A method for predicting hydraulic pressure drop in irregularly packed particle beds

Abstract

This invention proposes a method for predicting the hydraulic pressure drop of irregularly packed particle beds, comprising the following steps: establishing the motion control equations of a particle model using the discrete element method (DEM), generating the packed particle bed through calculation; deriving the STL patch model of the packed particle bed; repairing the STL patch model into a solid bed geometry model; establishing a fluid domain and creating a discrete mesh on the fluid domain; and calculating the resistance of the solid bed geometry model to water flow using computational fluid dynamics (CFD). This method can predict the resistance entirely through numerical calculation in advance without any physical experiments, selecting the particle morphology with the lowest resistance, greatly reducing experimental costs and accelerating development; furthermore, it can calculate the pressure drop of the particle bed, providing theoretical support for subsequent hydraulic calculations of the reactor, pump head selection, and energy consumption calculations.

Description

Technical Field

[0001] This invention belongs to the technical field of lithium extraction equipment for electro-deintercalation in salt lakes, specifically relating to a method for predicting the hydraulic pressure drop of irregularly packed particle beds. Background Technology

[0002] Electrochemical lithium extraction technology currently primarily utilizes electrode-coated equipment, which suffers from low lithium extraction efficiency and difficulties in electrode disassembly and reassembly. To address these shortcomings, millimeter-sized spheres and cylinders can be produced using granulation technology. These particles are then stacked in a lithium extraction reactor, and a graphite electrode is energized to form a bed of deposited particles for electrochemical lithium extraction. (See [link to relevant documentation]). Figure 1 .

[0003] However, predicting the resistance of packed particle beds is a critical issue. Because the shapes of the packed particles are varied—including spheres, cylinders, plates, cloverleaf columns, and tetracloverleaf columns—and their dimensions are also variable, the resulting bed structure, bulk density, and porosity differ significantly. These factors all cause substantial variations in the resistance to liquid flow. Furthermore, even within the same bed, the resistance varies depending on the properties of the liquid. The viscosity and density of the liquid greatly influence the resistance.

[0004] If we first prepare a large number of granules, build a reactor for filling, and then install pressure gauges at the reactor inlet and outlet to measure the pressure difference, this method of measuring resistance would consume a lot of money and time: ① Granulation preparation is also a very difficult development process, requiring a lot of experimentation to find suitable granulation machines and granulation formulas to enable mass production of granules; ② Different granule shapes have different resistances. Optimizing the granule shape with the lowest resistance takes even longer. Summary of the Invention

[0005] This invention aims to solve at least one of the technical problems existing in the prior art. To this end, this invention proposes a method for predicting the hydraulic pressure drop of irregularly packed particle beds, which can predict the resistance in advance entirely through numerical calculations, without conducting any physical experiments, and select the particle morphology with the lowest resistance, greatly reducing experimental costs and accelerating development speed.

[0006] According to a first aspect of the present invention, a method for predicting the hydraulic pressure drop of an irregularly packed particle bed is proposed, comprising the following steps:

[0007] S100: Determine the shape and size of the particles and establish a geometric model of the particles, and use a combination of multiple spheres to perform a body-fit approximation on the geometric model to obtain the particle model;

[0008] S200: Establish the container wall, then generate a set amount of the particle model. Under the constraint of the container wall, the particle model falls freely from a set height and forms a stacked particle bed after stabilization. The particle motion control equation of the particle model is established by the discrete element method, and the shape of the stacked particle bed is obtained by iterative calculation.

[0009] S300: In the packed particle bed, each sphere in each particle model is approximated as a sphere using an STL triangular patch;

[0010] S400: Reduce all the spherical surfaces to a smaller size, and merge and connect the STL triangular facets of the reduced spherical surfaces that are in contact with each other to form a first triangular facet of multiple approximate particles;

[0011] S500: Reconstruct the first triangular facet of each of the approximate particles into a second triangular facet of uniform size, and generate a solid bed geometry model composed of smooth curved surfaces based on the second triangular facet.

[0012] S600: Establish a fluid domain, and then create a discrete mesh for the fluid domain;

[0013] S700: The dynamic equations of laminar flow are established using the finite volume method. The flow parameters are solved on the discrete grid to obtain the velocity field and pressure field. The inlet and outlet pressure difference is extracted from the pressure field, which is the hydraulic pressure drop.

[0014] Preferably, in S100, the particle is in the form of at least one of spheres, cylinders, four-leaf clover columns, or three-leaf clover columns.

[0015] Preferably, in step S200, the height to which the set amount of particle models freely stack after falling is 20% to 80% of the height of the container wall; and / or, the set height is not higher than the height of the container wall.

[0016] Preferably, in S300, the maximum side length of the stl triangular facet is 0.08 mm.

[0017] Preferably, in S400, the shrinkage process includes: all the spheres are reduced in volume by 1% to 5% with their center as the base point.

[0018] Preferably, in S500, the average side length of the second triangular facet is 0.02 mm, and the maximum allowable angle of the second triangular facet is 40 degrees.

[0019] Preferably, in step S600, establishing the fluid domain includes the following steps:

[0020] S610: Create fluid domain geometry without particles;

[0021] S620: Remove the solid bed geometry model from the particle-free fluid domain geometry.

[0022] In S600, establishing the discrete mesh includes the following steps:

[0023] S630: Generates a triangular mesh;

[0024] S640: Improve the quality of the triangular mesh;

[0025] S650: The improved triangular mesh is merged into a tetrahedral mesh;

[0026] S660: Improve the quality of the tetrahedral mesh;

[0027] S670: The improved tetrahedral mesh is merged into a polyhedral mesh.

[0028] Preferably, in S630, the average side length of the triangular mesh is 0.02 to 2 mm, the minimum curvature normal angle of the triangular mesh is 18°, the lower limit number of gap meshes in the triangular mesh is 2, the upper limit angle of the triangular mesh is 80°, and the upper limit of the twist degree of the triangular mesh is 0.8; in S650, the maximum diameter of the circumcircle of the tetrahedral mesh is 2.49 mm, and the lower limit of the orthogonality of the tetrahedral mesh is 0.05.

[0029] Preferably, in step S640, the quality improvement of the triangular mesh includes: triggering an improvement mechanism when the distortion of the triangular mesh exceeds 0.8, moving the unqualified mesh nodes to within the upper limit of the distortion, with a maximum of 5 improvements.

[0030] Preferably, in step S660, the quality improvement of the tetrahedral mesh includes: the orthogonality of the tetrahedral mesh being lower than 0.05 triggers an improvement mechanism, and the unqualified mesh nodes are moved to within the lower limit of orthogonality, with a maximum of 5 improvements.

[0031] According to a second aspect of the present invention, a method for manufacturing a packed particle bed is provided, comprising the following steps:

[0032] (1) Select particles of various shapes and sizes, calculate the hydraulic pressure drop of the accumulated particle bed formed by each type of particle, and obtain the shape and size of the particles corresponding to the lowest hydraulic pressure drop. The calculation method includes the steps of the hydraulic pressure drop prediction method for irregularly accumulated particle beds described in the first aspect of the present invention.

[0033] (2) Mix the active solid, organic solvent and binder to make a slurry, concentrate the slurry and then extrude and cut it to obtain solid particles with the shape and size described in step (1). Fill the solid particles into the lithium extraction electrolytic cell to obtain the packed particle bed.

[0034] The hydraulic pressure drop prediction method for irregularly packed particle beds of the present invention is used to calculate the hydraulic pressure drop of a packed particle bed formed by particles of different shapes and sizes. Based on the calculation results, the particle shape with the least resistance can be selected.

[0035] According to a third aspect of the present invention, a computer device is provided, comprising one or more processors; and a memory having stored one or more programs thereon, which, when executed by the one or more processors, cause the one or more processors to perform the steps of the method for predicting hydraulic pressure drop in irregularly packed particle beds as described in the first aspect of the present invention.

[0036] According to a fourth aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for predicting the hydraulic pressure drop of an irregularly packed particle bed as described in the first aspect of the present invention.

[0037] According to one embodiment of the present invention, at least the following beneficial effects are achieved:

[0038] 1. This invention does not require any physical experiments; the parameters can be obtained entirely through simulation calculations. It can also simulate particles of any shape. In contrast, some existing analytical methods can only simulate the generation of spherical particles or require physical experiments and three-dimensional scanning to obtain the particle morphology.

[0039] 2. The absence of tangency between particles does not lead to distorted meshes, which will not affect the calculation accuracy. However, in some existing analysis methods for infilled particles, the particles have not been reduced in size, and there is contact (tangency) between the particles, which will generate a large number of distorted meshes during mesh generation.

[0040] 3. This invention employs unidirectional coupling, allowing for the arrangement of multiple meshes within tiny gaps to analyze the rich flow states within these gaps, thus improving computational accuracy. In contrast, some existing methods for analyzing fluid resistance in particle-filled beds employ bidirectional coupling, requiring the combination of particle and fluid motion to calculate the interaction force between particles and the fluid and convert it into fluid resistance. Such algorithms cannot generate a large number of dense meshes within the particle gaps to analyze the flow; they are merely approximations. However, in reality, the mass of particles is much greater than that of the fluid, and they are stationary. Therefore, calculating particle motion is unnecessary; the particle surface can be considered a stationary wall. This allows for the thorough analysis of the flow by constructing a large number of dense meshes on the particle surface and within the fluid. Attached Figure Description

[0041] The present invention will be further described below with reference to the accompanying drawings and embodiments, wherein:

[0042] Figure 1 A schematic diagram of the electrochemical lithium extraction and deintercalation technology in a stacked particle bed;

[0043] Figure 2 This is a flowchart of an embodiment of the present invention;

[0044] Figure 3 A schematic diagram showing the fitting of particles with different shapes;

[0045] Figure 4 A schematic diagram of a bed of packed particles formed by particles of different shapes;

[0046] Figure 5 This is a schematic diagram of the force-displacement relationship in a hysteretic linear spring model.

[0047] Figure 6 This is a schematic diagram of the sphere geometric model of the present invention after approximation and fitting using STL triangular facets.

[0048] Figure 7 This is a schematic diagram of the spherical surface after scaling down according to the present invention;

[0049] Figure 8 This is a schematic diagram of the spherical surface before and after scaling down according to the present invention;

[0050] Figure 9 This is a schematic diagram of the mesh shape at the tangent point before the spherical surface is reduced in size according to the present invention;

[0051] Figure 10 This is a schematic diagram of the mesh shape at the original tangent point after the sphere is reduced in size according to the present invention;

[0052] Figure 11 This is a schematic diagram showing the merging and connection of triangular facets of overlapping spheres according to the present invention;

[0053] Figure 12 This is a schematic diagram showing the reconstruction of the triangular facets of the particles before and after the present invention.

[0054] Figure 13 This is a schematic diagram showing the solid particles with smooth curved surfaces generated according to the present invention before and after generation.

[0055] Figure 14 A geometric model of the solid bed layer after generating a smooth curved surface for all solid particles in this invention;

[0056] Figure 15 This is a schematic diagram of the fluid domain obtained by removing the solid bed layer from the fluid geometry of a particle-free fluid geometry according to the present invention.

[0057] Figure 16 This is a schematic diagram illustrating the spatial discretization of the fluid domain geometry according to the present invention;

[0058] Figure 17 A schematic diagram illustrating the principle of the improved mechanism;

[0059] Figure 18 This is a velocity distribution diagram of the packed particle bed using cylindrical particles in this invention.

[0060] Figure 19 This is a pressure distribution diagram of the packed particle bed using cylindrical particles in this invention;

[0061] Figure 20 This is a velocity distribution diagram of the packed particle bed using spherical particles in this invention;

[0062] Figure 21 This is a pressure distribution diagram of the spherical particle bed used in this invention. Detailed Implementation

[0063] The following will describe the concept and technical effects of the present invention clearly and completely with reference to the embodiments, so as to fully understand the purpose, features and effects of the present invention.

[0064] It should be noted that the terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0065] This invention proposes a method for predicting the hydraulic pressure drop of irregularly packed particle beds, comprising the following steps:

[0066] S100: Determine the shape and size of the particles and establish a geometric model of the particles, and use a combination of multiple spheres to perform a body-fit approximation on the geometric model to obtain the particle model;

[0067] S200: Establish the container wall, then generate a set amount of the particle model. Under the constraint of the container wall, the particle model falls freely from a set height and forms a stacked particle bed after stabilization. The particle motion control equation of the particle model is established by the discrete element method, and the shape of the stacked particle bed is obtained by iterative calculation.

[0068] S300: In the packed particle bed, each sphere in each particle model is approximated as a sphere using an STL triangular patch;

[0069] S400: Reduce all the spherical surfaces to a smaller size, and merge and connect the STL triangular facets of the reduced spherical surfaces that are in contact with each other to form a first triangular facet of multiple approximate particles;

[0070] S500: Reconstruct the first triangular facet of each of the approximate particles into a second triangular facet of uniform size, and generate a solid bed geometry model composed of smooth curved surfaces based on the second triangular facet.

[0071] S600: Establish a fluid domain, and then create a discrete mesh for the fluid domain;

[0072] S700: The dynamic equations of laminar flow are established using the finite volume method. The flow parameters are solved on the discrete grid to obtain the velocity field and pressure field. The inlet and outlet pressure difference is extracted from the pressure field, which is the hydraulic pressure drop.

[0073] In S200, the particle motion control equations of the particle model are established by the discrete element method, which can yield the interaction between the particle models and thus accurately simulate the morphology of the accumulated particle bed formed after the particle models fall freely from a set height within the container wall.

[0074] Preferably, the normal force between particles is calculated using the hysteretic linear spring model:

[0075]

[0076] In the above formula, and These represent the lengths of the intersection between particles at the current and previous time steps, respectively. S represents the length of the intersection between particles when they intersect. n S is a positive value when the particles do not cross each other. n It is a negative value; and These represent the normal forces acting on the particle at the current moment and the previous moment, respectively; K nl and K nu λ represents the normal contact stiffness under loading and unloading conditions, respectively; λ is the unloading zeroing coefficient.

[0077] Preferably, the tangential force between particles is calculated using the linear spring coulomb limit model:

[0078]

[0079] In the formula, and K represents the tangential force acting on the particle at the current moment and the previous moment, respectively. nl It is the normal contact stiffness under load, r K It is the tangential stiffness coefficient, ΔS τ It is the tangential relative displacement that occurs between particles, where μ is the coefficient of friction. It is the normal force acting on the particle.

[0080] Preferably, the translational motion of the particles is calculated using Euler's first law of motion:

[0081]

[0082] Preferably, the rotation of the particles is calculated using Euler's second law of motion:

[0083]

[0084] In the formula, m p For particle mass, J p v is the moment of inertia of the particle. p w is the translational velocity of the particle. p F is the angular velocity of the particle's rotation. c M is the vector sum of the normal and tangential forces between particles. c is the tangential force of the particle, and g is the gravitational acceleration.

[0085] In the S700, the dynamic equations of laminar flow are established using the finite volume method, and the flow parameters are solved on the discrete grid. The flow can be fully analyzed by constructing a dense grid between the particle surface and the fluid, thereby improving the calculation accuracy.

[0086] Preferably, the mass conservation equation is as follows:

[0087]

[0088] In the formula, ρ is the density of water, and t is time. For divergence operators, velocity vector

[0089] Preferably, the momentum conservation equation is as follows:

[0090]

[0091] In the formula, For gradient operators, Let g be the stress tensor and g be the acceleration due to gravity.

[0092] Preferably, stress tensor It can be calculated using the following formula:

[0093]

[0094] In the formula, μ is the hydrodynamic viscosity, T represents the vector transpose, and I is the unit tensor.

[0095] Preferably, the pressure difference value is calculated by the following formula:

[0096] Δp=p outlet -p inlet

[0097] In the formula, Δp is the pressure difference value, p outlet p is the water pressure at the outlet of the material bed. inlet For the inlet water pressure of the material layer

[0098] Convert the pressure difference into water resistance:

[0099]

[0100] In the above formula, ΔH is the water resistance, ρ is the density of water, and g is the acceleration due to gravity.

[0101] By comparing the water resistance of different particle beds, particles with lower resistance can be selected intuitively.

[0102] Preferably, in S100, the particle is in the form of at least one of spheres, cylinders, four-leaf clover columns, or three-leaf clover columns.

[0103] Preferably, in step S200, the height to which the set amount of particle models freely stack after falling is 20% to 80% of the height of the container wall; and / or, the set height is not higher than the height of the container wall. It is understood that the number of particle models set in step S200 can be adjusted according to actual conditions; for example, the height to which the particle models freely stack after falling can be 10% to 90% of the height of the container wall.

[0104] Preferably, in S300, the maximum side length of the STL triangular facet is 0.08mm, for example, it can be 0.08mm, 0.07mm or 0.06mm, but it is not limited to the listed values. Other unlisted values ​​within the above range are also applicable.

[0105] Preferably, in S400, the shrinkage process includes: all the spheres are reduced in volume by 1% to 5% with their center as the base point. For example, it can be 1%, 2%, 3%, 4% or 5%, but it is not limited to the listed values. Other unlisted values ​​within the above range are also applicable.

[0106] Preferably, in S500, the average side length of the second triangular facet is 0.02 mm, and the maximum allowable angle of the second triangular facet is 40 degrees. For example, it can be 36 degrees, 37 degrees, 38 degrees, 39 degrees or 40 degrees, but it is not limited to the listed values. Other unlisted values ​​within the above range are also applicable.

[0107] Preferably, in step S600, establishing the fluid domain includes the following steps:

[0108] S610: Create fluid domain geometry without particles;

[0109] S620: Remove the solid bed geometry model from the particle-free fluid domain geometry.

[0110] In S600, establishing the discrete mesh includes the following steps:

[0111] S630: Generates a triangular mesh;

[0112] S640: Improve the quality of the triangular mesh;

[0113] S650: The improved triangular mesh is merged into a tetrahedral mesh;

[0114] S660: Improve the quality of the tetrahedral mesh;

[0115] S670: The improved tetrahedral mesh is merged into a polyhedral mesh.

[0116] Preferably, in step S630, the average side length of the triangular mesh is 0.02–2 mm, for example, 0.02 mm, 0.05 mm, 0.1 mm, 0.5 mm, 1 mm, or 2 mm. The minimum curvature normal angle of the triangular mesh is 18°, for example, 18°, 19°, or 20°. The lower limit of the number of gap meshes in the triangular mesh is 2, for example, 2, 3, 4, or 5. The upper limit of the angle of the triangular mesh is 80°, for example, 80°, 70°, or 60°. °, the upper limit of the twist of the triangular face mesh is 0.8, for example, it can be 0.8, 0.7, 0.6 or 0.5; in S650, the maximum diameter of the circumcircle of the tetrahedral mesh is 2.49 mm, for example, it can be 2.49 mm, 2.48 mm, 2.47 mm or 2.46 mm; and / or, the lower limit of the orthogonality of the tetrahedral mesh is 0.05, for example, it can be 0.05, 0.1, 0.2 or 0.3, but not limited to the listed values, other unlisted values ​​within the above range are also applicable.

[0117] Preferably, when the distortion of the triangular mesh exceeds 0.8, an improvement mechanism is triggered to move the unqualified mesh nodes to within the upper limit of distortion. The maximum number of improvements is 5, for example, 5, 4, 3, 2 or 1.

[0118] Preferably, the orthogonality of the tetrahedral mesh is less than 0.05, which triggers an improvement mechanism. The unqualified mesh nodes are moved to within the lower limit of orthogonality, and the maximum number of improvements is 5, such as 5, 4, 3, 2 or 1.

[0119] This invention also proposes a method for manufacturing a packed particle bed, comprising the following steps:

[0120] (1) Select particles of various shapes and sizes, calculate the hydraulic pressure drop of the particle bed formed by each type of particle, and obtain the shape and size of the particles corresponding to the lowest hydraulic pressure drop. The calculation method includes the steps of the above-mentioned method for predicting the hydraulic pressure drop of irregularly packed particle beds.

[0121] (2) Mix the active solid, organic solvent and binder to make a slurry, concentrate the slurry and then extrude and cut it to obtain solid particles with the shape and size described in step (1). Fill the solid particles into the lithium extraction electrolytic cell to obtain the packed particle bed.

[0122] The present invention also proposes a computer device, including one or more processors; a memory storing one or more programs, which, when executed by the one or more processors, cause the one or more processors to implement the steps of the hydraulic pressure drop prediction method for irregularly packed particle beds as described in the present invention.

[0123] The present invention also proposes a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the hydraulic pressure drop prediction method for irregularly packed particle beds described in the present invention.

[0124] The process of the present invention will be described in detail below with reference to specific embodiments. The generation of the packed particle bed is carried out using the open-source discrete element method software LIGGGHTS, and the resistance calculation is carried out using the open-source fluid calculation software OpenFOAM.

[0125] This invention proposes a method for predicting the hydraulic pressure drop of irregularly packed particle beds, such as... Figure 2 As shown, it includes:

[0126] S100: Determine the shape and size of the particles and establish a geometric model of the particles. Then, use a combination of multiple spheres to perform a body-fit approximation on the geometric model to obtain the particle model.

[0127] The shape of the granules can be selected from spheres, cylinders, four-leaf clover cylinders, or three-leaf clover cylinders. Among them, the diameter of the spheres can be 2mm; the diameter of the cylinders can be 2mm and the height can be 6mm; the diameter of the small circle of the four-leaf clover cylinder can be 1mm, the diameter of the circumscribed great circle can be 2.414mm, and the height can be 6mm; the diameter of the small circle of the three-leaf clover cylinder can be 1.2mm, the diameter of the circumscribed circle can be 2.275mm, and the height can be 6mm.

[0128] After establishing the geometric model of the particles, a combination of multiple spheres is used to perform a body-fit approximation of the particle's geometric model. The fitting method is the volume comparison method. First, the diameter and number of spheres used for fitting are manually set, and the software automatically fills the spheres into the particle's geometric model. After filling, the volume of the filling is calculated and compared with the volume of the particle's geometric model. For example... If the volume difference is small, the shape fit is considered high. If the volume ratio exceeds the upper or lower limit, the diameter of the sphere is reduced, the number of spheres is increased, and the fitting continues until the volume ratio is within the upper or lower limit.

[0129] In this embodiment, spherical particles are fitted with a single sphere with a diameter of 2 mm; cylindrical particles are fitted with 10 spheres with a diameter of 0.5 mm; four-leaf clover-shaped particles are fitted with 42 spheres with a diameter of 0.3 mm; and three-leaf clover-shaped particles are fitted with 42 spheres with a diameter of 0.3 mm. Figure 3 As shown.

[0130] S200: Establish the container wall, then generate a set amount of the particle model. Under the constraint of the container wall, the particle model falls freely from a set height and forms a stacked particle bed after stabilization. The particle motion control equation of the particle model is established by the discrete element method, and the shape of the stacked particle bed is obtained by iterative calculation.

[0131] In this embodiment, the container wall is constrained by a block wall with a length of 50mm, a width of 20mm, and a height of 80mm. The number of freely falling particle models in each bed layer is set to 500, the initial falling position height is set to 80mm, the particle model generation speed is 10kg / s, the time from falling to stable accumulation is 3s, and the falling acceleration is the gravitational acceleration of 9.81m / s². 2 . Figure 4 The diagram shows the morphology of the packed particle bed formed by particles of different shapes.

[0132] The true density of the granular material is 2320 kg / m³. 3 The elastic modulus is 2.5 GPa; the density of the wall material is 8000 kg / m³. 3 Its elastic modulus is 210 GPa.

[0133] The normal force between particles was calculated using the hysteretic linear spring model.

[0134]

[0135] Figure 5 A schematic diagram of the force-displacement relationship for the hysteretic linear spring model is shown. In the above equation, and These represent the lengths of the intersection between particles at the current and previous time steps, respectively. S represents the length of the intersection between particles when they intersect. n S is a positive value when the particles do not cross each other. n It is a negative value; and These represent the normal forces acting on the particle at the current moment and the previous moment, respectively; K nl and K nu λ represents the normal contact stiffness under loading and unloading conditions, respectively; λ is the unloading zeroing coefficient.

[0136] The tangential force between particles was calculated using the linear spring coulomb limit model.

[0137]

[0138]

[0139] In the formula, and k represents the tangential force acting on the particle at the current moment and the previous moment, respectively. nl It is the normal contact stiffness under load, r K It is the tangential stiffness coefficient, ΔS τ It is the tangential relative displacement that occurs between particles, where μ is the coefficient of friction. It is the normal force acting on the particle.

[0140] The translational motion of the particles is calculated using Euler's first law of motion:

[0141]

[0142] The rotation of the particles is calculated using Euler's second law of motion:

[0143]

[0144] In the formula, m p For particle mass, J p v is the moment of inertia of the particle. p w is the translational velocity of the particle. p F is the angular velocity of the particle's rotation. cM is the vector sum of the normal and tangential forces between particles. c is the tangential force of the particle, and g is the gravitational acceleration.

[0145] S300: In a packed particle bed, each sphere in each particle model is approximated as a sphere using an STL triangular patch.

[0146] Taking cylindrical particles as an example, we approximate the shape using STL triangular patches. It's important to note that after fitting, only the fitted surface is considered, neglecting the internal volume. Therefore, the concepts of spheres and cylinders no longer exist; instead, it becomes a sphere and the cylindrical surfaces it comprises. For example... Figure 6 As shown, each sphere is still independent, and the triangular facets are not connected together.

[0147] The maximum side length of the STL triangular facet can be 0.08 mm, and each sphere is composed of 240 triangular facets.

[0148] S400: Reduce all spherical surfaces and merge and connect the STL triangular facets of the reduced spherical surfaces that are in contact with each other to form a first triangular facet of multiple approximate particles.

[0149] Furthermore, the aforementioned reduction process includes reducing the volume of all spheres by 1% to 5% with their centers as the reference point.

[0150] There are two purposes to reduce the size of the sphere:

[0151] ① In order to geometrically separate the particle model

[0152] In the S300, after the packing stabilizes, the particle models are in contact with each other, and the entire bed is considered as a single, large mass of particles. However, when the spheres are reduced in size, those belonging to the same particle model still intersect and are considered as a single particle; spheres not belonging to the same particle model, due to the reduction in size, no longer contact each other, leaving a gap. This gap can be identified by the algorithm, thus determining them as different particles. Figure 7 As shown, spheres belonging to the same particle model remain overlapping, while spheres not belonging to the same particle model are completely separated, leaving a gap. Figure 7 (The area circled in the image) This gap can be identified by the program as different particles.

[0153] ② To remove tangent points and prevent mesh distortion at tangent points.

[0154] like Figure 8-10As shown, for any two smoothly transitioning surfaces, such as circles or ellipses, a tangent will form when they come into contact. Geometrically, the gap at the tangent is infinitesimal, which leads to sharp and distorted elongated triangular meshes during mesh generation. Such distorted meshes can cause accuracy deviations in subsequent flow calculations, or even prevent calculations altogether.

[0155] When the surface is scaled down as a whole, a tiny gap is left in the middle. Although this gap is small, it is not infinitesimal, allowing for the placement of a high-quality mesh. This greatly increases the stability and accuracy of subsequent fluid dynamics calculations.

[0156] It is worth noting that reducing the size means that the particles no longer contact each other, resulting in less obstruction to the water flow. The larger the reduction ratio, the smaller the calculated resistance to the water flow; the smaller the reduction ratio, the closer the calculated resistance to the actual value, but the degree of mesh distortion will increase. To balance both, this embodiment uses 2% as the reduction ratio.

[0157] After the sphere is reduced in size, the triangular facets of all overlapping spheres are merged and connected, as follows: Figure 11 As shown, the triangular facets of overlapping spheres of the same particle model have been connected to form a whole. At this point, there are no longer triangular facets of individual spheres, but rather triangular facets of individual approximate particles.

[0158] S500: Reconstruct the first triangular facet of each of the approximate particles into a second triangular facet of uniform size, and generate a solid bed geometry model composed of smooth curved surfaces based on the second triangular facet.

[0159] In S400, due to the forced merging and connection of triangular facets, many triangular facets exhibit significant distortion and sharp corners, which is detrimental to the subsequent extraction of smooth surface geometry. Therefore, it is necessary to reconstruct the triangular facets.

[0160] In this embodiment, the average side length of the reconstructed triangular facet is 0.02 mm, and the maximum allowable angle of the triangular facet is 40 degrees.

[0161] like Figure 12 As shown, the topmost particles are the particle model after reconstructing the triangular faces. All triangular faces are smaller and more uniform in size, which is beneficial for subsequent geometry generation. The particles below are the particle model without reconstruction; the triangular faces are large and distorted in many places (e.g., Figure 12 (The circled area) cannot be used for subsequent geometry generation.

[0162] like Figure 13As shown, the topmost particle is the solid particle model with a smooth surface, while the particles below are triangular facets of the particles that have not yet been smoothed. This step converts the triangular facets of the particle model into smooth surfaces, making it easier to capture the boundaries of the surfaces during subsequent mesh generation.

[0163] Figure 14 The geometric model of the solid bed layer after all the particle models have been generated into smooth surfaces is shown.

[0164] S600: Establish a fluid domain, and then create a discrete mesh for the fluid domain.

[0165] After obtaining the solid bed geometry model, the fluid domain required for the calculation must be established. Creating the fluid domain involves the following steps:

[0166] S610: Create fluid domain geometry without particles;

[0167] S620: Remove solid bed geometry from a fluid domain geometry without particles.

[0168] In this embodiment, the particle-free fluid domain geometry is a cube with a length of 50mm, a width of 20mm, and a height of 80mm. The fluid domain inlet is located at the bottom of the fluid domain and is 20mm away from the bottom surface of the solid bed geometry model. Boolean subtraction is used to remove the solid bed geometry model from the particle-free fluid domain geometry, as follows: Figure 15 As shown, the fluid domain required for the calculation is obtained. Water flows into the fluid domain from the bottom inlet, encounters resistance in the particle bed, and flows out from the top.

[0169] After obtaining the fluid domain, it is necessary to spatially discretize the fluid domain and establish a grid.

[0170] In this embodiment, the steps for establishing the mesh are as follows:

[0171] S630: Generates a triangular mesh;

[0172] S640: Improves the quality of triangular meshes;

[0173] S650: The improved triangular mesh is merged into a tetrahedral mesh;

[0174] S660: Improves the quality of tetrahedral meshes;

[0175] S670: The improved tetrahedral mesh is merged into a polyhedral mesh.

[0176] In this embodiment, the average side length of the triangular mesh is a minimum of 0.02 mm and a maximum of 2 mm, with a growth rate of 1.2. The curvature normal angle is 18°, the lower limit for the number of gap meshes is 2, the upper limit for the triangle angle is 80°, and the upper limit for the twist is 0.8. When the twist exceeds 0.8, an improvement mechanism is triggered. The improvement mechanism involves a global check of the mesh twist, moving unqualified mesh nodes to within the twist limit, and then performing a global check to see if the twist of qualified meshes exceeds the twist limit due to node movement. If so, the unqualified mesh nodes are moved to within the twist limit, and the above process is repeated. The maximum number of improvements is 5. Of course, this is only one improvement step for triangular meshes. In other embodiments, the twist threshold can be set to other values, and the improvement mechanism can be triggered when this threshold is exceeded, moving unqualified mesh nodes to within the twist limit. The maximum number of improvements can also be set to other values, such as 4 or 6.

[0177] In this embodiment, the maximum diameter of the circumcircle of the tetrahedral mesh is 2.49 mm, and the lower limit of orthogonality is 0.05. When the orthogonality is below 0.05, an improvement mechanism is triggered. Unqualified mesh nodes are moved to within the lower limit of orthogonality, and then a global check is performed to see if the orthogonality of qualified meshes exceeds the lower limit due to node movement. If so, the unqualified mesh nodes are moved again, and the above process is repeated. The maximum number of improvements is 5. Of course, this is only one type of improvement step for tetrahedral meshes. In other embodiments, the orthogonality threshold can be set to other values, and an improvement mechanism can be triggered when this threshold is exceeded, moving unqualified mesh nodes to within the lower limit of orthogonality. The maximum number of improvements can also be set to other values, such as 4 or 6.

[0178] Figure 16 The mesh of the fluid domain between particle models is shown. The subsequent fluid control equations need to be discretized in the mesh, assembled into a large-scale matrix, and iteratively solved to obtain the variables such as velocity and pressure in the equations.

[0179] Figure 17 The process of improving the mechanism is shown.

[0180] S700: The dynamic equations of laminar flow are established using the finite volume method. The flow parameters are solved on the discrete grid to obtain the velocity field and pressure field. The inlet and outlet pressure difference is extracted from the pressure field, which is the hydraulic pressure drop.

[0181] The mass conservation equation is as follows:

[0182]

[0183] In the formula, ρ is the density of water, and t is time. For divergence operators, velocity vector

[0184] The equation for the conservation of momentum is as follows:

[0185]

[0186] In the formula, For gradient operators, Let g be the stress tensor and g be the acceleration due to gravity.

[0187] Stress tensor It can be calculated using the following formula:

[0188]

[0189] In the formula, μ is the hydrodynamic viscosity, T represents the vector transpose, and I is the unit tensor.

[0190] The differential pressure value is calculated using the following formula:

[0191] Δp=p outlet -p inlet

[0192] In the formula, Δp is the pressure difference value, p outlet p is the water pressure at the outlet of the material bed. inlet For the inlet water pressure of the material layer

[0193] Convert the pressure difference into water resistance:

[0194]

[0195] In the above formula, ΔH is the water resistance, ρ is the density of water, and g is the acceleration due to gravity.

[0196] In this embodiment, the fluid inlet velocity is 0.06 m / s, and the outlet pressure is atmospheric pressure. The fluid density is 1000 kg / m³. 3 The viscosity is 0.001 Pa·s, and the calculation model is a laminar flow model.

[0197] Figure 18-21 The flow velocity and pressure distribution diagrams for the packed particle beds of cylindrical particles and spherical particles are shown respectively.

[0198] Depend on Figure 18 , 20 It can be seen that in the velocity distribution between spherical and cylindrical particles, the average velocity in the cavity is 0.06 m / s, and the maximum velocity between particles can reach 0.55 m / s.

[0199] Depend on Figure 19It can be seen that the inlet pressure of the cylindrical particle bed is 198.74 Pa, and the outlet pressure is 0 Pa. The bed height is approximately 20 mm, meaning that a 20 mm high cylindrical particle bed generates a pressure difference of 198.74 Pa. This translates to a pressure difference of 9937 Pa for a 1-meter high bed. The water resistance is 1.013 meters of water resistance per meter of material bed height.

[0200] Depend on Figure 21 It can be seen that the spherical particle bed generates a total pressure difference of 232.02 Pa, which translates to a pressure difference of 11601 Pa for a 1-meter-high bed. This is further converted to water resistance, which is 1.182 meters of water resistance per meter of material bed height.

[0201] This shows that the bed resistance of spherical particles is about 16.7% higher than that of cylindrical particles.

[0202] This embodiment also provides a method for manufacturing a packed pellet bed, including the following steps:

[0203] (1) Select spherical particles (diameter of 2 mm) and cylindrical particles (diameter of 2 mm and height of 6 mm) for comparison. Calculate the hydraulic pressure drop generated by the bed formed by spherical particles and cylindrical particles respectively using the above-mentioned method for predicting the hydraulic pressure drop of irregularly packed particle beds. It is found that the bed resistance of cylindrical particles is lower.

[0204] (2) The active solids (iron phosphate or lithium iron phosphate, conductive carbon black, carbon nanotubes) and organic solvent (NMP) and binder (PVDF) are mixed at a solid content of 30% and stirred in a double planetary mixer to obtain a viscous slurry.

[0205] (3) Bake the above viscous slurry to remove some organic solvent. As the organic solvent is removed, the viscous slurry gradually solidifies until it becomes a mud cake with a certain plasticity. Then, put the mud cake into a twin-screw extruder with a rotating cutter to extrude and shape it, and cut it into cylindrical particles with a diameter of 2 mm and a length of 6 mm.

[0206] (4) The cylindrical particles are further dried until completely dry, and the resulting solid particles are filled into the lithium extraction electrolytic cell to obtain a packed particle bed.

[0207] The lithium extraction electrolytic cell is 1 meter long, 15 millimeters wide, and 2 meters high.

[0208] On-site, cylindrical particles with a diameter of 2mm and a height of 6mm were used to fill a 400mm high material layer. The pressure drop measured with a pressure gauge was approximately 4300Pa, slightly higher than the theoretical calculation value of 4000Pa calculated by the above method. Due to some degree of accuracy loss during modeling and calculation, and the inherent errors of the instruments used on-site, the overall error between the theoretically calculated pressure drop and the actual measured value of the prediction method of this invention is within 10%, which can be considered relatively close to reality and has a good prediction effect.

[0209] As can be seen, this invention provides a resistance prediction method that relies entirely on numerical calculations and requires no physical experiments. It can predict the hydraulic pressure drop of irregularly packed particle beds of any shape. This method is primarily applied to electrochemical lithium extraction technology using packed particle beds, but it can also be applied to particle bed packing reaction technologies in other industries. By calculating the pressure drop of the particle bed, it provides theoretical support for subsequent hydraulic calculations of the reactor, selection of pump head, and energy consumption calculations.

[0210] The embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention. Furthermore, the embodiments of the present invention and the features thereof can be combined with each other unless otherwise specified.

Claims

1. A method for predicting the hydraulic pressure drop of an irregularly packed granular bed, characterized in that, Includes the following steps: S100: Determine the shape and size of the particles and establish a geometric model of the particles, and use a combination of multiple spheres to perform a body-fit approximation on the geometric model to obtain the particle model; S200: Establish the container wall, then generate a set amount of the particle model. Under the constraint of the container wall, the particle model falls freely from a set height and forms a stacked particle bed after stabilization. The particle motion control equation of the particle model is established by the discrete element method, and the shape of the stacked particle bed is obtained by iterative calculation. S300: In the packed particle bed, each sphere in each particle model is approximated as a sphere using an STL triangular patch; S400: Reduce all the spherical surfaces to a smaller size, and merge and connect the STL triangular facets of the reduced spherical surfaces that are in contact with each other to form a first triangular facet of multiple approximate particles; S500: Reconstruct the first triangular facet of each of the approximate particles into a second triangular facet of uniform size, and generate a solid bed geometry model composed of smooth curved surfaces based on the second triangular facet. S600: Establish a fluid domain, and then create a discrete mesh for the fluid domain; S700: The dynamic equations of laminar flow are established using the finite volume method. The flow parameters are solved on the discrete grid to obtain the velocity field and pressure field. The inlet and outlet pressure difference is extracted from the pressure field, which is the hydraulic pressure drop.

2. The method for predicting hydraulic pressure drop in an irregularly packed particle bed according to claim 1, characterized in that, In S100, the particle is in the form of at least one of spheres, cylinders, four-leaf clover columns, or three-leaf clover columns.

3. The method for predicting hydraulic pressure drop in an irregularly packed particle bed according to claim 1, characterized in that, In S300, the maximum side length of the stl triangular facet is 0.08 mm.

4. The method for predicting hydraulic pressure drop in an irregularly packed particle bed according to claim 1, characterized in that, In S400, the shrinkage process includes: all the spheres are reduced in volume by 1% to 5% with their center as the base point.

5. The method for predicting hydraulic pressure drop in an irregularly packed particle bed according to claim 1, characterized in that, In S500, the average side length of the second triangular facet is 0.02 mm, and the maximum allowable angle of the second triangular facet is 40 degrees.

6. The method for predicting hydraulic pressure drop in an irregularly packed particle bed according to claim 1, characterized in that, In step S600, establishing the fluid domain includes the following steps: S610: Create fluid domain geometry without particles; S620: Remove the solid bed geometry model from the particle-free fluid domain geometry; The process of establishing a discrete mesh includes the following steps: S630: Generates a triangular mesh; S640: Improve the quality of the triangular mesh; S650: The improved triangular mesh is merged into a tetrahedral mesh; S660: Improve the quality of the tetrahedral mesh; S670: The improved tetrahedral mesh is merged into a polyhedral mesh.

7. The method for predicting hydraulic pressure drop in an irregularly packed particle bed according to claim 6, characterized in that, In S630, the average side length of the triangular mesh is 0.02 to 2 mm, the minimum curvature normal angle of the triangular mesh is 18°, the lower limit of the number of gap meshes in the triangular mesh is 2, the upper limit of the angle of the triangular mesh is 80°, and the upper limit of the twist degree of the triangular mesh is 0.8; in S650, the maximum diameter of the circumcircle of the tetrahedral mesh is 2.49 mm, and the lower limit of the orthogonality of the tetrahedral mesh is 0.

05.

8. The method for predicting hydraulic pressure drop in an irregularly packed particle bed according to claim 7, characterized in that, In S640, the quality improvement of the triangular mesh includes: when the distortion of the triangular mesh exceeds 0.8, an improvement mechanism is triggered, and the unqualified mesh nodes are moved to within the upper limit of the distortion, with a maximum of 5 improvements.

9. The method for predicting hydraulic pressure drop in an irregularly packed particle bed according to claim 7, characterized in that, In S660, the quality improvement of the tetrahedral mesh includes: when the orthogonality of the tetrahedral mesh is lower than 0.05, an improvement mechanism is triggered, and unqualified mesh nodes are moved to within the lower limit of orthogonality, with a maximum of 5 improvements.

10. A method for manufacturing a packed pellet bed, characterized in that, Includes the following steps: (1) Select particles of various shapes and sizes, calculate the hydraulic pressure drop of the accumulated particle bed formed by each type of particle, and obtain the shape and size of the particles corresponding to the lowest hydraulic pressure drop. The calculation method includes the steps of the hydraulic pressure drop prediction method for irregularly accumulated particle beds as described in any one of claims 1-9. (2) Mix the active solid, organic solvent and binder to make a slurry, concentrate the slurry and then extrude and cut it to obtain solid particles with the shape and size described in step (1). Fill the solid particles into the lithium extraction electrolytic cell to obtain the packed particle bed.

Images