Thermal monitoring of iron making ladles in production is important since the energy that is stored in the ladle has an influence on the molten steel. A cold ladle will take a bit of thermal energy from the molten steel during the period between tapping and casting. At the same time the temperature of the steel at the casting phase has a direct influence on the quality of the final product. Thus good control of the temperature in the production process is needed.
A joint project between MAI and SSAB
Previously, in a joint project between Fredrik Berntsson and Patrik Wikström (SSAB), a mathematical model of the heat transfer in a standard steel making ladle has been developed. The mathematical model has been implemented as a simulation code that allows the thermal state of the ladle to be tracked during production. The input to the model is taken from the SSAB production monitoring system, that is time spent by the ladle in different configurations. The simulation software has been running at SSAB, Luleå, since late autumn 2021.
Certain physical parameters difficult to estimate
A problem during the development of the model was that certain physical parameters in the model are difficult to estimate. This includes the exact thermal conductivity of certain materials used and also a couple of heat transfer coefficients. In order to verify the accuracy of the model a special ladle has been prepared. The test ladle has several thermocouples built into it. In the photo below, we see one of thermocouples being inserted into the the wear lining of the Ladle. We also see the test ladle at the end of a casting cycle. The test ladle was constructed during spring 2022 and temperature data was collected during several production cycles. In total temperature measurements were taken during a little more than nine days until the ladle was taken out of production to be rebuilt.
Using measurements to verify accuracy of the model
In the current project the measurements have been used to verify the accuracy of the model. We have also tried to find optimal parameters, that fit the data in a least squares sense, by implementing a Gauss-Newton type algorithm. The results from the parameter fitting indicates that most of the physical parameters in the model of the ladle were essentially correct. However, one type of insulation material had a completely wrong thermal conductivity. With some of the physical parameters adjusted the simulation software accurately predicts the temperatures in the ladle for the duration of the experiment. In the photo below, we see both measured and simulated temperatures, in the ladle wall, during the time period 172-180 hours from the time when the ladle was initially put into production (black=measurement and blue=simulation). The thermocouple was located about 10 cm from the interior where the molten steel is held. Note that the only input to the simulation code is the production system that records the configuration of the ladle, for example empty, full, with or without lid, etcetera every 5 minutes.
Using simulation in production planning
Since the simulation software can predict a future thermal state of the ladle, including the temperature of the molten steel, our next step is to more actively use the simulation results in the production planning. The idea is to pick the temperature of the steel during the tapping phase in such a way that the desired temperature is obtained during the casting phase, given the current state of the ladle and detailed schedule for the next production cycle.