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 PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 106
- FYYHWMGAXLPEAU-UHFFFAOYSA-N Magnesium Chemical compound [Mg] FYYHWMGAXLPEAU-UHFFFAOYSA-N 0.000 title claims abstract description 71
- 239000011777 magnesium Substances 0.000 title claims abstract description 69
- 229910052749 magnesium Inorganic materials 0.000 title claims abstract description 69
- 238000004088 simulation Methods 0.000 title claims abstract description 43
- CPLXHLVBOLITMK-UHFFFAOYSA-N Magnesium oxide Chemical compound [Mg]=O CPLXHLVBOLITMK-UHFFFAOYSA-N 0.000 claims abstract description 131
- 239000013078 crystal Substances 0.000 claims abstract description 97
- 239000000395 magnesium oxide Substances 0.000 claims abstract description 76
- 235000012245 magnesium oxide Nutrition 0.000 claims abstract description 76
- 230000008569 process Effects 0.000 claims abstract description 75
- 230000012010 growth Effects 0.000 claims abstract description 74
- 238000004781 supercooling Methods 0.000 claims abstract description 60
- 238000007711 solidification Methods 0.000 claims abstract description 41
- 230000008023 solidification Effects 0.000 claims abstract description 41
- 239000000463 material Substances 0.000 claims abstract description 17
- 238000004458 analytical method Methods 0.000 claims abstract description 11
- 238000012546 transfer Methods 0.000 claims abstract description 11
- 238000012545 processing Methods 0.000 claims abstract description 5
- 230000006911 nucleation Effects 0.000 claims description 134
- 238000010899 nucleation Methods 0.000 claims description 134
- 238000001816 cooling Methods 0.000 claims description 61
- 230000008859 change Effects 0.000 claims description 33
- 238000002425 crystallisation Methods 0.000 claims description 26
- 230000008025 crystallization Effects 0.000 claims description 26
- 239000004576 sand Substances 0.000 claims description 26
- AXZKOIWUVFPNLO-UHFFFAOYSA-N magnesium;oxygen(2-) Chemical compound [O-2].[Mg+2] AXZKOIWUVFPNLO-UHFFFAOYSA-N 0.000 claims description 21
- 238000009826 distribution Methods 0.000 claims description 19
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- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 10
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- ZLNQQNXFFQJAID-UHFFFAOYSA-L magnesium carbonate Chemical compound [Mg+2].[O-]C([O-])=O ZLNQQNXFFQJAID-UHFFFAOYSA-L 0.000 description 3
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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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
Technical Field
The invention relates to the technical field of quality optimization of fused magnesium products, in particular to a numerical simulation method for improving the crystallization quality of a fused magnesium fused weight.
Background
The magnesium industry comprises three major industries of magnesium refractory materials, magnesium chemical materials and magnesium metal and magnesium alloy, and is generally called as the magnesium material industry. The magnesium resource refers to magnesium-containing mineral which can be used for producing products such as magnesium refractory materials, magnesium chemical materials, magnesium metal and the like, China is a magnesium resource kingdom, magnesite, dolomite, brucite and the like have abundant resource reserves, and the products are widely applied to the fields of metallurgy, building materials, chemical industry, automobiles, electronics, aerospace, medicine, food, agriculture and animal husbandry and the like.
The fused magnesia is also called fused MgO (fused magnesia for short), which is an alkaline magnesia refractory material with high purity, high melting point (2825 ℃), large crystal grain, compact structure, strong clarification resistance and stable chemical property, is an excellent high-temperature electrical insulating material, is also an important raw material for manufacturing high-grade magnesia bricks, magnesia carbon bricks and unshaped refractory materials, and is widely applied to the fields of metallurgy, building materials, glass, petrifaction, cement, national defense and the like.
In recent years, the development of refractory industry is promoted by the continuous development of high-temperature industries such as global metallurgy, cement, glass, petrifaction and the like, and fused magnesia has extremely unique performance, is a high-grade refractory material with irreplaceable advantages and is widely applied to countries around the world. With the continuous expansion of the application range of fused magnesia, the demand is increased year by year, the comprehensive price is continuously increased, the market is good, and the fused magnesia industry is facing great opportunity and development.
At present, due to the influences of global climate change, greenhouse effect, excessive resource consumption, energy crisis and the like, the strength of the international society on resource, energy and environment protection is increased, and the energy conservation and emission reduction work is highly concerned by various countries year by year. China is the biggest world-wide fused magnesia producing country and supplying country at present, but the current situations of high energy consumption, high pollution and low grade of the fused magnesia industry are caused by lagging of the domestic fused magnesia production process and staggering power consumption of the traditional smelting mode, and the current situations of high energy consumption, high pollution and low grade of the fused magnesia industry cause serious influence on the surrounding environment. The electric smelting magnesium industry in China is in the situation of 'material waiting, second-class processing and second-generation', and the resource waste is severe. The high energy consumption of the electric magnesium melting industry becomes a bottleneck problem restricting the development of the industry, and the reduction of the smelting unit consumption becomes a work of governments and enterprises. Meanwhile, the environmental pollution in production is treated, energy resource waste is recycled, and the quality of fused magnesia is improved. Therefore, the investment of scientific and technological force is increased, a new generation of fused magnesia energy-saving production process is developed, and the production of high-grade fused magnesia is imperative.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a numerical simulation method for improving the crystallization quality of an electric fused magnesium lump, which is characterized in that the numerical simulation is carried out on the heat exchange and microstructure forming process in the cooling and solidifying process of the electric fused magnesium lump, the microstructure formation is known and controlled on the solidification rule by controlling the parameters such as the heat exchange condition and the like, the preparation is made for producing high-grade periclase, the experiment times are reduced, the manpower and material resources are saved, and the product quality is improved.
A numerical simulation method for improving the crystallization quality of an electric fused magnesium fused weight comprises the following steps:
step 1, establishing a macro-micro unified model coupling macro heat transfer, micro nucleation and growth dynamics, and realizing mathematical physical description of the periclase solidification process, wherein the specific method comprises the following steps:
step 1.1, establishing a macroscopic model of the solidification process of the fused magnesium, wherein the macroscopic model comprises a macroscopic physical model and a macroscopic mathematical model;
step 1.1.1, establishing a macroscopic physical model, namely a physical model of the fused magnesia furnace in the cooling process, which sequentially comprises a fused magnesia pool, a sand coating and a metal outer wall from inside to outside, wherein the model is simplified into a cylinder after the smelting is finished, and the edges of the upper end and the lower end of the cylinder are rounded;
step 1.1.2, establishing a macroscopic mathematical model, determining a heat conduction differential equation of the fused magnesium, namely a dynamic temperature field control equation, and establishing a three-dimensional coordinate system by taking the central point of a cylinder as a point 0, the central line of the cylinder as a z-axis and a plane passing through the point 0 and perpendicular to the z-axis as a plane xov, wherein the dynamic temperature field control equation is as follows:
wherein rho is the density of magnesium oxide and the unit is kg/m3(ii) a c represents the specific heat capacity of magnesium oxide and the unit is J/(kg. K); t is the instantaneous temperature in units of; t is time, unit s; k is the thermal conductivity coefficient, and the unit is W/(m.K); r is the radius of the cylinder in m;the solid phase fraction is a solid phase fraction,in lattice micro-region with N being magnesium oxideAll atomic numbers, n being the atomic number that has grown; l is the latent heat of phase change of the magnesium oxide, and the unit is J/kg; theta is the minimum included angle between the normal vector of the solidification interface and the x, y and z axes;represents the second derivative; mu is a fixed coefficient of the coefficient,expressed as dendrite tip growth rate, i.e.Delta T is the supercooling degree; Δ x, Δ y, and Δ z are unit lengths of the x-axis, y-axis, and z-axis, respectively;
step 1.2, establishing a micro model of the fused magnesium cooling process, wherein the micro model comprises a nucleation model and a growth model;
step 1.2.1, establishing a nucleation model, and determining the nucleation density and the nucleation position by adopting a continuous nucleation model in heterogeneous nucleation, which comprises the following steps:
step 1.2.1.1, determining the nucleation density, wherein the function expression of the nucleation density is as follows:
wherein, Delta T is the supercooling degree;the solid phase ratio; dn/d (Δ T) is the variation in nucleation density, satisfying a Gaussian distribution, expressed as:
where dn is the increase in nucleation density caused by an increase in supercooling degree Δ T, nmaxIntegrated from 0 to ∞ for normal distributionMaximum nucleation density, surface shape nucleus in m-2The unit of the figure nucleus is m-3；ΔTσThe standard deviation nucleation supercooling degree is K; delta TmaxThe maximum nucleation supercooling degree is K;
step 1.2.1.2, determining a nucleation position;
for the determination of nucleation sites in a large volume of liquid, a random number of nucleation sites is used for representation, and the random selection process is determined by the following method:
in a time step t, the density n of the crystal nuclei is expressed as:
wherein (Δ T) is the supercooling degree increase;
nucleation position random number PvComprises the following steps:
wherein N isvThe number of crystal nuclei generated in t time is represented and is obtained by multiplying the increment of the crystal nucleus density by the sample volume; vCARepresenting the volume of each unit cell; n is a radical ofCARepresents the total number of cells of the sample; generating a random number r in each cell of the sample in a time step, when r is less than or equal to PvWhen this happens, the unit begins to nucleate;
for the crystal nucleus position of the surface nucleation, calculating the random number P of the nucleation by using the surface kernel functions；
If the generated crystal nucleus falls into the solidified crystal grain range, the crystal nucleus is abandoned, and the nucleation at the position is not considered;
step 1.2.2, establishing a growth model, simulating a microstructure by determining the growth speed of a dendritic crystal tip and the growth direction of the dendritic crystal tip, and fitting an KGT model, namely fitting the relation between the growth speed v of the dendritic crystal tip and the supercooling degree delta T into a cubic polynomial:
v＝a2ΔT2+a3ΔT3
wherein a is2、a3The growth kinetic coefficient is expressed in m/(s.K)3)；
2, carrying out numerical simulation on a temperature field and a microstructure in the cooling and solidification process of the fused magnesium by using PROCAST software based on the established mathematical physical model;
step 3, carrying out visual processing on the whole temperature field change of the fused weight and the growth process of the crystal grains by using a numerical simulation result to realize visual output of the result;
and 4, analyzing and discussing the grain microstructure simulation result, and analyzing the influence trend of the supercooling degree on the microstructure of the fused magnesia lump, including the analysis of temperature field distribution in different periods of the cooling process, the analysis of the grain microstructure evolution process of the fused magnesia in the solidification process and the analysis of the influence of nucleation parameters on the simulation result.
Further, the parameters of the physical model of the fused magnesia furnace are set as follows: the radius of the fused magnesia pool is 0.7m, the thickness of the sand coat layer is 0.294m, the thickness of the metal outer wall is 0.006m, the height of the furnace is 2.9m, the height of the fused magnesia pool is 2.4m, the distance between the fused magnesia pool and the furnace top is 0.25m, and the distance between the fused magnesia pool and the furnace bottom is 0.25 m.
Further, the step 2 of performing numerical simulation includes the following steps:
step 2.1, importing the physical model into PROCAST software, and carrying out grid division on the physical model of the electro-fused magnesia furnace;
step 2.2, setting boundary conditions and thermophysical parameters including furnace wall heat exchange coefficient h1Furnace top heat exchange coefficient h2Heat exchange coefficient h of furnace bottom3Heat exchange coefficient h of interface of molten pool and sand4；
The calculation formula of the heat exchange coefficient of the furnace wall is as follows:wherein T iswIndicating the temperature, T, of the outer surface of the furnace walleRepresenting the temperature of the environment surrounding the furnace wall;
the heat exchange coefficient of the furnace top, the heat exchange coefficient of the furnace bottom and the heat exchange coefficient of the interface of the molten pool and the sand coat are constants which are respectively as follows: h is2＝25w/(m2·K)、h3＝10w/(m2K) and h4＝500w/(m2·K)；
Step 2.3, setting initial conditions and feasibility, simulating a temperature field at the end of smelting, firstly setting constant temperature of a molten pool, and setting a simulated maximum time step length and iteration step number of the temperature field reaching a steady state;
step 2.4, setting material parameters, newly building three materials of magnesium oxide, sand and a steel plate in PRECAST, and matching the materials with a physical model;
step 2.5, setting the parameter values of the nucleation model, including the maximum nucleation density nmaxMaximum nucleation supercooling degree delta TmaxSum standard deviation nucleation supercooling degree delta TσWherein the maximum nucleation density nmaxIncluding the maximum surface shape nuclear density nmax，sAnd a maximum bulk nuclear density nmax，V；
Step 2.6, setting growth model parameters including growth kinetic coefficient a2And a3；
Step 2.7, setting for simulation nucleation in PROCAST softwareParameters of the module.
According to the technical scheme, the invention has the beneficial effects that: according to the numerical simulation method for improving the crystallization quality of the fused magnesium lump, mathematical physical modeling is carried out on the heat exchange and microstructure forming processes in the cooling and solidifying processes of the fused magnesium lump, the numerical simulation is carried out by using PROCAST software, the structure formation of the fused magnesium lump is known and controlled on the solidification rule through controlling the parameters such as the heat exchange condition and the like, the preparation is made for producing high-grade periclase, the experiment times are effectively reduced, and the manpower and material resources are saved, so that the quality of the periclase product in the actual production is improved.
Drawings
FIG. 1 is a flow chart of a numerical simulation method for improving the crystallization quality of an electrically fused magnesium fused weight according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a physical model of an electric smelting magnesium furnace according to an embodiment of the present invention;
FIG. 3 is a grid drawing of an electro-fused magnesia furnace face according to an embodiment of the present invention;
fig. 4 is a mesh division diagram of an electric smelting magnesium furnace body according to an embodiment of the present invention;
FIG. 5 is a graph showing the temperature of the furnace wall of the fused magnesia furnace according to an embodiment of the present invention after reaching a steady state;
fig. 6 is a schematic view of the temperature field distribution of the fused magnesia furnace provided in an embodiment of the present invention after reaching a steady state;
fig. 7 is a schematic diagram of a simulation result of a temperature field according to an embodiment of the present invention, wherein (a) to (f) are schematic diagrams of temperature field distributions of an electrofusion magnesium furnace in different periods from the beginning to the end of melting;
fig. 8 is a schematic diagram of a simulation result of a solidification field according to an embodiment of the present invention, in which (a) and (b) are schematic diagrams of a solidification field in an x-axis direction and an oblique 45-degree direction under a natural condition, respectively, (c) and (d) are schematic diagrams of a solidification field in an x-axis direction and an oblique 45-degree direction under an air-cooling condition, respectively, and (e) and (f) are schematic diagrams of a solidification field in an x-axis direction and an oblique 45-degree direction under a water-cooling condition, respectively;
FIG. 9 is a schematic diagram showing the results of a microstructure simulation according to an embodiment of the present invention, wherein (a), (b), and (c) are schematic diagrams showing the microstructure along the z-axis, the x-axis, and three directions obliquely above;
FIG. 10 is a schematic diagram of the distribution of the nucleation temperature field under three conditions of natural conditions, air cooling and water cooling after 1h of the cooling process according to an embodiment of the present invention; wherein, (a) is under the natural condition, (b) is under the air-cooled condition, and (c) is under the water-cooled condition;
FIG. 11 is a schematic diagram showing the distribution of the temperature field during nucleation, after the cooling process for 3 hours, i.e., under the three conditions of natural conditions, air cooling and water cooling, in the crystal growth stage according to an embodiment of the present invention; wherein, (a) is under the natural condition, (b) is under the air-cooled condition, and (c) is under the water-cooled condition;
FIG. 12 is a schematic diagram illustrating temperature field distribution during nucleation after 5h of cooling process, i.e., under natural conditions, air cooling and water cooling, when the crystallization process is finished; wherein, (a) is under the natural condition, (b) is under the air-cooled condition, and (c) is under the water-cooled condition;
FIG. 13 is a schematic diagram of the growth of the microstructure crystals during the crystallization process under the three conditions of natural conditions, air cooling and water cooling according to an embodiment of the present invention; wherein, (a) is under the natural condition, (b) is under the air cooling condition, and (c) is under the water cooling condition.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
As shown in fig. 1, the method of this embodiment is a numerical simulation method for improving the crystallization quality of the electrically fused magnesium fused mass as follows.
Step 1: establishing a macro-micro unified model coupling macro heat transfer, micro nucleation and growth dynamics, and realizing mathematical and physical description of the periclase solidification process.
The fused magnesium lump is doped with heat transfer analysis and crystallization analysis in the crystallization process, and a macroscopic heat transfer model and a microscopic crystallization model are related to phase field change. The internal heat source in the cooling process of the fused magnesium comes from latent heat released by phase change, the crystallization process is the phase change process of the fused magnesium from a molten phase to a solid phase, and the solid phase rate of the fused magnesium connects a macroscopic model and a microscopic model in the cooling process of the fused magnesium. Therefore, when modeling the cooling process of the fused magnesium, the phase field change must be analyzed first, and the influence of the phase field change on the temperature field distribution and the crystal nucleation growth is mastered. A phase field variable reflecting the phase field change is introduced into the model, and the solid fraction is generally selected as the phase field variable to realize the unification of a macro model and a micro model.
Step 1.1: establishing a macroscopic model of the cooling process of the fused magnesium, which comprises a macroscopic physical model and a macroscopic mathematical model;
step 1.1.1: and establishing a macroscopic physical model, namely a physical model of the electro-fused magnesia furnace in the cooling process, wherein the model comprises a molten pool part, a skin sand layer and a metal outer wall. The electric melting magnesium molten pool after the smelting is finished is simplified into a cylinder, and the edge of the molten pool can be in an irregular shape due to the influence of the change of a temperature field in the smelting process, so that the edge of the molten pool is rounded. The data of the electro-fused magnesia furnace are measured in the field, the physical model of the electro-fused magnesia furnace is shown in figure 2, and the parameter settings are shown in table 1.
TABLE 1 electro-fused magnesia furnace physical model parameter set
| Parameter(s) | Measured value (m) |
| Half of the bathDiameter of a pipe | 0.7 |
| Sand layer of skin | 0.294 |
| Furnace wall | 0.006 |
| Furnace blast | 2.9 |
| Height of the molten bath | 2.4 |
| Distance between molten pool and furnace top | 0.25 |
| Distance between molten pool and furnace bottom | 0.25 |
Step 1.1.2: establishing a macroscopic mathematical model;
the fused magnesium releases a large amount of latent heat in the cooling process, the release of the latent heat has important influence on the change of a temperature field in the cooling process, and in a dynamic temperature field model, the accurate reflection of a latent heat release rule and the calculation of the latent heat release amount are very critical to obtaining the correct temperature field distribution. According to a phase change latent heat processing method and model software used, an enthalpy method is finally selected to process the latent heat in the cooling process of the fused magnesium in heat transfer analysis.
Because the heat productivity of the internal heat source mainly comes from the phase change latent heat of the fused magnesium, the heat productivity item of the internal heat source, namely the latent heat item, is processed by an enthalpy method, and the heat entropy function is introduced into a heat conduction differential equation after being derived:
the method comprises the following steps of establishing a three-dimensional coordinate system by taking a cylinder central point as a point 0, a cylinder central line as a z-axis and a plane which passes through the point 0 and is vertical to the z-axis as an xoy plane; rho is the density of the material in kg/m3(ii) a H is the enthalpy of matter, in kJ/kg; t is time, unit s; k is the thermal conductivity coefficient, and the unit is w/(m.K); r is the radius of the cylinder in m; t is the instantaneous temperature in units of;the solid phase fraction is a solid phase fraction,n is all atomic numbers in a crystal lattice micro-area of the magnesium oxide, N is a grown atomic number, and in the embodiment, the value of N is 2-6;
the heat conservation equation in the micro-zone is:
wherein,represents the second derivative;
according to the thermodynamic rule, the following components are obtained:
wherein S is the entropy of solidification,the variation of the enthalpy of latent heat of crystallization in a time period,the influence of the variation of the enthalpy H of latent heat of crystallization, specific heat c and solidification entropy S on latent heat release is a source item,is a diffusion item, which is the influence of the latent heat and enthalpy of crystallization of peripheral micro-regions on the local region; f (T, H …) is a function of temperature T and enthalpy H.
Since the crystal lattice of magnesium oxide is a face-centered cubic crystal lattice, when the number of atoms in the domain is N and the number of atoms grown is N according to the analysis of the face-centered cubic system, the solid fraction isLet the latent heat per atom be L0η for coordination number, η for base coordination number0Coordination number of η in the same layer1Then η is 2 η0+η1It is known that the coordination number η of a magnesium oxide crystal is 12 and the coordination number η of a bottom layer0Coordination number of the same layer η of 414, the latent heat E released at any moment during the growth phase is:
therefore, the latent heat of crystallization enthalpy H, and the derivative with time can be obtainedAndsubstituting into the heat conservation equation to obtain:
wherein,the medium specific heat c has little effect, the main influencing factor is the solidification entropy S,with respect to temperature T and solid fractionAs a function of (c).
The rate of change of the freezing entropy is determined by the rate of change of the thermal entropy Δ SrAnd rate of change of entropy of mixing Δ ShComposition, i.e. Δ S ═ Δ Sr+ΔShWherein the rate of change of thermal entropy Δ SrComprises the following steps:rate of change of mixed entropy Δ ShComprises the following steps:where ψ denotes a mixed entropy change coefficient. As can be seen, the entropy of the mixture is related to the current state. The rate of change of the entropy of solidification is therefore:
substituting the above formula into the heat conservation equation due toFor high order small quantities, negligible, the entropy of freezing of the above equation reduces to:
in the above formula, the first and second carbon atoms are,embodies the solid phase ratioThe change of the heat transfer coefficient is related to the heat transfer physical quantity and the thermodynamic physical quantity,then, the solid phase ratio is reflectedThe change of (A) is also related to the crystallography physical quantities such as the growth speed of the crystal, the supercooling degree, the temperature gradient and the like. To obtain an accurate phase change control equation, the method must be solved by using the crystallography theoryTo solid fractionThe relational expression (c) of (c).
When the crystal grows, the old interface in the micro-area continuously disappears, a new interface is continuously generated, and the interface can block the growth speed; and the free energy accelerates the growth of the crystal as the solid phase ratio becomes larger. The growth rate of a known crystal can be expressed as:
v1＝μ1ΔT
wherein, mu1Is a first fixed coefficient, Δ T is the degree of supercooling, v1For the growth rate of the principal axis of the crystal, branching may also occur during the actual cooling.
The distance of the secondary branches reflects the length of one period of the secondary branch growth, and the growth speed of the secondary branches of the crystal is in direct proportion to the evolution of the supercooling degree, namely:
wherein, mu2Denotes a second fixed coefficient, v2Is the growth rate of the secondary branching of the crystal; the secondary and tertiary branches of the crystal are calculated according to the above formula.
Assuming that the interface energy will reduce the crystal growth rate by half; solid fraction of free energyAt 0, the rate of increase in the crystal growth rate is 0, and the solid fractionAt 1, the rate of increase in the crystal growth rate is 1 times, becauseOrWhen v is 0, the expression of the crystal growth rate is in the form shown in the following formula.
Where μ is a fixed coefficient. And the microcell cells centered on the X-axis are examined, so that a phase change control equation is obtained as shown in the following formula.
Each crystal grain can be regarded as a single crystal, atoms in the crystal are regularly arranged according to a lattice, and the relationship among the atoms has difference in different directions, so that physical parameters are different, namely the anisotropy of the crystal. Magnesium oxide belongs to the cubic system, and its heat transfer coefficient can be calculated at different positions by the following formula:
k(θ)＝k(1+cosθ)n
in the formula, theta is the minimum included angle between the normal vector of the solidification interface and the x, y and z axes; and n is the grown atomic number and takes a value of 2-6.
The final phase change control equation is:
therefore, the dynamic temperature field control equation is:
wherein rho is the density of magnesium oxide and the unit is kg/m3(ii) a c represents the specific heat capacity of magnesium oxide and the unit is J/(kg. K); t is the instantaneous temperature in units of; t is time, unit s; k is the thermal conductivity coefficient, and the unit is w/(m.K); r is the radius of the cylinder in m;the solid phase fraction is a solid phase fraction,n is all atomic numbers in the crystal lattice micro-area of the magnesium oxide, and N is the grown atomic number; l is the latent heat of phase change of the magnesium oxide, and the unit is J/kg; theta is the minimum included angle between the normal vector of the solidification interface and the x, y and z axes;represents the second derivative; mu is a fixed coefficient; AT is supercooling degree; Δ x, Δ y, and Δ z are unit lengths of the x-axis, y-axis, and z-axis, respectively.
Step 1.2: and establishing a micro model of the cooling process of the fused magnesium, wherein the micro model comprises a nucleation model and a growth model, and the specific process is as follows.
Step 1.2.1: and establishing a nucleation model.
The nucleation solid-liquid phase conversion process includes two principles of mean nucleation and non-mean nucleation. Wherein the non-mean nucleation can occur through foreign particles or substrates, such as impurities in magnesite, so the non-mean nucleation is easier to occur and more practical. The embodiment adopts a non-mean continuous nucleation model to determine the nucleation density and the nucleation position, and specifically comprises the following steps:
step 1.2.1.1, determining nucleation density;
the non-mean continuous nucleation model assumes that the nucleation occurs at different nucleation sites and that the variation dn/d (Δ T) of the nucleation density satisfies a gaussian distribution, and thus the grain density can be described as follows using the gaussian distribution:
where dn is the increase in nucleation density caused by an increase in supercooling degree Δ T; n ismaxThe maximum nucleation density obtained by integration from 0 to infinity in normal distribution, and the unit of surface shape nucleus is m-2The unit of the figure nucleus is m-3；ΔTσThe standard deviation nucleation supercooling degree is K; delta TmaxThe maximum nucleation supercooling degree is K;
the nucleation nucleus density is obtained by integration, since the solid fraction follows the growth of the magnesium oxide crystal grainsAt increasing levels, nucleation density improves as:
because the release of latent heat of crystallization during cooling can lead to the remelting phenomenon of crystals, the density of crystal nuclei is far less than the maximum nucleation density nmax；
The liquid metal forms crystal nuclei in certain areas through the fluctuation effect of energy, and only the areas meeting the energy condition can form the crystal nuclei and stably grow;
step 1.2.1.2, after the number of crystal nuclei is determined, the nucleation positions are also determined;
for the determination of nucleation positions in a large amount of liquid, the random numbers of the nucleation positions are adopted for representation; in the liquid metal, the appearance of the nuclei is random without fixed positions, and the random selection of the nucleation sites is determined by the following method:
in a time step T, the sample temperature decreases by T, the supercooling degree increases by (Δ T), and the density of crystal nuclei is:
the increase of the crystal nucleus density is multiplied by the sample volume to obtain the number N of crystal nuclei generated in the time tvThe total number of cells of the sample is NCADetermining a random number PvComprises the following steps:
in the formula, VCAIs the volume of each unit cell; generating a random number r in each cell of the sample in a time step, when r is less than or equal to PvWhen, the unit begins to nucleate;
for the crystal nucleus position of the surface nucleation, calculating the random number P of the nucleation by using the surface kernel functions；
If the nuclei produced fall within the range of the solidified grains, they are discarded and nucleation at this point is no longer taken into account.
Step 1.2.2: and establishing a growth model.
After solid phase nucleation, the microstructure begins to grow. Experimental studies have shown that the main direction of each dendrite is unlikely to be exactly the same, with dendrites that grow most rapidly with a main direction parallel to the direction of heat flow. They preferentially grow and inhibit the growth of adjacent dendrites, thereby achieving the growth of columnar crystals. The key to the microstructure simulation is therefore to determine the growth rate of the dendrite tip and the growth direction of the dendrite tip.
The supercooling degree of dendrites generally consists of four parts:
AT＝ΔTc+ΔTt+ΔTk+ΔTr
wherein, Delta Tc、ΔTt、ΔTk、ΔTrRespectively, the composition supercooling degree, the thermal supercooling degree, the dynamic supercooling degree and the curvature supercooling degree.
Usually the last three phase ratio Δ TcAre small and are therefore often ignored in the calculation. According to the KGT model, the relationship between the dendritic crystal tip radius R and the growth rate v is obtained as follows:
wherein r is a Gibbs-Thompson coefficient (ratio of interfacial energy of a solid-liquid interface to entropy of each volume of a melting zone); m is the slope of the liquidus; gcThe concentration gradient of the solute in the liquid phase of the dendrite front, ξ is a function of the Peclet number, 1 is taken at low growth speed, G is a temperature gradient, Pe is the Peclet number of the solute and is used for expressing the relative proportion of convection and diffusion, iv (Pe) is the Ivantsov function of the Peclet number (Ivantsov of presorts assumes that solid and liquid are in solid and liquidThe interface is a steady state diffusion solution of the dendritic crystal tip strictly obtained mathematically on the basis of an isothermal or isoconcentration parabola); d is the solute diffusion coefficient in the liquid phase; delta TαThe supercooling degree of the dendritic crystal tip; gamma is the equilibrium partition coefficient.
Iv (pe) in the equation can also be expressed as a continuous fraction:
during calculation, a certain number of terms is usually intercepted as an approximation according to needs, and the more the number of terms is taken, the more the dendrite approaches to the rotating parabola. Usually, a first approximation is taken:
or a second order approximation:
fitting the KGT model, namely fitting the relationship between the dendritic crystal tip growth speed v and the supercooling degree delta T into a cubic polynomial, which is shown as the following formula:
v＝a2ΔT2+a3ΔT3
wherein a is2、a3The growth kinetic coefficient is expressed in m/(s.K)3)。
The growth direction is simulated by software after a model is built, is uncertain and has certain randomness.
Step 2: and (3) carrying out numerical simulation on a temperature field and a microstructure in the cooling and solidification process of the electro-fused magnesium by using PROCAST software based on the established mathematical physical model, wherein the specific method is as follows.
Step 2.1: inputting a macro-micro mathematical physical model, and dividing a grid of the physical model.
The physical model is imported into PROCAST software, and the electric magnesium melting furnace is subjected to grid division as shown in figures 3 and 4, wherein the number of the grids after the division is 1234087, and the number of the nodes is 249864.
Step 2.2: setting boundary conditions and thermophysical parameters including furnace wall heat exchange coefficient h1Furnace top heat exchange coefficient h2Heat exchange coefficient h of furnace bottom3Heat exchange coefficient h of interface of molten pool and sand4。
The furnace wall temperature is very high at the initial moment of the cooling process, so that not only is heat conduction between the sand and the raw material layer exist, but also convection and radiation heat exchange with the external atmosphere exists. The heat exchange coefficient of the furnace wall is calculated by the formula:
in the formula,wis the emissivity of the outer surface of the furnace wall,w0.85; σ is the Stefan-Boltzmann constant; t iswIs the temperature of the outer surface of the furnace wall; t iseIs the temperature of the surrounding environment, Te＝293K。
The top of the fused magnesia furnace is uncovered, the fused weight is directly exposed in the atmosphere, and the heat transfer coefficient of the furnace top is taken as constant h due to weak heat conduction capability of the skin sand and the raw material layer and unobvious change along with the temperature2＝25W/(m2·K)。
The bottom of the electric smelting magnesium furnace is contacted with the furnace platform, because the furnace platform has thermal resistance, the heat insulation effect is better than that of the top, and the heat exchange coefficient of the furnace bottom is h3＝10w/(m2·K)。
It is known that the skin sand and raw material layer are mainly unmelted and sintered raw materials, and the heat exchange coefficient of the interface of the molten pool and the skin sand is h4＝500W/(m2·K)。
Step 2.3: setting initial conditions and feasibility; simulating a temperature field when smelting is finished, assuming constant temperature of a molten pool, changing the temperature into a steady-state heat conduction problem, wherein a heat conduction differential equation is as follows:
the boundary conditions and thermophysical parameters are set in the same way as in step 2.2.
Setting the simulation maximum time step length as 1s, and after iterating 10000 steps, the temperature field reaches a steady state. The furnace wall temperature was at 610 ℃ and the curve of the furnace wall temperature is shown in FIG. 5. The temperature data of the furnace wall obtained by the field after the smelting is finished is about 600 ℃, and the two results are in an error range, so that the simulation is effective. After reaching the steady state, the temperature field distribution of the fused magnesia furnace is shown in fig. 6.
Step 2.4: setting material parameters;
since there is no magnesia data in PRECAST, three materials were created and matched to physical models, with relevant parameters as shown in tables 2, 3 and 4.
TABLE 2 magnesium oxide, sand, steel plate specific correlation parameter table
TABLE 3 specific Heat Capacity of magnesium oxide
TABLE 4 thermal conductivity of magnesium oxide
Step 2.5: setting a parameter value of a nucleation model;
according to modeling, the grain nucleation density is as follows:
in a large volume of liquid, the nucleation site random number is:
wherein the parameter setting comprises a maximum nucleation density nmaxMaximum nucleation supercooling degree delta TmaxSum standard deviation nucleation supercooling degree delta TσWherein the maximum nucleation density nmaxIncluding the maximum surface shape nuclear density nmax，SAnd a maximum bulk nuclear density nmax，VAs shown in table 5.
TABLE 5 nucleation model parameter Table
| nmax，S(m-2) | 1.0e+7 |
| nmax，V(m-3) | 1.0E+8 |
| ΔTmax(℃) | 4.0 |
| ΔTσ(℃) | 7.0 |
Step 2.6: setting growth model parameters;
the relationship between the growth rate v and the supercooling degree DeltaT is fitted to
v＝a2ΔT2+a3ΔT3
Wherein, a2、a3For growth dynamics coefficient, the two parameters are respectively set as a2＝1.05×10-6，a3＝8.768×10-6And is also input to PROCAST.
Step 2.7: setting for simulated nucleation in PROCAST softwareParameters of the module;
in the CA method, continuous nucleation is adopted, a Gaussian distribution function is adopted for describing the distribution relation of nucleation particle density along with temperature, the growth dynamics of the tip of a crystal and the crystal orientation in the preferred growth direction [ 100 ] are considered simultaneously in a crystal grain growth model, macroscopic finite element grid division is carried out in the first step, and then the macroscopic finite element grid is subdivided into a microcosmic cubic unit cell grid.
The parameters are set as follows:
CA unit1000um in size, 1000 CA in each block, 5000 crystal orientation, 4.0 deg.C in average surface nucleation degree, 1.0 deg.C in standard surface variance degree, and 1.0 × 10 in heterogeneous surface nucleation number7The average supercooling degree of the nucleation of the body is 7.0 ℃, the standard variance supercooling degree of the body is 1.0 ℃, and the number of the nucleation of the heterogeneous body is 1.0 × 107。
And step 3: and carrying out PROCAST software visualization processing on the overall temperature field change of the fused weight and the growth process of the crystal grains by using a numerical simulation result, and realizing the visualization output of the result.
And 4, step 4: and analyzing and discussing the grain microstructure simulation result, and analyzing the influence trend of the supercooling degree on the microstructure of the fused magnesium lump.
Step 4.1: and analyzing the simulation result of the dynamic temperature field.
The temperature field distribution after the completion of melting is taken as the initial condition of the solidification process, and the temperature field distributions in different periods of the cooling process are intercepted, as shown in fig. 7(a) to (f). Under the condition of natural cooling, the heat dissipation of the fused magnesia is uniform, and the heat dissipation of the central fused weight is faster than that of the external sand coat at the same time interval, because the sand coat is qualitatively conveyed and has good heat conductivity. The melting point of magnesite is very high, and the temperature of a molten pool can reach 3000 ℃, so the cooling solidification process takes longer time. To better simulate our longer simulation time, from the beginning of solidification (melting initial temperature field shown in fig. 7 (a)) to the end of 2.5 hours, at t 2.5 hours, the sand layer is basically cooled to the ambient temperature, the center of the fused magnesium lump is completely solidified (melting end temperature field shown in fig. 7 (f)), but because of its high melting point, the temperature is still high. The external furnace wall and the sand coating can be removed in the industry, so that the fused magnesium lump is further cooled.
The change in the coagulation field is shown in figure 8. As can be seen from FIG. 8, the solidification fraction of the fused magnesium lump varies with the temperature field. When the temperature of the molten pool is lower than the liquidus temperature of 2825 ℃, crystallization is started; when the average temperature of the molten pool is reduced to 2400 ℃, the average tibial fraction is 40%; continuing to 1900 ℃, and increasing the solidification fraction to 70%, wherein the contact surface of the molten pool and the sand is completely solidified; finally, when the temperature of the molten pool is reduced to 1500 ℃, the average solidification fraction reaches 100 percent. Thus 1500 ℃ was taken as the maximum temperature for the crushing process, at which the furnace wall temperature was approximately 600 ℃.
At the initial stage of the solidification process, the temperature is obviously reduced, the average temperature of the melt is reduced to be below a liquid phase line along with the progress of the solidification process, a liquid phase is gradually changed into a solid phase, the temperature of a solidification region is improved due to the release of latent heat to the surrounding environment, the latent heat is reduced along with the increasing of the fraction of the solid phase, the conductive capacity of the fused mass is increased, and the temperature is rapidly reduced.
Step 4.2: and analyzing the microstructure simulation result.
Built up according to the method of the embodimentThe model (i.e. setting corresponding parameters in the PROCAST software) and the nucleation and growth model calculate the microstructure of the fused magnesium lump, and the evolution process of the grain structure of the fused magnesium in the solidification process can be seen, as shown in fig. 9. The temperature of the fused mass gradually decreases along with the outward diffusion of heat, and when the temperature of a certain part of a solidification region is lower than the nucleation supercooling degree, the solidification process starts at the first place of the part. As can be seen from fig. 9, the crystal grains formed on the mold wall have a crystal orientation in an arbitrary direction. As the growth process proceeds, the crystal grains with the growth crystal orientation parallel to the heat flow direction are preferentially grown, i.e. the crystal grains are generated in the shape of columnar crystals. During the growth of columnar crystal, the solid-liquid interface has raised supercooling degree, which is caused by the supercooling degree and heat diffusion of redistribution common front. When the supercooling degree reaches the predefined nucleation supercooling degree, nucleation cells in the melt are excited to nucleate, and equiaxed crystals begin to form. The equiaxed crystal grains grow to the surrounding supercooling melt, release a large amount of latent heat, reduce the temperature gradient, slow the growth speed of the newly generated crystal nucleus, continue the growth of the original crystal grains, generate new nucleation when reaching the nucleation supercooling degree again, and finally grow in the fused lumpThe core forms an equiaxed region.
Step 4.3: and analyzing the influence of the nucleation parameters on the simulation result.
The solidification process mainly comprises the nucleation and growth processes of microscopic grains, but the nucleation capability is difficult to control, and the difficulty in obtaining parameters through experiments is also high. However, the different nucleation parameters have a great influence on the morphology of the grains, so that the microstructure of the grains can be effectively controlled only by determining the appropriate nucleation parameters and mastering the influence trend of the parameters on the microstructure. Six nucleation parameters are respectively surface average nucleation supercooling degree, body average nucleation supercooling degree, surface shape nucleation supercooling degree variance, surface maximum nucleation density and body maximum nucleation density in the Rappaz continuous nucleation model, wherein the surface represents nucleation on the furnace wall, and the body represents nucleation in the molten pool.
According to the traditional solidification theory, the heat exchange coefficient has obvious influence on the characteristic value of the solidified grain structure. This is because in a volume of liquid metal, the nucleation rate is inversely proportional to the nucleated grain size, while the growth rate of the grains is directly proportional to the grain size, both the nucleation rate and the growth rate being closely related to the degree of supercooling in the melt. In the crystallization process, the greater the supercooling degree is, the greater the number of nucleation is, and the slower the growth of the crystal nuclei is. Therefore, the supercooling degree can be increased in the nucleation stage and reduced in the growth stage, so that large-size crystals can be obtained. The method for adjusting the supercooling degree is to adjust the cooling rate.
In order to obtain the influence of the cooling speed and the grain size, the change of the microstructure appearance of the grains under different cooling speed conditions is simulated. The method of air cooling and water cooling the furnace wall is adopted to change the supercooling degree of the furnace wall in the nucleation and growth processes. Comparing the changes of the nucleation process temperature field under the three conditions of natural condition, air cooling and water cooling, the situation after 1h of the cooling process is shown in fig. 10, and it is found that the central temperature of the molten pool under the natural cooling condition is still quite high, while under the air cooling and water cooling conditions, the temperature of the molten pool is obviously lower than that of the natural cooling, and the temperature field is superior to that of the natural cooling condition. After 3h of the cooling process, i.e. during the crystal growth phase, the temperature field changes under the three conditions are more obvious, as shown in fig. 11. After 5h of the cooling process, i.e. when the crystallization process is finished, the temperature field is substantially stable, as shown in fig. 12.
Under the three conditions of natural condition, air cooling and water cooling, the growth condition of the crystal is shown in figure 13, and the crystallization process is characterized in that the supercooling degree is larger, the growing number of crystal nuclei is larger, and the growth of the crystal nuclei is slower. Therefore, the supercooling degree is increased at the nucleation stage and decreased at the growth stage, so that high-purity large-size electrofused magnesium crystals can be obtained.
Therefore, the cooling speed is enhanced, the number and the size of columnar crystals in a microstructure are obviously increased, the number of equiaxed crystals in a central area is reduced, the equiaxed crystals in a melt are difficult to nucleate due to the fact that the supercooling degree of the nucleation process is increased, the columnar crystals grow continuously without being hindered by the equiaxed crystals at the front edge of a solid-liquid interface, and the product quality is optimized. Under the water cooling condition, the effect is optimal, the growth of equiaxial crystals is almost stopped, columnar crystals are fully developed, and the columnar crystal area can be greatly increased by changing the condition. Not only is the columnar crystal size increased, but the equiaxed crystal size is also decreasing.
The numerical simulation method for improving the crystallization quality of the fused magnesium lump provided by the embodiment is characterized in that the heat exchange and microstructure forming process in the cooling and solidification process of the fused magnesium lump are subjected to numerical simulation, the formation of the microstructure of the fused magnesium lump is known and controlled on the solidification rule of the fused magnesium lump through the control of parameters such as heat exchange conditions, the experiment frequency is reduced, the manpower and the material resources are saved, and the product quality is improved.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (3)
1. A numerical simulation method for improving the crystallization quality of an electric fused magnesium fused weight is characterized by comprising the following steps: the method comprises the following steps:
step 1, establishing a macro-micro unified model coupling macro heat transfer, micro nucleation and growth dynamics, and realizing mathematical physical description of the periclase solidification process, wherein the specific method comprises the following steps:
step 1.1, establishing a macroscopic model of the solidification process of the fused magnesium, wherein the macroscopic model comprises a macroscopic physical model and a macroscopic mathematical model;
step 1.1.1, establishing a macroscopic physical model, namely a physical model of the fused magnesia furnace in the cooling process, which sequentially comprises a fused magnesia pool, a sand coating and a metal outer wall from inside to outside, wherein the model is simplified into a cylinder after the smelting is finished, and the edges of the upper end and the lower end of the cylinder are rounded;
step 1.1.2, establishing a macroscopic mathematical model, determining a heat conduction differential equation of the fused magnesium, namely a dynamic temperature field control equation, and establishing a three-dimensional coordinate system by taking the central point of a cylinder as a point 0, the central line of the cylinder as a z-axis and a plane passing through the point 0 and vertical to the z-axis as an xoy plane, wherein the dynamic temperature field control equation is as follows:
wherein rho is the density of magnesium oxide and the unit is kg/m3(ii) a c represents the specific heat capacity of magnesium oxide and the unit is J/(kg. K); t is the instantaneous temperature in units of; t is time, unit s; k is the thermal conductivity coefficient, and the unit is w/(m.K); r is the radius of the cylinder in m;the solid phase fraction is a solid phase fraction,n is all atomic numbers in the crystal lattice micro-area of the magnesium oxide, and N is the grown atomic number; l is the latent heat of phase change of the magnesium oxide, and the unit is J/kg; theta is the minimum included angle between the normal vector of the solidification interface and the x, y and z axes;represents the second derivative; mu is a fixed coefficient of the coefficient,expressed as dendrite tip growth rate, i.e.Delta T is the supercooling degree; Δ x, Δ y, and Δ z are unit lengths of the x-axis, y-axis, and z-axis, respectively；
Step 1.2, establishing a micro model of the fused magnesium cooling process, wherein the micro model comprises a nucleation model and a growth model;
step 1.2.1, establishing a nucleation model, and determining the nucleation density and the nucleation position by adopting a continuous nucleation model in heterogeneous nucleation, which comprises the following steps:
step 1.2.1.1, determining the nucleation density, wherein the function expression of the nucleation density is as follows:
wherein, Delta T is the supercooling degree;the solid phase ratio; dn/d (Δ T) is the variation in nucleation density, satisfying a Gaussian distribution, expressed as:
<mrow> <mfrac> <mrow> <mi>d</mi> <mi>n</mi> </mrow> <mrow> <mi>d</mi> <mrow> <mo>(</mo> <mi>&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>&pi;</mi> </mrow> </msqrt> <msub> <mi>&Delta;T</mi> <mi>&sigma;</mi> </msub> </mrow> </mfrac> <mi>exp</mi> <mo>&lsqb;</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>T</mi> <mo>-</mo> <msub> <mi>&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>&Delta;T</mi> <mi>&sigma;</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>&rsqb;</mo> </mrow>
where dn is the increase in nucleation density caused by an increase in supercooling degree AT, and nmaxThe maximum nucleation density obtained by integration from 0 to infinity in normal distribution, and the unit of surface shape nucleus is m-2The unit of the figure nucleus is m-3；ΔTσThe standard deviation nucleation supercooling degree is K; delta TmaxThe maximum nucleation supercooling degree is K;
step 1.2.1.2, determining a nucleation position;
for the determination of nucleation sites in a large volume of liquid, a random number of nucleation sites is used for representation, and the random selection process is determined by the following method:
in a time step t, the density n of the crystal nuclei is expressed as:
wherein (AT) is the increment of supercooling degree;
nucleation position random number PvComprises the following steps:
<mrow> <msub> <mi>P</mi> <mi>v</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&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>&delta;n</mi> <mi>v</mi> </msub> <msub> <mi>V</mi> <mrow> <mi>C</mi> <mi>A</mi> </mrow> </msub> </mrow>
wherein N isvRepresents the time of tThe number of generated crystal nuclei is obtained by multiplying the increment of the crystal nucleus density by the sample volume; vCARepresenting the volume of each unit cell; n is a radical ofCARepresents the total number of cells of the sample; generating a random number r in each cell of the sample in a time step, when r is less than or equal to PvWhen this happens, the unit begins to nucleate;
for the crystal nucleus position of the surface nucleation, calculating the random number P of the nucleation by using the surface kernel functions；
If the generated crystal nucleus falls into the solidified crystal grain range, the crystal nucleus is abandoned, and the nucleation at the position is not considered;
step 1.2.2, establishing a growth model, simulating a microstructure by determining the growth speed of a dendritic crystal tip and the growth direction of the dendritic crystal tip, and fitting an KGT model, namely fitting the relation between the growth speed v of the dendritic crystal tip and the supercooling degree delta T into a cubic polynomial:
v＝a2ΔT2+a3ΔT3
wherein a is2、a3The growth kinetic coefficient is expressed in m/(s.K)3)；
2, carrying out numerical simulation on a temperature field and a microstructure in the cooling and solidification process of the fused magnesium by using PROCAST software based on the established mathematical physical model;
step 3, carrying out visual processing on the whole temperature field change of the fused weight and the growth process of the crystal grains by using a numerical simulation result to realize visual output of the result;
and 4, analyzing and discussing the grain microstructure simulation result, and analyzing the influence trend of the supercooling degree on the microstructure of the fused magnesia lump, including the analysis of temperature field distribution in different periods of the cooling process, the analysis of the grain microstructure evolution process of the fused magnesia in the solidification process and the analysis of the influence of nucleation parameters on the simulation result.
2. The numerical simulation method for improving the crystallization quality of the fused magnesium lump melt according to claim 1, which is characterized in that: the parameters of the physical model of the electro-fused magnesia furnace are set as follows: the radius of the fused magnesia pool is 0.7m, the thickness of the sand coat layer is 0.294m, the thickness of the metal outer wall is 0.006m, the height of the furnace is 2.9m, the height of the fused magnesia pool is 2.4m, the distance between the fused magnesia pool and the furnace top is 0.25m, and the distance between the fused magnesia pool and the furnace bottom is 0.25 m.
3. The numerical simulation method for improving the crystallization quality of the fused magnesium lump melt according to claim 1, which is characterized in that: the process of numerical simulation in the step 2 comprises the following steps:
step 2.1, importing the physical model into PROCAST software, and carrying out grid division on the physical model of the electro-fused magnesia furnace;
step 2.2, setting boundary conditions and thermophysical parameters including furnace wall heat exchange coefficient h1Furnace top heat exchange coefficient h2Heat exchange coefficient h of furnace bottom3Heat exchange coefficient h of interface of molten pool and sand4；
The calculation formula of the heat exchange coefficient of the furnace wall is as follows:wherein T iswIndicating the temperature, T, of the outer surface of the furnace walleRepresenting the temperature of the environment surrounding the furnace wall;
the heat exchange coefficient of the furnace top, the heat exchange coefficient of the furnace bottom and the heat exchange coefficient of the interface of the molten pool and the sand coat are constants which are respectively as follows: h is2＝25W/(m2·K)、h3＝10w/(m2K) and h4＝500W/(m2·K)；
Step 2.3, setting initial conditions and feasibility, simulating a temperature field at the end of smelting, firstly setting constant temperature of a molten pool, and setting a simulated maximum time step length and iteration step number of the temperature field reaching a steady state;
step 2.4, setting material parameters, newly building three materials of magnesium oxide, sand and a steel plate in PRECAST, and matching the materials with a physical model;
step 2.5, setting the parameter values of the nucleation model, including the maximum nucleation density nmaxMaximum nucleation supercooling degree delta TmaxSum standard deviation nucleation supercooling degree delta TσWherein the maximum nucleation density nmaxIncluding the maximum surface shape nuclear density nmax，SAnd a maximum bulk nuclear density nmax，V；
Step 2.6, setting growth model parameters including growth kinetic coefficient a2And a3；
Step 2.7, setting for simulation nucleation in PROCAST softwareParameters of the module.
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