Method for optimizing slag-iron separation of high-carbon chromite hot slag

By constructing a density ratio function and calculating the shear disturbance intensity to optimize the iron slag outlet opening ratio, the problem of unstable layer interface control in the slag-iron separation of high-carbon chromite ore hot furnace was solved, thus achieving stability in slag-iron separation and equipment protection.

CN121362879AActive Publication Date: 2026-01-20INNER MONGOLIA XINTAIYUAN NEW MATERIALS CO LTD
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Patent Information

Application Number
CN202511946663.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-12-23
Publication Date
2026-01-20
Estimated Expiration
2045-12-23

AI Technical Summary

Technical Problem

In the smelting process of high-carbon chromite submerged arc furnace, slag-iron separation relies on operator experience and fixed structure adjustment, which cannot achieve dynamic response control of the layering interface height. It is easily affected by factors such as interface disturbance and temperature gradient, which can lead to layering failure, resulting in slag-iron mixing and equipment wear.

Method used

By constructing a density ratio function and a shear disturbance intensity calculation formula based on temperature data, density differences and shear disturbances are dynamically sensed, and the opening ratio of molten iron slag outlet is optimized, thereby achieving real-time control and stability improvement of the layered interface.

Benefits of technology

It can detect density differences on a millisecond timescale, prevent slag-iron mixing, improve the stability of stratification control, reduce equipment wear, and increase alloy purity and resource recovery rate.

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Abstract

The invention relates to the technical field of iron smelting, in particular to a slag-iron separation optimization method for high-carbon chromite hot slag. The method comprises the steps that the molten iron temperature and the slag temperature are obtained, instantaneous density values of molten iron and slag are estimated respectively, and the density ratio of the molten iron to the slag is obtained; based on the density ratio of the molten iron to the slag, an interface height dynamic positioning model is constructed, and the layered interface height is obtained; a layered shear disturbance intensity calculation formula is introduced to quantify the shear force, and the shear disturbance intensity is obtained; and based on the shear disturbance intensity, the molten iron and slag outlet opening ratio is adjusted in combination with the layered interface height, and separation optimization is conducted based on the molten iron and slag outlet opening ratio. The problem that in the slag separation process, dynamic response control over the layered interface height cannot be achieved mainly depending on operator experience and fixed structure adjustment is solved; and layering failure and frequent mixed flow phenomena are caused by the influence of factors such as interface disturbance and temperature gradient.
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Description

Technical Field

[0001] This invention relates to the field of iron smelting technology, and in particular to an optimized method for separating iron from slag in a high-carbon ferrochrome ore furnace. Background Technology

[0002] In the smelting process of high-carbon ferrochrome submerged arc furnaces, slag-iron separation is a crucial step before molten iron tapping, and its efficiency directly determines the alloy purity, resource recovery rate, and energy utilization level of the final product. Currently, most enterprises still use physical separation methods based primarily on gravity settling, supplemented by slag baffles or grate structures. In traditional processes, operators rely on their experience to judge the stratification state and manually adjust the iron and slag tapping processes, which has significant limitations. Specifically, the physical properties of molten iron and slag are not significantly different at high temperatures; for example, the density and viscosity differences change dynamically with temperature fluctuations, making it difficult to accurately determine the stratification interface. Furthermore, during iron tapping, the height of the stratification interface often fluctuates with changes in flow rate and furnace temperature, and is easily damaged by shear disturbances and fluid instability, leading to slag mixing into the molten iron or molten iron flowing into the slag pool. This reduces the purity of the molten iron or wastes alloy resources, and causes erosion and wear on equipment such as grates, increasing operation and maintenance costs. Summary of the Invention

[0003] This invention provides an optimized method for separating slag and iron in a high-carbon chromite submerged arc furnace, which solves the technical problems of relying mainly on operator experience and fixed structure adjustment during slag separation, making it impossible to achieve dynamic response control of the layering interface height; and being easily affected by factors such as interface disturbance and temperature gradient, leading to layering failure and frequent mixing phenomena.

[0004] An optimized method for separating slag and iron in a high-carbon ferrochrome submerged arc furnace, according to the present invention, includes the following steps: S1. Obtain the temperatures of molten iron and slag, and estimate the instantaneous density values ​​of molten iron and slag respectively to obtain the density ratio of molten iron to slag; based on the density ratio of molten iron to slag, and combined with a density ratio threshold, determine the density separation potential between molten iron and slag; when stable stratification physical conditions are met, based on the density ratio of molten iron to slag, combined with dynamic viscosity and flow velocity, construct a dynamic positioning model of the interface height to obtain the stratification interface height; the specific construction formula of the dynamic positioning model of the interface height is as follows: , in, At any moment The instantaneous height of the slag-iron stratification interface relative to the bottom in the slag grate represents the stratification interface height; This refers to the working depth of the slag grate; At any moment The weighted fusion temperature of molten iron temperature and slag temperature; It is molten iron at all times Weighted fusion temperature The dynamic viscosity at the following levels; It is the slag at all times Weighted fusion temperature The dynamic viscosity at the following levels; It is a moment The flow rate of molten iron; It is a moment The slag flow rate; It is gravitational acceleration; At any moment The density ratio of molten iron to slag; It is to prevent Regularization parameters that cause numerical divergence; It is the viscosity ratio weighting coefficient; It is the velocity difference weighting coefficient; It is the viscosity ratio term; It is the flow rate difference time correction term; It is the baseline flow velocity difference.

[0005] S2. The shear force is quantified by introducing a formula for calculating the layered shear disturbance intensity, and the shear disturbance intensity is obtained. Based on the shear disturbance intensity and the layered interface height, the opening ratio of the molten iron and slag outlet is adjusted, and separation optimization is performed based on the opening ratio of the molten iron and slag outlet.

[0006] Preferably, S1 specifically includes: Based on the molten iron temperature, a molten iron temperature decay term is constructed, and the instantaneous density value of the molten iron is obtained; based on the slag temperature, combined with logarithmic calculation, the instantaneous density value of the slag is obtained.

[0007] Preferably, S1 specifically includes: Based on the density ratio of molten iron to slag and the density ratio threshold, the density separation potential between molten iron and slag is judged: when the density ratio of molten iron to slag is greater than or equal to the density ratio threshold, it indicates that the physical conditions for stable stratification are currently available; when the density ratio of molten iron to slag is less than the density ratio threshold, it indicates that stratification is difficult to form.

[0008] Preferably, S2 specifically includes: The formula for calculating the layered shear disturbance intensity calculates the layered shear force by calculating the vertical velocity gradient between molten iron and slag at the layered interface and combining it with the dynamic viscosity of slag and molten iron, thus obtaining the shear disturbance intensity.

[0009] Preferably, S2 specifically includes: Based on the layered interface height, a layered sensitivity index is introduced to generate a layered ratio term.

[0010] Preferably, S2 specifically includes: Based on the shear disturbance intensity, a disturbance index weight is introduced to generate an exponential disturbance decay term.

[0011] Preferably, S2 specifically comprises: The layered proportion term and the exponential disturbance decay term are taken as nonlinear modulation factors to calculate the molten iron slag outlet opening ratio, and the tapping and slagging are regulated, and the specific calculation formula is: , Wherein, is the molten iron slag outlet opening ratio at time t; is the numerical stability correction term; is the layered sensitivity index; is the disturbance index weight; is the shear disturbance intensity at time t; is the shear disturbance intensity threshold value; is the reference temperature; represents the height of the slag layer; is the layered proportion term; is the exponential disturbance decay term. The beneficial effects of the technical scheme of the present application are: 1、Traditional slag-iron separation mainly relies on operator experience and fixed structure adjustment, and cannot realize dynamic response control of the layered interface height, the present application can perceive the evolution trend of the density difference between molten iron and slag in milliseconds time scale based on the density ratio function constructed based on temperature data, and use it as the preliminary judgment basis of the layered feasibility, ensure that the prerequisite physical conditions of the layered behavior are met, once the density ratio reaches the density ratio threshold value, the subsequent height positioning process is started, effectively avoiding the mixed flow problem caused by blind tapping under adverse conditions, and improving the stability of layered control.

[0012] 2、The traditional slag-iron separation process is easily affected by interface disturbance, temperature gradient and other factors, resulting in layered failure, the present application realizes quantitative judgment of the mechanical stability of the layered interface by introducing the shear disturbance intensity calculation formula; the shear disturbance intensity is calculated by the vertical direction velocity gradient and temperature viscosity coupling term, which can dynamically reflect the relative slip state of the molten fluid in the furnace, and is used as an important intervention variable of system response opening adjustment, especially in the case of high temperature or high flow rate difference, the potential interface instability risk can be found in advance, and adjustment action can be made in advance, thereby effectively preventing interface collapse or mixed flow accident.

[0013] 2、The traditional slag-iron separation process is easily affected by interface disturbance, temperature gradient and other factors, resulting in layered failure, the present application realizes quantitative judgment of the mechanical stability of the layered interface by introducing the shear disturbance intensity calculation formula; the shear disturbance intensity is calculated by the vertical direction velocity gradient and temperature viscosity coupling term, which can dynamically reflect the relative slip state of the molten fluid in the furnace, and is used as an important intervention variable of system response opening adjustment, especially in the case of high temperature or high flow rate difference, the potential interface instability risk can be found in advance, and adjustment action can be made in advance, thereby effectively preventing interface collapse or mixed flow accident.

[0014] ​3、The formula for calculating the opening ratio of the iron and slag outlets of the furnace is designed with double nonlinear modulation factors, the position sensitivity of the layered interface is controlled by a power function, and the disturbance risk is suppressed by an exponential function, so that real-time collaborative control between the iron outlet and the slag outlet is realized, and the fixed baffle position or manual adjustment is no longer relied on, but the opening of the fluid channel is adjusted according to the physical state variables such as the calculated layered interface height and shear disturbance intensity, so that the functions of closed-loop operation, adaptive adjustment and disturbance suppression are realized. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 A high-carbon chromium iron ore hot furnace slag iron separation optimization method flow chart. DETAILED DESCRIPTION

[0016] In order to further illustrate the technical means and effects adopted by the present application to achieve the predetermined object of the application, the technical solutions in the embodiments of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor belong to the scope of protection of the present application.

[0017] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs.

[0018] The specific scheme of the high-carbon chromium iron ore hot furnace slag iron separation optimization method provided by the present application will be specifically described below in combination with the drawings.

[0019] Referring to the drawings Figure 1 It shows a high-carbon chromium iron ore hot furnace slag iron separation optimization method flow chart provided by an embodiment of the present application, and the method comprises the following steps: S1. Obtain the temperature of molten iron and the temperature of slag, and respectively estimate the instantaneous density values of molten iron and slag to obtain the density ratio of molten iron and slag; based on the density ratio of molten iron and slag, a dynamic positioning model of the interface height is constructed to obtain the layered interface height; Before the whole separation process starts, the temperature data of molten iron and slag at the inlet of the slag grating is collected by the on-site temperature sensor. Since temperature directly affects the density and viscosity of molten fluid, based on the temperature data, combined with the laboratory thermal expansion experiment, a density ratio function is constructed as the basic input for subsequent layered interface judgment, and the specific formula of the density ratio function is as follows: , Wherein, is the time at which the temperature data is collected, The density ratio of molten iron and slag reflects the density difference between molten iron and slag at this moment, and the larger the density ratio, the larger the value, which generally means that the molten iron and slag are better layered, and the layering interface is more obvious. The initial density of molten iron is obtained by searching standard literature, and the initial density of slag is obtained by standard data provided by standard literature. The initial density of molten iron is obtained by searching standard literature, and the initial density of slag is obtained by standard data provided by standard literature. The initial density of molten iron is obtained by searching standard literature, and the initial density of slag is obtained by standard data provided by standard literature. The temperature of molten iron at time is measured by a temperature sensor in real time, wherein the temperature unit of the temperature sensor is set to Kelvin. The temperature of molten iron at time is measured by a temperature sensor in real time. The standard temperature value can be the melting point temperature or a common smelting temperature, such as 298K, K representing the temperature unit of Kelvin. The decay coefficient of molten iron density with temperature rise reflects the influence degree of molten iron temperature on molten iron density, and the reference value range is . The logarithmic response coefficient of slag density with temperature change describes the logarithmic change law of slag density with temperature rise, and the reference value range is . , The experimental data of molten iron density and slag density at different temperatures are obtained by existing nonlinear least squares method. The molten iron temperature decay term is used to describe the influence of molten iron temperature change on molten iron density, and the density of molten iron gradually decreases with the increase of temperature. The logarithmic response of slag temperature to slag density is used to describe how the density of slag changes with the change of temperature, that is, the density of slag decreases with the increase of temperature, but the decreasing rate is slow. The density reduction process of molten iron caused by thermal expansion under high temperature smelting conditions is described, which is used to dynamically estimate the instantaneous density value of molten iron. The instantaneous density value of slag is The density ratio output by the above formula is the main control parameter of the interface height dynamic positioning model, and its purpose is to judge the density separation potential between molten iron and slag. Specifically, based on the historical smelting working condition data obtained from the existing database, the density ratio threshold is set by empirical regression method, and the density ratio is compared with the density ratio threshold : when If the temperature is too high, it indicates that stratification is difficult to form, and the process enters the preparation stage for temperature or flow regulation, such as reducing the tapping speed and appropriately increasing the temperature difference, in order to wait for the ideal stratification conditions to form.

[0020] when Based on the density ratio of molten iron to slag, a dynamic positioning model for the interface height is constructed. This model dynamically adjusts the height of the stratified interface according to factors such as temperature, flow rate, and density differences. Specifically, because the molten fluid exhibits a stratified flow state driven by gravity, the denser molten iron lies in the lower layer, while the less dense slag floats in the upper layer. The height of the stratified interface fluctuates over time and is limited by the viscosity ratio and flow rate differences of the molten fluid. Therefore, the specific formula for constructing the dynamic positioning model for the interface height is as follows: , in, At any moment The instantaneous height of the slag-iron stratification interface relative to the bottom in the slag grate is the stratification interface height, which is also the height of the molten iron layer. It is the working depth of the grate (total liquid column height), which is a design parameter of the equipment; At any moment The weighted fusion temperature of molten iron temperature and slag temperature is calculated by using an attention mechanism. The methods used in the calculation of the weighted fusion temperature are all well-known to those skilled in the art and will not be described in detail here. It is molten iron at all times Weighted fusion temperature The dynamic viscosity was measured under controlled temperature conditions using a high-temperature rotational viscometer or crucible rheometer, and obtained by fitting multi-point data using a nonlinear model such as the Arrhenius equation. The reference range is as follows: ; It is the slag at all times Weighted fusion temperature The dynamic viscosity was measured under controlled temperature conditions using a high-temperature rotational viscometer or crucible rheometer, and obtained by fitting multi-point data using a nonlinear model such as the Arrhenius equation. The reference range is as follows: ; It is a moment The molten iron flow rate can reflect the sinking and discharge capacity of molten iron, and is obtained through a flow rate sensor in front of the furnace; It is a moment The slag flow velocity is an important source of the velocity difference at the stratification interface, which is obtained through the furnace front flow velocity sensor. It is gravitational acceleration; It is to prevent The regularization parameter that causes numerical divergence can make the formula stable at the initial time, and can be taken as 0.06; is a viscosity ratio weight coefficient, used to control the degree of contribution of the viscosity ratio to the layering process, embodying the nonlinear influence of viscosity difference on interface stability, based on historical smelting condition data (such as layering interface height) obtained from the existing database, determined by the existing multivariate nonlinear least squares regression method, and the reference value range is ; is a flow rate difference weight coefficient, used to control the excitation effect of the flow rate difference in the layering process, which can affect the sensitivity of the layering interface rising, based on historical smelting condition data (such as molten iron flow rate and slag flow rate) obtained from the existing database, determined by the existing multivariate nonlinear least squares regression method, and the reference value range is ; is a viscosity ratio term, representing the dynamic viscosity ratio between slag and molten iron, used to measure the difference in flow performance between the two melts; is a flow rate difference time correction term, used to measure the dynamic contribution of the molten physical state (speed + density + time) to the change in layering interface height; represents the coupling effect of the viscosity difference, flow rate difference, density contrast and time evolution at a given temperature; is a reference flow rate difference, which is a small constant greater than 0, and can be valued at , which ensures that even if the macro flow rate difference is zero, will not completely disappear, thus reserving a basic contribution for the dynamic calculation of the interface height.

[0021] S2. Introduce the layering shear disturbance intensity calculation formula to quantify the shear force, and obtain the shear disturbance intensity; based on the shear disturbance intensity, adjust the molten iron and slag outlet opening ratio combining with the layering interface height, and perform separation optimization based on the molten iron and slag outlet opening ratio.

[0022] After the instantaneous height of the interface is positioned, due to the strong shear force difference between the molten iron and the slag in the molten flow state, it will cause the instability of the layering interface, therefore, based on the interlayer shear stress theory and the double-layer immiscible fluid interface calculation model based on the Navier-Stokes equation, a layering shear disturbance intensity calculation formula is constructed to quantify the shear disturbance intensity, and the specific formula is: , wherein, is the layering shear force at time , i.e. the shear disturbance intensity; , respectively represent the vertical velocity gradient of slag and molten iron at the interface, i.e. the rate of change of velocity per unit height, which is calculated based on the multi-point laser Doppler velocimeter (LDA) combined with numerical differentiation algorithm. The velocity gradient of the lower layer of the interface is , and the velocity gradient of the upper layer of the interface is ; represents the shear stress in the molten iron layer close to the interface region; represents the shear stress in the slag layer close to the interface position.

[0023] Further, based on the interface height and the shear disturbance intensity, the angle opening ratio of the taphole and the slag hole, i.e. the molten iron and slag outlet opening ratio, is calculated to realize accurate regulation and control of tapping and slagging. The specific calculation formula is as follows: , wherein, is the molten iron and slag outlet opening ratio at time ; is a numerical stability correction term, which is used to avoid the denominator or numerator being zero in the limit state to prevent numerical singularity, and can be taken as 0.01; is a stratification sensitivity index, which is used to control the nonlinearity degree of the outlet opening ratio to the stratification ratio response, the greater the index is, the more sensitive the molten iron is to the regulation; is a disturbance index weight, which is used to control the influence degree of the disturbance factor on the exponential decay term, and determines the feedback strength; is a shear disturbance intensity threshold value, which is obtained by simulation using numerical simulation tools such as ANSYS Fluent, OpenFOAM and COMSOL. When the shear disturbance intensity exceeds the shear disturbance intensity threshold value, the outlet opening ratio should be controlled in time to prevent slag and molten iron from mixing; is a reference temperature, i.e. the full-power furnace temperature measured by an infrared thermometer, which is used as a benchmark for temperature weight normalization; represents the height of the slag layer; is a stratification ratio term, which is a nonlinear modulation factor in the form of a power function, and represents the relative relationship between the thickness of the molten iron layer and the thickness of the slag layer. If , it means that the molten iron proportion is high, and the molten iron outlet opening ratio should be increased; is an exponential disturbance decay term, which is a nonlinear modulation factor in the form of an exponential decay, and can quickly respond to and suppress high disturbance and high risk states. When the shear disturbance intensity is high or the temperature is high, the exponential term tends to zero, and the molten iron outlet opening ratio is automatically reduced; The theoretical basis of the above formula is derived from the approximate functional relationship of the opening flow rate changing with the outlet angle in fluid dynamics, and by introducing a nonlinear modulation factor, the slag-iron separation process is robust to disturbances. The control logic is: the higher the stratification interface, i.e. the more molten iron, the larger the opening degree of the iron notch, and the stronger the shear disturbance, so as to reduce the outlet opening degree of the molten iron, further reduce the overall opening degree, and prevent the stratification interface from collapsing. Through this adjustment, the separation effect of molten iron and slag can be maximized, and the mixing of slag and iron can be reduced.

[0024] In summary, a high-carbon chromite hot stove slag-iron separation optimization method is completed.

[0025] The order of the embodiments is merely for description, and does not represent the advantages and disadvantages of the embodiments. The processes depicted in the drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multi-task processing and parallel processing are also possible or can be advantageous.

[0026] Each embodiment in the specification is described in a progressive manner, and the same or similar parts between each embodiment can be referred to each other. Each embodiment mainly describes the difference from other embodiments.

[0027] The above embodiments are only used to illustrate the technical solutions of the present application, but not limit the present application; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features can be replaced by equivalent ones; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.

Claims

1. A high carbon chromite hot furnace slag iron separation optimization method, characterized by, Comprise the following steps: S1. Obtain the temperature of molten iron and slag, and estimate the instantaneous density value of molten iron and slag respectively, obtain the density ratio of molten iron and slag; Based on the density ratio of molten iron and slag, combined with the density ratio threshold, judge the density separation potential between molten iron and slag; When the physical conditions for stable stratification are met, based on the density ratio of molten iron and slag, combined with dynamic viscosity, flow rate, construct the dynamic positioning model of interface height, obtain the stratification interface height; The specific construction formula of the dynamic positioning model of interface height is as follows: , in, At any moment The instantaneous height of the slag-iron stratification interface relative to the bottom in the slag grate represents the stratification interface height; This refers to the working depth of the slag grate; At any moment The weighted fusion temperature of molten iron temperature and slag temperature; It is molten iron at all times Weighted fusion temperature The dynamic viscosity at the following levels; It is the slag at all times Weighted fusion temperature The dynamic viscosity at the following levels; It is a moment The flow rate of molten iron; It is a moment The slag flow rate; It is gravitational acceleration; At any moment The density ratio of molten iron to slag; It is to prevent Regularization parameters that cause numerical divergence; It is the viscosity ratio weighting coefficient; It is the velocity difference weighting coefficient; It is the viscosity ratio term; It is the flow rate difference time correction term; It is the reference flow rate difference; S2. Introduce the stratification shear disturbance intensity calculation formula to quantify the shear force, and obtain the shear disturbance intensity; Based on the shear disturbance intensity, combined with the stratification interface height, adjust the molten iron and slag outlet opening ratio, and based on the molten iron and slag outlet opening ratio, optimize the separation.

2. A high carbon chromitite hot furnace slag iron separation optimization method according to claim 1, characterized by, The S1, specifically includes: Based on the temperature of molten iron, construct the temperature attenuation term of molten iron, and obtain the instantaneous density value of molten iron; Based on the temperature of slag, combined with logarithmic operation, obtain the instantaneous density value of slag.

3. A high carbon chromitite hot furnace slag iron separation optimization method according to claim 1, characterized by, The S1, specifically includes: Based on the density ratio of molten iron and slag and the density ratio threshold, judge the density separation potential between molten iron and slag: when the density ratio of molten iron and slag is greater than or equal to the density ratio threshold, it indicates that the current physical conditions for stable stratification are met; When the density ratio of molten iron and slag is less than the density ratio threshold, it indicates that it is difficult to form stratification.

4. A high carbon chromitite hot furnace slag iron separation optimization method according to claim 1, characterized by, The S2, specifically includes: The stratification shear disturbance intensity calculation formula calculates the vertical velocity gradient of molten iron and slag at the stratification interface, combined with the dynamic viscosity of slag and molten iron, calculates the stratification shear force, and obtains the shear disturbance intensity.

5. A high carbon chromitite hot furnace slag iron separation optimization method according to claim 1, characterized by, The S2, specifically includes: Based on the stratification interface height, introduce stratification sensitivity index to generate stratification proportion term.

6. A high carbon chromitite hot furnace slag iron separation optimization method according to claim 5, characterized by, The S2, specifically includes: Based on the shear disturbance intensity, introduce disturbance index weight to generate exponential disturbance attenuation term.

7. A high carbon chromitite hot furnace slag iron separation optimization method according to claim 6, characterized by, The S2, specifically includes: Take the stratification proportion term and exponential disturbance attenuation term as nonlinear modulation factors, calculate the molten iron and slag outlet opening ratio, and regulate the tapping and slag tapping, and the specific calculation formula is: , wherein, is the molten iron slag outlet opening ratio at the time ; is the numerical stability correction term; is the stratification sensitivity index; is the disturbance index weight; is the shear disturbance intensity at the time ; is the shear disturbance intensity threshold value; is the reference temperature; denotes the height of the slag layer; is the stratification proportionality term; is the exponential disturbance decay term.

Citation Information

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