CASTMANAGER

A lot of heat transfer models have been developed for continuous casting. Most of them are for steady state purposes (see our TEMPSINU tool) but also many real-time models are presented and applied in steel industry. In real-time calculation, many practical requirements will be set for the model. The computing time must, for instance, be short enough and the special process conditions, such as the start and the end of casting as well as the ladle change, steel grade and possible width changes must be included in the model. Due to the increasing power of modern computers available, the requirements concerning the computing time can today, however, be met more and more easily, but anyhow a lot of attention must be paid on numerical solution algorithms.

Our CastManager and Tempsimu tools are heat transfer modelling software for continuous steel casting. CastManager is a software for transient online applications, while Tempsimu is a software for steady-state modelling. Basically, the tools are very similar and the theory presented for Tempsimu (see Temspsimu tool) are also valid for CastManager. The equations differ only a bit because in the CastManager tool also the time derivative needs to be considered (first term in the equation). Also in the mould equation, time derivative needs to be added. Hence, the heat transfer equation for strand can be defined by the following equation:

The accuracy of the predictions is governed by numerical accuracy, the boundary conditions, and the materials properties. Of particular importance is the choice of numerical parameters such as the mesh refinement and time-step size. After finding the limits after which the results do not change (within a selected tolerance limit), the software is ready to be used for optimization, development, research, and for on-line applications.

Determination of the heat transfer coefficients. For the correct simulation of heat transfer, the determination of the boundary conditions describing the heat transfer phenomena taking place along the strand surface is of crucial importance. In the mold, there exists a thermal resistance between the shell and the mold because of the powder lubrication and the formation of an air gap due to the steel shrinkage during cooling. Heat transfer in the mold is controlled mainly by heat conduction across the interface between the surface of the solidifying shell and the mold. It is quite difficult to determine the heat transfer across this gap, which varies with time and position of the mold. The gap is a function of casting variables as casting speed, superheat, casting powder, steel composition, mold taper, etc.  Advanced models, as our Tempsimu and CastManager tools, simulate not only the strand but also the mold around the strand and the heat transfer across the gap is determined by the gap heat transfer coefficient. These models consist of two models: the mold model and the strand model. The gap heat transfer coefficient can be determined with the help of the experimental measurements as the mold thermocouple measurements and the heat flux measurements from the mold cooling water. The average heat flux extracted from the mold calculated from the heat balance of the mold cooling water could be directly applied as the boundary condition in the mold. Anyhow, for on-line models, the response of the mold cooling water measurements to rapid changes in casting condition is too low. CastManager tool uses gap heat transfer coefficient as a function of the strand surface temperature. The profiles, which are validated with experimental data (mold thermoelements, mold water heat flux measurements), are defined in input data tables, including the effects of casting powder used.

Materials data. To obtain reliable results from the heat transfer simulations, accurate data on the thermophysical material properties are also needed. Typical data needed are the density, the thermal conductivity, and the specific heat. Other important data are the phase transformation temperatures and the corresponding latent heats, and the way in which the latent heats are released during the phase transformations. If the enthalpy formulation is used, the enthalpy values can be used directly if they are known. The enthalpy then includes all the other data except the thermal conductivity and the density. The material data are not only functions of the temperature and the chemical composition but also of the cooling rate. This is because the kinetics of phase transformations depends on the cooling rate and the thermophysical properties are related to the phases formed. Thus, for accurate simulation of solidification and cooling processes, one should know the material data as a function of temperature, composition, and cooling rate. Although material data have been measured for a great number of steel grades, most of these data are valid only for special steel grades and/or for the low temperature region only and there is only a little data for higher temperatures up to the liquid phase. So, it is seldom possible to find all the data needed. This is especially the case for carbon and low alloyed steel grades, because in these steels even smaller variations in the composition might have a significant effect on the phase transformations and thus on the thermophysical material properties.

In the heat transfer simulations, the equations are usually solved using fixed grids, i.e., the strand dimensions are the same everywhere in the machine. This means that the contraction of the steel is not calculated and considered. In these kinds of models, it is important to take care of the correct mass and heat balance. One method to take care of this is that the density is not varied either. In such cases the density should be that of the initial liquid and constant. However, during solidification the fluid in the interdendritic space is free to move and it more or less compensates the solidification contractions. To take this feeding into account, the density should be constant and that at the solidus temperature.

Two calculations for a slab caster were made to test the effect of the density. The first calculation with the changing density gave 17.50 m for pool length and the second with the constant density 20.85 m. So, the difference in the pool length was over three meters. So, it is important to take care of the correct mass and heat balance.

Our tools Tempsimu and CastManager use fixed grid concept and the width and thickness dimensions of the strand are given as the mould inner dimensions at the bottom of the mould and density is that of the solidus density. This concept meets the mass and energy balance of the steel in casting machines.

Model validation. The heat transfer models can be validated using strand surface temperature and shell thickness measurements. The mold model can be validated using mold thermocouple measurements. The strand surface temperature can be measured by pyrometers or by thermocouples. In the case of thermocouples, these are fed into the strand surface in the upper part of the machine, and they move with the strand through the machine. The strand surface measurements are quite sensitive to external disturbance and the scale on the strand surface also affects the results. Usually, peak temperatures are used in the validation. The shell thickness can be measured with some methods, as with the rivet pin shooting method, the so-called wedge method and adding alloying element into liquid pool. In the wedge method, a wedge is fed between two rolls of a caster. As the strand moves on, the wedge moves between the roll and the strand. The wedge causes tensile stress resulting in cracks in the solidification front of the strand. Shell thickness is then determined from the crack tip locations in the strand specimens.

Calculation example of CastManager (Figure 1) shows an example of the bloom casting case where steel grade and tundish were changed during which the casting has been stopped for some minutes [9]. A plate is also placed in the mold to prevent the mixing of the steel grades. When the casting starts again, there is a danger of secondary pipe formation, i.e., the solidifying fronts meet at the center line of the bloom while there is still liquid steel below. When this entrapped steel finally solidifies, a cavity or mini-ingot is formed, because the feeding of liquid steel to compensate the solidifying shrinkage is prevented. A pipe is a severe quality risk, and this part of the bloom must be scrapped. By correct cooling of the bloom, the length of the pipe can be minimized.

Figure 1. A simulation example with the CastManager tool. Steel grade and tundish were changed, and the casting was stopped for some minutes. A plate was also placed in the mold to prevent the mixing of the steel grades. There is a risk to the formation of a long mini-ingot, which should be avoided. Figures from left to right: before the grade change; a plate was placed; casting speed was increased again, formation of mini-ingot.

Especially in slab casters, it is also important to avoid a “dog bone” pool shape (Figure 2) . This may occur when the off-corner areas of the wide face are clearly less cooled than the mid-face area.

Figure 2. CastManager results. “Dog bone” pool shape. This example case was calculated using the CastManager  tool for continuous casting. The “dog bone” shape in slabs should be avoided.

CastManager + onlineIDS -system. Figure 3 shows the online CastManager + IDS -system.  CastManager has special conditions needed in online calculations such as the start and the end of casting as well as the ladle change, steel grade and possible width changes. The calculation of the system is very fast for online applications.  In addition to the normal CPU (central processing unit) version, also an CPU + GPU (GPU = graphics processing unit) version is developed and is available. GPU is very fast compared with CPU.

Figure 3. CastManager + IDS online system.  CastManager + IDS system is running in industrial slab casters. For quality prediction concept, see the Tempsimu chapter.