Nucleation Model Research Articles

Exploring the role of Type-II residual stresses in a laser powder bed fusion nickel-based superalloy using measurement and modeling

Far-field high-energy X-ray diffraction microscopy (ff-HEDM) and the crystal plasticity finite element method (CPFEM) are used to investigate the role of grain-scale (Type-II) residual stresses on the fatigue life of additively manufactured (AM) Inconel alloy 625 (IN-625). Grain-averaged orientations, centroids, and residual elastic strain tensors from ff-HEDM data are used to instantiate a crystal plasticity model to simulate the effect of residual stresses at the grain scale. Simulation results indicate that the presence of tensile residual strains increase stress localization and heterogeneity within grains, triggering an earlier onset of plasticity. A microscale fatigue indicator parameter (FIP) is computed to model the impact of these residual strains on the cycles to fatigue crack nucleation. The crack nucleation model, based on the computed FIPs, predicts a significant reduction in the number of cycles for fatigue crack nucleation for mid- and high-cycle fatigue due to the residual strain induced localization, while the residual strains have minimal impact on low-cycle fatigue life.

Modeling the effect of prior austenite grain size on bainite formation kinetics

While experiments show that refining the prior austenite grain size can either accelerate or decelerate bainite formation in steels, kinetic models based on the successive nucleation of bainitic ferrite subunits can only predict an acceleration. In this work we develop a physically-based model for bainite kinetics assuming a displacive growth mechanism which is able to reproduce both faster and slower bainite formation kinetics induced by austenite grain refinement. A theoretical analysis of the model and comparison against published experimental data show that slower kinetics for smaller grains is favored as the difference between the activation energy for grain boundary and autocatalytic nucleation of bainite increases, and as the austenite grain refinement results in finer bainite sub-units. We also theoretically analyze the density of initially present potential nucleation sites for bainite and show that the values of density used in other published bainite nucleation models are mostly underestimated. After using physically consistent values for the density of potential nucleation sites, we were able to calculate the apparent lengthening rate of bainite sheaves which were in line with experimentally measured lengthening rates.

Dynamics analysis of twin formation for InP and preparation of 6 inch InP single crystals

Twin-free InP crystals can be grown under suitable growth conditions. A kinetic model for twin nucleation is proposed.

Physicochemical mechanisms of aggregation and fibril formation of α-synuclein and apolipoprotein A-I.

Deposition and accumulation of amyloid fibrils is a hallmark of a group of diseases called amyloidosis and neurodegenerative disorders. Although polypeptides potentially have a fibril-forming propensity, native proteins have evolved into proper functional conformations to avoid aggregation and fibril formation. Understanding the mechanism for regulation of fibril formation of native proteins provides clues for the rational design of molecules for inhibiting fibril formation. Although fibril formation is a complex multistep reaction, experimentally obtained fibril formation curves can be fitted with the Finke-Watzky (F-W) two-step model for homogeneous nucleation followed by autocatalytic fibril growth. The resultant F-W rate constants for nucleation and fibril formation provide information on the chemical kinetics of fibril formation. Using the F-W two-step model analysis, we investigated the physicochemical mechanisms of fibril formation of a Parkinson's disease protein α-synuclein (αS) and a systemic amyloidosis protein apolipoprotein A-I (apoA-I). The results indicate that the C-terminal region of αS enthalpically and entropically suppresses nucleation through the intramolecular interaction with the N-terminal region and the intermolecular interaction with existing fibrils. In contrast, the nucleation of the N-terminal fragment of apoA-I is entropically driven likely due to dehydration of large hydrophobic segments in the molecule. Based on our recent findings, we discuss the similarity and difference of the fibril formation mechanisms of αS and the N-terminal fragment of apoA-I from the physicochemical viewpoints.

A Hybrid ANN Multiaxial Fatigue Model for the Assessment of Fretting Fatigue under Variable Amplitude Shear Loading.

To foresee the life of fretting fatigue with variable shear amplitude loading, a hybrid model incorporating non-local multiaxial fatigue parameters and artificial neural networks (ANN) in conjunction with cumulative damage models has been proposed. The model has been developed based on equivalent stress parameters associated with crack nucleation and Miner's cumulative damage rule-inspired models, enabling the assessment of the impact of variable amplitude loading. To validate the models, fretting fatigue tests conducted under variable shear loading amplitude are employed to compare the predictions of four different models. The results demonstrate that while all models provide satisfactory estimates falling within the two-band limit, the hybrid model combining two ANN models outperforms the others and emerges as the most effective in predicting fretting fatigue life under these conditions. The proposed methodology effectively addresses the inherent complexities of fretting fatigue under variable amplitude stress, while also examining the influence of load block order on material behavior. Additionally, these types of fatigue ANN models have been demonstrating a strong capacity for generalization, making them highly promising for future industrial applications.

Grain Boundary Slip and a Grain Boundary Triple Junction Crack Nucleation Model for Nanocrystals Under the Influence of Hydrogen

Grain Boundary Slip and a Grain Boundary Triple Junction Crack Nucleation Model for Nanocrystals Under the Influence of Hydrogen

Phenalenyl growth reactions and implications for prenucleation chemistry of aromatics in flames.

The energetics and kinetics of phenalene and phenalenyl growth reactions were studied theoretically. Rate constants of phenalene and phenalenyl H-abstraction and C2H2 addition to the formed radicals were evaluated through quantum-chemical and rate-theory calculations. The obtained values, assigned to all π radicals, were tested in deterministic and kinetic Monte Carlo simulations of aromatics growth under conditions of laminar premixed flames. Kekulé and non-Kekulé structures of the polycyclic aromatic hydrocarbons (PAHs) evolving in the stochastic simulations were identified by on-the-fly constrained optimization. The numerical results demonstrated an increased PAH growth and qualitatively reproduced experimental observations of Homann and co-workers of non-decaying PAH concentrations with nearly equal abundances of even and odd carbon-atom PAHs. The analysis revealed that the PAH growth proceeds via alternating and sterically diverse acetylene and methyl HACA additions. The rapid and diverse spreading in the PAH population supports a nucleation model as PAH dimerization, assisted by the non-equilibrium phenomena, forming planar aromatics first and then transitioning to the PAH-PAH stacking with size.

Induced seismicity in the Changning salt mining zone, China, could be driven by the pore-pressure diffusion

The detailed mechanism of induced seismicity associated with salt mining remains elusive. Herein we compile the geological, industrial data, and seismic records within the Changning salt mining zone, China, and simulate the changes in crustal stresses and seismicity rate based on the physics-based poroelastic model and rate-and-state earthquake nucleation model. Our models reveal that the regional induced seismicity, including the 2019 Ms. 6.0 Changning earthquake, which might be one of the largest induced events by industrial exploitation ever recorded, is mainly driven by the pore-pressure diffusion, but suppressed by pumping operations. Motivated by the injection-extraction scenario, we further investigate the effect of wells' locations on stress changes, which could be potentially used for well site optimization to minimize the poroelastic response. A simple mode of setting extraction wells around the injection well could reduce the seismicity rate by a factor of two. These results collectively advance the understanding of physics and hazards associated with injection-extraction-induced earthquakes, and help design or guide industrial well deployment.

Crystallization thermodynamic properties and nucleation kinetics of Sr(OH)2·8H2O in an Sr(OH)2·8H2O-H2O system

There have been few reports in literature on the crystallization thermodynamic properties and nucleation kinetics of strontium hydroxide octahydrate despite their great importance to the reactor design and the regulation of crystal properties. In this work, the crystallization thermodynamic properties of Sr(OH)2·8H2O in pure water were investigated using a dynamic temperature-controlled process and an equilibrium process. The metastable zone width (MSZW) was examined under different crystallization process conditions including stirrer speed, solution concentration, cooling rate, and different strategies in adding seed crystals. In addition, models for the nucleation kinetics and MSZW were successfully constructed based on the classical nucleation model. Based on the data provided, it can be concluded that the dissolution of Sr(OH)2·8H2O in pure water is an entropy-driven endothermic process and its MSZW was gradually narrowed with an increase in stirring speed and concentration and with a decrease in cooling rate. Additionally, adding seeds was an effective strategy to narrow the metastable zone. Therefore, this endeavor provided a rational principle for subsequential investigations of Sr(OH)2·8H2O and other compounds.

Development of a multi-stage model for freezing of a suspended binary solution droplet

The importance of developing spray freeze-drying technology for extending the shelf life of biological and pharmaceutical materials has never been greater, given the increasing food shortage and the strong demand for pharma processes. In particular, the optimal thermal design and application of spray freeze-drying technologies now depend on the estimation of nucleation behavior for droplet solidification (especially the droplets of binary mixtures). Although earlier nucleation models could estimate the nucleation rate and temperature of solidifying droplets, few considered extreme environmental factors, such as extremely low ambient temperatures below −60C∘. To ensure the preservation and storage of biological and pharmaceutical products, such as vaccines and protein drugs, these conditions are essential. Hence, developing an accurate and trustworthy mathematical framework for simulating nucleation is paramount. In this study, a multi-stage, hybrid analytical-numerical model for droplet solidification is developed while coupled with a gradient-based optimization algorithm. Specifically, the five-stage solidification of binary mixtures is simulated (including supercooling of liquid, nucleation, recalescence, equilibrium freezing, and subcooling of solid), which captures the dynamic behaviors of temperature and composition or solute concentration during phase change. The heterogeneous nucleation of a binary-mixture droplet in a frigid environment is predicted and validated against a series of experiments on single suspended droplets at a wide range of ambient temperatures between −20 and −160C∘. The freezing curves of different solute concentrations are also validated against experimental data. It is found that significant variations in interfacial tension lead to abrupt changes in nucleation temperature for extremely cold environments. Further, the effects of the concentration, contact angle, droplet size, and heat transfer coefficient are investigated.

Size-Independent Nucleation and Growth Model of Potassium Sulfate from Supersaturated Solution Produced by Stirred Crystallization.

This paper explores the kinetics of the crystallization of potassium sulfate in a stirred bed crystallizer through experimental investigation. Employing classical nucleation theory, the homogeneous and heterogeneous nucleation mechanisms of potassium sulfate were investigated. The induction time and critical nucleation parameters, including the surface tension (γ), critical nucleation radius (r*), critical nucleation free energy (ΔG*), and critical nucleation molecule number (i*), were meticulously determined under varying temperatures and supersaturation ratios. The experimental findings revealed that as the temperature and supersaturation ratio increased, the induction time, critical nucleation free energy, critical nucleation radius, and critical molecule number decreased whereas the nucleation rate increased. The crystalline shape remains relatively unaltered with respect to temperature and supersaturation ratio, yet the particle size (D10, D50, D90) increases as the supersaturation and temperature increase. The variations in the measured nucleation parameters align well with the predictions of classical nucleation theory. Furthermore, the kinetic equations of crystal nucleation and the growth rate in a stirred crystallization system were fitted using population balance equations. The results demonstrate that the growth rate increases with increasing supersaturation and stirring rates. Additionally, the effects of the parameters in the nucleation rate equation suggested that the suspension density exerted the greatest influence, followed by the supersaturation ratio and stirring rate. This extensive research provides invaluable theoretical guidance for optimizing the crystallization process and designing industrial crystallizers.

Computer Simulation of Pitting Corrosion in Galvanostatic Conditions

Pitting corrosion of stainless steels has been the subject of substantial research over many years. The overall mechanism can be separated into nucleation and propagation stages, and the development of a reliable predictive model requires a robust treatment for both these processes. Over the years, several purely stochastic models have been developed, including those by Shibata and Takeyama [1], Williams et al. [2], Baroux [3] and Wu et al. [4]. Alternatively, Macdonald and co-workers [e.g., 5] have focused on a deterministic approach, based on the point defect model of passivity breakdown. Newman, Laycock and co-workers developed a deterministic model for the propagation of individual corrosion pits [6-8], which was then combined with a stochastic model of pit nucleation to enable simulation of pitting potential measurements [9]. Li, Scully and Frankel later published a series of papers based on a similar approach [e.g., 10-11].The majority of the prior modelling work has focused on potential-controlled conditions, where the pitting outcomes are determined mainly by the pit propagation element; for example, a limiting lower bound distribution of the pitting potential can be calculated without any consideration of pit nucleation processes [9]. However, real corrosion does not occur under potential control; rather, there is a limited supply of cathodic current that must be shared between all simultaneously propagating pits [12,13]. This situation is closer to that of experiments under galvanostatic control [14]. Krouse et al [15] described simulations that included possible interactions between multiple simultaneously propagating pits under galvanostatic conditions, supporting earlier suggestions that pits compete for the available current, and that ‘champion pits’ will ultimately use all available resources (see, e.g., Figure 1).In more recent work [16], we have further developed the earlier propagation model [6-9] to include the interactions and possible mergers between two simultaneously propagating pits. Here we expand on the work of Krouse et al [15] to carry out simulations of galvanostatic experiments that now incorporate the possibility of mergers between propagating pits. References Shibata, T. Takeyama, Corrosion 33 (1997) 243.E. Williams, C. Westcott, M. Fleischmann, J. Electrochem. Soc. 132 (1985) 1796.Baroux, Corros. Sci. 28 (1988) 969.Wu, J.R. Scully, J.L. Hudson, A.S. Mikhailov, J. Electrochem. Soc. 144 (1997) 1614.Engelhardt, D.D. Macdonald, Corrosion 54 (1998) 469.Ernst, N.J. Laycock, M.H. Moayed, R.C. Newman, Corros. Sci. 39 (1997) 1133.J. Laycock, S.P. White, J.S. Noh, P.T. Wilson, R.C. Newman, J. Electrochem. Soc. 145 (1998) 1101.J. Laycock, S.P. White, J. Electrochem. Soc. 148 (2001) B264.J. Laycock, J.S. Noh, S.P. White and D.P. Krouse, Corros. Sci, 47, 3140 (2005).S. Frankel, T. Li, and J. R. Scully, Journal of the Electrochemical Society, 164, C180 (2017).Li, J. R. Scully, and G. S. Frankel, Journal of The Electrochemical Society, 165, C484 (2018).Y. Chen, F. Cui and R.G. Kelly, J. Electrochem. Soc., 155, C360-C368 (2008).Y. Chen and R.G. Kelly, J. Electrochem. Soc., 157, C69 (2010).I. Suleiman and R. C. Newman, Corros. Sci., 36, 1657 (1994).Krouse, P. McGavin and N. Laycock, in Proceedings of Corrosion & Prevention 2008, Paper # 97, ACA, Wellington, 16-19 November (2008).A Nguyen, R.C. Newman and N.J. Laycock, J. Electrochem. Soc., 169, 081503 (2022) Figure 1

A new hydration kinetic model based on boundary nucleation and growth mechanism with time-dependent growth rate: Application to quantitively characterize the influence of alkali on the early hydration of cement

In this study, a boundary nucleation and growth model with a time-dependent growth rate was proposed to quantitively characterize the precipitation of CSH. The newly constructed model was typically applied to quantitively analyse the influence of alkali content on the growth of CSH, and the value-taking equations of the time-dependent growth rate of CSH in various alkali content systems were proposed and verified. The experimental and simulation results proved that a high soluble alkali content stimulated early hydration (within the initial several hours) and inhibited the late growth of CSH (>20 h) in cement paste. The time-varying ion concentrations in cement solutions were the main driving force for the change in the growth rate of CSH with time. Likewise, the variation in the aqueous phase properties of cement pastes also explains the influence of alkali content on the growth rate of CSH, i.e., the high initial pH of the solution with high soluble alkali led to the high supersaturation degree and high growth rate of CSH, consuming large amounts of calcium ions and in turn reducing the later supersaturation degree and growth rate. The newly constructed model is also expected to precisely characterize the factors that have a significant influence on the precipitation of cement hydrates.

Induced Seismicity Forecasting with Uncertainty Quantification: Application to the Groningen Gas Field

Abstract Reservoir operations for gas extraction, fluid disposal, carbon dioxide storage, or geothermal energy production are capable of inducing seismicity. Modeling tools exist for seismicity forecasting using operational data, but the computational costs and uncertainty quantification (UQ) pose challenges. We address this issue in the context of seismicity induced by gas production from the Groningen gas field using an integrated modeling framework, which combines reservoir modeling, geomechanical modeling, and stress-based earthquake forecasting. The framework is computationally efficient thanks to a 2D finite-element reservoir model, which assumes vertical flow equilibrium, and the use of semianalytical solutions to calculate poroelastic stress changes and predict seismicity rate. The earthquake nucleation model is based on rate-and-state friction and allows for an initial strength excess so that the faults are not assumed initially critically stressed. We estimate uncertainties in the predicted number of earthquakes and magnitudes. To reduce the computational costs, we assume that the stress model is true, but our UQ algorithm is general enough that the uncertainties in reservoir and stress models could be incorporated. We explore how the selection of either a Poisson or a Gaussian likelihood influences the forecast. We also use a synthetic catalog to estimate the improved forecasting performance that would have resulted from a better seismicity detection threshold. Finally, we use tapered and nontapered Gutenberg–Richter distributions to evaluate the most probable maximum magnitude over time and account for uncertainties in its estimation. Although we did not formally account for uncertainties in the stress model, we tested several alternative stress models, and found negligible impact on the predicted temporal evolution of seismicity and forecast uncertainties. Our study shows that the proposed approach yields realistic estimates of the uncertainties of temporal seismicity and is applicable for operational forecasting or induced seismicity monitoring. It can also be used in probabilistic traffic light systems.

Multi-scale spallation model for single-crystal ductile metals incorporating microscopic mechanism of void nucleation

Spall strength characterizes the tensile performance of materials under high strain rates. However, theoretical prediction of the spall strength has long been a big challenge since it involves information on the damage evolution at multiple length scales. In this work, a multi-scale model is proposed for the spallation of single-crystal ductile metals, which includes both a microscopic model of damage nucleation and an effective correlation between the microscopic physical mechanisms and the macroscopic mechanical behaviors. An energy criterion to predict the threshold stress for damage nucleation is firstly proposed based on a near-realistic three-dimensional configuration of dislocation emission. The statistical characteristics of the damage nucleation threshold are analyzed, based on which a multi-scale spall model is proposed to couple the physical essence at the micro-scale to the macro-scale, revealing the influences of temperature, vacancy concentration, and strain rate on spall strength. An approximate form of the multi-scale model is proposed by dimensional analysis and reasonable approximation, which is consistent with the empirical model summarized from experimental results, and further deduced to a simple scaling law that predicts the transition in the strain rate-sensitivity of spall strength.

Multi-physics multi-scale simulation of microstructure evolution in entire welds of 2219-T6 aluminum alloy: An MPF-LBM study

The microstructure of fusion welds significantly affects its mechanical properties. Existing studies on the dynamic evolution of welding molten pools have exposed great limitations in considering the flow field and the solid motion of free dendrites. In this paper, a multi-physics multi-scale coupling simulation of thermal-mass-flow was conducted to study the solidification behavior during the welding of 2219-T6 aluminum alloy. The developed multi-phase field lattice Boltzmann model realized the direct full coupling of phase, temperature, solute, solid motion, and flow fields. It is also combined with a continuous nucleation model to simulate heterogeneous nucleation and columnar-to-equiaxed transition (CET), and a transient growth-condition model to simulate the movement and solidification of the entire molten pool. The model and simulation results were verified by welding experiments, electron back-scattered diffraction, and scanning electron microscopy tests. Good agreements are achieved in terms of grain structure, dendrite morphology, and grain size. The undercooling field, fluid flow, solid motion, dendrite morphology, solute distribution, and quantitative parameters during the whole solidification process were analyzed in detail to reveal the true evolution of thousands of dendrites in fusion welds. The results show that solute convection caused by fluid flow significantly affects the dendrite morphology. The solid motion of equiaxed dendrites squeezes the solute enrichment layer and forms a solute hysteresis transport effect. A band of equiaxed dendrites gathers in front of the columnar dendrites and blocks their growth, forming a mechanical blockade mechanism of the CET process. The equiaxed dendrites dominated the subsequent solidification after CET is complete, and the final microstructure consists of brief-growth columnar dendrites and dense equiaxed dendrites. The top tangential flow causes a band of equiaxed dendrites with large gaps in the upper weld, which was presumed to be the source of surface cracks in welds with high residual stress.

Effects of heterogeneous nucleation model on computational fluid dynamics simulation of flow boiling heat transfer in the mini-channel

Bubble nucleation is the initial stage of flow boiling and plays an important role in boiling heat transfer. However, bubble nucleation occurs at a microscopic scale, rendering it challenging for the macroscopic computational fluid dynamics method to realistically simulate this intricate process. In this paper, based on the coupled volume-of-fluid and level set method, a heterogeneous nucleation model is improved and conducted to simulate the subcooled flow boiling in a rectangular mini-channel, considering these conditions both in the presence and absence of a microlayer. The coefficient of the original heterogeneous nucleation model is adjusted across a range from 0.1 to 10.0 times its previous value to establish multiple new nucleation models for illustrating their effects on flow patterns and heat transfer characteristics. For flow boiling without a microlayer, when the coefficient of the original heterogeneous nucleation model is halved, the nucleate boiling intensity upstream of the channel diminishes, resulting in a reduction in the heat transfer coefficient. Nevertheless, this alteration mitigates the formation of slug flow and the appearance of dry patches near the channel outlet, consequently averting a sharp increase in outlet wall superheat. Quantitatively, relative differences of 23.83% and 90.48% in average and local maximum wall superheat are observed, respectively. In contrast, the presence of a very thin microlayer beneath the growing and slipping bubble in flow boiling with a microlayer is notable. This microlayer quickly evaporates, dissipating more than 77% of the input heat flux and substantially expanding the bubble volume. Consequently, under identical wall superheat conditions, the influence of variations in the number of activated bubbles induced by different heterogeneous nucleation models on heat transfer and flow patterns in flow boiling is significantly attenuated. Specifically, when the difference in nucleus site density remains within a tenfold range, the differences in the average and maximum wall superheat are limited to just 16.78% and 33.86%, respectively. Concerning flow boiling in a mini-channel featuring a microlayer, the simulation results verify that large deviations in the activated bubble number have few effects on the flow pattern and wall superheat, greatly reducing heterogeneous nucleation model requirement and promoting the numerical study of flow boiling.

Interactions between Gravity Waves and Cirrus Clouds: Asymptotic Modeling of Wave-Induced Ice Nucleation

Abstract We present an asymptotic approach for the systematic investigation of the effect of gravity waves (GWs) on ice clouds formed through homogeneous nucleation. In particular, we consider high- and midfrequency GWs in the tropopause region driving the formation of ice clouds, modeled with a double-moment bulk ice microphysics scheme. The asymptotic approach allows for identifying reduced equations for self-consistent description of the ice dynamics forced by GWs including the effects of diffusional growth and nucleation of ice crystals. Further, corresponding analytical solutions for a monochromatic GW are derived under a single-parcel approximation. The results provide a simple expression for the nucleated number of ice crystals in a nucleation event. It is demonstrated that the asymptotic solutions capture the dynamics of the full ice model and accurately predict the nucleated ice crystal number. The present approach is extended to allow for superposition of GWs, as well as for variable ice crystal mean mass in the deposition. Implications of the results for an improved representation of GW variability in cirrus parameterizations are discussed.

Phase Transformation Under High Pressure Radiates as a Double Couple Deep Earthquake

AbstractDeep‐focus earthquakes (DFEs) originating at the Mantle‐Transition‐Zone (MTZ) (400–700 km) have a Double Couple (DC) radiation pattern similar to crustal earthquakes; however, their mechanism is different and governed by high pressures (15–25 GPa) at nucleation depths. We present a model of nucleation and growth of regions of phase transformation, undergoing a sudden reduction in volume (5%–10%), “volume collapse.” Successive symmetry‐breaking instabilities minimize the energy spent to move the boundary of phase discontinuity and a collapsing volume expands as a flattened pancake‐like self‐similarly expanding Eshelby ellipsoidal inclusion. At the vanishing of the M integral, expressing the balance of flows of energy across the inclusion boundary, at a critical value of the pressure, an arbitrarily small inclusion nucleates and grows at constant potential energy driven by the pressure acting on the change in volume. The inclusion develops shear eigenstrains that decompose into two DC, placing one on the basal plane to radiate without energy losses. The symmetric volume collapse radiates out as an anti‐symmetric DC, and the radiated energy is obtained as the “excess energy,” of the ambient pressure acting on the “volume collapse,” reduced by the energy consumed for the growth of the pancake surfaces, with a “pressure drop” (p0 − pcr) driving the expansion emitting a DC, even under full isotropy. The solution explains some features of the DFEs, (a) the DC radiation, (b) their large energies (the Mw 8.3 Okhotsk earthquake [2013]), (c) the absence of volumetric radiation, and (d) why they can originate in the MTZ, a long‐standing open problem.

Numerical simulation of VAR for large-scale TC4 alloy during the solidification process

ABSTRACT A three-dimensional multi-physics model of the effect of process parameters on the evolution of the solid–liquid interface during solidification of large-scale Ti-6 wt% Al-4 wt% V (TC4) alloy by[Ballantyne, 1977 #483] (VAR) and a macroscopic model of grain nucleation and growth was established. The simulation results qualitatively reveal the evolution of solid–liquid interface and central cross-sectional solidification structure under various melting conditions, indicating that the melting zone depth increased while the mushy zone width and the number of grains decreased with the increase of melting power; the depth of the melting zone and the width of the mushy zone increase sharply with the increase in solidification velocity, the average grain radius increased, while the number of grains decreased; when the ingot diameter increased from 260 mm to 660 mm, the depth of the melting zone increased and gradually remained stable, and the width of the mushy zone gradually decreased.