TEMPSIMU tool

OUR TOOL 3: TEMPSIMU is a 3D steady state heat transfer modelling software for continuous casting of steel. It calculates strand temperatures, mould temperatures and temperature related data (as the shell thickness and total mould heat flux) as a function of:

·   Secondary cooling components: rolls, nozzles and radiation zones

·   Steel grade (thermophysical material properties)

·   Strand geometry

·   Mould geometry and material properties

·   Casting variables: casting speed, super heat, cooling water temperature and flow rates

·   Mould cooling variables: cooling water temperature and the boundary condition between the mould and water

TEMPSIMU can be applied to the casting of rectangular sections (slabs, blooms, billets). It can be used, for instance, to analyse the existing secondary cooling system and to study new alternatives (spray configurations, cooling water flow rates). The program consists of the graphical user interface and two separate modules: the three-dimensional mould model and the three-dimensional strand model. They are run iteratively, and the so called gap heat transfer coefficient as a function of the strand temperature is used to couple them. In addition, Leidenfrost effect and effect of convection (fluid flow) is taken into account in the calculations. Material data can be calculated with the Solidification and Microstructure Model, IDS, which gives directly the data file needed in TEMPSIMU.

The gap heat transfer coefficient profile is a function of the strand surface temperature, and it depends on steel grade, mould material properties and mould powder. There are three unknown variables: strand surface temperatures, mould inner surface temperatures and heat transfer coefficients between them, but all of the variables can be calculated iterating between the strand model and the mould model.

Figure 1.  Interdependencies between TEMPSIMU and IDS modules

Figure 2. Example of the mould gap heat transfer profiles

Tempsimu consists of two separate modules: the three-dimensional mould model and the three-dimensional strand model. They are run iteratively, and the so called gap heat transfer coefficient as a function of the strand temperature is used to couple them. The strand model calculates the steady state strand temperatures and the shell thickness 3-dimensionally throughout the strand. Hence the heat flow along the casting direction is also taken into account. The mould model calculates the mould temperatures 3-dimensionally and the total amount of heat flux extracted from the mould. The following assumptions are made for the calculations:

·   Cross section of the strand along the casting direction is symmetric across x- and y-directions.

·   The solidus and the liquidus temperature, as well as other phase transformation temperatures, are constant

·   The solidification takes place by directional growth.

·   The material behaviour is isotropic.

Let z be the casting direction, x the direction of wide side and y the direction of narrow side. The heat transfer within the calculation domain of the strand is written by Equations 1. Where ρ is the density, v the casting speed and k the thermal conductivity. Function H is the enthalpy, and it is defined as to be the sum of sensible and latent heats. Here c is the specific heat capacity, L the latent heat and fs the solidified fraction in the mushy zone. The solidified fraction describes the manner in which the latent heat is released between the solidus and liquidus temperatures. This manner depends strongly on the chemical composition of the steel to be cast. The solid state phase transformations can be treated similarly. 

The convective heat transfer in the liquid pool due to the liquid flow is quite difficult  and slow to calculate using deferential equations. The technique most often used to account for the convective heat transfer is effective thermal conductivity. This technique is also used in Tempsimu.

The model equations are discretized using fully implicit three-dimensional finite difference (FDM) and upwind schemes. The resulting algebraic equations are solved using parallel Gauss–Seidel–Newton–Rhapson method. Cross section of the strand along the casting direction is supposed to be symmetric across x- and y-directions. Hence the calculation domain is one quarter of the strand and one quarter of the mould. See Figure.

Figure 3. The calculation domains of the strand and the mould schematically presented.

In the secondary cooling area, the strand is held with rolls, and between the rolls, the nozzles spray water or water-air mixture on the strand. When the strand passes between two rolls, four different cooling regions are accounted for in the model:

1. Roll contact area

2. Pre-nozzle area

3. Spraying area

4. Post-nozzle area

Figure 4.  Schematic of cooling regions between rolls.

Roll contact area: this region indicates heat conduction from the strand to the roll. Roller heat transfer depends on the roll contact length in casting direction as well as the roll type. Three different roll types are considered in the tool. See the figure.  The internal roll is cooled internally by water (=standard center bore design), the revolver is also internally cooled by water, but the water channels are closer to the surface (peripheral-bore design), the solid roll is not cooled by water internally or externally. In the model, the contact length in the casting direction is constant for each roll. The default boundary condition values are defined for each roll type based on validation measurement.

Figure 5. Different roll types considered in Tempsimu.

The regions 2 and 4 are the pre- and post-nozzle cooling areas respectively which account for the indirectly cooled space between roller pairs. The boundary equation for these areas consists of two parts: the convection term and the radiation term. Default values are also defined for these areas. So called flowing water from the spray nozzle can be considered.

Spraying area: The strand is usually cooled in the secondary cooling zone by sprays of water or water-air mixture. The tool has a spray nozzle database. Each nozzle in the database has its water distribution profiles and other important data affecting the cooling efficiency. The database is typically specific for each steel plant for their nozzles. The data can be defined based for instance on laboratory measurements or information from the nozzle suppliers.

One important factor which needs to be considered is the Leidenfrost phenomenon, which also influences the heat transfer. Above a temperature called Leidenfrost point, the surface is totally covered by a vapor film  and the increase of surface temperature has not clear effects on the heat transfer. Below the Leidenfrost temperature, the heat transfer increases strongly when the surface temperature decreases. The Leidenfrost temperature  typically occurs in the range of 700-900 °C, depending on the surface quality and the water flow rates. It is evident that the powder scale on the surface shifts the Leidenfrost point to higher values. In the Tempsimu tool, the effect of Leidenfrost phenomenon is considered in spray cooling areas.

TEMPSIMU tool is validated in many steel plants using pyrometer measurements and it is used in many steel plants, research institutes and universities.

Figure 6. TEMPSIMU user interface consists of two main windows: Machine building window and Results window. The machine building window and its menu bar item descriptions are presented In Figure 6. 

Tempsimu is a fast model, the calculation times for one continuous casting case last typically about 10-30 seconds

SIGNIFICANCE

•     Industry is more capable of developing new advanced steel grades and to solve their production problems

•       Faster R&D cycle and minimisation of their costs

•       With the model, it is easy to test new ideas

Figure 1 .  Interdependencies between TEMPSIMU and IDS modules

Figure 2. Example of the mould gap heat transfer profiles

Equations 1 .The heat transfer within the calculation domain of the strand is written by these equations. Here ρ is the density, v the casting speed and k the thermal conductivity. Function H is the enthalpy, and it is defined as to be the sum of sensible and latent heats. Here c is the specific heat capacity, L the latent heat and fs the solidified fraction in the mushy zone.

Figure 3. The calculation domains of the strand and the mould schematically presented.

Figure 4.  Schematic of cooling regions between rolls.

Figure 5. Different roll types considered in Tempsimu

Figure 6. TEMPSIMU user interface consists of two main windows: Machine building window and Results window. The machine building window and its menu bar item descriptions are presented in this figure