Evaluation of Heat Transfer Coefficients along the Secondary Cooling Zones in the Continuous Casting of Steel Billets

In the present work, heat transfer coefficients (h) along different cooling zones of a continuous caster billet machine were determined during casting of low and medium carbon steels. The effects of casting parameters, such as machine characteristics, the ingot dimension, mold, sprays zones, radiant cooling, melt composition and casting temperature were investigated and correlated with heat transfer coefficients. By using industrial measured billet surface temperatures, linked with a numerical solution of the solidification problem, ingot/cooling zones heat transfer coefficients were quantified based on the solution of the inverse heat conduction problem (IHCP). The experimental temperatures were compared with simulations furnished by an explicit finite difference numerical model, and an automatic search has selected the best theoreticalexperimental fit from a range of values of h. The computer software algorithm has been developed to simulate temperature profiles, solid shell growth, phase transformations and the point of complete solidification in continuous casting of steel billets and blooms. Industrial experiments were monitored with an optical infrared pyrometer to analyze the evolution of surface temperatures during solidification along the machine. The results permitted the establishment of expressions of h as a function of position along the caster, for different steel compositions, casting parameters and melt superheats. INTRODUCTION The continuous casting process is responsible by most of the steel production in the world, and has largely replaced conventional ingot casting/rolling for the production of semi-finished steel shaped products. The process is essentially a process of heat transfer between the metal and different cooling zones. Fig. 1 shows a schematic representation of a continuous caster and the different cooling zones along the machine. The casters have been implemented with modern equipments for billets, slabs or blooms, multiple casting and process control. Figure 1. Representation of the continuous casting process of steel. For the purpose of accurate mathematical modeling of solidification in the continuous casting of steel, it is essential that correct boundary conditions be established along the caster machine during casting operations. Heat transfer at the metal/cooling interface is one of these boundary conditions, which is of central importance when considering the magnitude of heat transfer during the stages of solidification in the mold, spray zones or natural cooling. Inverse Problems, Design and Optimization Symposium Rio de Janeiro, Brazil, 2004 The present study describes a method for obtaining transient interfacial heat transfer coefficients as a function of position along the caster, from temperature experimental data concerning the solidification of steel during continuous casting. Ingot surface experimental temperatures obtained by optical pyrometers are compared with simulations furnished by a numerical model, and an automatic search selects the best fit from a range of values of interfacial heat transfer coefficients by IHCP procedure (Inverse Heat Conduction Problem). The effects of alloy composition, casting and dimensions of the ingot are also investigated. HEAT TRANSFER COEFFICIENT Several studies have attempted to quantify the metal/cooling transient interfacial heat transfer during solidification in continuous casting processes during operation in terms of a heat transfer coefficient . These studies have highlighted the different factors affecting heat flow across metal/cooling interface during solidification. These factors include the thermophysical properties of the contacting materials, the casting and mold geometry, melt superheat, and mainly the specific configurations of each machine, as well as the operational casting parameters and solidification conditions. The heat transfer coefficients vary for each region along the machine . Most of the methods of calculation of h existing in the literature are based on temperature histories at points of the casting or mold together with mathematical models of heat transfer during solidification. Among these methods, those based on the solution of the inverse conduction problem have been widely used in the quantification of the transient interfacial heat transfer . This method makes a complete mathematical description of the physics of the process and is supported by temperatures measurements at known locations inside the heat conducting body. The temperature files containing the experimentally monitored temperatures are used in a finite difference heat flow model to determine h, as described in a previous article. The process at each time step included the following: a suitable initial value of h is assumed and with this value, the temperature of each reference location in casting at the end of each time interval ∆t is simulated by using an explicit finite difference technique. The correction in h at each interaction step is made by a value ∆h, and new temperatures are estimated [Test(h+∆h)] or [Test(h-∆h)]. With these values, sensitivity coefficients (φ) are calculated for each interaction, given by: h ) h ( T ) h h ( T est est ∆ − ∆ + = φ (1) In the present work, a similar procedure determines the values of h, which minimizes an objective function defined by: