A mixing process prediction method based on particle contact number
By obtaining particle contact number in a small-scale rotary drum reactor and establishing a mixing equation through numerical simulation, the problems of low mixing efficiency and inaccurate prediction in industrial-scale rotary drum reactors are solved. This achieves accurate simulation and prediction of the mixing process, optimizes mixing efficiency, and reduces costs.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- EAST CHINA UNIV OF SCI & TECH
- Filing Date
- 2024-07-29
- Publication Date
- 2026-07-03
AI Technical Summary
Existing mixing technologies suffer from low mixing efficiency, high energy consumption, and long mixing time in industrial-scale rotary drum reactors. Furthermore, existing prediction methods lack precision and are difficult to accurately predict mixing effects.
By conducting particle mixing experiments in a small-scale benchmark drum reactor, the particle contact number was obtained, the mixing equation was fitted, and models under different scale scaling factors were established by combining numerical simulation. The mixing equation of the drum reactor under study was determined, thus realizing the accurate simulation and prediction of the particle mixing process in an industrial-scale drum reactor.
It effectively overcomes the shortcoming of unpredictable particle mixing in industrial-scale rotary drum reactors, and can accurately simulate and predict the mixing process, optimize mixing efficiency and reduce production costs.
Smart Images
Figure CN119007846B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the fields of powder engineering and particle technology, and in particular to a method for predicting mixing processes based on particle contact number. Background Technology
[0002] In many industrial applications, such as pharmaceutical manufacturing, food processing, and the chemical industry, particle mixing is a critical process. The quality of particle mixing directly affects the quality of the final product. Currently, rotary drum reactors are commonly used in industry to achieve uniform mixing of particulate systems. However, existing mixing technologies face several challenges, mainly including low mixing efficiency, high energy consumption, and long mixing times.
[0003] Traditional particle mixing processes rely on empirically set operating parameters, such as equipment rotation speed and particle loading. These parameters are often determined through trial and error, lacking precise scientific calculation support. Furthermore, existing mixing process prediction techniques mainly depend on simplified physical models and laboratory-scale testing, which often fail to accurately predict mixing effects in industrial-scale drum reactors.
[0004] Scaling up a laboratory-scale rotary drum reactor to an industrial-scale reactor involves a "scale-up effect," altering material flow patterns and particle stress characteristics, making it difficult to predict the degree and duration of mixing. Due to the complexity of particle properties, particle contact number is a suitable parameter for quantitatively characterizing particle mixing, directly reflecting the actual contact between particles and applicable to particle systems of different sizes and types. Therefore, it is necessary to develop a new particle mixing prediction method to more accurately simulate, characterize, and predict the mixing process of particles in industrial-scale rotary drum reactors, optimizing mixing efficiency and reducing production costs. Summary of the Invention
[0005] The purpose of this application is to provide a mixing process prediction method based on particle contact number, which can accurately simulate and predict the particle mixing process from small-scale drum reactors to large-scale drum reactors.
[0006] To achieve the above objectives, this application provides the following solution:
[0007] In a first aspect, this application provides a method for predicting mixing processes based on particle contact number, comprising: conducting particle mixing experiments using a benchmark drum reactor to obtain particle contact number at different times during the mixing process; the scale of the benchmark drum reactor is smaller than a scale threshold; fitting the relationship between particle contact number and time during the mixing process to obtain the mixing equation of the benchmark drum reactor, which is used as the benchmark mixing equation; establishing a numerical model of the benchmark drum reactor under different scale scaling factors and performing numerical simulation of the particle mixing process to obtain the mixing equation of the drum reactor under different scale scaling factors; comparing the benchmark mixing equation with the mixing equation of the drum reactor under different scale scaling factors to confirm the variation law of parameters in the mixing equation; determining the mixing equation of the drum reactor to be studied based on the variation law of parameters in the benchmark mixing equation and the mixing equation; the scale of the drum reactor to be studied is larger than a scale threshold; and obtaining the particle mixing process characteristics of the drum reactor to be studied based on the mixing equation of the drum reactor to be studied.
[0008] According to the specific embodiments provided in this application, the following technical effects are disclosed:
[0009] This application provides a method for predicting mixing processes based on particle contact number. By conducting particle mixing experiments using a benchmark drum reactor, a benchmark mixing equation is determined. Then, by establishing numerical models at different scale-up factors, the particle mixing process is numerically simulated, yielding mixing equations for the drum reactor at different scale-up factors. By comparing the benchmark mixing equation with the mixing equations for the drum reactor at different scale-up factors, the variation law of the parameters in the mixing equation is discovered. This variation law is then applied to the drum reactor under study to determine its mixing equation, enabling the prediction of the mixing process in an industrial-scale drum reactor. This application, through the combination of experimental and numerical simulation methods, effectively overcomes the difficulty in predicting particle mixing in industrial-scale drum reactors, and can accurately simulate and predict particle mixing in drum reactors scaled up to industrial scale. Attached Figure Description
[0010] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0011] Figure 1 This is an application environment diagram of a mixing process prediction method based on particle contact number in one embodiment of this application. Detailed Implementation
[0012] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0013] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0014] In one exemplary embodiment, such as Figure 1 As shown, a mixing process prediction method based on particle contact number is provided, including steps 101 to 106. Wherein:
[0015] Step 101: Conduct particle mixing experiments using a reference drum reactor to obtain the number of particle contacts at different times during the mixing process; the scale of the reference drum reactor is smaller than the scale threshold.
[0016] Step 102: Fit the relationship between the number of particles in contact with time during the mixing process to obtain the mixing equation of the reference drum reactor, which serves as the reference mixing equation.
[0017] Step 103: Establish numerical models of the benchmark drum reactor under different scale-up factors, and perform numerical simulation of the particle mixing process to obtain the mixing equations of the drum reactor under different scale-up factors.
[0018] Step 104: Compare the baseline mixing equation with the mixing equations of the drum reactors under different scale-up factors to confirm the variation law of the parameters in the mixing equation.
[0019] Step 105: Based on the baseline mixing equation and the variation law of the parameters in the mixing equation, determine the mixing equation of the drum reactor to be studied; the scale of the drum reactor to be studied is greater than the scale threshold.
[0020] Step 106: Based on the mixing equation of the drum reactor under study, obtain the particle mixing process characteristics of the drum reactor under study.
[0021] By implementing steps 101 to 106 above, and combining experimental and numerical simulation methods, the particle mixing process, which is difficult to observe in experiments, was understood. Particle coordinates at different times were obtained, and the particle contact number was determined based on this data. A mixing equation was derived, and the curve of particle contact number versus time after scaling up was fitted to obtain the equation. Finally, the parameter variation law was determined according to the equipment scale. This method effectively overcomes the shortcoming of unpredictable particle mixing state in industrial-scale rotary drum reactors, and can accurately predict particle mixing in rotary drum reactors scaled up to industrial scale, providing a valuable reference for the design and production of industrial-scale rotary drum reactors.
[0022] In another exemplary embodiment of this application, in order to accurately obtain the number of particle contacts at different times during the mixing process, the number of particle contacts at different times is calculated through a combination of experiments and simulations. Then, step 101 above is replaced by steps 201 to 203:
[0023] Step 201: Determine the particle feeding sequence, particle properties, and particle filling factor. Particle properties include particle type, size, shape, and physical properties.
[0024] Step 202: Establish a numerical model of the benchmark rotary drum reactor, and perform numerical simulation based on the particle feeding sequence, particle properties and particle filling coefficient to obtain the coordinates of all particles at different times during the simulated mixing process.
[0025] Step 203: Conduct particle mixing experiments in a benchmark rotary drum reactor according to the particle feeding sequence.
[0026] Step 204: Use a high-speed camera to capture images of particle distribution during the particle mixing process in the reference drum reactor, and use image analysis to obtain the coordinates of some particles at each time point during the particle mixing process; the partial particles are the unobstructed particles captured by the high-speed camera.
[0027] Step 205: If the error between the particle coordinates of a portion of the particles at the same time and the corresponding particle coordinates obtained from the numerical simulation is less than the error threshold, then all particle coordinates at different times during the simulated mixing process will be used as the particle coordinates of the reference drum reactor at different times during the mixing process.
[0028] Step 206: Based on the particle size and the particle coordinates at different times during the mixing process in the reference drum reactor, calculate the number of particle contacts at different times during the mixing process by means of contact judgment.
[0029] Furthermore, the contact determination in step 206 above specifically involves defining the criterion for contact between two particles as the center-to-center distance |r| between the two particles. i (t)-r j(t)| is less than or equal to the set threshold, which can be adjusted according to the actual application needs. The center distance is calculated as shown in equation (1):
[0030]
[0031] The threshold setting is shown in equation (2):
[0032] R i +R j (2)
[0033] The contact determination is shown in equation (3):
[0034] |r i (t)-r j (t)|≤R i +R j (3)
[0035] Therefore, step 206 above can be replaced by the following steps 301 to 302:
[0036] Step 301: Based on the particle size and the particle coordinates at different times during the mixing process in the reference drum reactor, determine the particle pairs that meet the contact criterion as being in contact; where the contact criterion is r i (t)-r j (t)|≤R i +R j ,|r i (t)-r j (t)| represents the center-to-center distance between particle i and particle j at time t, R i Let R be the particle size of particle i. j Let j be the particle size.
[0037] Step 302: Count the number of particle pairs that are identified as being in contact at the same time, and use this number as the particle contact count at the same time.
[0038] In another exemplary embodiment of this application, step 102 described above may be specifically implemented by the following steps 401 to 402:
[0039] Step 401: Based on the number of particle contacts at different times during the mixing process, plot the curve of the number of particle contacts changing over time.
[0040] Step 402: Perform linear fitting on the curve of the particle contact number changing over time to obtain the mixing equation of the rotary drum reactor.
[0041] The above hybrid equation includes the parameters of the fitted baseline equation. The baseline linear equation is shown in equation (4):
[0042] y = Ax + B (4)
[0043] A and B in equation (4) are the baseline equation parameters obtained from the experiment.
[0044] In another exemplary embodiment of this application, in order to evaluate the dynamic characteristics and system stability of the particle flow, after step 102 above, the method may further include: analyzing the changing trend of the particle contact number over time in the plotted particle contact number versus time curve to evaluate the dynamic characteristics and system stability of the particle flow.
[0045] In another exemplary embodiment of this application, a numerical simulation is performed based on the structure and dimensions of the drum reactor in step 101 to establish a particle mixing numerical model. The geometric model needs to be simplified based on the actual equipment, typically based on the internal space of the drum reactor. Mesh generation must ensure that the mesh retains the basic geometric structure; if necessary, mesh independence verification should be performed to ensure that the mesh can be used for simulation studies. The flow model is usually determined based on the Reynolds number to analyze whether the flow is laminar or turbulent. The particle contact model generally requires the setting of a normal force model and a tangential force model; the contact model can be adjusted according to different properties, and other models, such as a breakup model, can also be added. Therefore, step 103 can be replaced by the following steps 501 to 503:
[0046] Step 501: Establish numerical models of the scaled-up rotary drum reactor according to different scale-up factors; the numerical models include geometric models, flow models and particle contact models.
[0047] Step 502: Using the amplified numerical model, numerical simulation is performed based on the same particle feeding sequence, particle properties, and particle filling coefficient as the benchmark rotary drum reactor experiment to obtain the number of particle contacts at different times during the mixing process in the rotary drum reactor under different scale amplification factors.
[0048] Step 503: Fit the relationship between particle contact number and time in the mixing process of the drum reactor under different scale-up factors to obtain the mixing equation of the drum reactor under different scale-up factors.
[0049] The mixing equations for the rotary drum reactors under different scale-up factors are as shown in equation (5).
[0050] y = A * x+B * (5)
[0051] A in equation (5) * and B * These are the equation parameters obtained from the simulation.
[0052] In another exemplary embodiment of this application, after step 104, it is necessary to compare the parameters obtained from the numerical simulation with the parameters obtained from the experiment in step 102 to make a corresponding accuracy judgment and verify whether the numerical model or the variation law of the parameters is accurate. Therefore, the method in an exemplary embodiment further includes: according to the variation law of the parameters in the mixing equation, based on the mixing equation of the rotary drum reactor under a certain scale factor, obtaining the calculated value of the parameters in the mixing equation of the benchmark rotary drum reactor; comparing the experimental value and the calculated value of the parameters in the benchmark mixing equation to obtain the parameter error; if the parameter error is less than or equal to a preset threshold, it is determined that the variation law of the parameters is correct; if the parameter error is greater than the preset threshold, the amplified numerical model is corrected, and the process returns to step "using the amplified numerical model, according to the same particle feeding sequence, particle properties and particle filling coefficient as the benchmark rotary drum reactor experiment, to perform numerical simulation to obtain the number of particle contacts at different times during the mixing process of the rotary drum reactor under different scale scale factors".
[0053] Through repeated processes, a suitable prediction model for the mixing system is finally obtained. The determined parameter variation patterns are applied to the required large-scale rotary drum reactor to obtain a new prediction equation. Based on the particle contact number, the mixing effect and mixing process of the required industrial-scale rotary drum reactor are predicted, and the final prediction equation is shown in equation (6):
[0054] y = ax + b (6)
[0055] In equation (6), a and b are the equation parameters obtained based on the parameter variation law.
[0056] Typically, the particle contact number eventually reaches a stable value during the mixing process (fluctuating around this stable value). The mixing progress is mainly reflected indirectly through the mixing equation of the rotary drum reactor under study. Before mixing is complete, the predicted value gradually approaches the stable value of the particle contact number as the mixing process continues.
[0057] The aforementioned benchmark drum reactor is a small-scale drum reactor, while drum reactors with different scale-up factors are large-scale drum reactors. This prediction method can solve the simulation and prediction problems of mixing processes in drum reactors scaled up from small-scale to large-scale, and guide the prediction of mixing processes in scaled-up reactors.
[0058] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0059] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A method for predicting mixing processes based on particle contact number, characterized in that, include: Particle mixing experiments were conducted using a benchmark rotary drum reactor to obtain the number of particle contacts at different times during the mixing process; The size of the reference drum reactor is smaller than the size threshold; By fitting the relationship between the number of particles in contact with time during the mixing process, the mixing equation of the benchmark rotary drum reactor is obtained and used as the benchmark mixing equation. Numerical models of the benchmark rotary drum reactor under different scale-up factors were established, and numerical simulations of the particle mixing process were performed to obtain the mixing equations of the rotary drum reactor under different scale-up factors. By comparing the baseline mixing equation with the mixing equations of drum reactors under different scale-up factors, the variation law of parameters in the mixing equation is confirmed; Based on the baseline mixing equation and the variation law of the parameters in the mixing equation, the mixing equation of the drum reactor to be studied is determined; the scale of the drum reactor to be studied is greater than the scale threshold. Based on the mixing equation of the drum reactor under study, the particle mixing process characteristics of the drum reactor under study are obtained.
2. The mixing process prediction method based on particle contact number according to claim 1, characterized in that, Particle mixing experiments were conducted using a benchmark rotary drum reactor to obtain the number of particle contacts at different times during the mixing process, specifically including: Determine the particle feeding sequence, particle properties, and particle filling coefficient; A numerical model of a benchmark rotary drum reactor was established, and numerical simulations were performed based on the particle feeding sequence, particle properties, and particle filling coefficient to obtain the coordinates of all particles at different times during the simulated mixing process. Particle mixing experiments were conducted in a benchmark rotary drum reactor according to the particle feeding sequence. The particle distribution during the particle mixing process inside a reference rotary drum reactor was captured using a high-speed camera, and the coordinates of some particles at each time point during the particle mixing process were obtained using image analysis; the partial particles were unobstructed particles captured by the high-speed camera. If the errors between the particle coordinates of a portion of the particles at the same time and the corresponding particle coordinates obtained from the numerical simulation are all less than the error threshold, then all particle coordinates at different times during the simulated mixing process will be used as the particle coordinates of the reference drum reactor at different times during the mixing process. Based on the particle size and the particle coordinates at different times during the mixing process in the reference rotary drum reactor, the number of particle contacts at different times during the mixing process is calculated by contact judgment.
3. The mixing process prediction method based on particle contact number according to claim 2, characterized in that, Based on the particle size and particle coordinates at different times during the mixing process in the benchmark rotary drum reactor, the number of particle contacts at different moments during the mixing process is calculated through contact determination, specifically including: Based on the particle size and the particle coordinates at different times during the mixing process in the reference rotary drum reactor, particle pairs that meet the contact criterion are determined to be in contact; the contact criterion is |r i (t)-r j (t)|≤R i +R j , where r i (t)-r j (t)| represents the center-to-center distance between particle i and particle j at time t, R i Let R be the particle size of particle i. j Let j be the particle size. The number of particle pairs identified as being in contact at the same time is counted as the particle contact count at that time.
4. The mixing process prediction method based on particle contact number according to claim 1, characterized in that, By fitting the relationship between the number of particles in contact with time during the mixing process, the mixing equation of the rotary drum reactor is obtained, specifically including: Based on the number of particles in contact at different times during the mixing process, plot the curve of the number of particles in contact with time. The mixing equation of the rotary drum reactor is obtained by fitting the curve of the particle contact number changing over time.
5. The mixing process prediction method based on particle contact number according to claim 4, characterized in that, Based on the number of particle contacts at different times during the mixing process, a curve showing the change of the number of particle contacts over time is plotted, followed by: The trend of particle contact number over time is analyzed from the plotted particle contact number curve to evaluate the dynamic characteristics of the particle flow and the system stability.
6. The mixing process prediction method based on particle contact number according to claim 1, characterized in that, Numerical models of the benchmark rotary drum reactor under different scale-up factors were established, and numerical simulations of the particle mixing process were performed to obtain the mixing equations of the rotary drum reactor under different scale-up factors, specifically including: Numerical models of the scaled-up rotary drum reactor were established according to different scale-up factors; the numerical models included equipment geometry models and particle motion models. Using the amplified numerical model, numerical simulations were performed based on the same particle feeding sequence, particle properties, and particle filling coefficient as the benchmark rotary drum reactor experiment, to obtain the number of particle contacts at different times during the mixing process in the rotary drum reactor under different scale amplification factors. By fitting the relationship between particle contact number and time during the mixing process in a rotary drum reactor with different scale-up factors, the mixing equations of the rotary drum reactor under different scale-up factors are obtained.
7. The mixing process prediction method based on particle contact number according to claim 6, characterized in that, By comparing the baseline mixing equation with the mixing equations of drum reactors at different scale-up factors, the variation patterns of the parameters in the mixing equations are confirmed, and the process further includes: Based on the variation law of parameters in the mixing equation, the calculated values of parameters in the mixing equation of the benchmark drum reactor are obtained based on the mixing equation of the drum reactor under a scale-up factor. By comparing the experimental and calculated values of the parameters in the baseline mixture equation, the parameter error can be obtained. If the parameter error is less than or equal to the preset threshold, then the parameter change pattern is considered correct. If the parameter error is greater than the preset threshold, the amplified numerical model is corrected and the process returns to step "Using the amplified numerical model, numerical simulation is performed based on the same particle feeding sequence, particle properties and particle filling coefficient as the benchmark drum reactor experiment, to obtain the number of particle contacts at different times during the mixing process in the drum reactor under different scale amplification factors".