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.

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.

A coupled model of TiN inclusion growth in GCr15SiMn during solidification in the electroslag remelting process

TiN inclusions observed in an ingot produced by electroslag remelting （ESR） are extremely harmful to GCrl5SiMn steel. Therefore, accurate predictions of the growth size of these inclusions during steel solidification are significant for clean ESR ingot production. On the basis of our previous work, a coupled model of solute microsegregation and TiN inclusion growth during solidification has been established. The results demonstrate that compared to a non-coupled model, the coupled model predictions of the size of TiN inclusions are in good agreement with experimental results using scanning electron microscopy with energy disperse spectroscopy （SEM-EDS）. Because of high cooling rate, the sizes of TiN inclusions in the edge area of the ingots are relatively small compared to the sizes in the center area. During the ESR process, controlling the content of Ti in the steel is a feasible and effective method of decreasing the sizes of TiN inclusions.

Recent research progress on the phase-field model of microstructural evolution during metal solidification

Solidification structure is a key aspect for understanding the mechanical performance of metal alloys,wherein composition and casting parameters considerably influence solidification and determine the unique microstructure of the alloys.By following the principle of free energy minimization,the phase-field method eliminates the need for tracking the solid/liquid phase interface and has greatly accelerated the research and development efforts geared toward optimizing metal solidification microstructures.The recent progress in the application of phasefield simulation to investigate the effect of alloy composition and casting process parameters on the solidification structure of metals is summarized in this review.The effects of several typical elements and process parameters,including carbon,boron,silicon,cooling rate,pulling speed,scanning speed,anisotropy,and gravity,on the solidification structure are discussed.The present work also addresses the future prospects of phase-field simulation and aims to facilitate the widespread applications of phase-field approaches in the simulation of microstructures during solidification.

Study of ultrahigh-purity copper billets refined by vacuum melting and directional solidification

The purpose of this paper is to study large-sized copper billets refined with 5N ultrahigh purity after vacuum melting and directional solidifi-cation （VMDS）. The precise impurity analysis of copper billets was carried out with a glow discharge mass spectrometer （GDMS）. The re-sults demonstrate that the total concentration of twenty-two impurities is decreased by 63.1wt.%-66.5 wt.%. Ag, P, S, Na, Mg, Se, Zn, In and Bi are easy to be removed due to lgPimp - lgPCu 1.5, and they can be removed effectively under the vacuum condition of 1650-1700 K for 30 min. The electrical conductivity of 5N copper is higher than that of the raw material as the impurity concentrations decrease. The segrega-tion effect in directional solidification can be remarkable when the equilibrium distribution coefficient （k0） value is less than 0.65 due to the strong affinity of Cu for some metallic and non-metallic impurities.

Numerical and Experimental Studies of Substrate Melting and Resolidification during Thermal Spraying

A good understanding of melting and resolidification of the substrate will help us to achieve better bonding.Anumerical model is developed to investigate the solidification of the droplet,and melting and resolidification of thesubstrate.The molybdenum powder spraying onto three different substrates:a stainless steel,brass(70%Cu)andaluminum by atmospheric plasma spraying has been investigated.The maximum melting depth of the substrate hasbeen measured and compared with the numerical prediction.Experimental results show that the material propertiesof the splat and substrate and melting temperature of the substrate play the important roles on substrate melting.A dimensionless parameter,temperature factor,has been proposed and served as an indicator for substrate melting.

Melting Reconstruction Features and Solidification Mechanism of Heavy Metal-containing Slag

The relationships between microstructure and melting temperature of slag containing different heavy metals （Zn, Cu, Pb and Cr） were studied. Furthermore, the corresponding solidification mechanism and rule of heavy metals were analyzed by microscopic tests during melting and reconstructing process. Based on preliminary results, three conclusions were derived. Firstly, pure slag would begin to melt when the temperature reached 1 180℃; however, Zn did not play any fluxing action. Secondly, upon adding Cu and Pb, the initial melting temperature of slag decreased by 5-8℃ and their fluxing effect was observed. Thirdly, the initial melting temperature and the reaction time for slag decreased by 22℃ and 6 s respectively after adding Cr; the fluxing action was significant under Cr. The results of X-ray diffraction （XRD） and Fourier transform infrared spectroscope （FTIR） analyses showed that the above heavy metals had little influence on the reconstruction of slag. Toxicity characteristic leaching procedure （TCLP） leaching tests showed a good solidification effect of the heavy metals with melting slag, fixation rate of Zn, Cu, Pb and Cr was 36.3%, 24.6%, 9.2% and 93.2%, respectively. The leaching toxicity of the heavy metals met the requirements for environmental emission after solidification treatment.

Functionally Gradient Material Made by IncrementalMelting and Solidification Process

A new technique IMS (Incremental Melting and Solidification Process) has been introduced. A kind of cast steel high Mn foundry alloy gradient rnalerial was produced by this process. The microstructure and mechanical properties of the alloy were tested. Fe and Mn in the samples were measured by EPMA. The experimental results show that the content and hardness of Fe-Mn alloy vary continuously and the IMS process is an alternative way in producing metal matrix gradient material. It is possible for these materials to be made into some parts such as camshaft.

Numerical prediction of the incremental melting and solidification process

A mathematical formulation is applied to represent the phenomena in theincremental melting and solidification process (IMSP), and the temperature and electromagneticfields and the depth of steel liquid phase are calculated by a finite difference technique using thecontrol volume method. The result shows that the predicted values are in good agreement with theobservations. In accordance with the calculated values for different kinds of materials anddifferent size of molds, the technological parameter of the IMS process such as the power supply andthe descending speed rate can be determined.

Partial melting and re-solidification in partially melted zone during gas tungsten arc welding of AZ91 cast alloy

During the welding of AZ91 cast alloy,the presence of eutectic β-Mg17Al12 phase results in constitutional liquation in the original interdendritic regions and in the formation of a partially melted zone(PMZ). In this study,gas tungsten arc welding(GTAW) and partial melting(simulated using furnace,salt bath and Gleeble) experiments were conducted. The results show that practically there would not be a critical heating rate during the welding to prevent constitutional liquation. The gradual change of the re-solidification microstructure within PMZ from base metal side to weld metal side was characterized. A sharp transition from base metal to PMZ has been observed. It is found that the original partially divorced eutectic has become a more regular eutectic in most of the PMZ,although close to the fusion boundary the re-solidified eutectic is again a more divorced one. Proceeding the eutectic re-solidification,α-Mg re-solidified with a cellular growth resulting in a serrated interface. The morphological change affected by the peak temperature and cooling rate will be presented and explained.

Numerical simulation on rapid melting and nonequilibrium solidification of pure metals and binary alloys

A heat and mass transfer modelling containing phase transformation dynamics is made for pure metals and binary alloys under pulsed laser processing. The nonequilibrium effects of processing parameters and physical properties are evaluated on the melting and solidification of pure metals (Al, Cu, Fe and Ni) and Al Cu alloys. It is shown that the energy intensity of laser beam and physical properties of metals and the solute concentration of alloys have important effect on the interface temperature, melting and solidification velocity, melting depth and non equilibrium partition coefficient. This situation is resulted from the interaction of heat transfer, redistribution of solute, solute trapping and growth kinetics.

Si purification by solidification of Al-Si melt with super gravity

The investigation on purification of metallurgical grade silicon by solidification of hypereutectic Al-Si melt with super gravity as an intensified separation way was carried out.The results indicate that the refined silicon grains are successfully enriched at the bottom of the Al-Si alloy along the direction of super gravity.Then the refined silicon was collected by aqua regia leaching.The purity of the collected silicon is analyzed as 99.92%,which is obviously improved compared with the purity of the metallurgical grade silicon of 99.59%,proving the feasibility of this purification method.Furthermore,the mass fraction of B is reduced from 8.33×10-6 to 5.25×10-6 and that of P from 33.65×10-6 to13.50×10-6.

Comparative analysis of isothermal and non-isothermal solidification of binary alloys using phase-field model

Based on the entropy function, a two-dimensional phase field model of binary alloys was established. Meanwhile, an explicit difference method with uniform grid was adopted to solve the phase field and solute field controlled equations. And the alternating direction implicit(ADI) algorithm for solving temperature field controlled equation was also employed to avoid the restriction of time step. Some characteristics of the Ni-Cu alloy were captured in the process of non-isothermal solidification, and the comparative analysis of the isothermal and the non-isothermal solidification was investigated. The simulation results indicate that the non-isothermal model is favorable to simulate the real solidification process of binary alloys, and when the thermal diffusivity decreases, the non-isothermal phase-field model is gradually consistent with the isothermal phase-field model.

Effect of melt superheat on structural uniformity of lotus-type porous metals prepared by unidirectional solidification

Structural uniformity is an important parameter influencing physical and mechanical properties of lotus-type porous metals prepared by directional solidification of metal-gas eutectic (Gasar). The effect of superheat on structural uniformity as well as average porosity, pore morphology of porous metals was studied. The experimental results show that, when the superheat is higher than a critical value (ΔTc), the bubbling or boiling phenomenon will occur and the gas bubbles will form in the melt and float out of the melt. As a result, the final porosity will decrease. In addition, a higher superheat will simultaneously cause a non-uniform porous structure due to the pores coalescence and bubbling phenomenon. Finally, a theoretical model was developed to predict the critical superheat for the hydrogen to escape from the melt and the corresponding escapement ratio of hydrogen content. Considering the escapement of hydrogen, the predicted porosities are in good agreement with the experimental results.

Mathematical Model for Electroslag Remelting Process

A mathematical model, including electromagnetic field equation, fluid flow equation, and temperature field equation, was established for the simulation of the electroslag remelting process. The distribution of temperature field was obtained by solving this model. The relationship between the local solidification time and the interdendritic spacing during the ingot solidification process was established, which has been regarded as a criterion for the evaluation of the quality of crystallization. For a crucible of 950 mm in diameter, the local solidification time is more than 1 h at the center of the ingot with the longest interdendritic spacing, whereas it is the shortest at the edge of the ingot according to the calculated results. The model can be used to understand the ESR process and to predict the ingot quality.

Fluid Flow and Solidification Simulation in Beam Blank Continuous Casting Process With 3D Coupled Model

Based on turbulent theory, a 3D coupled model of fluid flow and solidification was built using finite difference method and used to study the influence of superheating degree and casting speed on fluid flow and solidification, analyze the interaction between shell and molten steel, and compare the temperature distribution under different technological conditions. The results indicate that high superheating degree can lengthen the liquid-core depth and make the crack and breakout possible, so suitable superheating should be controlled within 35℃ according to the simulation results. Casting speed which is one of the most important technological parameters of improving production rate, should be controlled between 0. 85 m/min and 1.05 m/min and the caster has great potential in the improvement of blank quality.

Progress on modeling and simulation of directional solidification of superalloy turbine blade casting

Directional solidified turbine blades of Ni-based superalloy are widely used as key parts of the gas turbine engines.The mechanical properties of the blade are greatly influenced by the final microstructure and the grain orientation determined directly by the grain selector geometry of the casting.In this paper,mathematical models were proposed for three dimensional simulation of the grain growth and microstructure evolution in directional solidification of turbine blade casting.Ray-tracing method was applied to calculate the temperature variation of the blade.Based on the thermo model of heat transfer,the competitive grain growth within the starter block and the spiral of the grain selector,the grain growth in the blade and the microstructure evolution were simulated via a modified Cellular Automaton method.Validation experiments were carried out,and the measured results were compared quantitatively with the predicted results.The simulated cooling curves and microstructures corresponded well with the experimental results.The proposed models could be used to predict the grain morphology and the competitive grain evolution during directional solidification.

Numerical simulation of solidification morphologies of Cu-0.6Cr casting alloy using modified cellular automaton model

The purpose of this study is to predict the morphologies in the solidification process for Cu-0.6Cr(mass fraction,%)alloy by vacuum continuous casting(VCC)and verify its accuracy by the observed experimental results.In numerical simulation aspect, finite difference(FD)method and modified cellular automaton(MCA)model were used to simulate the macro-temperature field, micro-concentration field,nucleation and grain growth of Cu-0.6Cr alloy using real data from actual casting operations.From the observed casting experiment,the preliminary grain morphologies are the directional columnar grains by the VCC process.The solidification morphologies by MCAFD model are in agreement with the result of actual casting experiment well.

Numerical Evaluation of Two k-εTurbulence Model for Predicting Flow and Solidification in Continuous Casting Slab

A steady three-dimensional fluid flow and solidification model was built based on CFD software by high-Reynolds-number and Lam-Bremhorst low-Reynolds-number k-ε model.During the simulation,the fixed-grid enthalpy-porosity technique was used to represent the solidification,and Darcy law was adopted to simulate the flow in mushy region.The prediction for steel flow and solidification was evaluated by the comparison of two turbulence models.It is found that both Lam-Bremhorst low-Reynolds-number and high-Reynolds-number k-ε models predict the same trend of the steel flow and temperature distribution.However,due to the effect of turbulent flow on heat transfer,the low-Reynolds-number turbulence model predicts longer penetration depth of molten steel in sub-mold region,less shell growth and higher shell surface temperature at the narrow face compared with standard k-ε model.

Phase field modeling of multiple dendrite growth of Al-Si binary alloy under isothermal solidification

Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model. The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification. With the increase of growing time, the grains begin to coalesce and impinge the adjacent grains. When the dendrites start to impinge, the dendrite growth is obviously inhibited.