CN107423460A - A kind of method for numerical simulation for improving electrically fused magnesium fused weight crystalline quality - Google Patents

A kind of method for numerical simulation for improving electrically fused magnesium fused weight crystalline quality Download PDF

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CN107423460A
CN107423460A CN201710186987.4A CN201710186987A CN107423460A CN 107423460 A CN107423460 A CN 107423460A CN 201710186987 A CN201710186987 A CN 201710186987A CN 107423460 A CN107423460 A CN 107423460A
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magnesium
forming core
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supercooling
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CN107423460B (en
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张颖伟
王建鹏
许晶
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Northeastern University China
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Abstract

The present invention provides a kind of method for numerical simulation for improving electrically fused magnesium fused weight crystalline quality, is related to electric-melting magnesium product quality optimisation technique field.This method initially sets up a grand microcosmic unified model that macroscopic view heat transfer, microcosmic forming core are coupled with growth kinetics, then numerical simulation is carried out to the temperature field during electric-melting magnesium cooled and solidified and microstructure using PROCAST softwares, and then visualization processing and interpretation of result discussion, effect tendency of the analysis degree of supercooling to electrically fused magnesium fused weight microstructure are carried out to molten Tuo Zhengtiwenduchang changes and Growing Process of Crystal Particles.The present invention carries out mathematical physics modeling and numerical simulation to the heat exchange during electricity melt magnesium lump cooled and solidified and microstructure forming process, by the control for exchanging the parameters such as heat condition, on its solidification law, understand and control it to organize the formation of, prepared for production high-grade periclase, experiment number is effectively reduced, human and material resources are saved, so as to improve the quality of periclase product in actual production.

Description

A kind of method for numerical simulation for improving electrically fused magnesium fused weight crystalline quality
Technical field
The present invention relates to electric-melting magnesium product quality optimisation technique field, more particularly to a kind of raising electrically fused magnesium fused weight crystalline The method for numerical simulation of amount.
Background technology
Magnesium industry includes magnesia refractories, Magnesium Chemical Materials and magnesium metal and magnesium alloy three industries, is referred to as magnesia Materials industry.Magnesium resource refers to the ore deposit containing magnesium that can be used for the products such as production magnesia refractories, Magnesium Chemical Materials, magnesium metal Thing, China are that the resource reserve such as magnesium resource big country, magnesite, dolomite, shepardite enriches, its product be widely used in it is metallurgical, The fields such as building materials, chemical industry, automobile, electronics, Aero-Space, medicine, food, agriculture and animal husbandry.
Fused magnesite is also known as fusion-cast MgO (abbreviation electric-melting magnesium), and it is both a kind of high purity, fusing point high (2825 DEG C), crystallization Grain is big, compact structure, resists that clear property is strong, the alkaline magnesia refractories of stable chemical performance, is that a kind of excellent high temperature is electric again Insulating materials, while be also the important source material for making high-grade magnesia brick, magnesia carbon brick and unshape refractory, it is widely used in The fields such as metallurgy, building materials, glass, petrochemical industry, cement, national defence.
In recent years, the sustainable development of the hot industry such as global metallurgy, cement, glass, petrochemical industry, promotes refractory material industry Development, and the performance of fused magnesite is extremely unique, is a kind of high grade refractory for having irreplaceable advantage, each by the world The extensive use of institute of state.Constantly expanding with the application of fused magnesite, demand increases year by year, and composite price constantly rises, Market is had an optimistic view of, and electric-melting magnesium industry is just welcoming great opportunity and development.
At present because Global climate change, greenhouse effects, resource consumption excessively influence with energy crisis etc., international community pair Resource, the energy, the dynamics of environmental protection are increasingly big, and various countries are paid high attention to year by year to " energy-saving and emission-reduction " work.China is complete at present Ball maximum fused magnesite producing country and supply country, but because current domestic electric-melting magnesium production technology falls behind, traditional smelting side Formula power consumption is surprising, result in electric-melting magnesium industry " high energy consumption ", " pollution is high ", the present situation of " grade is low ", surrounding enviroment are caused Have a strong impact on.The electric-melting magnesium industry in China is in the condition of " wait and expect, second-class processing, two produce ", and the wasting of resources is tight.Electric-melting magnesium is produced The high energy consumption of industry turns into the bottleneck problem for restricting the industry development, reduces smelting unit consumption and does not allow at one quarter as government, enterprise Slow work.The environmental pollution in production is administered simultaneously, energy resources waste is recycled, improves electric-melting magnesium Sand grade is also the task of top priority.Therefore, science and technology strength input is increased, develops electric-melting magnesium energy-saving processing technique of new generation, output is high The molten magnesia of grade electricity is imperative.
The content of the invention
The defects of for prior art, the present invention provide a kind of numerical simulation side for improving electrically fused magnesium fused weight crystalline quality Method, by carrying out numerical simulation to the heat exchange during electricity melt magnesium lump cooled and solidified and microstructure forming process, pass through The control of the parameters such as heat condition is exchanged, on its solidification law, understands and controls it to organize the formation of, to produce high-grade side's magnesium Stone is prepared, and reduces experiment number, saves human and material resources, improves product quality.
A kind of method for numerical simulation for improving electrically fused magnesium fused weight crystalline quality, comprises the following steps：
Step 1, a grand microcosmic unified model that macroscopic view heat transfer, microcosmic forming core are coupled with growth kinetics is established, Realize and the mathematical physics of periclase process of setting is described, specific method is as follows：
Step 1.1, establish electric-melting magnesium process of setting macromodel, including Macroscopic physical model and macroscopical mathematical model；
Step 1.1.1, Macroscopic physical model, i.e. cooling procedure electric melting magnesium furnace physical model are established, is wrapped successively from inside to outside Electric-melting magnesium molten bath, skin layer of sand and metal outer wall are included, the model is reduced to a cylinder after melting terminates, the cylinder The edge rounding of upper and lower ends；
Step 1.1.2, macroscopical mathematical model is established, determines the Heat Conduction Differential Equations of electric-melting magnesium, be i.e. dynamic temperature field controls Equation using its center point is 0 point, using the center line of cylinder as z-axis, using by 0 point and perpendicular to the face of z-axis as xov Three-dimensional system of coordinate is established in face, then dynamic temperature field governing equation is：
Wherein, ρ is magnesia density, unit kg/m3；C represents the specific heat capacity of magnesia, and unit is J/ (kgK)；T is Transient temperature, unit are DEG C；T is the time, unit s；K is thermal conductivity factor, and unit is W/ (mK)；R be cylinder radius, unit For m；For solid rate,N is atomicities all in the lattice microcell of magnesia, and n is the atomicity grown；L is The latent heat of phase change of magnesia, unit J/kg；θ is the minimum angle of freezing interface normal vector and x, y, z axle；Represent that second order is led Number；μ is fixed coefficient,For dentrite tip speed of growth expression formula, i.e., Δ T is degree of supercooling；Δ x, Δ y and Δ z are respectively the unit length of x-axis, y-axis and z-axis；
Step 1.2, electric-melting magnesium cooling procedure micromodel is established, micromodel includes Nucleation Model and growth model；
Step 1.2.1, establish Nucleation Model, using the nucleation model in Heterogeneous Nucleation, determine Enhancing Nucleation Density and Nucleation site, specifically include following steps：
Step 1.2.1.1, Enhancing Nucleation Density is determined, its function expression is：
Wherein, Δ T is degree of supercooling；For solid rate；Dn/d (Δ T) is the change of Enhancing Nucleation Density, meets Gaussian Profile, table It is shown as：
Wherein, dn is Enhancing Nucleation Density incrementss, n as caused by degree of supercooling Δ T increasemaxAccumulated for normal distribution from 0 to ∞ The maximum Enhancing Nucleation Density got, the unit of face forming core is m-2, the unit of bodily form core is m-3；ΔTσIt is subcooled for standard variance forming core Degree, unit K；ΔTmaxFor maximum forming core degree of supercooling, unit K；
Step 1.2.1.2, nucleation site is determined；
Determination for the nucleation site in big quantity of fluid, using nucleation site random number represent, random selection process by Following method determines：
In a time step δ t, the density δ n of nucleus are expressed as：
Wherein, δ (Δ T) is degree of supercooling incrementss；
Nucleation site random number PvFor：
Wherein, δ NvThe nucleus number of generation in the δ t times is represented, is that incrementss and the volume of sample of grain density are mutually multiplied Arrive；VCARepresent the volume of each unit cell units；NCARepresent the whole unit number of sample；It is every in sample in a time step A random number r is produced in individual unit, as r≤PvWhen, the unit starts forming core；
For the nucleation sites in surface forming core, the random number P of its forming core is calculated with surface forming core functions；
If the nucleus of generation falls into the grain colony solidified, it will be abandoned, do not consider further that the forming core of the position；
Step 1.2.2, growth model is established, by determining the speed of growth of dentrite tip and the direction of growth of dentrite tip To simulate microstructure, KGT models are fitted, i.e., are fitted to dentrite tip speed of growth v and degree of supercooling Δ T relation Cubic polynomial：
V=a2ΔT2+a3ΔT3
Wherein a2、a3To grow kinetic coefficient, unit is m/ (sK3)；
Step 2, using PROCAST softwares, based on the mathematics physics model established, during electric-melting magnesium cooled and solidified Temperature field and microstructure carry out numerical simulation；
Step 3, using numerical simulation result, to melting, Tuo Zhengtiwenduchang changes and Growing Process of Crystal Particles visualizes Processing, realize the visualization output to result；
Step 4, carry out analysis discussion to crystal grain Microstructure Simulation result, analysis degree of supercooling is to microcosmic group of electrically fused magnesium fused weight The effect tendency knitted, including analysis to cooling procedure different periods thermo parameters method, to electric-melting magnesium in process of setting crystal grain The analysis of influence of the analysis and forming core parameter of Microstructural Evolution process to analog result.
Further, the parameter setting of electric melting magnesium furnace physical model is as follows：Electric-melting magnesium molten bath radius 0.7m, skin layer of sand are thick 0.294m, metal outer wall thickness 0.006m, the high 2.9m of stove, electric-melting magnesium melt pool height 2.4m, electric-melting magnesium molten bath and furnace roof distance 0.25m, electric-melting magnesium molten bath and furnace bottom distance 0.25m.
Further, the process of the step 2 progress numerical simulation comprises the following steps：
Step 2.1, physical model is imported into PROCAST softwares, mesh generation is carried out to electric melting magnesium furnace physical model；
Step 2.2, conditions setting and thermal physical property parameter, including furnace wall coefficient of heat transfer h1, furnace roof coefficient of heat transfer h2, stove Bottom coefficient of heat transfer h3With molten bath and skin sand interface coefficient of heat transfer h4；
Furnace wall Formulas of Heat Transfer Coefficient is：Wherein TwTable Show the temperature of furnace wall outer surface, TeRepresent the temperature of furnace wall surrounding environment；
The furnace roof coefficient of heat transfer, the furnace bottom coefficient of heat transfer and molten bath and the skin sand interface coefficient of heat transfer are constant, are respectively：h2 =25w/ (m2·K)、h3=10w/ (m2) and h K4=500w/ (m2·K)；
Step 2.3, setting primary condition and feasibility, simulate the temperature field at the end of melting, and it is permanent first to set bath temperature It is fixed, and set simulation maximum time step-length and temperature field to reach the iterative steps of stable state；
Step 2.4, setting material parameter, three kinds of newly-built magnesia, skin sand and steel plate materials in PRECAST, and by material Material matches with physical model；
Step 2.5, setting Nucleation Model parameter value, including maximum Enhancing Nucleation Density nmax, maximum forming core degree of supercooling Δ TmaxWith Standard variance forming core degree of supercooling Δ Tσ, wherein maximum Enhancing Nucleation Density nmaxIncluding largest face Enhancing Nucleation Density nMax, sWith largest body forming core Density nMax, V；
Step 2.6, setting growth model parameter, including growth kinetics coefficient a2And a3；
It is used to simulate forming core in step 2.7, setting PROCAST softwaresThe parameter of module.
As shown from the above technical solution, the beneficial effects of the present invention are：A kind of raising fused magnesium fusing provided by the invention Stick together the method for numerical simulation of crystalline quality, by being formed to the heat exchange during electricity melt magnesium lump cooled and solidified and microstructure Process carries out mathematical physics modeling, and numerical simulation is carried out using PROCAST softwares, by exchanging the control of the parameters such as heat condition, On its solidification law, understand and control it to organize the formation of, prepared for production high-grade periclase, effectively reduce experiment time Number, human and material resources are saved, so as to improve the quality of periclase product in actual production.
Brief description of the drawings
Fig. 1 is the method for numerical simulation flow for the raising electrically fused magnesium fused weight crystalline quality that an embodiment of the present invention provides Figure；
Fig. 2 is the electric melting magnesium furnace physical model schematic diagram that an embodiment of the present invention provides；
Fig. 3 is the electric melting magnesium furnace surface grids division figure that an embodiment of the present invention provides；
Fig. 4 is the electric melting magnesium furnace volume mesh division figure that an embodiment of the present invention provides；
Fig. 5 is that the electric melting magnesium furnace that an embodiment of the present invention provides reaches furnace wall temperature curve map after stable state；
Fig. 6 is that the electric melting magnesium furnace that an embodiment of the present invention provides reaches the thermo parameters method schematic diagram after stable state；
Fig. 7 be an embodiment of the present invention provide temperature field simulation result schematic diagram, wherein, (a)~(f) be respectively from The thermo parameters method schematic diagram for terminating different periods electric melting magnesium furnace natural cooling process is initially arrived in melting；
Fig. 8 is the solidification field stimulation result schematic diagram that an embodiment of the present invention provides, wherein, (a) and (b) is respectively certainly The solidification field schematic diagram in x-axis direction and oblique 45 degree directions under the conditions of so, (c) and (d) be respectively it is air-cooled under the conditions of x-axis direction and oblique The solidification field schematic diagram in 45 degree of directions, (e) and (f) be respectively under the conditions of water cooling the solidification field in x-axis direction and oblique 45 degree of directions show It is intended to；
Fig. 9 is the Microstructure Simulation result schematic diagram that an embodiment of the present invention provides, wherein, (a), (b) and (c) point Wei not be along the heterogeneous microstructure schematic diagram of z-axis, x-axis and the direction of oblique upper three；
After Figure 10 is the cooling procedure 1h that an embodiment of the present invention provides under the conditions of natural conditions, air-cooled, three kinds of water cooling Nucleation process thermo parameters method schematic diagram；Wherein, (a) is under natural conditions, and under the conditions of (b) is air-cooled, (c) is water cooling condition Under；
Figure 11 be an embodiment of the present invention provide cooling procedure 3h after i.e. crystal growth phase natural conditions, it is air-cooled, Nucleation process thermo parameters method schematic diagram under the conditions of three kinds of water cooling；Wherein, (a) be under natural conditions, (b) under the conditions of air-cooled, (c) under the conditions of water cooling；
Figure 12 be an embodiment of the present invention provide cooling procedure 5h after i.e. crystallization process terminate natural conditions, it is air-cooled, Nucleation process thermo parameters method schematic diagram under the conditions of three kinds of water cooling；Wherein, (a) be under natural conditions, (b) under the conditions of air-cooled, (c) under the conditions of water cooling；
Figure 13 be an embodiment of the present invention provide natural conditions, crystallization process is microcosmic under the conditions of air-cooled, three kinds of water cooling Organize crystal growth condition schematic diagram；Wherein, (a) is under natural conditions, and under the conditions of (b) is air-cooled, (c) is under the conditions of water cooling.
Embodiment
With reference to the accompanying drawings and examples, the embodiment of the present invention is described in further detail.Implement below Example is used to illustrate the present invention, but is not limited to the scope of the present invention.
As shown in figure 1, a kind of method for numerical simulation of raising electrically fused magnesium fused weight crystalline quality of the method for the present embodiment is as follows It is described.
Step 1：A grand microcosmic unified model that macroscopic view heat transfer, microcosmic forming core are coupled with growth kinetics is established, Realize and the mathematical physics of periclase process of setting is described.
Electricity melt magnesium lump adulterates analysis of Heat Transfer and crystal analysis in crystallization process, regardless of whether macroscopical heat transfer model or micro- Seeing crystal model will be relevant with the change of phase field.The latent heat that the endogenous pyrogen of electric-melting magnesium cooling procedure discharges from phase transformation, and crystallize Process is exactly phase transition process of the electric-melting magnesium from melting behaviors to solid phase, and the solid rate of electric-melting magnesium is by macroscopical mould of electric-melting magnesium cooling procedure Type connects with micromodel.So when being modeled to electric-melting magnesium cooling procedure, it is necessary to first the change of phase field is analyzed, slapped Hold the influence that the change of phase field grows to thermo parameters method and crystal nucleation.The phase field change for embodying the change of phase field is introduced in a model Amount, general solid rate of choosing is the unification that phase field variable realizes macromodel and micromodel.
Step 1.1：Establish electric-melting magnesium cooling procedure macromodel, including Macroscopic physical model and macroscopical mathematical model；
Step 1.1.1：Macroscopic physical model, i.e. cooling procedure electric melting magnesium furnace physical model are established, the model includes molten bath Partly, skin layer of sand and metal outer wall.Electric-melting magnesium molten bath after wherein melting terminates is simplified to a cylinder, due in melting Irregular shape occurs in Cheng Zhong, the influence of change of temperature field, melt tank edge, so to melt tank edge rounding.Electric melting magnesium furnace Data measured by scene, its physical model is as shown in Fig. 2 its parameter setting is as shown in table 1.
The electric melting magnesium furnace physical model statistic property of table 1 is set
Parameter Measured value (m)
Molten bath radius 0.7
Skin layer of sand 0.294
Furnace wall 0.006
Stove is high 2.9
Melt pool height 2.4
Molten bath and furnace roof distance 0.25
Molten bath and furnace bottom distance 0.25
Step 1.1.2：Establish macroscopical mathematical model；
Electric-melting magnesium can discharge a large amount of latent heat in cooling procedure, and the change of the release of latent heat to the temperature field of cooling procedure has weight Influence, in dynamic temperature field model, accurately reflect latent heat treatment rule, calculate latent heat treatment amount to obtaining correct temperature Field distribution is very crucial.According to latent heat of phase change processing method, the prototype software used, the final choice Enthalpy method in analysis of Heat Transfer Electric-melting magnesium cooling procedure latent heat is handled.
Because endogenous pyrogen caloric value is essentially from the latent heat of phase change of electric-melting magnesium, so to endogenous pyrogen caloric value item, i.e. latent heat Item is handled using Enthalpy method, is had being brought into after hot entropy function derivation in Heat Conduction Differential Equations：
Wherein, be 0 point using cylindrical center's point, using the center line of cylinder as z-axis, with by 0 point and perpendicular to the face of z-axis Three-dimensional system of coordinate is established for xoy faces；ρ is density of material, unit kg/m3；H be material heat content, unit kJ/kg；When t is Between, unit s；K is thermal conductivity factor, and unit is w/ (mK)；R be cylinder radius, unit m；T is transient temperature, unit For DEG C；For solid rate,N is atomicities all in the lattice microcell of magnesia, and n is the atomicity grown, In the present embodiment, n values 2~6；
Heat conservation equation is in microcell：
Wherein,Represent second dervative；
Obtained according to Thermodynamic Law：
In formula, S is solidification entropy,For the variable quantity of latent heat heat content in the period,For latent heat heat Influence of the enthalpy H variable quantity, specific heat c, solidification entropy S to latent heat treatment, is source item,It is diffusion term, is periphery microcell knot Influence of the brilliant latent heat heat content to local area；F (T, H ...) is the function on temperature T and heat content H.
Because the lattice of magnesia is face-centered cubic lattice, so analyzed according to centroid cubic crystal system, it is all in microcell Atomicity is N, and the atomicity grown is n, then solid rateIf the latent heat of each atom is L0, ligancy η, bottom Layer ligancy is η0, it is η with layer ligancy1, then the η of η=20+η1, it is known that the ligancy η of magnesia crystal is 12, bottom ligancy η0For 4, with layer ligancy η1For 4, the latent heat E that any time is discharged within growth period is：
So latent heat heat content H can be obtained, and the derivative to the timeAndHeat is updated to keep Permanent equation obtains：
Wherein,Middle specific heat c effect very little, main influent factor are solidification entropy S,For on Temperature T and solid rateFunction.
Rate of entropy change is solidified by hot rate of entropy change Δ SrWith mixing rate of entropy change Δ ShComposition, i.e. Δ S=Δs Sr+ΔSh, its In, hot rate of entropy change Δ SrFor：Mix rate of entropy change Δ ShFor：Wherein, ψ Represent, entropy of mixing variation coefficient.It can be seen that the entropy of mixing is relevant with current state.So solidification rate of entropy change is：
Above formula is substituted into heat conservation equation, due toIt is a small amount of for high-order, it can neglect Slightly, the solidification entropy of institute's above formula is reduced to：
In above formula,Embody solid rateChange it is relevant with thermal conduction study physical quantity, thermodynamics physical quantity,Then reflect, solid rateChange also with the crystallography physics such as the speed, degree of supercooling, thermograde of crystal growth Measure relevant.Expect accurate phase transformation governing equation, it is necessary to obtain using crystallographic theoriesWith solid rate's Relational expression.
When crystal growth, old interface is constantly disappeared in microcell, and new interface is continuously generated, and interface will can hinder to grow Speed；And free energy constantly becomes the growth that will accelerate crystal greatly with solid rate.The speed of growth of known crystal can be expressed as：
v1=μ1ΔT
Wherein, μ1For the first fixed coefficient, Δ T is degree of supercooling, v1For the speed of growth of crystal main shaft, in the cooling of reality During, also have branch generation.
What the spacing of Secondary branches reflected is a cycle length of Secondary branches growth, and the growth of crystal Secondary branches is fast Degree is directly proportional to the evolution of degree of supercooling, i.e.,：
Wherein, μ2Represent the second fixed coefficient, v2For the speed of growth of crystal Secondary branches；Secondary, the tertiary branching of crystal All calculated by above formula.
Assuming that interface can will make rate of crystalline growth drop by half；The solid rate of free energyFor 0 when, rate of crystalline growth Increased speed is 0, and solid rateFor 1 when, the increased speed of rate of crystalline growth be 1 times, and becauseOrWhen, v =0, therefore the expression formula of rate of crystalline growth is the form being shown below.
Wherein μ is fixed coefficient.And the microcell unit being centrally located in X-axis is investigated, so obtaining phase transformation governing equation It is shown below.
Each crystal grain can regard monocrystal as, and atom is regularly arranged according to lattice in crystal, the connection between atom System has differences in a different direction, causes physical parameter also can be different, here it is the anisotropy of crystal.Magnesia belongs to Cubic system, its heat transfer coefficient can be calculated on diverse location with following formula：
K (θ)=k (1+ δ cos θ)n
In formula, θ is the minimum angle of freezing interface normal vector and x, y, z axle；N is the atomicity that has grown, value 2~6.
The phase transformation governing equation being finally completed is：
So dynamic temperature field governing equation is：
Wherein, ρ is magnesia density, unit kg/m3；C represents the specific heat capacity of magnesia, and unit is J/ (kgK)；T For transient temperature, unit is DEG C；T is the time, unit s；K is thermal conductivity factor, and unit is w/ (mK)；R is the radius of cylinder, Unit is m；For solid rate,N is atomicities all in the lattice microcell of magnesia, and n is the atom grown Number；L be magnesia latent heat of phase change, unit J/kg；θ is the minimum angle of freezing interface normal vector and x, y, z axle；Represent Second dervative；μ is fixed coefficient；AT is degree of supercooling；Δ x, Δ y and Δ z are respectively the unit length of x-axis, y-axis and z-axis.
Step 1.2：Electric-melting magnesium cooling procedure micromodel is established, micromodel includes Nucleation Model and growth model, tool Body process is as described below.
Step 1.2.1：Establish Nucleation Model.
Due to including two kinds of principles of average forming core and non-average forming core during forming core solid, liquid phase in version.Wherein non-average Forming core can be occurred by external particle or substrate, such as the impurity in magnesite, so non-average forming core is easier to occur, also more Tally with the actual situation.The present embodiment uses non-average nucleation model, determines Enhancing Nucleation Density and nucleation site, specifically include with Lower step：
Step 1.2.1.1, Enhancing Nucleation Density is determined；
Non- average nucleation model assumes that forming core phenomenon occurs on different nucleation sites, the change of Enhancing Nucleation Density Dn/d (Δ T) meets Gaussian Profile, therefore grain density Gaussian Profile can be described as：
In formula, dn is the Enhancing Nucleation Density incrementss as caused by degree of supercooling Δ T increase；nmaxAccumulated for normal distribution from 0 to ∞ The maximum Enhancing Nucleation Density got, the unit of face forming core is m-2, the unit of bodily form core is m-3；ΔTσIt is subcooled for standard variance forming core Degree, unit K；ΔTmaxFor maximum forming core degree of supercooling, unit K；
The grain density of forming core is obtained by integration, due to magnesia grain growth, solid rateConstantly increasing Greatly, then Enhancing Nucleation Density is improved to：
Because in cooling procedure, the release of latent heat can cause crystal remelting phenomenon occur, and grain density is much smaller than Maximum Enhancing Nucleation Density nmax；
Liquid metal is acted on by fluctuation of energy forms nucleus in some regions, only meet the region of energy condition Nucleus and stable growth can be formed；
Step 1.2.1.2, it is determined that after nucleus number, nucleation site is also predefined；
Determination for the nucleation site in big quantity of fluid, represented using nucleation site random number；It is brilliant in liquid metal The no fixed position of appearance of core, is random, the random selection process of nucleation site determines using the following method：
In a time step δ t, specimen temperature reduces δ T, degree of supercooling increase δ (Δ T), and the density of nucleus is：
The incrementss of grain density are multiplied with volume of sample, obtain the nucleus number δ N generated within the δ t timesv, sample it is whole Individual unit number is NCA, determine random number PvFor：
In formula, VCAIt is the volume of each unit cell units；In a time step, one is produced in sample in each unit Random number r, as r≤Pv, when, the unit starts forming core；
For the nucleation sites in surface forming core, the random number P of its forming core is calculated with surface forming core functions；
If the nucleus of generation falls into the grain colony solidified, it will be abandoned, do not consider further that the forming core of the position.
Step 1.2.2：Establish growth model.
After solid phase nucleus is formed, microstructure begins to growth course.Experimental study show that each dendrite trunk direction is not May be identical, wherein the trunk direction dendritic growth parallel with direction of heat flow obtains the rapidest.So they are preferential raw Grow and suppress the growth of adjacent dendrite, so as to realize the growth of column crystal.Therefore the key of Microstructure Simulation is to determine dendrite The speed of growth at tip and the direction of growth of dentrite tip.
The degree of supercooling of dendrite is generally made up of four parts：
AT=Δs Tc+ΔTt+ΔTk+ΔTr
Wherein, Δ Tc、ΔTt、ΔTk、ΔTrRespectively constitutional supercooling degree, hot degree of supercooling, kinetic undercooling degree and curvature mistake Cold degree.
Δ T is compared after generally for threecFor very little, so calculate in usually ignore.According to KGT models, obtained dendrite Tip radius R and growth rate v relation have：
Wherein, r is Gibbs-Thompson coefficients (interface of solid liquid interface can be with the ratio of the entropy of every volume fusion zone)； M is liquidous slopes；GcFor the solute concentration gradient in the liquid phase of dendrite forward position；ξ is the function of Peclet numbers, in bradyauxesis Take 1；G is thermograde；Pe is the Peclet numbers of solute, for representing the relative scale of convection current and diffusion；Iv (Pe) is (former Soviet Union mathematician Ivantsov is it is assumed that solid liquid interface is isothermal or isoconcentration parabola to the Ivantsov functions of Peclet numbers On the basis of, the stable state diffusion solution of the dentrite tip strictly mathematically obtained)；D is the solutes accumulation coefficient in liquid phase；Δ TαFor the degree of supercooling of dentrite tip；γ is equilibrium distribution coefficient.
Iv (Pe) in equation can also be expressed as the form of continuous fraction：
Certain item number is often intercepted during calculating as needed as approximate, takes item number the more, represent dendrite be cured to Rotary parabolic line approaches.Generally take first approximation：
Or two stage approach：
KGT models are fitted, i.e., are fitted to dentrite tip speed of growth v and degree of supercooling Δ T relation more three times Item formula, is shown below：
V=a2ΔT2+a3ΔT3
Wherein a2、a3To grow kinetic coefficient, unit is m/ (sK3)。
The direction of growth is simulated after establishing model by software, and the direction of growth is uncertain, is had certain random Property.
Step 2：Using PROCAST softwares, based on the mathematics physics model established, during electric-melting magnesium cooled and solidified Temperature field and microstructure carry out numerical simulation, specific method is as follows.
Step 2.1：Grand microcosmic mathematics physics model is inputted, and the division of grid is carried out to physical model.
Physical model is imported into PROCAST softwares, mesh generation is carried out as shown in Figure 3 and Figure 4 to electric melting magnesium furnace, division Lattice number is 1234087 afterwards, nodes 249864.
Step 2.2：Conditions setting and thermal physical property parameter, including furnace wall coefficient of heat transfer h1, furnace roof coefficient of heat transfer h2, stove Bottom coefficient of heat transfer h3With molten bath and skin sand interface coefficient of heat transfer h4。
Cooling procedure initial time furnace wall temperature is very high, does not only exist the heat transfer with skin sand and raw material layer, also exist with The convection current and radiation heat transfer that ambient atmosphere occurs.The Formulas of Heat Transfer Coefficient of furnace wall is：
In formula, εwIt is furnace wall outer surface radiance, εw=0.85；σ is Stefan-Boltzmann constants；TwIt is outside furnace wall The temperature on surface；TeIt is the temperature of surrounding environment, Te=293K.
It is uncovered at the top of electric melting magnesium furnace, molten stick together is directly exposed in air, due to skin sand and the heat conduction energy of raw material layer Power is weaker, varies with temperature unobvious, so the furnace roof coefficient of heat transfer is taken as constant, h2=25W/ (m2·K)。
The bottom of electric melting magnesium furnace contacts with table, because table has thermal resistance, effect of heat insulation is better than top, varied with temperature It is less obvious, so the furnace bottom coefficient of heat transfer takes h3=10w/ (m2·K)。
Known skin sand and raw material layer are mainly raw material that is unfused and being sintered, and molten bath takes with the skin sand interface coefficient of heat transfer h4=500W/ (m2·K)。
Step 2.3：Set primary condition and feasibility；The temperature field at the end of melting is simulated, first assumes that bath temperature is permanent It is fixed, steady heat conduction problem is changed into, Heat Conduction Differential Equations are：
The setting of boundary condition and thermal physical property parameter with step 2.2.
It is 1s to set simulation maximum time step-length, and after the step of iteration 10000, temperature field reaches stable state.Now at furnace wall temperature In 610 DEG C, furnace wall temperature curve is as shown in Figure 5.The temperature data that the melting obtained by scene terminates furnace wall is about 600 DEG C, Two results are in error range, and simulation is effective.After reaching stable state, the thermo parameters method of electric melting magnesium furnace is as shown in Figure 6.
Step 2.4：Set material parameter；
Due to there is no the data of magnesia in PRECAST, so newly-built three kinds of materials, and by material and physical model Match somebody with somebody, its relevant parameter is as shown in table 2, table 3 and table 4.
The magnesia of table 2, skin sand, the particularly relevant parameter list of steel plate
The magnesia specific heat capacity of table 3
The magnesia thermal conductivity factor of table 4
Step 2.5：Set Nucleation Model parameter value；
Understand that grain nucleation density is according to modeling：
In big quantity of fluid, nucleation site random number is：
Parameter setting therein includes maximum Enhancing Nucleation Density nmax, maximum forming core degree of supercooling Δ TmaxWith standard variance forming core mistake Cold degree Δ Tσ, wherein maximum Enhancing Nucleation Density nmaxIncluding largest face Enhancing Nucleation Density nMax, SWith largest body Enhancing Nucleation Density nMax, VSuch as the institute of table 5 Show.
The Nucleation Model parameter list of table 5
nMax, S(m-2) 1.0e+7
nMax, V(m-3) 1.0E+8
ΔTmax(℃) 4.0
ΔTσ(℃) 7.0
Step 2.6：Set growth model parameter；
Speed of growth v and degree of supercooling Δ T relation are fitted to
V=a2ΔT2+a3ΔT3
Wherein, a2、a3To grow kinetic coefficient, it is respectively a to set the two parameters2=1.05 × 10-6, a3=8.768 ×10-6, and PROCAST input.
Step 2.7：It is used to simulate forming core in setting PROCAST softwaresThe parameter of module；
In CA methods, the heterogeneous forming core phenomenon major way for handling liquid metal is to use continuous nucleation, is described simultaneously The distribution relation of equiax crystal density with temperature then uses gauss of distribution function, and the model of grain growth considers crystal tip simultaneously Growth kinetics and selecting excellence evaluation [1 0 0] crystal orientation, the first step carry out macroscopic finite unit mesh generation, are then sub-divided into Microcosmic cubic cell grid.
Parameter setting is as follows：
CA cell sizes are 1000um；The CA numbers included in each block are 1000；Crystal orientation number is 5000；The average forming core mistake in face Cold degree is 4.0 DEG C；Face standard variance degree of supercooling is 1.0 DEG C；The heterogeneous forming core number in face is 1.0 × 107；The average forming core degree of supercooling of body For 7.0 DEG C；Body standard variance degree of supercooling is 1.0 DEG C；The heterogeneous forming core number of body is 1.0 × 107。
Step 3：PROCAST is carried out to molten Tuo Zhengtiwenduchang changes and Growing Process of Crystal Particles using numerical simulation result Software visualization processing, realize the visualization output to result.
Step 4：Carry out analysis discussion to crystal grain Microstructure Simulation result, analysis degree of supercooling is to microcosmic group of electrically fused magnesium fused weight The effect tendency knitted.
Step 4.1：Analyze dynamic temperature field analog result.
Using the thermo parameters method after melting as the primary condition of process of setting, cooling procedure different periods are intercepted Thermo parameters method, as shown in Fig. 7 (a)~(f).Under conditions of natural cooling, fused magnesite radiating is uniform, between same time Under, the molten center radiating that sticks together is rapid compared with external skin layer of sand, and this is due to the conveying of skin layer of sand quality, and thermal conductivity is good.Magnesite The fusing point of ore deposit is very high, and the temperature in molten bath is up to 3000 DEG C, so cooled and solidified process is time-consuming longer.In order to more preferable simulation we Using longer simulated time, since solidification (the melting initial temperature field as shown in Fig. 7 (a)) to terminating 2.5 hours, in t During=2.5h, skin layer of sand is cooled to environment temperature substantially, and electrically fused magnesium fused weight center has also been solidified (as shown in Fig. 7 (f) completely Melting end temp field), but because of its high-melting-point, now temperature is still very high.Outside furnace wall and skin can be removed in the industry Layer of sand, electrically fused magnesium fused weight is set further to cool down.
The change for solidifying field is as shown in Figure 8.As shown in Figure 8, the solid fraction of electrically fused magnesium fused weight is the change with temperature field And change.When bath temperature is less than 2825 DEG C of liquidus temperature, start to crystallize；When the mean temperature in molten bath drops to 2400 DEG C When, mean tibial fraction is 40%；Continue near 1900 DEG C after temperature, solid fraction rises to 70%, now molten bath and skin sand Contact surface solidifies completely；When finally grade bath temperature drops to 1500 DEG C, average solid fraction reaches 100%.Therefore take 1500 DEG C of maximum temperatures for crushing process, now furnace wall temperature is about 600 DEG C.
At process of setting initial stage, temperature declines obvious, and as process of setting is carried out, the mean temperature of melt drops to liquid phase Below line, liquid phase gradually becomes solid phase, due to discharging latent heat into surrounding environment, so the temperature of resolidified region is improved, As fraction solid is increasing, latent heat tails off, and the molten conductive capability to stick together becomes big, temperature rapid decrease.
Step 4.2：Analyze Microstructure Simulation result.
Established according to the present embodiment methodModel (parameter corresponding to being set i.e. in PROCAST softwares) and shape Core, growth model are calculated the microstructure of electricity melt magnesium lump, it can be seen that electric-melting magnesium grain structure in process of setting Evolutionary process, as shown in Figure 9.The molten temperature to stick together is gradually reduced with heat to external diffusion, when some portion of temperature of resolidified region When degree is less than forming core degree of supercooling, process of setting takes the lead in starting in this part.As shown in Figure 9, the crystal grain tool formed on type wall There is the crystal orientation of any direction.With the progress of growth course, the growth crystal orientation crystal grain parallel with direction of heat flow has obtained preferred growth, I.e. crystal grain is with the morphogenesis of column crystal.When column crystals growth, solid liquid interface degree of supercooling is also increasing, and this is due to again Caused by the general character forward position degree of supercooling of distribution and thermal diffusion.Just swash when this degree of supercooling reaches pre-defined forming core degree of supercooling Forming core occurs for the forming core cell element sent out in melt, and equiaxed crystal initially forms.These equi-axed crystal grow into subcooling films around, Discharge a large amount of latent heat, thermograde is diminished, newly-generated nucleus growth slows, but original grain growth also after It is continuous, when reaching forming core degree of supercooling again, there is new forming core generation again, be finally centrally formed an isometric crystalline region in molten stick together.
Step 4.3：Analyze influence of the forming core parameter to analog result.
Process of setting mainly includes the forming core and growth course of microcosmic crystal grain, but nucleation ability is difficult control, passes through reality The difficulty for testing acquisition parameter is also very big.But pattern influence of the forming core parameter difference on crystal grain is very big, it is thus determined that appropriate forming core Parameter and effect tendency of these parameters to microstructure is grasped, could effectively control the microscopic appearance of crystal grain.In Rappaz There are six forming core parameters in nucleation model, be the average forming core degree of supercooling in face, the average forming core degree of supercooling of body, face forming core mistake respectively Cold degree variance, face forming core degree of supercooling variance, face maximum Enhancing Nucleation Density, body maximum Enhancing Nucleation Density, wherein face represent the shape on furnace wall Core, body are represented in bath forming core.
According to traditional solidification theory, the coefficient of heat transfer has on the characteristic value of solidification grain structure and obviously influenceed.This is Because in the liquid metal of certain volume, forming core speed is inversely proportional with forming core crystallite dimension, and the coarsening rate of crystal grain and crystalline substance Particle size is directly proportional, and core forming speed and coarsening rate are all closely related with the degree of supercooling in melt.In crystallization process, degree of supercooling Bigger, the number of raw core is more, and nuclei growth is slower.Therefore degree of supercooling can be increased in the forming core stage, reduced in growth phase Degree of supercooling, so as to obtain large-sized crystalline solid.The method for adjusting degree of supercooling is exactly to adjust cooling velocity.
To grind the influence for drawing cooling velocity and crystallite dimension, simulate under the conditions of different cooling velocities, crystal grain it is micro- See the change of tissue topography.The present embodiment uses changes it in forming core and growth course to furnace wall air-cooled and water cooling the method for progress Degree of supercooling.Compare the change in nucleation process temperature field under the conditions of natural conditions, air-cooled, three kinds of water cooling, after cooling procedure 1h Situation is as shown in Figure 10, it is found that the molten bath central temperature under the conditions of natural cooling is still at a relatively high, and under the conditions of air-cooled and water cooling, Bath temperature is significantly lower than natural cooling, and temperature field is also superior to natural cooling condition.After cooling procedure 3h, i.e., when crystal growth rank Section, the change of temperature field under the conditions of three kinds is more obvious, as shown in figure 11.After cooling procedure 5h, i.e., when crystallization process terminates, temperature Degree field is substantially at stabilization, as shown in figure 12.
Under the conditions of natural conditions, air-cooled, three kinds of water cooling, the growing state of crystal is as shown in figure 13, crystallization process, degree of supercooling Bigger, nucleus growth number is more, and nuclei growth is slower.Therefore, increase degree of supercooling in the forming core stage, reduce in growth phase Degree of supercooling, so it is obtained with the large-sized electric smelting magnesium crystal of high-purity.
It is therefore seen that strengthening cooling velocity, the quantity and size of the column crystal in microstructure substantially increase, central area Equiax crystal quantity reduce, this is due to the degree of supercooling for increasing nucleation process, causes equiax crystal forming core in melt difficult, and The growth of column crystal does not run into the obstruction of solid liquid interface forward position equiax crystal and persistently grown up, and optimizes product quality.Water cooling bar Under part, effect is optimal, and the growth of equiax crystal is almost stagnated, and column crystal attains full development, it is seen then that the condition of change can be big Increase and add columnar zone domain.Not only column crystal size increases, and the size of equiax crystal is also being reduced.
The method for numerical simulation for a kind of raising electrically fused magnesium fused weight crystalline quality that the present embodiment provides, by electricity melt magnesium lump Heat exchange and microstructure forming process during cooled and solidified carry out numerical simulation, by exchanging the parameters such as heat condition Control, on its solidification law, understands and controls it to organize the formation of, and is prepared for production high-grade periclase, reduces experiment Number, human and material resources are saved, improve product quality.
Finally it should be noted that：The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although The present invention is described in detail with reference to the foregoing embodiments, it will be understood by those within the art that：It still may be used To be modified to the technical scheme described in previous embodiment, either which part or all technical characteristic are equal Replace；And these modifications or replacement, the essence of appropriate technical solution is departed from the model that the claims in the present invention are limited Enclose.

Claims (3)

  1. A kind of 1. method for numerical simulation for improving electrically fused magnesium fused weight crystalline quality, it is characterised in that：Comprise the following steps：
    Step 1, a grand microcosmic unified model that macroscopic view heat transfer, microcosmic forming core are coupled with growth kinetics is established, realized The mathematical physics of periclase process of setting is described, specific method is as follows：
    Step 1.1, establish electric-melting magnesium process of setting macromodel, including Macroscopic physical model and macroscopical mathematical model；
    Step 1.1.1, Macroscopic physical model, i.e. cooling procedure electric melting magnesium furnace physical model are established, includes electricity successively from inside to outside Molten magnesium molten bath, skin layer of sand and metal outer wall, the model are reduced to a cylinder after melting terminates, the cylinder up and down The edge rounding at both ends；
    Step 1.1.2, macroscopical mathematical model is established, determines the Heat Conduction Differential Equations of electric-melting magnesium, i.e. dynamic temperature field governing equation, It is 0 point using its center point, is established using the center line of cylinder as z-axis, using 0 point of process and perpendicular to the face of z-axis as xoy faces Three-dimensional system of coordinate, then dynamic temperature field governing equation be：
    Wherein, ρ is magnesia density, unit kg/m3；C represents the specific heat capacity of magnesia, and unit is J/ (kgK)；T is instantaneous temperature Degree, unit are DEG C；T is the time, unit s；K is thermal conductivity factor, and unit is w/ (mK)；R be cylinder radius, unit m； For solid rate,N is atomicities all in the lattice microcell of magnesia, and n is the atomicity grown；L is magnesia Latent heat of phase change, unit J/kg；θ is the minimum angle of freezing interface normal vector and x, y, z axle；Represent second dervative；μ is solid Determine coefficient,For dentrite tip speed of growth expression formula, i.e., Δ T is degree of supercooling；Δ x, Δ y and Δ z are respectively the unit length of x-axis, y-axis and z-axis；
    Step 1.2, electric-melting magnesium cooling procedure micromodel is established, micromodel includes Nucleation Model and growth model；
    Step 1.2.1, Nucleation Model is established, using the nucleation model in Heterogeneous Nucleation, determines Enhancing Nucleation Density and forming core Position, specifically include following steps：
    Step 1.2.1.1, Enhancing Nucleation Density is determined, its function expression is：
    Wherein, Δ T is degree of supercooling；For solid rate；Dn/d (Δ T) is the change of Enhancing Nucleation Density, meets Gaussian Profile, is expressed as：
    <mrow> <mfrac> <mrow> <mi>d</mi> <mi>n</mi> </mrow> <mrow> <mi>d</mi> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <msub> <mi>n</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> <msub> <mi>&amp;Delta;T</mi> <mi>&amp;sigma;</mi> </msub> </mrow> </mfrac> <mi>exp</mi> <mo>&amp;lsqb;</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>T</mi> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&amp;Delta;T</mi> <mi>&amp;sigma;</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow>
    Wherein, dn is Enhancing Nucleation Density incrementss, n as caused by degree of supercooling AT increasemaxIntegrated for normal distribution from 0 to ∞ The maximum Enhancing Nucleation Density arrived, the unit of face forming core is m-2, the unit of bodily form core is m-3；ΔTσFor standard variance forming core degree of supercooling, Unit is K；ΔTmaxFor maximum forming core degree of supercooling, unit K；
    Step 1.2.1.2, nucleation site is determined；
    Determination for the nucleation site in big quantity of fluid, represent that random selection process is by as follows using nucleation site random number Method determines：
    In a time step δ t, the density δ n of nucleus are expressed as：
    Wherein, δ (AT) is degree of supercooling incrementss；
    Nucleation site random number PvFor：
    <mrow> <msub> <mi>P</mi> <mi>v</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;delta;N</mi> <mi>v</mi> </msub> </mrow> <msub> <mi>N</mi> <mrow> <mi>C</mi> <mi>A</mi> </mrow> </msub> </mfrac> <mo>=</mo> <msub> <mi>&amp;delta;n</mi> <mi>v</mi> </msub> <msub> <mi>V</mi> <mrow> <mi>C</mi> <mi>A</mi> </mrow> </msub> </mrow>
    Wherein, δ NvThe nucleus number of generation in the δ t times is represented, is multiplied to obtain with volume of sample for the incrementss of grain density；VCA Represent the volume of each unit cell units；NCARepresent the whole unit number of sample；In a time step, each unit in sample One random number r of middle generation, as r≤PvWhen, the unit starts forming core；
    For the nucleation sites in surface forming core, the random number P of its forming core is calculated with surface forming core functions；
    If the nucleus of generation falls into the grain colony solidified, it will be abandoned, do not consider further that the forming core of the position；
    Step 1.2.2, establish growth model, by determine dentrite tip the speed of growth and dentrite tip the direction of growth come mould Intend microstructure, KGT models are fitted, i.e., are fitted to dentrite tip speed of growth v and degree of supercooling Δ T relation three times Multinomial：
    V=a2ΔT2+a3ΔT3
    Wherein a2、a3To grow kinetic coefficient, unit is m/ (sK3)；
    Step 2, using PROCAST softwares, based on the mathematics physics model established, to the temperature during electric-melting magnesium cooled and solidified Spend field and microstructure carries out numerical simulation；
    Step 3, using numerical simulation result visualization processing is carried out to molten Tuo Zhengtiwenduchang changes and Growing Process of Crystal Particles, Realize the visualization output to result；
    Step 4, analysis discussion is carried out to crystal grain Microstructure Simulation result, analysis degree of supercooling is to electrically fused magnesium fused weight microstructure Effect tendency, including analysis to cooling procedure different periods thermo parameters method, to electric-melting magnesium, crystal grain is microcosmic in process of setting The analysis of influence of the analysis and forming core parameter of microstructure Evolution process to analog result.
  2. A kind of 2. method for numerical simulation for improving electrically fused magnesium fused weight crystalline quality according to claim 1, it is characterised in that： The parameter setting of the electric melting magnesium furnace physical model is as follows：Electric-melting magnesium molten bath radius 0.7m, skin layer of sand thickness 0.294m, metal outer wall Thick 0.006m, the high 2.9m of stove, electric-melting magnesium melt pool height 2.4m, electric-melting magnesium molten bath and furnace roof distance 0.25m, electric-melting magnesium molten bath and stove Bottom distance 0.25m.
  3. A kind of 3. method for numerical simulation for improving electrically fused magnesium fused weight crystalline quality according to claim 1, it is characterised in that： The process that the step 2 carries out numerical simulation comprises the following steps：
    Step 2.1, physical model is imported into PROCAST softwares, mesh generation is carried out to electric melting magnesium furnace physical model；
    Step 2.2, conditions setting and thermal physical property parameter, including furnace wall coefficient of heat transfer h1, furnace roof coefficient of heat transfer h2, furnace bottom changes Hot coefficient h3With molten bath and skin sand interface coefficient of heat transfer h4；
    Furnace wall Formulas of Heat Transfer Coefficient is：Wherein TwRepresent stove The temperature of wall outer surface, TeRepresent the temperature of furnace wall surrounding environment；
    The furnace roof coefficient of heat transfer, the furnace bottom coefficient of heat transfer and molten bath and the skin sand interface coefficient of heat transfer are constant, are respectively：h2= 25W/(m2·K)、h3=10w/ (m2) and h K4=500W/ (m2·K)；
    Step 2.3, setting primary condition and feasibility, simulate the temperature field at the end of melting, and first setting bath temperature is constant, and Simulation maximum time step-length and temperature field is set to reach the iterative steps of stable state；
    Step 2.4, setting material parameter, three kinds of newly-built magnesia, skin sand and steel plate materials in PRECAST, and by material with Physical model matches；
    Step 2.5, setting Nucleation Model parameter value, including maximum Enhancing Nucleation Density nmax, maximum forming core degree of supercooling Δ TmaxAnd standard Variance forming core degree of supercooling Δ Tσ, wherein maximum Enhancing Nucleation Density nmaxIncluding largest face Enhancing Nucleation Density nMax, SWith largest body Enhancing Nucleation Density nMax, V；
    Step 2.6, setting growth model parameter, including growth kinetics coefficient a2And a3；
    It is used to simulate forming core in step 2.7, setting PROCAST softwaresThe parameter of module.
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