WO2009141205A1 - Method for the continuous casting of a metal strand - Google Patents

Abstract

The invention relates to a method for the continuous casting of a metal strand in a continuous casting plant, according to which a strand comprising a liquid core enclosed by a strand shell is withdrawn from a cooled in-line die, supported in a strand support unit downstream of said die and cooled using a coolant, the thermodynamic changes in the entire strand being calculated in a mathematical simulation model. The aim of the invention is to create a method which can be used to increase the accuracy of the simulation of the thermodynamic changes in the entire strand and to improve both the product quality of the metal strand in conjunction with the strand cooling process and the production output of the continuous casting process. This is achieved by a method, according to which a three-dimensional thermal conduction equation is solved numerically in real time in the mathematical simulation model and the cooling of the strand is set by taking into consideration the calculated changes.

Description

 Method for continuous casting of a metal strand

The present invention relates to a method for continuously casting a metal strand.

Specifically, the invention relates to a method for continuously casting a metal strand, in particular a steel strand, in a continuous casting, wherein a strand with a trapped by a strand shell, liquid core drawn from a cooled continuous casting mold, supported in a continuous casting mold downstream strand support means and cooled with coolant , where thermodynamic state changes of the entire strand in a mathematical simulation model, taking into account the physical parameters of the metal, the thickness of the strand and the constantly measured extraction speed are also calculated.

From DE 4417808 A1 a method for the continuous casting of a metal strand is known, in which a strand with drawn from a strand shell liquid core extracted from a cooled mold, then supported in a strand support device and cooled with coolant. The state changes occurring in the course of the continuous casting process are also calculated in real time for the entire strand by means of a mathematical simulation model, including the two-dimensional heat equation, and the cooling of the strand is set as a function of the calculated thermodynamic state changes.

Due to the two-dimensionality of the heat equation used, it has not been possible to calculate the heat conduction and the associated state changes in all directions (the strand thickness, the strand width and the strand extraction direction) of the metal strand and adjust the temperature profile depending on the calculated state changes by means of strand cooling targeted. In addition, there were differences between the calculated and the actual thermodynamic effects, which were not taken into account in the simulation model By freezing point.

The object of the invention is to provide a method of the type mentioned, with which the accuracy of the simulation of the thermodynamic state changes of the entire strand can be further increased and in connection with the cooling of the product quality of the metal strand and the production efficiency of the continuous casting process can be improved.

This object is achieved by a method of the type mentioned, in which in the mathematical simulation model, a three-dimensional

Heat equation is solved numerically in real time and the cooling of the strand is adjusted taking into account the calculated state changes.

By means of the method from DE 4417808 A1, it is possible to calculate thermodynamic state changes as a function of the two-dimensional heat conduction in real time and to influence the temperature profile of the strand by means of strand cooling. According to the method of the invention, it is possible thermodynamic state changes by means of a non-linear, transient heat equation as a function of the three-dimensional heat conduction, namely in strand thickness direction, in the strand width direction and in the strand longitudinal direction, ie. in the extension direction of the strand to calculate in real time and to influence by means of strand cooling targeted. As a result, the thermodynamic changes in state can be calculated with greater accuracy and be specifically influenced by means of a coordinated strand cooling. In the mathematical simulation model, the strand is divided into individual volume elements, i. so-called discretized, wherein each discrete volume element has an extension in the longitudinal direction of the strand, in the strand thickness direction and in the strand width direction. By means of this discretization, individual nozzles of the strand cooling can discrete one or more

Volume elements of the strand are assigned and thereby, first, the thermodynamic state changes in these volume elements, taking into account the heat conduction in all spatial dimensions and the determined by the strand cooling heat quantity can be determined with high accuracy, and secondly, by means of these nozzles, the thermodynamic properties of the strand can be influenced very targeted and with high efficiency.

In a particularly advantageous embodiment, in the mathematical simulation model of the method according to the invention, the three-dimensional heat equation is solved numerically taking into account the temperature-dependent change in the density of the metal strand. It is known to the person skilled in the art that the change in density of metal as a function of the temperature can assume significant proportions. So m ³ at 1550 ⁰ C (temperature of the melt in the distribution trough) increases for example in the continuous casting process, the density of steel of about 7000 kg / 7800 kg to about / m ³ at 300 ⁰ C (durcherstarrter strand). The density changes are in the continuous casting process in conjunction with the heat equation also in the determination of

Solidification point relevant. As Durcherstarrungspunkt that point in strand extraction direction is referred to, from which the metal strand is completely solidified, ie. the metal strand no longer has a liquid core. The most accurate calculation of the solidification point is extremely advantageous in any case. If the location of the solidification point underestimated, ie. if the calculated point is less far removed from the mold than the actual point in the direction of extension, this can lead to very dangerous casting situations (for example also strand penetration). On the other hand, the allowable casting speed is unnecessarily limited in overestimating the through-solidification point, which in turn would degrade the productivity of the equipment.

A further, particularly advantageous embodiment of the method according to the invention can be achieved if in the numerical solution of the heat equation, taking into account temperature-dependent

Density changes of the metal strand approximated equations are used for the enthalpy, which have the exact mass and the exact enthalpy for the entire strand. It should be noted at this point that the exact three-dimensional, nonlinear and unsteady heat equation with regard to the temperature-dependent density change is still unsolved. The thermal equation used today without taking into account the temperature-dependent density change are only rough approximations of the exact equation and their solutions may differ significantly from the exact solution. By using approximate equations for the enthalpy with global - ie. however, if the entire strand is considered - the exact mass and the exact enthalpy - it is ensured that these essential thermodynamic state variables correspond to the exact values.

The method according to the invention can be carried out particularly favorably if either a finite volume method or a finite element method is used to solve the heat equation in the mathematical simulation model. The heat equation is a parabolic partial differential equation that can be solved by standard methods of numerical mathematics, in particular the finite volume method or finite element method (see Chapter 19: Numerical Mathematics by IN Bronstein, KA Semendjajew, G. Musiol , H. Mühlig: Paperback of Mathematics, Verlag Harri Deutsch, 6th edition, 2005).

In a particularly favorable manner, the method according to the invention is carried out when the thermodynamic state changes due to the spatial symmetry are calculated only for a quarter of the strand cross-section. This simplification can be made due to the spatial symmetry of the strand cross-section and the time-varying boundary conditions without loss of accuracy and allows the three-dimensional heat equation can be solved with high accuracy even by relatively low-performance process computers.

The method according to the invention can be used without restrictions when casting metal strands with billet, billet, slab or thin slab cross section Any dimensions can be used to improve the quality of the cast metal strands.

Further advantages and features of the present invention will become apparent from the following description of non-limiting embodiments, reference being made to the following figures, which show the following:

1 shows a continuous casting plant in a schematic side view FIG. 2 shows a schematic representation of the discretized metal strand FIG. 3 shows a comparison of solutions of different formulations of heat conduction equations

A cooled mold 1 is fed with liquid steel 2, which is supplied from an intermediate vessel 3. The forming in the mold 1, a liquid core 4 and initially only a thin strand shell 5 having, strand 6 is an arcuate strand support means 7, which is provided with support rollers 8 and supports the strand at the top and at the bottom, redirected to the horizontal where, after solidification, it is either cut up or transported further as a continuous strand. For the cooling of the strand 6 7 coolant-supplying nozzles 10 are provided along the strand support means, of which in the drawing only those are drawn on the strand top at the beginning of the strand support means 7. In this case, one or more nozzles 10 are connected to a respective supply line 11. The amount of coolant applied by the nozzles to the strand can be changed by means of a continuously adjustable valve 12, which has a

Flow meter 13 is arranged downstream. Each valve 12 is adjustable via an actuator 14 that can be actuated via a control element 16 controlled by a central process computer 15. Each flow measuring device is coupled via an input unit 17 to the process computer 15, which in turn drives all control elements 16 via an output unit 18. In the input unit 17 of the process computer 15, for example, the physical parameters of the metal to be cast, in the present case of the steel 2, namely the temperature-dependent values of the density, the specific Heat capacity and thermal conductivity, further the flow-dependent spray pattern of the location-dependent arranged nozzles 10, the location-dependent role division 9, the optionally location-dependent strand thickness, the strand width and the continuously measured casting speed of the continuous casting plant are entered.

According to the invention, the strand 6 is cooled in a controlled manner at specific, either fixed or variable, positions of the strand support device 7. The control of the strand cooling takes place taking into account the thermodynamic state changes of the entire strand 6 by the release in real time of a three-dimensional heat equation using the process computer 15th

For example, a three-dimensional, nonlinear and transient heat equation in an enthalpy formulation is pE _mass {x, t) _(f) dE _mass (x, t)) d ² u (x, t), d ² u (x, t), d ² u (x, t)

^P {dt ^caΛ) dz) dx ² dy ² dz ² where t is the time in [s] x is the coordinate in strand thickness direction in [m] y is the coordinate in the strand width direction [m] z the coordinate in the extension direction and the strand longitudinal axis in [m ] d - partial derivative after time t dt

-, -, - partial derivatives according to the location x, y, z dx dy dz x position vector in a rectangular coordinate system in [m] p density in [kg / m ³ ]

E _mass ix't) mass-enthalpy at point x at time t in [J / kg]

ξ Dimensionless run variable

^v _ca Λ ^t ) Extraction speed of the strand at time t in [m / s]

In this heat equation, temperature-dependent changes in density of the strand 6 are disregarded. Since the density of steel 2 increases from 7000 kg / m ³ at 1550 ⁰ C to 7800 kg / m ³ at 300 ⁰ C, this leads

Simplification of inaccuracies in the calculation of thermodynamic state changes. It has been found that in this heat equation, the Durcherstarrungspunkt is underestimated, ie. that the actual through-solidification point is farther from the mold 1 than the calculated through-solidification point. In order to avoid disadvantageous and possibly even dangerous casting situations, it is necessary to use a density value p in the region of the maximum density of the steel 2, which subsequently results in the max. permissible casting speed significantly reduced.

wobei τ(x,t) Temperatur an der Stelle x zur Zeit t in [° K]A second formulation of a nonlinear, three-dimensional and transient heat equation is d ² un {x2, t)

where τ (x, t) temperature at the point x at time t in [° K]

p (τ (x, t)) Density of the metal strand at the temperature T in [kg / m ³ ]

This formulation of the heat equation is global, i. if the entire strand is considered, correct in mass, but incorrect in terms of the enthalpy. It has been shown that in this heat equation, the through-solidification point is overestimated, ie. that the actual

The solidification point is less far from the mold than the calculated through-solidification point. Thus, the use of this equation is indeed problematic with respect to any adverse casting situations, however, the max. allowable casting speed unnecessarily limited, resulting in reduced productivity of the plant.

wobeiAdvantageously, the heat equation is used

in which

E _trans iX't) Transformed mass-enthalpy at point x at time t

Two approaches are used for a globally correct transformed enthalpy E _trans (x, t) with respect to mass and enthalpy. The thermodynamic

Conditions in the strand 6 change significantly at the through-solidification point 19, since the strand 6, viewed in the casting direction, above the through-solidification point has a liquid core 4, which communicates with the liquid steel 2 of the mold 1. The ferrostatic pressure in this area presses the already solidified strand shell 5 against the rollers 8 of the strand support device 7, whereby the strand shrinkage due to the temperature-dependent change in density of the steel 2 is compensated by inflowing, liquid steel 2 in this area. Below the Durcherstarrungspunkts 19 such compensation does not take place.

Above the Durcherstarrungspunkts 19 is the approach

dξ .

E _tans (x, 0 - E _m Λξ) -

dξ.

On the other hand, below the solidification point 19, the following approach is used

Herein mean

T _{ref is} an arbitrary but constant reference temperature (usually 25

⁰ C) ^τ _{t and} temperature of the metal in the pouring mirror in [° K]

E _mass &'t) Time derivative of mass enthalpy

The heat conduction equation is transformed to Lagrangian coordinates x _lag , ie viewed by an observer moving along with the strand extraction movement. The transformation is

CastLg (t) = [v _cast (ζ) - dζ

wobei tstart Zeitpunkt der Entstehung des diskreten Volumenelements in der Kokille in [S]

where tstart is the time of formation of the discrete volume element in the mold in [S]

The heat equation in Lagrange coordinates is then

dt dx ² dy ² dz ²

This heat equation is solved by the process computer 15 in real time by means of the finite volume method. This standard method of numerical mathematics is known to the person skilled in the art and works with discrete volume elements of the strand 6. For each volume element 20, therefore, the simple three-dimensional heat equation described in the v- _cast moving element-fixed coordinate system is to be solved. This is performed periodically for a plurality of volume elements 20, resulting in the time-varying temperature field of the entire strand 6. From Fig. 2 it can be seen that the strand 6 is divided into discrete volume elements 19, for example, 10 cm edge length. The volume elements 19 are produced in the mold and tracked in accordance with the casting speed through the continuous casting plant. As shown in FIG. 2, the strand thickness axis x and the strand width axis y are symmetrical to the edges of the solidifying strand 6. Because of this spatial symmetry in strand width and strand thickness direction, it is advantageous to change the thermodynamic state changes only in one quadrant 20, ie one quarter, of the strand cross section.

To solve the heat equation, however, the initial and - depending on the movement of the volume elements through the mold and through different cooling zones - temporally variable boundary conditions are needed.

The initial condition for a newly created volume element is

- * \ ^X Lag V Start)) ^~ * tund

The boundary condition is general

^λ (T) - \ _Whether erflache = Φ) where

W

A (T) Temperature-dependent thermal conductivity in [] mK dT

- o i _f i _{over surface} temperature degrees ient normal to the surface dn q (t) Specific heat flow at time t

In order to model the heat flow q (t), the following approach is used within the cooled mold 1: q (t) = a _mold (τ _surf (t)) ^■ (τ _surf (t) _{-τ mold} )

Outside the mold, q (t) = a _water (sw (t)) ^■ (T _surf (t) _{-T wat} J + a _roU (t) ^■ (T _surf (t) _{-T roll} ) + σ ^■ ε ^■ (T _su (t) ⁴ - T _amt} ⁴ ) radiation where a _mold {T _surf (t)) _Heat dissipation function of the mold a _water (sw (t)) heat dissipation function of the strand cooling system sw (t) cooling water quantity of the strand cooling a _m u ( ^t ) heat dissipation function of the support rollers σ Stefan-Boltzmann constant ε the emissivity

T _surf (t) Surface temperature of the strand 6 τ _amb Ambient temperature

Since the three-dimensional heat equation is still unsolved, the high accuracy of the formulation according to the invention of the

Heat equation with a transformed enthalpy E _tra ns be checked using a one-dimensional example. The exact solution of the heat equation, taking into account the temperature-dependent density change (solid line) is known in the one-dimensional case and is compared in Fig. 3 with a mass correct formulation (dashed line) and a mass and enthalpierichtichtung formulation (dotted, solid line). In Fig. 3, the ordinate in the strand separation direction of the mold and on the abscissa, the thickness of a metal strand is applied in the direction of Strandickenrichtung. As can be seen in FIG. 3, in the case of a formulation of the heat conduction equation in mass and enthalpy, the actual through-solidification point is slightly further from the mold than the calculated through-solidification point, ie. the solidification point is slightly overestimated. In comparison, the solidification point is significantly underestimated in a mass correct formulation of the heat equation, which can lead to critical situations in the continuous casting process. LIST OF REFERENCE NUMBERS

1 mold

2 steel

3 mixing bowl

4 Liquid core of the strand

5 strand shell

6 strand

7 strand support device

8 support rollers

9 role division

10 cooling nozzles

11 Supply of coolant

12 valve

13 flow measuring device

14 actuator

15 process computers

16 control element

17 input unit

18 output unit

19 Discrete volume element

20 quadrant of the strand

Claims

Claims / Patent Claims 1 . A process for the continuous casting of a metal strand, in particular a steel strand, in a continuous casting plant, wherein a strand having a, from a strand shell enclosed liquid core of a cooled Continuous mold drawn, supported in a continuous casting mold downstream strand support device and cooled with coolant, wherein thermodynamic state changes of the entire strand in a mathematical simulation model taking into account the physical parameters of the metal, the thickness of the strand and constantly measured Discharge speed be calculated, characterized in that in the mathematical simulation model, a three-dimensional heat equation is solved numerically in consideration of temperature-dependent density changes of the metal strand in real time and the cooling of the strand is adjusted taking into account the calculated state changes. 2. A method according to claim 1, characterized in that in the numerical solution of the heat equation, taking into account temperature-dependent density changes of the metal strand approximated equations are used for the enthalpy, which have the exact mass and the exact enthalpy for the entire strand. 3. The method according to any one of the preceding claims, characterized in that the heat conduction equation is solved numerically by a finite volume method or by a finite element method. 4. Method according to one of the preceding claims, characterized in that the thermodynamic state changes due to the spatial symmetry are calculated only for a quarter of the strand cross-section.