Method for constructing a wet particle agglomeration criterion model based on critical coagulation velocity

Abstract

A wet particle adhesion coagulation criterion model construction method based on critical coagulation velocity belongs to the technical field of particle processing. The purpose of the present application is to establish a wet particle adhesion coagulation criterion model construction method based on critical coagulation velocity which can evaluate the coagulation between particles and the coagulation between particles and wall simultaneously according to the mechanical characteristics of particle size. The present application constructs a wet particle-wet particle model, and then adopts wet particle-wet particle and wet particle-wall to carry out joint evaluation. The present application obtains an efficient model which can jointly evaluate wet particle-wet particle and wet particle-wall based on critical coagulation velocity. According to the method, the coagulation between particles can be directly and efficiently regulated according to the velocity of particles, the coagulation efficiency between particles and wall can be influenced by the initial velocity of wet particle group, and the coagulation between particles and wall can be efficiently judged.

Description

Technical Field

[0001] This invention belongs to the field of particulate matter treatment technology. Background Technology

[0002] The movement of wet particle groups is frequently involved in industrial production, such as in food, chemical, transportation, and pharmaceutical industries, where wet, sticky particles often occur. In some processes, particle-particle adhesion is necessary, such as wet granulation. However, in other cases, particle aggregation can have negative effects, impacting particle-fluid interactions, reducing mass and heat transfer efficiency, and even causing other more serious problems. During the movement of wet particle groups, the particle-wall interaction cannot be ignored in many situations, such as in fluidized beds and turbulent aggregation in containers. However, a model that can comprehensively evaluate the correlation between particle-particle and particle-wall interactions is currently lacking.

[0003] Most current models for wet particle aggregation focus on the aggregation of wet particles themselves. They improve the computational accuracy and simulate the motion of wet particles more realistically by describing the forces acting on the particles more comprehensively or by introducing dimensionless quantities. However, this also makes the models more complex. While these models can achieve very high accuracy in predicting wet particle aggregation, they also result in low computational efficiency. Summary of the Invention

[0004] The purpose of this invention is to establish a wet particle adhesion and aggregation criterion model based on critical aggregation velocity, which can simultaneously evaluate the aggregation between particles and the aggregation between particles and walls, based on the mechanical characteristics at the particle scale.

[0005] The wet particle-wet particle model of this invention is constructed as follows:

[0006] Criterion for efficiently determining the work done to overcome the hydraulic bridge force:

[0007] (16)

[0008] in, For liquid surface tension, For the equivalent radius, The volume of the dimensionless liquid bridge;

[0009] The kinetic energy of the particles during the collision is:

[0010] (17)

[0011] in and These represent the velocities of the two colliding particles;

[0012] Critical coalescence rate obtained from the criterion Obtaining:

[0013] Let W = ,Pick We obtain the following formula:

[0014] (18)

[0015] After rearranging and simplifying, we get The expression:

[0016] (19)

[0017] Add a correction value δ to the model:

[0018] (20)

[0019] Where ρ refers to particle density.

[0020] This invention provides a joint evaluation method for wet particle-wet particle and wet particle-wall surfaces, wherein... The initial particle velocity at which the aggregation peak occurs:

[0021] (1) To determine the aggregation of two particles, then:

[0022] ;

[0023] (2) If it is necessary to determine the separation of two particles, then:

[0024] ;

[0025] (3) If it is necessary to promote particle group-wall aggregation, then:

[0026] ;

[0027] (4) If it is necessary to avoid particle cluster-wall aggregation while promoting particle cluster aggregation, then:

[0028] ;

[0029] (5) If it is necessary to avoid particle cluster-wall aggregation while simultaneously avoiding particle cluster aggregation, then:

[0030] .

[0031] This invention provides an efficient model for jointly evaluating wet particle-wet particle and wet particle-wall aggregation based on critical coalescence velocity. This method allows for direct and efficient control of particle-particle coalescence based on particle velocity, and the initial velocity of the wet particle group can influence the coalescence efficiency between particles and the wall, thus efficiently determining particle-particle and particle-wall coalescence. Attached Figure Description

[0032] Figure 1 This is a flowchart illustrating how the criterion method of this invention is used. Detailed Implementation

[0033] Based on DEM simulation, the liquid bridge force model and particle motion model are combined to simplify the complex wet particle collision process into a combination of the Hertz-Mundling particle contact model and a dynamic normal force. First, the energy dissipation caused by the liquid bridge is determined using Simons' simplified liquid bridge energy dissipation expression. Second, the energy contained in the two particles is derived based on the harmonic values ​​of the particle geometry and mechanical parameters. Finally, the critical state is obtained when the energy dissipation caused by the liquid bridge equals the kinetic energy of the particles. The calculated particle velocity at this point is the critical coalescence velocity. When the particle velocity is less than the critical coalescence velocity, the particles will coalesce after the collision; otherwise, they will bounce off. After obtaining the coalescence criterion between particles, numerical studies show that in the case of head-on collisions, the number of particles adhering to the wall first increases and then decreases with the initial particle velocity, leading to the appearance of a particle-wall coalescence peak. Numerical analysis reveals that the particle-wall coalescence peak always occurs between six and seven times the critical coalescence velocity under this condition, thus obtaining the particle-wall coalescence evaluation criterion.

[0034] Figure 1 This is a flowchart illustrating how to use the model. The specific usage method is as follows: First, the equivalent radius of the particles needs to be obtained. Surface tension of liquid on particle surface Dimensionless liquid bridge volume Equivalent quality and interparticle restitution coefficient Substitute these parameters into the formula The critical coalescence velocity of the particles can then be obtained. Based on the value of the critical coalescence velocity, particle coalescence can be controlled under different scenarios. In the case of two particles colliding, it is only necessary to compare the initial velocities of the particles. With critical coalescence rate The size is fine, when At that time, particles coalesce after the collision. Individual particles will bounce off after a collision. However, in the case of particle swarm collisions, if the goal is to maximize particle adhesion to the wall, the initial velocity of the particle swarm should be... However, if it is necessary to reduce particle-wall adhesion while promoting particle-particle aggregation, then the initial velocity of the particle group should be... If we want to avoid both particle-particle and particle-wall aggregation, then the initial velocity of the particle swarm is... .

[0035] This invention relates to a method for constructing a wet particle-wet particle and wet particle-wall aggregation criterion model based on critical aggregation velocity:

[0036] 1. Couple the particle motion model with the liquid bridge force model to obtain the motion and collision model between wet particles (Equations 1-15);

[0037] 2. Determine the kinetic energy of the wet particles based on the harmonic values ​​of the particle geometry and mechanical parameters (Equation 17);

[0038] 3. Based on previous research, an efficient model for the energy required to overcome the liquid bridge force was obtained (Equation 16).

[0039] 4. By comparing the energy possessed by the particles with the energy required to overcome the liquid bridge force, and setting the two equations equal, the value of the critical coalescence velocity can be obtained. By simply comparing the magnitude of the critical velocity and the particle velocity, it can be determined whether the wet particles coalesce or separate after a collision (Equations 18-20).

[0040] 5. Based on simulation and numerical analysis, the aggregation law of wet particle groups and the wall surface based on the critical aggregation velocity is obtained.

[0041] Particle motion model construction:

[0042] 1) According to Newton's second law, the motion of the particle in Cartesian coordinates is as follows:

[0043] (1)

[0044] 2) According to the angular momentum balance, the angular velocity of the particle is:

[0045] (2)

[0046] in, For particle mass, For particle velocity, For gravity, For normal contact force, For tangential contact force, For drag force, For liquid bridge force, For rotational inertia, For torque, Let ω be the particle angular velocity and T be time.

[0047] Particle contact model construction:

[0048] 1) The normal contact force is:

[0049] (3)

[0050] in This represents the overlap of normal vectors between particles, where n is the normal vector. The normal component of the relative velocity. For the equivalent Young's modulus, For the equivalent radius, For the equivalent mass, β is the damping coefficient. Normal stiffness: , , , , Where e is the coefficient of restitution. , , , These are Young's modulus, Poisson's ratio, radius, and mass of the particle itself. , , , These are the Young's modulus, Poisson's ratio, radius, and mass of the other particle that comes into contact with this particle. This represents the normal overlap between particles.

[0051] 2) The tangential contact force is:

[0052] (4)

[0053] This represents the tangential overlap between particles; t is the tangential vector, representing the direction of this component. The tangential component of the relative velocity. For equivalent shear modulus, Tangential stiffness: , .

[0054] 3) The liquid bridge force is:

[0055] (5)

[0056] (6)

[0057] (7)

[0058] (8)

[0059] (9)

[0060] in For liquid surface tension, The interparticle spacing is dimensionless. h is the distance between particles. For the wetted angle of the particles, The volume of the dimensionless liquid bridge is given.

[0061] The dimensionless liquid bridge volume is defined as:

[0062] (10)

[0063] Where V is the volume of the liquid bridge.

[0064] The volume of the liquid bridge is defined as:

[0065] (11)

[0066] (12)

[0067] (13)

[0068] (14)

[0069] (15)

[0070] , These represent the liquid bridge volumes provided by particle 1 and particle 2, respectively. , , , Let represent the volume of liquid adhering to the surface of particle 1, the ratio of the mass of liquid on the particle surface to the mass of the particle, the mass of the particle, and the density of the liquid, respectively. , , , Let $\mathbf$ represent the volume of liquid adhering to the surface of particle 2, the ratio of the mass of liquid on the particle surface to the mass of the particle, the mass of the particle, and the density of the liquid, respectively.

[0071] Simulations using the coupled model of the particle motion model and the liquid bridge force model (Equations 1-15) can yield the simulated critical coalescence velocity. The squeeze method was used to obtain... Two wet particles are given the same initial velocity and collide head-on. It is observed whether they coalesce. If the two particles do not coalesce, the initial velocity is decreased; otherwise, it is increased. This process continues until an initial velocity accurate to three decimal places is obtained. This velocity is the critical coalescing velocity under this condition. .

[0072] Wet particle-wet particle criterion model construction:

[0073] 1) Based on previous scientific research findings, a highly efficient criterion for determining the work done to overcome the liquid bridge force is derived:

[0074] (16)

[0075] in, For liquid surface tension, For the equivalent radius, The volume of the dimensionless liquid bridge is given.

[0076] 2) According to the work-energy theorem, the kinetic energy of the particles during the collision is:

[0077] (17)

[0078] in and These represent the velocities of the two colliding particles.

[0079] 3) Take the critical case to obtain the critical aggregation rate. The expression:

[0080] Let W = You can take We get the following formula

[0081] (18)

[0082] After rearranging and simplifying, we get The expression:

[0083] (19)

[0084] 4) Based on experimental data analysis, a correction value δ is added to the model to improve its prediction accuracy:

[0085] (20)

[0086] Where ρ refers to particle density.

[0087] In millimeter-level applications, δ is typically taken as 0.015.

[0088] Wet particle-wall model construction:

[0089] In the simulation software EDEM, we introduced 100 particles with a radius of 0.5 mm each into a container from an 8×8 mm plane, causing them to collide. We counted the number of particles adhering to the container wall when entering with different initial velocities and humidity levels. The results showed that within a certain range, the number of particles adhering to the wall initially increased and then decreased with increasing initial velocity, reaching a peak at a certain initial velocity. Changes in humidity also affected the timing of the coalescence peak. Further analysis revealed a correlation between the timing of the peak and the critical coalescence velocity. Specifically, the coalescence peak occurs when the initial velocity of the particle group is between 6 and 7 times the critical coalescence velocity. ∈[6 7 At a certain point, the particle-wall aggregation reaches its maximum value. Thus, particle-wall aggregation can be controlled by the critical aggregation rate.

[0090] The critical coalescence velocity in Table 1 is obtained using a squeeze test method: two wet particles are given different initial velocities and collide head-on. Whether they coalesce is observed. If the two particles do not coalesce, the initial velocity is decreased; otherwise, it is increased, until an initial velocity accurate to three decimal places is obtained. This velocity is the critical coalescence velocity under that condition. .

[0091] Table 1. Relationship between the number of particles adhering to the wall surface and the critical aggregation rate under different humidity levels.

[0092]

[0093] Joint evaluation methods for wet particle-wet particle and wet particle-wall:

[0094] 1) To determine the aggregation of two particles, then:

[0095] ;

[0096] 2) If it is necessary to determine the separation of two particles, then:

[0097] ;

[0098] 3) If it is necessary to promote particle cluster-wall aggregation, then:

[0099] ;

[0100] 4) If it is necessary to avoid particle cluster-wall aggregation while simultaneously promoting particle cluster aggregation, then:

[0101] ;

[0102] 5) If it is necessary to avoid both particle cluster-wall aggregation and particle cluster aggregation, then:

[0103] .

[0104] Table 2 compares the numerical values ​​of the critical coalescence velocity obtained from the simulation experiment with the numerical values ​​of the critical coalescence velocity predicted by the model under different operating conditions. The critical coalescence velocity was obtained in the same way as in Table 1. Under this operating condition, the equivalent radius... The value is between 0.45 and 0.70 mm, the liquid surface tension γ is 0.073 N / m, and the dimensionless liquid bridge volume is... The value is 0.00786. Overall, in the critical cases under these simulated operating conditions, the error of this model is less than 3% in all cases, which means that the prediction results of this model can be considered relatively accurate.

[0105] Table 2. Simulation results under different working conditions Comparison of the value with the value calculated by the criterion.

[0106] .

Claims

1. A method for constructing a wet particle adhesion and aggregation criterion model based on critical aggregation velocity, wherein the kinetic energy at particle collision is: （17） in and These represent the velocities of the two colliding particles; Its features are: The wet particle-wet particle model is constructed as follows: Criterion for efficiently determining the work done to overcome the hydraulic bridge force: （16） in, For liquid surface tension, For the equivalent radius, The volume of the dimensionless liquid bridge; Critical coalescence rate obtained from the criterion Obtaining: Let W = ,Pick We obtain the following formula: （18） After rearranging and simplifying, we get The expression: （19） Add a correction value δ to the model: （20） Where ρ refers to particle density; A joint evaluation method for wet particle-wet particle and wet particle-wall, wherein... The initial particle velocity at which the aggregation peak occurs: (1) To determine the aggregation of two particles, then: ； (2) If it is necessary to determine the separation of two particles, then: ； (3) If it is necessary to promote particle group-wall aggregation, then: ； (4) If it is necessary to avoid particle cluster-wall aggregation while promoting particle cluster aggregation, then: ； (5) If it is necessary to avoid particle cluster-wall aggregation while simultaneously avoiding particle cluster aggregation, then: 。

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