A method for analyzing a crystallizer-steel slag interface roll-up behavior based on wave stability

Abstract

This invention relates to a method for analyzing slag entrainment behavior at the slag interface in a crystallizer based on fluctuation stability, belonging to the field of continuous casting technology. The method first constructs a fluctuation model of the slag interface and establishes control equations; derives a mechanistic calculation formula for the critical slag entrainment velocity based on linear stability theory; dynamically obtains the interface wavenumber through spectral analysis of the liquid level fluctuation signal; calculates the slag entrainment frequency index by combining the real-time liquid level characteristic amplitude; triggers an early warning when the slag entrainment frequency index exceeds a critical threshold, and automatically calculates and executes adjustments to the casting speed or nozzle insertion depth based on the deviation of the slag entrainment frequency index through a closed-loop control model. This invention is the first to integrate fluid dynamics stability theory with online monitoring and closed-loop control, achieving real-time quantitative assessment and active suppression of slag entrainment risk at the mechanistic level, breaking through the limitations of existing empirical formulas, and significantly improving the intelligence level of process control and the stability of billet quality.

Description

Technical Field

[0001] This invention belongs to the field of continuous casting technology and relates to a method for analyzing the slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability. Background Technology

[0002] During the continuous casting process of slabs, factors such as nozzle blockage, argon blowing, and casting speed fluctuations can cause fluctuations in the liquid level in the crystallizer, resulting in the entrapment of protective slag at the steel-slag interface and causing slag entrapment. Slag entrapment not only affects the heat transfer uniformity between the solidified slab shell and the copper plate of the crystallizer, but also directly leads to slag inclusion defects under the slab surface, seriously affecting product quality.

[0003] The existing technologies for analyzing and controlling slag entrapment behavior have the following main shortcomings: 1) Empirical models have significant limitations: For example, patent CN113305277A discloses a method for judging shear slag entrainment, the core of which is an empirical formula obtained by fitting a water model experiment under specific working conditions ( Such formulas have unclear physical meanings and can only reflect parameter relationships within a specific experimental range. They lack the universality and extrapolation prediction ability at the mechanistic level for the complex changes in steel grades, protective slag properties, and operating parameters in actual production.

[0004] 2) Lack of theoretical criteria for slag entrainment: Existing technologies fail to reveal the intrinsic connection between interface wave instability and slag entrainment from the perspective of hydrodynamic instability, and cannot provide a method for calculating the critical slag entrainment velocity based on first principles.

[0005] 3) Disconnect between monitoring and control: For example, although patent CN103341609A discloses a method for monitoring liquid level fluctuations using spectral analysis, it only stops at monitoring and passive adjustment. It does not establish a quantitative mapping relationship between fluctuation characteristics and slag entrapment risk, nor does it propose a closed-loop, quantitative automatic control method. As a result, process adjustment relies on manual experience, which is lagging and inaccurate.

[0006] 4) Insufficient utilization of online data: Existing technologies have failed to effectively integrate mechanistic models with real-time liquid level fluctuation data to achieve real-time quantitative assessment and prediction of slag entrapment risk.

[0007] Therefore, there is an urgent need for a method for analyzing the slag entrainment behavior at the interface of the crystallizer steel slag, which is based on a theoretical model, can be quantitatively evaluated, and can guide online closed-loop control. Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide a method for analyzing the slag entrainment behavior of the slag interface in a crystallizer based on wave stability. This method introduces the theory of interface wave linear stability from fluid mechanics into the analysis of slag entrainment in a crystallizer, derives a theoretical model of the critical slag entrainment velocity based on physical mechanisms, and defines the slag entrainment frequency index Ds. This model is then coupled with the real-time liquid level fluctuation detection value. A real-time risk assessment and closed-loop control method for process parameters based on the Ds index is established, achieving a leap from empirical judgment to mechanism quantification and then to intelligent control.

[0009] To achieve the above objectives, the present invention provides the following technical solution: A method for analyzing slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability, the method comprising: S1. Construct a wave model of the interface between steel and slag in the crystallizer. Treat the two phases of steel and slag as liquid-liquid stratified flow in a finite space. Assume that the initial shape of the interface wave is a sine wave and establish the Laplace control equation to describe its motion. S2. Based on the small amplitude wave theory, the interface wave control equation is linearized to obtain linearized kinematic boundary conditions and dynamic boundary conditions. S3. Based on linear stability theory, the kinematic and dynamic boundary conditions are solved, and the critical condition for the interface wave to transition from a stable to an unstable state is derived, as well as the critical slag entrainment velocity. Theoretical calculation model; S4. The liquid level fluctuation time-series signal at the meniscus is acquired in real time through the crystallizer liquid level detection system, and the frequency spectrum of the time-series signal is analyzed using Fast Fourier Transform to extract the dominant frequency. The interface wave number under the current operating condition is dynamically calculated based on the dispersion relation. ; S5. Dynamically calculate the interface wave number under the current operating conditions. Substitute the critical slag entrainment speed The theoretical calculation model calculates the current critical slag entrainment speed. And thus calculate the slag frequency index. ; S6, calculate the obtained Exponent and critical threshold When comparing, When a risk of slag accretion is detected, an early warning signal is triggered and an activation mechanism based on [the relevant technology] is initiated. Closed-loop control procedure for exponential deviation.

[0010] Furthermore, in step S1, the constructed Laplace governing equation is expressed as:

[0011]

[0012]

[0013] in, Let be a scalar function of the velocity potential. and For fluid along and The velocity component in the direction, It is the Laplace differential operator.

[0014] Furthermore, in step S2, the linearized kinematic boundary conditions and dynamic boundary conditions are expressed as follows:

[0015]

[0016]

[0017] in, For the amplitude of the interface wave, For the interface wave number, The angular frequency of the interface wave. For time, This is the acceleration due to gravity.

[0018] Furthermore, in step S3, the critical slag entrainment speed... The theoretical calculation model is expressed as follows:

[0019] in, and These are the densities of the protective slag and the molten steel, respectively. To protect the viscosity of the slag, For the interfacial tension of steel slag, The angle between the liquid-liquid interface and the horizontal direction. To protect the thickness of the slag layer, The influencing factor of interfacial active elements related to steel composition.

[0020] Furthermore, in step S4, the interface wave number under the current operating condition... The calculation method is as follows:

[0021] in, λ is the wavelength.

[0022] Furthermore, in step S5, the calculated Substituting the values ​​into the above velocity theory calculation model, the critical slag entrainment velocity is obtained. Then calculate the slag frequency index. :

[0023] in, The characteristic amplitude of liquid level fluctuation is calculated in real time from the time-series signal.

[0024] Furthermore, the characteristic amplitude of liquid level fluctuation The effective or maximum value of the liquid level fluctuation signal within a specified time window.

[0025] Furthermore, in step S6, when it is determined that there is a risk of slag buildup, an activation based on... The closed-loop control program for exponential deviation, based on the current... Values ​​and thresholds The difference The reduction in pulling speed is automatically calculated through a preset control model. Or the increase in the insertion depth of the submersible nozzle The adjustment command is then sent to the continuous casting machine PLC system for execution until... The index fell to the following.

[0026] Furthermore, the preset control model in step S6 is established based on historical process data. and The linear or nonlinear functional relationship.

[0027] Furthermore, the critical threshold in step S6 Adjustments should be made based on the actual steel grade and the properties of the protective slag.

[0028] The beneficial effects of this invention are as follows: This invention systematically applies the linear stability theory of fluid mechanics to the analysis of slag entrainment in crystallizers, and establishes a critical slag entrainment velocity mechanism model based on first principles. This model is fundamentally different from existing empirical fitting formulas, has clear physical meaning, and has stronger universality and extrapolation prediction capabilities for different steel grades and operating conditions.

[0029] This invention dynamically determines the wavenumber of the interface wave through spectrum analysis. And combined with the real-time liquid level fluctuation characteristic amplitude calculate The index ensures that risk assessments are highly synchronized with current real-world conditions, significantly improving the accuracy of the assessments.

[0030] The Ds index proposed in this invention is not only a basis for judgment but also an input variable for closed-loop control. By establishing a quantitative relationship between the Ds index deviation and the adjustment amount of process parameters, online early warning and automatic elimination of slag entrapment risk are achieved, freeing operators from passive and lagging experience-based adjustments and providing key technical support for the intelligent control of the continuous casting process.

[0031] This invention can provide quantitative guidance for optimizing casting speed, adjusting nozzle insertion depth, and selecting protective slag, effectively suppressing slag entrapment defects and stabilizing billet quality, and has extremely high industrial application value.

[0032] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0033] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a schematic diagram of the overall process of the crystallizer steel slag interface entrapment behavior analysis method based on fluctuation stability according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the interface fluctuations near the crystallizer bulge in an embodiment of the present invention; Figure 3 This is a schematic diagram of liquid-liquid interface fluctuations under shearing action in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the relationship between the critical slag winding speed and the viscosity of the protective slag in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the relationship between the critical slag entrainment speed and the interfacial tension of steel slag in an embodiment of the present invention. Figure 6 This is a schematic diagram illustrating the relationship between the Ds index and the amplitude of liquid level fluctuations in an embodiment of the present invention. Figure 7 This is a schematic diagram illustrating the criteria and control effects of slag entrapment behavior under different working conditions in embodiments of the present invention. Detailed Implementation

[0034] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0035] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0036] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0037] Please see Figures 1 to 7 This is a method for analyzing the slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability.

[0038] Example 1 This embodiment first describes in detail the specific process of the crystallizer steel slag interface entrapment behavior analysis method based on fluctuation stability proposed in this invention, such as... Figure 1 As shown, it includes at least the following steps: S1. Construct a wave model of the interface between steel and slag in the crystallizer. Treat the two phases of steel and slag as liquid-liquid stratified flow in a finite space. Assume that the initial shape of the interface wave is a sine wave and establish the Laplace control equation to describe its motion. S2. Based on the small amplitude wave theory, the interface wave control equation is linearized to obtain linearized kinematic boundary conditions and dynamic boundary conditions. S3. Based on linear stability theory, the kinematic and dynamic boundary conditions are solved, and the critical condition for the interface wave to transition from a stable to an unstable state is derived, as well as the critical slag entrainment velocity. Theoretical calculation model; S4. The liquid level fluctuation time-series signal at the meniscus is acquired in real time through the crystallizer liquid level detection system, and the frequency spectrum of the time-series signal is analyzed using Fast Fourier Transform (FFT) to extract the dominant frequency. The interface wave number under the current operating condition is dynamically calculated based on the dispersion relation. ; S5. Dynamically calculate the interface wave number under the current operating conditions. Substitute the critical slag entrainment speed The theoretical calculation model calculates the current critical slag entrainment speed. And thus calculate the slag frequency index. ; S6, calculate the obtained Exponent and critical threshold When comparing, When a risk of slag accretion is detected, an early warning signal is triggered and an activation mechanism based on [the relevant technology] is initiated. Closed-loop control procedure for exponential deviation.

[0039] In step S1 of this embodiment, the constructed Laplace governing equation is expressed as:

[0040]

[0041]

[0042] in, Let be a scalar function of the velocity potential. and For fluid along and The velocity component in the direction.

[0043] like Figure 2 and Figure 3 As shown, Figure 2 The morphology of interface fluctuations near the crystallizer bulge is shown. Figure 3 A schematic diagram of liquid-liquid interface fluctuations under shear is shown. Both are used together to construct a steel-slag interface fluctuation model, reflecting the assumption that the actual interface wave is initially a sine wave.

[0044] In step S2 of this embodiment, the linearized kinematic boundary conditions and dynamic boundary conditions are expressed as follows:

[0045]

[0046]

[0047] in, For the amplitude of the interface wave, For the interface wave number, The angular frequency of the interface wave. For time, This is the acceleration due to gravity.

[0048] In step S3 of this embodiment, the critical slag entrainment speed The theoretical calculation model is expressed as follows:

[0049] in, and These are the densities of the protective slag and the molten steel, respectively. To protect the viscosity of the slag, For the interfacial tension of steel slag, The angle between the liquid-liquid interface and the horizontal direction. To protect the thickness of the slag layer, The value of the interfacial active element influence factor related to the steel composition ranges from 0.25 to 0.35.

[0050] like Figure 4 and Figure 5 As shown, Figure 4 The relationship between the critical slag swirling speed and the viscosity of the protective slag is given. Figure 5 The relationship between the critical slag entrainment speed and the interfacial tension of the steel slag is given, which demonstrates the sensitivity of the derived model to key physical property parameters and verifies the theoretical rationality of the model.

[0051] In step S4 of this embodiment, the liquid level fluctuation time-series signal at the meniscus is acquired in real time by the crystallizer liquid level detection system. The time-series signal is then subjected to spectrum analysis using Fast Fourier Transform to extract the dominant frequency and wavelength. Finally, the interface wavenumber is dynamically calculated based on the dispersion relation. :

[0052] in, λ is the wavelength.

[0053] In step S5 of this embodiment, the calculated Substituting the values ​​into the above velocity theory calculation model, the critical slag entrainment velocity is obtained. Then calculate the slag frequency index. :

[0054] in, In this embodiment, the characteristic amplitude of liquid level fluctuation (such as the effective value or the maximum value within a certain time window) is calculated in real time from the time-series signal. The effective or maximum value of the liquid level fluctuation signal within a specified time window; critical threshold. The value is 13.4 Pa·s, and can be adjusted according to the actual cast steel grade and the properties of the protective slag.

[0055] like Figure 6 As shown in the figure, this diagram illustrates... The relationship between the index and the amplitude of liquid level fluctuations: when the amplitude increases... The index rises linearly, and once it exceeds the threshold, it is determined that there is a risk of slag buildup, providing an intuitive criterion for risk assessment.

[0056] In step S6 of this embodiment, when it is determined that there is a risk of slag buildup, the process based on... The closed-loop control program for exponential deviation, based on the current... Values ​​and thresholds The difference The reduction in pulling speed is automatically calculated through a preset control model. Or the increase in the insertion depth of the submersible nozzle The adjustment command is then sent to the continuous casting machine PLC system for execution until... The index fell to The following is a preset control model based on historical process data. and The linear or nonlinear functional relationship.

[0057] like Figure 7 As shown in the figure, this diagram illustrates the different operating conditions. The correlation between the index and slag-carrying behavior, as well as the effect of closed-loop control, verified the effectiveness of the proposed method and the reliability of the control strategy under different process conditions.

[0058] Example 2 This embodiment uses a slab continuous casting machine in a steel plant as an example to demonstrate the above process.

[0059] In this embodiment, the density of molten steel is 7000 kg / m³, the density of the protective slag is 2600 kg / m³, the viscosity of the protective slag is 0.192 Pa·s, the interfacial tension between steel and slag is 0.96 N / m, and the thickness of the molten steel-slag layer is 10 mm. (Influence factor of active elements) Set it to 0.3.

[0060] First, the meniscus level fluctuation signal is acquired through a level detection system. The dominant fluctuation frequency under the current operating condition is obtained using FFT analysis, and the interface wave number is calculated based on the dispersion relation. .

[0061] Secondly, substitute the critical slag entrainment speed. The theoretical calculation model calculates the critical slag entrainment speed. Jet tilt angle hyperbolic cotangent function value The critical slag entrainment speed was calculated. .

[0062] Then, during the stable casting stage, the system monitors and calculates the characteristic amplitude of liquid level fluctuations in real time. At a certain moment, the flow field changes due to nozzle clogging. The thickness increased from 4 mm when it was stable to 16 mm.

[0063] Next, calculate index: When stable:

[0064] When fluctuations intensify:

[0065] Will The index and the preset critical threshold Compare them. When stable. The system does not respond; when When it rises to 16mm, The system immediately determined that there was a serious risk of debris accumulation and triggered an audible and visual alarm.

[0066] At the same time, the closed-loop control program automatically starts. The program detects... According to the preset speed control model (This model is built based on a process database, for example) The recommended reduction in pulling speed was calculated. The control system sends the command to the continuous casting machine PLC, automatically reducing the casting speed from the current 1.2 m / min to 1.11 m / min. The system continuously monitors the process, and after 10 seconds, the liquid level fluctuations stabilize. It fell back to 5mm. The index fell to If the speed is below the threshold, the risk of slag buildup is eliminated, the alarm is automatically cleared, and the pulling speed is maintained at a new stable level.

[0067] This embodiment clearly demonstrates how the present invention integrates theoretical models, online monitoring, and automatic control to achieve accurate prediction and proactive intervention of slag entrapment behavior, effectively ensuring the smooth operation of continuous casting production and the stability of billet quality.

[0068] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for analyzing slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability, characterized in that: The method includes: S1. Construct a wave model of the interface between steel and slag in the crystallizer. Treat the two phases of steel and slag as liquid-liquid stratified flow in a finite space. Assume that the initial shape of the interface wave is a sine wave and establish the Laplace control equation to describe its motion. S2. Based on the small amplitude wave theory, the interface wave control equation is linearized to obtain linearized kinematic boundary conditions and dynamic boundary conditions. S3. Based on linear stability theory, the kinematic and dynamic boundary conditions are solved, and the critical condition for the interface wave to transition from a stable to an unstable state is derived, as well as the critical slag entrainment velocity. Theoretical calculation model; S4. The liquid level fluctuation time-series signal at the meniscus is acquired in real time through the crystallizer liquid level detection system, and the frequency spectrum of the time-series signal is analyzed using Fast Fourier Transform to extract the dominant frequency. The interface wave number under the current operating condition is dynamically calculated based on the dispersion relation. ; S5. Dynamically calculate the interface wave number under the current operating conditions. Substitute the critical slag entrainment speed The theoretical calculation model calculates the current critical slag entrainment speed. And thus calculate the slag frequency index. ; S6, calculate the obtained Exponent and critical threshold When comparing, When a risk of slag accretion is detected, an early warning signal is triggered and an activation mechanism based on [the relevant technology] is initiated. Closed-loop control procedure for exponential deviation.

2. The method for analyzing slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability, as described in claim 1, is characterized in that: In step S1, the constructed Laplace governing equation is expressed as: in, Let be a scalar function of the velocity potential. and For fluid along and The velocity component in the direction, It is the Laplace differential operator.

3. The method for analyzing slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability, as described in claim 2, is characterized in that: In step S2, the linearized kinematic boundary conditions and dynamic boundary conditions are expressed as follows: in, For the amplitude of the interface wave, For the interface wave number, The angular frequency of the interface wave. For time, This is the acceleration due to gravity.

4. The method for analyzing slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability, as described in claim 3, is characterized in that: In step S3, the critical slag entrainment speed The theoretical calculation model is expressed as follows: in, and These are the densities of the protective slag and the molten steel, respectively. To protect the viscosity of the slag, For the interfacial tension of steel slag, The angle between the liquid-liquid interface and the horizontal direction. To protect the thickness of the slag layer, The influencing factor of interfacial active elements related to steel composition.

5. The method for analyzing slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability, as described in claim 4, is characterized in that: In step S4, the interface wave number under the current operating condition is... The calculation method is as follows: in, λ is the wavelength.

6. The method for analyzing slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability, as described in claim 5, is characterized in that: In step S5, the calculated Substituting the values ​​into the above velocity theory calculation model, the critical slag entrainment velocity is obtained. Then calculate the slag frequency index. : in, The characteristic amplitude of liquid level fluctuation is calculated in real time from the time-series signal.

7. The method for analyzing slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability, as described in claim 6, is characterized in that: Liquid level fluctuation characteristic amplitude The effective or maximum value of the liquid level fluctuation signal within a specified time window.

8. The method for analyzing slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability, as described in claim 6, is characterized in that: In step S6, when a risk of slag buildup is determined, the process based on... The closed-loop control program for exponential deviation, based on the current... Values ​​and thresholds The difference The reduction in pulling speed is automatically calculated through a preset control model. Or the increase in the insertion depth of the submersible nozzle The adjustment command is then sent to the continuous casting machine PLC system for execution until... The index fell to the following.

9. The method for analyzing slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability, as described in claim 8, is characterized in that: The preset control model in step S6 is established based on historical process data. and The linear or nonlinear functional relationship.

10. The method for analyzing slag entrainment behavior at the interface of steel slag in a crystallizer based on fluctuation stability, as described in claim 8, is characterized in that: Critical threshold in step S6 Adjustments should be made based on the actual steel grade and the properties of the protective slag.

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