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Mathematical Models For Calculating The Value Of Dynamic Viscosity Of A Liquid

Ślęzak M.

Archives of Metallurgy and Materials

2015

Vol. 60, iss. 2A

581--589

The objective of this article is to review models for calculating the value of liquid dynamic viscosity. Issues of viscosity and rheological properties of liquid ferrous solutions are important from the perspective of modelling, along with the control of actual production processes related to the manufacturing of metals, including iron and steel. Conducted analysis within literature indicates that there are many theoretical considerations concerning the effect of viscosity of liquid metals solutions. The vast majority of models constitute a group of theoretical or semi-empirical equations, where thermodynamic parameters of solutions, or some parameters determined by experimental methods, are used for calculations of the dynamic viscosity coefficient. This article presents equations belonging to four groups of models for calculating the value of the dynamic viscosity coefficient: rheological models, non-rheological models, non-rheological and rheological models for calculating viscosity of metals. The last group of equations is developed by own experiments – high temperature rheological liquid steel measurements.

Celem prezentowanego artykułu jest dokonanie przeglądu modeli służących do obliczania wartości współczynnika lepkości dynamicznej cieczy. Zagadnienia lepkości oraz właściwości reologicznych ciekłych roztworów żelaza są ważne z punktu widzenia modelowania, a także sterowania rzeczywistymi procesami technologicznymi w odniesieniu do wytwarzania metali, w tym surówki i stali. Z przeprowadzonej analizy literaturowej wynika, że istnieje wiele teoretycznych rozważań nad zjawiskiem lepkości ciekłych roztworów metali. Zdecydowana większość modeli stanowi grupę równań teoretycznych, bądź półempirycznych, w których do obliczania wartości współczynnika lepkości dynamicznej wykorzystywane są wielkości termodynamiczne roztworów lub pewne wielkości wyznaczane metodami eksperymentalnymi. W artykule zaprezentowano równania należące do czterech grup modeli służących do obliczania wartości współczynnika lepkości dynamicznej: modele reologiczne, modele niereologiczne oraz modele niereologiczne oraz reologiczne wykorzystywane do obliczania lepkości metali. Ostatnia grupa równań została opracowana w ramach badań własnych – wysokotemperaturowych pomiarów reologicznych ciekłej stali.

Viscosity calculations of mold slag in continuous casting

Kalisz D.

Archives of Materials Science and Engineering

2012

Vol. 58, nr 2

164--170

Purpose: This paper deals with the mold slag viscosity calculations. Design/methodology/approach: The study involved the analysis of the impact of the chemical composition and temperature on the viscosity. Calculations were performed using models Riboud - Zhao, Urbain, Kondratiev and the computer program FactSage using module viscosity. The results of this works charakterize the effect of temperature, addition of CaF2 and Na2O on the viscosity for two types of slag. Findings: Slag 1 contained CaO/SiO2 = 0.78 and the addition of Na2O, slag 2 contained CaO/SiO2 = 1.32 wihout Na2O addition. Computer simulations revealed differences in the obtained values of viscosity. The use of the classical models: Riboud - Zhao and Urbain showed that at temperature 1200°C slag 2 contains larger content of CaO has the lowest viscosity at temperature 1500°C. The addition CaF2 causes a similar effect on viscosity of both slags. The use of the Fact Sage software showed that the addition of Na2O has a large influence on the viscosity. Slag 2 CaO/SiO2 = 1.32 although more than slag 1 is obtained at temperature 1500°C higher viscosity values. Research limitations/implications: Mathematical modeling of liquid mold slag viscosity based on classical and structural models and with the use of commercial software requires verification methods using scanning microscopy and nuclear magnetic resonance. Practical implications: The computer calculations of the mold slag viscosity shown that the selection of the chemical composition of the slag is important for the species of the cast steel and the speed of casting. Results of calculations show that the change in viscosity of the slag in the process result from the content composition: CaO/SiO2, CaF2 and Na2O content. Originality/value: The results of the calculations indicate the reaction of CaF2 with Na2O, probably results of this reaction is NaF, which prevents the formation of cuspidine which has a high melting point, its presence increases the melting point of the slag.