Simulation of macrosegregation in a 36-t steel ingot using a multiphase model

Macrosegregation is the major defect in large steel ingots caused by solute partitioning and melt convection during casting.In this study,a three-phase(liquid,columnar dendrites,and equiaxed grains)model is proposed to simulate macrosegregation in a 36-t steel ingot.A supplementary set of conservation equations are employed in the model such that two types of equiaxed grains,either settling or adhering to the solid shell,are well simulated.The predicted concentration agrees quantitatively with the experimental value.A negative segregation cone was located at the bottom owing to the grain settlement and solute-enriched melt leaving from the mushy zone.The interdendritic liquid flow was carefully analyzed,and the formation of A-type segregations in the mid-height of the ingot is discussed.Negative segregation was observed near the riser neck due to the specific relationship between flow direction and temperature gradient.Additionally,the as-cast macrostructure of the ingot is presented,including the grain size distribution and columnar–equiaxed transition.

Volume-averaged modeling of multiphase solidification with equiaxed crystal sedimentation in a steel ingot

Macrosegregation is a critical factor that limits the mechanical properties of materials.The impact of equiaxed crystal sedimentation on macrosegregation has been extensively studied,as it plays a significant role in determining the distribution of alloying elements and impurities within a material.To improve macrosegregation in steel connecting shafts,a multiphase solidification model that couples melt flow,heat transfer,microstructure evolution,and solute transport was established based on the volume-averaged Eulerian-Eulerian approach.In this model,the effects of liquid phase,equiaxed crystals,columnar dendrites,and columnar-to-equiaxed transition(CET)during solidification and evolution of microstructure can be considered simultaneously.The sedimentation of equiaxed crystals contributes to negative macrosegregation,where regions between columnar dendrites and equiaxed crystals undergo significant A-type positive macrosegregation due to the CET.Additionally,noticeable positive macrosegregation occurs in the area of final solidification in the ingot.The improvement in macrosegregation is beneficial for enhancing the mechanical properties of connecting shafts.To mitigate the thermal convection of molten steel resulting from excessive superheating,reducing the superheating during casting without employing external fields or altering the design of the ingot mold is indeed an effective approach to control macrosegregation.

Exploration of the coupled lattice Boltzmann model based on a multiphase field model:A study of the solid-liquid-gas interaction mechanism in the solidification process

A multiphase field model coupled with a lattice Boltzmann(PF-LBM)model is proposed to simulate the distribution mechanism of bubbles and solutes at the solid-liquid interface,the interaction between dendrites and bubbles,and the effects of different temperatures,anisotropic strengths and tilting angles on the solidified organization of the SCN-0.24wt.%butanedinitrile alloy during the solidification process.The model adopts a multiphase field model to simulate the growth of dendrites,calculates the growth motions of dendrites based on the interfacial solute equilibrium;and adopts a lattice Boltzmann model(LBM)based on the Shan-Chen multiphase flow to simulate the growth and motions of bubbles in the liquid phase,which includes the interaction between solid-liquid-gas phases.The simulation results show that during the directional growth of columnar dendrites,bubbles first precipitate out slowly at the very bottom of the dendrites,and then rise up due to the different solid-liquid densities and pressure differences.The bubbles will interact with the dendrite in the process of flow migration,such as extrusion,overflow,fusion and disappearance.In the case of wide gaps in the dendrite channels,bubbles will fuse to form larger irregular bubbles,and in the case of dense channels,bubbles will deform due to the extrusion of dendrites.In the simulated region,as the dendrites converge and diverge,the bubbles precipitate out of the dendrites by compression and diffusion,which also causes physical phenomena such as fusion and spillage of the bubbles.These results reveal the physical mechanisms of bubble nucleation,growth and kinematic evolution during solidification and interaction with dendrite growth.

Application of different CFD multiphase models to investigate effects of baffles and nanoparticles on heat transfer enhancement

In this work, the effect of baffles in a pipe on heat transfer enhancement was studied using computa- tional fluid dynamics （CFD） in the presence of Al2O3 nanoparticles which are dispersed into water. Fluid flow through the horizontal tube with uniform heat flux was simulated numerically and three dimensional governing partial differential equations were solved. To find an accurate model for CFD simulations, the results obtained by the single phase were compared with those obtained by three different multiphase models including Eulerian, mixture and volume of fluid （VOF） at Reynolds numbers in range of 600 to 3000, and two different nanoparticle concentrations （1% and 1.6%）. It was found that multi- phase models could better predict the heat transfer in nanofluids. The effect of baffles on heat transfer of nanofluid flow was also investigated through a baffled geometry. The numerical results show that at Reynolds numbers in the range of 600 to 2100, the heat transfer of nanofluid flowing in the geometry without baffle is greater than that of water flowing through a tube with baffle, whereas the difference between these effects （nanofluid and baffle） decreases with increasing the Reynolds number. At higher Reynolds numbers （2100-3000） the baffle has a greater effect on heat transfer enhancement than the nanofluid.

Multiphase modeling of fluid dynamic in ladle steel operations under non-isothermal conditions

A numerical simulation was performed to study the flow pattern,mixing time and open-eye slag produced by argon gas injection in an industrial scale steel ladle under non-isothermal conditions.The liquid steel remains 5min before the injection,and thermal stratification and convective flows were analyzed.Three different sequences in stages employing various argon-gas flow rates were simulated.In the first case,a sequence with the highest flow rates of argon was applied,while in the second and the third sequences,the intermediate and the lowest flow rates of argon gas were used,respectively.For determining the chemistry homogenization,the mixing time was computed and analyzed in all three cases.It was found that the cold steel is located near the walls while the steel with a high temperature is accumulated in the center of the ladle above the argon-gas tuyere.The higher and lower flows promote a faster chemistry homogenization owing to the secondary recirculations that are developed closer to the walls.The results from steel temperature drop show a good concordance with plant trial measurements.

Multiphase equilibrium modeling of oxygen bottom-blown copper smelting process

A computational thermodynamics model for the oxygen bottom-blown copper smelting process(Shuikoushan,SKS process)was established,based on the SKS smelting characteristics and theory of Gibbs free energy minimization.The calculated results of the model show that,under the given stable production condition,the contents of Cu,Fe and S in matte are71.08%,7.15%and17.51%,and the contents of Fe,SiO2and Cu in slag are42.17%,25.05%and3.16%.The calculated fractional distributions of minor elements among gas,slag and matte phases are As82.69%,11.22%,6.09%,Sb16.57%,70.63%,12.80%,Bi68.93%,11.30%,19.77%,Pb19.70%,24.75%,55.55%and Zn17.94%,64.28%,17.79%,respectively.The calculated results of the multiphase equilibrium model agree well with the actual industrial production data,indicating that the credibility of the model is validated.Therefore,the model could be used to monitor and optimize the industrial operations of SKS process.

A Multiphase Wellbore Flow Model for Sour Gas “Kicks”

This study presents a new multiphase flow model with transient heat transfer and pressure coupling to simulate HTHP(high temperature and high pressure)sour gas“kicks”phenomena.The model is intended to support the estimation of wellbore temperature and pressure when sour gas kicks occur during drilling operation.The model considers sour gas solubility,phase transition and effects of temperature and pressure on the physical parameters of drilling fluid.Experimental data for a large-diameter pipe flow are used to validate the model.The results indicate that with fluid circulation,the annulus temperature with H2S kicks is the highest,followed by CO_(2),and CH_(4) is the lowest.The phase transition point of H2S is closer to wellhead compared with CO_(2),resulting in a faster expansion rate,which is more imperceptible and dangerous.With fluid circulation,the drilling fluid density and plastic viscosity both first decrease and then increase with the increase in the well depth.The bottom hole pressure when H2S kicks is greater than that for CO_(2) with the same amount of sour gas,and the pressure difference gradually increases with the increase of H2S/CO_(2) content.In addition,a parametric sensitivity analysis has been conducted to evaluate qualitatively and rank the influential factors affecting the bottom hole temperature and pressure.

A multicomponent multiphase lattice Boltzmann model with large liquid–gas density ratios for simulations of wetting phenomena

A multicomponent multiphase（MCMP） pseudopotential lattice Boltzmann（LB） model with large liquid–gas density ratios is proposed for simulating the wetting phenomena. In the proposed model, two layers of neighboring nodes are adopted to calculate the fluid–fluid cohesion force with higher isotropy order. In addition, the different-time-step method is employed to calculate the processes of particle propagation and collision for the two fluid components with a large pseudoparticle mass contrast. It is found that the spurious current is remarkably reduced by employing the higher isotropy order calculation of the fluid–fluid cohesion force. The maximum spurious current appearing at the phase interfaces is evidently influenced by the magnitudes of fluid–fluid and fluid–solid interaction strengths, but weakly affected by the time step ratio.The density ratio analyses show that the liquid–gas density ratio is dependent on both the fluid–fluid interaction strength and the time step ratio. For the liquid–gas flow simulations without solid phase, the maximum liquid–gas density ratio achieved by the present model is higher than 1000：1. However, the obtainable maximum liquid–gas density ratio in the solid–liquid–gas system is lower. Wetting phenomena of droplets contacting smooth/rough solid surfaces and the dynamic process of liquid movement in a capillary tube are simulated to validate the proposed model in different solid–liquid–gas coexisting systems. It is shown that the simulated intrinsic contact angles of droplets on smooth surfaces are in good agreement with those predicted by the constructed LB formula that is related to Young＇s equation. The apparent contact angles of droplets on rough surfaces compare reasonably well with the predictions of Cassie＇s law. For the simulation of liquid movement in a capillary tube, the linear relation between the liquid–gas interface position and simulation time is observed, which is identical to the analytical prediction. The simulation results regarding the wetting phenomena of droplets on smooth/rough surfaces and the dynamic process of liquid movement in the capillary tube demonstrate the quantitative capability of the proposed model.

Elliptic Flow Splitting between Particles and their Antiparticles in Au＋Au Collisions from a Multiphase Transport Model

The elliptic flow v2, for π±, K±, p and p in Au＋Au collisions at center-of-mass energies √sNN=7.7, 11.5, 14.5 and 19.6 GeV, is analyzed using a multiphase transport model. A significant difference in the v2 values for p and p is observed, and the values of v2 splitting are larger compared with π＋ and π-, K＋ and K-. The difference increases with decreasing the center-of-mass energy. The effect of the quark coalescence mechanism in a multi-phase transport model to the value of elliptic difference △v2 between p and p- has been discussed. The simulation of Au＋Au collisions at 14.5 GeV shows that the effect of hadron cascade to △v2 is not obvious, and a larger patton-scattering cross section can lead to a larger △v2.

Influences of Co-Flow and Counter-Flow Modes of Reactant Flow Arrangement on a PEMFC at Start-Up

To investigate the influences of co-flowand counter-flowmodes of reactant flowarrangement on a proton exchange membrane fuel cell(PEMFC)during start-up,unsteady physical and mathematical models fully coupling the flow,heat,and electrochemical reactions in a PEMFC are established.The continuity equation and momentum equation are solved by handling pressure-velocity coupling using the SIMPLE algorithm.The electrochemical reaction rates in the catalyst layers(CLs)of the cathode and anode are calculated using the Butler-Volmer equation.The multiphase mixture model describes the multiphase transport process of gas mixtures and liquid water in the fuel cell.After validation,the influences of co-flow and counter-flow modes on the PEMFC performance are investigated,including the evolution of the current density,flow field,temperature field,and reactant concentration field during start-up,as well as the steady distribution of the current density,reactant concentration,andmembrane water content when the start-up stabilizes.Co-flow and counter-flow modes influence the current density distribution and temperature distribution.On the one hand,the co-flow mode accelerates the start-up process of the PEMFC and leads to a more evenly distributed current density than the counter-flow mode.On the other hand,the temperature difference between the inlet and outlet sections of the cell is up to 10.1℃ under the co-flow mode,much larger than the 5.0℃ observed in the counter-flow mode.Accordingly,the counter-flowmode results in a more evenly distributed temperature and a lower maximum temperature than the co-flow case.Therefore,in the flow field design of a PEMFC,the reactant flow arrangements can be considered to weigh between better heat management and higher current density distribution of the cell.

Analysis of Snow Distribution and Displacement in the Bogie Region of a High-Speed Train

Snow interacting with a high-speed train can cause the formation of ice in the train bogie region and affect its safety.In this study,a wind-snow multiphase numerical approach is introduced for high-speed train bogies on the basis of the Euler-Lagrange discrete phase model.A particle-wall impact criterion is implemented to account for the presence of snow particles on the surface.Subsequently,numerical simulations are conducted,considering various snow particle diameter distributions and densities.The research results indicate that when the particle diameter is relatively small,the distribution of snow particles in the bogie cavity is relatively uniform.However,as the particle diameter increases,the snow particles in the bogie cavity are mainly located in the rear wheel pairs of the bogie.When the more realistic Rosin-Rammler diameter distribution is applied to snow particles,the positions of snow particles with different diameters vary in the bogie cavity.More precisely,smaller diameter particles are primarily located in the front and upper parts of the bogie cavity,while larger diameter snow particles accumulate at the rear and in the lower parts of the bogie cavity.

A generalized CFD model for evaluating catalytic separation process in structured porous materials

A hybrid multiphase model is developed to simulate the simultaneous momentum, heat and mass transfer and heterogeneous catalyzed reaction in structured catalytic porous materials. The approach relies on the combination of the volume of fluid(VOF) and Eulerian–Eulerian models, and several plug-in field functions. The VOF method is used to capture the gas–liquid interface motion, and the Eulerian–Eulerian framework solves the temperature and chemical species concentration equations for each phase.The self-defined field functions utilize a single-domain approach to overcome convergence difficulty when applying the hybrid multiphase for a multi-domain problem. The method is then applied to investigate selective removal of specific species in multicomponent reactive evaporation process. The results show that the coupling of catalytic reaction and interface species mass transfer at the phase interface is conditional, and the coupling of catalytic reaction and momentum transfer across fluid–porous interface significantly affects the conversion rate of reactants. Based on the numerical results, a strategy is proposed for matching solid catalyst with operating condition in catalytic distillation application.

Uncertainty analysis of flow rate measurement for multiphase flow using CFD

The venturi meter has an advantage in its use,because it can measure flow without being much affected by the type of the measured fluid or flow conditions.Hence,it has excellent versatility and is being widely applied in many industries.The flow of a liquid containing air is a representative example of a multiphase flow and exhibits complex flow characteristics.In particular,the greater the gas volume fraction（GVF）,the more inhomogeneous the flow becomes.As a result,using a venturi meter to measure the rate of a flow that has a high GVF generates an error.In this study,the cause of the error occurred in measuring the flow rate for the multiphase flow when using the venturi meter for analysis by CFD.To ensure the reliability of this study,the accuracy of the multiphase flow models for numerical analysis was verified through comparison between the calculated results of numerical analysis and the experimental data.As a result,the Grace model,which is a multiphase flow model established by an experiment with water and air,was confirmed to have the highest reliability.Finally,the characteristics of the internal flow Held about the multiphase flow analysis result generated by applying the Grace model were analyzed to find the cause of the uncertainty occurring when measuring the flow rate of the multiphase flow using the venturi meter.A phase separation phenomenon occurred due to a density difference of water and air inside the venturi,and flow inhomogeneity happened according to the flow velocity difference of each phase.It was confirmed that this flow inhomogeneity increased as the GVF increased due to the uncertainty of the flow measurement.

Study of acoustic bubble cluster dynamics using a lattice Boltzmann model

The search for the development of a reliable mathematical model for understanding bubble dynamics behavior is an ongoing endeavor.A long list of complex phenomena underlies the physics of this problem.In the past decades,the lattice Boltzmann method has emerged as a promising tool to address such complexities.In this regard,we have applied a 121-velocity multiphase lattice Boltzmann model to an asymmetric cluster of bubbles in an acoustic field.A problem as a benchmark is studied to check the consistency and applicability of the model.The problem of interest is to study the deformation and coalescence phenomena in bubble cluster dynamics,as well as the screening effect on an acoustic multibubble medium.It has been observed that the LB model is able to simulate the combination of the three aforementioned phenomena for a bubble cluster as a whole and for every individual bubble in the cluster.

Three-dimensional Simulation of Gas/Solid Flow in Spout-fluid Beds with Kinetic Theory of Granular Flow

A three-dimensional Eulerian multiphase model, with closure law according to the kinetic theory of granular flow, was used to study the gas/solid flow behaviors in spout-fluid beds. The influences of the coefficient of restitution due to non-ideal particle collisions on the simulated results were tested. It is demonstrated that the simulated result is strongly affected by the coefficient of restitution. Comparison of simulations with experiments in a small spout-fluid bed showed that an appropriate coefficient of restitution of 0.93 was necessary to simulate the flow characteristics in an underdesigned large size of spout-fluid bed coal gasifier with diameter of lm and height of 6m. The internal jet and gas/solid flow patterns at different operating conditions were obtained. The simulations show that an optimal gas/solid flow pattern for coal gasification is found when the spouting gas flow rate is equal to the fluidizing gas flow rate and the total of them is two and a half times the minimum fluidizing gas flow rate. Besides, the radial distributions of particle velocity and gas velocity show similar tendencies; the radial distributions of particle phase pressure due to particle collisions and the particle pseudo-temperature corresponding to the macroscopic kinetic energy of the random particle motion also show similar tendencies. These indicate that both gas drag force and particle collisions dominate the movement of particles.

2D-simulation of wet steam flow in a steam turbine with spontaneous condensation

Removal of condensates from wet steam flow in the last stages of steam turbines significantly promotes stage efficiency and prevents erosion of rotors. In this paper, homogeneous spontaneous condensation in transonic steam flow in the 2-D rotor-tip section of a stage turbine is investigated. Calculated results agree with experimental data reasonably well. On the basis of the above work, a 2-D numerical simulation of wet steam flow in adjacent root sections of a complex steam turbine stage was carded out. Computational results were analyzed and provide insights into effective removal of humidity.

A review on prediction of casting defects in steel ingots:from macrosegregation to multi-defect model

Due to the nature of the solute redistribution,the reduction in the solidification rate with time in a square root relationship,and the multiphase melt flow during the solidification,casting defects such as macrosegregation,shrinkage cavity,and porosity will inevitably occur in the steel ingot and intensify with the increase in ingot size.These defects directly affect the performance of the final product and severely restrict the choice of subsequent thermal processing methods and process windows.Therefore,the solidification defects including macrosegregation,shrinkage/porosity,and inclusions encountered in the preparation of large steel ingots and their formation mechanisms were reviewed.The development progress and the latest development of the macrosegregation model for steel ingots were introduced in detail,especially the latest progress in the coupling prediction of macrosegregation and shrinkage as well as macrosegregation and inclusions.Some methods to reduce macrosegregation of ingots were discussed as well.Finally,a new casting method called layered casting was introduced in detail.This method can effectively improve the uniformity of the macrostructure and reduce the macrosegregation of the large ingots and therefore is a promising method for preparing large ingots with high homogeneity.

Modeling and simulation of circulating fluidized bed reactors applied to a carbonation/calcination loop

A fluid dynamic model for a gas-solid circulating fluidized bed （CFB） designed using two coupled riser reactors is developed and implemented numerically with code programmed in Matlab. The fluid dynamic model contains heat and species mass balances to calculate temperatures and compositions for a carbonation/calcination loop process. Because of the high computational costs required to resolve the three-dimensional phenomena, a model representing a trade-offbetween computational time requirements and accuracy is developed. For dynamic processes with a solid flux between the two reactor units that depends on the fluid dynamics of both risers, a dynamic one-dimensional two-fluid model is sufficient. A two-fluid model using the constant particle viscosity closure for the stress term is used for the solid phase, and an algebraic turbulence model is applied to the gas phase. The numerical model implementa- tion is based on the finite volume method with a staggered grid scheme. The exchange of solids between the reactor units constituting the circulating fluidized bed （solid flux） is implemented through additional mass source/sink terms in the continuity equations of the two phases, For model validation, a relevant experimental analysis provided in the literature is reproduced by the numerical simulations, The numerical analysis indicates that sufficient heat integration between the two reactor units is important for the performance of the circulating fluidized bed system, The two-fluid model performs fairly well for this chemical process operated in a CFB designed as two coupled riser reactors. Further analysis and optimization of the solution algorithms and the reactor coupling strategy is warranted.

Numerical approach for modeling particle transport phenomena in a closed loop of a circulating fluidized bed

Numerical modeling of a large scale circulating fiuidized bed （CFB） imposes many complexities and difficulties. Presence of a dense solid phase, a variety of spatial and time scales as well as complex model geometries requires advanced numerical techniques. Moreover, the appropriate selection of a numerical model capable of solving granular flow, and geometrical model simplification can have a huge impact on the predicted flow field within the CFB boiler. In order to reduce the cost of the numerical simulations, the complex CFB boiler geometry is reduced to that of the combustion chamber. However, a question arises as to bow much one can simplify the geometrical model without losing accuracy of numerical simulations. To accurately predict the gas-solid and solid-solid mixing processes within subsequent sections of the CFB boiler （combustion chamber, solid separator, drain section）, a complete 3D geometrical model should be used. Nevertheless, because of the presence of various spatial and temporal scales within subsequent boiler sections, the complete model of the 3D CFB boiler is practically unrealizable in numerical simulations. To resolve the aforementioned problems, this paper describes a new approach that can be applied for complete boiler modeling. The proposed approach enables complex particle transport and gas flow problems within each of the boiler sections to be accurately resolved, It has been achieved by dividing the CFB boiler geometry into several submodels, where different numerical approaches can be used to resolve gas-solid transport. The interactions between computational domains were taken into account by connecting the inlets/outlets of each section using a set of user-defined functions implemented into the solution procedure. The proposed approach ensures stable and accurate solution within the separated boiler zones.

Modelling the bed characteristics in fluidised-beds for top-spray coating processes

A particle sub-model describing the bed characteristics of a bubbling fluidised bed is presented. Atomisation air, applied at high pressures via a nozzle positioned above the bed for spray formation, is incorporated in the model since its presence has a profound influence on the bed characteristics, though the spray itself is not yet considered. A particle sub-model is developed using well-known empirical relations for particle drag force, bubble growth and velocity and particle distribution above the fluidised-bed surface. Simple but effective assumptions and abstractions were made concerning bubble distribution, particle ejection at the bed surface and the behaviour of atomisation air flow upon impacting the surface of a bubbling fluidised bed, The model was shown to be capable of predicting the fluidised bed characteristics in terms of bed heights, voidage distributions and solids volume fractions with good accuracy in less than 5 min of calculation time on a regular desktop PC. It is therefore suitable for incorporation into general process control models aimed at dynamic control for process efficiency and product quality in top-spray fluidised bed coating processes.