Different-weight Monte Carlo fusion method for particle crushing

Abstract

The invention relates to the technical field of particle crushing, in particular to a different-weight Monte Carlo fusion method for particle crushing, which comprises the following steps: collecting emission data of particulate matters in pollutants; constructing a different-weight Monte Carlo fusion model: performing MC circulation on the virtual particle swarm, and calculating the time step length of the breaking probability of the virtual particles; simulating the crushing process of the virtual particles to obtain crushed virtual particles, and performing volume merging operation on the sub-particles and the virtual particles; and performing repeated iteration or iteration termination judgment by using the time step length. According to the method, the problem that the relative error is large due to the fact that the total volume conservation cannot be guaranteed in the particle crushing process through a different-weight Monte Carlo method is solved.

Description

Technical Field

[0001] The invention relates to the technical field of particle crushing, and in particular to a Monte Carlo fusion method for particle crushing with different weights. Background Art

[0002] Particle formation and prediction technology has a wide range of applications in many engineering fields, such as controlling the emission of soot pollutants, regulating the morphology, structure and properties of particle products when synthesizing nanoparticles, etc. The generation and evolution process of particles is a key factor in determining the characteristics of particles. In order to more accurately predict the concentration and particle size distribution of particles, it is necessary to simulate and calculate the particle evolution process, particle size distribution characteristics and dispersion characteristics.

[0003] The Population Balance Equation (PBE) describes the change process of the particle size distribution function in time and space. The evolution process of particles is described as a series of dynamic events (nucleation, agglomeration, fragmentation, oxidation, etc.). By solving the PBE equation, we can obtain information such as particle number density, volume (or mass) fraction, and particle size distribution.

[0004] The patent with publication number CN117875143A uses heterogeneous weighted Monte Carlo to analyze the agglomeration process of particles, but cannot analyze the fragmentation process.

[0005] Although the Monte Carlo method can obtain multi-dimensional information of particles, its disadvantage is that it usually consumes more computing resources. The more popular Monte Carlo method is the weighted Monte Carlo method, which can greatly improve the computing efficiency. However, when dealing with the particle crushing process, the total volume conservation cannot be guaranteed, resulting in errors in the calculated total volume. Summary of the invention

[0006] In view of the shortcomings of the existing methods, the present invention mainly solves the problem that the different-weighted Monte Carlo method cannot ensure the conservation of the total volume when processing the particle crushing process, resulting in large relative errors.

[0007] The technical solution adopted by the present invention is: a particle crushing different-weighted Monte Carlo fusion method comprises the following steps:

[0008] Step 1: Collect emission data of particulate matter in pollutants;

[0009] Step 2: Construct a Monte Carlo fusion model with different weights, including: performing MC cycles on the virtual particle group to calculate the time step of the virtual particle fragmentation probability; simulating the fragmentation process of the virtual particles to obtain the virtual particles after fragmentation, and performing volume merging operations on the sub-particles and virtual particles; and using the time step to perform repeated iterations or iterative termination judgments.

[0010] As a preferred embodiment of the present invention, the different-weighted Monte Carlo fusion model includes:

[0011] Step 21, setting the total number of Monte Carlo cycles, the total simulation time and the initial conditions of the simulation conditions;

[0012] As a preferred embodiment of the present invention, the initial conditions of the simulated working condition include: actual particle size spectrum, initial particle number concentration, particle breakup nucleus and particle breakup time scale.

[0013] Step 22, generating virtual particle groups with different numbers and weights;

[0014] As a preferred embodiment of the present invention, step 22 specifically includes:

[0015] The actual particle size spectrum is divided into C particle classes, and the number and representative size of each type of particles in the regional volume V are obtained;

[0016] Calculate the temporary public weight of the virtual particles, w = N / N f0 ; where N is the total number of actual particles in the calculation area volume V, N f0 The total number of virtual particles that are preset.

[0017] Step 23, perform MC cycle and set the number of cycles;

[0018] Step 24, setting the time step according to the probability of virtual particle breakage;

[0019] As a preferred embodiment of the present invention, the formula of the time step is:

[0020]

[0021] Among them, α≤0.01 is the multiplication factor, S i is the crushing core of virtual particle i, N f is the number of virtual particles.

[0022] Step 25, simulating the crushing process of virtual particles;

[0023] As a preferred embodiment of the present invention, step 25 specifically includes:

[0024] Based on its breakage probability, a random method is used to determine whether a virtual particle i has a breakage event within the time step Δt. The formula is:

[0025] r≤1-exp(-S i Δt)≈S i Δt (2)

[0026] Among them, Δt is the time step, S iis the broken core of virtual particle i.

[0027] Step 26: After the virtual particle fragmentation process occurs, the virtual particle weight value and the number of primary particles are updated for the fragmentation events occurring within the time step;

[0028] As a preferred embodiment of the present invention, step 26 specifically includes:

[0029] Virtual particle i undergoes binary fragmentation to obtain sub-particles A and B. A and B inherit the weight of i and their scale is half of i.

[0030] Replace i with A;

[0031] For B, traverse the existing virtual particle groups and find the virtual particle j with the smallest volume difference with B;

[0032] Merge j and B, and update the weight values ​​and number of original particles of i and j after condensation. The formula is:

[0033]

[0034] Among them, w i ,w j and w i ',w j 'represents the weight values ​​of virtual particle i and virtual particle j before and after crushing respectively; w A ,w B represents the weight value of particle A and particle B after crushing; v i ,v j and v i ',v j 'represents the volume of virtual particle i and virtual particle j before and after crushing, respectively; v A ,v B Represents the volume of particles A and B after crushing.

[0035] Step 27: Use the time step to perform iterative judgment;

[0036] As a preferred embodiment of the present invention, step 27 specifically includes:

[0037] If the accumulated value of the time step Δt exceeds the initially set simulation time length, proceed to step 28 , otherwise return to step 24 .

[0038] Step 28, determine the number of MC cycles, when the number of MC cycles exceeds the total number of cycles, average the results of several MC cycles.

[0039] As a preferred embodiment of the present invention, a particle crushing different-weight Monte Carlo fusion system includes: a memory for storing instructions executable by a processor; a processor for executing the instructions to implement a particle crushing different-weight Monte Carlo fusion method.

[0040] As a preferred embodiment of the present invention, a computer readable medium stores a computer program code, and the computer program code implements a different-weighted Monte Carlo fusion method for particle crushing when executed by a processor.

[0041] Beneficial effects of the present invention:

[0042] 1. Compared with the Monte Carlo model with different weights, the model of the present invention can ensure the conservation of the total volume of particles;

[0043] 2. Compared with numerical simulation methods, random probability is used to meet actual conditions, reduce simulation errors, save simulation time, and improve efficiency;

[0044] 3. The present invention simulates the generation and synthesis process of pollutants or nanoparticles, customizes initial data, and adds more initial conditions, i.e., influencing factors, after determining that the simulation results are consistent with the actual results, to determine the impact of external conditions on particle generation, thereby controlling particle generation at the source and improving efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flow chart of the different-weighted Monte Carlo fusion algorithm for describing particle crushing of the present invention;

[0046] Figure 2 It is a comparison of the description accuracy of the particle number concentration by the different-weighted Monte Carlo fusion algorithm, the different-weighted Monte Carlo algorithm and the theoretical analytical solution of the present invention;

[0047] Figure 3 It is a comparison of the description accuracy of the particle mass concentration by the different-weighted Monte Carlo fusion algorithm of the present invention and the different-weighted Monte Carlo algorithm;

[0048] Figure 4 It is the evolution process of the total particle density and the average radius over time obtained by the different-weighted Monte Carlo fusion algorithm, the different-weighted Monte Carlo algorithm and the theoretical analytical solution of the present invention. DETAILED DESCRIPTION

[0049] The present invention is further described below in conjunction with the accompanying drawings and embodiments. This figure is a simplified schematic diagram, which only illustrates the basic structure of the present invention in a schematic manner, and therefore it only shows the components related to the present invention.

[0050] like Figure 1 As shown, a particle-crushing Monte Carlo fusion method with different weights includes the following steps:

[0051] Step 1: Collect the emission data of particulate matter in the pollutants, input the heterogeneous weighted Monte Carlo fusion model, and output the total number density of particles, the geometric mean radius of particles and the mass concentration of particles;

[0052] Step 2: Construct a Monte Carlo fusion model with different weights, including:

[0053] Step 21: Set the total number of Monte Carlo cycles N MC , total simulation time T, input the initial conditions of the simulation conditions;

[0054] The initial conditions of the simulation include: the actual particle size spectrum at the initial moment satisfies monodispersity, that is, all particle sizes are v0 = 1 (dimensionless), the initial particle number concentration N0 = 1000m -3 The calculation area is a 1m*1m*1m cube, the particle breakup kernel is S(v)=1, and the particle breakup time scale is defined as τ brk =1 / S(v0)=1s.

[0055] Step 22, generating virtual particle groups with different numbers and weights;

[0056] This embodiment uses "weighted virtual particles" to generate a virtual particle group, including:

[0057] Discretize the scale spectrum of the actual particle group into C particle classes, and obtain the number and representative scale of each type of particles in the calculation area volume V, where C is 1 to 200; calculate the temporary public weight w = N / N of the virtual particles f0 , where N is the total number of actual particles in the calculation area volume V, N f0 is the total number of virtual particles set in advance; for particle class m, the actual total number of particles is N m , representing the scale v m , generating N fm virtual particles to represent this class N m actual particles, the weight of the virtual particle is w m =N m / N fm , with a scale of v m .

[0058] Step 23, perform Monte Carlo (MC) cycle and set the number of cycles;

[0059] Step 24, setting the time step Δt according to the probability of breakage of the virtual particles;

[0060] The formula for Δt is:

[0061]

[0062] Among them, α≤0.01 is the multiplication factor, S i is the crushing core of virtual particle i, N f is the number of virtual particles.

[0063] Step 25, simulating the crushing process of virtual particles;

[0064] Considering the morphological diversity of virtual particles, a random method is adopted to deal with it; taking the two-dimensional algorithm as an example: for a virtual particle i, a random method is used based on its breakage probability to determine whether it has a breakage event within the time step Δt. The judgment formula is:

[0065] r≤1-exp(-S i Δt)≈S i Δt (2)

[0066] Where r is a random number that satisfies uniform distribution and is located in [0,1]; Δt is the time step and has a dimension of s; if the formula requirements are met, virtual particle i is broken, and a broken particle j is generated, and various state parameters of virtual particles i and j are temporarily saved; if virtual particle i does not participate in the breakage event, the virtual particle group is traversed to continue to determine whether other particles are broken until all virtual particles are determined;

[0067] Step 26: After the virtual particle fragmentation process occurs, the virtual particle weight value and the number of primary particles are updated for the fragmentation events occurring within the time step Δt;

[0068] When virtual particle i undergoes binary breakage, two daughter particles are obtained, namely particle A and particle B. The daughter particles inherit the weight of the parent particle i and have a scale half of the parent particle. When processing the breakage event of virtual particle i, particle A replaces the position of parent particle i. For particle B, find the virtual particle j with the same or closest scale to particle B in the existing virtual particle group, that is, traverse the virtual particle group and find the virtual particle j with the smallest volume difference with particle B. Merge particle B and virtual particle j. The formula for updating the weight value and the number of primary particles of particles i and j after agglomeration is:

[0069]

[0070] Among them, w i ,w j and w i ',w j 'represents the weight values ​​of virtual particle i and virtual particle j before and after crushing respectively; w A ,w B represents the weight value of particle A and particle B after crushing; v i ,v j and v i ',vj 'represents the volume of virtual particle i and virtual particle j before and after crushing, respectively; v A ,v B Represents the volume of particles A and B after crushing.

[0071] When updating the volume of virtual particle j, the fusion algorithm is used to solve the problem that the existing algorithm cannot ensure the conservation of the total volume of particles; that is, the existing method directly replaces particle B with particle j, while the fusion algorithm merges the volumes of particles B and j.

[0072] Step 27, judging the time length, if the accumulated value of the time step Δt exceeds the initially set simulation time length T, proceed to step 28, otherwise return to step 24;

[0073] Step 28: Determine the number of cycles. If the number of MC cycles exceeds the total number of MC cycles N set initially, MC , go to step nine, otherwise return to step 23;

[0074] Step 29: Average the results of multiple MC cycles, output the final simulation result, and end.

[0075] Figure 2 , Figure 3 and Figure 4 The description accuracy of the algorithm of the present invention and the Monte Carlo algorithm with different weights for the total number density N / N0 of particles, the geometric mean radius v / v0 and the particle mass concentration M1(t) are compared. 0exact and M 1exact are the theoretical analytical solutions of the total number density N / N0 of particles and the total volume M1(t) of particles respectively; Figure 2 and Figure 3 It can be seen that for the total number density N / N0 of particles, the relative error between the fusion algorithm of the present invention and the analytical solution is small, both within 2%, while the relative error of the heterogeneous Monte Carlo algorithm is within 2.5%; for the particle mass concentration M1, the accuracy of the fusion algorithm of the present invention is obviously better than that of the heterogeneous Monte Carlo algorithm, and its relative error is 0, while the relative error of the heterogeneous Monte Carlo algorithm is within 0.2%; Figure 4 It can be seen that the changes in the total number density N / N0 and the geometric mean radius v / v0 of the particles obtained by the algorithm of the present invention over time are in good agreement with the theoretical analytical solution; it can be seen that the fusion algorithm of the present invention has higher accuracy than the existing heterogeneous-weighted Monte Carlo algorithm, ensuring the volume conservation of the particle crushing process.

[0076] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A particle-crushing Monte Carlo fusion method with different weights, characterized in that: The following steps are involved: Step 1: Collect the original data of particulate matter; Step 2: Construct a Monte Carlo fusion model with different weights, including: performing MC cycles on the virtual particle group to calculate the time step of the virtual particle fragmentation probability; simulating the fragmentation process of the virtual particles to obtain the virtual particles after fragmentation, and performing volume merging operations on the sub-particles and virtual particles; and using the time step to perform repeated iterations or iterative termination judgments.

2. The particle crushing different-weighted Monte Carlo fusion method according to claim 1 is characterized in that: The different-weighted Monte Carlo fusion model includes: Step 21, setting the total number of Monte Carlo cycles, the total simulation time and the initial conditions of the simulation conditions; Step 22, generating virtual particle groups with different numbers and weights; Step 23, perform MC cycle and set the number of cycles; Step 24, setting the time step according to the probability of virtual particle breakage; Step 25, simulating the crushing process of virtual particles; Step 26: After the virtual particle fragmentation process occurs, the virtual particle weight value and the number of primary particles are updated for the fragmentation events occurring within the time step; Step 27: Use the time step to perform iterative judgment; Step 28, determine the number of MC cycles, when the number of MC cycles exceeds the total number of cycles, average the results of several MC cycles.

3. The Monte Carlo fusion method for particle crushing according to claim 2 is characterized in that: Step 22 specifically includes: The actual particle size spectrum is divided into C particle classes, and the number and representative size of each type of particles in the regional volume V are obtained; Calculate the temporary public weight of the virtual particles, w = N / N f0 ; where N is the total number of actual particles in the calculation area volume V, N f0 is the total number of virtual particles that are preset.

4. The Monte Carlo fusion method for particle crushing according to claim 3 is characterized in that: The formula for the time step is: Among them, α≤0.01 is the multiplication factor, S i is the crushing core of virtual particle i, N f is the number of virtual particles.

5. The Monte Carlo fusion method for particle crushing according to claim 4 is characterized in that: Step 25 specifically includes: Based on its breakage probability, a random method is used to determine whether a virtual particle i has a breakage event within the time step Δt. The formula is: r≤1-exp(-S i Δt)≈S i Δt (2) Among them, Δt is the time step, S i is the broken core of virtual particle i.

6. The Monte Carlo fusion method for particle crushing according to claim 5, characterized in that: Step 26 specifically includes: Virtual particle i undergoes binary fragmentation to obtain sub-particles A and B. A and B inherit the weight of i and their scale is half of i. Replace i with A; For B, traverse the existing virtual particle groups and find the virtual particle j with the smallest volume difference with B; Merge j and B, and update the weight values ​​and number of original particles of i and j after condensation. The formula is: Among them, w i ,w j and w i ',w j 'represents the weight values ​​of virtual particle i and virtual particle j before and after crushing respectively; w A ,w B represents the weight value of particle A and particle B after crushing; v i ,v j and v i ',v j 'represents the volume of virtual particle i and virtual particle j before and after crushing, respectively; v A ,v B Represents the volume of particles A and B after crushing.

7. The Monte Carlo fusion method for particle crushing according to claim 2, characterized in that: Step 27 specifically includes: If the accumulated value of the time step Δt exceeds the initially set simulation time length, proceed to step 28 , otherwise return to step 24 .

8. The Monte Carlo fusion method for particle crushing according to claim 2, characterized in that: The initial conditions of the simulation include: actual particle size spectrum, initial particle number concentration, particle breakup nucleus and particle breakup time scale.

9. The particle crushing heterogeneous weighted Monte Carlo fusion system is characterized by: include: a memory for storing instructions executable by a processor; A processor, configured to execute instructions to implement the Monte Carlo fusion method for particle crushing according to any one of claims 1 to 8.

10. A computer readable medium storing computer program code, characterized in that: The computer program code, when executed by a processor, implements the different-weighted Monte Carlo fusion method for particle crushing as claimed in any one of claims 1 to 8.

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