Wet particle adhesion coalescence criterion model construction method based on critical coalescence speed

Abstract

The invention discloses a wet particle adhesion coalescence criterion model construction method based on a critical coalescence speed, and belongs to the technical field of particulate matter treatment. The invention aims to establish a wet particle adhesion coalescence criterion model construction method based on the critical coalescence speed, which can be used for simultaneously evaluating coalescence between particles and coalescence between particles and wall surfaces according to mechanical characteristics of particle sizes. According to the method, a wet particle-wet particle model is constructed, and then wet particle-wet particle and wet particle-wall surface combined evaluation is carried out. According to the method, an efficient model capable of jointly evaluating wet particles-wet particles and wet particles-wall surfaces is obtained on the basis of the critical coalescence speed, and coalescence between particles can be directly and efficiently regulated and controlled according to the speed of the particles on the basis of the method; and the coalescence efficiency between the particles and the wall surface can be influenced through the initial velocity of the wet particle swarms, and the particle-particle coalescence and particle-wall surface coalescence conditions can be efficiently judged.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of particle processing. BACKGROUND

[0002] In industrial production, the movement of wet particles is often involved, such as food, chemical industry, transportation and pharmaceutical industry, etc. Wet sticky particles will appear. In some processes, particle-particle adhesion is necessary, such as wet granulation. However, in some other cases, the coalescence of particles will have a negative impact on the interaction between particles and fluid, reduce the efficiency of mass and heat transfer, and even cause other more serious problems. In the process of wet particle group movement, the particle-wall interaction cannot be ignored in many cases, such as fluidized bed and turbulent coalescence in the container. However, there is currently a lack of a model that can evaluate the particle-particle and particle-wall interaction.

[0003] Most of the current wet particle coalescence models focus on the wet particle coalescence itself, and by more comprehensively describing the force condition in the process of wet particle movement or introducing dimensionless quantity to improve the calculation accuracy of the model and more truly simulate the movement process of wet particles, but this also leads to the complexity of the model. If these models are used to predict wet particle coalescence, although very high accuracy can be achieved, the operation efficiency is low. SUMMARY

[0004] The purpose of the present application is to establish a wet particle adhesion coalescence criterion model construction method based on the critical coalescence velocity according to the mechanical characteristics of particle size, which can evaluate the particle-particle coalescence and particle-wall coalescence at the same time.

[0005] The wet particle-wet particle model of the present application is constructed as follows: The criterion formula for efficiently judging the work done by liquid bridge force: (16) Wherein, is the liquid surface tension, is the equivalent radius, is the dimensionless liquid bridge volume; The kinetic energy of particle collision is: (17) Wherein and respectively represent the velocity of the two particles colliding; The critical coalescence velocity obtained by the criterion is The acquisition: Let W= , take , the following formula is obtained: (18) After moving the term, the expression is simplified as (19) A correction value δ is added to the model: (20) Where ρ is the particle density.

[0006] The present application is a combined evaluation method for wet particles-wet particles and wet particles-wall surfaces, wherein is the initial velocity of the particles when the coalescence peak occurs: (1) If two particles need to be coalesced, then: ; (2) If two particles need to be separated, then: ; (3) If the coalescence of the particle group-wall surface needs to be promoted, then: ; (4) If the coalescence of the particle group-wall surface needs to be avoided while promoting the coalescence of the particle group, then: ; (5) If the coalescence of the particle group-wall surface needs to be avoided while avoiding the coalescence of the particle group, then: .

[0007] Based on the critical coalescence velocity, the present application has obtained an efficient model for combined evaluation of wet particles-wet particles and wet particles-wall surfaces. Based on this method, the coalescence between particles can be directly and efficiently regulated according to the velocity of the particles, and the coalescence efficiency between particles and wall surfaces can be affected by the initial velocity of the wet particle group, so as to efficiently determine the coalescence between particles and wall surfaces. BRIEF DESCRIPTION OF DRAWINGS

[0008] Figure 1 is the flow chart of the criterion method used in the present application. DETAILED DESCRIPTION

[0009] ​The liquid bridge force model is combined with the particle motion model based on DEM simulation, and the complex wet particle collision process is simplified to the Hertz-Mindlin particle contact model and a dynamic normal force. Firstly, the energy dissipation caused by the liquid bridge is determined, and this part uses Simons' simplified liquid bridge energy dissipation expression. Secondly, the energy contained in two particles is derived based on the harmonic value of the particle geometry and mechanical parameters. Finally, as long as the energy dissipation caused by the liquid bridge is equal to the kinetic energy possessed by the particles, the critical state can be obtained, and the calculated particle speed is the critical coalescence velocity. When the particle speed is less than the critical coalescence velocity, the particles will coalesce after collision, otherwise they will bounce off. After obtaining the coalescence criterion between particles, it is found through numerical research that in the case of head-on collision, the number of particles adhering to the wall increases first and then decreases with the initial speed of the particles, which leads to the appearance of the particle-wall coalescence peak. After numerical analysis, it is found that the particle-wall coalescence peak always appears between six to seven times the critical coalescence velocity under this working condition, and thus the particle-wall coalescence criterion is obtained.

[0010] Figure 1 The flow chart of the method for using the model is shown in the figure, and the specific use method is as follows: firstly, the equivalent radius of the particle , the surface tension of the liquid on the surface of the particle , the dimensionless liquid bridge volume , the equivalent mass and the inter-particle restitution coefficient are obtained. The critical coalescence velocity of the particle can be obtained by substituting these parameters into the formula, and the coalescence of the particles can be regulated under different conditions according to the numerical value of the critical coalescence velocity. If it is a two-particle collision, only the initial speed of the particles and the critical coalescence velocity need to be compared. When , the particles coalesce after collision, and when , the particles are bounced off after collision. For the collision of a particle group, if it is necessary to promote the adhesion of the particles to the wall to the maximum extent, the initial speed of the particle group should be , if it is necessary to reduce the adhesion between the particles and the wall and promote the coalescence of the particles, the initial speed of the particle group should be , and if it is necessary to avoid the coalescence of the particles and the wall, the initial speed of the particle group should be .

[0011] The construction method of the wet particle-wet particle and wet particle-wall coalescence criterion model based on the critical coalescence velocity is as follows: 1. The particle motion model is coupled with the liquid bridge force model to obtain the motion and collision model of wet particles (formula 1-15); 2. Determine the kinetic energy of wet particles according to the harmonic value of particle geometry and mechanical parameters (equation 17); 3. Obtain the high-efficiency model of energy required to overcome liquid bridge force according to previous research (equation 16); 4. Compare the energy possessed by the particles and the energy required to overcome the liquid bridge force, and set the two equations equal to obtain the value of the critical coalescence velocity. Only by comparing the critical velocity and the particle velocity can we determine whether the wet particles will coalesce or separate after collision (equations 18-20); 5. According to the simulation analysis and numerical analysis, obtain the coalescence rule of wet particle group and wall surface based on the critical coalescence velocity.

[0012] Particle motion model construction: 1. According to Newton's second law, the motion of particles in Cartesian coordinates is: (1) 2. According to angular momentum balance, the angular velocity of the particle is: (2) Where, is the mass of the particle, is the particle velocity, is the gravity, is the normal contact force, is the tangential contact force, is the drag force, is the liquid bridge force, is the moment of inertia, is the torque, is the particle angular velocity, and T is time.

[0013] Particle contact model construction: 1. The normal contact force is: (3) Where is the normal overlap between particles, n is the normal vector, is the normal component of relative velocity, is the equivalent Young's modulus, is the equivalent radius, is the equivalent mass, β is the damping coefficient, is the normal stiffness: , , , , where e is the restitution coefficient, 、 、 、 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.

[0014] 2) The tangential contact force is: (4) 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: , .

[0015] 3) The liquid bridge force is: (5) (6) (7) (8) (9) 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.

[0016] The dimensionless liquid bridge volume is defined as: (10) Where V is the volume of the liquid bridge.

[0017] The volume of the liquid bridge is defined as: (11) (12) (13) (14) (15) , 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.

[0018] 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. .

[0019] Wet particle-wet particle criterion model construction: 1) Based on previous scientific research findings, a highly efficient criterion for determining the work done to overcome the liquid bridge force is derived: (16) in, For liquid surface tension, For the equivalent radius, The volume of the dimensionless liquid bridge is given.

[0020] 2) According to the work-energy theorem, the kinetic energy of the particles during the collision is: (17) in and These represent the velocities of the two colliding particles.

[0021] 3) Take the critical case to obtain the critical aggregation rate. The expression: Let W = You can take We get the following formula (18) After rearranging and simplifying, we get The expression: (19)

[0022] 4) Based on experimental data analysis, a correction value δ is added to the model to improve its prediction accuracy: (20) where p refers to the particle density.

[0023] In the millimeter scale, δ is usually 0.015.

[0024] Wet particle-wall model construction: We use the simulation software EDEM to let the left and right sides of the 100 particles with a radius of 0.5 mm from the 8x8 mm plane into the container and collide, and we count the number of particles adhering to the wall when the particles enter the container at different initial speeds and humidity. The results show that within a certain range, the number of particles adhering to the wall increases first and then decreases with the increase of the initial speed, and there is a peak value when the initial speed reaches a certain size. The change of humidity also affects the timing of the appearance of the aggregation peak, and further analysis shows that the timing of the appearance of the peak value is related to the critical aggregation speed. It can be found that the timing of the appearance of the aggregation peak is the initial speed of the particle group between 6-7 times the critical aggregation speed. That is, ∈[6 ,7 ], the particle-wall will appear the maximum value of the aggregation number. Thus, the critical aggregation speed can be used to regulate the aggregation of particle-wall.

[0025] The critical aggregation speed in Table 1 is obtained by using the pinch method: giving two wet particles different initial speeds for forward collision, observing whether they aggregate or not, if the two particles do not aggregate, reducing the initial speed, otherwise increasing, until the initial speed is accurate to the third decimal place, which is the critical aggregation speed under this condition .

[0026] Table 1 Relationship between the number of particles adhering to the wall and the critical aggregation speed under different humidity

[0027] Wet particle-wet particle and wet particle-wall joint evaluation method: 1) If two particles need to be aggregated, then: ; 2) If two particles need to be separated, then: ; 3) If the particle group-wall aggregation needs to be promoted, then: ; 4) If the particle group-wall aggregation needs to be avoided while promoting the aggregation of the particle group, then: ; 5) If both particle cluster-wall coalescence and particle cluster coalescence should be avoided, then: .

[0028] Table 2 shows the comparison between the critical coalescence velocity obtained from the simulation and the critical coalescence velocity predicted by the model under different conditions. The critical coalescence velocity is obtained in the same way as in Table 1. In this condition, the equivalent radius of the liquid bridge is in the range of 0.45-0.70 mm, the liquid surface tension γ is 0.073 N / m, and the dimensionless liquid bridge volume V is 0.00786. Overall, in the critical conditions under these simulation conditions, the error of the model is less than 3%, and it can be considered that the prediction result of the model is more accurate.

[0029] Table 2 Comparison of the critical coalescence velocity obtained from the simulation and the critical coalescence velocity calculated by the criterion under different conditions .​​​

Claims

1. A method for constructing a wet particle adhesion and aggregation criterion model based on critical aggregation velocity, characterized in that: 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; The kinetic energy of the particles during the collision is: （17） in and These represent the velocities of the two colliding particles; 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.

2. The method for constructing a wet particle adhesion and aggregation criterion model based on critical aggregation velocity according to claim 1, characterized in that: 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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