A Three-dimensional Mathematical Modelling of Drainage Behavior in Blast Furnace Hearth

Abstract

Stable blast furnace operation is required to reduce energy consumption in iron and steelmaking industry. For the stable blast furnace operation, precise controlled drainage is one of the important factors. However, the effects of the various in-furnace conditions on the stable operation were not examined well. Therefore, in this work, basic characteristic features of drainage in a blast furnace hearth were examined.Two-and three-dimensional mathematical model were developed based on the finite difference method to simulate molten iron and slag flow in a hearth of a blast furnace. Pressure drop evaluation model in a taphole was developed to reflect pressure variation in a blast furnace hearth on drainage rate of molten iron and slag for the three-dimensional mathematical model.The two-dimensional mathematical model results were validated with measured interfaces shapes obtained using an experimental model. The three-dimensional mathematical model results were validated with measured total, iron and slag drainage rate of Chiba No. 6 blast furnace. The results indicate that the drainage behavior and residual iron and slag volume were affected by the conditions in the hearth. The taphole conditions dominate the total drainage rate under the term of assumed blast furnace conditions. In order to reduce the residual slag volume, the taphole diameter change during the tap should be controlled. The decrease of the coke diameter causes increase of the residual slag volume, decrease of the residual iron volume.KEY WORDS: iron and slag flow; residual slag volume; numerical simulation; VOF method; blast furnace hearth; ironmaking.faces shapes of immiscible fluids having different properties. Two-dimensional Mathematical ModellingThe governing equations for fluid flow used in the twodimensional mathematical model are based on the HSMAC method, 8) ... (3) where u is the horizontal velocity (m/s), v is vertical velocity (m/s), x and y are coordinates (m), t is time (s), r is density of fluids (kg/m 3 ), p is pressure of fluids (Pa), m is viscosity (Pa · s), g is acceleration due to gravity (m/s 2 ), and S is an interaction force between fluid and 2 flat parallel plates (m/s 2 ). In the two-dimensional mathematical model, gas, slag and iron were treated as one fluid having local properties, which correspond to each phase. Representation of InterfacesFor the determination of the fluid properties in each computational cell, it is necessary to compute the proportion of gas, iron and slag in each cell. Therefore, gas-slag and slag-iron interfaces should be identified exactly. To distinguish the interfaces, the VOF method 9) was applied for the calculation of interfaces (gas-slag, slag-iron). Generally, the VOF method is used to track free boundaries in two-or three-dimensional meshes. Although, in this work, VOF is also used to identify slag-iron interface, as shown in Fig. 1. A unit value of VOF 1 would correspond to a cell full of liquid. A unit value of VOF 2 would correspond to a cell full of iron. Cells with VOF 2 values betw...

Pressure Drop in the Blast Furnace Hearth with a Sitting Deadman

“…An efficient and strictly controlled tapping is necessary for guaranteeing a stable operation and high productivity of the BF. Many recent investigations [1][2][3][4][5][6][7][8][9] on this subject have revealed that the pressure drop caused by fluid flow through the deadman in the hearth is a significant factor governing hearth drainage. However, due to the hostile environment, the possibilities to directly measure internal variables are practically nonexistent.…”

Modelling of Multiphase Flow in a Blast Furnace: Recent Developments and Future Work

“…38,134) Recently, attempts have also been made to model the gas-liquid-solid flow in BF hearth, where the effects of coke free zone, 85) natural convection and turbulent model 86,88) are investigated. Mathematical models have also been extended to identify the interface between slag and hot metal, 90) and establish the interrelationships between operation parameter, hearth condition and drainage behaviour. 91,92) The work described in this section may offer various methods to study the multiphase flow in a BF.…”

“…Numerical predictions of liquid levels or liquid flow distributions in the hearth are usually based on the static equilibrium of forces acting on the submerged solid particles or an assumed position of deadman and porosity distribution in the submerged solid region. [83][84][85][86][87][88][89][90][91][92] The prediction of the deadman profile and its relation to solid or liquid flow pattern overcomes these deficiencies. Due to the discontinuous stress distribution between solid particles in the hearth, a continuum-based approach is difficult to apply.…”

Effect of FeO in Dripping Slag on Drainage Ability of Slag

“…In a previous paper, 11) we developed a three-dimensional mathematical model, which can predict gas-slag and slag-iron interfaces shapes, total drainage rate, iron and slag drainage rates during a tap affected by various hearth conditions. The effect of various in-furnace conditions on drainage rates, gas-slag and slag-iron interfaces shapes and maximum gas-slag interfaces height were examined in another previous paper.…”

“…[1][2][3][4] Many researchers attempted to solve the issues by using experimental and mathematical models. [1][2][3][4][5][6][7][8][9][10][11] However, there are many problems to understand drainage behavior in a blast furnace hearth because several important hearth values such as coke diameter, void fraction, temperature of iron and slag in the hearth, and levels of iron and slag cannot be measured during a tap. Because of these issues, there are many unrevealed phenomena in the blast furnace hearth.…”