An Improved Model of Cored Wire Injection in Steel Melts

Abstract

Mathematical models for tracking the melting of cored wire during its injection into the steel bath have been developed in the past though important aspects of the formulations have not been discussed in sufficient detail. As a result, it is difficult to use the results of these models to derive benefits for a specific steel melting shop.A general purpose mathematical model has been developed at R & D, Tata Steel, using the finite difference approach with a fully implicit scheme to simulate the process of cored wire injection taking into account the different operating practices encountered in the steel shop. Numerical simulation of this kind of problem, involving moving boundary, typically suffers from the limitation that the progressive solidification of frozen layers that takes place is not made part of the thermal balance till it attains the size of a full node and thus the heat gained or lost by this "partial node" is not accounted for till such time. An alternative numerical formulation has been developed to rectify this.Owing to the difficulty in making a direct validation, this model has been verified through a novel approach. This work suggests that the use of different wire dimensions (13-18 mm diameter and 0.4-0.6 mm casing), depending on the steel grades to be processed, is necessary in order to extract the maximum benefit.KEY WORDS: mathematical model; steelmaking; calcium treatment; cored wire; injection metallurgy; deoxidation; alloy addition.

A Lump-Integral Model for Freezing and Melting of a Bath Material Onto a Plate Shaped Solid Additive in an Agitated Bath

“…In this situation, it is observed that the increased heat transfer coefficient of the bath reduces the frozen layer thickness and time taken in the first step for the plate [1], spherical [6] and cylindrical [3] additives. This prediction is implicit in [2,5] whereas in [4] only instant equilibrium temperature at the interface between the additive and the bath immediately after the immersion of the additive in the bath is found. Closed-form solutions for the growth of the maximum frozen layer thickness, its time of development and the total time of freezing and melting of the bath material onto the cylindrical additive in an agitated bath [7] is also reported recently.…”

“…Investigation of such a situation that leads to thermal resistance of the frozen layer negligible with respect to that of the bath seldom appears in the literature. However, the occurrence of the first step for plate [1], cylindrical [2][3][4] and spherical [5,6] shaped solid additives is analyzed when the frozen layer formed on these additives has their thermal resistances comparable with those of their bath. In this situation, it is observed that the increased heat transfer coefficient of the bath reduces the frozen layer thickness and time taken in the first step for the plate [1], spherical [6] and cylindrical [3] additives.…”

Model Based Optimisation of Aluminium Wire Injection in Steel Melts

“…It is also possible to represent the same heat transfer phenomena by the following one dimensional unsteady state heat conduction equation. An earlier work 1) of this author had detailed the procedure. Equation (1) has been used for the present study and solved with the relevant initial and boundary conditions to determine 1. the temperature distribution inside the Al wire and the solidified shell, 2. the total time taken for the melting of the shell and Al wire.…”

“…The imperfect contact between the wire surface and this shell results in a thermal contact resistance (R T ) between the two. [1][2][3][4][5][8][9][10][11][12][13][14] These values for different metal combinations have been derived experimentally, [15][16] which vary from 1.9ϫ10 Ϫ4 to 9.1ϫ10 Ϫ4 m 2 s K/J. The authors have considered the value as 2.4ϫ10 Ϫ4 m 2 s K/J for the present study.…”

“…In a fashion similar to the case of cored wire, 1) when an aluminium (Al) wire at room temperature is injected into the liquid steel solidifies on itself a layer of the steel from the melt. This layer, referred to as a shell, grows to a maximum thickness and thereafter melts back leaving the original wire (either solid or molten depending on the prevailing thermal condition) surface uncovered.…”