Method and device for predicting trajectory of flaky particle based on steady-state database algorithm

Abstract

The application discloses a kind of sheet particle motion trajectory prediction method and device based on steady-state database algorithm.The method is characterized by sheet particle and constructs steady-state database, queries database interpolation calculation to obtain particle force and moment and substitutes into particle translation and rotation equation, respectively in global coordinate system and local coordinate system under the solution of sheet particle position and attitude.The application is aimed at the low calculation accuracy of high Reynolds number and non-spherical particle in the traditional gas-solid two-phase flow numerical simulation research, accurately describes the shape of sheet particle by establishing hyperellipsoidal model, and the calculation accuracy is high;Overcome the deficiency of traditional CFD-DEM method in the calculation accuracy of non-spherical particle, fill the blank of CFD-DEM method in solving the motion of sheet particle under high Reynolds number.

Description

Technical Field

[0001] This invention belongs to the field of computational fluid dynamics, specifically relating to a method and apparatus for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm. Background Technology

[0002] Flaky particles have a wide range of engineering applications in energy, chemical, pharmaceutical, and process equipment fields. The development and utilization of new and renewable energy sources, such as biomass, municipal solid waste, and solar energy, is a crucial measure for achieving clean, efficient, and low-carbon energy use. Unlike traditional coal, biomass, municipal solid waste, and discarded solar panels often exhibit a flaky shape after crushing or compression. However, the varied attitudes of flaky particles in flow fields, the difficulty in controlling them using traditional experimental methods, and the significant errors caused by limitations in measurement techniques make analyzing the motion trajectory and forces acting on flaky particles extremely challenging.

[0003] With the development of computer hardware technology and software algorithms, numerical simulation has become an important research tool for developing new processes utilizing particulate materials and optimizing existing processes. However, current simulation studies mostly adopt the assumption of spherical particles, and there is still no universal and high-precision method for predicting the motion trajectory of sheet-like particles. This is mainly because the shape and orientation of sheet-like particles significantly affect the flow field, thereby affecting the interaction between particles and fluid, making accurate prediction of drag difficult. In addition, the traditional computational fluid dynamics-discrete element method (CFD-DEM) suffers from relatively coarse analytical accuracy of the flow field when simulating sheet-like particles with large aspect ratios due to the accuracy requirements between the computational grid size and the particle (equivalent) diameter, further increasing the calculation error of particle-fluid interaction.

[0004] Therefore, this invention proposes a method for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm. This method can overcome the limitations of traditional CFD-DEM methods in calculating the accuracy of non-spherical particles and realize numerical simulation research on the prediction of the motion trajectory of sheet-like particles in the fluidized bed industry. Summary of the Invention

[0005] To address the problem that traditional CFD-DEM methods cannot accurately calculate the motion trajectory of sheet-like particles with large aspect ratios, this invention provides a method for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm. This method constructs a steady-state database, queries the database for interpolation calculations to obtain the forces and moments acting on the particles, and substitutes these into the particle translation and rotation equations to solve for the position and orientation of the sheet-like particles in both global and local coordinate systems.

[0006] The objective of this invention is achieved through the following technical solution: Firstly, this invention proposes a method for predicting the trajectory of sheet-like particles based on a steady-state database algorithm. The steps of this method are as follows:

[0007] Step 1: Characterize the plate-like particles: Determine the particle geometry parameters according to the calculation requirements and construct a three-dimensional model of the plate-like particles, and calculate the particle mass and moment of inertia;

[0008] Step 2: Database Construction: Based on the range of incoming Reynolds numbers in the calculated flow field and the combinations of pitch, roll, and heading angles of the plate-like particles under different attitudes in the flow field, the data points required for database construction are designed; the Latin hypercube sampling method is used to perform stratified random sampling of the database to extract key calculation points; according to the attitude of the plate-like particles in the flow field, the flow field mesh is divided, and the mesh around the particles is refined by boundary layer; for different incoming Reynolds numbers, laminar or turbulent flow models are selected, and the forces and moments on each surface of the plate-like particles are solved by integration, and the net external force and net moment on the plate-like particles are obtained by vector summation; the data points in the database are refined based on the Kriging model, and finally a dynamic database of plate-like particles containing different incoming flow velocities and attitude angles is constructed.

[0009] Step 3: Calculate and read the flow field information: Based on the Eulerian simulation framework, a large eddy simulation turbulence model is introduced to calculate the flow field information and perform a grid independence check until the grid is refined to meet the calculation accuracy requirements; the particle positions are mapped to the flow field grid, and the three-dimensional flow field velocity information at the particle locations is read.

[0010] Step 4: Calculate the particle's attitude in the flow field and its relative velocity with the fluid: Convert the particle's local coordinates to global coordinates using quaternions, and calculate the relative velocity and relative angle between the particle and the flow field based on the flow field velocity information read in Step 3.

[0011] Step 5: Calculate particle mechanics data: Based on the relative angle and relative velocity between the particle and the flow field, query the granular particle dynamics database constructed in Step 2 to obtain the forces and torques acting on the particle;

[0012] Step 6: Update the position and orientation of the plate-like particles: Using the above-mentioned mechanical and particle property information as input parameters for the Newton-Euler equations, calculate the position and orientation information of the particles at the next moment;

[0013] Step 7: Iterative calculation of the complete trajectory: Repeat steps 4 to 6 iteratively to obtain the complete trajectory and attitude evolution information of the sheet-like particles over a period of time.

[0014] Furthermore, in step one, a hyperellipsoidal model is used to geometrically characterize the sheet-like particles.

[0015] Furthermore, in step two, the maximum cell length of the dense grid around the particle should be less than or equal to the thickness of the sheet-like particle.

[0016] Furthermore, in step two, when the Reynolds number is below 1000, the flow field solution uses a steady-state laminar flow model to calculate the forces and moments acting on the particles.

[0017] Furthermore, in step two, when the Reynolds number is higher than 1000, the steady-state turbulence model Realizable k-ε is used to solve the flow field, and the inlet turbulence intensity is calculated and set.

[0018] Furthermore, in step two, the SIMPLEC algorithm is used to calculate and solve the forces and torques on the particles.

[0019] Furthermore, in step six, the trajectory of the sheet-like particles is tracked within the Lagrange framework according to Newton's second law.

[0020] Furthermore, in step six, the position and orientation of the sheet-like particles are solved in the global and local coordinate systems, respectively, based on the particle translation and rotation equations.

[0021] Secondly, the present invention also provides an apparatus for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm, comprising a memory and one or more processors, wherein the memory stores executable code, and when the processor executes the executable code, it implements the aforementioned method for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm.

[0022] Thirdly, the present invention also provides a computer-readable storage medium having a program stored thereon, wherein when the program is executed by a processor, it implements the aforementioned method for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm.

[0023] The beneficial effects of this invention are as follows: Addressing the low accuracy of traditional numerical simulation studies of gas-solid two-phase flow for high Reynolds numbers and non-spherical particles, this invention establishes a hyperellipsoidal model to accurately describe the shape of sheet-like particles, achieving high computational accuracy. Furthermore, constructing a particle dynamics database using a parameterized method significantly reduces computation time, resulting in high computational efficiency. Additionally, by tracking the forces and motion of each particle based on Newton's second law, rich particle-scale information can be obtained. Solving for the position and orientation of sheet-like particles in both global and local coordinate systems based on the particle translation and rotation equations overcomes the shortcomings of traditional CFD-DEM methods in calculating the accuracy of non-spherical particles, filling the gap in predicting the motion trajectory of sheet-like particles at high Reynolds numbers using the CFD-DEM method. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a flowchart illustrating a method for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm.

[0026] Figure 2 This provides a simulation framework for a method to predict the motion trajectory of sheet-like particles based on a steady-state database algorithm.

[0027] Figure 3 A schematic diagram of sampling points for constructing a dynamic database of sheet-like particles;

[0028] Figure 4 This is a schematic diagram of the attitude of sheet-like particles at different simulation times based on the steady-state database algorithm;

[0029] Figure 5 This is a structural diagram of a device for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm. Detailed Implementation

[0030] The present invention will be further described below with reference to the accompanying drawings and examples.

[0031] This invention proposes a method for predicting the trajectory of sheet-like particles based on a steady-state database algorithm. The method involves establishing a hyperellipsoidal model to describe the shape of the sheet-like particles; constructing a dynamic database of the particles using a parametric method; simultaneously reading the flow field velocity information using a center interpolation method; tracking the forces and motion of each particle based on Newton's second law to obtain rich particle-scale information; and solving for the position and attitude of the sheet-like particles in both global and local coordinate systems based on the particle translational and rotational equations. Numerical simulation studies of a gas-solid two-phase flow system involving sheet-like particles verify the feasibility of this method for simulating the trajectory of sheet-like particles using a steady-state database algorithm.

[0032] The following section applies the method for predicting the trajectory of sheet-like particles based on a steady-state database. The specific process is as follows: Figure 1 As shown, a numerical simulation of a gas-solid two-phase flow system of sheet-like particles in a wind tunnel is performed. The simulation framework of this prediction method is as follows: Figure 2 As shown, after determining the shape of the sheet-like particles, the position, angular velocity, and linear velocity of the particles are calculated based on their motion model. Additionally, the velocity and pressure information of the flow field are calculated and read to construct a dynamic database. Finally, the position and attitude of the sheet-like particles are updated and calculated. The specific steps are as follows:

[0033] (1) Characterizing plate-like particles. The shape model of plate-like particles adopts a hyperellipsoidal model, and the shape is described by the hyperquadratic surface equation, the standard equation of which is:

[0034]

[0035] Where f is the surface function, x, y, and z are three coordinate variables, a, b, and c are the semi-axis lengths along the main axis of the particle, and s1 and s2 are shape indices.

[0036] In addition, it is necessary to calculate the inherent properties of the sheet-like particles, such as the mass (m) required for trajectory simulation. p ) and moment of inertia (I p ),Right now:

[0037] m p =ρ p V p (2)

[0038] I p =∫r 2 ·dm=∫ρ p r 2 ·dv (3)

[0039] Where, m p For particle mass, ρ p V is the particle density. p I represents the particle volume. p Let dm be the moment of inertia, dm be the infinitesimal element, and r be the distance between dm and the rotation axis. For a three-dimensional object, when choosing itself as the reference frame, there are generally three rotation axes, and its moment of inertia matrix is ​​expressed as:

[0040]

[0041] Where x, y, and z represent coordinate variables in space; dx, dy, and dz represent derivatives with respect to x, y, and z, respectively.

[0042] For symmetrically shaped sheet-like particles, the inertial matrix has elements only on its diagonal, therefore the above formula can be simplified to:

[0043] m p =ρ p l p w p h p (5)

[0044]

[0045] Among them, l p w p h pThese are the length, width, and height of the flaky particles, respectively.

[0046] (2) Establish a database. This is based on the range of the incoming Reynolds number Re from the simulation and the combinations of pitch, roll, and heading angles of the plate-like particles under different attitudes in the flow field. For example... Figure 3 As shown, the parameters for constructing the database include relative velocity (range 0–75 m / s, interval 5 m / s), pitch angle (range 0–90°, interval 10°), roll angle (range 0–90°, interval 10°), and yaw angle (range 0–90°, interval 10°). The data points required for database construction are designed. Latin hypercube sampling is used to perform stratified random sampling on the database to extract key calculation points.

[0047] The flow field is meshed to generate an unstructured mesh, and the boundary layer around the particles is refined. The largest cell of the refined mesh is selected as the thickness of the plate-like particles (i.e. the length of the shortest side of the plate-like particles) after mesh independence analysis.

[0048] For different incoming Reynolds numbers Re, appropriate laminar or turbulent flow models are selected, and the particle forces and moments are obtained using the SIMPLEC algorithm. When the incoming Reynolds number is below 1000, a steady-state laminar flow model is used; when the incoming Reynolds number is above 1000, a steady-state Realizable k-ε model is used. The turbulence intensity I is calculated by the following formula:

[0049]

[0050]

[0051] Where, ρ g For fluid density, u g For the incoming flow velocity, l p The characteristic length of the sheet-like particles, μ g This refers to the fluid dynamic viscosity.

[0052] The forces and moments acting on the particle surface are solved by integration, and vector summation yields the net external force and net moment acting on the sheet-like particles by the fluid. Finally, the raw data obtained from Latin hypercube sampling is used to train a Kriging model. The spatial interpolation technique of the Kriging model allows for estimation and interpolation of values ​​at unknown locations without direct access to the raw data. Data points in the database are then densified based on the Kriging model. Ultimately, a dynamic database of sheet-like particles containing different incoming flow velocities, pitch angles, roll angles, and heading angles is constructed.

[0053] (3) Calculate and read the flow field information. Based on the Eulerian simulation framework, the large eddy turbulence model is introduced to calculate the flow field information and perform the independent verification of the computational grid until the calculation accuracy is met. After the gas flow in the flow field reaches a steady state, the flow field information such as velocity and pressure in each grid is saved. The particle position information is mapped to the flow field, and the fluid velocity at the center of the flow field grid is interpolated to the particle location. Since the sheet-like particles may cover multiple grids, it is necessary to calculate the average velocity of the fluid at the particle location based on the interpolation data.

[0054] (4) Calculate the particle's attitude in the flow field and its relative velocity with the fluid. Based on the flow field velocity information and the particle's attitude and velocity information, calculate the relative velocity and relative angle between the particle and the flow field. The relative velocity is obtained by subtracting the particle's velocity vector from the flow field velocity vector in global coordinates and taking the modulus, i.e.:

[0055]

[0056] Among them, v rel For relative velocity, u g u is the velocity vector of the flow field in the global coordinate system. p This is the particle velocity vector in the global coordinate system.

[0057] The calculation of the relative angle requires transforming the three particle surface vectors in the local coordinate system into surface vectors in the global coordinate system using quaternions. Then, the relative angle between the particle and the flow field is calculated using the law of cosines. The conversion formula for transforming the local surface vectors into surface vectors in the global coordinate system using quaternions is as follows:

[0058]

[0059] V global =Q·v local (11)

[0060] Where Q is a quaternion, q0 is the real part of the quaternion, also called the scalar part; q1, q2, and q3 are the imaginary parts of the quaternion, also called the vector parts; V global v is a surface vector in global coordinates. local It is a surface vector in local coordinates.

[0061] After transforming the local surface vector into a surface vector in global coordinates, the relative angle between the particle and the flow field is calculated using the law of cosines, i.e.:

[0062]

[0063] Where angle is the relative angle between the particle and the flow field. The velocity vector of the flow field in the global coordinate system. Let be the surface vector of the particle in the global coordinate system.

[0064] (5) Calculate particle mechanics data. Based on the relative angle and relative velocity between the particle and the flow field, query the database constructed in step (2) to perform interpolation calculations at a certain point within the unit and obtain the force and torque acting on the particle;

[0065] (6) Update the position and orientation of the sheet-like particles. The motion of the particles can be tracked within the Lagrange framework according to Newton's second law. The control equations for the position, translation, and rotation of the particles can be expressed as:

[0066]

[0067]

[0068]

[0069] Where, m p X p U p ω p These represent the particle's mass, position, linear velocity, and angular velocity, respectively. F p Let M be the net force on the particle excluding its own weight, g be the acceleration due to gravity, and M be the net force on the particle. p I is the total torque acting on the particle. p It is the moment of inertia on the particle.

[0070] The position and orientation of the sheet-like particles are solved in both the global and local coordinate systems based on the particle translation and rotation equations. The forces and moments in the three directions are expressed as follows:

[0071]

[0072]

[0073] Based on the forces and torques acting on the particle, the position and attitude information of the particle at the next moment can be calculated.

[0074] (7) Iteratively calculate the complete trajectory. Using the above mechanical information and particle property information as inputs to the Newton-Euler equations, repeat iterative calculation steps (4) to (6) to obtain the complete trajectory of the sheet-like particle and its attitude information such as rotation angle and velocity over a period of time. The attitude of the sheet-like particle at different simulation moments over a period of time is as follows: Figure 4 As shown.

[0075] This invention proposes a method for predicting the trajectory of sheet-like particles based on a steady-state database algorithm. The method involves establishing a hyperellipsoidal model to describe the shape of the sheet-like particles; constructing a dynamic database of the particles using a parametric method; simultaneously reading the flow field velocity information using a center interpolation method; and tracking the forces and motion of each particle based on Newton's second law to obtain rich information such as the particle's trajectory, attitude, and forces. The position and attitude of the sheet-like particles are solved in both the global and local coordinate systems based on the particle translation and rotation equations. Simulation and analysis of the trajectories of sheet-like particles in flow fields with different incoming Reynolds numbers verify the feasibility of this method for simulating the trajectory of sheet-like particles using a steady-state database algorithm.

[0076] Corresponding to the aforementioned embodiment of a method for predicting the trajectory of sheet-like particles based on a steady-state database algorithm, the present invention also provides an embodiment of a device for predicting the trajectory of sheet-like particles based on a steady-state database algorithm.

[0077] See Figure 5 The present invention provides a device for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm, comprising a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it is used to implement a method for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm as described in the above embodiment.

[0078] The embodiment of the sheet-like particle trajectory prediction device based on a steady-state database algorithm provided by this invention can be applied to any device with data processing capabilities, such as a computer. The device embodiment can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 5 The diagram shown is a hardware structure diagram of any device with data processing capabilities, including the sheet-like particle trajectory prediction device based on a steady-state database algorithm provided by this invention. (Except for...) Figure 5 In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0079] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0080] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0081] This invention also provides a computer-readable storage medium storing a program thereon, which, when executed by a processor, implements a method for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm as described in the above embodiments.

[0082] The computer-readable storage medium can be an internal storage unit of any data processing device as described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device of any data processing device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units and external storage devices of any data processing device. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0083] The above embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A method for predicting the trajectory of sheet-like particles based on a steady-state database algorithm, characterized in that, The steps of this method are as follows: Step 1: Geometric characterization of the plate-like particles using a hyperellipsoidal model: Determine the particle geometric parameters according to the calculation requirements and construct a three-dimensional model of the plate-like particles to calculate the particle mass and moment of inertia; Step 2: Database Construction: Based on the range of incoming Reynolds numbers in the calculated flow field and the combinations of pitch, roll, and heading angles of the plate-like particles under different attitudes in the flow field, the data points required for database construction are designed; the Latin hypercube sampling method is used to perform stratified random sampling of the database to extract key calculation points; according to the attitude of the plate-like particles in the flow field, the flow field mesh is divided, and the mesh around the particles is refined by boundary layer; for different incoming Reynolds numbers, laminar or turbulent flow models are selected, and the forces and moments on each surface of the plate-like particles are solved by integration, and the net external force and net moment on the plate-like particles are obtained by vector summation; the data points in the database are refined based on the Kriging model, and finally a dynamic database of plate-like particles containing different incoming flow velocities and attitude angles is constructed. Step 3: Calculate and read the flow field information: Based on the Eulerian simulation framework, a large eddy simulation turbulence model is introduced to calculate the flow field information and perform a grid independence check until the grid is refined to meet the calculation accuracy requirements; the particle positions are mapped to the flow field grid, and the three-dimensional flow field velocity information at the particle locations is read. Step 4: Calculate the particle's attitude in the flow field and its relative velocity with the fluid: Convert the particle's local coordinates to global coordinates using quaternions, and calculate the relative velocity and relative angle between the particle and the flow field based on the flow field velocity information read in Step 3. Step 5: Calculate particle mechanics data: Based on the relative angle and relative velocity between the particle and the flow field, query the granular particle dynamics database constructed in Step 2 to obtain the forces and torques acting on the particle; Step 6: Update the position and orientation of the plate-like particles: Using the above-mentioned mechanical and particle property information as input parameters for the Newton-Euler equations, the position and orientation of the plate-like particles are solved in the global and local coordinate systems according to the particle translation and rotation equations, respectively, to obtain the position and orientation information of the particles at the next moment. Step 7: Iterative calculation of the complete trajectory: Repeat steps 4 to 6 iteratively to obtain the complete trajectory and attitude evolution information of the sheet-like particles over a period of time.

2. The method for predicting the trajectory of sheet-like particles based on a steady-state database algorithm according to claim 1, characterized in that, In step two, the maximum cell length of the dense grid around the particle should be less than or equal to the thickness of the sheet-like particle.

3. The method for predicting the trajectory of sheet-like particles based on a steady-state database algorithm according to claim 1, characterized in that, In step two, when the Reynolds number is below 1000, the flow field solution uses a steady-state laminar flow model to calculate the forces and moments acting on the particles.

4. The method for predicting the trajectory of sheet-like particles based on a steady-state database algorithm according to claim 1, characterized in that, In step two, the flow field solution for Reynolds numbers above 1000 uses the Realizable steady-state turbulence model. k-ε Calculate and set the inlet turbulence intensity.

5. The method for predicting the trajectory of sheet-like particles based on a steady-state database algorithm according to claim 1, characterized in that, In step two, the SIMPLEC algorithm is used to calculate and solve the forces and torques on the particles.

6. The method for predicting the trajectory of sheet-like particles based on a steady-state database algorithm according to claim 1, characterized in that, In step six, the trajectory of sheet-like particles is tracked within the Lagrange framework according to Newton's second law.

7. A device for predicting the trajectory of sheet-like particles based on a steady-state database algorithm, comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that... When the processor executes the executable code, it implements a method for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm as described in any one of claims 1-6.

8. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements a method for predicting the motion trajectory of sheet-like particles based on a steady-state database algorithm as described in any one of claims 1-6.

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