Thermal Analysis of Continuous Casting Process

Thermal Analysis of Continuous Casting Process
Belete Kiflie and Dr.-Ing. Demiss Alemu
Faculty of Technology, Addis Ababa University, Ethiopia
ESME 5th Annual Conference on Manufacturing and Process Industry, September 2000
Reprinted with ESME permission by the African Technology Forum

Continuous casting is one of the prominent methods of production of casts. Effective design and operation of continuous casting machines needs complete analysis of the continuous casting process. In this paper the basic principles of continuous casting and its heat transfer analysis using the finite element method are presented. In the analysis phase change is assumed to take place at constant temperature. A front tracking algorithm has been developed to predict the position of the solidification front at each step. Finally, examples that are solved by the proposed algorithm are discussed. The results show that there is a good agreement between the method developed in this work and other previously reported works.

Continuous casting is the process whereby molten metal is solidified into a "semifinished" billet, bloom, slab or beam blank. Prior to the introduction of continuous casting in the 1950s, steel was poured into stationary moulds to form "ingots". Since then, "continuous casting" has evolved to achieve improved yield, quality, productivity and cost efficiency. Nowadays, continuous casting is the predominant way by which steel is produced in the world. Continuous casting is used to solidify most of the 750 million tons of steel, 20 million tons of aluminum, and many tons of other alloys produced in the world every year [1].

In the continuous casting process, illustrated in Figure 1, molten metal is poured from the ladle into the tundish and then through a submerged entry nozzle into a mould cavity. The mould is water-cooled so that enough heat is extracted to solidify a shell of sufficient thickness. The shell is withdrawn from the bottom of the mould at a "casting speed" that matches the inflow of metal, so that the process ideally operates at steady state. Below the mould, water is sprayed to further extract heat from the strand surface, and the strand eventually becomes fully solid when it reaches the ''metallurgical length''.

Solidification begins in the mould, and continues through the different zones of cooling while the strand is continuously withdrawn at the casting speed. Finally, the solidified strand is straightened, cut, and then discharged for intermediate storage or hot charged for finished rolling.

To start a cast, the bottom of the mould is sealed by a steel dummy bar. This bar prevents liquid metal from flowing out of the mould and the solidifying shell until a fully solidified strand section is obtained. The liquid poured into the mould is partially' solidified in the mould, producing a strand with a solid outer shell and a liquid core. In this primary cooling area, once the steel shell has a sufficient thickness, the partially solidified strand will be withdrawn out of the mould along with the dummy bar at the casting speed. Liquid metal continues to pour into the mould to replenish the withdrawn metal at an equal rate. Upon exiting the mould, the strand enters a roller containment section and secondary cooling chamber in which the solidifying strand is sprayed with water, or a combination of water and air (referred to as "air-mist") to promote solidification. Once the strand is fully solidified and has passed through the straightener, the dummy bar is disconnected, removed and stored.

The shape of the tundish is typically rectangular. Nozzles are located along its bottom to distribute liquid steel to the mould. The tundish also serves several other key functions:

- Enhances oxide inclusion separation.
- Provides a continuous flow of liquid steel to the mould during ladle exchanges.
- Maintains a steady metal height above the nozzles to the mould, thereby keeping steel flow uniform.
- Provides more stable stream patterns to the mould.

The main function of the mould is to establish a solid shell sufficient in strength to support its liquid core upon entry into the secondary spray cooling zone.

The mould is basically an open-ended box structure, containing a water-cooled inner lining fabricated from a high purity copper alloy. The inner face of the copper mould is often plated with chromium or nickel to provide a harder working surface, and to avoid copper pickup on the surface of the cast strand, which can otherwise facilitate surface cracks on the product.

Mould oscillation is necessary to minimize friction and sticking of the solidifying shell, and avoid shell tearing, and liquid steel breakouts, which can wreak havoc on equipment and machine downtime due to clean up and repairs. Friction between the shell and mould is reduced through the use of mould lubricants such as oils or powdered fluxes. Oscillation is achieved either hydraulically or via motor-driven cams or levers which support and reciprocate (or oscillate) the mould.

Depending on the design of the casting machine, the as-cast products of the continuous cast process are slabs, blooms, billets, or beam blanks. The cross sections of these products are shown in Figure 2.

Billets have cast section sizes up to about 200 mm square. Bloom section sizes typically range from approximately 200 mm to 400 mm by 600 mm. Round billets include diameters of approximately 140 mm to 500 mm. Slab castings range in thickness from 50 mm to 400 mm, and over 2500 mm wide. The aspect ratio (width-to-thickness ratio) is used to determine the dividing line between blooms and slabs. An aspect ratio of 2.5:1 or greater constitutes an as-cast product referred to as a slab.

By its nature, continuous casting is primarily a heat-extraction process. The conversion molten metal into a solid semi-finished shape involves the removal of the following forms of heat:

- superheat from the liquid entering the mould from the tundish.
- the latent heat of fusion at the solidification front as liquid is transformed solid, and finally
- the sensible heat (cooling below the solidus temperature) from the solid shell

These heats are extracted by a combination of the following heat-transfer mechanisms:

- convection in the liquid pool.
- heat conduction down temperature gradients in the solid shell from the solidification
front to the colder outside surface of the cast, and
- external heat transfer by radiation, conduction and convection to surroundings.

Also not less important is heat transfer before the molten metal is poured into the mould. or instance, in the casting of steel, heat transfer is important before the steel enters the mould because control of superheat in the molten steel is vital to the attainment of a predominantly equiaxed structure and good internal quality. Thus, conduction of heat into ladle and tundish linings, the preheat of these vessels, convection of the molten steel and heat losses to the surroundings also play an important role in continuous casting.

Because heat transfer is the major phenomenon occurring in continuous casting, it is also the limiting factor in the operation of a casting machine. The distance from the meniscus to the cut-off stand should be greater than the metallurgical length, which is dependent on the rate of heat conduction through the solid shell and of heat extraction from the outside surface, in order to avoid cutting into a liquid core. Thus, the casting speed must be limited to allow sufficient time for the heat of solidification to be extracted from the strand.

Heat transfer not only limits maximum productivity but also profoundly influences cast quality, particularly with respect to the formation of surface and internal cracks. In part, this is because metals expand and contract during periods of heating or cooling. That is, sudden changes in he temperature gradient through the solid shell, resulting from abrupt changes in surface heat extraction, causes differential thermal expansion and the generation of tensile strains. Depending on the magnitude of the strain relative to the strain-to-fracture of the metal and the proximity' of the strain to the solidification front, cracks may form in the solid shell. The rate of heat extraction also influences the ability of the shell to withstand the bulging force due to the ferrostatic pressure owing to the effect of temperature on the mechanical properties of the metal. Therefore, heat transfer analysis of the continuous casting process should not be overlooked in the design and operation of a continuous casting machine.

The importance of mathematical modeling of the continuous casting process can be seen in situations where the following are necessary.

i)              Simulation of an existing casting machine with a view to learning more about its operation;
ii)             Prediction of effects of a change in a casting parameter on the performance of an operating caster;
iii)            Design of new casting machines.

In particular, most process engineers are probably interested in the effect of increasing the casting speed on machine operation as higher output is sought to match planned or existing production capacity. Do changes then need to be made to the mould length, spray system, and position of the cut-off strand? Another area of interest to the process engineer is the minimization of interna1 cracks such as halfway or centerline cracks. These points are discussed in this section to show the importance of a mathematical model, based on heat-transfer principles, in adjusting casting conditions and improving overall machine performance.

Increasing the casting speed will have the effect of decreasing the time that the strand spends in the mould and spray zones, and also of increasing the depth of the liquid pool. Looking first at the mould, a decrease in the mould dwell time will result in a thinner shell at the bottom of the mould. Since this may increase the danger of break-outs, an increase in the mould length should be considered. Here the mathematical model can assist us since it can calculate the shell thickness for different casting speeds and mould lengths.

Halfway or midway cracks are the result of reheating of the surface of the strand due to a sudden reduction in the rate of surface heat extraction as the strand moves into the secondary cooling zone. So, if the spray system is to be altered to avoid midway cracks, reheating of the surface of the strand must be minimized as much as is practicable. How can this be achieved? A mathematical model can give part of the answer. For example, if the surface temperature distribution to be maintained through the sprays is specified, the mathematical model can provide the spray heat-flux distribution that is required to achieve it.

The following basic assumptions were made during the formulation of the mathematical model:

- The continuous casting process is steady state.
- A round billet is considered and radial symmetry assumed.
- Energy dissipation due to internal friction in the liquid state is neglected.
- The melt free surface is assumed to be covered with a protective slag layer,
through which negligible heat is assumed to be lost.

Taking the above assumptions into account, the governing equation will be reduced to:

The axial heat conduction is negligible compared to that convected due to the bulk motion of the moving strand. Thus, heat conduction is important solely in the radial direction. Under this condition the governing equation becomes:

The differential equation given in eq. 3 along with the boundary conditions in eqs. 4 through 7 is solved by the finite element method. The finite element solution approximates temperature at any point in an element as a function of nodal temperatures as follows:

After going through the finite element discretization, the following set of simultaneous equations which are to be solved for the nodal temperatures are obtained:

where K is the conductivity matrix, C is the heat capacity matrix, and Q is the nodal point heat flow input matrix. For a node on the solidification front:

Once the temperature distribution is found for the n^th step, the nodal heat flux for the node on the solidification front will be found from eq. 7. Then, the location of the solidification front at the next step will be found from:

Since the algorithm calculates Q from the temperature distribution of the n^th step, it is necessary to assume initial solidification to start the calculation process.

Equation 9 is solved by Euler's algorithm for unsteady and non-linear problems using the substitution method, in which:

A computer program with the above algorithm was developed and a number of test problems have been run.

A one dimensional solidification problem was solved for a slab-like region of water with initial temperature of 10 ºC when a temperature of -20 ºC is applied on the outer surface shown in Figure 4. The slab was modeled by using 20 two-node linear elements, 10 for the liquid part and 10 for the solid part. As solidification progresses, the mesh on the water is compressed and on the ice side is expanded; i.e., the interface moves.

In Figure 5, the result of the simplified front tracking FEM method presented in this paper is compared to Neuman's exact solution for a semi-infinite medium [2], the perturbation method, and the finite difference method [3]. Although there is no exact solution for this problem, it can be seen that the method presented in this paper is almost identical with the Neuman solution in the time range where the later is known to be exact.

The algorithm has also been applied to solve a two dimensional continuous casting problem of copper with the following thermal properties:

Property	Liquid state	Solid state
Thermal conductivity, k	370 W/m-K	370 W/m-K
Specific heat capacity, c	400 J/kg-K	400 J/kg-K
Density, r	8900 kg/m³	8900 kg/m³

In addition to these, the temperature of phase change T_m = 1083 ºC, a pouring temperature of T = 1150 ºC, and latent heat Q_L = 2 x 10⁵ J/kg were taken.

A constant heat flux of a value q = 1 x 10⁵ W/m² was prescribed within the mould. Outside the mould, the heat flux is assumed to vary with surface temperature T according to the following equation:

Results of calculations for casting speeds of 0.001 m/s, 0.002 m/s and 0.003 m/s are shown in Figure 7. It can be seen that the result well compares with that found by the boundary element method [4].

Figure 7: Shell profile for speeds 0.001 m/s (dotted line),
0.002 m/s (dashed line), and 0.003 m/s (solid line)

The continuous casting process is introduced. One and two dimensional heat transfer analyses of the process are discussed. Results showed that such mathematical analysis of the process can help to control and optimize the process and to investigate the consequences of parameter changes without the safety and cost limitations of in-plant experiments. The proposed algorithm can be used for the analysis of both stationary and moving solidification problems in which phase change occurs at a specific temperature.

T – Temperature
T_p – Pouring temperature
T_m – Solidification temperature
u - Casting speed
r - Density
c - Specific heat capacity
k - Thermal conductivity
q_s - Surface heat flux
Q_L - Latent heat
r_i - Interface position
N - Shape function
t - time
V - velocity vector
n - number of nodes