Viscosity models for molten slags

The understanding and optimisation of the metallurgical processes require access to accurate data of the physical properties of slags. Viscosity is one of the most important properties in the case of metallurgical melts, in view of its direct effect on the kinetic conditions of the processes, and is one of the key factors to be taken into consideration in process modeling. The difficulty and high cost of measuring the viscosity of slags has led to development of number of viscosity models. Most of these models employ parameters extracted from experimental data of viscosity, which ensure the validity of the models in viscosity estimation. In this report models developed to estimate the viscosity of fully molten oxide slags were discussed. In addition viscosities of converter slags (Basic Oxygen Furnace, Argon-Oxygen Decarburization furnace) predicted with different models were compered. In the case of BOF-slag the Iida and the modified Urbain models seemed to be more reliable than the other models in predicting the viscosities. The values calculated by KTH model were too high for this high basic slag whereas in the case of NPL model the slag composition was observed to be outside of the working range of the model. Urbain model modified by Forsbacka as well as the modified Iida models takes account of chromium oxide as a separate component in the calculations and are thus assumed to be more reliable than the other models in predicting viscosities of chromium containing slags. However the reliability of these models is debatable in the case of high chromium containing slags e.g. AOD-slag after oxidising period due to existing of solid phases in the slag. Iida as well as the Urbain model modified by Forsbacka are also assumed to be reliable predicting viscosity of slag composition corresponding the AOD-slag after reduction period. Also NPL-model seemed to give reliable viscosity values, since in this case the slag composition is inside the working range of the model. Although there are plenty of experimentally measured viscosity data available for ternary systems, less data in limited ranges are available as the order of the system gets higher. Also lack of experimental data of very basic slag compositions as well as slags containing iron and chromium oxides is apparent. Due to lack of experimental data the performance of these models in predicting viscosities of converter slags was not able to evaluate. Thus more experimental work is necessary to provide the data to test and optimise the models for these very complex slag compositions

A simple mathematical model for estimating plume hydrodynamics of metallurgical ladles

In secondary steelmaking, the refining operation is typically carried out in a metallurgical ladle that is commonly furnished with gas injection facilities. Since gas injection plays an intrinsic role in determining the efficiency of secondary steelmaking and thus the quality of final products, a great volume of work has been conducted mostly utilizing air-water systems at room temperature. Despite a portion of the air-water correlations have been adopted in the literature, their applicability to the real argon-metal system is still questionable. The main motivation behind this paper is to present a simple mathematical model for plume hydrodynamics of metallurgical ladles based on the characteristic phenomena and underlying mechanisms of a buoyant plume, where bubble breakup and coalescence occur simultaneously. The main assumptions/simplifications and governing equations are firstly introduced. After that, the accuracy of the model is demonstrated by comparing predicted plume velocities with the ones measured in an industrial ladle.Peer reviewe

Optimization of the CCT curves for steels containing Al, Cu and B

Abstract New continuous cooling transformation (CCT) equations have been optimized to calculate the start temperatures and critical cooling rates of phase formations during austenite decomposition in low-alloyed steels. Experimental CCT data from the literature were used for applying the recently developed method of calculating the grain boundary soluble compositions of the steels for optimization. These compositions, which are influenced by solute microsegregation and precipitation depending on the heating/cooling/holding process, are expected to control the start of the austenite decomposition, if initiated at the grain boundaries. The current optimization was carried out rigorously for an extended set of steels than used previously, besides including three new solute elements, Al, Cu and B, in the CCT-equations. The validity of the equations was, therefore, boosted not only due to the inclusion of new elements, but also due to the addition of more low-alloyed steels in the optimization. The final optimization was made with a mini-tab tool, which discarded statistically insignificant parameters from the equations and made them prudently safer to use. Using a thermodynamic-kinetic software, IDS, the new equations were further validated using new experimental CCT data measured in this study. The agreement is good both for the phase transformation start temperatures as well as the final phase fractions. In addition, IDS simulations were carried out to construct the CCT diagrams and the final phase fraction diagrams for 17 steels and two cast irons, in order to outline the influence of solute elements on the calculations and their relationship with literature recommendations

Gradient boosted regression trees for modelling onset of austenite decomposition during cooling of steels

Abstract Continuous cooling transformation (CCT) diagrams can be constructed by empirical methods, which is expensive and time consuming, or by fitting a model to available experimental data. Examples of data-driven models implemented so far include regression models, artificial neural networks, k-Nearest Neighbours and Random Forest. Gradient boosting machine (GBM) has been succesfully used in many machine learning applications, but has not been used before in modelling CCT-diagrams. This article presents a novel way of predicting ferrite start temperatures for low alloyed steels using gradient boosting. First, transformation onset temperatures are predicted over a grid of values with a trained GBM-model after which a physically-based model is fitted to the piecewise constant curve obtained as output from the model. Predictability of the GBM-model is tested with two sets of CCT-diagrams and compared to Random Forest and JMatPro software. GBM outperforms its competitors under all tested model performance metrics: e.g. R² for test data is 0.92, 0.87 and 0.70 for GBM, Random Forest and JMatPro respectively. Output from the GBM-model is used for fitting a physically based model, which enables the estimation of transformation start for any linear or nonlinear cooling path. This can be further converted to Time-Temperature-Transformation (TTT) diagram

Optimization of CCT equations using calculated grain boundary soluble compositions for the simulation of austenite decomposition of steels

Abstract New CCT equations have been developed and optimized to simulate the start temperatures of the austenite decomposition process in low-alloyed steels using experimental CCT data published in the literature. Exceptionally, this optimization does not apply the nominal compositions of the steels, but the corresponding soluble compositions of the grain boundaries calculated using IDS software, depending on the reported austenitization treatments of the steels. These compositions, rather than the nominal ones, are expected to control the start of the austenite decomposition, which usually initiates at the grain boundaries. The new optimization treatment takes into account the solute microsegregation and the possible precipitate formation. Using IDS software, the new equations were validated with new experimental CCT data. Agreement was good not only for the austenite decomposition start temperatures, but also for the final phase fractions, indicating fairly reasonable predictions of phase transformation kinetics by the IDS. In addition, IDS simulations were compared with the experimental CCT data of five high-carbon steels, applying both the new equations based on grain boundary soluble compositions as well as the equations based on the nominal compositions. With the same experimental CCT data used in optimization, better agreement was obtained with the new equations, indicating the importance of determining the soluble compositions at the grain boundaries where the austenite decomposition process is likely to begin

New phenomenological quality criteria for continuous casting of steel based on solidification and microstructure tool IDS

Abstract The aim of this work was to derive new quality criteria based on steel composition and cooling pattern for continuous casting and for the subsequent cooling and reheating processes. The criteria were devised based on the outputs of multiphysics simulation tools for casting applications. The criteria were found to be good predictors of whether a steel grade combined with a given cooling pattern is prone to a specific defect. The criteria are useful in providing a theoretical justification as to why certain defects form or would form, and can be used for devising practical solutions to avoid them. In practice, the final determination of whether a defect will form depends on the cumulative impact of various single quality criteria combined with the models/data describing the developing mechanical and thermal stresses. In this paper, new quality criteria are proposed for different kinds of cracking-related and gas defects along with case examples