A discrete element simulation method and system for paste-powder mixing and stirring in a vertical kneader

Abstract

A kind of slurry-powder mixing stirring system in vertical kneader, vertical kneader stirrer includes first paddle, second paddle, paddle center is paddle shaft, the first paddle and second paddle are symmetrically arranged in pairs, revolve around common center and each self-rotate;The first paddle and second paddle all include horizontal section profile, propeller body, three parts of stirring base circle;Steps: (1) based on the kneading principle design stirring paddle horizontal section curve and establish its three-dimensional discrete element model;(2) based on material formula generates glue-containing phase discrete element particles and solid-phase discrete element particles to be mixed;(3) to solid paddle and hollow paddle, planetary motion mixes material is applied.This application provides a discrete element numerical simulation method and system for the non-uniform mixing stage of high-viscosity slurry-powder system.

Description

Technical Field

[0001] This invention relates to a method for simulating the mixing of slurry and powder, particularly a slurry mixing system and a three-dimensional discrete element numerical simulation method. Background Technology

[0002] Solid propellant mixing is a highly complex process. During mixing, the proportion of solid components gradually increases, eventually exceeding 80%. The viscosity of the entire mixed material system also gradually increases with increasing density. This type of mixture is typically classified as a high-viscosity fluid mixture. Planetary vertical kneaders are key equipment in the research and production of solid propellants. Vertical kneaders used for solid propellant mixing generally employ a combination of hollow and solid blades, with the two blades undergoing complex planetary motion under the action of a transmission device. Numerical simulation is an excellent means of revealing the microscopic mechanisms of the mixing process. Using computational fluid dynamics theory and finite element analysis tools, it is possible to analyze the pressure field, velocity field, and viscosity distribution field during complex mixing processes, assess the uniformity of material mixing, and further optimize geometric parameters such as the blade drive ratio and mixing gap of the vertical kneader, as well as process parameters such as rotational speed and solid component content.

[0003] During the mixing process in a vertical kneader, the materials undergo agglomeration, heterogeneous mixing, and homogeneous mixing stages. Especially during the initial agglomeration stage after adding a large amount of solid components, conventional computational fluid dynamics (CFD) theory struggles to effectively simulate the process of powder components being gradually enveloped and uniformly mixed by the fluid.

[0004] Solid propellant slurries are high-solids, high-viscosity non-Newtonian fluids (including solids from various particles or powders mixed into slurries; these can be materials prepared before coating or spraying, such as positive and negative electrode slurries for secondary batteries, and various applications in textiles, metallurgy, power, and daily chemicals). The mixing process requires strong shear, strong distribution, and strong convection (including stirring, kneading, and homogenization). Currently, vertical planetary kneaders are commonly used in the industry. Their core working components are a pair of stirring blades, usually a hollow blade and a solid blade, which complete kneading and stirring through a combination of revolution and rotation. Existing publicly available technologies, such as CN106000187A, describe a stirring mixer suitable for energetic materials. This mixer is a vertical double-blade (hollow + solid) mixer used for stirring high-solids energetic materials. The blades perform a combination of rotation and revolution, and it can be used for mixing high-viscosity materials such as solid propellants. Only the structure and transmission are disclosed; discrete element simulation and blade trajectory equation design are not disclosed. CN210252054U discloses a vertical kneader with dual impellers, featuring a compact structure with vertical dual impellers and planetary motion; it represents a structural improvement without impeller trajectory equations or numerical simulation methods. CN101954255B discloses a method for designing the impeller profile of a vertical kneader, optimizing the impeller contour and motion clearance.

[0005] However, none of the aforementioned existing technologies disclose a dual-paddle cross-section design method based on the tip trajectory equation, nor do they propose a three-dimensional discrete element numerical simulation method for slurry, thus failing to simulate the entire heterogeneous mixing process from particle scale to agglomeration → wetting → dispersion.

[0006] The dual-blade propeller employs a Z-shaped or sigma-shaped structure, relying on the gap between the outer edge of the blade and the inner wall of the feed pan to achieve wall scraping and shearing. However, in practical engineering applications, the following drawbacks still exist: 1. The horizontal cross-section of the blades is mostly designed empirically, resulting in mismatched blade tip trajectories and low shearing efficiency at the kneading surface; 2. The risk of interference between paired blade movements is high, and the mixing dead zone is difficult to eliminate; 3. The helix angle and cross-sectional curve are mismatched, leading to incoordination between axial material transport and radial dispersion; 4. For the initial mixing of agglomerated materials, the particle wetting and dispersion capabilities are insufficient. These problems result in poor mixing uniformity and long cycles, making it difficult to meet the high consistency manufacturing requirements of solid propellants. Summary of the Invention

[0007] The purpose of this invention is to overcome the problems of existing paired impeller agitators, such as unreasonable trajectory, easy interference, large mixing dead zone, and poor dispersion of agglomerated materials. It provides a method that uses discrete element particles to construct the slurry to be mixed and the solid component particles to be added, and proposes a three-dimensional discrete element simulation method suitable for the mixing process of a vertical kneader. This results in a vertical kneader paired impeller agitator with accurate trajectory, no interference, and efficient mixing throughout the entire mixing range.

[0008] To solve the above problems, the technical solution of the present invention is a slurry-powder mixing system in a vertical kneader, comprising a first impeller (hollow or solid distal impeller), a second impeller (solid or hollow proximal impeller), and an impeller shaft at the center of the impeller. The first and second impellers are arranged symmetrically in pairs, revolving around a common center and rotating on their own axes. Both the first and second impellers comprise a horizontal cross-sectional profile, a propeller body, and a mixing base circle. The horizontal cross-sectional profile is smoothly closed by a distal tip trajectory segment, a proximal tip trajectory segment, a (Bezier) shaping segment, and a base circle arc segment. The steps include:

[0009] (1) Input geometric parameters: Input the volume, diameter and height of the kneader, as well as the diameter of the stirring blade and the helix angle, etc., as basic geometric parameters for the design of the horizontal cross section curve of the blade and the modeling of the kneader.

[0010] (2) Design the horizontal cross-sectional curve of the blade. Based on the kneading principle, calculate the trajectory equation of the blade kneading surface based on the blade tip motion trajectory. The non-kneading surface is modified to form a closed horizontal cross-sectional curve of the blade.

[0011] (3) Modeling of stirring blades and kneader: Based on the principle of spiral, the geometric model of the blade is generated based on the horizontal cross-section curve and the spiral angle of the blade. At the same time, the discrete element model of the kneader pot is established based on the geometric parameters.

[0012] (4) Generate sample particles of the slurry to be mixed. Generate slurry samples according to the material formula and solid content. Group the sample particles and set the material parameters based on the mixing conditions.

[0013] (5) Apply planetary motion to mix the slurry. Apply different rotational angular velocities to the hollow and solid blades according to the transmission ratio, and simultaneously apply a revolution angular velocity to both blades. The blades drive the slurry to be mixed under the planetary compound motion.

[0014] Beneficial effects: Precise matching of paired blade trajectories: cross-section design based on equations improves kneading efficiency by over 20%; Interference-free global mixing: optimized speed ratio and center distance eliminate dead zones and material jamming; Strong adaptability to high viscosity: helical structure enhances axial circulation, suitable for propellant slurries; Strong agglomeration and dispersion capabilities: shear and extrusion coupling significantly improves initial mixing quality. Using discrete element methods (DEMs) to simulate the slurry and solid component particles, rather than the pure fluid characterization in traditional numerical simulations, effectively simulates the agglomerate state in the initial stage of mixing, exploring the wetting and homogenization process of colloidal components and solid particles from a particle perspective. Attached Figure Description

[0015] Figure 1 Discrete element simulation method and system implementation flowchart for slurry-powder mixing in a vertical kneader;

[0016] Figure 2 Flowchart of the process for designing the horizontal cross-section curve of the blade;

[0017] Figure 3 Modeling flowchart of mixing blades and kneader;

[0018] Figure 4 Flowchart of applying planetary motion to mix the slurry. Detailed Implementation

[0019] Figure 1 This document presents a discrete element method for slurry-powder mixing in a vertical kneader, along with a flowchart of its implementation.

[0020] The vertical kneader includes a first blade (hollow or solid distal blade), a second blade (solid or hollow proximal blade), and a blade shaft at the center of the blades. The first and second blades are arranged symmetrically in pairs, revolving around a common center and rotating on their own axes. Both the first and second blades consist of a horizontal cross-sectional profile, a propeller body, and a mixing base circle. The horizontal cross-sectional profile is smoothly closed by a distal blade tip trajectory segment, a proximal blade tip trajectory segment, a (Bezier) shaping segment, and a base circle arc segment. The first and second blades satisfy a fixed or variable speed ratio: a rotation ratio of 2:1 and a rotation / revolution ratio. The minimum gap between the blades and the mixing bowl is 1–5 mm. The paired blades can be either active and passive or have no motion interference.

[0021] The paired blades consist of one hollow and one solid blade, with helix angles of [missing information]. and This process creates an axial differential conveying system. The horizontal cross-section of the blades generates a contact motion envelope based on the tip trajectory equation. The kneading surface is shaped using Bezier curves to reduce resistance and enhance turbulence. Scraping chamfers are provided on both the outer edge and bottom of the blades to eliminate dead zones on the walls and bottom. Through discrete element modeling of the sides and bottom of the material pot, the blade shape, material pot fit, and minimum clearance of the combined kneader are derived.

[0022] Step 01: Input geometric parameters. Input the kneader volume V, the inner diameter of the feed pan D, and the height of the feed pan H. Design based on experience. The inner diameter of the feeding pot is calculated by back-calculating the volume formula of a cylinder:

[0023]

[0024] impeller diameter Input minimum gap Take 3mm, center distance of the far (hollow) propeller :

[0025]

[0026] Take the center distance of the near (solid) propeller stirring base circle diameter :

[0027]

[0028] Without loss of generality, assuming a kneader volume of 5L, the inner diameter of the mixing bowl is 204mm, the bowl height is 153mm, and the impeller diameter is 102mm. Taking a minimum clearance of 3mm, the center-to-center distance between the distal and proximal impellers is 48mm, the center-to-proximal distance is 24mm, and the base circle diameter of the agitator is 36mm. Other geometric parameters include:

[0029] Blade center distance

[0030]

[0031] Blade pinch angle

[0032]

[0033] The speed ratio k between the proximal and distal blades is set to 2.

[0034] Step 02: Design the horizontal cross-sectional curve of the blade. The kneader blade consists of solid and hollow blades, and the blade cross-section is symmetrical. This example will specifically illustrate the modeling of one of the blades.

[0035] Figure 2 This is a schematic diagram of the segmented horizontal cross-sectional curve of the blade.

[0036] like Figure 2 The schematic diagram shows that segments 1 and 2 are the kneading surfaces of the two blades, which can be calculated based on the kneading principle. Segment 3 is the non-kneading surface, which is modified through shaping. Segment 4 is part of the stirring base circle curve. Based on the kneading principle, segment 1 is part of the motion trajectory of the distal (hollow) blade tip, determined according to the following parametric equations:

[0037]

[0038] Segment 2 is part of the near-solid blade tip motion trajectory, determined according to the following parametric equations:

[0039]

[0040] Segment 3 is reshaped using Bézier curves based on control points. Segment 4 has a diameter of... The arc curve of (the diameter of the stirring base circle).

[0041] Step 03: Modeling the mixing blades and kneader

[0042] Figure 3 Flowchart for modeling the mixing blades and kneader.

[0043] Step 31: Discretization of the cross-sectional curve and discrete element modeling. Based on the cross-sectional curve obtained in Step 02, the discrete length (element diameter) is set according to the simulation accuracy. Simultaneously, equal-sized spheres are used to fill the interior of the cross-sectional polygon to establish the cross-sectional discrete element model. Without loss of generality, the element diameter is set to 4mm in this example.

[0044] Step 32: Hollow Propeller Discrete Element Modeling. Based on the cross-sectional discrete element model from Step 31, a single-wing hollow propeller propeller is generated according to the propeller height and helix angle. The points on the propeller are determined by the following parametric equations:

[0045]

[0046] in For points on the discrete element model of the section in step 31, The height of the helix. The radius of the agitator is... The helical lift angle of the hollow propeller is given. Based on symmetry, the propellers on both sides are generated, and the central hollow stirring base circle is combined to establish a discrete element model of the hollow propeller.

[0047] Step 33 Solid propeller discrete element modeling. Based on the cross-sectional discrete element model from Step 31, a single-wing solid propeller propeller is generated according to the solid propeller height and helix angle. The propeller equation is similar to that in Step 32 and will not be repeated here. Based on symmetry, the propellers on the opposite sides are generated, and the solid stirring base circle in the middle is combined to establish the solid propeller discrete element model.

[0048] Step 34 Discrete Element Modeling of the Material Pot and Assembly of the Kneader. Based on the diameter and height of the kneader, establish discrete element models of the side and bottom surfaces of the material pot. Simultaneously, combine the hollow paddle from Step 32 and the solid paddle from Step 33 to construct the discrete element geometric model of the kneader.

[0049] Step 04: Generate sample particles of the slurry to be mixed.

[0050] Step 51: Modeling and Grouping of Drug Slurry Particles. Based on the mass and volume of the mixed drug slurry, randomly distributed discrete element particle samples of the drug slurry are generated. To improve the computational scale and efficiency, based on coarsening theory, a single discrete element is used to characterize micron-sized powder particle agglomerates. Without loss of generality, in this example, the average diameter of the element is taken as 4 mm, and the maximum-to-minimum particle size ratio of the element is 1.56, so the sample particle size range is 3.2~5.0 mm. According to the stirring conditions, the lower layer is set as premixed drug slurry (liquid phase or colloidal phase) discrete element particles, and the upper layer is set as the drug slurry powder (solid phase) discrete element particles to be mixed. The method of the first group of this invention is used for verification.

[0051] Step 52: Setting the material parameters for the slurry particles. Based on the state of the slurry particles, set the rheological and mechanical parameters of the lower colloidal phase particles, including the viscosity coefficient. etc.; Set the mechanical parameters of the upper solid phase particles, based on the linear elastic contact model, including the particle normal stiffness kn and tangential stiffness ks, normal fracture force bF, initial shear force Fs0, and friction coefficient. wait.

[0052] Step 05: Apply planetary motion mixed syrup

[0053] Figure 4 A flowchart for applying planetary motion to mix the slurry.

[0054] Step 53: Apply impeller rotation displacement. Set the rotation speed ratio k between the hollow and solid impellers to 2, and the rotation speed ratio C between the hollow impeller and its revolution speed to 8.1304, so that the impellers sweep across as much of the stirring area as possible and avoid [unclear - possibly "avoiding"]. Without loss of generality, let's take the single rotation angular displacement of the hollow impeller as 1°, then the single rotation angular displacement of the solid impeller as 0.5°. Apply the corresponding rotation angular displacement to each impeller around its center to achieve stirring rotation.

[0055] Step 54: Apply blade angular displacement. Without loss of generality, the single revolution angular displacement of the blade is 0.1223°.

[0056] Step 55: Discrete Element Method (DEM) Iterative Calculation of Particles. Using a conventional DEM iterative calculation process, the forces acting on the sample particles are updated based on the contact model, the resultant force of the sample particles is calculated, and the acceleration, velocity, and position of the sample particles are calculated according to Newton's second law of motion, thus realizing the mixing process after a single planetary motion. Steps 53-55 are repeated until the preset stirring displacement or uniform mixing of the slurry is achieved.

[0057] This invention achieves uniformity in less time, using SPAN = (D90−D10) / D50 or the Cu coefficient for detection. It outputs the change in mixing uniformity over time during rotation. Furthermore, this invention can optimize rotation speed, resulting in a significant reduction in mixing time. Conventional methods use fluid dynamics, while this invention uses particle discrete element methods. Compared to similar equipment, the mixing time to achieve the same mixing uniformity is reduced by 10%-20%, greatly improving mixing efficiency and quality.

[0058] The above-disclosed embodiments are merely one or more preferred embodiments of this application and should not be construed as limiting the scope of this application. Those skilled in the art can understand that implementing all or part of the above embodiments and making equivalent changes in accordance with the claims of this application still fall within the scope of this application.

Claims

1. A slurry-powder mixing system in a vertical kneader, wherein the vertical kneader agitator includes a first blade, a second blade, and a blade shaft at the center of the blades; the first and second blades are arranged symmetrically in pairs, revolving around a common center and rotating independently; both the first and second blades comprise a horizontal cross-sectional profile, a propeller body, and a mixing base circle; the horizontal cross-sectional profile is smoothly closed by a distal tip trajectory segment, a proximal tip trajectory segment, a shaping segment, and a base circle arc segment; characterized in that, the steps... include: (1) Input geometric parameters: including the volume, diameter, height, diameter of the stirring blade, helix angle and minimum clearance of the vertical kneader; (2) Design the horizontal section curve of the blade: Based on the kneading principle, calculate the trajectory equation of the kneading surface based on the movement trajectory of the blade tip, and form a closed curve by modifying the non-kneading surface; (3) Modeling of stirring blades and kneader: Based on the horizontal cross-section curve and the helical rise angle, a geometric model of the blades is generated, and a discrete element model of the material pot is established.

2. The method according to claim 1, characterized in that: The kneading surface trajectory equations mentioned in step (2) include the distal propeller tip trajectory and the proximal propeller tip trajectory, which are determined by the following parametric equations: Telecentric propeller tip trajectory: X=a·cos(t)-(d / 2+e)·cos(t+t·k-β) Y=-a·sin(t)+(d / 2+e)·sin(t+t·k-β) t∈[0, β / k] Proximal propeller tip trajectory: X=a·cos(t)-(d / 2+e)·cos(tt / k+β) Y=-a·sin(t)+(d / 2+e)·sin(tt / k+β) t∈[0, β / k].

3. The system according to claim 1, characterized in that: The impeller modeling in step (3) includes: Discretize the cross-sectional curve and establish a discrete element model of the cross-section by filling the interior of the polygon with spheres of equal size. Hollow and solid propellers are generated based on the helix angle and blade height. Discrete element models of the hollow impeller and the solid impeller are established for the combined stirring base circle part. Discrete element models of the side and bottom surfaces of the material pot are established and combined to construct a complete geometric model of the kneader blades.

4. The system according to claim 1, characterized in that: In step (4), the slurry particles to be mixed are distributed in layers, with the lower layer being premixed colloidal particles and the upper layer being solid particles to be mixed, and their rheological or particle mechanical parameters are set respectively.

5. The system according to claim 1, characterized in that: The planetary motion described in step (5) includes: The rotational speed ratio between the hollow propeller and the solid propeller is set to 2; The rotational speed ratio of the hollow propeller to its revolution speed is set to 8.1304; Apply rotational and revolution angular displacements respectively, and iterate until the preset mixing degree is reached.

6. The system according to claim 1, characterized in that: Generate sample particles for the slurry to be mixed: Generate colloidal and solid discrete element particles according to the material formula and set material parameters; Apply planetary motion to mix the slurry: Apply rotational and revolutionary motion to hollow and solid blades to achieve mixing; The method is used to simulate the particle motion and mixing process of the slurry-powder system from the agglomerated state to the heterogeneous mixing stage.

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