A method for predicting the discharge performance of a semi-autogenous mill by fusing multiphase flow simulation and screening mathematical model
By integrating the multiphase flow simulation method of DEM-CFD-VOF and Solvinger screening model, the problems of accuracy and generalization ability in predicting the discharge performance of semi-autogenous mills were solved. High-precision prediction of discharge rate and particle size distribution was achieved, supporting intelligent control and improving production efficiency and stability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- KUNMING UNIV OF SCI & TECH
- Filing Date
- 2026-02-06
- Publication Date
- 2026-06-02
AI Technical Summary
Existing semi-autogenous mill discharge performance prediction technologies suffer from low accuracy and poor generalization ability, making it difficult to meet actual industrial needs. Traditional models lack mechanistic support, and multiphase flow simulation methods fail to fully couple the interaction between particles, fluid, and air and the dynamic screening process.
By integrating DEM-CFD-VOF multiphase flow simulation with the Soldinger sieving mathematical model, a three-phase flow coupling and dynamic sieving integrated prediction framework is constructed. Particle motion is calculated by DEM, fluid motion is simulated by CFD, gas-liquid interface is tracked by VOF, and the sieving process is described by the Soldinger model, realizing the momentum exchange between particles, fluid and gas and the coupling of the sieving process.
It enables high-precision prediction of discharge rate and particle size distribution of semi-autogenous mills, provides mechanistic support, lays the foundation for intelligent control of the grinding process, and improves production efficiency and stability.
Smart Images
Figure CN122133545A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of mineral processing equipment technology, specifically to a method for predicting the discharge performance of a semi-autogenous mill that integrates multiphase flow simulation and screening mathematical model. Background Technology
[0002] As a core piece of equipment in the mineral processing field, the discharge performance of a semi-autogenous grinding mill directly determines the processing efficiency, separation accuracy, and mineral recovery rate of subsequent flotation, gravity separation, and other beneficiation operations. It has an irreplaceable impact on the overall beneficiation process's capacity release, energy consumption control, and product quality stability. Accurate and real-time discharge performance prediction is a crucial prerequisite for achieving load optimization, adaptive parameter adjustment, and intelligent management of the entire semi-autogenous grinding mill process. It is also a key technological bottleneck in the current transformation of the mineral processing industry towards "high efficiency, low carbon emissions, and intelligence." Existing technologies for predicting the discharge performance of semi-autogenous mills have significant shortcomings and are difficult to meet actual industrial needs. Traditional empirical models heavily rely on historical production data under specific operating conditions, and the model parameters lack mechanistic support. When parameters such as ore properties and mill operation fluctuate, the prediction accuracy drops sharply, and the generalization ability is extremely poor. Although discrete element method (DEM) simulation can simulate the collision, grinding, and motion trajectory of solid particles such as ore and steel balls in detail, it generally ignores the key role of slurry in the mill. In actual operating conditions, slurry not only changes the suspension state and motion trajectory of particles through drag and buoyancy, but its flow characteristics also directly affect the entrainment and conveying of fine-grained materials and the screening efficiency of the discharge end liner. Some existing multiphase flow simulation methods only achieve unidirectional coupling between discrete element method (DEM) and computational fluid dynamics (CFD), but do not combine dynamic screening models, making it difficult to accurately replicate the synergistic mechanism of "particle-fluid-screening" at the discharge end. Therefore, there is an urgent need in industrial settings for a prediction method that combines mechanistic and practical approaches, capable of fully coupling the interaction between particles, fluid, and air phases and the dynamic screening process, to achieve high-precision prediction of discharge rate and particle size distribution in semi-autogenous mills, providing core model support for intelligent control of semi-autogenous mills, and addressing the industry pain points of existing technologies such as "weak generalization ability, low prediction accuracy, and insufficient mechanistic aspects". Summary of the Invention
[0003] To address the aforementioned problems, this invention provides a method for predicting the discharge performance of a semi-autogenous mill that integrates multiphase flow simulation and screening mathematical models.
[0004] To achieve the above objectives, the present invention provides the following technical solution: a method for predicting the discharge performance of a semi-autogenous mill that integrates multiphase flow simulation and screening mathematical model, specifically including the following steps: S1. Establish a three-dimensional geometric model of the discharge end of the semi-autogenous mill and the ore steel ball based on the actual parameters of the semi-autogenous mill and the parameter information of the ore steel ball particles; S2, Integration of DEM-CFD-VOF (Discrete Element Method) Computational Fluid Dynamics A coupled model of the semi-autogenous mill discharge process was constructed using the multiphase flow simulation method (fluid volume method) and the Solvinger screening mathematical model, and the parameters of the coupled model were set for numerical simulation calculation of discharge volume data. Specifically, the following steps are included: S2.1, DEM is used for numerical simulation calculations of the motion of solid particles, including the equations of translational motion, rotational motion, normal contact force, and tangential contact force. The expression for the translational motion equation is as follows: In the formula: For particle mass, For particle velocity, To preset the gravitational acceleration, This refers to the normal contact force between particles. This refers to the tangential contact force between particles.
[0005] The equation of rotational motion is expressed as follows: In the formula: For rotational inertia, Angular velocity, This represents the torque between particles.
[0006] The expression for the normal contact force equation is as follows: In the formula: For normal spring stiffness, For normal overlap, The normal damping coefficient is... This is the relative normal velocity.
[0007] The expression for the tangential contact force equation is as follows: In the formula: To preset the static friction coefficient, For tangential spring stiffness, For tangential overlap, The tangential damping coefficient is... This represents the relative tangential velocity.
[0008] The expressions for normal spring stiffness, normal damping coefficient, tangential spring stiffness, and tangential damping coefficient are as follows: In the formula: For equivalent Young's modulus, For the equivalent contact radius, For equivalent quality, To preset the collision recovery coefficient, This is the equivalent shear modulus.
[0009] S2.2 CFD is used for numerical simulation calculation of liquid phase fluid motion, including the fluid mass conservation equation, momentum conservation equation, drag force equation, momentum source phase equation, and grid porosity calculation equation; The expression for the mass conservation equation is as follows: In the formula: For grid porosity, For fluid density, The fluid velocity.
[0010] The equation for the conservation of momentum is expressed as follows: In the formula: For fluid pressure, For stress tensor, It is the acceleration due to gravity. It is the momentum source phase.
[0011] The expression for the drag force equation is as follows: In the formula: This represents the drag force exerted by the fluid on the particles. The interphase momentum transfer coefficient, For the velocity of the particles, This represents the particle volume.
[0012] The expression for the momentum source phase equation is as follows: In the formula: The surface tension coefficient of the gas-liquid two-phase system. This represents the liquid phase volume fraction.
[0013] The expression for the equation for calculating mesh porosity is as follows: In the formula: Let V be the volume of the particles within the grid. The number of particles within the grid. Let be the volume of the grid.
[0014] S2.3 and VOF are used for numerical simulation to calculate the free surface between the gas and liquid phases. By solving the transport equations of the gas and liquid volume fractions, the advection motion of the interface is tracked, thereby reconstructing the dynamic changes of the free surface.
[0015] The expressions for the volume fractions of the gas and liquid phases are as follows: In the formula: This refers to the gas phase volume fraction. It is the liquid volume fraction. For gas phase volume, This represents the volume of the liquid phase.
[0016] Meanwhile, the volume fractions and volumes of the gas and liquid phases satisfy the following constraints: The transport equation for volume fraction is expressed as follows: S2.4, the Solvinger screening mathematical model is used to describe the dynamic screening process at the discharge end of the semi-autogenous mill. It includes the stratification equation, the material balance equation, and the cumulative screening equation. By solving its mathematical model, the screening probability and discharge rate of materials of different particle sizes can be calculated.
[0017] The layered equation is expressed as follows: In the formula: The content of screenable particles, To preset the stratification coefficient, For the CFD time step, select the larger of the DEM and CFD time steps. n and n+ 1 represents the time step number. The material balance equation is expressed as follows: In the formula: The particle content on the sieve surface. The preset screening coefficient is used. The cumulative screening equation is expressed as follows: In the formula: This represents the total content of particles that have passed through the sieve. The S2.5 semi-autogenous mill discharge process coupling algorithm is used to realize the momentum exchange between particles, fluids, and gases in multiphase flow simulation, as well as the coupling between multiphase flow simulation and screening mathematical model. During DEM calculation, the position and velocity information of particles are updated based on CFD calculation results; during CFD and VOF calculations, the velocity, density, and pressure information of the gas and liquid phases are updated based on DEM calculation results; finally, the output particle information is used to solve the Solvinger screening mathematical model to obtain the screening probability and discharge rate of materials of different particle sizes. S3. Based on the coupled model parameters, initialize the coupled model parameters and set the initial ore filling rate, initial steel ball filling rate, initial gas phase volume fraction and liquid phase volume fraction of the model. S4. Perform numerical simulation to obtain data on the discharge rate and particle size distribution of the semi-autogenous mill. Compare with the actual data and calculate the relative error. If the relative error is ≤5%, save the coupled model parameters and execute step S5. If the relative error is >5%, correct the coupled model parameters and continue to execute step S2 to set the coupled model parameters. S5. Output the final semi-autogenous mill discharge rate and discharge particle size distribution data.
[0018] Compared with existing technologies, this invention provides a method for predicting the discharge performance of a semi-autogenous mill that integrates multiphase flow simulation and screening mathematical models, and has the following beneficial effects: This invention is the first to deeply couple DEM-CFD-VOF multiphase flow simulation with a Solderinger dynamic screening mathematical model, constructing an integrated prediction framework of "three-phase flow coupling + dynamic screening". This systematically solves the technical defects of traditional methods that ignore fluid effects and lack consideration of screening mechanisms. Through a two-way coupling algorithm, it not only accurately captures the drag, buoyancy, and entrainment effects of fluid on particles, but also fully considers the obstruction and disturbance effects of particle presence on fluid flow and the dynamic evolution of the gas-liquid interface. It completely replicates the coordinated physical process of "particle grinding - fluid transport - dynamic screening" at the discharge end of a semi-autogenous mill, providing solid mechanistic support for the prediction of discharge performance. This invention can more comprehensively and accurately output the two key process indicators, discharge rate and discharge particle size distribution. It provides a solid technical foundation for intelligent control of the grinding process, helping to improve production efficiency and stability. Attached Figure Description
[0019] Figure 1 This is a schematic diagram of the steps of the present invention; Figure 2 Figure (a) shows a three-dimensional geometric model of the discharge end of the semi-autogenous mill of the present invention, wherein Figure (b) is a three-dimensional model of the cylinder liner and Figure (a) is a three-dimensional model of the discharge end liner. Figure 3This is a coupled flowchart of the semi-autogenous mill discharge process coupling model of the present invention; Figure 4 The above are particle and fluid motion cloud diagrams of the present invention, wherein part (a) is a solid phase particle motion cloud diagram and part (b) is a liquid phase fluid motion cloud diagram. Figure 5 This is a comparison chart of the predicted and actual data of the present invention. In the chart, part (a) is a comparison chart of the discharge rate and part (b) is a comparison chart of the discharge particle size distribution. Figure 6 This is a graph showing the final predicted ore discharge rate of this invention. Figure 7 This is a diagram showing the final predicted result of the particle size distribution of the discharged ore according to the present invention. Detailed Implementation
[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0021] like Figure 1 As shown, a method for predicting the discharge performance of a semi-autogenous mill that integrates multiphase flow simulation and screening mathematical modeling includes the following steps: S1. Establish a three-dimensional geometric model of the discharge end of the semi-autogenous mill and the ore steel ball based on the actual parameters of the semi-autogenous mill and the parameter information of the ore steel ball particles; The actual parameters of the semi-autogenous mill include the three-dimensional geometric model of the cylinder, the three-dimensional geometric model of the discharge end, and the material properties of the liner. The three-dimensional geometric model of the cylinder includes: an effective radius of 1.6m, an axial thickness of 0.8m, 60 evenly distributed lifting bars of varying heights (175mm and 90mm respectively), and a 15° inclined angle for the lifting bars to facilitate the dropping motion of particles at the discharge end. The three-dimensional geometric model of the discharge end includes: an inner liner, a grid plate, and a discharge chute, used for forced ore discharge and screening of ore particles. The material properties of the liner include shear modulus, which is set to 7×10 in this embodiment. 10 Pa and Young's modulus are set to 1.82 × 10⁻⁶ in this embodiment. 11 Density, in this embodiment, is set to 7800 kg / m³. 3 The Poisson's ratio is set to 0.3 in this embodiment; finally, a three-dimensional geometric model of the discharge end of the semi-autogenous mill is built using Solidworks, as shown below. Figure 2 As shown, Figure (a) is a three-dimensional model of the cylinder liner, and Figure (b) is a three-dimensional model of the discharge end liner.
[0022] The parameter information of the ore steel ball particles includes their geometric structure and material properties. The ore geometry has five particle size classes with diameters of 20mm, 30mm, 40mm, 60mm, and 100mm. The first three particle size classes can be discharged by the discharge end liner, and their masses are 0.02kg, 0.06kg, 0.15kg, 0.51kg, and 2.35kg, respectively, all in a spherical rigid body shape. The steel ball geometry has one particle size class with a diameter of 150mm and a mass of 13.78kg, also in a spherical rigid body shape. The ore material properties include shear modulus, which is set to 1×10⁻⁶ in this embodiment. 8 Pa and Young's modulus are set to 2.6 × 10 in this embodiment. 8 The material density is set to 2600 kg / m³ in this embodiment. 3 The Poisson's ratio is set to 0.3 in this embodiment; the steel ball material properties include shear modulus, which is set to 7 × 10⁻⁶ in this embodiment. 10 Pa and Young's modulus are set to 1.82 × 10⁻⁶ in this embodiment. 11 The material density is set to 7800 kg / m³ in this embodiment. 3 The Poisson ratio is set to 0.3 in this embodiment; S2. A coupled model of the discharge process of a semi-autogenous mill is constructed by integrating the DEM-CFD-VOF multiphase flow simulation method with the Solvinger screening mathematical model, and the parameters of the coupled model are set for numerical simulation calculation of discharge volume data. Specifically, the following steps are included: S2.1 and DEM are used for numerical simulation calculations of the motion of solid particles, including the equations of translational motion, rotational motion, normal contact force, and tangential contact force of the particles. The equation of translational motion is expressed as follows: In the formula: For particle mass, For particle velocity, The acceleration due to gravity is set to 9.81 in this embodiment. This refers to the normal contact force between particles. This refers to the tangential contact force between particles.
[0023] The equation of rotational motion is expressed as follows: In the formula: For rotational inertia, Angular velocity, This represents the torque between particles.
[0024] The expression for the normal contact force equation is as follows: In the formula: For normal spring stiffness, For normal overlap, The normal damping coefficient is... This is the relative normal velocity.
[0025] The expression for the tangential contact force equation is as follows: In the formula: The static friction coefficient is set to 0.25 in this embodiment. For tangential spring stiffness, For tangential overlap, The tangential damping coefficient is... This represents the relative tangential velocity.
[0026] The expressions for normal spring stiffness, normal damping coefficient, tangential spring stiffness, and tangential damping coefficient are as follows: In the formula: For equivalent Young's modulus, For the equivalent contact radius, For equivalent quality, The collision recovery factor is set to 0.5 in this embodiment. This is the equivalent shear modulus.
[0027] S2.2 CFD is used for numerical simulation calculation of liquid phase fluid motion, including the fluid mass conservation equation, momentum conservation equation, drag force equation, momentum source phase equation, and grid porosity calculation equation; The expression for the mass conservation equation is as follows: In the formula: For grid porosity, For fluid density, The fluid velocity.
[0028] The equation for the conservation of momentum is expressed as follows: In the formula: For fluid pressure, For stress tensor, It is the acceleration due to gravity. It is the momentum source phase.
[0029] The expression for the drag force equation is as follows: In the formula: This represents the drag force exerted by the fluid on the particles. The interphase momentum transfer coefficient is set to 0.85 in this embodiment. For the velocity of the particles, This represents the particle volume.
[0030] The expression for the momentum source phase equation is as follows: In the formula: The surface tension coefficient for the gas-liquid two-phase system is set to 0.072 in this embodiment. This represents the liquid phase volume fraction.
[0031] The expression for the equation for calculating mesh porosity is as follows: In the formula: Let V be the volume of the particles within the grid. The number of particles within the grid. Let be the volume of the grid.
[0032] S2.3 and VOF are used for numerical simulation to calculate the free surface between the gas and liquid phases. By solving the transport equations of volume fraction, the advection motion of the interface is tracked, thereby reconstructing the dynamic changes of the free surface.
[0033] The expressions for the volume fractions of the gas and liquid phases are as follows: In the formula: This refers to the gas phase volume fraction. It is the liquid volume fraction. For gas phase volume, The volume of the liquid phase; Simultaneously, the volume fractions of the gas and liquid phases, along with the volume, satisfy the following constraints: The transport equation for volume fraction is expressed as follows: .
[0034] S2.4, the Solvinger screening mathematical model is used to describe the dynamic screening process at the discharge end of the semi-autogenous mill. It includes the stratification equation, the material balance equation, and the cumulative screening equation. By solving its mathematical model, the screening probability and discharge rate of materials of different particle sizes can be calculated.
[0035] The layered equation is expressed as follows: In the formula: The content of screenable particles, The stratification factor is set to 0.5 in this embodiment. For the CFD time step, select the larger of the DEM and CFD time steps. n and n+ 1 represents the time step number.
[0036] The material balance equation is expressed as follows: In the formula: The particle content on the sieve surface. The sieve penetration coefficient is set to 0.3 in this embodiment.
[0037] The cumulative equation for sieve penetration is expressed as follows: In the formula: This represents the total content of particles that have passed through the sieve. S2.5, the semi-autogenous mill discharge process coupling algorithm is used to realize the momentum exchange between particles, fluids and gases in multiphase flow simulation, as well as the coupling between multiphase flow simulation and screening mathematical model. The coupling flowchart is as follows. Figure 3 As shown. To set the simulation time, it is set to 30 in this embodiment. To simulate time, The DEM time step is set to 0.0001 in this embodiment. The CFD time step is set to 0.001 in this embodiment. During the DEM calculation, the particle position and velocity information are updated based on the CFD calculation results, particle contact is detected, contact force and contact torque are calculated, and the particle motion equations are solved. During the CFD and VOF calculations, the momentum source term is calculated based on the DEM calculation results. and mesh porosity The gas-liquid two-phase velocity, density, and pressure information are updated, and the mass and momentum conservation equations are solved. The final output particle information is used to solve the Solvinger screening mathematical model to obtain the screening probability and discharge rate of materials of different particle sizes. The parameters set for the coupling model include: static friction coefficient. Collision recovery coefficient Interphase momentum transfer coefficient Surface tension coefficient of gas-liquid two phases Stratification coefficient and sieve penetration coefficient ; S3. Based on the coupled model parameters, initialize the coupled model parameters and set the initial ore filling rate, initial steel ball filling rate, initial gas phase volume fraction and liquid phase volume fraction of the model. The initialization of the coupled model parameters includes the following parameters: static friction coefficient. Collision recovery coefficient Interphase momentum transfer coefficient Surface tension coefficient of gas-liquid two phases Stratification coefficient and sieve penetration coefficient ; The initial ore filling rate of the coupled model was 25%, the initial steel ball filling rate of the coupled model was 10%, the gas phase volume fraction was 65%, and the liquid phase volume fraction was 35%. S4. Perform numerical simulation; particle and fluid motion cloud maps are shown below. Figure 4 As shown in the figure, part (a) is the solid phase particle motion cloud map, and part (b) is the liquid phase fluid motion cloud map. Simultaneously, data on the discharge rate and discharge particle size distribution during the 10-second steady-state discharge process of the semi-autogenous mill were selected and compared with actual data. The comparison figure between predicted and actual data is shown in the figure below. Figure 5 As shown, the relative error is calculated simultaneously. If the relative error is ≤5%, the coupling model parameters are saved, and step S5 is executed; if the relative error is >5%, the coupling model parameters are corrected, and step S2 is executed to set the coupling model parameters. Figure (a) shows the comparison of discharge rates, and Figure (b) shows the comparison of discharge particle size distribution. In the figures, the predicted discharge mass fractions of different particle size classes (D20, D30, D40) are consistent with the actual values, and the prediction errors of each particle size class are all less than the threshold, further verifying the effectiveness of the fusion model proposed in this invention in characterizing particle size selective discharge behavior. In particular, the prediction accuracy for the dominant particle size class (such as D40) is high, indicating that the model can reliably capture the screening mechanism and multiphase flow coupling effect at the discharge end.
[0038] S5. Output the final semi-autogenous mill discharge rate and discharge particle size distribution data. The final prediction results are as follows: Figure 6 , Figure 7 As shown in the curve, during the stable phase of the simulation (after about 10 seconds), the total discharge volume tends to stabilize, indicating that the system has reached dynamic equilibrium and the discharge rate remains stable. The discharge quality of D40 particles is the highest, indicating that this particle size is the easiest to pass through the screen during the discharge process of the semi-autogenous mill and has the largest contribution to the discharge. The discharge quality of D30 and D20 particles decreases in that order.
[0039] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A method for predicting the discharge performance of a semi-autogenous mill by integrating multiphase flow simulation and screening mathematical model, characterized in that, Includes the following steps: S1. Based on the actual parameters of the semi-autogenous mill and the parameters of the ore steel ball particles, establish a three-dimensional geometric model of the discharge end of the semi-autogenous mill and the ore steel ball. S2. Based on the three-dimensional geometric model, a coupled model of the semi-autogenous mill discharge process is constructed by integrating the DEM-CFD-VOF multiphase flow simulation method with the Solvinger screening mathematical model, and the parameters of the coupled model are set. S3. Based on the coupled model parameters, initialize the coupled model parameters and set the initial ore filling rate, initial steel ball filling rate, initial gas phase volume fraction and liquid phase volume fraction of the model. S4. Based on the initialization of the coupled model parameters and the initial ore filling rate, initial steel ball filling rate, initial gas phase volume fraction, and liquid phase volume fraction, numerical simulation is performed to obtain the discharge rate and discharge particle size distribution data of the semi-autogenous mill. By comparing with the real data, the relative error is calculated. When the relative error is ≤5%, the discharge rate and discharge particle size distribution data of the semi-autogenous mill are saved. When the relative error is >5%, the coupled model parameters are corrected, and the process of setting the coupled model parameters in S2 is continued. S5. Based on the semi-autogenous mill discharge rate and discharge particle size distribution data with a relative error of ≤5%, output the final semi-autogenous mill discharge rate and discharge particle size distribution data results, and complete the semi-autogenous mill discharge performance prediction method that integrates multiphase flow simulation and screening mathematical model.
2. The method for predicting the discharge performance of a semi-autogenous mill by integrating multiphase flow simulation and screening mathematical model as described in claim 1, characterized in that, S2 specifically includes the following steps: S2.1 Calculate the motion of solid particles using DEM; Specifically, this includes: the equations of translational motion, rotational motion, normal contact force, and tangential contact force of solid particles; S2.2 Calculate the motion of liquid phase fluid using CFD; Specifically, this includes: the mass conservation equation, momentum conservation equation, drag force equation, momentum source phase equation, and grid porosity calculation equation for liquid phase fluids; S2.3 Calculate the free surface between the gas and liquid phases using VOF; Specifically, this includes solving for the gas phase volume fraction and the liquid phase volume fraction; S2.4 Describe the dynamic screening process at the discharge end of the semi-autogenous mill using a Solvinger screening mathematical model; Specifically, these include: stratification equations, material balance equations, and cumulative sieve penetration equations; S2.
5. A bidirectional momentum exchange between DEM, CFD and VOF is realized through a coupling algorithm, and the output particle information is input into the Soldinger screening model to obtain the screening probability and discharge rate of materials of different particle sizes. Specifically, during the DEM calculation process, the position and velocity information of the particles are updated based on the CFD calculation results; during the CFD and VOF calculation processes, the gas-liquid two-phase velocity, density, and pressure information are updated based on the DEM calculation results; finally, the output particle information is used to solve the Solvinger screening mathematical model to obtain the screening probability and discharge rate of materials of different particle sizes.
3. The method for predicting the discharge performance of a semi-autogenous mill by integrating multiphase flow simulation and screening mathematical model according to claim 2, characterized in that, In S2.1, the expression for the translational motion equation is as follows: In the formula: For particle mass, For particle velocity, To preset the gravitational acceleration, This refers to the normal contact force between particles. This refers to the tangential contact force between particles; The equation of rotational motion is expressed as follows: In the formula: For rotational inertia, Angular velocity, The torque between particles; The expression for the normal contact force equation is as follows: In the formula: For normal spring stiffness, For normal overlap, The normal damping coefficient is... The relative normal velocity; The expression for the tangential contact force equation is as follows: In the formula: To preset the static friction coefficient, For tangential spring stiffness, For tangential overlap, The tangential damping coefficient is... Relative tangential velocity; The expressions for the normal spring stiffness, normal damping coefficient, tangential spring stiffness, and tangential damping coefficient are as follows: In the formula: For equivalent Young's modulus, For the equivalent contact radius, For equivalent quality, To preset the collision recovery coefficient, This is the equivalent shear modulus.
4. The method for predicting the discharge performance of a semi-autogenous mill by integrating multiphase flow simulation and screening mathematical model according to claim 2, characterized in that, In S2.2, the expression for the mass conservation equation is as follows: In the formula: For grid porosity, For fluid density, For fluid velocity; The equation for the conservation of momentum is expressed as follows: In the formula: For fluid pressure, For stress tensor, It is the acceleration due to gravity. It is a momentum source phase; The expression for the drag force equation is as follows: In the formula: This represents the drag force exerted by the fluid on the particles. To preset the interphase momentum transfer coefficient, For the velocity of the particles, The particle volume; The expression for the momentum source phase equation is as follows: In the formula: To preset the surface tension coefficients of the gas-liquid two phases, It represents the liquid volume fraction; The expression for the equation for calculating mesh porosity is as follows: In the formula: Let V be the volume of the particles within the grid. The number of particles within the grid. For indexing, Let be the volume of the grid.
5. The method for predicting the discharge performance of a semi-autogenous mill by integrating multiphase flow simulation and screening mathematical model according to claim 2, characterized in that, In S2.3, the expressions for the volume fractions of the gas phase and the liquid phase are as follows: In the formula: This refers to the gas phase volume fraction. It is the liquid volume fraction. For gas phase volume, The volume of the liquid phase; Simultaneously, the volume fractions of the gas and liquid phases, along with the volume, satisfy the following constraints: The transport equation for volume fraction is expressed as follows: 。 6. The method for predicting the discharge performance of a semi-autogenous mill by integrating multiphase flow simulation and screening mathematical model according to claim 2, characterized in that, In S2.4, the layered equation is expressed as follows: In the formula: The content of screenable particles, To preset the stratification coefficient, For CFD time step, n and n+ 1 represents the time step number; The material balance equation is expressed as follows: In the formula: The particle content on the sieve surface. This is the preset sieve penetration coefficient. The cumulative equation for sieve penetration is expressed as follows: In the formula: This represents the total content of particles that have passed through the sieve.
7. The method for predicting the discharge performance of a semi-autogenous mill by integrating multiphase flow simulation and screening mathematical model as described in claim 1, characterized in that, In step S3, the initialization of the coupled model parameters specifically includes: static friction coefficient. Collision recovery coefficient Interphase momentum transfer coefficient Surface tension coefficient of gas-liquid two phases Stratification coefficient and sieve penetration coefficient The 6 parameters are initialized.
8. The method for predicting the discharge performance of a semi-autogenous mill by integrating multiphase flow simulation and screening mathematical model according to claim 1, characterized in that, In S4, the initial ore filling rate is 25%, the initial steel ball filling rate is 10%, the gas phase volume fraction is 65%, and the liquid phase volume fraction is 35%.