CN109446748B - Method for simulating solidification process of continuous casting round billet - Google Patents
Method for simulating solidification process of continuous casting round billet Download PDFInfo
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Abstract
The invention discloses a method for simulating a continuous casting round billet solidification process, belongs to the technical field of metallurgy, and aims to solve the problem that no process or method can provide basis for the design and optimization of round billet continuous casting process parameters at present. Step a, establishing a round billet continuous casting solidification heat transfer mathematical model; step b, determining model solution conditions; step c, verifying a heat transfer model; step d, simulation results and analysis; and comparing the model calculation with the casting blank surface temperature measured by on-site production, verifying whether the selected parameters are reliable, and judging whether the calculated temperature of the heat transfer model is close to the actual temperature, wherein if the calculated and actual errors are controlled to be about 5% at maximum, the engineering requirements can be met. The final simulation result of the method for simulating the continuous casting round billet solidification process can better reflect the round billet temperature distribution of solidification heat transfer, and provides a direction for parameter design optimization of continuous casting technology.
Description
Technical Field
The invention relates to a method for simulating a round billet solidification process, in particular to a method for simulating a continuous casting round billet solidification process, and belongs to the technical field of metallurgy.
Background
Continuous casting is a complex high-temperature process in which liquid molten steel is continuously solidified into a solid state and is accompanied by various phenomena such as heat transfer, mass transfer, phase change, flow and the like. The molten steel is sequentially subjected to primary cooling, secondary cooling and radiation air cooling of a crystallizer, and overheated, latent heat and sensible heat are released, so that a continuous casting blank with a certain organization structure is formed. The solidification and heat transfer process of the casting blank has a direct influence on the quality of the continuous casting blank, and the formation of various defects (including internal cracks, surface cracks, diamond changes, shrinkage cavities, segregation and the like) of the casting blank is usually related to unreasonable temperature distribution. The modern continuous casting technology level is greatly improved, and new technologies including continuous temperature measurement of a tundish, automatic control of the liquid level of a crystallizer, prediction of bonding steel leakage, electromagnetic stirring, dynamic soft reduction, continuous casting and rolling, near-net-shape continuous casting and the like are presented. Wherein, the end electromagnetic stirring (F-EMS) gathers solute elements in a dispersed and solidified two-phase region on the casting blank, thereby reducing center segregation; the central solidification structure is improved, and the central looseness is reduced; reducing the semi-macrosegregation (V-type) caused by the slip of the central equiaxial crystal, and the like. But the F-EMS installation position is important to the effect. It is considered that the casting blank should be installed at the position with the liquid core diameter of more than or equal to 40mm, that fs=0.7-0.8, and that the central liquid phase of the casting blank is 40-55%. However, these data cannot be measured directly in actual production, so it is necessary to build a mathematical model of heat transfer for calculation. The setting model and the actual measurement are generally adopted to find the F-EMS installation position, and the proper technological parameters are obtained through the heat transfer model so that the F-EMS can better play a role.
The prior art is that the temperature distribution can not be obtained in real time when parameters such as the pulling speed of a continuous casting machine are changed by manual real-time monitoring and temperature change measurement, and no process or method can provide basis for the design and optimization of the technological parameters of round billet continuous casting at present.
Disclosure of Invention
The invention aims to provide a method for simulating a continuous casting round billet solidification process, so as to solve the problem that no process or method can provide basis for the design and optimization of round billet continuous casting process parameters at present.
A method for simulating the solidification process of a round billet for continuous casting, comprising the following steps:
step a, establishing a round billet continuous casting solidification heat transfer mathematical model;
step b, determining model solution conditions;
step c, verifying a heat transfer model;
step d, simulation results and analysis; and comparing the model calculation with the casting blank surface temperature measured by on-site production, verifying whether the selected parameters are reliable, and judging whether the temperature calculated by the heat transfer model is close to the actual temperature, wherein if the error between the calculation and the actual temperature is less than 5%, the engineering requirement can be met.
Preferably: the establishing a round billet continuous casting solidification heat transfer mathematical model in the step a comprises the following steps:
step a1, establishing a round billet continuous casting solidification heat transfer mathematical model coordinate system; regarding the continuous casting process as a process that a two-dimensional slice of a casting blank cross section moves downwards along the direction of drawing the blank of a casting machine at the speed of drawing the blank, updating the temperature field and boundary conditions once every time step, namely the distance corresponding to the motion V.Deltaτ of the slice, wherein the slice respectively transfers heat through a crystallizer, a secondary cooling area and a radiation air cooling area in the continuous casting machine, the boundary conditions are continuously changed, the temperature field information of the slice is also continuously updated, the central point of a molten steel meniscus in the crystallizer is taken as the origin of a space-time coordinate system gamma theta Z τ, the direction of drawing the blank is Z, the imaginary time axis QT coincides with the OZ axis, the upper boundary of a certain length which is larger than the metallurgical length L is taken as Z, and the metallurgical length L is taken as the cutting position of the casting blank from the length L of the meniscus of the crystallizer 0 Correspondingly, there is a temporal upper bound tau 0 The casting blank temperature field function T (gamma, theta, Z, tau) is defined on the space-time coordinate system, and the radius r, the angle theta, the Z phase length and the time T are: gamma is more than or equal to 0 and less than or equal to (D/2), D is the diameter, and tau is more than or equal to 0 and less than or equal to tau o The method comprises the steps of carrying out a first treatment on the surface of the For solid phase, liquid phase and solid-liquid two-phase regions of a continuous casting blank, the heat transfer of the casting blank meets a unified form of unsteady heat transfer partial differential equation:
wherein: gradT temperature gradient, DEG C/m; div divergence symbols; density of rho steel Kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the c constant pressure specific heat, J/(kg. DEG C))，λ - Thermal conductivity, W/(m·deg.C); τ time, s; a temperature T;
the general differential equation is very difficult to directly solve under the complex boundary condition of continuous casting, namely, the solution is difficult to solve, and the general processing method is to make reasonable assumptions aiming at specific continuous casting process conditions so as to solve;
according to the above assumed conditions, the basic differential equation based on the round billet continuous casting solidification heat transfer in the polar coordinate system is:
the deduction is carried out:
and (3) finishing to obtain:
wherein the density of rho-steel Kg/m3; ce-specific heat, J/(Kg. Deg.C); λe-coefficient of thermal conductivity, W/(m·deg.C); tau-time; a temperature T; angle θ;
step a2, variable-pitch meshing; for a round billet, because the established heat transfer differential equation is in a polar coordinate form, the cross section of the round billet is generally divided into grids according to the radial direction and the tangential direction or the circumferential direction, and because the round billet is closer to the center of a casting blank after being determined by the radial step delta r and the tangential angle delta theta, the grids are finer, and the stability of differential equation calculation is poor and difficult to converge due to the tiny grids; increasing the tangential angle can increase the central tangential step length, but the surface tangential step length is too large at the moment, so that the calculation accuracy is poor;
dividing the cross section of the round billet into grids with different tangential angles, wherein the junction position of the inner ring and the outer ring can be selected by oneself, the position of the junction position is 1/4 of the cross section diameter, the tangential angle of the inner ring is large, the tangential angle of the outer ring is small, the grid division with variable spacing is adopted, the grid division is denser in the surface area of a casting blank with sensitive temperature change, and the grid division is sparse in the central area of the casting blank with gentle temperature change;
step a3, establishing a differential equation; the heat transfer differential equation is discretized and solved by utilizing a finite difference method, six different differential equations can be established according to the grid division in the step a2, and the differential equations are sequentially a central node, an inner ring internal node, an inner ring junction node, an outer ring internal node and a surface node;
step a4, determining equation stability conditions; the calculation proves that the stability requirement of the center differential equation is the most strict in six differential equations in the model, and the differential equations are as follows based on two types of nodes i=0 and i=1:
to converge the differential equation calculation, one of the two equations above
The coefficients of the terms must be greater than or equal to zero, thus resulting in the following stability conditions:
step a5, selecting a space and a time step; for the explicit finite difference method, when the numerical solution is carried out, the grid division has a certain influence on the calculation result, generally, when the time step delta tau is fixed, the larger the space step value is, the faster the calculation process is, but the error is increased and the accuracy is reduced; in contrast, the smaller the space step length is, the smaller the calculation error is, the high precision is, but the calculation is slow, even the calculation is not converged, and the result is paradoxical, so that the step length is selected to be comprehensively considered;
the radial step length is selected, other conditions are fixed, different radial step lengths are selected for simulation calculation, the calculation result obtained by the large radial step length is found to be higher than that obtained by the small radial step length, the tangential step length is reduced, finer temperature field data in the circumferential direction can be obtained, and meanwhile, the load of the simulation calculation is increased; in addition, for round billets, the stability problem of a difference equation is considered, especially the problem that the tangential step length is small when the difference equation is close to a central node, and the phenomenon of calculation non-convergence is easy to occur;
the tangential step length is selected, so that the effect on the result is not as obvious as the radial step length, because for the round billet, the heat transfer is mainly carried out through radial transfer, the tangential heat transfer only plays a role in uniform axial temperature, if the boundary conditions of the surface of the round billet are inconsistent, the temperature of the surface of the round billet is not uniform, and at the moment, the finer the tangential grid is, the higher the calculation result precision is; if the surface cooling conditions of the round billets are the same, the surface temperature is uniform, tangential heat transfer does not exist, and the division of tangential grids has no influence on the calculation result;
the model ignores heat transfer in the running direction of the casting blank, considers that the surface of the round blank is uniformly cooled, and comprehensively considers that the inner ring delta theta is taken 1 Taken to be 0.524, the outer ring delta theta 2 Taking the angle as 0.0524, and taking larger tangential angles of the inner ring, mainly considering the convergence of the core nodes; meanwhile, as the core nodes mostly exist in the liquid core in the continuous casting process, the convection heat transfer of the molten steel is strong, the temperature gradient is much smaller than that of the conduction heat transfer, and the tangential temperature non-uniformity of the nodes is much smaller than that of the surface nodes, so that the tangential step length does not need to be too fine;
time step selection
After determining the space step length, substituting the space step length into the thermophysical parameters of the continuous casting blank to be researched according to the stability condition of the differential equation, and taking the maximum value of the heat conductivity coefficient; the density and the specific heat take the minimum value, and the value range of the time step delta tau can be determined according to the stability condition of the differential equation;
the method of changing the time step at the fixed slice position is adopted in calculation, namely, the same moving distance of the casting blank in the blank drawing direction in each time step is ensured under different drawing speeds, v is taken as delta tau=0.08, the unit of v is m/min, and the unit of delta tau is s.
Preferably: the model solution conditions in the step b comprise initial conditions, boundary conditions and thermophysical parameters.
Preferably: the assumptions made in step a1 for model simplification include:
(1) the heat transfer problem of continuous casting is simplified into a two-dimensional problem, and the heat transfer in the running direction of the casting blank can be ignored because the length of the casting blank is much larger than the cross section size of the casting blank, and the surface of the round blank is uniformly cooled;
(2) assuming that the temperature of the meniscus molten steel of the crystallizer is the same as the casting temperature;
(3) ignoring the dimensional change of the casting blank caused by solidification, cooling and shrinkage;
(4) the temperature of a certain space point in the direction of drawing the blank does not change with time, namely, the continuous casting solidification heat transfer is considered to be a steady heat transfer process;
(5) considering the influence of forced convection of molten steel on heat transfer of casting blank, the influence of forced convection is processed into effective heat conductivity coefficient lambda of molten steel e The thermal conductivity of the region with liquid phase is larger than that of the solid phase region;
(6) neglecting the influence of the vibration of the crystallizer and the electromagnetic stirring on solidification heat transfer.
Preferably: six different differential equations in step a3 are:
assume that:
wherein: Δθ 1 -circumferential angle of the inner ring; Δθ 2 -circumferential angle of the outer ring, moment K, temperature at point i+1, moment j, temperature at point i-1, j; a is a code number, which represents the calculation result of the following formula;
(1) center node (i=0, j=0):
at this time have
Because the center r=0, so
(according to the lobida rule)
The equation becomes
The display differential format of the equation is:
(symmetrical at the center, so there is
)
So that:
i.e.
(2) Inner ring internal nodes (i=1 to M1-1, j=1 to N1):
the display differential format of the equation is:
and (3) finishing to obtain:
(3) inner ring interface nodes (i=m1, j=1 to N1):
the difference equation is the same as that shown in (2), except that when i+1, the point runs from the inner ring to the outer ring, and the axial mesh numbers of the inner ring and the outer ring are different, so that the size of j is also changed, and the difference can be obtained according to the same angle: (j' -1) Δθ 2 ＝(j-1)Δθ 1
Obtaining the product
The differential equation is:
wherein the method comprises the steps of
The other of the two is not changed,
(4) outer ring interface nodes (i=m1+1, j=1 to N2):
as the difference equation in (2) is the same, when i-1, the points run from the outer ring to the inner ring, and the axial grids of the inner ring and the outer ring are different, so that the j is also changed, and the j is obtained according to the same angle: (j-1) Δθ 2 ＝(j′-1)Δθ 1
Obtaining the product
And is the outer ring at this time, the tangential step length is delta theta 2 ，A 2 Becomes A 3 ，
The differential equation is:
wherein:
(5) outer ring internal nodes (i=m1+2 to M-1, j=1 to N2):
the difference equation is the same as that in (2), except that the tangential step is delta theta due to the outer ring at this time 2 ，A 2 Becomes A 3 ，
(6) Surface node (i=m, j=1 to N2):
at this time have no
So T in the differential equation in (5) 2 And T 5 Is->
The differential equation at the time of availability is eliminated,
the boundary condition is the Neumann boundary condition (the heat flux density q is obtained), and the expression is:
representing the difference as a second-order precision center difference;
is deformed and then is brought into the following formula T 2 And T 5 In (a) and (b)
Has the following components
Is available in the form of
At this point, the expression is again:
expressed by backward differential:
finally, the method can obtain:
in the above formulae, lambda 1 ～λ 6 Effective heat conduction system at two temperatures in Ti (i=1 to 5)A weighted average of the numbers, n being the ratio of the number of outer circumferential meshes to the number of inner circumferential meshes, n=Δθ 1 /Δθ 2 ，Δθ 1 Is the tangential step length of the inner ring, delta theta 2 The tangential step length of the outer ring is expressed in radians.
Compared with the existing products, the invention has the following effects:
the heat transfer problem of continuous casting is simplified into a two-dimensional problem, a two-dimensional solidification heat transfer mathematical model of a continuous casting round billet is established, the temperature distribution of molten steel at the meniscus of a crystallizer is used as an initial condition of time, and a temperature change model in the continuous casting operation process is established by combining a finite difference method;
the continuous casting round billet two-dimensional solidification heat transfer model adopts variable-spacing grid division, solves by using a finite difference method, and develops round billet continuous casting solidification heat transfer simulation calculation. The simulation result can better reflect the round billet temperature distribution of solidification heat transfer through comparison and correction of the surface temperature of the casting billet measured by actual production; providing basis for the design optimization of the round billet continuous casting process parameters.
Drawings
FIG. 1 is a schematic diagram of space-time coordinates of a cast strand;
FIG. 2 is a schematic illustration of finite difference meshing;
fig. 3 is a graph of v=0.20 m/min, Δt=24 ℃ pull rate versus Φ650mm round billet surface temperature;
FIG. 4 is a graph of the effect of pull rate on solid phase rate of a phi 650mm round billet;
FIG. 5 is a graph of the effect of pull rate on the length of a phi 650mm round billet liquid core;
FIG. 6 is a graph of the effect of pull rate on the thickness of a phi 650mm round blank shell;
FIG. 7 is a graph showing the effect of superheat on the surface temperature of a phi 650mm round blank;
FIG. 8 is a graph showing the effect of superheat on solids fraction;
FIG. 9 is a graph showing the effect of superheat on wick length;
FIG. 10 is a graph showing the effect of superheat on the thickness of a phi 650mm round green shell.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
As shown in fig. 1 to 10, the method for simulating the solidification process of the continuous casting round billet according to the invention comprises the following steps:
step a, establishing a round billet continuous casting solidification heat transfer mathematical model;
step b, determining model solution conditions;
step c, verifying a heat transfer model;
step d, simulating results and analyzing.
Further: the establishing a round billet continuous casting solidification heat transfer mathematical model in the step a comprises the following steps:
step a1, establishing a round billet continuous casting solidification heat transfer mathematical model coordinate system; regarding the continuous casting process as a process that a two-dimensional slice of a casting blank cross section moves downwards along the casting machine withdrawal direction at withdrawal speed, the temperature field and boundary conditions are updated once every time step (the distance corresponding to the slice movement V.DELTA.tau), the slice respectively transfers heat through a crystallizer, a secondary cooling zone and a radiation air cooling zone in the continuous casting machine, the boundary conditions are continuously changed, the temperature field information of the slice is also continuously updated, the central point of a molten steel meniscus in the crystallizer is taken as the origin of a space-time coordinate system gamma theta tau, the withdrawal direction is Z, the imaginary time axis O tau coincides with the OZ axis, and a certain length larger than the metallurgical length L is taken (the casting blank cutting position is taken to be away from the length L of the crystallizer meniscus) 0 ) Being the upper bound of Z, there is a corresponding upper bound of time τ 0 The casting blank temperature field function T (gamma, theta, Z, tau) is defined on the space-time coordinate system, and the radius r, the angle theta, the Z phase length and the time T are: gamma is more than or equal to 0 and less than or equal to (D/2), D is the diameter, and tau is more than or equal to 0 and less than or equal to tau e The method comprises the steps of carrying out a first treatment on the surface of the For solid phase, liquid phase and solid-liquid two-phase regions of a continuous casting blank, the heat transfer of the casting blank meets a unified form of unsteady heat transfer partial differential equation:
wherein: gradT temperature gradient, DEG C/m; div divergence symbols; density of rho steel Kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the C constant pressure specific heat, J/(Kg. DEG C), lambda-heat conductivity coefficient, W/(m. DEG C);τ time, s; a temperature T;
it is very difficult to directly solve the general differential equation under the complex boundary condition of continuous casting, namely, it is difficult to solve the solution, and the general processing method makes reasonable assumptions for specific continuous casting process conditions, and makes numerical solutions, and the assumptions made for model simplification herein include:
(1) the heat transfer problem of continuous casting is simplified into a two-dimensional problem, and the heat transfer in the running direction of the casting blank can be ignored because the length of the casting blank is much larger than the cross section size of the casting blank, and the surface of the round blank is uniformly cooled;
(2) assuming that the temperature of the meniscus molten steel of the crystallizer is the same as the casting temperature;
(3) ignoring the dimensional change of the casting blank caused by solidification, cooling and shrinkage;
(4) the temperature of a certain space point in the direction of drawing the blank does not change with time, namely, the continuous casting solidification heat transfer is considered to be a steady heat transfer process;
(5) considering the influence of forced convection of molten steel on heat transfer of casting blank, the influence of forced convection is processed into effective heat conductivity coefficient lambda of molten steel e The thermal conductivity of the region with liquid phase is larger than that of the solid phase region;
(6) neglecting the influence of the vibration of the crystallizer and the electromagnetic stirring on solidification heat transfer,
according to the above assumed conditions, the basic differential equation based on the round billet continuous casting solidification heat transfer in the polar coordinate system is:
the deduction is carried out:
and (3) finishing to obtain:
wherein the density of rho-steel Kg/m3; ce-specific heat, J/(Kg. Deg.C); λe-coefficient of thermal conductivity, W/(m·deg.C); tau-time; a temperature T; angle θ;
step a2, variable-pitch meshing; for a round billet, because the established heat transfer differential equation is in a polar coordinate form, the cross section of the round billet is generally divided into grids according to the radial direction and the tangential direction (circumferential direction), and because the round billet is smaller when being closer to the center of a casting blank after being determined by the radial step delta r and the tangential angle delta theta, the stability of differential equation calculation is poor and is not easy to converge due to the fact that the grids are too small; increasing the tangential angle can increase the central tangential step length, but the surface tangential step length is too large at the moment, so that the calculation accuracy is poor;
in order to solve the contradiction, the difference equation is converged, meanwhile, the calculation precision is ensured, the cross section of the round billet is divided into grids with different tangential angles, the junction position of the inner ring and the outer ring can be selected by self, the junction position is taken as 1/4 of the cross section diameter, the tangential angle of the inner ring is large, the tangential angle of the outer ring is small, the variable-spacing grid division is adopted, the grid division is denser in the surface area of the casting billet with sensitive temperature change, the grid division is sparse in the central area of the casting billet with gentle temperature change,
step a3, establishing a differential equation; and d, discretizing and solving a heat transfer differential equation by using a finite difference method, and establishing six different differential equations, namely a center node, an inner ring inner node, an inner ring junction node, an outer ring inner node and a surface node, according to the grid division in the step f, wherein the specific deduction process is as follows:
to facilitate the expression of the differential equation, the following assumptions are made:
wherein: Δθ 1 -circumferential angle of the inner ring;
Δθ 2 the circumferential angle of the outer ring,
(1) center node (i=0, j=0):
at this time have
Because the center r=0, so
(according to the lobida rule)
The equation becomes
The display differential format of the equation is:
(symmetrical at the center, so there is
)
So that:
i.e.
(2) Inner ring internal nodes (i=1 to M1-1, j=1 to N1):
the display differential format of the equation is:
and (3) finishing to obtain:
(3) inner ring interface nodes (i=m1, j=1 to N1):
the difference equation is the same as that shown in (2), except that when i+1, the point runs from the inner ring to the outer ring, and the axial mesh numbers of the inner ring and the outer ring are different, so that the size of j is also changed, and the difference can be obtained according to the same angle: (j' -1) Δθ 2 ＝(j-1)Δθ 1
Obtaining the product
The differential equation is:
wherein the method comprises the steps of
The other of the two is not changed,
(4) outer ring interface nodes (i=m1+1, j=1 to N2):
as the difference equation in (2) is the same, when i-1, the points run from the outer ring to the inner ring, and the axial grids of the inner ring and the outer ring are different, so that the j is also changed, and the j is obtained according to the same angle: (j-1) Δθ 2 ＝(j′-1)Δθ 1
Obtaining the product
And is the outer ring at this time, the tangential step length is delta theta 2 ，A 2 Becomes A 3 ，
The differential equation is:
wherein:
(5) outer ring internal nodes (i=m1+2 to M-1, j=1 to N2):
the difference equation is the same as that in (2), except that the tangential step is delta theta due to the outer ring at this time 2 ，A 2 Becomes A 3 ，
(6) Surface node (i=m, j=1 to N2):
at this time have no
So T in the differential equation in (5) 2 And T 5 Is->
The differential equation at the time of availability is eliminated,
the boundary condition is the Neumann boundary condition (the heat flux density q is obtained), and the expression is:
representing the difference as a second-order precision center difference;
is deformed and then is brought into the following formula T 2 And T 5 In (a) and (b)
Has the following components
Is available in the form of
At this point, the expression is again:
expressed by backward differential:
finally, the method can obtain:
in the above formulae, lambda 1 ～λ 6 Weighted average of effective thermal conductivity at two temperatures in Ti (i=1 to 5), respectivelyThe value n is the ratio of the number of outer circumferential meshes to the number of inner circumferential meshes, n=Δθ 1 /Δθ 2 ，Δθ 1 Is the tangential step length of the inner ring, delta theta 2 The tangential step length of the outer ring is radian;
step a4, determining equation stability conditions; the calculation proves that the stability requirement of the center differential equation is the most strict in six differential equations in the model, and the differential equations are as follows based on two types of nodes i=0 and i=1:
to converge the differential equation calculation, one of the two equations above
The coefficients of the terms must be greater than or equal to zero, thus resulting in the following stability conditions:
step a5, selecting a space and a time step; for the explicit finite difference method, when the numerical solution is carried out, the grid division has a certain influence on the calculation result, generally, when the time step delta tau is fixed, the larger the space step value is, the faster the calculation process is, but the error is increased and the accuracy is reduced; in contrast, the smaller the space step length is, the smaller the calculation error is, the high precision is, but the calculation is slow, even the calculation is not converged, and the result is paradoxical, so that the step length is selected to be comprehensively considered;
the radial step length is selected, other conditions are fixed, different radial step lengths are selected for simulation calculation, the calculation result obtained by the large radial step length is found to be higher than that obtained by the small radial step length, the tangential step length is reduced, finer temperature field data in the circumferential direction can be obtained, and meanwhile, the load of the simulation calculation is increased; in addition, for round billets, the stability problem of a difference equation is considered, especially the problem that the tangential step length is small when the difference equation is close to a central node, and the phenomenon of calculation non-convergence is easy to occur;
comprehensively considering, and simultaneously, in order to ensure the uniformity of grid division, the radial step length in table 1 is adopted by the model.
TABLE 1 radial step sizes for different sections
The tangential step length is selected, so that the effect on the result is not as obvious as the radial step length, the heat transfer is mainly carried out through radial transfer for the round billet, the tangential heat transfer only plays a role in uniform axial temperature, if the boundary conditions of the surface of the round billet are inconsistent, the temperature of the surface of the round billet is not uniform, and the smaller the tangential grid is, the higher the calculation result precision is; if the surface cooling conditions of the round billets are the same, the surface temperature is uniform, tangential heat transfer does not exist, and the division of tangential grids has no influence on the calculation result;
the model ignores heat transfer in the running direction of the casting blank, considers that the surface of the round blank is uniformly cooled, and comprehensively considers the inner ring taking delta theta 1 Taken to be 0.524, the outer ring delta theta 2 Taking the inner ring tangential angle to be 0.0524, and taking more than one inner ring tangential angle to mainly consider ensuring the convergence of the core node; meanwhile, as the core nodes mostly exist in the liquid core in the continuous casting process, the convection heat transfer of the molten steel is strong, the temperature gradient is much smaller than that of the conduction heat transfer, and the tangential temperature non-uniformity of the nodes is much smaller than that of the surface nodes, so that the tangential step length does not need to be too fine;
time step selection
After determining the space step length, substituting the space step length into the thermal physical property parameters (the thermal conductivity coefficient takes the maximum value; the density and the specific heat take the minimum value) of the continuous casting blank to be researched according to the stability condition of the difference equation, and determining the value range of the time step length delta tau according to the stability condition of the difference equation;
the method of changing the time step at the fixed slice position is adopted in calculation, namely, the same moving distance of the casting blank in the blank drawing direction in each time step is ensured under different drawing speeds, v is taken as delta tau=0.08, the unit of v is m/min, and the unit of delta tau is s.
Further: the model solution conditions in the step b comprise initial conditions, boundary conditions and thermophysical parameters;
initial conditions
The mathematical model of two-dimensional solidification heat transfer of the continuous casting round billet takes the temperature distribution of molten steel at the meniscus of a crystallizer as an initial condition when time tau=0. Assuming uniform temperature distribution at the meniscus of molten steel in the mold, the temperature at this point is generally considered to be the casting temperature Tc (liquidus temperature+superheat), namely:
T(x，y)＝Tc(0≤r≤D/2,0≤θ≤2,τ＝0)
boundary conditions
Heat flux density of a crystallizer
Calculating the average heat flux density of the crystallizer by using the on-site measured cooling water flow and water inlet and outlet temperature difference of the crystallizer:
q＝Cw·qw·pw·(ΔT)w/Seff
wherein the average density of heat flow of the q-crystallizer is w/m2; cw-is the specific heat of water, 4180J/(kg. Deg.C); qw-crystallizer cooling water flow, m3/s; the pw-cooling water density is 1000kg/m3; (delta T) w-crystallizer cooling water inlet and outlet temperature difference, DEG C; seff-crystallizer effective heat transfer area, m2.
The instantaneous heat flux density qm distribution of the crystallizer along the direction of drawing is calculated by the following formula:
wherein:
wherein the effective length of the L-crystallizer, m; v-pull speed, m/s; n-constant, which varies with the cross-sectional diameter;
L m -distance from the meniscus, m.
b heat flux density of second cold area
This is generally described in terms of the two-cold integrated heat transfer coefficient h:
h＝A·Wn
wherein h-is the comprehensive heat transfer coefficient, W/(m2· ℃ C); w-is the water flow density, L/(m2.s); A. n-coefficient.
Then the secondary cold zone heat flux density q (w/m 2):
q＝h·(Tb-Tw)
tb-is the surface temperature of a casting blank and is at the temperature of DEG C; tw-is the spray water temperature, DEG C;
c air cooling zone
The heat transfer of the air cooling section is calculated by adopting a radiation heat transfer formula:
qrad＝εδ[(Ts+273)4-(T0+273)4)]
wherein qrad-is radiant heat transfer quantity, W/m2; epsilon-is the blackness of the surface of a casting blank and is taken as 0.8; for the heat preservation section, 0.75 is taken; delta-is the Stefan-Boltzmann constant, 5.67X10-8W/(m2.K4); t0-is the ambient temperature, DEG C.
Determination of thermophysical parameters
Liquid-solidus temperature of steel a
The liquidus and solidus of steel are related to the chemical composition of the steel, generally using the empirical formula:
TL＝1539-(70％C+8％Si+5％Mn+30％P+5％S+4％Ni+1.5％Cr)
TS＝1536-(41.5％C+12.3％Si+6.8％Mn+12.4％+18.3％P+4.3％S+1.4％Ni+4.1％Cr)
b specific heat Cp and latent heat of solidification Lf
The specific heat capacity increases with an increase in temperature, but the specific heat capacity does not change much at high temperatures, so the specific heat is treated as a constant.
Latent heat of solidification refers to the heat evolved from cooling from the liquidus temperature to the solidus temperature. For the solidification latent heat Lf, an equivalent specific heat method is adopted, and the solidification latent heat is calculated in the specific heat of the two-phase region, namely the equivalent specific heat of the two-phase region is as follows:
wherein Cs, cl-steel has a solid-state, liquid-state specific heat, J/(kg. DEG C); lf-latent heat of solidification, J/kg;
c coefficient of thermal conductivity
The thermal conductivity is related to the steel grade and temperature, and the thermal conductivity to the solid phase region is considered herein to be a constant λ.
For the liquid phase region and the liquid-solid two-phase region, because of the influence of forced convection of molten steel, the problem of convection heat transfer of the liquid phase is equivalent to a heat conduction process by utilizing an equivalent heat conduction coefficient method, namely using an amplification coefficient m. The equivalent heat conductivity of the liquid phase region is 1-7 times of that of the solid phase region, namely lambda e In this model, the value of m varies in different cooling sections because the convective intensity of molten steel is different in different regions and the intensity thereof decreases from top to bottom. In the two-phase region, lambda is taken here e Is half of the sum of the thermal conductivity of the solid phase region and the effective thermal conductivity of the liquid phase region.
d density of
The density of steel is related to both steel type and temperature, but the variation is not very large, and some studies consider that the effect of the density of steel on the model is small, so it is treated as a constant.
Verification of heat transfer model
The model is built to play a role in actual production, and only the model subjected to verification and correction can be applied. And comparing the calculated temperature with the surface temperature of the casting blank measured by on-site production through model calculation, verifying whether the selected parameters are reliable, and judging whether the calculated temperature of the heat transfer model is close to the actual temperature, wherein if the calculated and actual errors are controlled to be about 5% at maximum, the engineering requirements can be met.
Taking the continuous casting billet with the section phi of 650mm as an example for producing S45CB steel, the working conditions of a casting machine are shown in Table 2.
Table 2 process parameters of s45cb
According to the technological parameters of the casting machine during the field temperature test, the calculation is simulated on the heat transfer model, and the obtained calculation result is compared with the actually measured temperature, and the comparison result is shown in Table 3. As can be seen from the table, the corrected model calculation result is compared with the actual measured temperature, the calculation result of the second cooling zone is better than that of the air cooling zone, the maximum difference of the air cooling zone is 40 ℃, the maximum error is 4.9%, and the model calculation result is closer to the surface temperature of the casting blank in actual production as a whole. Therefore, when the section diameter is 650mm, the parameters of the heat transfer coefficient of the selected secondary cooling zone are suitable.
Table 3 comparison of calculated and measured temperatures
The compiling of the temperature numerical simulation software in the round billet continuous casting process is completed, and the next step can be used for researching the influence of various parameters (such as drawing speed, superheat degree and the like) on the surface temperature of the round billet, the solid phase rate, the length of the liquid core and the thickness of the solidified billet shell, so that the support for the improvement of the continuous casting process is facilitated. And the position of the solidification end point is determined to have important significance for the efficient utilization of the electromagnetic stirring of the secondary cooling end point.
When the section of the continuous casting blank is phi 650mm, taking C45Cr as an example, other process parameters are not changed, the drawing speed is 0.20m/min, the superheat degree is 24 ℃ as a standard, and the influence of the drawing speed or the superheat degree is compared by changing.
Influence of pull-out speed
a influence of the pull rate on the surface temperature
FIG. 3 is a graph showing the effect of pull rate on the surface temperature of a phi 650mm round billet. As can be seen from the figure, the cooling intensity of the crystallizer is higher than that of other cooling sections, and the temperature drops most rapidly. The increase of the pulling rate in the crystallizer has little influence on the surface temperature, and is mainly reflected in the tail end of the crystallizer, and the temperature is increased. As the secondary cooling water quantity is unchanged, the surface temperature is also increased along with the increase of the pulling speed in the secondary cooling area, and the influence in the air cooling area is also great. In short, as the pulling speed increases, the surface temperature of the round billet correspondingly increases.
b influence of pull rate on the solid fraction of the center two-phase region
FIG. 4 shows the effect of pull rate on the solid fraction, and Table 4 shows the data for the two-phase region at different pull rates. From the above, the influence of the pulling speed on the two-phase region and the solid phase rate in the center of the round billet is obvious, and the larger the pulling speed is, the more the solid phase rate curve moves backwards, which shows that the two-phase region appears later when the pulling speed is larger, the pulling speed is increased by 0.02m/min, and the appearance position of the two-phase region moves backwards by about 0.83 m. The larger the pulling speed is, the longer the length of the two-phase region is, and the length of the two-phase region is increased by about 0.9m every 0.02m/min of the pulling speed is increased.
TABLE 4 data for two-phase regions at different pull rates
| Pulling speed (m/min) | Two-phase region initiation (m) | Two-phase zone endpoint (m) | Length of two-phase region (m) |
| 0.18 | 8.18 | 16.21 | 8.03 |
| 0.20 | 9.38 | 18.32 | 8.94 |
| 0.22 | 10.65 | 20.51 | 9.86 |
Table 5 shows the distances from the meniscus, i.e., the lengths, at solid phases of 0.3 and 0.8. It can be seen that the larger the pull rate, the longer the length between 0.3 and 0.8 for the solid phase ratio, the higher the pull rate by 0.02m/min, and the longer the length by about 0.17 m.
TABLE 5 data for solid phases at 0.3 and 0.8
| Pulling speed (m/min) | fs=0.3 distance from meniscus (m) | fs=0.8 distance from meniscus (m) | Length (m) |
| 0.18 | 14.58 | 16.08 | 1.5 |
| 0.20 | 16.5 | 18.17 | 1.67 |
| 0.22 | 18.5 | 20.35 | 1.85 |
c influence of pulling speed on liquid core length and blank shell thickness
Fig. 5 shows the influence of the pull rate on the length of the liquid core, and it can be seen from the figure that the length of the liquid core becomes longer as the pull rate increases, and the relationship substantially conforms to the linear increase. Every time the pulling speed is increased by 0.02m/min, the length of the liquid core is increased by 1.87m.
Fig. 6 is a graph showing the effect of pull rate on the thickness of the blank. From the graph, the thickness change of the blank shell accords with the law of the square root of solidification, the pulling speed has obvious influence on the thickness of the solidified shell, the pulling speed is improved, and the thickness of the blank shell at the same distance from the liquid level is thinned.
Influence of the degree of superheat
a influence of the degree of superheat on the surface temperature
Superheating is the heat evolved from the molten steel as it enters the mold to the liquidus temperature of the steel. Fig. 7 shows the effect of superheat on surface temperature. As can be seen from the figure, the degree of superheat is increased, the surface temperature is also increased, but the influence is not great, the degree of superheat is increased by 10 ℃, the surface temperature is increased by about ten degrees at most, the surface temperature is mainly represented in a crystallizer and a secondary cooling zone, and the surface temperature curves of the air cooling zone are basically overlapped.
b influence of the degree of superheat on the two-phase region, solid fraction
FIG. 8 shows the effect of superheat on the solid fraction, and Table 6 shows the data for the two-phase region at different superheat. From the result, the influence of the degree of superheat on the two-phase region and the solid phase rate in the center of the round billet is smaller, the degree of superheat is increased by 10 ℃, the solid phase rate curve is slightly moved backwards, the occurrence position of the two-phase region is moved backwards by about 0.63m, and the length of the two-phase region is reduced by about 0.4 m.
TABLE 6 data for two-phase regions at different superheat levels
| Degree of superheat (. Degree. C.) | Two-phase region initiation (m) | Two-phase zone endpoint (m) | Length of two-phase region (m) |
| 14 | 8.64 | 18.06 | 9.42 |
| 24 | 9.38 | 18.32 | 8.94 |
| 34 | 9.91 | 18.53 | 8.62 |
Table 7 shows the distances from the meniscus, i.e., the lengths, at solid phases of 0.3 and 0.8. As can be seen from the table, the increase in superheat is 10℃and the positions where the solid phase ratio is 0.3 and 0.8 appear later, the length between them increasing slightly.
TABLE 7 data for solid phases at 0.3 and 0.8
| Degree of superheat (. Degree. C.) | fs=0.3 distance from meniscus (m) | fs=0.8 distance from meniscus (m) | Length (m) |
| 14 | 16.23 | 17.9 | 1.58 |
| 24 | 16.5 | 18.17 | 1.67 |
| 34 | 16.7 | 18.39 | 1.69 |
c influence of superheat on liquid core length and solidified shell thickness
Fig. 9 is a graph showing the effect of superheat on wick length. From the figure, the influence of the degree of superheat on the length of the liquid core is small, the degree of superheat is increased, and the solidification time is prolonged. The superheat degree is increased by 10 ℃, and the length of the liquid core is increased by about 0.23 m.
Fig. 10 shows the effect of superheat on shell thickness. The change of the superheat degree can be seen from the graph, the thickness change of the shell at the same distance from the liquid level is small, the curves basically coincide in the early stage of continuous casting, and the thickness change slightly occurs in the later stage of continuous casting.
The present embodiment is only exemplary of the present patent, and does not limit the scope of protection thereof, and those skilled in the art may also change the part thereof, so long as the spirit of the present patent is not exceeded, and the present patent is within the scope of protection thereof.
Claims (4)
1. A method for simulating the solidification process of a round billet for continuous casting, comprising the steps of:
step a, establishing a round billet continuous casting solidification heat transfer mathematical model;
step b, determining model solution conditions;
step c, verifying a heat transfer model;
step d, simulation results and analysis; comparing the model calculation with the casting blank surface temperature measured by on-site production, verifying whether the selected parameters are reliable, and judging whether the temperature calculated by the heat transfer model is close to the actual temperature, wherein if the error between the calculation and the actual temperature is less than 5%, the engineering requirement can be met;
the establishing a round billet continuous casting solidification heat transfer mathematical model in the step a comprises the following steps:
step a1, establishing a round billet continuous casting solidification heat transfer mathematical model coordinate system; regarding the continuous casting process as a process that a two-dimensional slice of a casting blank cross section moves downwards along the direction of drawing the blank of a casting machine at the speed of drawing the blank, updating the temperature field and boundary conditions once every time step, namely, the distance corresponding to the motion V.Deltaτ of the slice, wherein the slice respectively transfers heat through a crystallizer, a secondary cooling area and a radiation air cooling area in the continuous casting machine, the boundary conditions are continuously changed, the temperature field information of the slice is also continuously updated, the center point of a molten steel meniscus in the crystallizer is taken as the origin of a space-time coordinate system Y theta Z τ, the direction of drawing the blank is Z, the imaginary time axis O tau coincides with the OZ axis, the upper boundary of a certain length which is larger than the metallurgical length L is taken as Z, and the metallurgical length L is taken as the cutting position of the casting blank from the length L of the meniscus of the crystallizer 0 Correspondingly, there is a temporal upper bound tau 0 The casting blank temperature field function T (gamma, theta, Z, tau) is defined on the space-time coordinate system, and the gamma radius, the theta angle, the Z phase length and the tau time are as follows: beta is more than or equal to 0 and less than or equal to (D/2), D is the diameter, and tau is more than or equal to 0 and less than or equal to tau o The method comprises the steps of carrying out a first treatment on the surface of the For solid phase, liquid phase and solid-liquid two-phase regions of a continuous casting blank, the heat transfer of the casting blank meets a unified form of unsteady heat transfer partial differential equation:
wherein: gradT temperature gradient, DEG C/m; div divergence symbols; ρDensity of steel Kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the C constant pressure specific heat, J/(Kg. DEG C); lambda-coefficient of thermal conductivity, W/(m·deg.C); τ time, s; a temperature T;
the general differential equation is very difficult to directly solve under the complex boundary condition of continuous casting, namely, the solution is difficult to solve, and the general processing method is to make reasonable assumptions aiming at specific continuous casting process conditions so as to solve;
according to the above assumed conditions, the basic differential equation based on the round billet continuous casting solidification heat transfer in the polar coordinate system is:
the deduction is carried out:
and (3) finishing to obtain:
wherein the density of rho-steel Kg/m3; ce-specific heat, J/(Kg. Deg.C); λe-effective thermal conductivity, W/(m·deg.C); angle θ;
step a2, variable-pitch meshing; for a round billet, because the established heat transfer differential equation is in a polar coordinate form, the cross section of the round billet is generally divided into grids according to the radial direction and the tangential direction or the circumferential direction, and because the round billet is closer to the center of a casting blank after being determined by the radial step delta r and the tangential step delta theta, the grids are finer, and the stability of differential equation calculation is poor and difficult to converge due to the tiny grids; increasing the tangential angle can increase the central tangential step length, but the surface tangential step length is too large at the moment, so that the calculation accuracy is poor;
dividing the cross section of the round billet into grids with different tangential angles, wherein the junction position of the inner ring and the outer ring can be selected by oneself, the position of the junction position is 1/4 of the cross section diameter, the tangential angle of the inner ring is large, the tangential angle of the outer ring is small, the grid division with variable spacing is adopted, the grid division is denser in the surface area of a casting blank with sensitive temperature change, and the grid division is sparse in the central area of the casting blank with gentle temperature change;
step a3, establishing a differential equation; the heat transfer differential equation is discretized and solved by utilizing a finite difference method, six different differential equations can be established according to the grid division in the step a2, and the differential equations are sequentially a central node, an inner ring internal node, an inner ring junction node, an outer ring internal node and a surface node;
step a4, determining equation stability conditions; the calculation proves that the stability requirement of the center differential equation is the most strict in six differential equations in the model, and the differential equations are as follows based on two types of nodes i=0 and i=1:
to converge the differential equation calculation, one of the two equations above
The coefficients of the terms must be greater than or equal to zero, thus resulting in the following stability conditions:
step a5, selecting a space and a time step; for the explicit finite difference method, when the numerical solution is carried out, the grid division has a certain influence on the calculation result, generally, when the time step delta tau is fixed, the larger the space step value is, the faster the calculation process is, but the error is increased and the accuracy is reduced; in contrast, the smaller the space step length is, the smaller the calculation error is, the high precision is, but the calculation is slow, even the calculation is not converged, and the result is paradoxical, so that the step length is selected to be comprehensively considered;
the radial step length is selected, other conditions are fixed, different radial step lengths are selected for simulation calculation, the calculation result obtained by the large radial step length is found to be higher than that obtained by the small radial step length, the tangential step length is reduced, finer temperature field data in the circumferential direction can be obtained, and meanwhile, the load of the simulation calculation is increased; in addition, for round billets, the stability problem of a difference equation is considered, especially the problem that the tangential step length is small when the difference equation is close to a central node, and the phenomenon of calculation non-convergence is easy to occur;
the tangential step length is selected, so that the effect on the result is not as obvious as the radial step length, because for the round billet, the heat transfer is mainly carried out through radial transfer, the tangential heat transfer only plays a role in uniform axial temperature, if the boundary conditions of the surface of the round billet are inconsistent, the temperature of the surface of the round billet is not uniform, and at the moment, the finer the tangential grid is, the higher the calculation result precision is; if the surface cooling conditions of the round billets are the same, the surface temperature is uniform, tangential heat transfer does not exist, and the division of tangential grids has no influence on the calculation result;
the model ignores heat transfer in the running direction of the casting blank, considers that the surface of the round blank is uniformly cooled, and comprehensively considers tangential step length delta theta of the inner ring 1 Taken to be 0.524, the tangential step delta theta of the outer ring 2 Taking the angle as 0.0524, and taking larger tangential angles of the inner ring, mainly considering the convergence of the core nodes; meanwhile, as the core nodes mostly exist in the liquid core in the continuous casting process, the convection heat transfer of the molten steel is strong, the temperature gradient is much smaller than that of the conduction heat transfer, and the tangential temperature non-uniformity of the nodes is much smaller than that of the surface nodes, so that the tangential step length does not need to be too fine; Δθ 1 Is the tangential step length of the inner ring, delta theta 2 The tangential step length of the outer ring is expressed in radians.
Time step selection
After determining the space step length, substituting the space step length into the thermophysical parameters of the continuous casting blank to be researched according to the stability condition of the differential equation, and taking the maximum value of the heat conductivity coefficient; the density and the specific heat take the minimum value, and the value range of the time step delta tau can be determined according to the stability condition of the differential equation;
the method of changing the time step at the fixed slicing position is adopted in calculation, namely, the same moving distance of the casting blank in the blank drawing direction in each time step is ensured under different drawing speeds, and V.delta tau=0.8 is taken, wherein V is m/min, and delta tau is s.
2. A method of simulating a solidification process of a continuously cast round billet according to claim 1, wherein: the model solution conditions in the step b comprise initial conditions, boundary conditions and thermophysical parameters.
3. A method of simulating a solidification process of a continuously cast round billet according to claim 1, wherein: the assumptions made in step a1 for model simplification include:
(1) the heat transfer problem of continuous casting is simplified into a two-dimensional problem, and the heat transfer in the running direction of the casting blank can be ignored because the length of the casting blank is much larger than the cross section size of the casting blank, and the surface of the round blank is uniformly cooled;
(2) assuming that the temperature of the meniscus molten steel of the crystallizer is the same as the casting temperature;
(3) ignoring the dimensional change of the casting blank caused by solidification, cooling and shrinkage;
(4) the temperature of a certain space point in the direction of drawing the blank does not change with time, namely, the continuous casting solidification heat transfer is considered to be a steady heat transfer process;
(5) considering the influence of forced convection of molten steel on heat transfer of casting blank, the influence of forced convection is processed into effective heat conductivity coefficient lambda of molten steel e The thermal conductivity of the region with liquid phase is larger than that of the solid phase region;
(6) neglecting the influence of the vibration of the crystallizer and the electromagnetic stirring on solidification heat transfer.
4. A method of simulating a solidification process of a continuously cast round billet according to claim 1, wherein: the six different differential equations in the step a3 are as follows:
assume that:
wherein: Δθ 1 -tangential step of the inner ring; Δθ 2 The tangential step size of the outer ring,
at the moment, the temperatures at points i +1, j,
the temperature of points i-1 and j at the moment; a is a code number, which represents the calculation result of the following formula;
(1) center node i=0, j=0:
at this time have
Because the center r=0, so
According to the lobida law:
the equation becomes
The display differential format of the equation is:
symmetrical at the center, so there is
So that:
i.e.
(2) Inner ring internal node: i=1 to M 1 -1，j＝1～N 1 ：
The display differential format of the equation is:
and (3) finishing to obtain:
(3) inner ring interface node i=m 1 ，j＝1～N 1 ：
The difference equation is the same as that shown in (2), except that when i+1, the point runs from the inner ring to the outer ring, and the axial grid of the inner and outer ringsThe number is different, so the size of j also changes, and the same angle can be obtained: (j' -1) Δθ 2 ＝(j-1)Δθ 1
Obtaining the product
The differential equation is:
wherein the method comprises the steps of
T 1 、T 3 、T 4 The temperature of the liquid crystal is not changed,
(4) outer ring interface node i=m 1 +1，j＝1～N 2 ：
As the difference equation in (2) is the same, when i-1, the points run from the outer ring to the inner ring, and the axial grids of the inner ring and the outer ring are different, so that the j is also changed, and the j is obtained according to the same angle: (j-1) Δθ 2 ＝(j′-1)Δθ 1
Obtaining the product
And is the outer ring at this time, the tangential step length of the outer ring is delta theta 2 ，A 2 Becomes A 3 ，
The differential equation is:
wherein:
(5) outer ring internal node: i=m 1 +2～M-1，j＝1～N 2 ：
The difference equation is the same as that in (2), except that the tangential step is delta theta due to the outer ring at this time 2 ，A 2 Becomes A 3 ，
(6) Surface node: i=m, j=1 to N 2 ：
At this time have no
So T in the differential equation in (5) 2 And T 5 Is->
The differential equation at the time of availability is eliminated,
at this time, the boundary condition is a Neumann boundary condition, and the heat flux density q can be obtained, and the expression is:
representing the difference as a second-order precision center difference;
is deformed and then is brought into the following formula T 2 And T 5 Medium elimination
Has the following components
Is available in the form of
At this point, the expression is again:
expressed by backward differential:
finally, the method can obtain:
in the above formulae, lambda 1 ～λ 5 Respectively, is a weighted average value of effective heat conductivity coefficients at two temperatures in Ti (i=1-5), n is a ratio of the number of outer ring circumferential grids to the number of inner ring circumferential grids, and n=delta theta 1 /Δθ 2 。
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102110188A (en) * | 2009-12-25 | 2011-06-29 | 鞍钢股份有限公司 | Method for calculating continuous casting flow temperature and solid phase rate distribution |
| CN107052292A (en) * | 2017-01-04 | 2017-08-18 | 东北大学 | It is a kind of that the Hot Charging of Continuous Casting Slab tracking and calculating method calculated is distributed based on thermal physical property parameter |
| CN108647376A (en) * | 2018-03-23 | 2018-10-12 | 东北大学 | A kind of analogy method of continuous casting billet gross segregation |
-
2018
- 2018-12-28 CN CN201811624680.9A patent/CN109446748B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102110188A (en) * | 2009-12-25 | 2011-06-29 | 鞍钢股份有限公司 | Method for calculating continuous casting flow temperature and solid phase rate distribution |
| CN107052292A (en) * | 2017-01-04 | 2017-08-18 | 东北大学 | It is a kind of that the Hot Charging of Continuous Casting Slab tracking and calculating method calculated is distributed based on thermal physical property parameter |
| CN108647376A (en) * | 2018-03-23 | 2018-10-12 | 东北大学 | A kind of analogy method of continuous casting billet gross segregation |
Non-Patent Citations (3)
| Title |
|---|
| 合金钢连铸坯动态凝固过程数值模拟;贾光霖等;《东北大学学报(自然科学版)》;20040215;第25卷(第02期);30-33 * |
| 圆坯连铸温度场模拟;卫超等;《铸造》;20020222;第51卷(第02期);44-46 * |
| 大圆坯连铸传热数值模拟;郭春等;《连铸》;20160215;第41卷(第01期);41-45 * |
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