Mathematical Modeling of Iron and Steel Making Processes. Mathematical Model for Transient Erosion Process of Blast Furnace Hearth.

Takatani, Kouji; Inada, Takanobu; Takata, Kouzo

doi:10.2355/isijinternational.41.1139

Cited by 63 publications

(52 citation statements)

References 7 publications

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“…The model thus provides a measure of the extent of the coke-free region, the important role of which on iron flow and hearth refractory wear has been stressed by several investigators. [24][25][26][27] …”

Section: Discussionmentioning

confidence: 99%

Model Analysis of the Operation of the Blast Furnace Hearth with a Sitting and Floating Dead Man

Brännbacka

Saxén

2003

ISIJ International

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The phenomena in the blast furnace hearth are extremely complex and the possibilities to directly measure its internal state are practically non-existent. In order to control the process to achieve smooth operation and long campaigns, a thorough understanding of the conditions in the hearth is required. Such knowledge can be gained through mathematical modeling of the internal conditions. Since the properties of the dead man are known to considerably affect the hearth conditions, a model describing the operation of the hearth with a sitting, partially or completely floating dead man has been developed. Simulation of the tap cycle of a one-taphole blast furnace shows the effect of boundary conditions, hearth geometry, coke voidage and dead-man floating state on the evolution of the liquid levels and the slag delay. On the basis of the computed inner geometry of the hearth, the model has been applied to data from a six-year period of a Finnish blast furnace, and it has been found to accurately predict the long-term variations in the slag delay.KEY WORDS: blast furnace hearth; tap cycle; dead man floating; slag delay. scend further to a certain (given or calculated) level below the taphole at the end of each tap. Under these assumptions, the voidage of the dead man can be estimated once in every tap cycle from produced and tapped quantities of iron.According to Zulli, 13) a coke-free zone at the bottom of the hearth does not influence the cyclic behavior of the liquid levels as long as its volume is constant and it does not extend above the surface of the iron phase. However, if a coke-free zone below the dead man exists, the reason must be that the dead man is (at least partially) floating, so the position of the dead man, and thus also the size of the free space below it, depends on the volume of the liquids in the hearth. From this it follows that it is likely that the volume of the free space varies and affects the liquid levels. Therefore, the methods for estimating the dead-man voidage reviewed above apply only for a hearth with a sitting dead man. This is one of the motivations behind the modeling effort presented in the present paper, where the effect of a floating dead man on the liquid levels is investigated. In particular, the implications of dead-man floating on the slag delay, t sl , i.e., the time of iron-only flow in the beginning of the tap, is studied. Modeling The Tap CycleIn blast furnaces with one taphole, the tapping of iron and slag from the hearth follows a typical cycle, schematically illustrated in Fig. 1. When the taphole is closed both iron and slag accumulate in the hearth because of the progress of reduction and smelting of iron and slag formation. In the hearth the two liquids form separate layers, the dense iron on the bottom and the light slag layer floating on top of the iron bath. The taphole is generally kept plugged for at least 20-30 min to let the injected taphole mud solidify properly. Thus, as the tapping begins the iron-slag interface, henceforth called the iron level, is us...

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Section: Discussionmentioning

confidence: 99%

Model Analysis of the Operation of the Blast Furnace Hearth with a Sitting and Floating Dead Man

Brännbacka

Saxén

2003

ISIJ International

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“…Though, the particle size and void ratio of deadman were assumed to be 20 mm and 0.4, respectively, since the permeability of the deadman is supposed to be good in the target period. The simulation was made by use of the mathematical model developed by Takatani et al 22) The erosion profile was successively updated in the reiterative calculation process where temperature distribution evaluation by flow and heat transfer analysis of the hearth and removal of refractory pieces based on erosion criteria shown in Table 8 were made, and finally, the "thermo-equilibrium" erosion profile was obtained when no removal process of refractory was required.…”

Section: Simulation Of the Erosion Profile Of Hearth Refractorymentioning

confidence: 99%

Dissection Investigation of Blast Furnace Hearth—Kokura No. 2 Blast Furnace (2nd Campaign)

Inada¹,

Kasai²,

Nakano³

et al. 2009

ISIJ Int.

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“…On the other hand, it is also noted that the powder flow pattern has not been affected much by F l f , which explains why reasonable results can still be obtained even the liquid-powder interaction force was ignored in other studies. 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.…”

Section: Simulation Of the Multiphase Flowmentioning

confidence: 99%

“…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.…”

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

et al. 2007

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An ironmaking blast furnace is a complex multiphase flow reactor involving gas, powder, liquid and solid phases. Understanding the flow behaviour of these phases is of paramount importance to the control and optimization of the process. Mathematical modelling, often coupled with physical modelling, plays an important role in this development. Yagi 1) gave a comprehensive review of the early studies in this area in 1993. Significant progress has since been made, partially driven by the needs in research but mainly as a result of the rapid development of computer and computational technologies. This paper reviews these developments, covering the formulation, validation and application of mathematical models for gas-solid, gas-liquid, gas-powder and multiphase flows. The need for further developments is also discussed.KEY WORDS: ironmaking; blast furnace; multiphase flow; two fluid model; discrete element method. Review development. Mathematical ModellingGenerally speaking, the existing approaches to modelling the multiphase flow in a BF can be classified into two categories: continuum approach at a macroscopic level and discrete approach at a microscopic level. In the continuum approach, phases are generally considered as fully interpenetrating continuum media and described by separate conservation equations with appropriate constitutive relations and interaction terms representing the coupling between phases. The general governing equations are based on the so-called two fluid model (TFM), originally developed for gas-particle flow, [29][30][31] given by:Conservation The so-called Model A and Model B result from the treatment of the fluid pressure. For example, for gas-solid flow, Model A assumes the pressure is shared between the two phases, while in Model B, the pressure is attributed to gas phase only. 31) Model A formulation has been widely used in multiphase modelling, especially in process metallurgy. Model B formulation was recently used in the so called combined continuum and discrete method for coupled flow of continuum fluid and discrete particles. 32) The continuum approach is suitable for process modelling and applied research because of its computational convenience and efficiency. Indeed, most of the BF modelling is based on this approach. However, its effective use heavily depends on constitutive or closure relations and the momentum exchange between phases. For Newtonian fluids (gas and liquid here), these relations can be readily determined. For non-Newtonian fluids such as solids and powder, general theories are not yet available. In the past, various theories have been devised for different flow regimes (three flow regimes have been identified: quasi-static regime, rapid flow regime and a transitional regime that lies inbetween). For example, models have been proposed to derive the constitutive equations for the rate-independent deformation of granular materials based on either the plasticity theory or the double shearing theory; the rapid flow of granular materials has been described by extend...

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Mathematical Modeling of Iron and Steel Making Processes. Mathematical Model for Transient Erosion Process of Blast Furnace Hearth.

Cited by 63 publications

References 7 publications

Model Analysis of the Operation of the Blast Furnace Hearth with a Sitting and Floating Dead Man

Model Analysis of the Operation of the Blast Furnace Hearth with a Sitting and Floating Dead Man

Dissection Investigation of Blast Furnace Hearth—Kokura No. 2 Blast Furnace (2nd Campaign)

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

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