CN110970095A - Method for calculating stress of forced convection on AlN dendrites in molten steel solidification process in metallurgical field - Google Patents
Method for calculating stress of forced convection on AlN dendrites in molten steel solidification process in metallurgical field Download PDFInfo
- Publication number
- CN110970095A CN110970095A CN201911036081.XA CN201911036081A CN110970095A CN 110970095 A CN110970095 A CN 110970095A CN 201911036081 A CN201911036081 A CN 201911036081A CN 110970095 A CN110970095 A CN 110970095A
- Authority
- CN
- China
- Prior art keywords
- aln
- growth
- interface
- calculated
- solute
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 90
- 210000001787 dendrite Anatomy 0.000 title claims abstract description 59
- 238000007711 solidification Methods 0.000 title claims abstract description 56
- 230000008023 solidification Effects 0.000 title claims abstract description 56
- 229910000831 Steel Inorganic materials 0.000 title claims abstract description 45
- 239000010959 steel Substances 0.000 title claims abstract description 45
- 230000008569 process Effects 0.000 title claims abstract description 41
- 230000012010 growth Effects 0.000 claims abstract description 71
- 210000004027 cell Anatomy 0.000 claims abstract description 59
- 238000001556 precipitation Methods 0.000 claims abstract description 15
- 238000005272 metallurgy Methods 0.000 claims abstract description 10
- 238000012546 transfer Methods 0.000 claims abstract description 9
- 230000006911 nucleation Effects 0.000 claims abstract description 7
- 238000010899 nucleation Methods 0.000 claims abstract description 7
- 230000000007 visual effect Effects 0.000 claims abstract description 7
- 229910018509 Al—N Inorganic materials 0.000 claims abstract description 6
- 229910002059 quaternary alloy Inorganic materials 0.000 claims abstract description 6
- 239000000203 mixture Substances 0.000 claims abstract description 4
- 239000007791 liquid phase Substances 0.000 claims description 61
- 238000004364 calculation method Methods 0.000 claims description 47
- 238000009826 distribution Methods 0.000 claims description 47
- 239000007790 solid phase Substances 0.000 claims description 44
- 238000004781 supercooling Methods 0.000 claims description 40
- 239000012530 fluid Substances 0.000 claims description 25
- 239000011159 matrix material Substances 0.000 claims description 24
- 230000001413 cellular effect Effects 0.000 claims description 19
- 239000007788 liquid Substances 0.000 claims description 19
- 238000005315 distribution function Methods 0.000 claims description 16
- 230000000694 effects Effects 0.000 claims description 15
- 239000002245 particle Substances 0.000 claims description 15
- 230000003993 interaction Effects 0.000 claims description 13
- 239000012071 phase Substances 0.000 claims description 8
- 238000004088 simulation Methods 0.000 claims description 8
- 238000004458 analytical method Methods 0.000 claims description 7
- 238000006243 chemical reaction Methods 0.000 claims description 6
- 239000002184 metal Substances 0.000 claims description 6
- 229910052751 metal Inorganic materials 0.000 claims description 6
- 239000007787 solid Substances 0.000 claims description 6
- 239000000126 substance Substances 0.000 claims description 6
- 230000006870 function Effects 0.000 claims description 5
- 230000005540 biological transmission Effects 0.000 claims description 3
- 229910052799 carbon Inorganic materials 0.000 claims description 3
- 230000010261 cell growth Effects 0.000 claims description 3
- 230000008859 change Effects 0.000 claims description 3
- 238000012937 correction Methods 0.000 claims description 3
- 230000001419 dependent effect Effects 0.000 claims description 3
- 238000009792 diffusion process Methods 0.000 claims description 3
- 230000004907 flux Effects 0.000 claims description 3
- 230000005012 migration Effects 0.000 claims description 3
- 238000013508 migration Methods 0.000 claims description 3
- 239000002904 solvent Substances 0.000 claims description 3
- 238000005266 casting Methods 0.000 abstract description 9
- 238000005516 engineering process Methods 0.000 abstract description 5
- 238000009749 continuous casting Methods 0.000 abstract description 2
- 238000001816 cooling Methods 0.000 abstract description 2
- 238000007405 data analysis Methods 0.000 abstract 1
- 238000003384 imaging method Methods 0.000 abstract 1
- 239000013078 crystal Substances 0.000 description 9
- 238000010586 diagram Methods 0.000 description 3
- 229910001209 Low-carbon steel Inorganic materials 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000009851 ferrous metallurgy Methods 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 238000007670 refining Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 239000002344 surface layer Substances 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
- G16C10/00—Computational theoretical chemistry, i.e. ICT specially adapted for theoretical aspects of quantum chemistry, molecular mechanics, molecular dynamics or the like
-
- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
- G16C20/00—Chemoinformatics, i.e. ICT specially adapted for the handling of physicochemical or structural data of chemical particles, elements, compounds or mixtures
- G16C20/10—Analysis or design of chemical reactions, syntheses or processes
Landscapes
- Theoretical Computer Science (AREA)
- Computing Systems (AREA)
- Engineering & Computer Science (AREA)
- Chemical & Material Sciences (AREA)
- Bioinformatics & Cheminformatics (AREA)
- Bioinformatics & Computational Biology (AREA)
- Life Sciences & Earth Sciences (AREA)
- General Health & Medical Sciences (AREA)
- Spectroscopy & Molecular Physics (AREA)
- Health & Medical Sciences (AREA)
- Physics & Mathematics (AREA)
- Analytical Chemistry (AREA)
- Chemical Kinetics & Catalysis (AREA)
- Crystallography & Structural Chemistry (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention provides a method for calculating the stress of AlN dendrite by forced convection in the process of molten steel solidification in the field of metallurgy, and relates to the field of metallurgy. The method comprises the steps of firstly collecting steel components and solidification conditions, then calculating heat transfer and mass transfer in the solidification process, growth of interface cells in the solidification process and AlN nucleation and growth in the solidification process, and further establishing an AlN precipitation model in the solidification of the Fe-C-Al-N quaternary alloy. And predicting the precipitation rule of the AlN precipitation model according to the continuous casting process conditions such as casting temperature, solute composition, cooling rate and the like, and displaying the precipitation position, size, shape and size of the AlN in an imaging manner by utilizing data analysis and visual processing software data, and quantifying the precipitation amount of the AlN. The method for predicting the AlN inclusion precipitation condition in the molten steel solidification process provides theoretical guidance for optimizing the solidification technology, controlling the size of the AlN inclusion in the steel and improving the quality of casting blanks.
Description
Technical Field
The invention belongs to the technical field of ferrous metallurgy, and particularly relates to a method for calculating the stress of AlN dendrites by forced convection in a molten steel solidification process in the field of metallurgy.
Background
The steel industry is an important pillar type basic industry of national economy. In the process of molten steel solidification, the surface layer of a casting blank begins to nucleate and grow to form columnar crystals along with the reduction of temperature, and the solute concentration at the front edge of a solid-liquid interface is serious along with the growth of the columnar crystals. AlN inclusions with different sizes play different roles in the performance of steel. Therefore, the prediction of the precipitation of the inclusions in the molten steel solidification process has important significance for controlling the cracks of the casting blank and improving the quality of the casting blank. In the continuous casting process, molten steel in the casting blank can continuously flow, and certain influence is generated on the growth and the appearance of the microscopic dendritic crystal. At the same time, the flow of molten steel is also made more complex by the presence of dendrites. The traditional flow field numerical simulation is mainly to solve the pressure field iteratively through a Navier-Stokes (N-S) equation. However, the method is complex to solve, large in calculation amount and poor in numerical stability, and a wall function is needed to be used when the dendritic crystal curved edge boundary is processed, so that the solving error is increased. Therefore, accurately describing the flow field distribution is extremely important for dendrite solution. A method for solving a flow field around dendrites by using a lattice Boltzmann method which has been developed in recent years is introduced. The lattice Boltzmann method is derived from the Boltzmann equation. The Boltzmann equation is mainly used for describing the change rule of the system in the nonequilibrium state.
Disclosure of Invention
The invention aims to solve the problem of the prior solidification technology and provides a method for calculating the stress of AlN dendrites by forced convection in the molten steel solidification process. The stress condition of forced convection on the AlN dendrites under the condition of different processes is predicted, and the solidification technology and the theoretical guidance of forced growth of the dendrites under the forced convection are optimized.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a method for calculating the stress of AlN dendrite by forced convection in the process of molten steel solidification comprises the following steps:
step 2.1, in order to enable the cellular automaton model to have certain physical significance, introducing a metal solidification theory, and calculating the growth direction and curvature supercooling of an interface by adopting a sharp interface model;
step 2.2, determining a fluid flow boundary, and calculating the velocity distribution of the flow field by adopting a D2Q9 model;
step 2.3, calculating a liquid phase temperature field by adopting a cellular automaton model in combination with the velocity distribution of the flow field;
step 2.4, combining the flow field velocity distribution, and calculating solute distribution of the liquid phase region and the solid phase region by adopting a cellular automaton model;
and 3, for the complex boundary flow, correcting an F-H format by adopting Mei, adding a free boundary condition on the right side along the speed of the complex boundary flow along the x direction, and establishing a stress growth model of the lower dendrite of the Fe-C-Al-N quaternary alloy flow field by combining a lattice Boltzmann method. And displaying the shape, the size and the stress condition of the AlN dendrite by using data and analysis and visual processing software images.
A method for calculating the stress of AlN dendrites by forced convection in the process of molten steel solidification in the field of metallurgy is characterized by comprising the following steps: the specific method of the step 2.1 comprises the following steps:
firstly, supposing that the solid-liquid interface is in a thermodynamic equilibrium state, according to the law of conservation of solute at the interface, the growth direction of the interface
Calculated by the following formula:
wherein 
Indicating the direction of interfacial growth, curvature overcoolingK is calculated by the following formula:
wherein ,
and
respectively representing first-order partial derivatives of the solid phase ratio on an x axis and a y axis;
firstly, solving the second-order partial derivative of the y axis after solving the partial derivative of the solid phase ratio on the x axis;
and
respectively is a second order partial derivative of the solid fraction on an x axis and a y axis;
the state of the cells is detected and the fluid flow boundary and its boundary conditions are determined as described in step 2.2. In the two-dimensional numerical simulation calculation, a D2Q9 model is generally used to calculate the flow field distribution, while ignoring the external force, the velocity distribution of the flow field is calculated by the following formula:
wherein τ is the dimensionless single-step relaxation time, fi(x+ciΔt,t+Δt)、fi(x, t) is a liquid phase fluid particle distribution function,
is in equilibrium with liquid phase fluid particlesA distribution function; wherein c isiThe migration velocity of liquid phase fluid particles in the direction of the grid i, and delta t is a time step; due to the adoption of the D2Q9 model, wherein ciThe sum of the calculation formula is the weight coefficient wiCalculated by the following formula:
wherein c and csThe lattice velocity and the lattice sound velocity are respectively; the macroscopic density ρ, the macroscopic velocity u, and the hydrodynamic viscosity v are calculated by the following equations:
wherein fiIs an entrance node distribution function, i (values of 0,1,2,3,4,5,6,7 and 8) is an angular step node ordinal number, and entrance density rhoinOutlet density ρoutThe velocity u of the fluid particles in the x-axis directionxAnd the velocity u of the fluid particles in the y-axis directionyThe calculation formula is calculated by the following formula:
f1＝f3,f2＝f4,f8＝f6(19)
a method for calculating the stress of AlN dendrites by forced convection in the process of molten steel solidification relates to the field of metallurgy, and step 2.3, a cellular automaton model is adopted to calculate a liquid phase temperature field in combination with flow field velocity distribution; the specific method is calculated by the following method:
firstly, the calculation of the liquid phase temperature field is the calculation in the heat transfer process, so the liquid phase region temperature field is calculated by adopting the following formula:
wherein T is time, ρ is matrix density, λ is thermal conductivity, T is cell temperature, cpThe specific heat capacity of the matrix, fs the cellular solid phase rate and L the latent heat; q. q.sw,w、qw,e、qw,n、qw,sThe heat flux densities of the left boundary, the right boundary, the upper boundary and the lower boundary in four directions respectively; for the sake of simplifying the calculation, it is assumed that the thermal conductivity λ of the matrix in the x-axis and y-axis directions is equal;
the supercooling degree at the solid-liquid interface consists of component supercooling, curvature supercooling, thermal supercooling and dynamic supercooling degree, and the dynamic supercooling degree is neglected because the dynamic supercooling degree is smaller relative to other supercooling degrees in the solidification process; therefore, the supercooling degree is calculated by the following equation:
ΔT＝ΔTc+ΔTr+(Tbulk-TL) (22)
wherein ,ΔTrIs undercooling of curvature, TbulkTemperature of liquid phase, T, at solidification frontLIs the liquidus temperature, Δ TcIs the supercooling of the components; the liquidus temperature, curvature supercooling and composition supercooling are respectively solved by the following formulas:
TL＝1535-65[％C]-2.7[％Al]-90[％N](23)
wherein gamma is a Gibbs-Thomson coefficient; m isL,iIs the liquidus slope of element i; c. CL,iRepresents the liquid phase concentration of element i;
the concentration of the solid-liquid interface front edge of the element i;
because the heat transfer density and the mass transfer density are inseparable in the forced convection AlN dendrite stress calculation method, the solute distribution of the liquid phase region and the solid phase region is calculated by adopting a cellular automaton model according to the flow field velocity distribution in the step 2.4; the interaction between solutes on the growth of dendrites is considered in the liquid phase, and the solute transport in the solid phase is smaller than that in the liquid phase by several orders of magnitude, so the solute interaction in the solid phase is ignored, and the solute transport in the solid phase and the solute transport in the liquid phase are respectively calculated by adopting the following formulas:
wherein ,CL,i、CS,iRespectively representing the concentration of the element i in the liquid phase and the solid phase; cS,iIs the transmission coefficient of the element i in the solid phase matrix; n-1, wherein n is the total number of elements in the molten steel, and the nth element represents a solvent;
representing the Darken coefficient matrix in the liquid phase, assuming the directions of the x-axis and the y-axis in the matrix for simplifying the calculation
The values are the same, and the following formula is utilized to solve:
wherein R represents a gas constant, akIndicates the activity of the element k, xkDenotes the molar fraction of the element k, xjRepresents the molar fraction of the element j, δkiDenotes the Kronector delta function, when k is i, δkiTake 1, otherwise deltakiTaking 0; mkRepresenting the mobility of the element k in the system, which is solved according to the Einstein formula, e.g.The following equation is shown:
wherein ,
representing the diffusion coefficient of the tracking element k. Assuming that a solid-liquid interface is in a thermodynamic equilibrium state, the solute distribution law is satisfied at the interface:
according to the law of conservation of solute at the interface, the growth speed of interface cells in a thermodynamic equilibrium state is solved according to the following formula:
wherein, the right side
The solute transport item only considers the influence of the liquid phase solute interaction on the growth of dendrites;
representing the growth speed of the interface cell solidification front; by solving the growth speed of the solidification front of the interface cells, the growth of the interface cells in unit time step is calculated by increasing the solid phase rate, and the following formula is shown:
wherein ,
and
the cell solid phase ratio Δ f of AlN at the previous time and this time, respectivelys,AlNIncrease in solid fraction of (2); Δ t is a unit time step;
indicating edge
Unit length of direction through the center of the cell; Δ l ═ 1 μm for the grid cell length; theta represents the angle between the dendrite growth direction and the x-axis direction.
A method for calculating the stress of AlN dendrites by forced convection in the process of molten steel solidification in the field of metallurgy is characterized by comprising the following steps:
the specific method of the step 2.4 comprises the following steps: the following assumptions are calculated and simulated for the calculation of the stress of the forced convection on the AlN dendrites: AlN precipitated in the steel does not contain other phases; only AlN precipitation in the liquid phase is considered; neglecting the increase of interface energy in the growth process; neglecting the heat change when AlN is precipitated; based on the above assumptions, the thermodynamic and kinetic conditions for AlN nucleation in steel are first calculated; when the nucleation condition is met, nucleation is carried out in the cell and the surrounding solute field is updated and calculated, as the AlN interface keeps a thermodynamic equilibrium state, the solute is continuously diffused to the interface, forced convection is carried out on the stress calculation simulation of the AlN dendrite according to the thermodynamic equilibrium state, and the solid-liquid interface normal phase and the growth direction function
Calculated by the following formula:
whereinθ and
the included angles between the interface growth normal direction and the preferred growth direction and the positive direction of the x axis are respectively. ε represents the anisotropy parameter, where the angle between the preferential growth direction and the positive x-axis direction
Calculated by the following formula:
the reaction formula for generating AlN in the solid-liquid two-phase region and the calculation formula for activity and activity coefficient are as follows:
[Al]+[N]＝(AlN) (39)
a[M]＝[％M]f[M](40)
wherein ,a[M]Representing the Henry activity of element M; m represents an element Al or N, [ M ]]Indicates that the element M is dissolved in the steel; [% M]Represents the concentration of the element M based on a mass 1% standard; f. of[Al] and f[N]Activity coefficients of elements Al and N, respectively, based on a mass 1% standard;
representing the interaction coefficient of element j to element i; when a certain cell in the calculation region meets the AlN precipitation condition, marking the cell, carrying out 3 x 3 grid refinement division on the cell, and simultaneously calculating the growth of the cell according to dynamic chemical equilibrium, wherein the formula is as follows:
MAlNrepresents the relative molecular mass of AlN; Δ x represents the reaction amount;
a method for calculating the stress of AlN dendrites by forced convection in the process of molten steel solidification in the field of metallurgy is characterized in that Mei is adopted to correct the F-H format, the speed in the x direction is added, the free boundary condition is added on the right side, and a stress growth model of the lower dendrite of a Fe-C-Al-N quaternary alloy flow field is established by combining a lattice Boltzmann method.
Therefore, according to the Mei, the F-H format is modified by first aligning the solid phase boundary points xbAssume that it has a virtual state equilibrium distribution function as follows:
wherein ufIs xfFluid velocity of (u)bfFor undetermined virtual velocity, to solve for ubfConstructing an interpolation factor α and xwPosition dependent, ubfThe following formula is used to obtain:
wherein β is for calculating xfInterpolation factor, u, of the rebound distribution structurewIs xwThe moving speed of the interface; according to the formula, a virtual state balance distribution function can be solved; therefore, the solute field distribution and the solid phase region solute distribution under the Mei correction F-H format are obtained by the following formulas:
when the cell growth is calculated according to the dynamic chemical balance, in order to reduce the calculation error caused by the larger time step, the cells are subjected to spatial 3 x 3 refinement time division and time division, and are subjected to refinement time division at the same time, and the growth in a time step is subjected to multiple circulating calculation when the forced convection is calculated and calculated to stress the AlN dendrite for growth, so that the calculation error caused by the time step is reduced; when the volume of AlN in the matrix cell is increased and the matrix cell is contacted with the adjacent liquid-phase cell, the adjacent liquid-phase cell is subdivided into 3 multiplied by 3F-H format lower boundary AlN precipitation cells, and AlN growth is continued. And displaying the shape, the size and the stress condition of the AlN dendrite by using data and analysis and visual processing software images.
Adopt above-mentioned technical scheme to adopt the produced beneficial effect of above-mentioned technical scheme to lie in: the invention provides a method for calculating the stress of AlN dendrite by forced convection in the process of molten steel solidification. Dendritic crystal growth is carried out under the condition of calculating the forced convection, and the calculation precision is improved by refining the time step. Showing the shape, size and stress of the AlN dendrite. The invention optimizes the solidification technology, predicts the stress analysis of the dendrite under the forced convection and provides theoretical guidance for improving the quality of the casting blank.
Drawings
FIG. 1 is a flow chart of a method for calculating the stress on AlN dendrites by forced convection in a molten steel solidification process according to an embodiment of the present invention;
FIG. 2 is a flow chart of the procedure for computing the stress on the AlN dendrite by forced convection according to the embodiment of the present invention;
fig. 3 is a schematic diagram of a general D2Q9 model of a lattice Boltzmann method according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a Mei modified F-H format according to an embodiment of the present invention;
FIG. 5 is a simulated graph of dendrite morphology evolution and Al solute distribution in a flow field according to an embodiment of the present invention;
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.
In the embodiment, ordinary low-carbon steel is taken as an example, and the method for calculating the stress of the forced convection to the AlN dendrite crystal in the molten steel solidification process is adopted to calculate the stress of the forced convection to the AlN dendrite crystal in the molten steel solidification process.
A method for calculating the stress of AlN dendrites by forced convection in the process of molten steel solidification is shown in figure 1 and comprises the following steps:
TABLE 1 Steel species main Components
step 2.1, in order to enable the cellular automaton model to have certain physical significance, introducing a metal solidification theory, and calculating the growth direction and curvature supercooling of an interface by adopting a sharp interface model;
firstly, assuming that a solid-liquid interface is in a thermodynamic equilibrium state, and according to the solute conservation law at the interface, the growth direction of the interface is calculated by the following formula:
wherein 
Expressing the interface growth direction, the curvature undercooling K is calculated by the following formula:
wherein ,
and
respectively representing first-order partial derivatives of the solid phase ratio on an x axis and a y axis;
firstly, solving the second-order partial derivative of the y axis after solving the partial derivative of the solid phase ratio on the x axis;
and
respectively is a second order partial derivative of the solid fraction on an x axis and a y axis;
step 2.2, determining a fluid flow boundary, and calculating the velocity distribution of the flow field by adopting a D2Q9 model; the fluid flow boundary and its boundary conditions are determined. In the two-dimensional numerical simulation calculation, a D2Q9 model is generally used to calculate the flow field distribution, while ignoring the external force, and the liquid phase fluid particle calculation expression and the equilibrium state distribution function are calculated by the following formulas:
wherein τ is the dimensionless single-step relaxation time, fi(x+ciΔt,t+Δt)、fi(x, t) is a liquid phase fluid particle distribution function,
is an equilibrium distribution function of liquid phase fluid particles; wherein c isiIs the migration velocity, Δ t, of liquid phase fluid particles in the direction of lattice iIs the time step; due to the adoption of the D2Q9 model, wherein ciThe sum of the calculation formula is the weight coefficient wiCalculated by the following formula:
wherein c and csThe lattice velocity and the lattice sound velocity are respectively; the macroscopic density ρ, the macroscopic velocity u, and the hydrodynamic viscosity v are calculated by the following equations:
wherein fiIs an entrance node distribution function, i (values of 0,1,2,3,4,5,6,7 and 8) is an angular step node ordinal number, and entrance density rhoinOutlet density ρoutThe velocity u of the fluid particles in the x-axis directionxAnd the velocity u of the fluid particles in the y-axis directionyThe calculation formula is calculated by the following formula:
f1＝f3,f2＝f4,f8＝f6(19)
step 2.3, calculating a liquid phase temperature field by adopting a cellular automaton model in combination with the velocity distribution of the flow field; the specific method is calculated by the following method:
firstly, the calculation of the liquid phase temperature field is the calculation in the heat transfer process, so the liquid phase region temperature field is calculated by adopting the following formula:
wherein T is time, ρ is matrix density, λ is thermal conductivity, T is cell temperature, cpThe specific heat capacity of the matrix, fs the cellular solid phase rate and L the latent heat; q. q.sw,w、qw,e、qw,n、qw,sLeft, right, upper and lower boundaries, respectivelyThe heat flux density of the boundary in four directions; for the sake of simplifying the calculation, it is assumed that the thermal conductivity λ of the matrix in the x-axis and y-axis directions is equal;
the supercooling degree at the solid-liquid interface consists of component supercooling, curvature supercooling, thermal supercooling and dynamic supercooling degree, and the dynamic supercooling degree is neglected because the dynamic supercooling degree is smaller relative to other supercooling degrees in the solidification process; therefore, the supercooling degree is calculated by the following equation:
ΔT＝ΔTc+ΔTr+(Tbulk-TL) (22)
wherein ,ΔTrIs undercooling of curvature, TbulkTemperature of liquid phase, T, at solidification frontLIs the liquidus temperature, Δ TcIs the supercooling of the components; the liquidus temperature, curvature supercooling and composition supercooling are respectively solved by the following formulas:
TL＝1535-65[％C]-2.7[％Al]-90[％N](23)
wherein gamma is a Gibbs-Thomson coefficient; m isL,iIs the liquidus slope of element i; c. CL,iRepresents the liquid phase concentration of element i;
the concentration of the solid-liquid interface front edge of the element i;
step 2.4, combining the flow field velocity distribution, and calculating solute distribution of the liquid phase region and the solid phase region by adopting a cellular automaton model; the specific method is as follows:
the interaction between solutes on the growth of dendrites is considered in the liquid phase, and the solute transport in the solid phase is smaller than that in the liquid phase by several orders of magnitude, so the solute interaction in the solid phase is ignored, and the solute transport in the solid phase and the solute transport in the liquid phase are respectively calculated by adopting the following formulas:
wherein ,CL,i、CS,iRespectively representing the concentration of the element i in the liquid phase and the solid phase; cS,iIs the transmission coefficient of the element i in the solid phase matrix; n-1, wherein n is the total number of elements in the molten steel, and the nth element represents a solvent;
representing the Darken coefficient matrix in the liquid phase, assuming the directions of the x-axis and the y-axis in the matrix for simplifying the calculation
The values are the same, and the following formula is utilized to solve:
wherein R represents a gas constant, akIndicates the activity of the element k, xkDenotes the molar fraction of the element k, xjRepresents the molar fraction of the element j, δkiDenotes the Kronector delta function, when k is i, δkiTake 1, otherwise deltakiTaking 0; mkRepresents the mobility of the element k in the system, which is solved according to the einstein formula, as shown in the following formula:
wherein ,
representing the diffusion coefficient of the tracking element k. Assuming that a solid-liquid interface is in a thermodynamic equilibrium state, the solute distribution law is satisfied at the interface:
according to the law of conservation of solute at the interface, the growth speed of interface cells in a thermodynamic equilibrium state is solved according to the following formula:
wherein, the right side
The solute transport item only considers the influence of the liquid phase solute interaction on the growth of dendrites;
representing the growth speed of the interface cell solidification front; by solving the growth speed of the solidification front of the interface cells, the growth of the interface cells in unit time step is calculated by increasing the solid phase rate, and the following formula is shown:
wherein ,
and
the cell solid phase ratio Δ f of AlN at the previous time and this time, respectivelys,AlNIncrease in solid fraction of (2); Δ t is a unit time step;
indicating edge
Unit length of direction through the center of the cell; Δ l ═ 1 μm for the grid cell length; theta represents the angle between the dendrite growth direction and the x-axis direction.
Function of normal phase and growth direction of solid-liquid interface
Calculated by the following formula:
wherein, θ and
the included angles between the interface growth normal direction and the preferred growth direction and the positive direction of the x axis are respectively. ε represents the anisotropy parameter, where the angle between the preferential growth direction and the positive x-axis direction
Calculated by the following formula:
the reaction formula for generating AlN in the solid-liquid two-phase region and the calculation formula for activity and activity coefficient are as follows:
[Al]+[N]＝(AlN) (39)
a[M]＝[％M]f[M](40)
wherein ,a[M]Representing the Henry activity of element M; m represents an element Al or N, [ M ]]Indicates that the element M is dissolved in the steel; [% M]Represents the concentration of the element M based on a mass 1% standard; f. of[Al] and f[N]Activity coefficients of elements Al and N, respectively, based on a mass 1% standard;
representing the interaction coefficient of element j to element i; (as shown in table 2);
TABLE 2 solute interaction coefficients
When a certain cell in the calculation region meets the AlN precipitation condition, marking the cell, carrying out 3 x 3 grid refinement division on the cell, and simultaneously calculating the growth of the cell according to dynamic chemical equilibrium, wherein the formula is as follows:
MAlNrepresents the relative molecular mass of AlN; Δ x represents the reaction amount;
and for the complex boundary condition, the method is characterized in that Mei is adopted to correct the F-H format, the speed is increased along the x direction, the free boundary condition is added on the right side, and a lattice Boltzmann method is combined to establish a stress growth model of the lower dendrite of the Fe-C-Al-N quaternary alloy flow field.
Therefore, according to the Mei, the F-H format is modified by first aligning the solid phase boundary points xbAssume that it has a virtual state equilibrium distribution function as follows:
wherein ufIs xfFluid velocity of (u)bfFor undetermined virtual velocity, to solve for ubfConstructing an interpolation factor α and xwPosition dependent, ubfThe following formula is used to obtain:
wherein β is for calculating xfInterpolation factor, u, of the rebound distribution structurewIs xwThe moving speed of the interface; according to the formula, a virtual state balance distribution function can be solved; therefore, the solute field distribution and the solid phase region solute distribution under the Mei correction F-H format are obtained by the following formulas:
when the cell growth is calculated according to the dynamic chemical balance, in order to reduce the calculation error caused by the larger time step, the cells are subjected to spatial 3 x 3 refinement time division and time division, and are subjected to refinement time division at the same time, and the growth in a time step is subjected to multiple circulating calculation when the forced convection is calculated and calculated to stress the AlN dendrite for growth, so that the calculation error caused by the time step is reduced; when the volume of AlN in the matrix cell is increased and the matrix cell is contacted with the adjacent liquid-phase cell, the adjacent liquid-phase cell is subdivided into 3 multiplied by 3F-H format lower boundary AlN precipitation cells, and AlN growth is continued. And displaying the shape, the size and the stress condition of the AlN dendrite by using data and analysis and visual processing software images.
In this embodiment, the model parameter values involved in the calculation process are shown in table 3:
TABLE 3 model parameters in the calculation process
The embodiment is implemented by writing a numerical simulation program shown in figure 2 on a mathematical model for computing the stress of the forced convection to the AlN dendrites by using a C + + language based on a Visual Studio 2015 platform to obtain a simulation diagram of dendrite morphology evolution and Al solute distribution in a molten steel solidification flow field shown in figure 5; and (3) obtaining a branch crystal growth model under the flow field through numerical simulation, and providing theoretical guidance for optimizing the solidification technology, predicting the stress analysis of the dendritic crystal under the forced convection and improving the casting blank quality.
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 (5)
1. A method for calculating the stress of AlN dendrites by forced convection in the process of molten steel solidification in the field of metallurgy is characterized by comprising the following steps: the method comprises the following steps:
step 1, collecting steel grade components, thermodynamic and kinetic parameters in a solidification process and flow field boundary conditions;
step 2, based on a metal solidification theory, calculating the interface growth direction, the distribution of a liquid phase solute field and a temperature field and the distribution of a solid phase region solute field by using a cellular automaton model; meanwhile, a classical model D2Q9 model in a lattice Boltzmann method is coupled to calculate the velocity distribution of the flow field;
step 2.1, in order to enable the cellular automaton model to have certain physical significance, introducing a metal solidification theory, and calculating the growth direction and curvature supercooling of an interface by adopting a sharp interface model;
step 2.2, determining a fluid flow boundary, and calculating the velocity distribution of the flow field by adopting a D2Q9 model;
step 2.3, calculating a liquid phase temperature field by adopting a cellular automaton model in combination with the velocity distribution of the flow field;
step 2.4, combining the flow field velocity distribution, and calculating solute distribution of the liquid phase region and the solid phase region by adopting a cellular automaton model;
and 3, for the complex boundary flow, correcting an F-H format by adopting Mei, adding a free boundary condition on the right side along the speed of the complex boundary flow along the x direction, and establishing a stress growth model of the lower dendrite of the Fe-C-Al-N quaternary alloy flow field by combining a lattice Boltzmann method. And displaying the shape, the size and the stress condition of the AlN dendrite by using data and analysis and visual processing software images.
2. The method for calculating the stress of the AlN dendrites by forced convection in the process of molten steel solidification in the field of metallurgy according to claim 1 is characterized in that: the specific method of the step 2.1 comprises the following steps:
firstly, assuming that a solid-liquid interface is in a thermodynamic equilibrium state, and according to the solute conservation law at the interface, the growth direction of the interface is calculated by the following formula:
wherein 
Expressing the interface growth direction, the curvature undercooling K is calculated by the following formula:
wherein ,
and
respectively representing first-order partial derivatives of the solid phase ratio on an x axis and a y axis;
firstly, solving the second-order partial derivative of the y axis after solving the partial derivative of the solid phase ratio on the x axis;
and
respectively is a second order partial derivative of the solid fraction on an x axis and a y axis;
the state of the cells is detected and the fluid flow boundary and its boundary conditions are determined as described in step 2.2. In the two-dimensional numerical simulation calculation, a D2Q9 model is generally used to calculate the flow field distribution, while ignoring the external force, the velocity distribution of the flow field is calculated by the following formula:
wherein τ is the dimensionless single-step relaxation time, fi(x+ciΔt,t+Δt)、fi(x, t) is the distribution function of the liquid phase fluid particles, fi eq(x, t) is the liquid phase fluid particle equilibrium distribution function; wherein c isiThe migration velocity of liquid phase fluid particles in the direction of the grid i, and delta t is a time step; due to the adoption of the D2Q9 model, wherein ciThe sum of the calculation formula is the weight coefficient wiCalculated by the following formula:
wherein c and csThe lattice velocity and the lattice sound velocity are respectively; the macroscopic density ρ, the macroscopic velocity u, and the hydrodynamic viscosity v are calculated by the following equations:
wherein fiIs an entrance node distribution function, i (values of 0,1,2,3,4,5,6,7 and 8) is an angular step node ordinal number, and entrance density rhoinOutlet density ρoutThe velocity u of the fluid particles in the x-axis directionxAnd the velocity u of the fluid particles in the y-axis directionyThe calculation formula is calculated by the following formula:
f1＝f3,f2＝f4,f8＝f6(19)
3. the method for calculating the stress on the AlN dendrite by the forced convection in the molten steel solidification process in the metallurgical field according to claim 1, wherein in the step 2.3, a cellular automaton model is adopted to calculate a liquid phase temperature field in combination with the velocity distribution of a flow field; the specific method is calculated by the following method:
firstly, the calculation of the liquid phase temperature field is the calculation in the heat transfer process, so the liquid phase region temperature field is calculated by adopting the following formula:
wherein T is time, ρ is matrix density, λ is thermal conductivity, T is cell temperature, cpIs the specific heat capacity of the matrix, fs is the cellular solid phase rate,l is latent heat; q. q.sw,w、qw,e、qw,n、qw,sThe heat flux densities of the left boundary, the right boundary, the upper boundary and the lower boundary in four directions respectively; for the sake of simplifying the calculation, it is assumed that the thermal conductivity λ of the matrix in the x-axis and y-axis directions is equal;
the supercooling degree at the solid-liquid interface consists of component supercooling, curvature supercooling, thermal supercooling and dynamic supercooling degree, and the dynamic supercooling degree is neglected because the dynamic supercooling degree is smaller relative to other supercooling degrees in the solidification process; therefore, the supercooling degree is calculated by the following equation:
ΔT＝ΔTc+ΔTr+(Tbulk-TL) (22)
wherein ,ΔTrIs undercooling of curvature, TbulkTemperature of liquid phase, T, at solidification frontLIs the liquidus temperature, Δ TcIs the supercooling of the components; the liquidus temperature, curvature supercooling and composition supercooling are respectively solved by the following formulas:
TL＝1535-65[％C]-2.7[％Al]-90[％N](23)
wherein gamma is a Gibbs-Thomson coefficient; m isL,iIs the liquidus slope of element i; c. CL,iRepresents the liquid phase concentration of element i;
the concentration of the solid-liquid interface front edge of the element i;
because the heat transfer density and the mass transfer density are inseparable in the forced convection AlN dendrite stress calculation method, the solute distribution of the liquid phase region and the solid phase region is calculated by adopting a cellular automaton model according to the flow field velocity distribution in the step 2.4; the interaction between solutes on the growth of dendrites is considered in the liquid phase, and the solute transport in the solid phase is smaller than that in the liquid phase by several orders of magnitude, so the solute interaction in the solid phase is ignored, and the solute transport in the solid phase and the solute transport in the liquid phase are respectively calculated by adopting the following formulas:
wherein ,CL,i、CS,iRespectively representing the concentration of the element i in the liquid phase and the solid phase; cS,iIs the transmission coefficient of the element i in the solid phase matrix; n-1, wherein n is the total number of elements in the molten steel, and the nth element represents a solvent;
representing the Darken coefficient matrix in the liquid phase, assuming the directions of the x-axis and the y-axis in the matrix for simplifying the calculation
The values are the same, and the following formula is utilized to solve:
wherein R represents a gas constant, akIndicates the activity of the element k, xkDenotes the molar fraction of the element k, xjRepresents the molar fraction of the element j, δkiDenotes the Kronector delta function, when k is i, δkiTake 1, otherwise deltakiTaking 0; mkRepresents the element k in the systemIs solved according to the einstein formula, as shown in the following formula:
wherein ,
representing the diffusion coefficient of the tracking element k. Assuming that a solid-liquid interface is in a thermodynamic equilibrium state, the solute distribution law is satisfied at the interface:
according to the law of conservation of solute at the interface, the growth speed of interface cells in a thermodynamic equilibrium state is solved according to the following formula:
wherein, the right side
The solute transport item only considers the influence of the liquid phase solute interaction on the growth of dendrites;
representing the growth speed of the interface cell solidification front; by solving the growth speed of the solidification front of the interface cells, the growth of the interface cells in unit time step is calculated by increasing the solid phase rate, and the following formula is shown:
wherein ,
and
the cell solid phase ratio Δ f of AlN at the previous time and this time, respectivelys,AlNIncrease in solid fraction of (2); Δ t is a unit time step;
indicating edge
Unit length of direction through the center of the cell; Δ l ═ 1 μm for the grid cell length; theta represents the angle between the dendrite growth direction and the x-axis direction.
4. The method for calculating the stress of the AlN dendrites by forced convection in the process of molten steel solidification in the field of metallurgy according to claim 3 is characterized in that:
the specific method of the step 2.4 comprises the following steps: the following assumptions are calculated and simulated for the calculation of the stress of the forced convection on the AlN dendrites: AlN precipitated in the steel does not contain other phases; only AlN precipitation in the liquid phase is considered; neglecting the increase of interface energy in the growth process; neglecting the heat change when AlN is precipitated; based on the above assumptions, the thermodynamic and kinetic conditions for AlN nucleation in steel are first calculated; when the nucleation condition is met, nucleation is carried out in the cell and the surrounding solute field is updated and calculated, as the AlN interface keeps a thermodynamic equilibrium state, the solute is continuously diffused to the interface, forced convection is carried out on the stress calculation simulation of the AlN dendrite according to the thermodynamic equilibrium state, and the solid-liquid interface normal phase and the growth direction function
Calculated by the following formula:
wherein, θ and
the included angles between the interface growth normal direction and the preferred growth direction and the positive direction of the x axis are respectively. ε represents the anisotropy parameter, where the angle between the preferential growth direction and the positive x-axis direction
Calculated by the following formula:
the reaction formula for generating AlN in the solid-liquid two-phase region and the calculation formula for activity and activity coefficient are as follows:
[Al]+[N]＝(AlN) (39)
a[M]＝[％M]f[M](40)
wherein ,a[M]Representing the Henry activity of element M; m represents an element Al or N, [ M ]]Indicates that the element M is dissolved in the steel; [% M]Represents the concentration of the element M based on a mass 1% standard; f. of[Al] and f[N]Activity coefficients of elements Al and N, respectively, based on a mass 1% standard; e.g. of the typei jRepresenting the interaction coefficient of element j to element i; when a certain cell in the calculation region meets the AlN precipitation condition, marking the cell, carrying out 3 x 3 grid refinement division on the cell, and simultaneously calculating the growth of the cell according to dynamic chemical equilibrium, wherein the formula is as follows:
MAlNrepresents the relative molecular mass of AlN; Δ x represents the reaction amount.
5. The method for calculating the stress of the AlN dendrites by forced convection in the molten steel solidification process in the metallurgical field according to claim 4 is characterized in that an F-H format is modified by Mei, the speed in the x direction is increased, a free boundary condition is added on the right side, and a stress growth model of the dendrites under the Fe-C-Al-N quaternary alloy flow field is established by combining a lattice Boltzmann method.
Therefore, according to the Mei, the F-H format is modified by first aligning the solid phase boundary points xbAssume that it has a virtual state equilibrium distribution function as follows:
wherein ufIs xfFluid velocity of (u)bfFor undetermined virtual velocity, to solve for ubfConstructing an interpolation factor α and xwPosition dependent, ubfThe following formula is used to obtain:
wherein β is for calculating xfInterpolation factor, u, of the rebound distribution structurewIs xwThe moving speed of the interface; according to the formula, a virtual state balance distribution function can be solved; therefore, the solute field distribution and the solid phase region solute distribution under the Mei correction F-H format are solved by the following formulasObtaining:
when the cell growth is calculated according to the dynamic chemical balance, in order to reduce the calculation error caused by the larger time step, the cells are subjected to spatial 3 x 3 refinement time division and time division, and are subjected to refinement time division at the same time, and the growth in a time step is subjected to multiple circulating calculation when the forced convection is calculated and calculated to stress the AlN dendrite for growth, so that the calculation error caused by the time step is reduced; when the volume of AlN in the matrix cell is increased and the matrix cell is contacted with the adjacent liquid-phase cell, the adjacent liquid-phase cell is subdivided into 3 multiplied by 3F-H format lower boundary AlN precipitation cells, and AlN growth is continued. And displaying the shape, the size and the stress condition of the AlN dendrite by using data and analysis and visual processing software images.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911036081.XA CN110970095B (en) | 2019-10-29 | 2019-10-29 | Method for calculating stress of forced convection on AlN dendrites in molten steel solidification process in metallurgical field |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911036081.XA CN110970095B (en) | 2019-10-29 | 2019-10-29 | Method for calculating stress of forced convection on AlN dendrites in molten steel solidification process in metallurgical field |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110970095A true CN110970095A (en) | 2020-04-07 |
| CN110970095B CN110970095B (en) | 2023-10-10 |
Family
ID=70029969
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911036081.XA Active CN110970095B (en) | 2019-10-29 | 2019-10-29 | Method for calculating stress of forced convection on AlN dendrites in molten steel solidification process in metallurgical field |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110970095B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112613202A (en) * | 2020-11-27 | 2021-04-06 | 东北大学 | Method for determining dendritic network permeability of steel solidification mushy zone |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20170147723A1 (en) * | 2015-11-20 | 2017-05-25 | Metal Industries Research & Development Centre | Method of simulatively predicting a metal solidification microstructure for a continuous casting process |
| CN109785907A (en) * | 2019-01-28 | 2019-05-21 | 东北大学 | The prediction technique of TiN Inclusion Precipitation situation during a kind of solidification of molten steel |
| CN109817284A (en) * | 2019-01-25 | 2019-05-28 | 东北大学 | The mobile prediction technique of dendrite in a kind of molten steel |
| CN110908973A (en) * | 2019-10-28 | 2020-03-24 | 东北大学 | Method for calculating stress of forced convection on MnS dendrite in molten steel solidification process |
-
2019
- 2019-10-29 CN CN201911036081.XA patent/CN110970095B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20170147723A1 (en) * | 2015-11-20 | 2017-05-25 | Metal Industries Research & Development Centre | Method of simulatively predicting a metal solidification microstructure for a continuous casting process |
| CN109817284A (en) * | 2019-01-25 | 2019-05-28 | 东北大学 | The mobile prediction technique of dendrite in a kind of molten steel |
| CN109785907A (en) * | 2019-01-28 | 2019-05-21 | 东北大学 | The prediction technique of TiN Inclusion Precipitation situation during a kind of solidification of molten steel |
| CN110908973A (en) * | 2019-10-28 | 2020-03-24 | 东北大学 | Method for calculating stress of forced convection on MnS dendrite in molten steel solidification process |
Non-Patent Citations (2)
| Title |
|---|
| XIANGNING MENG 等: "Cross-Scale Modeling of MnS Precipitation for Steel Solidification", vol. 8, no. 7, pages 529 - 542 * |
| 左晓静 等: "连铸低碳钢一次枝晶演变数值模拟及其受力分析", vol. 65, no. 16, pages 1 - 10 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112613202A (en) * | 2020-11-27 | 2021-04-06 | 东北大学 | Method for determining dendritic network permeability of steel solidification mushy zone |
| CN112613202B (en) * | 2020-11-27 | 2023-09-15 | 东北大学 | Determination method for dendrite network permeability of steel solidification pasty area |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110970095B (en) | 2023-10-10 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Takaki et al. | Phase-field lattice Boltzmann simulations of multiple dendrite growth with motion, collision, and coalescence and subsequent grain growth | |
| CN109785907B (en) | Method for predicting precipitation condition of TiN inclusion in molten steel solidification process | |
| Pickering | Macrosegregation in steel ingots: the applicability of modelling and characterisation techniques | |
| CN109817284B (en) | Prediction method for movement of dendritic crystal in molten steel | |
| CN110908973B (en) | Method for calculating stress of forced convection on MnS dendrites in molten steel solidification process | |
| Ares et al. | Influence of solidification thermal parameters on the columnar-to-equiaxed transition of aluminum-zinc and zinc-aluminum alloys | |
| Rátkai et al. | Phase-field lattice Boltzmann model for dendrites growing and moving in melt flow | |
| CN110765599A (en) | Prediction method for AlN inclusion precipitation condition in molten steel solidification process | |
| Wu et al. | Simulation of As‐Cast Steel Ingots | |
| CN111027172A (en) | Method for predicting dendritic crystal growth under molten steel convection condition | |
| CN105057642A (en) | Simulation method of casting grain structure formation related numerical value | |
| CN110970095A (en) | Method for calculating stress of forced convection on AlN dendrites in molten steel solidification process in metallurgical field | |
| Kihara et al. | Numerical simulation of macrosegregation in a continuous casting mold with electromagnetic stirring | |
| Lu et al. | Modeling of microstructure formation with gas porosity growth during columnar dendritic solidification of aluminum alloys | |
| Battaglioli et al. | Influence of natural and forced gravity conditions during directional columnar solidification | |
| CN113807033A (en) | Numerical simulation method for evolution of magnesium alloy selective laser melting microstructure | |
| Kumar et al. | Grain floatation during equiaxed solidification of an Al-Cu alloy in a side-cooled cavity: Part II—Numerical studies | |
| CN110993038A (en) | Prediction method for dendritic crystal growth in standing molten steel based on parallel computation | |
| Meng et al. | A CA-LBM model for simulating dendrite growth with forced convection | |
| Sharp et al. | Solute redistribution in cellular solidification | |
| CN110765598A (en) | Method for predicting MnS inclusion precipitation condition in molten steel solidification process | |
| CN110910967A (en) | Method for predicting CrN precipitation condition in molten steel solidification process | |
| Egole et al. | Micro-macro model for the transient heat and fluid transport in solidification structure evolution during static casting processes | |
| CN115455760A (en) | Casting blank on-line thermal state tracking method | |
| CN116796658A (en) | Method for calculating stress of forced convection on dendrites in BN precipitation process |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |