Hydraulic pressure drop prediction method for irregularly stacked particle bed

Abstract

The invention provides a hydraulic pressure drop prediction method for an irregular accumulation particle bed, which comprises the following steps of: establishing a motion control equation of a particle model by using a discrete element method, and generating an accumulation particle bed body through calculation; exporting an accumulated particle bed body stl patch model; repairing the stl patch model into a solid bed geometric model; establishing a fluid domain, and establishing a discrete grid on the fluid domain; and calculating the resistance of the solid bed geometric model to water flow by using a computational fluid mechanics method. According to the method, the resistance can be predicted in advance completely through numerical calculation, no entity experiment is performed, the particle form with the lowest resistance is selected, the experiment cost is greatly reduced, and the development speed is increased; moreover, the pressure drop of the granular bed can be calculated, and theoretical support is provided for subsequent hydraulic calculation of the reactor, lift of a selected pump, energy consumption calculation and the like.

Description

Technical Field

[0001] The invention belongs to the technical field of salt lake electric deintercalation and lithium extraction equipment, and in particular relates to a method for predicting hydraulic pressure drop of an irregularly stacked particle bed. Background Art

[0002] The current technology of electrochemical deintercalation and lithium extraction is mainly carried out by using electrode-coated electrochemical deintercalation equipment. This technology has problems such as low lithium extraction efficiency and difficulty in disassembling the electrode. In order to solve the defects of the electrode-type electrochemical deintercalation and lithium extraction technology, millimeter-level spheres, cylinders and other particles can be produced through granulation technology, and the particles are accumulated in the lithium extraction reactor, and the graphite electrode is set to be energized to form a piled particle bed for electrochemical deintercalation and lithium extraction. See Figure 1 .

[0003] However, how to predict the resistance of a bed of packed particles is a key issue. The shapes of the packed particles vary, including spheres, cylinders, sheets, three-leaf clover columns, four-leaf clover columns, etc., and the size is also a variable. Different shapes and sizes will result in different gap morphology, bulk density, porosity, etc. of the bed after stacking. These factors will greatly change the resistance to liquid passing through. In addition, even in the same bed, the resistance to the flow of liquids of different properties is different. The viscosity and density of the liquid will greatly affect the resistance.

[0004] If you need to prepare a large number of particles first, manufacture a reactor to fill it, and then install a pressure gauge at the reactor inlet and outlet to detect the pressure difference, using this method to measure the resistance will consume a lot of money and time costs: ① Preparing particles is also a very difficult development process, and it takes a lot of experiments to find a suitable granulation machine and granulation formula so that the particles can be formed and manufactured in large quantities; ② Particles of different shapes have different resistances. It takes longer to select the particle shape with the lowest resistance. Summary of the invention

[0005] The present invention aims to solve at least one of the technical problems existing in the above-mentioned prior art. To this end, the present invention proposes a method for predicting the hydraulic pressure drop of a bed of irregularly stacked particles, which can completely predict the resistance in advance through numerical calculation, and can select the particle shape with the lowest resistance without any physical experiment, greatly reducing the experimental cost and accelerating the development speed.

[0006] According to a first aspect of the present invention, a method for predicting hydraulic pressure drop of a randomly stacked particle bed is provided, comprising the following steps:

[0007] S100: determining the shape and size of the particle and establishing a geometric model of the particle, and performing body-fitting approximation fitting on the geometric model using a combination of multiple spheres to obtain a particle model;

[0008] S200: establishing a container wall, and then generating a set amount of the particle model, the particle model freely falls from a set height under the constraint of the container wall, and forms a piled particle bed after stabilization, the particle motion control equation of the particle model is established by discrete element method, and the shape of the piled particle bed is obtained by iterative calculation;

[0009] S300: In the stacked particle bed, each sphere in each particle model is fitted into a spherical surface by using an STL triangle patch approximation;

[0010] S400: reducing all the spherical surfaces, and merging and connecting the stl triangular facets of the spherical surfaces that are in contact with each other after reduction, to form a plurality of first triangular facets that approximate particles;

[0011] S500: reconstructing the first triangular facet of each of the approximate particles into a second triangular facet with uniform size, and generating a solid bed geometry model consisting of a smooth curved surface based on the second triangular facet;

[0012] S600: establishing a fluid domain, and then establishing a discrete grid for the fluid domain;

[0013] S700: using the finite volume method to establish the dynamic equation of laminar flow, solving the flow parameters on the discrete grid to obtain the velocity field and the pressure field, and extracting the inlet and outlet pressure difference from the pressure field, that is, the hydraulic pressure drop.

[0014] Preferably, in S100, the shape of the particles is at least one of a sphere, a cylinder, a four-leaf clover column or a three-leaf clover column.

[0015] Preferably, in S200, the height of the set amount of particle models that are freely piled up 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 shrinking process includes: all the spherical surfaces are reduced in volume by 1% to 5% with their centers as base points.

[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 S600, establishing the fluid domain comprises the following steps:

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

[0021] S620: Subtract the solid bed geometry model from the fluid domain geometry without particles.

[0022] In S600, the step of establishing a discrete grid includes the following steps:

[0023] S630: generating a triangular surface mesh;

[0024] S640: Improving the quality of the triangular surface mesh;

[0025] S650: merging the improved triangular face meshes into a tetrahedral mesh;

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

[0027] S670: Merging the improved tetrahedral meshes into polyhedral meshes.

[0028] Preferably, in S630, the average side length of the triangular face mesh is 0.02-2 mm, the minimum curvature normal angle of the triangular face mesh is 18°, the lower limit number of gap meshes of the triangular face mesh is 2, the upper limit of the angle of the triangular face mesh is 80°, and the upper limit of the distortion of the triangular face mesh is 0.8; in S650, the maximum diameter of the circumscribed circle 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 S640, the quality of the triangular face mesh is improved, including: when the distortion of the triangular mesh exceeds 0.8, an improvement mechanism is triggered, and unqualified mesh nodes are moved to within the upper limit of the distortion, and the maximum number of improvements is 5 times.

[0030] Preferably, in S660, the quality of the tetrahedral mesh is improved, including: 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 the orthogonality, and the maximum number of improvements is 5 times.

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

[0032] (1) selecting particles of various shapes and sizes, calculating the hydraulic pressure drop of a piled particle bed formed by each of the particles, and obtaining the shape and size of the particles corresponding to the lowest hydraulic pressure drop, wherein the calculation method includes the steps of the hydraulic pressure drop prediction method of the irregularly piled particle bed described in the first aspect of the present invention;

[0033] (2) The active solid, organic solvent and binder are mixed to form a slurry, and the obtained slurry is concentrated, extruded and cut to obtain solid particles having the shape and size described in step (1), and the solid particles are filled into a lithium extraction electrolytic cell to obtain the stacked particle bed.

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

[0035] According to the third aspect of the present invention, a computer device is proposed, comprising one or more processors; a memory on which one or more programs are stored, and when the one or more programs are executed by the one or more processors, the one or more processors implement the steps of the hydraulic pressure drop prediction method for an irregularly stacked particle bed 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, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method for predicting the hydraulic pressure drop of a randomly stacked particle bed described in the first aspect of the present invention are implemented.

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

[0038] 1. The present invention does not require any physical experiments, and can obtain parameters entirely through simulation calculations, and can simulate particles of any shape. However, some existing analysis methods can only simulate the generation of spherical particles, or require three-dimensional scanning through physical experiments to obtain the particle shape;

[0039] 2. The absence of tangency between particles will result in a deformed mesh, which will not affect the calculation accuracy. However, in some existing analysis methods for filling particles, the particles are not reduced in size and there is contact (tangency) between the particles, which will produce a large number of deformed meshes when generating the mesh;

[0040] 3. The present invention belongs to one-way coupling, and multiple grids can be arranged in a small gap to analyze the rich flow state in the gap and improve the calculation accuracy. Some existing analysis methods for the fluid resistance of a particle-packed bed are two-way coupling, which requires combining the movement of the particles with the movement of the fluid, calculating the interaction force of the particles on the fluid and converting it into the resistance value of the fluid. This algorithm cannot generate a large number of dense grids in the gap between the particles to analyze the flow, and is only an approximate processing method. But in fact, the mass of the particles is much larger than that of the fluid and is stationary. There is no need to calculate the movement of the particles. The surface of the particles is regarded as a stationary wall. In this way, a large number of dense grids can be constructed on the surface of the particles and the fluid to fully analyze the flow. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0042] Figure 1 Schematic diagram of the electrochemical deintercalation and lithium extraction technology of the stacked particle bed;

[0043] Figure 2 is a flow chart of an embodiment of the present invention;

[0044] Figure 3 It is a schematic diagram of the fitting of particles with different morphologies;

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

[0046] Figure 5 It is a schematic diagram of the force-displacement relationship of the hysteretic linear spring model;

[0047] Figure 6 It is a schematic diagram of the spherical geometric model of the present invention after being approximated and fitted by STL triangle patches;

[0048] Figure 7 It is a schematic diagram of a reduced spherical surface of the present invention;

[0049] Figure 8 It is a schematic diagram of the spherical surface of the present invention before and after reduction;

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

[0051] Fig.10 This is a schematic diagram of the mesh shape at the original tangent point after the spherical surface of the present invention is reduced;

[0052] Fig.11 It is a schematic diagram of the present invention after merging and connecting the triangular facets of overlapping spherical surfaces;

[0053] Fig.12 It is a schematic diagram of the present invention before and after the triangular facets of the particle are reconstructed;

[0054] Fig.13 A schematic diagram of a solid particle before and after generating a smooth curved surface according to the present invention;

[0055] Fig.14 A solid bed geometry model after smoothing the surface for all solid particles of the present invention;

[0056] Fig.15 It is a schematic diagram of a fluid domain obtained by removing a solid bed geometry model from a fluid geometry body without particles according to the present invention;

[0057] Fig.16 It is a schematic diagram of spatial discretization of fluid domain geometry in the present invention;

[0058] Fig.17 Schematic diagram of the principle of the improvement mechanism;

[0059] Fig.18 The flow velocity distribution diagram of the packed particle bed using cylindrical particles of the present invention;

[0060] Fig.19 This is a pressure distribution diagram of a packed particle bed using cylindrical particles of the present invention;

[0061] Fig. 20 The flow velocity distribution diagram of the packed particle bed using spherical particles in the present invention;

[0062] Fig.21 This is a pressure distribution diagram of a packed particle bed using spherical particles in the present invention. DETAILED DESCRIPTION

[0063] The concept and technical effects of the present invention will be clearly and completely described below in conjunction with embodiments 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 above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. Moreover, the terms "include", "comprises" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0065] The present invention proposes a method for predicting the hydraulic pressure drop of a irregularly stacked particle bed, comprising the following steps:

[0066] S100: determining the shape and size of the particle and establishing a geometric model of the particle, and performing body-fitting approximation fitting on the geometric model using a combination of multiple spheres to obtain a particle model;

[0067] S200: establishing a container wall, and then generating a set amount of the particle model, the particle model freely falls from a set height under the constraint of the container wall, and forms a piled particle bed after stabilization, the particle motion control equation of the particle model is established by discrete element method, and the shape of the piled particle bed is obtained by iterative calculation;

[0068] S300: In the stacked particle bed, each sphere in each particle model is fitted into a spherical surface by using an STL triangle patch approximation;

[0069] S400: reducing all the spherical surfaces, and merging and connecting the stl triangular facets of the spherical surfaces that are in contact with each other after reduction, to form a plurality of first triangular facets that approximate particles;

[0070] S500: reconstructing the first triangular facet of each of the approximate particles into a second triangular facet with uniform size, and generating a solid bed geometry model consisting of a smooth curved surface based on the second triangular facet;

[0071] S600: establishing a fluid domain, and then establishing a discrete grid for the fluid domain;

[0072] S700: using the finite volume method to establish the dynamic equation of laminar flow, solving the flow parameters on the discrete grid to obtain the velocity field and the pressure field, and extracting the inlet and outlet pressure difference from the pressure field, that is, the hydraulic pressure drop.

[0073] Among them, the particle motion control equation of the particle model is established by the discrete element method in S200, and the interaction between the particle models can be obtained, so as to accurately simulate the shape of the accumulated particle bed formed after the particle model freely falls from a set height in the container wall.

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

[0075]

[0076] In the above formula, and are the lengths of the particles crossing the particle model at the current moment and the previous moment, respectively. When the particles cross each other, S n is a positive value, when the particles do not intersect each other, S n is a negative value; and are the normal forces acting on the particle at the current moment and the previous moment respectively; K nl and K nu are the normal contact stiffnesses under loading and unloading respectively; λ is the unloading zeroing coefficient.

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

[0078]

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

[0080] Preferably, the translation 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 is the particle mass, J p is the particle moment of inertia, v p is the particle translation velocity, w p is the particle rotation angular velocity, F c is the vector sum of the normal force and tangential force between particles, M c is the tangential force on the particle and g is the acceleration due to gravity.

[0085] In the S700, the finite volume method is used to establish the dynamic equation of laminar flow, and the flow parameters are solved on the discrete grid. The dense grid constructed between the particle surface and the fluid can be used to fully analyze the flow and improve the calculation accuracy.

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

[0087]

[0088] Where ρ is the density of water, t is the time, is the divergence operator, is the velocity vector

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

[0090]

[0091] In the formula, is the gradient operator, is the stress tensor, g is the gravitational acceleration

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

[0093]

[0094] Where μ is the fluid dynamic viscosity, T represents the vector transpose, and I is the unit tensor

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

[0096] Δp=p outlet -p inlet

[0097] In the formula, Δp is the pressure difference, p outlet is the water pressure at the outlet of the material layer, p inlet The water pressure at the inlet of the material layer

[0098] Convert the pressure difference to 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 resistances corresponding to different particle beds, particles with smaller resistance can be intuitively selected.

[0102] Preferably, in S100, the shape of the particles is at least one of a sphere, a cylinder, a four-leaf clover column or a three-leaf clover column.

[0103] Preferably, in S200, the height of the set amount of particle models after falling freely 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 understandable that in S200, the set amount of the particle models can be adjusted according to actual conditions, for example, the height of the particle models after falling freely 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 0.08 mm, for example, it can be 0.08 mm, 0.07 mm or 0.06 mm, but is not limited to the listed values, and other unlisted values ​​within the above numerical range are also applicable.

[0105] Preferably, in S400, the shrinking process includes: the volume of all the spherical surfaces is reduced by 1% to 5% with the center of the spherical surface as the base point, for example, it can be 1%, 2%, 3%, 4% or 5%, but is not limited to the listed values, and other unlisted values ​​within the above numerical 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 is not limited to the listed values, and other unlisted values ​​within the above numerical range are also applicable.

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

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

[0109] S620: Subtract the solid bed geometry model from the fluid domain geometry without particles.

[0110] In S600, the step of establishing a discrete grid includes the following steps:

[0111] S630: generating a triangular surface mesh;

[0112] S640: Improving the quality of the triangular surface mesh;

[0113] S650: merging the improved triangular face meshes into a tetrahedral mesh;

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

[0115] S670: Merging the improved tetrahedral meshes into polyhedral meshes.

[0116] Preferably, in S630, the average side length of the triangular face 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 curvature normal angle of the triangular face mesh is at least 18°, for example, 18°, 19° or 20°, the lower limit number of gap meshes of the triangular face mesh is 2, for example, 2, 3, 4 or 5, and the upper limit of the angle of the triangular face mesh is 80°, for example, 80°, 70° or 60°. °, the upper limit of the distortion of the triangular face mesh is 0.8, for example, it can be 0.8, 0.7, 0.6 or 0.5; in the S650, the maximum diameter of the circumscribed circle of the tetrahedral mesh is 2.49mm, for example, it can be 2.49mm, 2.48mm, 2.47mm or 2.46mm; 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 is not limited to the listed values, and other values ​​not listed in the above numerical range are also applicable.

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

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

[0119] The present invention also proposes a method for making a piled particle bed, comprising the following steps:

[0120] (1) selecting particles of various shapes and sizes, calculating the hydraulic pressure drop of a piled particle bed formed by each of the particles, and obtaining the shape and size of the particles corresponding to the lowest hydraulic pressure drop, wherein the calculation method includes the steps of the hydraulic pressure drop prediction method of the irregularly piled particle bed;

[0121] (2) The active solid, organic solvent and binder are mixed to form a slurry, and the obtained slurry is concentrated, extruded and cut to obtain solid particles having the shape and size described in step (1), and the solid particles are filled into a lithium extraction electrolytic cell to obtain the stacked particle bed.

[0122] The present invention also proposes a computer device, comprising one or more processors; a memory on which one or more programs are stored, and when the one or more programs are executed by the one or more processors, the one or more processors implement the steps of the hydraulic pressure drop prediction method for an irregularly stacked particle bed as described in the present invention.

[0123] The present invention also proposes a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the method for predicting the hydraulic pressure drop of a randomly stacked particle bed described in the present invention are implemented.

[0124] The process of the present invention is described in detail below in conjunction with specific embodiments, wherein the generation of the stacked particle bed adopts the open source discrete element calculation software LIGGGHTS, and the resistance calculation adopts the open source fluid calculation software OpenFOAM.

[0125] The present invention proposes a method for predicting the hydraulic pressure drop of a irregularly stacked particle bed. Figure 2 As shown, including:

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

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

[0128] After the geometric model of the above particles is established, a combination of multiple spheres is used to perform body-fitting approximation fitting on the geometric model of the particles. 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 geometric model of the particles. After filling, the volume of the filled body is calculated and compared with the volume of the geometric model of the particles. If the volume ratio exceeds the upper and lower limits, the diameter of the sphere is reduced, the number of spheres is increased, and the fitting is continued until the volume ratio is within the upper and lower limits.

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

[0130] S200: Establish a container wall, and 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 piled particle bed after stabilization. The particle motion control equation of the particle model is established by the discrete element method, and the morphology of the piled particle bed is obtained by iterative calculation.

[0131] In this embodiment, the container wall is constrained to be a square wall with a length of 50 mm, a width of 20 mm, and a height of 80 mm. The number of free-falling particle models in each bed layer is set to 500, the height of the falling starting position is set to 80 mm, the particle model generation speed is 10 kg / s, the time from falling to stacking stability is 3 s, and the falling acceleration is the gravity acceleration of 9.81 m / s 2 . Figure 4 A morphological diagram showing a packed particle bed formed by particles of different morphologies.

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

[0133] The normal force between particles is calculated using the hysteretic linear spring model:

[0134]

[0135] Figure 5 Figure 2 shows the force-displacement relationship diagram of the hysteretic linear spring model. In the above formula, and are the lengths of the particles crossing the particle model at the current moment and the previous moment, respectively. When the particles cross each other, S n is a positive value, when the particles do not intersect each other, S n is a negative value; and are the normal forces acting on the particle at the current moment and the previous moment respectively; K nl and K nu are the normal contact stiffnesses under loading and unloading respectively; λ is the unloading zeroing coefficient.

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

[0137]

[0138]

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

[0140] The translation of the particle 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 is the particle mass, J p is the particle moment of inertia, v p is the particle translation velocity, w p is the particle rotation angular velocity, F cis the vector sum of the normal force and tangential force between particles, M c is the tangential force on the particle and g is the acceleration due to gravity.

[0145] S300: In the stacked particle bed, each sphere in each particle model is fitted into a spherical surface by using an STL triangle patch approximation.

[0146] Take cylindrical particles as an example, and use stl triangle patches for approximation fitting. It is worth noting that after fitting, only the fitted surface is taken, and the internal volume is ignored. At this time, the concept of sphere and cylinder no longer exists, but becomes a spherical surface and its composed cylindrical surface. Figure 6 As shown, each sphere is still independent and the triangles are not connected together.

[0147] The maximum side length of the stl triangle can be 0.08mm, and each sphere is composed of 240 triangles.

[0148] S400: All spherical surfaces are reduced, and the stl triangular facets of the spherical surfaces that are in contact with each other after reduction are merged and connected to form a plurality of first triangular facets that approximate the particles.

[0149] Furthermore, the shrinking process includes: all spherical surfaces are reduced in volume by 1% to 5% with their centers as base points.

[0150] There are two purposes for shrinking the sphere:

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

[0152] In S300, after the accumulation is stable, the particle models touch each other, and the entire bed is regarded as a huge mass of particles. After the spheres are reduced, the spheres belonging to the same particle model still cross and touch each other and are regarded as one particle; the spheres that do not belong to the same particle model no longer touch each other due to the reduction, but leave a gap. This gap can be identified by the algorithm and determined as different particles. Figure 7 As shown in the figure, the spheres belonging to the same particle model still overlap, while the spheres not belonging to the same particle model are completely separated, leaving a gap ( Figure 7 The gap can be identified as different particles by the program.

[0153] ② To remove the tangent points and prevent the mesh from being deformed at the tangent points

[0154] like Figure 8-10As shown in the figure, any two smooth transition surfaces, such as circles and ellipses, will form a tangent point when they touch each other. Geometrically, the gap at the tangent point is infinitesimal, which will result in sharp and deformed elongated triangular meshes when meshing. This deformed mesh will cause the subsequent flow calculation process to have accuracy deviations, or even make the calculation impossible.

[0155] When the surface is reduced as a whole, a tiny gap is left in the middle of the surface. Although the size of this gap is small, it is not infinitesimal, and a high-quality grid can be arranged on it. This greatly increases the stability and accuracy of subsequent fluid calculations.

[0156] It is worth noting that reducing the size means that the particles are no longer in contact with each other, and the resistance to the water flow will be smaller. The greater the reduction ratio, the smaller the calculated resistance of the water flow will be; the smaller the reduction ratio, the closer the calculated resistance of the water flow is to the actual value, but the degree of deformity of the grid will increase. In order to take both into account, this embodiment takes 2% as the reduction ratio.

[0157] After the sphere is reduced, all overlapping triangles of the sphere are merged and connected, as shown in Fig.11 As shown in the figure, the overlapping spherical triangular facets of the same particle model have been connected to form a whole. At this time, there is no single spherical triangular facet, but a single triangular facet approximating the particle.

[0158] S500: reconstructing the first triangular facet of each of the approximate particles into a second triangular facet with uniform size, and generating a solid bed geometry model consisting of a smooth curved surface based on the second triangular facet.

[0159] In S400, due to the forced merging and connection of triangular facets, many triangular facets have strong deformities and sharp corners, which is not conducive to the subsequent extraction of smooth surface geometry. Therefore, the triangular facets need to be reconstructed.

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

[0161] like Fig.12 As shown in the figure, the top particle is the particle model after the triangular facets are reconstructed. The size of all the triangular facets becomes small and uniform, which is conducive to the subsequent geometric body generation; the particle below is the particle model that has not been reconstructed. The size of the triangular facets is large and many places are deformed (such as Fig.12 The circled area) will not be able to generate geometry later.

[0162] like Fig.13As shown in the figure, the top particle is a solid particle model with a smooth surface, and the bottom particle is a particle triangular facet that has not yet generated a smooth surface. This step is to convert the triangular facets of the particle model into a smooth surface so that the boundary of the surface can be captured in the subsequent mesh division.

[0163] Fig.14 The solid bed geometry model is shown after all the particle models have been generated into smooth surfaces.

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

[0165] After having the solid bed geometry model, it is necessary to establish the fluid domain required for calculation. The creation of the fluid domain requires the following steps:

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

[0167] S620: Subtract the solid bed geometry from the fluid domain geometry without particles.

[0168] In this embodiment, the fluid domain geometry without particles is a block with a length of 50 mm, a width of 20 mm, and a height of 80 mm. The fluid domain inlet is located at the bottom of the fluid domain and is 20 mm away from the bottom surface of the solid bed geometry model. The subtraction operation in Boolean operation is used to remove the solid bed geometry model from the fluid domain geometry without particles, such as Fig.15 As shown in the figure, the fluid domain required for calculation is obtained. Water flows into the fluid domain from the bottom inlet, passes through the particle bed to generate resistance, 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 of establishing a grid are:

[0171] S630: generating a triangular surface mesh;

[0172] S640: Improve the quality of triangular surface meshes;

[0173] S650: The improved triangular meshes are merged into tetrahedral meshes;

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

[0175] S670: Merge the improved tetrahedral meshes into a polyhedral mesh.

[0176] In this embodiment, the average side length of the triangular face 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 of the number of gap meshes is 2, the upper limit of the triangle angle is 80°, and the upper limit of the distortion is 0.8. When the distortion exceeds 0.8, the improvement mechanism is triggered. The improvement mechanism is to globally check the mesh distortion, move the unqualified mesh nodes to within the upper limit of the distortion, and then globally check whether the qualified mesh distortion exceeds the upper limit of the distortion due to the node movement. If so, continue to move the unqualified mesh nodes to the upper limit of the distortion, and repeat the above process. The maximum number of improvements is 5 times. Of course, this is only one of the improvement steps of the triangular face mesh. In some other embodiments, the distortion threshold can also be set to other values, and the improvement mechanism is triggered when it exceeds this threshold, and the unqualified mesh nodes are moved to within the upper limit of the distortion. The maximum number of improvements can also be set to other values, such as 4 times or 6 times.

[0177] In this embodiment, the maximum diameter of the circumscribed circle of the tetrahedral mesh is 2.49 mm, and the lower limit of orthogonality is 0.05. When the orthogonality is lower than 0.05, the improvement mechanism is triggered, and the unqualified mesh nodes are moved to within the lower limit of orthogonality. Then a global check is performed to see whether the orthogonality of the qualified mesh exceeds the lower limit of orthogonality due to the node movement. If so, the unqualified mesh nodes are continued to be moved to within the lower limit of orthogonality, and the above process is repeated. The maximum number of improvements is 5 times. Of course, this is only one of the improvement steps for the tetrahedral mesh. In some other embodiments, the threshold of orthogonality can also be set to other values, and the improvement mechanism is triggered when this threshold is exceeded, and the unqualified mesh nodes are moved to within the lower limit of orthogonality. The maximum number of improvements can also be set to other values, such as 4 times or 6 times.

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

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

[0180] S700: using the finite volume method to establish the dynamic equation of laminar flow, solving the flow parameters on the discrete grid to obtain the velocity field and the pressure field, and extracting the inlet and outlet pressure difference from the pressure field, that is, the hydraulic pressure drop.

[0181] The mass conservation equation is as follows:

[0182]

[0183] Where ρ is the density of water, t is the time, is the divergence operator, is the velocity vector

[0184] The momentum conservation equation is as follows:

[0185]

[0186] In the formula, is the gradient operator, is the stress tensor, g is the gravitational acceleration

[0187] Stress Tensor It can be calculated by the following formula:

[0188]

[0189] Where μ is the fluid dynamic viscosity, T represents the vector transpose, and I is the unit tensor

[0190] The pressure difference is calculated by the following formula:

[0191] Δp=p outlet -p inlet

[0192] In the formula, Δp is the pressure difference, p outlet is the water pressure at the outlet of the material layer, p inlet The water pressure at the inlet of the material layer

[0193] Convert the pressure difference to 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 0.06m / s, and the outlet pressure is atmospheric pressure. The fluid density is 1000kg / m 3 , viscosity 0.001Pa·s, and the calculation model is laminar flow model.

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

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

[0199] Depend on Fig.19It can be seen that the inlet pressure of the cylindrical particle bed is 198.74Pa, and the outlet pressure of the bed is 0Pa; the bed height is approximately 20mm, that is, the 20mm high cylindrical particle bed produces a total pressure difference of 198.74Pa, which is converted to a 1-meter high bed and produces a pressure difference of 9937Pa, which is then converted into water resistance of 1.013 meters of water resistance per meter of material layer.

[0200] Depend on Fig.21 It can be seen that the spherical particle bed produces a total pressure difference of 232.02Pa, which is converted into a 1-meter-high bed and produces a pressure difference of 11601Pa, which is then converted into water resistance of 1.182 meters of water resistance per meter of material layer.

[0201] It can be seen 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 making a piled particle bed, comprising the following steps:

[0203] (1) Spherical particles (2 mm in diameter) and cylindrical particles (2 mm in diameter and 6 mm in height) were selected for comparison. The hydraulic pressure drop generated by the bed formed by the spherical particles and the cylindrical particles was calculated using the above-mentioned hydraulic pressure drop prediction method for the irregularly stacked particle bed. It was found that the bed resistance of the cylindrical particles was lower.

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

[0205] (3) drying out part of the organic solvent from the viscous slurry, and gradually solidifying the viscous slurry as the organic solvent is removed until it becomes a mud cake with a certain plasticity, and then placing the mud cake into a twin-screw extruder with a rotating cutter for extrusion molding, and cutting it into cylindrical particles with a diameter of 2 mm and a length of 6 mm;

[0206] (4) further drying the cylindrical particles until completely dry, and filling the obtained solid particles into a lithium extraction electrolytic cell to obtain a packed particle bed;

[0207] Among them, the lithium extraction electrolytic cell is 1 meter long, 15 mm wide and 2 meters high.

[0208] On-site selection of cylindrical particles with a diameter of 2 mm and a height of 6 mm to fill a material layer of 400 mm in height, the pressure drop measured by the pressure gauge is about 4300 Pa, which is slightly higher than the theoretical calculated value of 4000 Pa of the above method. Due to a certain degree of precision loss in the modeling and calculation process, the instrument actually used on site also has errors. Overall, the error between the theoretical calculated value of the pressure drop of the prediction method of the present invention and the actual measured value is within 10%, which can be considered to be more in line with reality and has a better prediction effect.

[0209] It can be seen that the present invention provides a resistance prediction method that completely relies on numerical calculation methods and does not require any physical experimental input, and can predict the hydraulic pressure drop of irregularly stacked particle beds of any shape. This method is mainly used in the electrochemical lithium extraction technology of stacked particle beds, but it can be understood that it can also be applied to particle bed stacking reaction technology in other industries. By calculating the pressure drop of the particle bed, theoretical support is provided for the subsequent hydraulic calculation of the reactor, the head of the pump selection, and the energy consumption calculation.

[0210] The above is a detailed description of the embodiments of the present invention, but the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in the relevant technical field without departing from the purpose of the present invention. In addition, the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

Claims

1. A method for predicting hydraulic pressure drop of irregularly stacked particle beds, characterized in that: The following steps are involved: S100: determining the shape and size of the particle and establishing a geometric model of the particle, and performing body-fitting approximation fitting on the geometric model using a combination of multiple spheres to obtain a particle model; S200: establishing a container wall, and then generating a set amount of the particle model, the particle model freely falls from a set height under the constraint of the container wall, and forms a piled particle bed after stabilization, the particle motion control equation of the particle model is established by discrete element method, and the shape of the piled particle bed is obtained by iterative calculation; S300: In the stacked particle bed, each sphere in each particle model is fitted into a spherical surface by using an STL triangle patch approximation; S400: reducing all the spherical surfaces, and merging and connecting the stl triangular facets of the spherical surfaces that are in contact with each other after reduction, to form a plurality of first triangular facets that approximate particles; S500: reconstructing the first triangular facet of each of the approximate particles into a second triangular facet with uniform size, and generating a solid bed geometry model consisting of a smooth curved surface based on the second triangular facet; S600: establishing a fluid domain, and then establishing a discrete grid for the fluid domain; S700: using the finite volume method to establish the dynamic equation of laminar flow, solving the flow parameters on the discrete grid to obtain the velocity field and the pressure field, and extracting the inlet and outlet pressure difference from the pressure field, that is, the hydraulic pressure drop.

2. The method for predicting hydraulic pressure drop of a randomly packed particle bed according to claim 1, characterized in that: In the S100, the shape of the particles is at least one of a sphere, a cylinder, a four-leaf clover column, or a three-leaf clover column.

3. The method for predicting hydraulic pressure drop of a randomly 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 of a randomly packed particle bed according to claim 1, characterized in that: In the S400, the shrinking process includes: all the spherical surfaces are reduced in volume by 1% to 5% with their centers as base points.

5. The method for predicting hydraulic pressure drop of a randomly 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 of a randomly packed particle bed according to claim 1, characterized in that: In S600, establishing the fluid domain includes the following steps: S610: Create the fluid domain geometry without particles; S620: subtracting the solid bed geometry model from the fluid domain geometry without particles; The discrete grid establishment comprises the following steps: S630: generating a triangular surface mesh; S640: Improving the quality of the triangular surface mesh; S650: merging the improved triangular face meshes into a tetrahedral mesh; S660: improving the quality of the tetrahedral mesh; S670: Merging the improved tetrahedral meshes into polyhedral meshes.

7. The method for predicting hydraulic pressure drop of a randomly packed particle bed according to claim 6, characterized in that: In the S630, the average side length of the triangular face mesh is 0.02 to 2 mm, the minimum curvature normal angle of the triangular face mesh is 18°, the lower limit number of gap meshes of the triangular face mesh is 2, the upper limit of the angle of the triangular face mesh is 80°, and the upper limit of the distortion of the triangular face mesh is 0.8; in the S650, the maximum diameter of the circumscribed circle 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 of a randomly packed particle bed according to claim 7, characterized in that: In the S640, the quality of the triangular face mesh is improved, including: when the distortion of the triangular mesh exceeds 0.8, an improvement mechanism is triggered, and unqualified mesh nodes are moved to within the upper limit of the distortion, and the maximum number of improvements is 5 times.

9. The method for predicting hydraulic pressure drop of a randomly packed particle bed according to claim 7, characterized in that: In the S660, the quality of the tetrahedral mesh is improved, including: 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 the orthogonality, and the maximum number of improvements is 5 times.

10. A method for making a piled particle bed, characterized in that: The following steps are involved: (1) selecting particles of various shapes and sizes, calculating the hydraulic pressure drop of a piled particle bed formed by each of the particles, and obtaining the shape and size of the particles corresponding to the lowest hydraulic pressure drop, wherein the calculation method comprises the steps of the hydraulic pressure drop prediction method for a randomly piled particle bed according to any one of claims 1 to 9; (2) The active solid, organic solvent and binder are mixed to form a slurry, and the obtained slurry is concentrated, extruded and cut to obtain solid particles having the shape and size described in step (1), and the solid particles are filled into a lithium extraction electrolytic cell to obtain the stacked particle bed.

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