# Measurement and Model-Based Control of Solidification in Continuous Casting of Steel Billets
## 1 Introduction  
The continuous casting (CC) of slabs or billets is a widespread process in the steel industry. Starting from liquid steel, a primary cooling zone constituted of a water-cooled mould achieves the solidification of a solid shell. This shell is thick enough to permit downwards extraction of the steel strand by supporting rolls which convey it through the secondary cooling zone, in which the product is submitted to intense water cooling. Hence, the solidification proceeds from surface towards the centre of the strand. All phases of the steel from liquid to completely solidified zones coexist in the process of continuous casting, i.e., from the meniscus to the end of the liquid pool (crater end, metallurgical length). For modelling the solidification process during continuous casting of steel, there are various commercial software packages available. These include Computational Fluid Dynamics (CFD, e.g., ANSYS/FLUENT) for modelling turbulent 3D flows with heat and mass transfer, which can be coupled to Finite Element Methods (FEM, e.g., ABAQUS) in order to determine stresses and strains in the strand [1,2]. There are a few commercial systems tailored to the modelling of continuous casting of steel [3], namely ProCAST (ESI), THERCAST (Transvador), MAGMA CC (MAGMA Giessereitech-nologie GmbH), FLOW-3D Cast (Flow Science Inc.) and CC Master (Expresslab). Only the first three aforementioned packages enable calculations on a number of processors. Based on such software packages, detailed numerical offline simulations ofcontinuous casting processes are possible in order to gain a better understanding of the influences of various casting conditions (mould design, mould water flow, casting speed, mould powder addition, spray water flows, spray nozzle configuration, electromagnetic stirring (EMS), etc.) on the temperature and fluid flow fields as well as on the shell thickness. These offline calculations may be used to optimise the design of mould and casting machine as well as to derive optimised cooling strategies for different (transient) casting conditions. For online monitoring and control of the continuous casting process, various numerical models have been developed based on the heat flow equation with (semi-)empirical sub-models for the boundary conditions [1; 4; 5; 6; 7; 8]. Some of them also include the Navier-Stokes equation for modelling of the fluid flow [1], while others just consider the mass flow in casting direction [5; 8]. They use explicit or implicit finite difference methods and thermophysical steel data (specific enthalpy, density, thermal conductivity, liquid phase fraction, etc.) depending on temperature and composition of the steel [5]. These models allow to monitor the casting process online, providing information about the 3D temperature (and fluid flow) fields and the related solidification front along the casting machine. With sufficiently powerful hard- and software architecture, the dynamic online solidification models can also be used in a predictive mode for determination of optimal cooling parameters under varying casting conditions. This model-based dynamic control has already been tested to achieve the best control capabilities compared to other methods such as fuzzy or PID control systems [9]. A vibrometer has been used for assessment of crater end position within first patented technologies. By enforcing a periodically forced vibration with certain frequency and amplitude on certain position of continuous casting process through the segment driven roller and applying the effect of different damping attenuation of vibration from liquid and solid phase, the final solidifying end can be detected online according to the feedback discrimination pattern of the exciting force signal and displacement signal [10]. The patent [11] describes a method of vibratory excitation realised by ultrasonic shear waves to detect the crater end. On the one hand, one attains a defined oscillation frequency which is proposed to be easily detectable.