A numerical calculation method for large-scale particle flow based on multi-sphere filling

Abstract

This invention relates to the field of multiphase numerical simulation and discloses a numerical calculation method for large-scale particle flow based on multi-sphere filling. The method includes: obtaining the fluid domain mesh size, fluid density, and large particle radius; calculating the radius of the filling spheres based on the fluid domain mesh size; determining the number and position of the filling spheres based on the golden-angle spiral distribution and minimum distance coverage judgment, generating a large-particle model with multi-sphere filling; obtaining the background flow field velocity of the large particles and filling spheres at the current time step, and calculating the background flow field velocity and drag force of the large particles; updating through iterative calculation to obtain the velocity and position of the large particles and filling spheres at the next time step; and adding the drag force as a source term to the momentum equation to solve for the fluid motion, obtaining the fluid computational domain mesh velocity at the next time step. This method achieves accurate numerical simulation of large-scale particles.

Description

Technical Field

[0001] This application relates to the field of multiphase numerical simulation, and in particular to a numerical calculation method for large-scale particle flow based on multi-sphere filling. Background Technology

[0002] Particle-fluid two-phase systems are complex multiphase systems that study the interaction between discrete particles and continuous fluids. Their core lies in revealing the mechanisms of momentum transfer and energy conversion between the solid and liquid phases. As a key area of ​​multiphase flow research, these phenomena are prevalent in nature and engineering applications. In recent years, thanks to advancements in high-performance computing technology, numerical simulation has become an important tool for exploring these systems. Through computational methods, we can not only gain a deeper understanding of the motion characteristics of particle swarms but also analyze the essential laws governing fluid-structure interaction. This simulation method provides a new research approach for understanding the dynamic behavior of two-phase systems.

[0003] In existing numerical simulations, the accuracy of flow field calculations depends on the fineness of the mesh. For traditional unanalytical methods, to ensure computational stability, the mesh size is typically required to be 3 to 5 times larger than the particle size. However, when simulating large-scale particle motion, the particle size often exceeds the mesh size. This contradiction makes it difficult to simultaneously meet the dual requirements of flow field accuracy and numerical stability, making the numerical simulation of large-scale particle motion a technical challenge that needs to be overcome. Summary of the Invention

[0004] To overcome the above problems, this application provides a numerical calculation method for large-scale particle flow based on multi-sphere filling. The present invention is based on the golden angle spiral distribution method and the minimum distance coverage determination method. It constructs a large particle model by using multi-sphere filling and corrects the background flow field velocity and particle frontal area in the drag calculation, thereby achieving accurate simulation in large-scale particle calculation.

[0005] According to a first aspect of the embodiments of this application, a numerical calculation method for large-scale particle flow based on multi-sphere filling is provided, comprising:

[0006] S1: Obtain fluid domain mesh size, fluid density, and large particle radius;

[0007] S2: The radius of the filling sphere is calculated based on the fluid domain mesh size;

[0008] S3: Based on the radius of the large particle and the radius of the filling spheres, determine the number and position vector of the filling spheres using the golden angle spiral method and the minimum distance coverage determination method, and generate the large particle;

[0009] S4: Obtain the velocity of the large particle and the background flow field velocity of the filling sphere at the current time step;

[0010] S5: Determine the background flow velocity of the large particles based on the background flow velocity and quantity of the filled spheres;

[0011] S6: Based on the fluid density, large particle radius, large particle velocity, and background flow field velocity of the filling spheres, calculate the corrected frontal area of ​​the large particles and determine the drag force of the large particles.

[0012] S7: The drag force of the large particle is calculated iteratively to obtain the velocity of the large particle in the next time step, as well as the velocity and position vector of the filling ball;

[0013] S8: Add the drag force as a source term to the momentum equation to iteratively calculate the fluid motion and obtain the fluid computational domain grid velocity for the next time step;

[0014] S9: Determine if the current time step is the last time step. If not, return to S4 to continue execution; if yes, terminate the operation process and obtain the final particle information and fluid computation domain grid velocity.

[0015] Optionally, based on the radius of the large particle and the radius of the filling spheres, the number and position vector of the filling spheres are determined using the golden angle spiral method and the minimum distance coverage determination method, including:

[0016] Based on the radius of the large particle and the radius of the filling spheres, determine the initial value of the number of filling spheres;

[0017] Based on the initial value of the number of filling balls, the position vector of the filling balls is determined by the golden angle spiral law;

[0018] Based on the position vectors of the filling spheres, a triangular mesh is constructed on the sphere surface. The number of filling spheres is determined using the minimum distance coverage method, including:

[0019] (1) Calculate the center point of each triangle using the following formula;

[0020] ;

[0021] in c i For the first i The position vector of the center point of each triangle p i,1 , p i,2 , p i,3 For the first i The position vectors of the filling spheres containing the three vertices of the triangle;

[0022] (2) Calculate the minimum distance between the center point of each triangle and the position of the filling ball:

[0023] ;

[0024] in, m The total number of triangles, p i，j For the first i The first triangle j The position vectors of the filling spheres where each vertex is located;

[0025] (3) If the minimum distance exceeds the radius r ,Right now If the distance is greater than r, then increase the number of filling balls and rearrange their positions until the minimum distance is less than or equal to the radius r, thus obtaining the final number of filling balls.

[0026] Optionally, the background flow field velocity of the large particles is determined by the following formula:

[0027] ;

[0028] in, N The number of balls to fill. U f The background flow field velocity is used to fill the small sphere. U f’ The background flow field velocity represents the velocity of large particles.

[0029] Optionally, the formula for calculating the drag force of the large particles is as follows:

[0030] ;

[0031] ;

[0032] in, F d For the drag force of large particles, C d This is the drag coefficient. ρ f For fluid density, U f’ The background flow field velocity is for large particles. U p For the speed of large particles, A ref For large particle frontal area, N The number of balls to fill. R For large particle radius, Number of small balls to fill the equator The distance between the centers of adjacent filled spheres. r The radius of the filling sphere.

[0033] The technical solutions provided by the embodiments of this application may include the following beneficial effects:

[0034] As can be seen from the above embodiments, the method proposed in this application is based on the golden spiral distribution method and the minimum distance coverage determination method, and constructs a large particle model using a multi-sphere filling method. The golden spiral distribution method enables the uniform arrangement of filling spheres on the spherical surface, while the minimum distance coverage determination method determines the minimum number of filling spheres required. The synergistic effect of these two methods significantly reduces model redundancy, significantly improves computational efficiency, and reduces resource consumption. This method uses the filling spheres as uniform sampling points on the surface of the large particles, acquires and averages the flow field information around the large particles, thereby constructing more accurate background flow field information. Furthermore, the correction of the particle's upstream area further improves the accuracy of the flow field in calculating particle drag. This method provides strong support for accurate numerical simulation of large-scale particle flow.

[0035] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0036] Figure 1 This is a flowchart illustrating a numerical calculation method for large-scale particle flow based on multi-sphere filling, according to an exemplary embodiment.

[0037] Figure 2 The grid position selection is based on the golden angle spiral law as illustrated in an exemplary embodiment.

[0038] Figure 3 This is a schematic diagram of a large-scale single-particle sedimentation calculation verification model according to an exemplary embodiment.

[0039] Figure 4 This is a comparison of large-scale single-particle sedimentation calculation verification results based on an exemplary embodiment.

[0040] Figure 5 This is a comparison of large-scale particle swarm calculation verification results illustrated by an exemplary embodiment.

[0041] Figure 6 This is a comparison of large-scale particle swarm calculation verification results illustrated by an exemplary embodiment. Detailed Implementation

[0042] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0043] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0044] Figure 1 This is a flowchart illustrating a numerical calculation method for large-scale particle flow based on multi-sphere filling, according to an exemplary embodiment. Figure 1 As shown, the method may include the following steps:

[0045] S1: Obtain fluid domain mesh size, fluid density, and large particle radius;

[0046] Specifically, Fluent software is used to obtain the mesh generation information of the internal flow field of the valve, including the fluid domain mesh and fluid density of key structures such as valve disc, valve seat, valve core and inner wall of flow channel. The large particle radius is determined by preset parameters, providing basic data for subsequent simulation of particle movement in valve pipeline and interaction with fluid.

[0047] S2: The radius of the filling sphere is calculated based on the fluid domain mesh size;

[0048] Specifically, in the EDEM, the radius of the filler spheres is set to 1 / 6 of the grid size, and the diameter is set to 1 / 3 of the grid size, which conforms to the particle size-to-grid ratio of traditional unanalyzed models. This allows the filler spheres to better capture the grid flow field velocity of large particles in regions such as the throat, throttling gap, and valve core-seat gap in valve pipelines, and to more accurately reflect the force and velocity distribution characteristics of particles in high-velocity shear zones and recirculation zones.

[0049] S3: Based on the radius of the large particle and the radius of the filling spheres, using the golden angle spiral method and the minimum distance coverage determination method, determine the number and position vector of the filling spheres, and generate the large particle; this step includes the following sub-steps:

[0050] S31: Determine the initial value of the number of filling spheres based on the radius of the large particle and the radius of the filling spheres;

[0051] Specifically, the number of small balls filled N The initial value is given by the particle size ratio:

[0052]

[0053] In the formula, R For large particle radius, r To fill the radius of the small sphere, N This represents the number of balls to fill the space.

[0054] S32: Based on the initial value of the number of filling balls, determine the position vector of the filling balls using the golden angle spiral rule;

[0055] Specifically, the coordinates of the filled ball's position are obtained using Matlab software based on the following mathematical expression, with the filling method as follows: Figure 2 As shown.

[0056]

[0057] In the formula, x n , y n , z n For the first n The components of the position vector of each filled sphere = ,in( R - r ) represents the radius of the sphere containing the center of the filling sphere.

[0058] S33: Based on the position vector of the filling spheres, construct a triangular mesh on the sphere surface, and determine the number of filling spheres using the minimum distance coverage determination method;

[0059] Specifically, in the Python environment, a spherical triangular mesh is constructed based on the aforementioned position vectors (each triangle corresponds to a spherical segment), and the minimum distance between the center point of each triangle and the position vector of the small sphere is calculated, including:

[0060] (1) Calculate the center point of each triangle using the following formula;

[0061] ;

[0062] in c i For the first i The position vector of the center point of each triangle p i,1 , p i,2 , p i,3 For the firsti The position vectors of the filling spheres where the vertices of the triangles are located;

[0063] (2) Calculate the minimum distance between the center point of each triangle and the position of the filling ball:

[0064] ;

[0065] in, m The total number of triangles, p i，j For the first i The first triangle j The position vectors of the filling spheres where each vertex is located;

[0066] (3) If the minimum distance exceeds the radius r ,Right now If the value is greater than r, the number of filling balls is increased and their positions are rearranged until the minimum distance is less than or equal to the radius r, at which point the final number of filling balls is obtained.

[0067] This method uses the golden angle spiral method to determine the particle arrangement and the minimum distance coverage method to determine the number of dynamically adjusted balls. In valve and pipeline simulation, it ensures simulation accuracy while effectively controlling computational costs.

[0068] S4: Obtain the velocity of the large particle and the background flow field velocity of the filling sphere at the current time step;

[0069] Specifically, a custom script was developed based on the API interface provided by EDEM to read and process the velocity of large particles and the mesh flow field information within the valve pipe where the filling spheres are located. This script can flexibly extract key parameters, thereby systematically obtaining the dynamic characteristic data of the particles.

[0070] S5: Determine the background flow velocity of the large particles based on the background flow velocity and quantity of the filled spheres;

[0071] Specifically, the velocity information of each filled sphere distributed on the surface of the large particle is averaged in the flow field grid to obtain the overall background flow field velocity of the large particle. The calculation formula is as follows:

[0072]

[0073] in, N To determine the number of balls to fill, U f The background flow field velocity is used to fill the small sphere. U f’ The background flow field velocity represents the velocity of large particles.

[0074] For particles larger than the fluid grid size, a more accurate background flow field velocity for large particles can be obtained by averaging the flow field information of multiple grid points in their neighborhood.

[0075] S6: Based on the fluid density, large particle radius, large particle velocity, and background flow field velocity of the filling spheres, calculate the corrected frontal area of ​​the large particles and determine the drag force of the large particles.

[0076] Specifically, first calculate the frontal area of ​​the large particles, and then, in combination with the total number of small spheres, use the following formula to roughly calculate the number of large particles at the equator.

[0077]

[0078] Calculate the distance between the centers of adjacent filled spheres;

[0079]

[0080] Calculate the area of ​​the great circle with radius (Rr):

[0081]

[0082] Calculate the total area of ​​the small circles with radius r:

[0083]

[0084] Calculate the sum of the overlapping areas between small circles of radius r:

[0085]

[0086] Calculate the area of ​​overlap between each smaller circle and the larger circle:

[0087]

[0088] Therefore, the total frontal area is A big + N equator ( A small - A small-overlap - A small∩big )as follows:

[0089]

[0090]

[0091] in, N To determine the number of balls to fill, N equator Number of small balls to fill the equatord The distance between the centers of adjacent filled spheres. A ref For large particle frontal area, R For large particle radius, C d This is the drag coefficient. ρ f For fluid density, U p For the speed of large particles, F d For large particle drag.

[0092] This step corrects the calculation of the frontal area of ​​large particles filled with multiple spheres, enabling it to more accurately characterize the flow characteristics of the particles under complex flow field conditions in valve pipes, thereby significantly improving the accuracy of subsequent drag force calculations.

[0093] S7: The drag force of the large particle is calculated iteratively to obtain the velocity of the large particle in the next time step, as well as the velocity and position vector of the filling ball;

[0094] Specifically, the EDEM is used to solve the motion equations of the particles in the valve pipeline based on the forces acting on the particles. Simultaneously, the collision forces between particles and between particles and the valve wall, as well as the dynamically coupled drag forces, are considered in relation to the particle motion. This yields the position vector of the large particles and the velocity and position vectors of the filling spheres for the next time step. This ensures that the dynamic response of the particles evolves synchronously with the fluid state inside the valve, providing support for high-fidelity CFD-DEM modeling.

[0095] S8: Add the drag force as a source term to the momentum equation to iteratively calculate the fluid motion and obtain the fluid computational domain grid velocity for the next time step;

[0096] Specifically, the forces are uniformly transformed into source terms and added to the control equations of the Fluent software. This is coupled with the momentum equations of the fluid inside the valve and pipeline to achieve multiphase mechanical linkage. During the numerical calculation, an iterative solution method is used to solve the updated momentum equations, thereby obtaining the flow field velocity of the particles in the next time step under the action of the valve. This updates the grid information of the entire fluid computational domain, providing a flow field basis for subsequent particle trajectory prediction.

[0097] S9: Determine if the current time step is the last time step. If not, return to S4 to continue execution; if yes, terminate the operation process and obtain the final particle information and fluid computation domain grid velocity.

[0098] Specifically, after each loop calculation is completed, the system will accumulate the time steps. When the accumulated time steps are less than the preset total time steps, the system returns to step S4 to continue the update and coupling calculation of particle information and fluid computational domain mesh information; if the accumulated time steps reach the preset total time steps, the loop terminates and the final particle state information and fluid computational domain mesh data are output.

[0099] As demonstrated by the above embodiments, this invention addresses the problem of insufficient accuracy in obtaining background flow field data when dealing with large-scale particle flow using traditional CFD-DEM methods. It proposes a numerical simulation method based on the coupling of multi-sphere filling modeling and dynamic verification, which is then applied to the background field calculation of valves. This method achieves uniform arrangement of the filling spheres through a golden-angle spiral distribution and optimizes the filling quantity using a minimum distance coverage criterion, reducing computational redundancy while ensuring geometric accuracy. Simultaneously, it extracts and corrects background flow field information based on the filling cells, improving the physical consistency and simulation accuracy of drag force calculations, and achieving accurate solutions for the flow behavior of large-scale particles.

[0100] To verify the effectiveness of the proposed large-scale particle calculation method, this study first validates the calculation accuracy of large-scale particles through single-particle sedimentation experiments. Figure 3 The diagram shows a single-particle sedimentation model. The experimental setup uses a 100mm×100mm square cross-section container, and the particles are released freely from a height of 120mm. Figure 4 The simulation results of different methods are compared with experimental data. The results show that the numerical simulation results of the method of the present invention are in high agreement with the experimental measurements, which verifies the calculation accuracy of the method for large-scale particles.

[0101] To further verify the applicability of the method to particle swarm optimization, this study conducted experiments in a vertically ascending pipe. For example... Figure 5 As shown, the experimental pipe has a diameter of 30.6 mm and a length of 3060 mm. Figure 6 The validation results of the particle swarm optimization calculation are presented, among which... r Indicates the distance between the particle (fluid) position and the pipe axis. R The radius of the pipe is given. The experimentally measured fluid and particle velocity distributions show good agreement with the numerical simulation results, fully demonstrating the effectiveness of the proposed method in large-scale particle swarm simulation.

[0102] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0103] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A numerical calculation method for large-scale particle flow based on multi-sphere filling, characterized in that, include: S1: Obtain fluid domain mesh size, fluid density, and large particle radius; S2: The radius of the filling sphere is calculated based on the fluid domain mesh size; S3: Based on the radius of the large particle and the radius of the filling spheres, determine the number and position vector of the filling spheres using the golden angle spiral method and the minimum distance coverage determination method, and generate the large particle; S4: Obtain the velocity of the large particle and the background flow field velocity of the filling sphere at the current time step; S5: Determine the background flow velocity of the large particles based on the background flow velocity and quantity of the filled spheres; S6: Based on the fluid density, large particle radius, large particle velocity, and background flow field velocity of the filling spheres, calculate the corrected frontal area of ​​the large particles and determine the drag force of the large particles. S7: The drag force of the large particle is calculated iteratively to obtain the velocity of the large particle in the next time step, as well as the velocity and position vector of the filling ball; S8: Add the drag force as a source term to the momentum equation to iteratively calculate the fluid motion and obtain the fluid computational domain grid velocity for the next time step; S9: Determine if the current time step is the last time step. If not, return to S4 to continue execution; if yes, terminate the operation process and obtain the final particle information and fluid computational domain grid velocity. Specifically, based on the radius of the large particle and the radius of the filling spheres, the number and position vectors of the filling spheres are determined using the golden angle spiral method and the minimum distance coverage determination method, including: Based on the radius of the large particle and the radius of the filling spheres, determine the initial value of the number of filling spheres; Based on the initial value of the number of filling balls, the position vector of the filling balls is determined by the golden angle spiral law; Based on the position vectors of the filling spheres, a triangular mesh is constructed on the sphere surface, and the number of filling spheres is determined by the minimum distance coverage method. The method for determining the number of filling balls using the minimum distance coverage criterion includes: (1) Calculate the center point of each triangle using the following formula; ； in c i For the first i The position vector of the center point of each triangle p i,1 , p i,2 , p i,3 For the first i The position vectors of the filling spheres containing the three vertices of the triangle; (2) Calculate the minimum distance between the center point of each triangle and the position of the filling ball: ； in, m The total number of triangles, p i，j For the first i The first triangle j The position vectors of the filling spheres where each vertex is located; (3) If the minimum distance exceeds the radius r ,Right now If the distance is greater than r, then increase the number of filling balls and rearrange their positions until the minimum distance is less than or equal to the radius r, thus obtaining the final number of filling balls.

2. The numerical calculation method for large-scale particle flow based on multi-sphere filling according to claim 1, characterized in that, The background flow field velocity of the large particles is determined by the following formula: ； in, N The number of balls to fill. U f The background flow velocity is used to fill the small sphere. U f’ The background flow field velocity represents the velocity of large particles.

3. The numerical calculation method for large-scale particle flow based on multi-sphere filling according to claim 1, characterized in that, The formula for calculating the drag force of the large particles is as follows: ； ； in, F d For the drag force of large particles, C d This is the drag coefficient. ρ f For fluid density, U f’ The background flow field velocity is for large particles. U p For the speed of large particles, A ref For large particle frontal area, N The number of balls to fill. R For large particle radius, Number of small balls to fill the equator The distance between the centers of adjacent filled spheres. r The radius of the filling sphere.

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