# Measurement and Model-Based Control of Solidification in Continuous Casting of Steel Billets
## 2 Materials and Methods  
Regarding the applied measurement technique, this paper lays the focus on the newly developed approach based on a laser vibrometer using Doppler interferometry with optimised head and data acquisition software to determine the solidification status of a strand section. It was constructed and tested in the laboratory of BFI. Afterwards, preliminary plant trials were undertaken on one strand at ESF with some first results on the determination of liquid and solid phases in the strand. An adaption of the system with water-cooled housing was necessary in order to perform two further plant trials at ESF. Figure 1 shows the laser vibrometer mounted on a rail to measure strand vibrations along the ESF billet caster. The Fast Fourier Transformed (FFT) vibrometer data over 60 measurement intervals of 1 s each are illustrated in Figure 2. The evaluation of these vibration spectra for stationary casting conditions along different positions below the meniscus revealed mainly signatures of the positions themselves (e.g., due to influences of descaler or other machine characteristics) instead of the solidification grade at these positions. Thus, it was decided to carry out a second vibrometer measurement campaign with fixed measurement position and application of stepwise increasing casting speeds. The recorded FFT vibration spectra were clustered by three different artificial intelligence (AI) methods: K-means, Gaussian mixture distribution and Ward method. Each method revealed a significant change in the population of the identified clusters after the emergence of a liquid core in the centre of the strand at the chosen measurement position (cf., results below). Figure 1: Laser vibrometer mounted on rail to measure strand vibrations along ESF billet caster. The dynamic real-time temperature and solidification model DynSolidCC of BFI is based on a state-of-the-art approach for solution of the heat flow equation with tailored submodels for the different boundary zones of the casting machine. In order to decouple the system of partial differential equations for fast numerical solutions, two approximations acceptable for the case of continuous casting have been made:  
* Neglection of heat conduction in the casting direction compared to convective heat transport and other heat conduction;
* Modelling of convective heat transport perpendicular to the casting direction in fluid phase by an effective thermal conductivity [5]. The model kernel was implemented with an application programming interface (API) for integration into online and offline applications and configured for simulations of the billet casting processes at ESF. The casting format of 160 \(\times\) 160 mm\({}^{2}\) billets was the focus of these simulations. The DynSolidCC model calculations for ESF caster were calibrated and validated based on the above-mentioned FOTS, infrared camera-based surface temperature and vibrometer measurement campaigns at the plant, which could be used for tuning related boundary condition model parameters. Offline parameter studies with the tuned casting process model revealed for the ESF billet caster only a minor influence of the initial superheat on the temperature field and solidification behaviour in the strand compared to the higher influence of spray water flows in secondary cooling and even stronger influence of the casting speed. A linear dependency of crater end position from casting speed and a quadratic dependency from spray water flows within a defined range the around defined reference casting conditions were found, which can be used for dynamic control of spray water flows and casting speed to adjust a target crater end position without iterative simulations of the whole resulting 3-dimensional stationary strand temperature field, which turned out to be too time-consuming for online application.