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Numerical Simulation of Phase Transitions in Type-II Annular Superconductor Using Time-dependent Ginzburg-Landau Equations
Time-dependent Ginzburg-Landau equations were solved by finite element method in two-dimensional space for order parameter and energy components of the annular superconducting sample in steady magnetic fields. Vortices preferred to penetrate from the inner surface of the annulus due to lesser energy required at the concave surface. A transition magnetic field strength was observed in spatial averages of carrier concentration and energy components, showing small bumps and abrupt variations, indicating phase transition from a non-vortex to vortex state. These effects were observed to repeat with every subsequent entry of a set of vortices into the sample; transition magnetic field strength was found to depend inversely on the annular width of the sample. The present work gives a better understanding of energy variations during phase transition from non-vortex to vortex state and predicts that vortex state can be avoided by tuning the wire thickness in practical applications, e.g., superconducting electromagnets.
Mechanism of Macrosegregation Formation in Continuous Casting Slab: A Numerical Simulation Study
Solidified shell bulging is supposed to be the main reason for slab center segregation, while the influence of thermal shrinkage rarely has been considered. In this article, a thermal shrinkage model coupled with the multiphase solidification model is developed to investigate the effect of the thermal shrinkage, solidification shrinkage, grain sedimentation, and thermal flow on solute transport in the continuous casting slab. In this model, the initial equiaxed grains contract freely with the temperature decrease, while the coherent equiaxed grains and columnar phase move directionally toward the slab surface. The results demonstrate that the center positive segregation accompanied by negative segregation in the periphery zone is mainly caused by thermal shrinkage. During the solidification process, liquid phase first transports toward the slab surface to compensate for thermal shrinkage, which is similar to the case considering solidification shrinkage, and then it moves opposite to the slab center near the solidification end. It is attributed to the sharp decrease of center temperature and the intensive contract of solid phase, which cause the enriched liquid to be squeezed out. With the effect of grain sedimentation and thermal flow, the negative segregation at the external arc side (zone A1) and the positive segregation near the columnar-to-equiaxed transition at the inner arc side (position B1) come into being. Besides, it is found that the grain sedimentation and thermal flow only influence solute transport before equiaxed grains impinge with each other, while the solidification and thermal shrinkage still affect solute redistribution in the later stage.
Numerical Simulation of Bulging Deformation for Wide-Thick Slab Under Uneven Cooling Conditions
In the present work, the bulging deformation of a wide-thick slab under uneven cooling conditions was studied using finite element method. The non-uniform solidification was first calculated using a 2D heat transfer model. The thermal material properties were derived based on a microsegregation model, and the water flux distribution was measured and applied to calculate the cooling boundary conditions. Based on the solidification results, a 3D bulging model was established. The 2D heat transfer model was verified by the measured shell thickness and the slab surface temperature, and the 3D bulging model was verified by the calculated maximum bulging deflections using formulas. The bulging deformation behavior of the wide-thick slab under uneven cooling condition was then determined, and the effect of uneven solidification, casting speed, and roll misalignment were investigated.
Numerical Simulation of Multiphase Magnetohydrodynamic Flow and Deformation of Electrolyte–Metal Interface in Aluminum Electrolysis Cells
A computational fluid dynamics based multiphase magnetohydrodynamic (MHD) flow model for simulating the melt flow and bath–metal interface deformation in realistic aluminum reduction cells is presented. The model accounts for the complex physics of the MHD problem in aluminum reduction cells by coupling two immiscible fluids, electromagnetic field, Lorentz force, flow turbulence, and complex cell geometry with large length scale. Especially, the deformation of bath–metal interface is tracked directly in the simulation, and the condition of constant anode–cathode distance (ACD) is maintained by moving anode bottom dynamically with the deforming bath–metal interface. The metal pad deformation and melt flow predicted by the current model are compared to the predictions using a simplified model where the bath–metal interface is assumed flat. The effects of the induced electric current due to fluid flow and the magnetic field due to the interior cell current on the metal pad deformation and melt flow are investigated. The presented model extends the conventional simplified box model by including detailed cell geometry such as the ledge profile and all channels (side, central, and cross-channels). The simulations show the model sensitivity to different side ledge profiles and the cross-channel width by comparing the predicted melt flow and metal pad heaving. In addition, the model dependencies upon the reduction cell operation conditions such as ACD, current distribution on cathode surface and open/closed channel top, are discussed.
A Numerical Simulation of Transport Phenomena During the Horizontal Single Belt Casting Process Using an Inclined Feeding System
Horizontal single belt casting (HSBC) has great potential to replace current conventional continuous casting (CCC) processes for sheet metal production, by directly casting 3 to 1 mm sheet for the automobile industry. In the present paper, two-dimensional mathematical models were developed to study transport phenomena, for the case of an inclined wall feeding system for a liquid aluminum wrought alloy (AA6111). Based on the commercial software ANSYS FLUENT 14.5 and user-defined functions, a two-layer turbulence model was used to examine the fluid flow emanating from a slot nozzle set above a water-cooled, high-speed, steel belt. The Volume of Fluid (VOF) method was used to predict the shape of the melt-air interface. A transformed coordinate system (x′, y′) was established in order to analyze the fluid flow on the inclined wall of the feeding system. The total pressure gauge gradient (∂p{sub total}/∂x) was used to describe the behavior of the melt film inside the slot nozzle of the head box. The modeling results show that during the melt film falling process, the total gauge pressure varies within the slot nozzle, which can decrease the stability of the falling film. The first impingement between the falling film and the inclined refractory wall of the feeding system gives rise to a local oscillation, and this influences the stability of the melt film moving downwards. At the rear meniscus position between the inclined wall and the moving belt, there is a clear vibration of the air-melt interface, together with a recirculation zone. The weak vibration of the air-melt interface could be induced by the periodic variation of the melt-air interface. Moreover, the formation of tiny air pockets is predicted. Finally, on the inclined wall of the feeding system, a suitable length of the transition area is needed to avoid over-acceleration of the melt film due to the force of gravity.
Numerical Simulation of Slag Eye Formation and Slag Entrapment in a Bottom-Blown Argon-Stirred Ladle
A transient mathematical model is developed for simulating the bubble-steel-slag-top gas four-phase flow in a bottom-blown argon-stirred ladle with a 70-ton capacity. The Lagrangian discrete phase model (DPM) is used for describing the moving behavior of bubbles in the steel and slag. To observe the formation process of slag eye, the volume of fluid (VOF) model is used to track the interfaces between three incompressible phases: metal/slag, metal/gas, and slag/gas. The complex multiphase turbulent flow induced by bubble-liquid interactions is solved by a large eddy simulation (LES) model. Slag eye area and slag droplet dispersion are investigated under different gas flow rates. The results show that the movement of bubbles, formation and collapse of slag eye, volatility of steel/slag interface and behavior of slag entrapment can be properly predicted in the current model. When the gas flow rate is 300 L/min, the circulation driven by the bubble plume will stir the entire ladle adequately and form a slag eye of the right size. At the same time, it will not cause strong erosion to the ladle wall, and the fluctuation of the interface is of adequate intensity, which will be helpful for improving the desulfurization efficiency; the slag entrapment behavior can also be decreased. Interestingly, with the motion of liquid steel circulation, the collision and coalescence of dispersed slag droplets occur during the floating process in the vicinity of the wall.
Numerical Simulation of V-shaped Segregation in Continuous Casting Blooms Based on a Microsegregation Model
This study establishes a volume-averaged model for transport phenomena to study V-shaped segregation in continuous casting blooms with different superheating and cooling rates by coupling fluid flow, macro-scale heat transfer, and solute transport. The results demonstrate that the modified Won–Thomas model considering back diffusion in the solid phase corresponds well with the measured carbon segregation. V-shaped segregation decreases with decreasing superheating and increases slightly with decreases in the cooling rate. The results of original position statistical distribution analysis correspond well with the simulation results. This phenomenon can be exploited to improve the quality of bloom.
Numerical Simulation of Recirculating Flow and Physical Model of Slag–Metal Behavior in an RH Reactor: Application to Desulfurization
Computational fluid dynamics (CFD) techniques and a 1:7.5 physical model of an RH degasser have been used to evaluate the flow of gas and metal inside an RH reactor for vacuum degassing of liquid steel. The effect of gas injection on the gas spatial distribution, steel circulation rate and flow field inside the ladle, snorkels and vacuum chamber have been assessed. N-pentane oil was employed to evaluate the average residence time as well as the slag droplet size distribution. The predicted radial gas distribution and liquid circulation rate have been validated against experimental data from a physical model. The results with incorporation of the virtual mass force coefficient of 0.25 and the turbulence dispersion force showed better predictions of gas distribution in the up-snorkel as well as circulation rate. Full-scale simulations were performed, and the predicted circulation rate was significantly affected by the argon bubble expansion. Data from these simulations were used to analyze the degree of desulfurization performed by the addition of desulfurizing agents inside the vacuum chamber. A model of the kinetics of desulfurization based on the results from the physical model and CFD simulation and on slag dispersion inside liquid steel yields degrees of desulfurization similar to the industrial trials reported in the literature.
Numerical Simulation of Gas and Liquid Two-Phase Flow in the RH Process
A mathematical model has been established to simulate the gas–liquid two-phase flow in the RH process. The effects of interphase forces and the bubble-induced turbulence on the fluid flow and motion of gas bubbles were investigated. The interphase forces include the drag force, the virtual mass force, the lift force, and the pressure gradient force, respectively. The prediction results of the liquid velocity and the recirculation rate were compared with the experimental data measured with a Particle Image Velocimetry technique. The results indicated that the drag force and the virtual mass force dominated the gas plume shape in the up-leg snorkel, and significantly influenced the liquid velocity and the distribution of the gas phase. The lift force mainly affected the spreading of gas bubbles in the radial direction of the snorkel. However, the pressure gradient force could be neglected because it had no effect on the liquid velocity and the gas volume fraction. The increase of the bubble-induced turbulence decreased the liquid velocity, and by adjusting the lift force, it widened the shape of the individual gas plumes. To accurately simulate the gas–liquid flow behavior in the RH degasser, these appropriate parameters, such as the drag coefficient, the virtual mass coefficient, the lift coefficient, and the bubble-induced turbulence coefficient, were determined by comparing the predicted results and the measured data.
Correction to: Numerical Simulation and Experimental Validation of Nondendritic Structure Formation in Magnesium Alloy Under Oscillation and Ultrasonic Vibration
The equation 1 “1 − ϕ” should be “1 − ϕ{sup 2}”.
Numerical Simulation of Residual Stress for Laser Welding of Ti-6Al-4V Alloy Considering Solid-State Phase Transformation
In the present work, a thermal-metallurgical-mechanical model which considered the influence of phase transformation was used to predict the residual stress field of Ti-6Al-4V after laser welding. In this model, the Johnson–Mehl–Avrami equation was used to predict diffusional solid-state phase transformations: α phase to β phase during heating and β phase to α phase during cooling. The Koistinen–Marburger equation was used to predict diffusionless solid-state phase transformation of β phase to martensite during cooling. The properties of material were obtained using a mixing rule based on the phase fraction and the property of each pure phase. By applying this model, the effect of solid-state phase transformations of Ti-6Al-4V alloy on temperature field and stress field during laser welding was considered in the simulation. In addition, experiments were carried out for comparison, which significantly verified the accuracy of the applied model.
Remedial Amendment Delivery near the Water Table Using Shear Thinning Fluids: Experiments and Numerical Simulations
The use of shear thinning fluids (STFs) containing xanthan is a potential enhancement for emplacing a solute amendment near the water table and within the capillary fringe. Most research to date related to STF behavior has involved saturated and confined conditions. A series of flow cell experiments were conducted to investigate STF emplacement in variable saturated homogeneous and layered heterogeneous systems. Besides flow visualization using dyes, amendment concentrations and pressure data were obtained at several locations. The experiments showed that injection of STFs considerably improved the subsurface distribution near the water table by mitigating preferential flow through higher permeability zones compared to no-polymer injections. The phosphate amendment migrated with the xanthan SFT without retardation. Despite the high viscosity of the STF, no excessive mounding or preferential flow were observed in the unsaturated zone. The STOMP simulator was able to predict the experimentally observed fluid displacement and amendment concentrations reasonably well. Cross flow between layers could be interpreted as the main mechanism to transport STFs into lower permeability layers based on the observed pressure gradient and concentration data in layers of differing hydraulic conductivity.
An explicit staggered-grid method for numerical simulation of large-scale natural gas pipeline networks
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Numerical simulation and optimization of an industrial fluid catalytic cracking regenerator
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Numerical simulations of significant orographic precipitation in Madeira island
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