Steel ladle constant flow pouring analytical model

Abstract

The invention discloses a steel ladle constant-current pouring analytical model, and establishes a constant-current pouring analytical model in order to realize accurate pouring of a steel ladle. By integrating a user-defined function (UDF), computational fluid dynamics (CFD) simulation is carried out on constant-flow pouring so as to research molten steel pouring behaviors under different inner wall inclination angles alpha, initial molten steel volume Vc and target flow qt, and finally, the accuracy of an analytical model and a simulation model is verified through experiments. Results show that experimental results are well matched with theoretical and simulation results. In order to realize constant-flow-speed pouring, the steel ladle angular speed changing along with time is obtained, and the steel ladle angular speed can be adjusted through the rotating speed of the motor. Therefore, different constant flow speeds can be obtained by adjusting the rotating speed of the motor, and guidance is provided for engineering application of the casting technology.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of metallurgy, and particularly relates to a ladle constant flow pouring analytical model. BACKGROUND

[0002] Precise pouring process plays a crucial role in casting technology. On the contrary, improper pouring, such as flow rate fluctuation or the presence of residual liquid steel, can lead to defects such as inclusions and porosity, thereby increasing the scrap rate and production cost. However, traditional pouring methods largely rely on the experience and skills of operators, which can result in a high defect rate. Therefore, in order to ensure high-quality casting production and reduce the influence of human factors, constant flow pouring technology has become a key focus of casting research. This technology includes various control methods, such as mass control, electrode control, volume control, time control, demonstration-based reproduction control, and image processing control.

[0003] Related technical personnel use computational fluid dynamics (CFD) simulation models to study the liquid steel pouring process. The results show that the two-phase flow model can effectively simulate the liquid steel pouring process, which confirms the feasibility of CFD simulation. Further analysis of the CFD simulation model shows that the dynamic changes of the flow field, temperature field, and phase interface during the ladle pouring process in a two-dimensional space at a constant rotational speed. It is found that operating the tilting pouring machine at a fixed angular velocity cannot achieve constant flow pouring, and continuously adjusting the angular velocity of the ladle can achieve this. However, stable and precise pouring has not yet been achieved by controlling the angular velocity of the ladle. SUMMARY

[0004] To solve the above problems, an embodiment of the present application proposes a ladle constant flow pouring analytical model.

[0005] The ladle constant flow pouring analytical model of the present application, the ladle pouring process is divided into three stages, the analytical model between the ladle rotation angle and the remaining liquid volume in the ladle during the ladle pouring process is:

[0006]

[0007] In the formula, r=D / 2, a=D / 2-h / tanθ, θ is the rotation angle of the ladle, D=(D1+D2) / 2, D1 and D2 respectively refer to the diameters of the top and bottom of the liquid in the ladle, a, r, D are all intermediate variables, H1-T is the height of the liquid in the ladle, H1 is the height of the liquid in the ladle to the bottom of the ladle, T is the thickness of the bottom of the ladle, h=H-T, h is the height of the interior of the ladle, i.e. the height of the inner cavity of the ladle, H is the height from the top to the bottom of the ladle.

[0008] During the pouring process, the analytical model between the rotation angle of the ladle, the angular velocity of the ladle and the flow rate is:

[0009]

[0010] In the formula, θ is the ladle rotation angle, ω is the ladle angular velocity, q is the flow rate, D=(D1+D2) / 2, D1 and D2 respectively refer to the diameters of the top and bottom of the liquid in the ladle, r=D / 2, h is the height inside the ladle, H is the height from the top to the bottom of the ladle, T is the thickness of the bottom of the ladle, h=H-T, e=tan 2 θ+1, f=(r-h / tanθ), g=r 2 -(r-h / tanθ) 2 The ladle angular velocity can be adjusted by the motor speed.

[0011] The three stages are: in the first stage, the remaining liquid volume in the ladle remains unchanged, and no liquid flows out of the ladle; in the second stage, the liquid begins to flow out of the ladle, the remaining liquid volume decreases, and the bottom of the ladle is still completely immersed in the liquid; in the third stage, the bottom of the ladle is exposed, the liquid continuously flows out of the ladle, and the remaining liquid volume continues to decrease.

[0012] When the initial liquid in the ladle is 70% of the total capacity of the ladle, a stable pouring process and a constant flow rate can be achieved.

[0013] When the inclination angle of the inner wall of the ladle is α=7.5°, a stable pouring process and a constant flow rate can be achieved.

[0014] When the target flow rate of the ladle is in the range of 0.10 cubic meters / second and 0.12 cubic meters / second, a stable pouring process and a constant flow rate can be achieved.

[0015] The ladle constant-flow pouring analysis model of the application comprises a device suitable for the ladle constant-flow pouring analysis model, the device comprises a shelf, two symmetrical support arms are arranged in the middle of the shelf, a pouring ladle is rotationally connected between the two support arms, one side of the bottom of the pouring ladle is connected with a motor through a steel wire rope, the pouring ladle is placed obliquely, and a liquid collecting barrel is placed below the outlet of the pouring ladle.

[0016] The motor is further connected with a PLC, the PLC is connected with a power supply and a switch, the power supply, the switch, the PLC and the motor are arranged on the rear side of the shelf, and the pouring ladle and the liquid collecting barrel are placed in the middle of the shelf.

[0017] One end of the steel wire rope is connected with the pouring ladle, and the other end is connected with the output shaft of the motor by passing through a fixed pulley arranged on the top of the shelf.

[0018] The rotation speed of the motor is used to control the constant flow rate of the liquid in the pouring ladle.

[0019] The beneficial effect of the present application is that, in order to realize accurate ladle pouring, an analytical model of constant flow pouring is established. Through the integration of user-defined function (UDF), the constant flow pouring is simulated by computational fluid dynamics (CFD) to study the pouring behavior of molten steel under different inner wall inclination angles α, initial molten steel volume Vc and target flow rate qt. Finally, the accuracy of the analytical model and the simulation model is verified by experiment. The results show that the experimental results are in good agreement with the theoretical and simulation results, verifying the accuracy of the analytical model and the simulation model. In order to realize constant flow pouring, the angular velocity of the ladle varying with time is obtained, and can be adjusted by the motor speed. Therefore, different constant flow rates can be obtained by adjusting the motor speed, which provides guidance for the engineering application of casting technology. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 is a schematic diagram of the ladle structure of the present application.

[0021] Figure 2 is a diagram of the change of the remaining liquid volume in the ladle of the present application.

[0022] Figure 3 is a simplified ladle coordinate system of the present application.

[0023] Figure 4 is a ladle model of the present application.

[0024] Figure 5 is a divided grid diagram of the present application.

[0025] Figure 6 is a curve of the change of the rotation angle of the ladle with time of the present application.

[0026] Figure 7 is a curve of the change of the angular velocity of the ladle with time of the present application.

[0027] Figure 8 is a transient phase interface in the constant flow pouring process of the present application.

[0028] Figure 9 is a transient liquid velocity in the constant flow pouring process of the present application.

[0029] Figure 10 is a diagram of the change of the remaining liquid volume and flow rate with the inner wall inclination angle α in the ladle of the present application.

[0030] Figure 11 is a diagram of the change of the remaining liquid volume and flow rate under different initial liquid volumes of the present application.

[0031] Figure 12 is a diagram of the change of the remaining liquid volume and flow rate under different target flow rates qt of the present application.

[0032] Figure 13 is a structural schematic diagram of an experimental device of the present application.

[0033] Figure 14 is a comparison chart of different initial liquid volumes in an embodiment of the present application.

[0034] Figure 15 is a comparison chart of different target flow rates in an embodiment of the present application. DETAILED DESCRIPTION

[0035] Embodiments of the present application are described in detail below with reference to the accompanying drawings. The embodiments described below by reference to the accompanying drawings are exemplary and are intended to explain the present application, and cannot be understood as a limitation of the present application.

[0036] The structural parameters of the ladle are shown in Figure 1 , wherein D1 and D2 represent the diameters of the top and bottom of the liquid in the ladle respectively, a is the inner wall inclination angle, H is the height of the ladle, H1 is the height from the top surface of the liquid in the ladle to the bottom of the ladle, H2 is the height from the half of the height of the inner cavity of the ladle to the bottom of the ladle, and T is the thickness of the bottom of the ladle. The structural parameters remain unchanged except the initial liquid volume.

[0037] The ladle pouring process can be divided into three stages. In the three stages, the remaining liquid volume in the ladle changes with time. In the first stage, the remaining liquid volume remains unchanged, and no liquid flows out of the ladle, as shown in Figure 2 (a). In the second stage, the liquid begins to flow out of the ladle, and the remaining liquid volume decreases, and the bottom of the ladle is still completely immersed in the liquid, as shown in Figure 2 (b). In the third stage, the bottom of the ladle is exposed. At the same time, the liquid continues to flow out of the ladle, and the remaining liquid volume continues to decrease, as shown in Figure 2 (c).

[0038] In the pouring process, the flow characteristics and the distribution of the liquid steel in each stage are different. Generally, the liquid steel flows out of the ladle in the form of a truncated cone or an irregular horse-shoe shape. Due to the lack of accurate volume calculation formula, the liquid steel is often modeled as a cylinder. The diameter D of the cylinder is calculated as D=(D1+D2) / 2, wherein D1 and D2 represent the diameters of the top and bottom of the liquid in the ladle respectively. In the design of the ladle, this assumption is reasonable due to the small taper. In addition, the initial liquid steel volume is usually assumed to be 70% of the total capacity of the ladle. By using the relationship between the rotation angle θ of the ladle and the remaining liquid steel volume, the remaining liquid steel volume at any given θ can be calculated after establishing an analytical model.

[0039] 1. The calculation process of the analytical model of the ladle constant flow pouring of the present application.

[0040] 1.1 Analytical model for the remaining liquid volume in a ladle during pouring

[0041] In the first stage (0° < θ < θ1), the ladle starts to rotate, but no liquid flows out because the liquid surface is at a distance from the outlet. θ1 is the critical angle of the first stage, when the ladle rotates to θ1, the liquid starts to flow out of the ladle. The remaining liquid volume in the first stage is set as V0, as shown in Fig. (a). Figure 2

[0042] The critical value of the ladle rotation angle θ1 is:

[0043] θ1 = arctan (2(H - H1) / D) (1)

[0044] At this time, the remaining liquid volume V0 in the ladle is:

[0045]

[0046] In the second stage (θ1≤θ<θ2), the liquid in the ladle is in the shape of a truncated cone, the remaining liquid volume in the second stage is set as V1, as shown in Fig. (b). Figure 2

[0047] The critical value of the ladle rotation angle θ2 is:

[0048] θ2 = arctan (h / D) (3)

[0049] In the formula, h = H - T, h is the height inside the ladle, i.e. the height of the ladle cavity.

[0050] At this time, the remaining liquid volume V1 in the ladle is:

[0051]

[0052] In the third stage (θ2≤θ<90°), the liquid continues to flow out of the ladle, the liquid in the ladle is in the shape of an irregular horse, until the pouring is completed, as shown in Fig. (c). Figure 2

[0053] To simplify the calculation, this shape is modeled as a right circular cylinder cut by the remaining diagonal tangent. The establishment of the coordinate axis is shown in Fig. (d). The remaining volume of the ladle is determined by calculus. Figure 3

[0054] There is a liquid surface plane 1 passing through point E (0, r, h) and point F (0, r - h tan θ, h). Let the equation of plane 1 be Ax + By + Cz = D. This equation of plane 1 can be solved by finding the normal vector of plane 1:

[0055] ​​​​

[0056] where r = D / 2, a = D / 2 - h / tanθ, a, r, D are all intermediate variables.

[0057] The remaining liquid volume V2 in the ladle is:

[0058]

[0059] Summarizing the above three stages, the analytical model of the remaining molten steel volume V in the ladle at any ladle rotation angle θ can be obtained.

[0060]

[0061] 1.2 Analytical model of flow rate during pouring

[0062] The flow rate q can be obtained by taking the first derivative of the remaining liquid volume with respect to time and then taking the absolute value of the derivative. Similarly, the flow rate varies with time during pouring and is different in the three stages q0, q1 and q2.

[0063] In the first stage (0° < θ < θ1), V0 = Vc. The flow rate q0 can be calculated as

[0064]

[0065] where Vc is the initial liquid volume and V0 represents the remaining molten steel volume in the first stage.

[0066] In the second stage (θ1≤θ<θ2), the flow rate q1 can be calculated as

[0067]

[0068] In the third stage (θ2≤θ<90°), the flow rate q2 can be calculated as follows:

[0069]

[0070] where ω is the angular velocity of the ladle, r, a, e, f, g are all intermediate variables,

[0071] e = tan 2 θ + 1, f = (r - h / tanθ), g = r 2 -(r - h / tanθ) 2 .

[0072] In summary, through the above three stages, the analytical model of the flow rate q at any ladle rotation angle θ and ladle angular velocity ω can be obtained.

[0073]

[0074] To achieve constant flow casting, a constant flow rate q over time is required. Therefore, the ladle angular velocity ω becomes a function of the ladle rotation angle θ, where ω can be calculated for any ladle rotation angle θ.

[0075] 2. Simulation model of ladle casting process

[0076] 2.1 Computational fluid dynamics (CFD) simulation settings

[0077] The simulation was performed using ANSYS Fluent 2022R1 on a workstation equipped with dual Intel Xeon Gold 6248R CPUs (48 cores) and 256 GB of memory. A user-defined function (UDF) for the ladle rotational speed was written using the compiler in Fluent. The convergence criterion was set to a residual less than 10 -4 .

[0078] To study the flow behavior during casting, a geometric model of the ladle was constructed (where D1 = 2305 mm, D2 = 2985 mm, H = 3740 mm, H1 = 2927 mm, T = 350 mm, and the inner wall inclination angle a = 7.5°), as shown in Figure 4 and Figure 5 The model consists of three regions: the liquid region inside the ladle, the air region inside the ladle, and the air region outside the ladle. During meshing, a patch conforming algorithm was used to generate tetrahedral meshes. For the ladle region, the mesh size was 70 mm, while for the air region, the mesh size was 200 mm. The total number of nodes was 173,699, and the total number of elements was 956,763. At the same time, the initial liquid volume Vc was set to 14226 liters, and the total casting time t was set to 110 seconds. The molten steel did not flow out of the ladle in the 0-20 second range, started to flow out at t = 20 seconds, and completely flowed out at t = 110 seconds.

[0079] To verify grid independence and eliminate the influence of the number of grids on the calculation accuracy, four groups of grids were generated. The number of grids in each group was 420,235, 550,378, 956,763, and 1,131,109, corresponding to numbers 1, 2, 3, and 4, respectively. Then, error analysis was performed on the casting flow rates calculated using the four groups of grids, and the results are shown in Table 1.

[0080] Table 1 Grid independence test results

[0081]

[0082] The results show that the flow calculation error between the first grid and the second grid is 0.79%; the flow calculation error between the second grid and the third grid is 0.95%; and the flow calculation error between the third grid and the fourth grid is 0.025%. By comparing the calculation errors, it is obvious that the calculation error between the third grid and the fourth grid is extremely small, which indicates that the influence of the number of grids on the solution result can be ignored. In view of the limitation of the calculation capacity, the third grid with the number of grids of 956,763 is selected for subsequent simulation calculation.

[0083] The viscosity and density of the liquid steel are set to be 0.0062 Pascal-second and 7138 kg / m3, respectively. Since the isothermal model is adopted, the thermal performance is irrelevant to the flow simulation. The initial temperature of 1600 K is only used for phase initialization (liquid steel). The air is regarded as an incompressible gas, and the viscosity, thermal conductivity, specific heat capacity and molar mass thereof are set to be 1.7894 x 10-5 Pascal-second, 0.0242 W / m-K, 1006.4 J / kg-K and 28.9 g / mol, respectively. The boundary conditions are defined as follows: (1) the upper surface boundary of the air domain is specified as a pressure outlet, and the value thereof is set to be the atmospheric pressure; (2) the boundary between the liquid domain inside the ladle and the air domain is defined as an internal boundary. In addition, the outlet surface of the ladle in contact with the air is also defined as an internal boundary; (3) all other boundaries are defined as stationary, no-slip, adiabatic walls. The available k-ε model and the volume of fluid (VOF) model are adopted to track the phase interface between the liquid steel and the air.

[0084] The initial temperature of the liquid phase region inside the ladle is set to be 1600 K (temperature of molten steel), and all other regions are set to be 300 K. The external pressure is set to be the standard atmospheric pressure 101325 Pa. The gravity is applied along the negative direction of the Y axis, and the value thereof is 9.8 m / s 2 . The pressure-velocity coupling is handled by using the SIMPLE algorithm. In order to study the flow behavior, the dynamic grid technology is used. The time step is 250 s, the time step length is 0.08 s, the maximum iteration number is 5, and the turbulence model is adopted. The diffusion smoothing method is applied, and the grid is regularly re-divided to maintain high quality. The geometric parameters are substituted into formula (7) to establish the relationship between the ladle rotation angle θ and the time, as shown in formula (8). Figure 6 At the same time, the geometric parameters are substituted into formula (11) to obtain the relationship between the angular velocity ω of the ladle and the time, as shown in formula (12). Figure 7

[0085] ​The ladle angular velocity remains constant in the range of 0 to 20 seconds, and the molten steel has not started to flow out of the ladle. In the range of 20 to 110 seconds, the angular velocity first decreases, then gradually increases, and finally sharply increases. To precisely determine the change in the ladle angular velocity with time, a user-defined function (UDF) was used. By defining the boundary as a rotating body around a fixed axis, the dynamic behavior during the pouring process can be accurately captured.

[0086] 2.2 Transient flow field during the constant flow pouring process

[0087] During the constant flow pouring process, the change in the phase interface is a key factor affecting the flow characteristics. The simulation results show that the entire pouring process can be divided into four stages. Each stage reflects different physical phenomena and flow characteristics of the molten steel. Next, the phases of the four stages are analyzed in detail, as shown in FIG. 2. Figure 8

[0088] (1) First stage of the pouring process (0-20 seconds). The ladle starts to rotate, and the angular velocity remains constant. The molten steel starts to flow slowly on the upper surface of the ladle, and the flow is mainly concentrated in a small area inside the ladle.(2) Second stage of the pouring process (20-56.8 seconds). The molten steel starts to flow out of the ladle, and the flow is concentrated around the outlet of the ladle.(3) Third stage of the pouring process (56.8-106.4 seconds). As the ladle rotation angle increases, the remaining amount of molten steel decreases, and the ladle bottom is exposed, so the ladle angular velocity gradually increases.(4) Fourth stage of the pouring process (106.4-110 seconds). The remaining amount of molten steel further decreases until the pouring is completed, and a small amount of molten steel remains in the ladle.

[0089] In addition, the cross-section of the ladle is given to observe the change in the velocity of the molten steel during the constant flow pouring process, as shown in FIG. 3. Figure 9 (1) First stage of the pouring process (0-20 seconds). Initially, the liquid velocity is zero. When the ladle starts to rotate, the liquid velocity is generated inside the ladle, while there is no liquid velocity outside the ladle.(2) Second stage of the pouring process (20-56.8 seconds). The molten steel starts to flow out of the ladle, so the liquid velocity is generated outside the ladle. Due to the effect of gravity, the liquid velocity gradually increases as the falling height increases. At the same time, due to the liquid diffusion, the liquid distribution area increases as the falling height increases. In order to achieve constant flow pouring, the maximum liquid velocity gradually decreases in this stage.(3) Third stage of the pouring process (56.8-106.4 seconds). Similarly, both the liquid velocity and the liquid distribution area increase as the falling height increases. On the contrary, in order to achieve constant flow pouring, the maximum liquid velocity gradually increases in this stage.(4) Fourth stage of the pouring process (106.4-110 seconds). When the ladle rotation angle approaches 90°, the remaining molten steel is very small, so although the ladle angular velocity rapidly increases, the maximum liquid velocity continues to decrease. ​

[0090] 2.3 Influence of the inner wall tilt angle α

[0091] During constant flow casting, according to formula (11), the inner wall inclination angle α and the initial liquid volume Vc significantly affect the instantaneous flow behavior and the remaining liquid volume. Constant flow casting simulations were performed for different inner wall inclination angles α of the ladle, and the curves showing the changes in the remaining liquid volume and instantaneous flow rate were obtained, as shown in the figure. Figure 10 As shown, regardless of the size of α, the remaining liquid volume and flow rate exhibit the same trend. The remaining liquid volume initially remains constant, then decreases to zero, while the flow rate initially reaches zero and then increases sharply to a near-constant value. With increasing α, the initial liquid volume Vc also increases, directly affecting the curve of the remaining liquid volume change. Both the initial volume and flow rate of the molten steel increase with increasing α. When α is in the range of 2.5° to 7.5°, the flow rate fluctuates; when α is in the range of 7.5° to 12.5°, the flow rate decreases slightly. However, when α = 7.5°, the flow rate curve is constant and stable. Therefore, to achieve a stable casting process and a constant flow rate value, a suitable inner wall inclination angle α should be selected in actual production.

[0092] 2.4. Effect of initial liquid volume Vc

[0093] Constant flow casting was simulated under different initial liquid volumes Vc, and the curves showing the changes in residual liquid volume and instantaneous flow rate were obtained, as shown below. Figure 11 As shown, regardless of the value of Vc, the residual liquid volume and flow rate exhibit the same trend. The residual liquid volume initially remains constant, then decreases to zero, while the flow rate initially reaches zero and then increases sharply to a near-constant value. With increasing Vc, the initial volume of molten steel, the residual liquid volume, and the flow rate all increase. Except when Vc = 70% of V capacity, the flow rate initially decreases slightly before completion of casting, then decreases significantly. However, when Vc = 70% of V capacity, the flow rate curve is constant and stable. Therefore, to achieve a stable casting process and a constant flow rate value, a suitable initial liquid volume Vc should be selected in actual production.

[0094] 2.5. Impact of target traffic qt

[0095] Since different target flow rates qt require different steel coil angular velocities, constant flow casting under different target flow rates qt was simulated, and the curves of change in remaining liquid volume and instantaneous flow rate were obtained, as shown in the figure. Figure 12The same trend of the remaining liquid volume and flow rate is observed regardless of qt. The remaining liquid volume remains constant first and then decreases to zero, while the flow rate is zero first and then increases sharply to a nearly constant value. With the increase of qt, the initial volume remains constant, the flow rate of liquid steel increases, the remaining liquid volume decreases more sharply, and the total pouring duration shortens. When qt is in the range of 0.10 m3 / s and 0.12 m3 / s, the flow rate curve is constant and stable. However, when qt is in the range of 0.16 m3 / s and 0.24 m3 / s, the flow rate decreases slightly. Therefore, in order to achieve a stable pouring process and a constant flow rate value, a suitable target flow rate qt should be selected in actual production.

[0096] 3. Experimental device and verification

[0097] 3.1 Experimental device

[0098] The molten steel is high in cost and has safety risks, so water is selected as the alternative fluid to verify the pouring process. The water model experiment is based on the Froude similarity criterion to ensure that the gravity-dominated flow is similar to the dynamics of molten steel. The dynamic viscosity difference is evaluated using the Reynolds number Re. In this application, Re> 105. In the condition of turbulent flow, the influence of viscosity can be ignored. Therefore, in the simulation of molten steel pouring, a water pouring experiment can be used to verify the flow behavior of molten steel instead of a molten steel pouring experiment. In order to verify the accuracy of the analytical model and the simulation model, an experimental device is constructed as shown in Figure 13 The experimental device suitable for the analytical model of ladle constant flow pouring includes a shelf with two symmetrical support arms in the middle, a pouring ladle rotatably connected between the two support arms, a motor connected to the bottom side of the pouring ladle through a steel wire rope, the pouring ladle being placed obliquely, and a liquid collecting barrel placed below the outlet of the pouring ladle. The motor is also connected to a PLC, and the PLC is connected to a power supply and a switch. The power supply, the switch, the PLC, and the motor are arranged on the back side of the shelf, and the pouring ladle and the liquid collecting barrel are arranged in the middle of the shelf. The liquid collecting barrel is used to collect the poured liquid, and the remaining liquid volume is used to verify the analytical model and the simulation model.

[0099] One end of the steel wire rope is connected to the pouring ladle, and the other end is wound around a fixed pulley fixed on the top of the shelf and connected to the output shaft of the motor. The rotational speed of the motor is used to control the constant flow rate of the liquid in the pouring ladle.

[0100] A pouring ladle with an inner wall inclination angle of 7.5° is selected. In the constant flow pouring experiment, the motor runs at a preset speed, and then drives the pouring ladle to rotate at a time-varying angular velocity, so accurate control of the motor speed is crucial to ensure a constant flow rate.

[0101] 3.2 Different initial liquid volumes

[0102] Three groups of constant flow rate casting experiments were conducted with initial liquid volumes Vc of 3.90 L, 4.50 L and 5.10 L, which are approximately 60%, 70% and 80% of the total liquid volume, respectively. The target flow rate qt was set to 50 cm 3 / s. The experimental residual liquid volume was obtained and compared with the results calculated by the analytical model and the simulation model, as shown in Figure 14 . It was observed that the experimental results agreed well with the theoretical and simulated results under different initial liquid volumes, which verified the accuracy of the analytical model and the simulation model. In addition, the experimental residual liquid volume approximately changed linearly, indicating that constant flow rate casting was achieved and constant flow rates could be obtained by adjusting the motor speed.

[0103] 3.3. Different target flow rates

[0104] Three groups of constant flow rate casting experiments were conducted with target flow rates qt of 50 cm3 / s, 45 cm3 / s and 40 cm3 / s, respectively. The initial liquid volume Vc was set to 4.5 L, which is approximately 70% of the total ladle volume. The experimental residual liquid volume was obtained and compared with the results calculated by the analytical model and the simulation model, as shown in Figure 15 . It was observed that the experimental results agreed well with the theoretical and simulated results under different target flow rates, which verified the accuracy of the analytical model and the simulation model. In addition, the experimental residual liquid volume approximately changed linearly, indicating that constant flow rate casting was achieved and different constant flow rates could be obtained by adjusting the motor speed.

[0105] To achieve precise ladle casting, an analytical model of constant flow casting was established. By integrating user-defined functions (UDFs), computational fluid dynamics (CFD) simulation of constant flow casting was conducted to study the behavior of steel liquid casting under different inner wall inclination angles a, initial liquid volumes Vc and target flow rates qt. Finally, the accuracy of the analytical model and the simulation model was verified by experiments. The results are as follows:

[0106] (1) The experimental results agreed well with the theoretical and simulated results, verifying the accuracy of the analytical model and the simulation model. (2) During the casting process, the residual liquid volume and the flow rate had the same trend. The residual liquid volume remained unchanged first, then decreased to zero, while the flow rate was zero first, then increased sharply to a value close to a constant. (3) Increasing a and Vc would result in an increase in flow rate. To achieve a stable casting process and a constant flow rate value, appropriate a, Vc and qt should be selected. In this application, a = 7.5°, Vc = 70% Vcapacity and q is in the range of 0.10-0.12 m 3The / s range is suitable.(4) In order to realize constant flow rate pouring, the ladle angular velocity changing with time is obtained, and can be adjusted by the motor speed. Therefore, different constant flow rates can be obtained by adjusting the motor speed, which provides guidance for engineering application of casting technology.

[0107] Although the above embodiments have been shown and described, it can be understood that the above embodiments are exemplary and cannot be understood as limiting the present application, and the changes, modifications, replacements and variations of the above embodiments made by those of ordinary skill in the art are within the protection scope of the present application.

Claims

1. A ladle constant flow pouring analysis model, characterized by, The ladle pouring process is divided into three stages, and the analytical model between the ladle rotation angle and the remaining liquid volume in the ladle in the ladle pouring process is: In the formula, r=D / 2, a=D / 2-h / tanθ, θ is the ladle rotation angle, V is the remaining liquid volume in the ladle, D=(D1+D2) / 2, D1 and D2 respectively refer to the diameters of the top and bottom of the liquid in the ladle, a, r and D are intermediate variables, H1-T is the height of the liquid in the ladle, H1 is the height of the liquid in the ladle to the bottom of the ladle, T is the thickness of the bottom of the ladle, H is the height from the top to the bottom of the ladle, and h is the height inside the ladle, h=H-T.

2. The ladle constant pouring analysis model according to claim 1, characterized in that, The analytical model between the ladle rotation angle, the angular velocity of the ladle and the flow rate in the pouring process is: where θ is the ladle rotation angle, ω is the ladle angular velocity, q is the flow rate, D = (D1+D2) / 2, D1 and D2 are the diameters of the top and bottom of the liquid in the ladle, respectively, r = D / 2, h is the height inside the ladle, h = H - T, e = tan 2 θ + 1, f = (r - h / tan θ), g = r 2 -(r - h / tan θ) 2 , and the ladle angular velocity can be adjusted by the motor speed.

3. The ladle constant pouring analysis model according to claim 1, characterized in that, The three stages are: in the first stage, the remaining liquid volume in the ladle remains unchanged, and no liquid flows out of the ladle; in the second stage, the liquid begins to flow out of the ladle, the remaining liquid volume decreases, and the bottom of the ladle is still completely immersed in the liquid steel; In the third stage, the bottom of the ladle is exposed, the liquid continuously flows out of the ladle, and the remaining liquid volume continues to decrease.

4. The ladle constant pouring analysis model according to claim 1, wherein, When the initial liquid in the ladle is 70% of the total capacity of the ladle, a stable pouring process and a constant flow rate can be achieved.

5. The ladle constant pouring analysis model according to claim 1, wherein, When the inclination angle of the inner wall of the ladle is α=7.5°, a stable pouring process and a constant flow rate can be achieved.

6. The ladle constant pouring analysis model of claim 1, wherein, When the target flow rate of the ladle is in the range of 0.10 cubic meters / second and 0.12 cubic meters / second, a stable pouring process and a constant flow rate can be achieved.

7. The ladle constant pouring analysis model according to claim 1, wherein, The device suitable for the analytical model of ladle constant flow pouring includes a shelf, two symmetrical support arms are arranged in the middle of the shelf, a pouring ladle is rotationally connected between the two support arms, one side of the bottom of the pouring ladle is connected with a motor through a steel wire rope, the pouring ladle is inclined, and a liquid collecting barrel is placed below the outlet of the pouring ladle.

8. The ladle constant pouring analysis model according to claim 7, wherein, The motor is further connected with a PLC, the PLC is connected with a power supply and a switch respectively, the power supply, the switch, the PLC and the motor are arranged on the rear side of the shelf, and the pouring ladle and the liquid collecting barrel are placed in the middle of the shelf.

9. The ladle constant pouring analysis model according to claim 8, wherein, One end of the steel wire rope is connected with the pouring ladle, and the other end is connected with the output shaft of the motor by passing through a fixed pulley on the top of the shelf.

10. The ladle constant pouring analysis model according to claim 9, wherein, The rotation speed of the motor is used to control the constant flow rate of the liquid in the pouring ladle.

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