Particle trajectory simulation method for mineral calcination digital twinning
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHENYANG UNIVERSITY OF TECHNOLOGY
- Filing Date
- 2026-04-02
- Publication Date
- 2026-06-19
AI Technical Summary
Numerical simulation of traditional mineral calcination processes is time-consuming and difficult to respond quickly to changes in process parameters. Furthermore, particle tracking methods have large errors and low computational efficiency in regions with large velocity field gradients, which cannot meet the real-time optimization requirements of digital twin systems.
A parameterized surrogate model is constructed and combined with adaptive step-size particle tracking technology. The target physical field is quickly generated through the parameterized surrogate model, and the adaptive step-size integral algorithm is combined to achieve efficient and high-precision prediction of particle motion trajectory, supporting process optimization and real-time monitoring.
It enables physical field response under new operating conditions to be completed within seconds or minutes, supports rapid scenario simulation and real-time process parameter adjustment of digital twin systems, improves computing efficiency and accuracy, and supports process optimization and real-time monitoring.
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Figure CN122242191A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of industrial process simulation and digital twin technology, and particularly relates to a particle trajectory simulation method for digital twins of mineral calcination. Background Technology
[0002] Mineral calcination is a crucial step in preparing high-purity oxides or activated mineral raw materials, typically carried out in equipment such as suspension roasters. During calcination, the trajectory, residence time, and thermal history of material particles in the high-temperature gas flow directly determine product quality (such as activity and crystal phase) and energy utilization efficiency. Traditionally, optimization of such processes relies on empirical trial and error, as well as offline simulations based on computational fluid dynamics (CFD). However, this approach has the following shortcomings:
[0003] First, direct numerical simulation (DNS) of complex geometries and transient multiphase flows is extremely time-consuming. Even with engineering simplification methods such as Reynolds-averaged (RANS), the computation time is still insufficient for the real-time or near-real-time operation requirements of digital twin systems.
[0004] Second, once a traditional CFD simulation is completed, the boundary conditions are fixed. If the effects of different adjustable process parameters such as inlet velocity, temperature, and particle feed rate are to be studied, a complete simulation must be performed again, which cannot meet the needs of digital twins for rapid extrapolation of process parameters.
[0005] Third, conventional particle tracking methods use fixed step-size integration of velocity field data, which can easily produce large errors in regions with large velocity field gradients, or be forced to use extremely small global step-sizes to control errors, resulting in low computational efficiency; while in flat regions, it causes a waste of computational resources. Summary of the Invention
[0006] This invention addresses the shortcomings of existing technologies by providing a particle trajectory simulation method for digital twins of mineral calcination. It rapidly generates the target physical field by constructing a parameterized surrogate model and combines it with adaptive step-size particle tracking technology to achieve efficient and high-precision prediction of particle motion trajectories under different operating conditions, thereby providing simulation support for process optimization and real-time monitoring.
[0007] To achieve the above objectives, the present invention adopts the following technical solution: a particle trajectory simulation method for digital twins of mineral calcination, comprising the following steps:
[0008] S1. Construct a parameterized proxy model; based on the three-dimensional digital geometric model of the calcining equipment and industrial adjustable parameters, establish a mapping relationship from spatial coordinates and boundary condition parameters to velocity vectors.
[0009] S2. Define boundary conditions in the three-dimensional digital geometric model and set particle simulation parameters, including the total number of particles, initial attributes, wall collision coefficient, integration step size range, error tolerance, and particle stagnation and oscillation determination parameters.
[0010] S3. Obtain the boundary condition parameters of the current target working condition, construct a velocity field query function, take the coordinates of any spatial location point and the boundary condition parameters as input, and output the predicted velocity vector value at that location in real time through parameterized surrogate model inference.
[0011] S4. Based on the velocity field query function constructed in step S3, release particles sequentially, establish the particle motion differential equation, calculate the net force on the particle and the resulting acceleration, and use an adaptive step-size integration algorithm to solve the problem to update the particle state. After each integration step, perform boundary condition judgment, stagnation judgment and oscillation processing until the termination condition is met.
[0012] S5. Trajectory data post-processing and output: Summarize the discrete trajectory sequences, dwell time, escape statistics, wall collision statistics, and spatial dwell density distribution information of all particles.
[0013] Furthermore, S1 specifically includes the following sub-steps:
[0014] S101. Based on the three-dimensional digital geometric model of the calcination equipment, perform mesh generation, define the set of node coordinates and topological relationships, and assign a type label to each node: the label for the inlet node is 1, the label for the outlet node is 2, the label for the wall node is 3, and the label for the internal node is 0.
[0015] S102. Based on the node type defined in S101, construct a set of boundary condition parameters including inlet wind speed, inlet wind temperature and particle feeding rate, and set the value range and discretization level of each parameter.
[0016] S103. Using the mesh model obtained in S101 and the parameter set constructed in S102, high-fidelity computational fluid dynamics methods are used to numerically simulate the physical field under different boundary condition combinations, and velocity vectors are extracted to construct a training dataset.
[0017] S104. Train a deep neural network based on the training dataset generated in S103, using mean squared error as the loss function, until the loss function converges or reaches the preset training rounds, thereby obtaining a parameterized surrogate model; wherein, the model input is a 6-dimensional vector containing three-dimensional spatial coordinates and boundary condition parameters, and the output is a 3-dimensional velocity vector at that spatial location.
[0018] Furthermore, in S104, a physical information neural network is used to replace the neural network model that only fits the training dataset, that is, the Navier-Stokes equation residual term is added to the loss function as a physical constraint; or a hybrid model is used, which introduces a physical regularization term on the basis of the neural network model that fits the training dataset.
[0019] Furthermore, the calling form of the velocity field query function in step S3 is as follows: there is no need to pre-calculate the full space velocity field, nor is there a need to perform interpolation processing; during the particle tracking process in step S4, whenever it is necessary to obtain the flow field velocity, the parameterized proxy model is directly called to perform forward inference calculation to obtain the velocity vector prediction value of the current position in real time.
[0020] Further, in step S4, the resultant acceleration described by the differential equation of particle motion is a vector synthesis of drag acceleration and gravitational acceleration; wherein, the drag acceleration is calculated according to the Schiller-Naumann model, which determines the Reynolds number by fluid density, fluid dynamic viscosity, particle diameter and particle relative velocity, and then calculates the drag coefficient, and then obtains the drag acceleration value by combining the particle density and particle relative velocity.
[0021] Furthermore, the step S4 step of updating the particle state using an adaptive step-size integration algorithm specifically includes:
[0022] S401. Define the state variables and their time derivatives, and use the fourth-order Runge-Kutta method to calculate the predicted state for the next time step, and the third-order Runge-Kutta method to calculate the low-order estimate.
[0023] S402. Based on the difference between the predicted state calculated in step S401 and the low-order estimate, calculate the local truncation error estimate.
[0024] S403. If the estimated value of the local truncation error is greater than the error tolerance, the current step is rejected, the integration step size is halved, and sub-step S401 is executed again; if the estimated value of the local truncation error is less than or equal to the error tolerance, the current step is accepted, and the integration step size is updated to the product of the original step size and the safety factor according to the error size, or the original step size is kept unchanged.
[0025] Furthermore, the boundary condition judgment and processing in step S4 includes the following sub-steps:
[0026] S411. If the node type label corresponding to the particle position is 2, or is within the tolerance range of the exit boundary, then the particle is determined to have escaped, relevant information is recorded, and tracking is terminated.
[0027] S412. If the node type label corresponding to the particle position is 3, or if the particle penetrates the wall / the distance is less than the tolerance, then calculate the velocity after the collision and reset the position.
[0028] If the velocity modulus after the collision is less than the preset stagnation velocity threshold, the particle is determined to be stagnant and marked as adsorbed onto the wall, and the tracking is terminated.
[0029] If more than two collisions are detected within a preset time window, it is determined to be an oscillation, and the particles are pushed tangentially along the wall a preset distance to avoid repeated collisions.
[0030] If stagnation or oscillation termination is not triggered, the integral step size will be halved and the calculation will be repeated.
[0031] S413. If the simulation time exceeds the maximum allowed simulation time, or the cumulative integration steps exceed the preset upper limit, it is determined that the particle has not escaped and the tracking is terminated.
[0032] Furthermore, in S412, the calculation of the velocity after the collision is as follows:
[0033] Based on the velocity vector before the collision, it is decomposed into normal and tangential components;
[0034] The normal component is multiplied by the normal restitution coefficient and then reversed, while the tangential component is adjusted according to the tangential friction coefficient. The resulting composite velocity vector is the velocity vector after the collision.
[0035] Furthermore, in S2, the particle simulation parameters also include:
[0036] Stagnation velocity threshold is used to determine whether a particle has stopped due to excessively low velocity.
[0037] The oscillation detection time window is used to determine whether particles repeatedly collide near the wall.
[0038] The upper and lower limits of the integration step size are used to constrain the adjustment range of the adaptive step size.
[0039] Boundary tolerance is used to determine whether a particle is close to the exit boundary.
[0040] Furthermore, the spatial dwell density distribution in step S5 is obtained by dividing the computational domain into statistical grids, traversing the discrete trajectory sequences of all particles, statistically analyzing the percentage of dwell time of particles in each grid cell, and generating a spatial dwell density distribution map.
[0041] Compared with the prior art, the present invention has the following advantages.
[0042] This invention replaces traditional real-time computational fluid dynamics calculations with a parametric proxy model. It takes boundary condition parameters and spatial coordinates as input and directly outputs the velocity vector at any spatial location. This "point-to-point" on-demand query mechanism avoids the computational overhead of pre-generating the entire spatial physics field, and can complete the physics response under new operating conditions within seconds or minutes, making rapid scenario simulation and real-time operating condition prediction possible for digital twin systems. Attached Figure Description
[0043] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The scope of protection of the present invention is not limited to the following description.
[0044] Figure 1 : Overall flowchart of the method in the embodiments of the present invention.
[0045] Figure 2 : A schematic diagram illustrating the construction and invocation of the parameterized proxy model in an embodiment of the present invention.
[0046] Figure 3 Detailed flowchart of the adaptive step-size particle trajectory tracking algorithm of this invention.
[0047] Figure 4 : Schematic diagram of the particle-wall collision processing mechanism in an embodiment of the present invention.
[0048] Figure 5 Example diagram of particle trajectory, residence time distribution and particle escape distribution in a certain type of suspension roasting furnace obtained by the method of the present invention. Detailed Implementation
[0049] The technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.
[0050] The terminology used in the embodiments of this disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of this disclosure. The singular forms “a,” “the,” and “the” as used in the embodiments of this disclosure and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.
[0051] Depending on the context, words such as “if” or “suppose” used here can be interpreted as “when”, “in response to determination”, or “in response to detection”.
[0052] For ease of understanding, the embodiments of this disclosure will be described in detail first.
[0053] like Figure 1-5 As shown, the particle trajectory simulation method for digital twins of mineral calcination in this embodiment can be divided into five core stages. First, a rapid mapping of the physical field is established by constructing a parameterized surrogate model; second, a specific particle simulation scenario and related parameters are defined; then, velocity field information under the target working condition is generated in real time based on the surrogate model; next, particle trajectory tracking including adaptive step size and complex boundary handling is performed; finally, the trajectory data generated by the simulation is post-processed and output.
[0054] The five stages described above will be explained in detail below with reference to the accompanying drawings.
[0055] Step 1: Construct a parameterized proxy model.
[0056] 1.1 Establish a three-dimensional digital geometric model of the calcination equipment, mesh the computational domain, define the set of mesh node coordinates and mesh topology, and clearly distinguish the inlet node set, outlet node set, wall node set, and internal node set to provide geometric identifiers for applying boundary conditions and determining particle boundaries in subsequent steps. Assume the total number of mesh nodes is... The coordinates of each node are represented as follows: , At the same time, each node is assigned a type label: the entry node type label is 1, the exit node type label is 2, the wall node type label is 3, and the internal node type label is 0.
[0057] 1.2 Constructing the Boundary Condition Parameter Set The boundary condition parameter set It should include at least the following industrial adjustable parameters: inlet air velocity , inlet air temperature Pellet feeding rate Each parameter has a preset value range and discretization level, forming a parameter space.
[0058] 1.3. For the boundary condition parameter set Each combination of values High-fidelity computational fluid dynamics methods are used for numerical simulation to obtain the corresponding steady-state or quasi-steady-state physical fields, from which velocity vector values on all grid nodes are extracted. This leads to the construction of a training sample set, where the input for each sample is a vector combining node coordinates and boundary condition parameters. The output is the velocity vector at that node. The training dataset consists of samples from all nodes under all operating conditions.
[0059] 1.4 Construct a parametric surrogate model, which is used to learn the mapping relationship from spatial coordinates and boundary condition parameters to velocity vectors. The specific construction method is as follows:
[0060] The model input is a 6-dimensional vector: three-dimensional spatial coordinates. With three boundary condition parameters .
[0061] The model output is a 3D vector: the velocity vector at that spatial location. .
[0062] A deep neural network is constructed, which adopts a multi-layer fully connected structure, takes the 6-dimensional input vector as input and the 3-dimensional velocity vector as output, and fits the nonlinear mapping relationship between the input and output through training.
[0063] Using the training dataset generated in step 1.3, with mean squared error as the loss function, the deep neural network is trained using an optimizer. The generalization error is monitored through the validation set until the loss function converges or the preset number of training rounds is reached.
[0064] After training, the parameterized surrogate model can receive any combination of spatial coordinates and boundary condition parameters as input and quickly output the predicted velocity vector value at that location.
[0065] 1.5 To improve the prediction accuracy of the model in regions with drastic changes in the physical field, a physical information neural network can be used to replace the pure data-driven model, that is, to add the Navier-Stokes equation residual term as a physical constraint to the loss function; or a hybrid model can be used, introducing a physical regularization term on the basis of the data-driven model.
[0066] Step 2: Define the particle simulation scene and parameters.
[0067] Based on the digital geometric model established in step one, the geometric boundaries and simulation parameters for particle trajectory simulation are defined:
[0068] 2.1 Definition of Geometric Boundary:
[0069] Entry boundary: Mark at least one entry surface in the digital geometry model to specify the spatial range of particle release locations.
[0070] Exit boundary: Mark at least one exit surface in the digital geometry model to determine the termination condition for particles leaving the computational domain.
[0071] Wall boundaries: Mark all internal surfaces of the equipment except for the inlet and outlet as wall boundaries, which are used to define the geometric constraints of particle collisions.
[0072] 2.2 Particle simulation parameter definitions, including:
[0073] Total number of particles , where is a positive integer.
[0074] Initial particle properties include initial position (random or uniformly distributed within the inlet boundary) and initial velocity vector (set to be the same as the local airflow velocity, or set according to process requirements for injection velocity).
[0075] Wall collision recovery coefficient The value ranges from 0 to 1 and is used to describe the degree of normal velocity recovery after a particle collides with a wall.
[0076] Wall tangential friction coefficient The value ranges from 0 to 1 and is used to describe the degree of attenuation of the tangential velocity after a particle collides with a wall.
[0077] Stagnation speed threshold It is used to determine whether a particle has stopped due to its low speed.
[0078] Oscillation detection time window It is used to determine whether particles repeatedly collide near the wall.
[0079] Maximum allowable simulation time This is used to limit the maximum tracking time for a single particle.
[0080] Upper limit of integral step and lower limit This is used to constrain the adjustment range of the adaptive step size.
[0081] Local truncation error tolerance It is used to control the integration accuracy.
[0082] Boundary tolerance It is used to determine whether a particle is close to the exit boundary.
[0083] Step 3: Quickly generate the physical field of the target working condition based on the parameterized proxy model.
[0084] 3.1 Obtain the boundary condition parameters of the current target working condition. The boundary condition parameters are collected in real time by the digital twin system or input by the user through an interactive interface.
[0085]
[0086] 3.2. Combine the target working condition boundary condition parameters with spatial coordinates to construct a velocity field query function. For any spatial location point Compare the coordinates of this point with The vectors are concatenated into a 6-dimensional input vector, which is then input into the parameterized surrogate model constructed in step one for forward inference calculation, directly outputting the predicted velocity vector value at that location.
[0087] 3.3, The velocity field query function It is used in the form of a function call for the particle tracking process in step four. It does not require pre-calculation of the full space velocity field or interpolation processing. It is obtained by the proxy model in real time during each query.
[0088] Step 4: Perform particle trajectory tracking with adaptive step size.
[0089] Release in sequence For each particle, perform the following tracking loop:
[0090] 4.1 Particle Initialization:
[0091] Based on the initial particle properties defined in step 2.2, set the current position of the particle. Current speed .
[0092] Set the current simulation time .
[0093] Set the current integration step size .
[0094] 4.2 Calculate the forces acting on the particle:
[0095] The motion of a particle is described by the following differential equation:
[0096]
[0097]
[0098] The resultant acceleration of a particle in a flow field Traction acceleration and gravitational acceleration composition:
[0099]
[0100] The drag acceleration is calculated using the following formula:
[0101]
[0102] Traction coefficient The Schiller-Naumann model was used for calculation:
[0103]
[0104] in: For fluid density; For fluid dynamic viscosity; Particle density; The diameter of the particle;
[0105] is the gravitational acceleration vector; Re represents the Reynolds number.
[0106] 4.3 The adaptive fourth-order Runge-Kutta method is used for integration:
[0107] Define state variables Its time derivative is:
[0108]
[0109] The predicted state for the next time step is calculated using the fourth-order Runge-Kutta method. :
[0110]
[0111] Meanwhile, a low-order estimate is calculated using the third-order Runge-Kutta method. It is used for local truncation error estimation.
[0112] 4.4 Adaptive step size adjustment:
[0113] Calculate the estimated value of the local truncation error:
[0114]
[0115] like If so, then reject the current step and... After halving, return to step 4.3 to recalculate;
[0116] like Then accept the current step and... Updated to ;
[0117] Otherwise, accept the current step and hold. constant.
[0118] 4.5 Boundary Condition Judgment and Handling:
[0119] Escape from the exit: If The corresponding node type label is 2 (exit node), or Located at the export boundary tolerance defined in step 2.1 If the particle is within the specified range, it is determined that it escaped from that exit, and the escape time is recorded. Escape location and escape velocity The tracking of the particle was terminated.
[0120] Wall collision detection: If The corresponding node type label is 3 (wall node), or Penetrating the wall, or The distance from the wall boundary is less than If the collision occurs, then collision handling will be performed.
[0121] 1. Calculate the collision location (Intersection of the ray and the wall) and velocity before the collision .
[0122] 2. Based on the normal coefficient of restitution and tangential friction coefficient Calculate the velocity after the collision :
[0123]
[0124]
[0125] 3. Reset the particle positions to Speed update to .
[0126] 4. If the velocity modulus after the collision is less than the preset stopping threshold If the speed is 0.01 m / s, the particle is determined to be "stationary", the tracking is terminated and it is marked as "wall adsorption".
[0127] 5. If it is detected within the preset time window If two or more collisions occur consecutively within 0.001 s, it is determined to be "oscillation," and the particles are pushed tangentially along the wall. To avoid repeated collisions.
[0128] 6. Adjust the integration step size Set the current step size to half and return to step 4.3 to recalculate.
[0129] Detention judgment: If Or the accumulated points and steps exceed the preset limit. If the particle does not escape (remains), its current position is recorded. Current speed The reason for termination and the termination of tracking.
[0130] 4.6 State Update and Looping:
[0131] If neither step 4.4 nor 4.5 triggers termination, then accept. As a new status update:
[0132]
[0133]
[0134]
[0135] Then continue executing steps 4.2 to 4.6 according to the step size updated in step 4.4, until the termination condition is triggered.
[0136] Step 5: Trajectory Data Post-processing and Output:
[0137] When all After each particle has been tracked, the following information is summarized and output:
[0138] Discrete trajectory sequence of each particle Stored in chronological order.
[0139] The dwell time of each particle (the time from release to escape or termination).
[0140] Escape exit statistics: the number and proportion of particles escaping from each exit.
[0141] Wall collision statistics: the number of collisions and the distribution of collision locations for each particle.
[0142] Spatial residence density distribution: The computational domain is divided into statistical grids, and the percentage of time particles spend in each grid cell is statistically analyzed.
[0143] This invention employs a modular design. In step one, a clear geometric identification system is established by assigning type labels such as inlet, outlet, wall, and interior to mesh nodes. In step two, the simulation parameters defined directly correspond to the adjustable parameters in the industrial field. In step three, the velocity field query function constructed interacts with the particle tracking engine in step four through a standardized interface. This design makes the method easy to integrate into existing digital twin architectures, supporting real-time process optimization and virtual experiments.
[0144] This invention directly addresses the optimization needs of high-temperature gas-solid two-phase flow processes such as mineral calcination. The output data, including particle trajectories, residence time distribution, escape outlet statistics, and wall collision distribution, are key indicators for evaluating and optimizing calcination uniformity, thermal efficiency, and product quality (such as activity and crystal phase), providing quantifiable decision support for process engineers.
[0145] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "preferred embodiment," "detailed description," or "preferred embodiment," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.
[0146] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Therefore, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.
Claims
1. A particle trajectory simulation method for digital twins of mineral calcination, characterized in that, Includes the following steps: S1. Construct a parameterized proxy model; based on the three-dimensional digital geometric model of the calcining equipment and the industrial adjustable parameters, establish a mapping relationship from spatial coordinates and boundary condition parameters to velocity vectors; S2. Define boundary conditions in the three-dimensional digital geometric model and set particle simulation parameters; Total number of particles, initial properties, wall collision coefficient, integration step size range, error tolerance, and particle stagnation and oscillation determination parameters; S3. Obtain the boundary condition parameters of the current target working condition, construct a velocity field query function, take the coordinates of any spatial location point and the boundary condition parameters as input, and output the predicted velocity vector value at that location in real time through parameterized proxy model inference. S4. Based on the velocity field query function constructed in step S3, release particles sequentially, establish the particle motion differential equation, calculate the net force on the particle and the resulting acceleration, and use an adaptive step-size integration algorithm to solve the problem to update the particle state. After each integration step, perform boundary condition judgment, stagnation judgment and oscillation processing until the termination condition is met. S5. Trajectory data post-processing and output: Summarize the discrete trajectory sequences, dwell time, escape statistics, wall collision statistics, and spatial dwell density distribution information of all particles.
2. The particle trajectory simulation method for mineral calcination digital twins according to claim 1, characterized in that, S1 specifically includes the following sub-steps: S101. Based on the three-dimensional digital geometric model of the calcining equipment, perform mesh generation, define the set of node coordinates and topological relationships, and assign a type label to each node: the label for the inlet node is 1, the label for the outlet node is 2, the label for the wall node is 3, and the label for the internal node is 0. S102. Based on the node type defined in S101, construct a set of boundary condition parameters including inlet wind speed, inlet wind temperature and particle feeding rate, and set the value range and discretization level of each parameter. S103. Using the mesh model obtained in S101 and the parameter set constructed in S102, high-fidelity computational fluid dynamics methods are used to numerically simulate the physical field under different boundary condition combinations, and velocity vectors are extracted to construct a training dataset. S104. Train a deep neural network based on the training dataset generated in S103, using mean squared error as the loss function, until the loss function converges or reaches the preset training rounds, thereby obtaining a parameterized surrogate model; wherein, the model input is a 6-dimensional vector containing three-dimensional spatial coordinates and boundary condition parameters, and the output is a 3-dimensional velocity vector at that spatial location.
3. The particle trajectory simulation method for mineral calcination digital twins according to claim 2, characterized in that, In S104, a physical information neural network is used to replace the neural network model that only fits the training dataset. That is, the Navier-Stokes equation residual term is added to the loss function as a physical constraint; or a hybrid model is used, which introduces a physical regularization term on the basis of the neural network model that fits the training dataset.
4. The particle trajectory simulation method for mineral calcination digital twins according to claim 1, characterized in that, The calling format of the velocity field query function in step S3 is as follows: No need to pre-calculate the velocity field across the entire space, nor to perform interpolation processing; During the particle tracking process in step S4, whenever the flow field velocity needs to be obtained, the parameterized proxy model is directly invoked to perform forward inference calculations and obtain the velocity vector prediction value of the current position in real time.
5. The particle trajectory simulation method for mineral calcination digital twins according to claim 1, characterized in that, In step S4, the resultant acceleration described by the differential equation of particle motion is a vector synthesis of drag acceleration and gravitational acceleration; wherein, the drag acceleration is calculated according to the Schiller-Naumann model, which determines the Reynolds number by fluid density, fluid dynamic viscosity, particle diameter and particle relative velocity, and then calculates the drag coefficient, and then obtains the drag acceleration value by combining the particle density and particle relative velocity.
6. The particle trajectory simulation method for digital twins of mineral calcination according to claim 1, characterized in that, The step S4, which uses an adaptive step-size integral algorithm to update the particle state, specifically includes: S401. Define the state variables and their time derivatives, and use the fourth-order Runge-Kutta method to calculate the predicted state for the next time step, and the third-order Runge-Kutta method to calculate the low-order estimate. S402. Based on the difference between the predicted state calculated in step S401 and the low-order estimate, calculate the local truncation error estimate. S403. If the estimated value of the local truncation error is greater than the error tolerance, the current step is rejected, the integration step size is halved, and sub-step S401 is executed again; if the estimated value of the local truncation error is less than or equal to the error tolerance, the current step is accepted, and the integration step size is updated to the product of the original step size and the safety factor according to the error size, or the original step size is kept unchanged.
7. The particle trajectory simulation method for mineral calcination digital twins according to claim 1, characterized in that, The boundary condition judgment and processing in step S4 includes the following sub-steps: S411. If the node type label corresponding to the particle position is 2, or is within the tolerance range of the exit boundary, then the particle is determined to have escaped, relevant information is recorded and tracking is terminated. S412. If the node type label corresponding to the particle position is 3, or if the particle penetrates the wall / the distance is less than the tolerance, calculate the velocity after the collision and reset the position. If the velocity modulus after the collision is less than the preset stagnation velocity threshold, the particle is determined to be stagnant and marked as wall adsorption, and the tracking is terminated. If more than two collisions are detected within a preset time window, it is determined to be an oscillation, and the particles are pushed tangentially along the wall a preset distance to avoid repeated collisions. If stagnation or oscillation termination is not triggered, the integral step size will be halved and the calculation will be repeated. S413. If the simulation time exceeds the maximum allowed simulation time, or the cumulative integration steps exceed the preset upper limit, it is determined that the particle has not escaped and the tracking is terminated.
8. The particle trajectory simulation method for mineral calcination digital twins according to claim 7, characterized in that, In S412, the calculation of the velocity after the collision is as follows: Based on the velocity vector before the collision, it is decomposed into normal and tangential components; The normal component is multiplied by the normal restitution coefficient and then reversed, while the tangential component is adjusted according to the tangential friction coefficient. The resulting composite velocity vector is the velocity vector after the collision.
9. A particle trajectory simulation method for mineral calcination digital twins according to claim 1, characterized in that, In S2, the particle simulation parameters also include: Stagnation velocity threshold is used to determine whether a particle has stopped due to excessively low velocity; The oscillation detection time window is used to determine whether particles repeatedly collide near the wall surface; The upper and lower limits of the integration step size are used to constrain the adjustment range of the adaptive step size; Boundary tolerance is used to determine whether a particle is close to the exit boundary.
10. A particle trajectory simulation method for mineral calcination digital twins according to any one of claims 1 to 9, characterized in that, The spatial dwell density distribution in step S5 is obtained by dividing the computational domain into statistical grids, traversing the discrete trajectory sequences of all particles, statistically analyzing the percentage of dwell time of particles in each grid cell, and generating a spatial dwell density distribution map.