CN100566888C - The formulating method of continuous casting mold of round billets stirring parameter - Google Patents

Abstract

The present invention relates to the formulating method of continuous casting mold of round billets stirring parameter.Less or research conclusion differs bigger problem to definite research of mixing parametric in order to overcome at present, invent a kind of in conjunction with steel grade, strand size, casting machine and electromagnetic stirring equipment, by Numerical Simulation Analysis and verification experimental verification, determine the current strength and the isoparametric formulating method of frequency of electromagnetic agitation.This method is on the basis of electromagnetic agitation Distribution of Magnetic Field analog result, to the calculating that is coupled of flow field, temperature field and the field trash movement locus of molten steel in the electromagnetic agitation process crystallizer, do at phenomenons such as the flowing of molten steel, solidification and heat transfer and field trash tracks and to investigate the reasonability of judging stirring parameter, and again result of calculation and field sampling test are fed back comparative analysis, to determine stirring parameter.Use method of the present invention, can determine the current strength and the frequency of electromagnetic agitation under the different condition fast, accurately and effectively, obviously reduce casting billet surface and subsurface inclusion thing and bubble, enlarge equiaxial crystal ratio, improve the core quality, improve dense structure's property and uniformity.

Description

The formulating method of continuous casting mold of round billets stirring parameter

Technical field

The present invention relates to the production Technology of continuous casting mold of round billets electromagnetic agitation, relate in particular to definite method of continuous casting mold electromagnetic agitation current strength and frequency.

Technical background

Along with the progress of the development of society and science and technology, to the strand internal soundness, particularly to the casting blank solidification structure refinement and homogenize and have higher requirement.The crystallizer electromagnetic agitating technology is a kind of effective means that metal solidification process is controlled, have a wide range of applications and deep industrial foundation, to the equiaxial crystal ratio, the thinning solidification structure that improve strand, improve field trash and distribute, promote homogenization of composition and improve dense structure's property etc. to have important function.The essence of electromagnetic agitation is to strengthen the motion of molten steel in the liquid core by the electromagnetic force of inducting in casting blank liquid core, strengthen convection current, heat transfer and the mass transport process of molten steel thus, thereby the process of setting of control strand, play important effect to improving slab quality, become a particularly important ring of circle/billet continuous casting technology of continuous casting.Its metallurgical mechanism and effect are seen Fig. 1.

The crystallizer electromagnetic agitation can be according to the change of working condition, and online adjusting stirring parameter makes strand all have good quality under different working conditions.The main technologic parameters of electromagnetic agitation is exciting current intensity and frequency.Have only the rational mixing parametric of determining just can reach the purpose of improving slab quality, otherwise slab quality can worsen on the contrary.

The relevant patent of having applied for is mostly at the equipment of realizing the crystallizer electromagnetic agitation, as patent CN2593937, CN2593938, CN2474252, CN2044898, CN2176821.And with the determining of equipment mixing parametric of equal importance, in publishing an article, only relevant for exciting current intensity and the frequency rule that influences to electromagnetic force, and various report conclusion differs bigger, the influence of mixing parametric stream field, temperature field and field trash, report are just seldom.Report to mixing parametric does not form final conclusion as yet at present, and the control method of mixing parametric was not reported.

As can be seen from Figure 1, the metallurgical effect of electromagnetic agitation is realized by stress effect and fuel factor, and the tie that connects stress effect and fuel factor is flowing of molten steel, thoroughly analyzes the influence of mixing parametric to this three so have only, and could determine the rational and effective technological parameter.

The present invention be overcome remedy at present big multiple enterprises or the inventor more to the equipment research of crystallizer electromagnetic agitation, less or research conclusion differs bigger problem and with definite research of equipment mixing parametric of equal importance, invent a kind of in conjunction with steel grade, casting blank cross-section size, casting machine and electromagnetic stirring equipment, by Numerical Simulation Analysis and verification experimental verification, determine the current strength and the isoparametric formulating method of frequency of a reliable crystallizer electromagnetic agitation, so that produce the more continuous casting billet of high-quality.

Summary of the invention

The present invention will provide a kind of formulating method of continuous casting mold of round billets stirring parameter, the technical issues that need to address are in conjunction with strand size, casting machine and electromagnetic stirring equipment, determine the optimum current intensity and the frequency of continuous casting mold of round billets electromagnetic agitation, thereby reduce surface and subsurface inclusion thing and bubble, enlarge equiaxial crystal ratio, improve the core quality, make continuous cast round billets slab quality be improved significantly.

The basic ideas of invention are, because strand is under the effect of electromagnetic agitation, many processes such as the molten steel in the process of setting flows, heat transfer and field trash movement locus all are nonlinear change, theory analysis to whole process is difficult to derive exactly with analytic method, can only calculate and analyze it by numerical computation method.This research method is carried out simulation calculation and analysis by numbered analog simulation to crystallizer electromagnetic agitation process exactly, and combines with produced on-site and to be verified.

The formulating method of continuous casting mold of round billets stirring parameter of the present invention is mainly realized by following method.Promptly on the basis of electromagnetic agitation Distribution of Magnetic Field analog result, to the calculating that is coupled of three-dimensional flow field, temperature field and the field trash movement locus of molten steel in the electromagnetic agitation process crystallizer, do at phenomenons such as the flowing of molten steel, solidification and heat transfer and field trash tracks and to investigate the reasonability of judging stirring parameter, and again result of calculation and field sampling test are fed back comparative analysis, with final definite rational stirring parameter.

The formulating method of above-mentioned continuous casting mold of round billets stirring parameter, crystallizer electromagnetic agitation electromagnetic field distribution simulation wherein, the magnetic field partial differential equation of employing and electric field partial differential equation are respectively:

${\▿}^{2}A-\mathrm{\μ\ϵ}\frac{{\∂}^{2}A}{\∂t^2}=-\mathrm{\μj}$

The strand flow field wherein and the governing equation in temperature field comprise continuity equation: $\frac{\∂\left(\mathrm{\ρ}{u}_i\right)}{\∂x_i}=0$

The equation of momentum: $\frac{\∂\left(\mathrm{\ρ}{u}_j{u}_i\right)}{\∂x_j}=-\frac{\∂p}{\∂x_i}+\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+{\mathrm{\μ}}_t)(\frac{\∂u_i}{\∂x_j}+\frac{\∂u_j}{\∂x_i})\right]+F_i$

Energy equation: $\frac{\∂\left(\mathrm{\ρ}{u}_{j}T\right)}{\∂x_j}=\frac{\∂}{\∂x_j}\left[(\frac{\mathrm{\μ}}{\mathrm{Pr}}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_T})\frac{\∂T}{\∂x_j}\right]-\frac{\∂\left(\mathrm{\ρ}{u}_j\mathrm{\ΔH}\right)}{\∂x_j}$

The k equation: $\frac{\∂\left(\mathrm{\ρ}{u}_{j}k\right)}{\∂x_j}=\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_k})\frac{\∂k}{\∂x_j}\right]+G-\mathrm{\ρ\ϵ}-D_k$

The ε equation: $\frac{\∂\left(\mathrm{\ρ}{u}_j\mathrm{\ϵ}\right)}{\∂x_j}=\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_{\mathrm{\ϵ}}})\frac{\∂\mathrm{\ϵ}}{\∂x_j}\right]{+f}_1{C}_{1}G\frac{\mathrm{\ϵ}}{k}-f_2{C}_2\mathrm{\ρ}\frac{{\mathrm{\ϵ}}^2}{k}{+E}_{\mathrm{\ϵ}}$

The calculating that is coupled of field trash movement locus wherein, on above-mentioned Flow Field Calculation result's basis, add field trash movement locus discrete model governing equation, associated clip foreign material parameter and divergent boundary condition are set, continuation is to the calculating that is coupled of the flow field under the electromagnetic agitation condition, temperature field and field trash track, the particle transmission equation: $m=\frac{d{V}_p}{\mathrm{dt}}=F_P+F_B+F_A+F_D.$

The data of magnetic field, flow field, temperature field and the field trash movement locus of the round mold electromagnetic agitation that goes out according to analog computation wherein, and in the crystallizer effectively the MOLTEN STEEL FLOW speed of stirring area between 0.2-0.25m/s, can produce enough big centrifugal force and shearing force; Can make the covering slag melt well; Can cause hot top effect; The time long enough that field trash is stopped in crystallizer, make its as far as possible phenomenon such as come-up do to investigate and judge, the data that go out with the correction analog computation.

Wherein adopting through analog computation, investigation, judgement and revising under resulting exciting current intensity in back and the frequency condition, detect the quality such as subcrack, core crackle, shrinkage cavity, center porosity, rimhole and equiaxial crystal ratio of strand, determine stirring parameter at last.

The invention has the beneficial effects as follows, adopt the control method of round mold electromagnetic agitation electrical quantity of the present invention, the reasonability of existing stirring parameter and the power of electromagnetic agitation intensity can be judged fast, accurately and effectively, to determine required optimum current intensity and the frequency of electromagnetic agitation under the different condition; Simultaneously, the parameter behind the optimizing application can obviously reduce casting billet surface and subsurface inclusion thing and bubble, enlarges equiaxial crystal ratio, improves the core quality, improves dense structure's property and uniformity and reduces the bleed-out probability.

Description of drawings

The metallurgical mechanism of accompanying drawing 1 crystallizer electromagnetic agitation and effect schematic diagram, accompanying drawing 2 round mold stirring parameter formulation process flow charts of the present invention, accompanying drawing 3 is to be round mold electromagnetic agitation schematic diagram of the present invention.

The specific embodiment

As accompanying drawing 2 are continuous casting mold of round billets stirring parameter formulating method implementing procedure figure of the present invention.Concrete steps are as follows.

1. crystallizer electromagnetic agitation electromagnetic field distributes.

Electromagnetic field phenomenon in the simulation crystallizer electromagnetic agitation process must be set up and describe this process mathematical model.In crystallizer electromagnetic agitation process, therefore the complexity of electromagnetic field and flow field coupled problem when setting up Mathematical Modeling, is easy to handle and don't lose its meaning in order to make problem, does following hypothesis:

1. the used alternating magnetic field frequency of electromagnetic agitation generally arrives 10Hz 1, belongs to the magnetic quasi-static field, so ignore displacement current.

2. in the electromagnetic agitation process, magnetic is very little, and document is estimated to be approximately 0.01, so ignore the influence of molten steel motion to electromagnetic field, in calculating electromagnetic problems, strand is considered as static.

The basic law that external electromagnetic field distributes is described by the Maxwell equation group, and the Maxwell differential equation group is as follows:

$\▿\×E=-\frac{\∂B}{\∂t}---\left(1\right)$

$\▿\×H=j---\left(2\right)$

$\▿\·B=0---\left(3\right)$

$\▿\·D={\mathrm{\ρ}}_e---\left(4\right)$

In the formula: E is the electric-field intensity in the medium; B is the magnetic induction intensity in the medium; H is the magnetic field intensity in the medium; J is the conduction current density in the medium; D is the dielectric displacement in the medium; ρ _eBe the electric charge volume density in the medium.

For being characterized in the macroscopic properties of medium under the electromagnetic field effect, outside last equation, also need replenish the constitutive equation of describing the material electromagnetic property:

D＝εE (5)

B＝μH (6)

j＝σE (7)

In the formula: ε is the dielectric constant of medium; μ is the medium magnetic conductivity; σ is the medium electrical conductivity.

By the Maxwell equation group as can be seen, the electromagnetism variable is interweaved together, has increased the difficulty to problem solving like this.For the simplification problem, usually, electric field variable and magnetic field variable are separated, thereby formed the independently partial differential equation in electric field or magnetic field, so that numerical computations by means of the method for a scalar electromotive force of definition and a vector magnetic potential.

Separating normally of electromagnetic problems tried to achieve by introducing various bit functions, adopts the magnetic vector potential method here, introduces vector magnetic potential A and scalar electromotive force

They are defined as follows:

$B=\▿\×A---\left(8\right)$

It should be noted that like that, only limit a curl of vector and can not determine this vector (being vector magnetic potential A here) uniquely,, also should its divergence be limited in order to guarantee the uniqueness of vector magnetic potential suc as formula (8).From the angle of mathematics, this restriction can be selected arbitrarily; From angle of practical application, then should choose suitable qualifications, thereby simplify the differential equation.Usually select Lorentz (Lorentz) condition for use, with vector magnetic potential A and scalar electromotive force

Connect, the Lorentz qualifications can be expressed as:

More than Ding Yi vector magnetic potential and scalar energy of position satisfy Faraday's electromagnetic induction law and Gauss's magnetic flux law automatically, and then are applied in the Ampere circuit law and the Gauss law of flux, through deriving magnetic field partial differential equation and electric field partial differential equation.

${\▿}^{2}A-\mathrm{\μ\ϵ}\frac{{\∂}^{2}A}{\∂t^2}=-\mathrm{\μj}---\left(11\right)$

Be Laplace operator

${\▿}^2=(\frac{{\∂}^2}{\∂x^2}+\frac{{\∂}^2}{\∂y^2}+\frac{{\∂}^2}{\∂z^2})---\left(13\right)$

Formula (11) has identical form with formula (12) obviously, is symmetrical fully, this means that the method for finding the solution them is identical.So far, we can carry out numerical solution to formula (11) and formula (12), as adopting FInite Element, solve the field distribution of magnetic potential and electromotive force, and then through transforming, can obtain the various physical quantitys of electromagnetic field, as magnetic induction intensity, energy storage etc.

Fig. 3 is a crystallizer electromagnetic agitation schematic diagram, does not wherein comprise the air part.Load three-phase current density on three pairs of stator winding coils, the phase difference of each phase current is 120 °, loads synchronous current density on two relative coils.Field boundary condition is: the magnetic line of force is parallel with the outer surface that surrounds the agitator air.

In the result of calculation, electromagnetic force is represented with hourly value: $F=\frac{1}{2}\mathrm{Re}(J\×B^{*})$

2. under the crystallizer electromagnetic agitation, flow field of molten steel and Numerical Simulation of Temperature Field in the crystallizer.

In crystallizer electromagnetic agitation process, the complexity of electromagnetic field and flow field coupled problem when setting up Mathematical Modeling, is easy to handle and don't lose its meaning in order to make problem, does following hypothesis:

1. the molten steel in the crystallizer flows and is steady-flow;

2. molten steel is pressed the homogeneous phase media processes in the crystallizer, and whole strand all is considered as liquid state;

3. the crystallizer inner fluid is incompressible Newtonian fluid, and its rerum natura is a constant;

4. ignore the tapering and the influence of vibration of crystallizer wall to flowing;

5. will the time electromagnetic force that becomes replace with hourly value.

Under the crystallizer electromagnetic agitation, the governing equation in strand flow field and temperature field comprises continuity equation, the equation of momentum, energy equation and k-ε turbulence model.

(1) continuity equation: $\frac{\∂\left(\mathrm{\ρ}{u}_i\right)}{{\∂x}_i}=0---\left(14\right)$

ρ is a density in the formula, kg/m ³, u _i(i=1,2,3) are the speed under the different coordinate directions, m/s.

(2) equation of momentum:

$\frac{\∂\left(\mathrm{\ρ}{u}_j{u}_i\right)}{\∂x_j}=-\frac{\∂p}{\∂x_i}+\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+{\mathrm{\μ}}_t)(\frac{\∂u_i}{\∂x_j}+\frac{\∂u_j}{\∂x_i})\right]+F_i---\left(15\right)$

μ is a dynamic viscosity in the formula, Pas; P is a pressure, Pa; μ _tBe turbulent viscosity

${\mathrm{\μ}}_t=\mathrm{\ρ}{C}_{\mathrm{\μ}}{f}_{\mathrm{\μ}}\frac{k^2}{\mathrm{\ϵ}}---\left(16\right)$

f _μ＝exp[-3.4/(1+Re _t/50) ²] (17)

${\mathrm{Re}}_t=\frac{{\mathrm{\ρk}}^2}{\mathrm{\μ\ϵ}}---\left(18\right)$

Wherein k is a Turbulent Kinetic, and ε is a turbulence dissipation rate, C _μ=0.09.

(3) energy equation:

$\frac{\∂\left(\mathrm{\ρ}{u}_{j}T\right)}{\∂x_j}=\frac{\∂}{\∂x_j}\left[(\frac{\mathrm{\μ}}{\mathrm{Pr}}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_T})\frac{\∂T}{\∂x_j}\right]-\frac{\∂\left(\mathrm{\ρ}{u}_j\mathrm{\ΔH}\right)}{\∂x_j}---\left(19\right)$

T is a temperature in the formula, and Pr is Prandtl number Pr=μ C _p/ λ, C _pHold for constant pressure specific heat, λ is a thermal conductivity.σ _T＝1.0。

(4) k equation:

$\frac{\∂\left(\mathrm{\ρ}{u}_{j}k\right)}{\∂x_j}=\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_k})\frac{\∂k}{\∂x_j}\right]+G-\mathrm{\ρ\ϵ}-D_k---\left(20\right)$

In the formula:

$G={\mathrm{\μ}}_t(\frac{{\∂u}_i}{{\∂x}_j}+\frac{{\∂u}_j}{\∂x_i})\frac{{\∂u}_i}{\∂x_j}---\left(21\right)$

$D_k=2\mathrm{\μ}{\left(\frac{\∂\sqrt{k}}{{\∂x}_i}\right)}^2$ σ wherein _k=1.0.(22)

(5) ε equation:

$\frac{\∂\left(\mathrm{\ρ}{u}_j\mathrm{\ϵ}\right)}{\∂x_j}=\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_{\mathrm{\ϵ}}})\frac{\∂\mathrm{\ϵ}}{\∂x_j}\right]{+f}_1{C}_{1}G\frac{\mathrm{\ϵ}}{k}-f_2{C}_2\mathrm{\ρ}\frac{{\mathrm{\ϵ}}^2}{k}{+E}_{\mathrm{\ϵ}}---\left(23\right)$

In the formula

$E_{\mathrm{\ϵ}}=2\frac{{\mathrm{\μ}}_t\mathrm{\μ}}{\mathrm{\ρ}}{\left(\frac{{\∂}^2{u}_i}{\∂x_j{\∂x}_k}\right)}^2---\left(24\right)$

f ₂＝1-0.3exp(-Re _t ²) (25)

F wherein ₁=1.0, C ₁=1.44, C ₂=1.92, σ _ε=1.3.Boundary condition is as follows:

1. wall: be treated to no slippage wall with the wall function method, it is given that temperature is pressed liquidus temperature.

2. top surface: normal velocity is zero, and the normal direction derivative of its dependent variable is zero, the temperature thermal insulation.

3. enter the mouth: entrance velocity is converted by casting rate, and temperature is given by pouring temperature.

4. outlet: get the mass flow boundary condition, to guarantee the molten steel conservation of mass of coming in and going out; The temperature thermal insulation.

Flow Field Calculation adopts the discrete flow field of the finite volume method differential equation, and with staggered-mesh storage speed component, Flow Field Calculation adopts the Simplec algorithm, when the quality source of continuity equation less than 10 ^-4The time, promptly think iteration convergence.Adopt the Fortran Programming with Pascal Language, the electromagnetic force that ANSYS is calculated adds the momentum source item.The crystallizer computational length is 1.8m.

3. field trash trace simulation.

On above-mentioned Flow Field Calculation result's basis, add field trash movement locus discrete model governing equation, associated clip foreign material parameter and divergent boundary condition are set, continue the calculating that is coupled of the flow field under the electromagnetic agitation condition, temperature field and field trash track.

The particle transmission equation:

$m\frac{{\mathrm{dV}}_p}{\mathrm{dt}}=F_P+F_B+F_A+F_D---\left(26\right)$

In the formula, m is a mass particle, V _pBe particle rapidity, t represents the time, F _DBe the suffered viscous drag of particle:

$F_D=\frac{1}{8}\mathrm{\π}{d}^2\mathrm{\ρ}{C}_D\left|V_p\right|V_p---\left(27\right)$

Wherein, viscous drag coefficient C _DDetermine by Reynolds number:

When 10 ^-3＜Re＜2 o'clock, C _D=24/Re (28)

When 2≤Re≤500, C _D=18.5/Re ^0.6(29)

When 500＜Re＜200000, C _D=0.44 (30)

When Re 〉=200000, C _D=0.09 (31)

The Reynolds number of ion is

$\mathrm{Re}=\frac{\mathrm{\ρd}\left|V_R\right|}{\mathrm{\μ}}---\left(32\right)$

Wherein, d is an ionic diameter, V _RBe the relative velocity of molten steel and particle two-phase, its mould is

$\left|V_R\right|=\sqrt{{(u-u_P)}^2+{(v-v_P)}^2+{(w-w_P)}^2}---\left(33\right)$

F _PThe power that causes for the molten steel barometric gradient: $F_P=-\frac{1}{4}\mathrm{\π}{d}^3\▿p---\left(34\right)$

F _BBe the buoyancy of molten steel to particle: $F_B=\frac{1}{6}\mathrm{\π}{d}^3({\mathrm{\ρ}}_P-\mathrm{\ρ})g---\left(35\right)$

F _ABe molten steel additional mass power: $F_A=-\frac{1}{12}\mathrm{\π}{d}^3\mathrm{\ρ}\frac{{\mathrm{dV}}_p}{\mathrm{dt}}---\left(36\right)$

Ion velocity and its position rate close

$u_p=\frac{{\mathrm{dx}}_p}{\mathrm{dt}},$ $v_p=\frac{d{y}_p}{\mathrm{dt}},$ $w_p=\frac{{\mathrm{dz}}_p}{\mathrm{dt}}---\left(37\right)$

(x wherein _P, y _P, z _P) be that particle is in t residing position of the moment.

Field trash relevant parameter: granularity 5～50 μ m, density 3500kg/m ³, mass flowrate 4 * 10 ^-5Kg/s.

4. investigate and judge correction.

Magnetic field, flow field, temperature field and field trash movement locus according to said method analog computation round mold electromagnetic agitation.Judge correction according to result of calculation by following standard or phenomenon:

(1) certain stirring intensity must be arranged, make the MOLTEN STEEL FLOW speed of effective stirring area in the crystallizer reach certain value, usually at 0.2～0.25m/s, to produce enough big centrifugal force and shearing force.

(2) should make near the stable molten steel of meniscus that makes again of meniscus that certain flowing velocity is arranged, make the covering slag melt well, both help improving covering slag and absorbed bubble and field trash, help improving its lubrication again.

(3) improve the position of hot-zone as far as possible, cause hot top effect, the degree of superheat is disappeared as early as possible.

(4) the time long enough that stops in crystallizer of field trash makes its come-up as far as possible.

5. field trial is fed back.

Field trial feedback: resulting optimal excitation current strength of numerical simulation and frequency application are arrived actual production, checking actual effect, the improvement degree of detection slab quality.

The concrete example of implementing: casting machine device parameter: the round billet continuous casting machine, type of stirrer is for as shown in Figure 3.Concrete parameter is as shown in table 1.

The parameter of table 1 strand size and crystallizer magnetic stirrer

Outer dia mm	Inside diameter mm	The high mm of agitator	Casting blank section diameter mm	The high mm of crystallizer	The coil turn circle	The thick mm of crystallizer
							890	498	430	150	800	120	18

The steel grade of test is 82B, and concrete composition and pouring condition see Table 2.

Steel grades in table 2 example and pouring condition

By the formulating method of continuous casting mold of round billets stirring parameter of the present invention, determine that exciting current intensity is 260A, frequency is 8.0Hz.

Produce 10 stoves continuously, production run is steady, with hot acid macroscopic examination strand internal soundness.The experimental result statistics shows: subcrack, core crackle, shrinkage cavity and rimhole are 0 grade, and center porosity is 1 grade, and equiaxial crystal ratio reaches 100%, and the strand internal soundness has obtained remarkable improvement.

Claims (1)

1, the formulating method of continuous casting mold of round billets stirring parameter is characterized in that:

(1) the magnetic field partial differential equation of Cai Yonging ${\▿}^{2}A-\mathrm{\μ\ϵ}\frac{{\∂}^{2}A}{\∂t^2}=-\mathrm{\μj},$ With the electric field partial differential equation

Determine electromagnetic agitation electricity, Distribution of Magnetic Field, in the formula, A is the vector magnetic potential; J is a current density; μ is a magnetic conductivity; ρ is a charge density; ε is the dielectric capacitance rate;

Be the scalar electromotive force; T is the time;

(2) under the crystallizer electromagnetic agitation, the governing equation in strand flow field and temperature field comprises:

Continuity equation: $\frac{\∂\left(\mathrm{\ρ}{u}_i\right)}{\∂x_i}=0,$

The equation of momentum: $\frac{\∂\left(\mathrm{\ρ}{u}_j{u}_i\right)}{\∂x_j}=-\frac{\∂p}{\∂x_i}+\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+{\mathrm{\μ}}_t)(\frac{\∂u_i}{\∂x_j}+\frac{\∂u_j}{\∂x_i})\right]+F_i,$

Energy equation: $\frac{\∂\left(\mathrm{\ρ}{u}_{j}T\right)}{\∂x_j}=\frac{\∂}{\∂x_j}\left[(\frac{\mathrm{\μ}}{\mathrm{Pr}}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_T})\frac{\∂T}{\∂x_j}\right]-\frac{\∂\left(\mathrm{\ρ}{u}_j\mathrm{\ΔH}\right)}{{\∂x}_j},$

And k equation: $\frac{\∂\left(\mathrm{\ρ}{u}_{j}k\right)}{\∂x_j}=\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_k})\frac{\∂k}{{\∂x}_j}\right]+G-\mathrm{\ρ\ϵ}-D_k,$

The ε equation: $\frac{\∂\left(\mathrm{\ρ}{u}_j\mathrm{\ϵ}\right)}{\∂x_j}=\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_{\mathrm{\ϵ}}})\frac{\∂\mathrm{\ϵ}}{\∂x_j}\right]+f_1{C}_{1}G\frac{\mathrm{\ϵ}}{k}-f_2{C}_2\mathrm{\ρ}\frac{{\mathrm{\ϵ}}^2}{k}+E_{\mathrm{\ϵ}}$

More than various in, ρ is a molten steel density; u _iAnd u _j(i, j=1,2,3) are the speed under the different coordinate directions; F _iBe electromagnetic force; μ is a dynamic viscosity; P is a pressure; μ _tBe turbulent viscosity; K is a Turbulent Kinetic; ε is a turbulence dissipation rate; T is a temperature; Pr is a Prandtl number; C _pFor constant pressure specific heat is held; λ is a thermal conductivity; σ _T=1.0, C ₁=1.44, C ₂=1.92, σ _k=1.0, σ _ε=1.3, f ₁=1.0; $G={\mathrm{\μ}}_t(\frac{\∂u_i}{\∂x_j}+\frac{{\∂u}_j}{\∂x_i})\frac{\∂u_i}{\∂x_j};$ $D_k=2\mathrm{\μ}{\left(\frac{\∂\sqrt{k}}{\∂x_i}\right)}^2;$ $E_{\mathrm{\ϵ}}=2\frac{{\mathrm{\μ}}_t\mathrm{\μ}}{\mathrm{\ρ}}{\left(\frac{{\∂}^2{u}_i}{\∂x_j\∂x_k}\right)}^2;$ f ₂＝1-0.3exp(-Re _t ²)，

Flow Field Calculation adopts the discrete flow field of the finite volume method differential equation, with staggered-mesh storage speed component, adopts the Simplec algorithm, when the quality source of continuity equation less than 10 ^-4The time, promptly to think and adopt the Fortran Programming with Pascal Language by iteration convergence, the electromagnetic force that ANSYS is calculated adds the momentum source item, and the crystallizer computational length is 1.8m;

(3) on above-mentioned Flow Field Calculation result's basis, add field trash movement locus discrete model governing equation $m\frac{{\mathrm{dV}}_p}{\mathrm{dt}}=F_P+F_B+F_A+F_D,$

In the formula, m is a mass particle; V _pBe particle rapidity; T represents the time; F _pThe power that causes for the molten steel barometric gradient; F _BBe the buoyancy of molten steel to particle; F _ABe molten steel additional mass power; F _DBe the suffered viscous drag of particle,

Field trash granularity 5～50 μ m are set, density 3500kg/m ³, mass flowrate 4 * 10 ^-5Kg/s parameter and divergent boundary condition continue the calculating that is coupled of the flow field under the electromagnetic agitation condition, temperature field and field trash track;

(4) data of magnetic field, flow field, temperature field and the field trash movement locus of the round mold electromagnetic agitation that goes out according to analog computation, and in the crystallizer effectively the MOLTEN STEEL FLOW speed of stirring area between 0.2-0.25m/s, can produce enough big centrifugal force and shearing force; Can make the covering slag melt well; Can cause hot top effect; The time long enough that field trash is stopped in crystallizer floats it as far as possible and does the investigation judgement, to revise the data that analog computation goes out;

(5) adopting through analog computation, investigation, judgement and revising under resulting exciting current intensity in back and the frequency condition, detect subcrack, core crackle, shrinkage cavity, center porosity, rimhole and the equiaxial crystal ratio of strand, determine stirring parameter at last.

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