Three-dimensional Transient Mathematical Model Research Articles

Experimental and numerical analysis on electrolytic bubble group dynamics in the aluminum electrolysis process using the slotted anode

The CuSO4 aqueous solution electrolysis experiment is conducted to investigate the electrical bubble dynamics using the slotted anode to reveal the gas removal mechanism. A three-dimensional transient mathematical model coupled discrete phase model (DPM) − discrete-continuum transition model (DCTM) − volume of fluid (VOF) method is developed to track the dispersed bubble trajectory, bridge the dispersed bubble to continuous gas, and resolve the deformed bubble surface, respectively. The slotted anode decreases the bubble diameter compared with the traditional anode because the slot shortens the bubble motion distance to decrease the bubble residence time. The slot width smaller than the detached bubble diameter can limit the bubble deformation. Increasing current plays a dual role in bubble motion in the experiment: it accelerates the bubble coalescence process but decreases the bubble collision probability. The longitudinal slot is more conducive to reducing the maximum bubble coverage and increasing the bubble release frequency than the transverse slot.

Numerical Simulation of the Slag Splashing Process in A 120 Ton Top-Blown Converter

Slag splashing operations at the end of the converter blow process can improve the furnace liner life and the converter operation rate. However, the effect of factors on slag splashing at actual dimensions is yet to be fully understood. A three-dimensional transient mathematical model coupled with the response surface analysis has been established to investigate the effects of the amount of remaining slag, oxygen lance height, and top-blowing nitrogen flowrate on the slag splashing process in a 120 ton top-blown converter. The predicted splashing density is validated by the experimental data. The numerical simulation results show that the splashing density and the splashing area ratio increase with the amount of remaining slag, which has the greatest effect on slag splashing. As the oxygen lance height decreases, the splashing density and the splashing area ratio first increase and then decrease. The top-blowing nitrogen flowrate is positively correlated with the splashing area ratio. When the oxygen lance height is high, the impact of the top-blowing nitrogen flowrate on the splashing density is not significant. The splashing density increases with increasing top-blowing nitrogen flowrate as the oxygen lance height is low.

Flow Field and Temperature Field in a Four-Strand Tundish Heated by Plasma

Tundish plasma heating is an effective method for achieving steady casting with low superheat and constant temperature. In order to study the flow field, temperature field in tundish heated by plasma, a three-dimensional transient mathematical model was established in the present work. A four-strand T-type tundish in a steelmaking plant was used to explore the changes in the flow field and temperature field of molten steel in the tundish under different plasma heating powers. The results showed that plasma heating affected the flow state of molten steel. It could eliminate the short-circuit flow at outlet. When the plasma heating was 500 kW, the molten steel had an obvious upward flow. The turbulence intensity was improved and distributed evenly with an increase in plasma heating power. In the prototype tundish, the temperature of the outlet was dropped by nearly 2–3 K within 300 s. With the increase of plasma heating power, the low temperature area in the tundish gradually was decreased. When the heating power was 1000 kW, the temperature difference of two outlets was 0.5 K and the overall temperature distribution was more uniform. The research results have a certain guiding significance for the selection of the actual plasma heating power on site.

Mathematical Modeling of Transport Phenomena in Multi-track and Multi-layer Laser Powder Deposition of Single-Crystal Superalloy

The transport phenomena in the multi-track and multi-layer laser powder deposition process of single-crystal superalloy were studied through an improved three-dimensional transient mathematical model. The effect of overlapping ratio on the transport phenomena such as temperature field, molten pool morphology, and thermal gradient distribution was discussed. Laser powder deposition experiments with single-crystal superalloy were conducted to verify the computational results. Results showed that temperature field and molten pool morphology are symmetric in the first track of the first layer, and then become asymmetric in the following tracks and layers due to the overlapping between tracks. The peak temperature in a layer increases quickly in the first three tracks and then gradually tends to steady state. For the same track number, the peak temperature in the second layer is higher than that in the first layer. The overlapping ratio has a predominant influence on the molten pool morphology and the distribution of normal thermal gradient at the solidification interface. With the increase of overlapping ratio, the melting depth of molten pool decreases, while the height of molten pool increases. Good agreement was obtained between the predicted and experimentally results. Under the given processing parameters, continuous epitaxial columnar dendrites were achieved in multi-track and multi-layer laser deposited SX superalloy with the optimized overlapping ratio = 34 pct.

Transient three-dimensional dynamics of argon plasma within the vacuum interface of the inductively coupled plasma mass spectrometer system

A three-dimensional transient mathematical model of the “inductively coupled plasma – vacuum interface of the mass spectrometer” system was developed. The model takes into account spatial and temporal dynamics of hot gas flow (plasma emulation) and allows calculation of evolution of spatial distribution of pressure, velocity and temperature fields outside and within the interface of the mass-spectrometer. The results of modeling are verified using the experimental setup of high-speed optical and schlieren visualization of gas flows.

FEATURES OF PARAMETER DETERMINATION OF THE INDUCTION MOTOR SUBSTITUTION CIRCUIT FOR SHORT-CIRCUIT MODE

Purpose. Development of a new method for determining the parameters of an induction motor, based on a three-dimensional transient mathematical model of the electrical and magnetic fields, that provides high accuracy and reliability of results and considering the design features of induction motors, nonlinearity of the electrophysical and magnetic properties of active and structural materials. Methods. Numerical simulation of the conjugate spatial transient electrical and magnetic fields of the induction motor in the short-circuit mode, with help methods of the theory of electromagnetic fields, finite element, theory of electrical machines and electrical circuits. Results. Theoretical researches and simulation results, which based on numerical realization of the finite element method of three-dimensional transient mathematical model of the electrical and magnetic fields in induction motor which displayed the features of the processes of AC energy conversion in the experimental short-circuit mode are obtained. The magnetic field energy is localized mainly in the area of the cores and slots of the stator and rotor of the low-power induction motors by researches was determined. In the zone of the frontal parts of the stator windings, up to 15% of the magnetic field energy of the induction motor is evolved. In the central area of the active part of the induction motor, a length up to 60% of the total length of the stator and rotor core, the magnetic field has plane-parallel form, but is transformed into zones of coil ends of the stator windings and near its end of the core. The influence of the characteristic features of the magnetic field distribution, its energy on the substitution circuit parameters of the low power induction motor and its operating modes are defined. The ratios between the resistances inductive coil ends zone of the stator windings and slots zone stator and rotor windings for an induction motor in short-circuit mode were respectively 14.7% and 85.3%. Originality. The regularities of the spatial distribution of induction and the energy of the magnetic field in the experimental short-circuit mode are defined. When the localization of the magnetic field energy in the frontal parts zone of the stator windings and in the cores and slots regions of the stator and rotor of low-power induction motors, the quantitative relations between the inductive resistances are determined. Practical value. Through the implementation of the dynamic spatial model of electromagnetic fields by the finite element method and numerical simulation data of the short-circuit dynamic mode of the induction motor, the parameters taking into account the structural features of the stator and rotor, and the nonlinear properties of active materials in the multicomponent modeling domain of its substitution circuit are determined. It is proved, that the new approach to the determination of the substitution circuit parameters of induction motors based on simulation data field provides a significant increase in accuracy compared to conventional iterative-empirical methods.

Numerical investigation of the influence of process conditions on the temperature variation in fused deposition modeling

An adaptable three-dimensional transient mathematical model of temperature variation with respect to space and time, during and after the fused deposition modeling (FDM), is proposed and applied with a boundary-adjusting finite difference method. This model enables researchers to study the influence of almost all other parameters on the temperature field and gradient variation when constructing any cuboid at fixed raster angle of 0(90)° and filling ratio of 100%. Some predicted but significant conclusions are reached: reheating of a deposited raster by a newly deposited one is universal and happens mainly in the layer thickness direction; temperature settings are the primary and direct factors determining temperature field variation, while layer thickness and printing speed can still exert their own influence; printing speed is predicted to be positively correlated to mechanical properties of FDM constructed components through the mechanism of thermal coalescence; strict energy management is required if a FDM printer of higher resolution is to be invented and applied. The technique of such mathematical model can provide immediate insights in the understanding of FDM process from the perspective of energy balance, many of which have never been revealed from previous reports yet.

Pyrolysis Characteristics of Municipal Solid Waste in Oxygen-free Circumstance

Abstract An oxygen-free pyrolysis technique employing Shenwu rotating bed reactor with regenerative radiant tube as high temperature heat source was investigated to recycle municipal solid waste. To obtain the optimum condition of this technique, the effects of heating source temperature, arrangement and material thickness on … were discussed, and the compositions and yields of products were studied experimentally. A three-dimensional transient mathematical model characterized with simultaneous fluid flow, heat and mass transfer was established to describe the pyrolysis process in a rotating bed reactor. The model was calibrated based on experimental data. Results show that this new technique has good commercial due to the possibility of avoiding the tar congestion problem effectively and obtaining clean gas with high caloricity.

Anaerobic Pyrolysis Characteristics of Municipal Solid Waste under High Temperature Heat Source

Abstract This study proposed a new pyrolysis technique for municipal solid waste under anaerobic environment with regenerative radiant tube as the high-temperature heat source within a rotating bed reactor. To obtain the optimum condition of this technique, the effect of heating source temperature, arrangement and bed thickness on the distribution, composition and yield of products was experimentally studied. A three-dimensional transient mathematical model was established to describe the pyrolysis process characterized with simultaneous fluid flow, heat and mass transfer in a rotating bed reactor. The simulation model parameters were also modified based on experimental data. Results showed that this new technique has commercial viability due to the possibility to effectively avoid the problem of tar congestion and obtain high caloricity clean gas.

Three-dimensional transient mathematical model to predict the heat transfer rate of a heat pipe

A three-dimensional model was developed to simulate the heat transfer rate on a heat pipe in a transient condition. This article presents the details of a calculation domain consisting of a wall, a wick, and a vapor core. The governing equation based on the shape of the pipe was numerically simulated using the finite element method. The developed three-dimensional model attempted to predict the transient temperature, the velocity, and the heat transfer rate profiles at any domain. The values obtained from the model calculation were then compared with the actual results from the experiments. The experiment showed that the time required to attain a steady state (where transient temperature is constant) was reasonably consistent with the model. The working fluid r134a (tetrafluoroethane) was the quickest to reach the steady state and transferred the greatest amount of heat.

Simulation of transport phenomena in coke oven with staging combustion

A three-dimensional transient mathematical model was developed for coupled coking chamber and staging combustion chamber in large-capacity coke ovens, to describe the flow–combustion–thermo behavior. The model was solved numerically using CFX CFD package and was validated by the central temperature evolution of coke bed. The fields of temperature, fluid flow and combustible gas concentration were analyzed, with special reference to the temperature difference of coke bed and NO concentration of exhaust. The results show that staging combustion plays an important role in improving temperature uniformity of the coke bed and reducing NO concentration of exhaust, especially for the large-capacity coke oven. It is beneficial for production optimization to decrease the gas mass flow rate at the bottom inlet while increase the rate at the upper inlet in the combustion chamber. In addition, it turns out that some measures such as coal preheating, adjustment of moisture content or/and coal densification may be used to improve the coke production efficiency. It is expected the developed model and relevant data in the present research will be beneficial to realize large-scale coke oven with a higher energy efficiency and lower emission.

Computational fluid dynamics integrated development of gerotor pump inlet components for engine lubrication

Generated rotor (gerotor) pumps are widely used in the automotive industry for engine oil lubrication. Computational fluid dynamics (CFD) can be utilized as a useful design tool not only to optimize the flow performance of gerotor pumps but also to develop and finalize specifications for the gerotor pump inlet components. In this paper, a CFD integrated development process for the gerotor pump inlet components such as the suction pipe, strainer, and ports has been executed using a three-dimensional transient mathematical model. The effects of the rotor speed, strainer porosity, and number of ports on the pump performance have been investigated. The results showed that the inlet pipe size, the free area ratio of the strainer, and the sizing of the ports have vital roles in the suction capacity, flow velocity, and volumetric efficiency of the gerotor pump. The selected pump components based on CFD simulation were validated using physical test data, and good agreement was found.

Three-dimensional double-diffusive convection and macrosegregation during non-equilibrium solidification of binary mixtures

A three-dimensional transient mathematical model (following a fixed-grid enthalpy-based continuum formulation) is used to study the interaction of double-diffusive natural convection and non-equilibrium solidification of a binary mixture in a cubic enclosure cooled from a side. Investigations are carried out for two separate test systems, one corresponding to a typical model “metal–alloy analogue” system and other corresponding to a real metal–alloy system. Due to stronger effects of solutal buoyancy in actual metal–alloy systems than in corresponding analogues, the convective transport mechanisms for the two cases are quite different. However, in both cases, similar elements of three-dimensionality are observed in the curvature and spacing of the projected streamlines. As a result of three-dimensional convective flow patterns, a significant solute macrosegregation is observed across the transverse sections of the cavity, which cannot be captured by two-dimensional simulations.