near-vertical configuration: existence of recirculating flow and very high volume fraction of bubbles near the top of the ACG. Both of these factors could lead to increased oxidation of aluminum and, therefore, to reduced current efficiency. Finally, comparison of results with Part I suggests that maximum energy efficiency should be obtained in retrofitted advanced Hall cells operated with this novel anode in the near-horizontal electrode configuration.     

Computational modeling of stationary gastungsten-arc weld pools and comparison to stainless steel 304 experimental results

A systematic study was carried out to verify the predictions of a transient multidimensional computational model by comparing the numerical results with the results of an experimental study. The welding parameters were chosen such that the predictions of the model could be correlated with the results of an earlier experimental investigation of the weld pool surface temperatures during spot gas-tungsten-arc (GTA) welding of Type 304 stainless steel (SS). This study represents the first time that such a comprehensive attempt has been made to experimentally verify the predictions of a numerical study of weld pool fluid flow and heat flow. The computational model considers buoyancy and electromagnetic and surface tension forces in the solution of convective heat transfer in the weld pool. In addition, the model treats the weld pool surface as a truly deformable surface. Theoretical predictions of the weld pool surface temperature distributions, the cross-sectional weld pool size and shape, and the weld pool surface topology were compared with corresponding experimental measurements. Comparison of the theoretically predicted and the experimentally obtained surface temperature profiles indicated agreement within ±8 pct for the best theoretical models. The predicted surface profiles were found to agree within ±20 pct on dome height and ±8 pct on weld pool diameter for the best theoretical models. The predicted weld cross-sectional profiles were overlaid on macrographs of the actual weld cross sections, and they were found to agree very well for the best theoretical models.     

Heat transfer in a direct-fired rotary kiln: II. Heat flow results and their interpretation

Heat flow rates from the gas to the wall and to the bed have been derived from temperature profiles measured in the UBC pilot rotary kiln. The experimental gas-to-wall heat flux has been found to agree closely with theoretical predictions based on a simple radiative model consisting of a grey gas surrounded by a grey surface at uniform temperature. Under identical conditions, the gas-to-solids heat flux is up to ten fold greater than the heat flux between the gas and wall. The gas-to-solids heat flux is a function of the solids feed rate at low throughputs but is constant at higher throughputs. At the lowest feed rates and corresponding rotation speeds heat flow to the bed is limited by mixing of the solids. Heat transfer control changes to the gas side of the bed at higher feed rates and rotation speeds. Under the latter conditions convection appears to account for the major fraction of heat flow to the bed. The heat flow measurements relate directly to observations of the bed motion which can be conveniently characterized by a “bed behavior” diagram. The low heat flux to the bed at low feed rates is due to a slumping action at the surface and concomitant poor mixing. The high heat flux obtained at high feed rates coincides with the observation of a rolling bed. Burden-side and gas-side convective heat transfer coefficients, calculated from the heat flux data, have values ranging from 700 to 1200 and 120 to 240 w/m²K respectively.     

Modeling superheat removal during continuous casting of steel slabs

To investigate superheat dissipation in a continuous slab casting machine, mathematical models have been developed to compute fluid flow velocities, temperature distribution within the liquid pool, heat transfer to the inside of the solidifying shell, and its effect on growth of the shell. Three-dimensional (3-D) velocity and heat-transfer predictions compare reasonably with pre-vious experimental measurements and two-dimensional (2-D) calculations. The results indicate that the maximum heat input to the shell occurs near the impingement point on the narrow face and confirm that most of the superheat is dissipated in or just below the mold. Superheat tem-perature and casting speed have the most important and direct influence on heat flux. The effects of other variables, including mold width, nozzle jet angle, and submergence depth, are also investigated. Calculated heat flux profiles are then input to a one-dimensional (1-D) solidifi-cation model to calculate growth of the shell. Shell thickness profiles down the wide and narrow faces are compared with the predictions of conventional heat conduction models and available measurements.     

A mathematical model of gas tungsten arc welding considering the cathode and the free surface of the weld pool

A two-dimensional axisymmetric numerical model, including the influence of the cathode and the free surface of the weld pool, is developed to describe the heat transfer and fluid flow in gas tungsten arc (GTA) welding. In the model, a boundary-fitted coordinate system is adopted to precisely describe the cathode shape and deformed weld-pool surface. The current continuity equation has been solved with the combined arc plasma-cathode system, independent of the assumption of current density distribution on the cathode surface, which was essential in the previous studies of arc plasma. It has been shown that the temperature profile, the current, and the heat flux to the anode show good agreement with the experimental data. Moreover, the current and the heat-flux distributions may be affected by the shape of the cathode and the free surface of the weld pool.     

Quantification of Input Uncertainty Propagation Through Models of Aluminum Alloy Direct Chill Casting

Insight into transport phenomena in complex solidification processes, such as direct chill (DC) casting, that cannot be found from experimental observation can be gained from numerical simulations. These predictions depend on material, process, and numerical parameters which contain inherit uncertainties due to experimental measurements or model assumptions. A fully transient numerical model of the direct chill casting process of Al-4.5 wt pct Cu was used to examine the propagation of input uncertainty to outputs of interest. The effect of microstructural model parameters, thermal boundary conditions, and material property input uncertainties were examined. Probability density functions were calculated based on these input uncertainties for metrics that characterize the ingot macrosegregation and sump depth. The macrosegregation-level predictions depend strongly on parameters that control the formation of the rigid mushy zone and shrinkage-driven flow. The heat release and transfer in the mushy zone are the dominant factors for determining the sump depth.

     

Experimental validation of flow and tracer-dispersion models in a four-strand billet-casting tundish

An exhaustive literature search indicates that, despite a large number of physical and mathematical model studies, very little efforts have been made to assess predicted flow and turbulence parameters in the tundish directly against equivalent experimental measurements until recently. Consequently, experimental measurements on the instantaneous velocity and residence-time distribution (RTD) were carried out in a scaled water model of a four-strand billet-casting tundish. While particle-image velocimetry (PIV) was applied to measure instantaneous flow, the electrical-conductivity measurement technique was applied to determine the RTD. Through PIV, the mean and the fluctuating components were derived along the central vertical plane of the tundish at two different liquid inflow rates: 1.55×10^?4 m³/s and 3.10×10^?4 m³/s, respectively. Similarly, RTD curves were obtained for tundish operations without and with a dam+turbulence inhibitor device (TID). Parallel to these operations, the flow and tracer dispersion were numerically predicted by FLUENT®. It is shown that the predicted time-average velocity components within the bath bear excellent correspondence with PIV measurements. On the assumption of isotropic fluctuations, turbulent kinetic energy was derived from experimental measurements, which agreed moderately with predictions. Furthermore, the experimentally derived fluctuating velocity components were compared with those obtained from the Reynolds stress model. This indicated very reasonable agreement between measurement and predictions (within ±20 pct). Despite such a difference, however, the extent of agreement between the measured and computed C curves was found to be excellent.     

Modeling of fluid flow and heat transfer in the plasma region of the dc electric arc furnace

A mathematical model describing the transport processes in the plasma arc in dc electric arc furnaces has been developed. The equations of conservation of mass, momentum, and energy are solved numerically in conjunction with Maxwell's equations of the electromagnetic field to calculate the velocity and temperature distributions in the plasma region. The heat transfer from the arc to a rigid anode surface is calculated. The model is applied to obtain quantitative results on the relative importance of the various modes of heat transfer from the electric arc to the anode surface. Computational results were obtained for varying arc current magnitudes and anode-cathode distances. The model predicts higher arc jet velocity and a broader arc core at higher arc current. The shorter arc length is more efficient for transferring heat to the anode.     

Mathematical simulation and experimental verification of melting resulting from the coupled effect of natural convection and exothermic heat of mixing

When melting processes are associated with an exothermic heat of mixing, unique coupled transport phenomena take place. In this article, a mathematical model has been developed to simulate these unique coupled heat and mass transfer events. The model was based on the control-volume finite difference approach and on an enthalpy method. In order to verify the mathematical model, a low-temperature physical model was established consisting of ice and sulfuric acid solutions. In this physical model, both temperature and velocity measurements were carried out. The model predictions were compared with experimental measurements, and they were found to be in good agreement. The model was also applied to a high-temperature system, namely, the melting of silicon metal in liquid high carbon iron. The predictions distinguished two periods present in the entire melting process. In the first period, the silicon was heated up. The second period, i.e., free melting period, occurred in tandem with the exothermic reaction, and consequently, the melting process was greatly accelerated. As was the case with the low-temperature physical model, as with the high-temperature system, good agreement was obtained between the predicted results and the experimental measurements.     

Fluid Flow Modeling of Arc Plasma and Bath Circulation in DC Electric Arc Furnace

 A mathematical model describing the flow field, heat transfer and the electromagnetic phenomenon in a DC electric arc furnace has been developed. First the governing equations in the arc plasma region are solved and the calculated results of heat transfer, current density and shear stresses on the anode surface are used as boundary conditions in a model of molten bath. Then a two dimensional time dependent model is used to describe the flow field and electromagnetic phenomenon in the molten bath. Moreover, the effect of bottom electrode diameter on the circulation of molten bath is studied.     

The role of transport phenomena in the plasma synthesis of fine particles: The production of silicon powder

A mathematical formulation has been developed to describe heat and fluid flow phenomena in a complex nontransferred are plasma jet system, and this information is then used to calculate the rate at which an injected silane stream decomposes. Problems of this type are important in the plasma synthesis of fine ceramic particles. The most important finding of the work is that swirl of the plasma jet plays a key role in determining the intermixing of the various streams and, hence, the overall process kinetics. The theoretical predictions were found to be in good agreement with measurements regarding the temperature fields. Furthermore, the capability of predicting temperature fields, residence times, and process kinetics should provide useful guidelines regarding reactor design such that the formation of monodispersed particles is favored. A.H. DILAWARI, formerly with the Massachusetts Institute of Technology This paper is based on a presentation made in the T.B. King Memorial Symposium on “Physical Chemistry in Metals Processing” presented at the Annual Meeting of The Metallurgical Society, Denver, CO, February, 1987, under the auspices of the Physical Chemistry Committee and the PTD/ISS.     

Heat transfer in a direct-fired rotary kiln: I. Pilot plant and experimentation

The characterization of heat flow processes in direct-fired rotary kilns requires detailed measurements of gas, solids and wall temperatures. This paper describes the construction, instrumentation and operation of a 5.5 m long x 0.406 m inside diam kiln designed for such measurements. The heating of inert sand was chosen for experimental study. Methods of calculating heat flows among solids, wall and gas from the measured axial and radial temperatures are presented and the heat balance calculations and other necessary checks on the validity of the data are given. The effects of the kiln operating variables on heat flow rates, and the implications of the results for modelling and scale-up to large kilns are discussed in Part II.     

The velocity field in the molten slag region of esr systems: a comparison of measurements in a model system with theoretical predictions

A comparison is presented between the experimentally measured velocity field in a room temperature model of an ESR system and theoretical predictions, obtained from the numerical solution of Maxwell’s equations and the turbulent Navier-Stokes equations. The experimental measurements were obtained in a horizontal trough, containing mercury, through which a current was being passedvia two electrodes. The velocity fields, which were measured, using a photographic technique were thought to model the electromagnetically driven component of the velocity field in the central plane of the slag phase in ESR systems. The agreement between the experimental measurements and the theoretical predictions is excellent, both regarding the absolute values of the velocities and the dependence of the velocity on the imposed current and on the electrode diameter. The calculations have shown that by the proper choice of the linear scale, and the current,. mercury may be used to model the electromagnetically driven flow in the slag phase of ESR systems. Furthermore, some general relationships have been developed showing the effect of the current on the velocity, the turbulence energy, and on the rate of turbulence energy dissipation. This work is thought to provide definite confirmation that the electromagnetically driven component of the velocity fields in ESR systems may be properly represented through the simultaneous solution of Maxwell’s equations and the turbulent NavierStokes equations.     

Mathematical Modelling of Water Sampler Filling

Steel samples taken from ladles or tundishes during the steel making process can be of significant importance when monitoring the inclusion size and distribution. In order to preserve the original size and distributions of inclusions in the extracted samples, it is important to avoid their collisions and coagulations inside samplers during filling. Thus, it is necessary to investigate the flow during a sampling process to make sure that this is minimized. In addition, it is important to study the turbulence characteristics, since it is known to influence the inclusion growth. This study presents mathematical modelling of sampler filling using water as a media and experimental results for verification. The study focuses on a lollipop‐shaped sampler since it is one of the most common in the industry. The sampler is filled from an inlet pin located at the bottom centre of the main body. In addition, two different turbulence models, the realizable k‐ε model and Wilcox k‐ω model, were used to study the flow pattern in the sampler. The predictions were compared to experimental results obtained by Particle Image Velocimetry (PIV) measurements. It was found that the flow field predictions using the Wilcox k‐ω model agreed best with the flow field obtained by PIV measurements. Furthermore, it was illustrated that the Wilcox k‐ω model can be used for predictions of the different flow regions as well as the positions of the centres of vortexes which are located near the free surface. Thus, it is concluded that the Wilcox k‐ω model can be used in the future to predict the filling of steel samplers.     

Simulating Bed-Load Transport in a Complex Gravel-Bed River

An existing two-dimensional mobile-bed hydrodynamic model has been modified to simulate bed-load transport in a complex gravel-bed river. We investigated the sensitivity of predicted bed load to control parameters, and compared model predictions of flow depth, shear stress, and gravel transport with field measurements made from the river. The predictions are based on concurrent field data of flow discharge, water level, and sediment for model input. The model takes into account multiple-fraction transport rates, and continuously updates the river bed and surface grain-size distribution. The model predictions are in reasonable agreement with field measurements.     

LDV measurements and computation of a turbulent circular jet placed non-concentrically in a confining pipe

Quantitative and nonintrusive fluid velocity and turbulence measurements obtained using laser Doppler velocimetry (LDV) in a circular jet that is positioned nonconcentrically in a confining pipe are presented. The experimental findings are compared with the results obtained by the finite-element computational simulation of the flow. The measured and predicted contours of the time-averaged axial velocity reveal the presence of a three-dimensional (3-D) asymmetric reverse-flow region, with its radial and circumferential extent depending on the axial position and the eccentricity ratio. Due to the weakened radial mixing and spreading of the jet for the higher eccentricities, the transition to the fully developed state is delayed for the high eccentricity cases. Measured and predicted contours of the axial turbulence fluctuations exhibit the ringlike distribution, although it is observed in an offset position for a given eccentricity ratio. At the downstream stations, the ringlike distribution tends to become more symmetric. The basic phenomena of flow reversal, preferential mixing, and shear layer growth are recovered by the computational predictions based on the high-Reynolds-number turbulence model. The time-averaged velocity measurements compare well with the predictions, whereas only qualitative comparison can be observed between the measured and predicted turbulence fluctuations.     

Analysis of the steady state molten pool obtained by heating a substrate with an electron beam

Surface melting and solidification with high powered beams can be used for enhancing surface properties. The dimensions of the molten zone define the extent of the modified properties and are critical parameters which must be predicted during process design. The flow field in the molten pool has been reported to be one of the key factors which controls the dimensions of the surface layer. However, the calculation of this is only possible through complex numerical schemes and there is a need to look for simple analytical expressions which may be adequate. One approach for this search involves the precise determination of the steady state stationary profiles and then developing a method for extending these values to include the effect of beam motion for predicting the pool dimensions during processing. In this paper, a study of the flow field and its effect on the depth and width of the steady state pool is presented, based on numerical and analytical methods. To validate the predictions, an experimental study is carried out using surface melting of Al-4.5 wt%Cu alloy an electron beam. The pool shapes are presented through optical micrographs and the depth and width of the pool is measured from these micrographs. The experiments are then simulated using a numerical model which includes fluid flow. The flow field is analyzed using streamline plots and the predicted pool shapes are compared with the micrographs. Further, the results are compared to an analytical method based on pure conduction and the pool depth and width are predicted when the liquid thermal conductivity is modified. The numerical and analytical predictions of the pool depth and width are found to be in good agreement with the experimental measurements (obtained from steady state stationary pools and from dimensions inferred on extrapolating moving beam measurements to zero velocity). The reasons for the success of the analytical model is discussed with reference to the two-dimensional flow fields and vortices predicted by the numerical model.