C-type particle flow state based on double euler model cae simulation method

Abstract

The application relates to the technical field of particle flow simulation, in particular to a CAE simulation method for C-type particle flow state based on a double Euler model, which defines model parameters under a secondary agglomeration theoretical model according to the agglomeration mechanism of C-type particles from initial agglomeration to secondary agglomeration, the model parameters including particle phase diameter, particle phase density, particle phase volume fraction and particle phase shear viscosity, thereby establishing a local dynamic agglomeration particle model (LDAP model) for C-type particles based on an Euler multiphase flow model, and performing C-type particle flow state simulation; the method can realize the setting of numerical simulation conditions and the simulation of the flow behavior of C-type particles through simple flow field calibration and parameter setting, can intuitively reflect the real-time state of the particle agglomerate diameter at any local position in the flow field, has higher accuracy in describing the motion state of particles and gas under the condition of particle agglomerate diameter difference, and can balance the calculation efficiency without increasing the number of particle phases for varying particle diameters.

Description

Technical Field

[0001] This invention relates to the field of particle flow simulation technology, specifically a CAE parameter acquisition and simulation method based on the double Euler model for the agglomeration problem of C-type particles. Background Technology

[0002] Geldart is based on particle density ( ) and fluid density ( The difference between () and particle size ( This paper systematically classifies the particle behavior in gas-solid fluidized beds, and this classification standard is widely used in industry and academia. Geldart Class C particles are defined as particles with a diameter of less than 40 micrometers (…). <40μm) and particle density less than 1400 kg / m³ ( <1400kg / m 3 Geldart C-type particles are fine particles. Due to their high specific surface area and small size effect, these particles have important applications in the preparation and processing of chemical materials such as cement, kaolin, titanium dioxide, alumina, talc, and graphite powder, involving multiple industrial fields such as chemical industry, coal, powder metallurgy, pharmaceutical preparations, and coatings. However, as the particle diameter decreases, the influence of interparticle forces such as van der Waals forces and electrostatic forces is significantly enhanced, leading to the agglomeration of Geldart C-type particles, forming dynamically changing agglomerates. This agglomeration behavior complicates the particle flow characteristics, especially when the particle phase volume fraction is high, making it difficult for traditional numerical simulation methods to accurately characterize the flow state.

[0003] In recent years, numerical simulation of particle-fluid coupled systems has become an important tool for industrial simulation in the field of CAE multiphase flow simulation (such as platforms like Fluent and Openform). Because the forces acting on particles in multiphase flows are extremely complex, it is crucial to accurately represent the influence of interparticle forces in the simulation calculations. Currently, numerical simulation of two-phase flows mainly employs the Euler-Lagrange model and the Two-Fluid Model (TMF). The Euler-Lagrange model includes the Discrete Phase Model (DPM) and the Discrete Element Model (DEM). While the DEM can simulate aggregation behavior by introducing interparticle forces, its computational complexity increases exponentially with the number of particles, making it difficult to meet the needs of industrial-scale simulations. The DPM, on the other hand, only considers the drag force of the fluid on the particles, neglecting interparticle and particle-wall interactions, and therefore cannot characterize aggregation phenomena. TFM treats both the gas and solid phases as continuous phases, simulating dense particle flows by solving the mass, momentum, and energy conservation equations. TFM can indirectly represent interparticle interactions through an interphase force model, offering high computational efficiency and suitability for industrial-scale simulations. However, traditional TFM methods suffer from the following problems when simulating Geldart C-type particles: 1. Aggregate diameter is typically assumed to be a global average, failing to reflect local dynamic changes; 2. The influence of gas-solid phase motion on aggregate diameter is not accurately modeled; 3. Reliable results are only obtained under specific operating conditions, lacking universality.

[0004] In summary, the current technological bottlenecks and research needs are: 1. Accuracy of macroscopic parameters, such as stable prediction of bed height, pressure drop, and volume fraction; 2. Dynamic characterization of aggregates, reflecting local changes in particle aggregate diameter in real time; 3. Precise description of motion state, accurately characterizing the motion behavior of the gas-solid two-phase system under different aggregate diameters. Therefore, developing a numerical simulation method based on the bi-Euler model that can dynamically characterize the aggregation behavior of Geldart C-type particles and adapt to multiple operating conditions has become an urgent technical problem to be solved in this field. Summary of the Invention

[0005] To address the problem of insufficient accuracy in flow field simulation of C-type powders due to their agglomeration characteristics in existing CAE technologies, the present invention aims to provide a CAE simulation parameter acquisition and simulation operation method for C-type particles under flow conditions based on a double Euler model, which can achieve stable prediction of macroscopic parameters, reflect local changes in particle agglomerate size in real time, and accurately characterize the motion state of agglomerates.

[0006] The technical solution adopted by this invention to solve its technical problem is:

[0007] A CAE simulation method for C-type particle flow based on a double Euler model includes the following steps:

[0008] S1: Based on the aggregation mechanism of C-type particles from initial aggregation to secondary aggregation, a secondary aggregation theoretical model is established and the model parameters under the secondary aggregation theoretical model conditions are defined. The model parameters include: particle phase diameter, particle phase density, particle phase volume fraction, and the relationship between particle phase shear viscosity and particle phase volume fraction under the secondary aggregation theoretical model conditions.

[0009] S2: Based on the principle of particle energy balance, a local dynamic diameter model is established. Then, based on the principle of energy balance, the relationship between the agglomerate diameter and the particle phase density, material properties, and flow field parameters is obtained.

[0010] S3: Based on the basic information of the gas-particle multiphase flow device, a geometric model of the gas-particle multiphase flow field is established using modeling software, thereby obtaining a simulation model of the gas-particle multiphase flow field; the simulation model of the gas-particle multiphase flow field is meshed to form a multiphase flow mesh model and imported into a computational fluid dynamics solver;

[0011] S4: In the computational fluid dynamics solver, set the corresponding material for the C-type particles involved and define the physical properties of the material;

[0012] S5: Set up the Euler multiphase flow model and phase interaction in the computational fluid dynamics solver. At the same time, set the boundary conditions of the Euler multiphase flow model, the model parameters under the secondary agglomerated theoretical model conditions, and the physical properties of the material. Import the local dynamic diameter model into the Euler multiphase flow model to enable the Euler multiphase flow model to obtain the dynamic characterization capability of particle phase diameter. Thus, a local dynamic agglomerated particle model (LDAP model) for flow simulation of C-type particles is obtained, and the simulation results are obtained.

[0013] S6: Multiphase flow calibration experiments were conducted on C-type particles, and the experimental results were obtained;

[0014] S7: Compare the simulation results with the experimental results. If the simulation results do not meet expectations, adjust the parameters in the agglomerate diameter relationship in the local dynamic diameter model and continue the simulation. If the simulation results meet expectations, use the LDAP model for subsequent simulation and analyze the variation law of the local dynamic particle phase diameter of C-type particles in post-processing.

[0015] The present invention, which adopts the above technical solution, has the following prominent features compared with the prior art:

[0016] This invention achieves a more accurate characterization of the flow behavior of Class C particles without significantly increasing computational load or reducing computational efficiency. It departs from traditional average particle size methods, providing a direct representation of the real-time state of particle agglomerate diameters in any local part of the flow field. It maintains stable characterization of macroscopic parameters such as bed height, pressure drop, and volume fraction under different operating conditions, adapting to changes in gas velocity. It offers higher accuracy in describing the motion of particles and gas under varying particle agglomerate diameters. This method balances accuracy and computational efficiency and can be integrated into multiphase flow simulation software as a calculation option or module for agglomerated powder multiphase flow in gas-solid multiphase flow. It is applicable to finite volume and finite difference numerical simulations involving Class C particles or particles with similar agglomerated characteristics, demonstrating broad applicability and versatility across various industrial scenarios. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the CAE simulation method for C-type particle flow based on the double Euler model in this invention.

[0018] Figure 2 Images of C-type particles from a macroscopic perspective in this invention;

[0019] Figure 3 These are images of the natural accumulation and aggregation of type C particles in this invention;

[0020] Figure 4 This describes the microscopic morphology of the basic unit of the aggregates formed by C-type particles in this invention.

[0021] Figure 5 This refers to the adhesion between particles of type C in this invention;

[0022] Figure 6 This is a schematic diagram of the stacking model of secondary agglomeration in this invention;

[0023] Figure 7 This is a schematic diagram of the structure when the aggregates in this invention are not in contact with each other;

[0024] Figure 8 This is a schematic diagram of the structure when the aggregates in this invention are mainly in contact relationship;

[0025] Figure 9 This is a schematic diagram of the equivalent apparent gas velocity relationship of the grid cells in the multiphase flow grid model of this invention;

[0026] Figure 10 This is a structural schematic diagram of the experimental apparatus in this invention;

[0027] Figure 11 This describes the friction pressure curve pattern for the corresponding volume fraction of C-type particles in this invention.

[0028] Figure 12 This is a schematic diagram of the three-dimensional mesh in this invention;

[0029] Figure 13 This is the pressure drop-bed height curve used for the mesh independence verification comparison in this invention;

[0030] Figure 14 This is a comparison of numerical simulation and experimental results for different particles in this invention;

[0031] Figure 15 This invention presents a comparison of the particle phase volume fraction cloud map and the particle phase volume fraction cloud map with the particle phase diameter contour lines using the LDAP model.

[0032] Figure 16 In this invention Volume fraction contour plots of the particle phase in the numerical simulation results of the three models: LDAP, etc.

[0033] Figure 17 In this invention The gas phase trajectory lines of the three models (LDAP, LP, and LP) in the flow plant;

[0034] Figure 18 In this invention The particle phase trajectory lines in the flow plant of the three models: LDAP, etc.

[0035] Figure 19 This invention relates to LDAP and Comparison of the variation patterns of bed height and average particle size under different apparent gas velocities in the model;

[0036] Figure 20 The LDAP model in this invention The differences between the model and experimental results regarding pressure drop variation under different apparent gas velocities.

[0037] Explanation of reference numerals in the attached diagram: 1. Air compressor; 2. Dryer; 3. Flow meter; 4. Differential pressure gauge; 5. High-speed camera; 6. Computer. Detailed Implementation

[0038] The present invention will be further illustrated below with reference to specific embodiments. The purpose of this illustration is solely to provide a better understanding of the invention. Therefore, the examples given do not limit the scope of protection of the present invention.

[0039] See Figure 1 The principle block diagram illustrates a CAE simulation method for Class C particle flow based on a double Euler model, comprising the following steps:

[0040] S1: Based on the aggregation mechanism of C-type particles from initial aggregation to secondary aggregation, a secondary aggregation theoretical model is established and the model parameters under the secondary aggregation theoretical model conditions are defined. The model parameters include: particle phase diameter, particle phase density, particle phase volume fraction, and the relationship between particle phase shear viscosity and particle phase volume fraction under the secondary aggregation theoretical model conditions.

[0041] Unlike particles of types A and B, the aggregation density of type C particles is much lower than their true density, and this cannot be adequately explained by coordination number alone or by the closest packing theory. Therefore, in our work, we utilize macroscopic morphology analysis and employ polarizing microscopy and scanning electron microscopy to understand the microscopic packing morphology of type C particles. Figure 2 The image is taken from a macroscopic perspective, showing aggregates of varying diameters dispersed within naturally accumulated Class C particle samples; through... Figure 3 It can be observed that the aggregation of particles in group C begins with the attachment and aggregation of small particles, forming smaller particle aggregates through natural accumulation. Subsequently, during the natural accumulation process, these smaller aggregates are influenced by external factors and further aggregate into larger particle clusters through secondary aggregation. Figure 4 , Figure 5 This study revealed the microscopic mechanism of particle aggregation.

[0042] After forming primary aggregates, group C particles exhibit similar packing behavior to group A and B particles. However, when multiple aggregates form secondary aggregates, the superposition of porosity results in a higher porosity in the secondary aggregates. Consequently, the actual volume fraction of group C particles during fluidization is lower than that of non-viscous particles such as group A and B. Therefore, we established a packing model for secondary agglomeration, as follows: Figure 6 As shown, due to the properties of the particles in group C, they agglomerate during natural deposition under the influence of their own gravity and interparticle forces, forming aggregates. Further external forces cause secondary agglomeration, resulting in larger and denser aggregates. Based on this, we assume that airflow can only pass beside the aggregates and cannot penetrate the secondary aggregates.

[0043] like Figure 6 As shown, firstly, under the influence of the surface energy of type C particles, the particles agglomerate into primary aggregates. At this point, the particles conform well to the natural packing model. Because the outer layers of the primary aggregates have sufficient surface area for the agglomeration to continue, the primary aggregates agglomerate again to form secondary aggregates. At this point, the packing model no longer conforms to natural packing but rather tends towards the natural packing of the aggregates. Therefore, the agglomeration density of type C particles at this stage is... Much smaller than its true density .

[0044] In summary, the secondary agglomeration theoretical model states that C-type particles first form small agglomerates, and then, under the influence of external pressure, undergo secondary agglomeration to form larger particle clusters, leading to an increase in the porosity between the agglomerates. Gas passes more easily from the periphery of the agglomerate particles than through them.

[0045] Therefore, the model parameter definition process includes:

[0046] S101: According to the C-type particle agglomeration process, as the particle diameter decreases, the surface energy relatively increases. Individual particles first form small agglomerates, and then form larger secondary agglomerates through secondary agglomeration. This phenomenon leads to porosity between the particles in the formed agglomerates, and its state differs from the physical meaning of the double Euler model; therefore, in the LDAP model, the particle phase diameter... The value does not take the particle diameter. And take the diameter of the aggregate ,like Figure 7 As shown, the diameter of the aggregates As particle phase diameter At that time, the particle phase density The value is not taken as the true density value of the particles. And take the aggregation density of the particles Correspondingly, the volume fraction of the particulate phase The value should be taken as the volume fraction under the condition of agglomerated particles. These parameter values ​​need to be obtained through specific calculation methods and experimental procedures.

[0047] S102: Determine the aggregation density under particle aggregation conditions based on the morphology and packing model of type C particles. .

[0048] In practice Updated continuously based on the reunion status;

[0049] (29)

[0050] in, The mapping scaling factor is set to 0.6; to ensure that the total particle mass remains constant within the mesh space, the particle phase volume fraction is... It also changed, becoming .

[0051] S103: Based on consolidation and compression experiments above 100 kPa, determine the approximate value of the closest packing model for type C particles, and obtain the true density of type C particles. Volume fraction of type C particles in contact with each other under certain conditions and ;

[0052] In a consolidation compression experiment, under conditions where no external force is present and the weight of the particles is negligible (true density conditions for C-type particles), the volume fraction of C-type particles in contact with each other is... ;Will Defined as the minimum volume fraction when particles activate frictional pressure.

[0053] S104: Based on true density With aggregation density Mapping ratio coefficient and volume fraction Calculate the minimum volume fraction of the activation frictional pressure of the aggregates. When the volume fraction of the particulate phase Less than or equal to the minimum volume fraction At that time, the particle phase shear viscosity in the LDAP model From collision viscosity Dynamic viscosity Composition; when the volume fraction of the particulate phase Greater than the minimum volume fraction At that time, the particle phase shear viscosity in the LDAP model From collision viscosity Dynamic viscosity and friction viscosity It consists of three parts;

[0054] Based on particle phase density With aggregation density Mapping ratio coefficient Calculate the minimum volume fraction of the activation frictional pressure of the aggregates. ,Right now When a pressure of 1000 kPa is applied to group C particles (far exceeding the external force experienced by the particles during fluidization), the volume fraction of group C particles increases from 0.28 to 0.6. At this point, compressing group C particles, such as cement, results in a blocky morphology. Although its density only reaches 60% of its true density, gas has difficulty circulating within the block. Therefore, this volume fraction is taken as... The value is set to 1. This also proves that it is essential to ignore the possibility of gas flow within the agglomerates. At this point, the variation law of the particle phase volume fraction under frictional pressure conditions still conforms well to the Johnson & Jackson model, and its variation law can be obtained through consolidation compression experiments.

[0055] When the relationship between aggregates is mainly based on contact, such as Figure 8As shown, interparticle frictional pressure can cause compressive deformation of aggregated particles, leading to changes in their packing structure. Under the relatively low frictional pressure conditions of a fluidized bed, dislocation behavior between particles is difficult to occur due to interparticle forces, and their packing pattern and the number of contact points are unlikely to change significantly. However, under the condition of C-type particle agglomeration, the shear resistance of the agglomerates depends on van der Waals forces rather than chemical bonds, making agglomerate deformation more likely. Under pressure, the deformation of the particle morphology to adapt to the pressure conditions significantly reduces the porosity around the agglomerates and significantly increases the volume fraction of the particles. This increase in volume fraction does not originate from changes in the lattice arrangement of particle packing under normal stress, but rather from changes in the shape of the agglomerates under shear stress. The energy consumption generated by this shear deformation also simultaneously reduces the collision recovery coefficient between agglomerate particles. Significantly reduced.

[0056] The states of Class C particle agglomerates in the flow field are mainly divided into two types: those where the relationship between agglomerates is mainly contact-based, and those where the relationship between agglomerates is mainly collision-based. This is the critical point for volume fraction.

[0057] a. In the volume fraction of the particulate phase The minimum volume fraction of activated frictional pressure of aggregates is less than or equal to the minimum value. At that time, the particle phase shear viscosity in the LDAP model From collision viscosity Dynamic viscosity Composition. Due to the volume fraction of the particulate phase. Particle phase density The mass of particles in the grid is expressed as the product of the mass conservation equation and the momentum conservation equation. The physical meaning of this relationship is related to the particle diameter. It is irrelevant. However, in the drag coefficient model (Equation 20), the collisional viscosity model (Equation 23), and the dynamic viscosity model (Equation 25), the volume fraction of the particle phase and the particle phase diameter have independent effects on these constitutive equations. The difference in their values ​​will lead to changes in the drag coefficient and the particle phase viscosity, which in turn will lead to differences in the flow field.

[0058] The volume fraction of the particulate phase is influenced by particle aggregation behavior, and its value depends on the particle packing state. The diameter of the particle phase in the aggregated state is influenced by particle aggregation and breakage behavior, and its value depends on the particle's binding energy and collision energy. The variation patterns of the particle phase volume fraction and particle phase diameter are not directly related, but there are differences in the simulation perspective. When class C particles are considered as individual particles, the particle phase density... The value should be taken as the true density of the particles. When class C particles are considered as aggregates, the particle phase density... The value should be taken as the particle aggregation density. Accordingly, to ensure that the total mass relationship of particles in space remains unchanged, the volume fraction of the particle phase is... The value also needs to be adjusted accordingly. Numerous studies have shown that in actual fluidization processes, C-type particles exist as aggregates. Therefore, when the volume fraction of the particle phase does not exceed... In numerical simulations, the volume fraction of the particle phase under agglomerated state needs to be considered. and particle diameter The changing pattern.

[0059] b. In terms of the volume fraction of the particulate phase Minimum volume fraction of activated frictional pressure greater than that of aggregates At this point, the triboviscosity and triboviscosity of the particulate phase are introduced. Under the influence of triboviscosity, the shear viscosity of the particulate phase in the LDAP model changes. From collision viscosity Dynamic viscosity and friction viscosity It consists of three parts, namely, the volume fraction of the particulate phase obeys the law of frictional pressure (Equation 29).

[0060] Regarding the volume fraction of the particulate phase, under frictional pressure, it is affected not only by the agglomeration behavior of type C particles but also by the particle pressure, leading to changes in the packing density per unit space and consequently, changes in the volume fraction of the particulate phase. Therefore, the value of the volume fraction of the particulate phase under frictional pressure also depends on the compression deformation law of the agglomerates. That is, under the condition of single particles of equal mass, the particle compression deformation law follows the packing model and the law of the number of contact points, exhibiting a very small range of volume change. However, under the condition of agglomerated particles of equal mass, during compression, the effect of changes in the packing pattern between agglomerates on volume compression is far less than the effect of changes in the packing pattern caused by shear deformation of agglomerates on volume compression. In other words, macroscopically, type C particles exhibit a unique characteristic of a large compressible volume range. Therefore, regarding the volume fraction of the particulate phase... The minimum volume fraction greater than the activation frictional pressure When doing so, frictional pressure needs to be considered. The changing pattern.

[0061] S105: Obtain the bulk volume fraction of agglomerated particles under various consolidation pressure conditions in the consolidation compression experiment, and fit the consolidation compression curve to obtain the particle phase volume fraction. The relationship between frictional pressure and particles.

[0062] S2: Based on the principle of particle energy balance, a local dynamic diameter model is established. Then, based on the principle of energy balance, the relationship between the agglomerate diameter and the particle phase density, material properties, and flow field parameters is obtained.

[0063] Based on the above analysis, we find that, firstly, particle diameter is a crucial factor not only in the drag coefficient model but also in the collision and dynamic viscosity models. Regarding the basic fluidization characteristics of Class C particles, we already understand that Class C particles are difficult to fluidize, with their minimum fluidization velocity significantly higher than that of Class A particles, which are larger and have relatively weaker interparticle forces. This means that to obtain effective numerical simulation results, the influence of drag needs to be reduced during the simulation process, requiring a higher apparent gas velocity to achieve fluidization. Therefore, modifying the equivalent agglomerate diameter based on the drag coefficient is both practical and necessary.

[0064] Secondly, we need to find more parameters to accurately describe the flow field. In the equilibrium equations, we find that the particle phase density... and volume fraction of particulate phase They always appear in pairs, representing the mass of a particle per unit space, which means that as long as... By maintaining consistency with reality, the two conservation equations can be closed. Furthermore, the particle phase volume fraction plays a crucial role in equations 20, 22, 24, and 28; therefore, we need to obtain a more reasonable particle phase density to accommodate a more reasonable particle phase volume fraction.

[0065] In actual fluidized beds, C-type particles exist in an aggregated state. We can assume that the airflow can only pass beside the aggregates but cannot penetrate them; that is, the aggregates can be considered as individual particles. Therefore, in the method proposed in this invention, the particle aggregation diameter is obtained by establishing a particle aggregation model. and aggregation density This leads to a particle phase viscosity that is more consistent with reality. and volume fraction of particulate phase This allows for a more accurate representation of the fluidization process through numerical simulation.

[0066] Based on the principle of energy balance, a local dynamic diameter model is established, which represents the relationship between agglomerate diameter and volume fraction, particle agglomeration density, and material properties.

[0067] (1)

[0068] In the formula, The diameter of the aggregate. The porosity of the aggregates. Hamek's constant, The viscosity is the gas phase viscosity. For gas phase density, The original diameter of the particle. This represents the initial distance between the two aggregates. For particle aggregation density, It is a dimensionless constant used to evaluate the relative collision velocity of particles, which can be obtained through fluidized bed calibration or particle cohesion-related experiments such as avalanche angle test and particle direct shear test. The average apparent gas velocity corresponding to the operating gas volume. The macroscopic minimum fluidization velocity was obtained experimentally. For gas phase velocity, For particle phase velocity;

[0069] The definition of is:

[0070] (2)

[0071] in, True density of C-type particles;

[0072] The derivation process of the aggregate diameter is as follows;

[0073] When C-type particles achieve a stable fluidized state, the size of the aggregates will reach equilibrium; the cohesive energy of two colliding aggregates... and collision energy The equilibrium equations between them are satisfied, that is:

[0074] (3)

[0075] Cohesive energy It is the energy required to overcome the tensile stress between two aggregates; while collision energy It is the energy generated during the compression of two aggregates in a collision; cohesive energy. The closed model can be represented as:

[0076] (4)

[0077] in, It is the tensile stress of the aggregate. This represents the actual separation distance between the two aggregates. This is the maximum separation distance, at which point the tensile stress of the aggregate remains constant; for spherical aggregates, the tensile stress... Given by the following formula:

[0078] (5)

[0079] in, It refers to interparticle forces. For dry, fine particles, the main component of these interparticle forces is van der Waals force, which can be calculated using the following formula. :

[0080] (6)

[0081] Substituting equations (5) and (6) into (4) yields the following:

[0082] (7)

[0083] neglect Equation (7) is further simplified as follows:

[0084] (8)

[0085] The closure equation is as follows:

[0086] (9)

[0087] in, Indicates compressive displacement. Indicates the maximum compressive displacement. The collision force is expressed as follows: assuming the collision is perfectly elastic and the aggregates of the two colliding particles are of uniform size and porosity, the collision force can be expressed as:

[0088] (10)

[0089] in, Let be an elastic constant, which can be expressed as:

[0090] (11)

[0091] in, Poisson's ratio, Young's modulus;

[0092] Maximum compressive displacement It can be represented as;

[0093] (12)

[0094] in Represents the relative collision velocity of two colliding aggregates;

[0095] (30)

[0096] This is a formula used to evaluate the intensity of motion. Most studies on agglomeration models calculate an equilibrium agglomeration size as the diameter of the agglomerates in the overall fluidized bed. However, in actual fluidization, particle agglomeration is a process of repeated breakup and agglomeration, and the agglomeration particle size is a constantly changing value. In our study, collision velocities are divided into microscopic and macroscopic components. The microscopic component assumes a single grid region as a small fluidized bed. To better reflect the characteristics of a fluidized bed, we use the particle phase motion as the relative motion coordinate system. At this point, the velocity of the particle phase in the small fluidized bed is 0, and the velocity of the gas phase relative to the particle phase is... This refers to the apparent gas velocity of a small fluidized bed, such as... Figure 9 As shown. Applying the relationship from Formula 30 to the microscopic level (i.e., within the region of a small fluidized bed), and defining the relative collision velocity under microscopic conditions: Update the formula:

[0097] (13)

[0098] in, The microscopic critical fluidization velocity is used. Since the relative collision velocity between aggregates is not only related to microscopic motion but also to macroscopic conditions, an evaluation factor for the intensity of macroscopic motion is incorporated. The ratio of apparent gas velocity to the macroscopic minimum fluidization velocity is introduced as a formula to evaluate the intensity of motion. Defined as:

[0099] (14)

[0100] Substituting formula 14 into formula 13, we get:

[0101] (15)

[0102] As a dimensionless empirical coefficient, in our work . It is the average apparent gas velocity corresponding to the operating gas volume. This is the macroscopic critical fluidization velocity, obtained experimentally. Because... It is a parameter determined by the average apparent gas velocity and the macroscopic critical fluidization velocity, and we use it as a standard for evaluating the fluidization state of a fluidized bed in this study.

[0103] Microcritical fluidization rate It is given by the following formula:

[0104] (16)

[0105] Substitute equations (12)-(16) into equation (10), and then obtain the result. Substituting into equation (9), we can obtain:

[0106] (17)

[0107] Substituting equations (8) and (17) into the energy balance equation (3), we obtain the final aggregate diameter function, i.e., Formula 1.

[0108] S3: Based on the basic information of the gas-particle multiphase flow field, a geometric model of the gas-particle multiphase flow field is established using modeling software, thereby obtaining a simulation model of the gas-particle multiphase flow field; the simulation model of the gas-particle multiphase flow field is meshed to form a multiphase flow mesh model and imported into a computational fluid dynamics solver.

[0109] S301: Use preprocessing software to perform unstructured polyhedral mesh generation on the gas-particle multiphase flow field simulation model, and perform physical property labeling and naming conventions on the flow field domain boundary. The flow field domain boundary includes the inlet, outlet, wall, and internal porous medium interface.

[0110] S302: After determining the optimal mesh size distribution through mesh independence verification, import the optimized multiphase flow mesh model into the computational fluid dynamics solver.

[0111] S4: In the computational fluid dynamics solver, set the corresponding material for the C-type particles involved, and define the physical properties of the material; the physical properties of the material should at least include the gas phase density. True density Gas phase viscosity Particulate phase viscosity .

[0112] S5: Set up the Euler multiphase flow model and phase interaction in the computational fluid dynamics solver. At the same time, set the boundary conditions of the Euler multiphase flow model, the model parameters under the secondary agglomeration theory model conditions, and the physical properties of the material. Import the local dynamic diameter model into the Euler multiphase flow model to enable the Euler multiphase flow model to obtain the dynamic characterization capability of particle diameter. This will result in a local dynamic agglomeration particle model for flow simulation of C-type particles, namely the LDAP model, and obtain the simulation results.

[0113] In the Euler multiphase flow model, the first phase is the gas phase and the second phase is the particulate phase. The gas-particle two-phase equilibrium equations include:

[0114] mass conservation equation:

[0115] (18)

[0116] In the formula, This refers to the gas phase volume fraction. This represents the volume fraction of the particulate phase. Particle phase density;

[0117] Momentum conservation equation:

[0118] (19)

[0119] In the formula, For gas phase viscous stress tensor, As gas phase pressure, For particle viscosity stress tensor, For particle phase pressure, It is the acceleration due to gravity. The drag coefficient is used to describe the momentum exchange between the gas and solid phases; the boundary conditions include inlet boundary conditions and outlet boundary conditions, with the inlet boundary condition being a velocity inlet.

[0120] Preferably, momentum exchange in momentum conservation mainly depends on the drag coefficient, and for the drag coefficient, we adopt the Gidaspow drag model; when the particle phase volume fraction The Wen-Yu expression is used when the gas phase volume fraction is... When using Ergun expressions, the expression is employed.

[0121] (20)

[0122] in, Represents the Reynolds number; the calculated traction coefficient or Substituting into formula 19 .

[0123] Preferably, momentum exchange in momentum conservation also depends on the gas phase viscous stress tensor and the particle phase viscous stress tensor;

[0124]

[0125] (twenty one)

[0126] in, For the deviatoric stress tensor, This refers to the gas phase volume viscosity. The bulk viscosity of the particulate phase. This refers to the gas phase shear viscosity. Particulate phase shear viscosity; gas phase shear viscosity Vapor volume viscosity All equal to gas phase viscosity ; Particulate phase shear viscosity From collision viscosity Dynamic viscosity and friction viscosity It consists of three parts, namely;

[0127] (twenty two)

[0128] The formula for calculating collision viscosity is:

[0129] (twenty three)

[0130] in, This is the collision recovery coefficient, with a value of 0.05. For particle temperature, the algebraic field function selected in the particle temperature model in the Euler multiphase flow tab of the solver is the Algebraic model. It is a radial distribution function;

[0131] (twenty four)

[0132] in, The volume fraction of closely packed particles is used; the dynamic viscosity is determined using the Gidaspow model.

[0133] (25)

[0134] The bulk viscosity of the particulate phase was determined using the Lun model.

[0135] (26)

[0136] The friction viscosity was modeled using the Schaeffer model.

[0137] (27)

[0138] in, Frictional pressure, It is the internal friction angle. It is the second invariant of the deviatoric stress tensor.

[0139] Substitute the agglomerate diameter formula into the definition of particle phase diameter in the Euler multiphase flow model, and set the friction pressure in the Euler multiphase flow model according to the secondary agglomeration theory model; thus constructing a local dynamic agglomeration particle model of type C particles, namely the LDAP model.

[0140] Substitute equation (1) into the definition of particle phase diameter in the Euler multiphase flow model; and define the friction pressure for C-type particles;

[0141] in, The frictional pressure is calculated using the Johnson & Jackson semi-empirical formula, which is as follows:

[0142] (28)

[0143] In the formula, Fr, n, and m are constants that are related to the particle properties. This represents the volume fraction of the particulate phase. The minimum volume fraction required to activate frictional pressure.

[0144] S6: Multiphase flow calibration experiments were conducted on C-type particles, and the experimental results were obtained;

[0145] S7: Compare the simulation results with the experimental results. If the simulation results do not meet expectations, adjust the parameters in the agglomerate diameter relationship in the local dynamic diameter model and continue the simulation. Specifically, adjust the parameters in the agglomerate diameter relationship in the local dynamic diameter model by adjusting the dimensionless constant used to evaluate the relative collision velocity of particles. When the simulation results meet expectations, the LDAP model is used for subsequent simulations, and the variation law of the local dynamic particle phase diameter of C-type particles is analyzed in post-processing.

[0146] The experiment using this method is as follows: Figure 10 This is a schematic diagram of the experimental setup consisting of a fluidized bed, an air compressor, a dryer, a differential pressure gauge, and a flow meter. The fluidized bed is made of plexiglass with an inner diameter of 100 mm and a height of 1500 mm, allowing observation of particle motion. Air is the fluidizing medium, and the air compressor controls the outflow of different gas flow rates. The air flows into the dryer for dehydration and drying, removing the influence of air humidity on particle agglomeration. After being metered by the flow meter, the air flows into the fluidized bed and passes through a porous medium that evenly distributes the air, achieving fluidization. Finally, the air is discharged through the porous medium at the top of the fluidized bed. Differential pressure measurement points are located below the porous medium for gas distribution and below the porous medium at the outlet. During the experiment, the differential pressure gauge outputs differential pressure data via a computer connection. The particle flow state during the experiment is recorded using a high-speed camera, and the bed height is measured and recorded using a scale. The experimental materials used in this paper are shown in Table 1, and the materials belong to both Class C and Class A particles.

[0147]

[0148] Table 1

[0149] The experiment recorded the bed height, bed pressure drop, and bed state of the particulate material under different operating conditions (0.248 m / s to 0.424 m / s) to obtain the performance of the particulate material under different operating conditions. The experimental results were compared and analyzed with the numerical simulation results to verify the effectiveness and accuracy of the method proposed in this work.

[0150] To understand the relationship between the volume fraction change of group C particles and the action of external force, a consolidation compression test was also conducted using a lever consolidation apparatus. First, the test material was placed in a metal compression container, with permeable stones placed above and below the material. After sealing the container and aligning it with the scale, it was placed in the lever. Finally, weights of different weights were added to obtain the volume compression change of the particle material under different pressures. The experimental results for groups A and C particles, and the frictional pressure curves for group C particles at corresponding volume fractions obtained using Formula 27, are shown below. Figure 11 As shown, the fitted values ​​of FR, n, and m are 0.05, 0.2, and 9.85, respectively.

[0151] A three-dimensional numerical simulation of the fluidized bed was performed using a double Euler model. The detailed simulation settings are summarized in Table 2.

[0152]

[0153] Table 2

[0154] The internal friction angle was determined by designing an experiment using the Mohr-Coulomb strength criterion. Due to the deformability of class C particles during aggregate collisions, their collision restitution coefficient is... The coefficient of restitution is 0.05, while the collision recovery coefficient of particles in group A is... Set it to 0.9. The model, used as a control, did not include the aggregate diameter compared to the LDAP model. Substitute the particle phase diameter Instead, it adopts the method based on the drag coefficient. Increase control coefficient before The method of controlling the traction coefficient to make the bed height closer to the experimental value was used, k=0.198; As another control model, the equilibrium agglomeration particle size was calculated using the equilibrium agglomeration particle size formula and substituted into the particle phase diameter. , The value is 0.1; the particle phase diameter of model A. Using aggregate diameter Traction coefficient The Gidaspow traction model was used for calculation. To control for variable A, model A was used. Model, The rest of the model settings are the same as the LDAP model. Model, The test particles for the model and LDAP model are cement (CaCO3) particles belonging to class C particles, and the test particles for model A are column chromatography silica gel particles belonging to class A particles. The material properties used in the experimental numerical simulation are shown in Table 3. The initial particle phase volume fraction values ​​are calculated from the weight and volume of the particle materials used in the experiment and the density set for the particle materials.

[0155]

[0156] Table 3

[0157] Before performing numerical simulations, comparisons should be made across different grid resolutions to obtain a suitable grid size, ensuring the accuracy of the calculation results. This paper uses simulations with three different grid sizes—419538 (coarse grid), 690161 (medium grid), and 940570 (fine grid)—to test grid independence. Figure 12 , 13 As shown, the pressure drop-height variation exhibits different behaviors under the same simulation parameter settings. The coarser mesh shows a more significant difference compared to the other meshes, while there is no significant difference between the results from the medium and fine mesh sizes. Therefore, to balance computational efficiency and accuracy, a medium mesh size is used for numerical simulation.

[0158] like Figure 14 As shown, for group A particles at an apparent gas velocity of 0.212 m / s, the bed height in the numerical simulation results without considering agglomeration is 0.45 m, while the bed height in the fluidized bed experiment is 0.47 m, with a bed height difference of 4.2%. For group C particles at an apparent gas velocity of 0.212 m / s, the bed height in the numerical simulation results without considering agglomeration is 0.91 m, while the bed height in the fluidized bed experiment is only 0.5 m, with no obvious fluidization behavior observed. For group C particles at an apparent gas velocity of 0.354 m / s, the bed height in the numerical simulation results considering particle agglomeration is 0.9 m, while the bed height in the fluidized bed experiment is 0.88 m.

[0159] Figure 14 -a indicates that under the condition of type A particles (250 μm, column chromatography silica gel), the column chromatography silica gel particles can be considered to have no aggregation characteristics. Under the numerical simulation conditions of the single particle model without considering aggregation characteristics, the difference in bed height between the numerical simulation and the experimental conditions is less than 5%, indicating that the TFM method has high effectiveness in characterizing multiphase flow. However, in cases such as Figure 14In the fluidized bed of C-type particles (22 μm, cement) shown at point -b, particle agglomeration is evident due to the dominant role of van der Waals forces between particles. In the numerical simulation of the model with the original particle size (22 μm), the fluidized bed only requires an apparent gas velocity of 0.1 m / s to achieve a fluidized bed height of 0.92 m. However, the corresponding experimental results show that the bed height is only 0.5 m, an increase of 0.13 m relative to the original bed height, and channeling occurs locally, failing to achieve effective fluidization. The numerical simulation and experimental results show a significant difference because, under particle agglomeration, the fluidization behavior is affected by the agglomeration diameter. The direct impact, namely the occurrence of agglomeration, is that it significantly increases the gas velocity required for particle fluidization behavior. And in cases such as... Figure 14 In the fluidized bed shown at -c, due to the adoption of the LDAP model, the influence of particle agglomeration on particle fluidization behavior is taken into account. The numerical simulation and experimental bed height show high consistency, with a bed height difference of less than 5%. This indicates that, under the condition of using the agglomeration model, this method can effectively characterize the fluidization behavior of C-type particles (22μm, cement).

[0160] like Figure 15 The images show a comparison of the particle phase volume fraction cloud map and the particle phase volume fraction cloud map with the particle phase diameter contour lines in the LDAP model. It can be seen that the agglomerated particle model can not only obtain an effective macroscopic characterization of the fluidized bed, but also obtain real-time, local particle phase diameters in the numerical simulation results. Patterns of change. Figure 15 The middle d indicates that, and There is a high correlation, which is related to the presence of more particles and a higher particle collision frequency in high volume fraction regions. The loss of particle kinetic energy and the decrease in relative particle velocity due to frequent collisions increase the likelihood of low-speed collisions between particles. These low-speed collisions are more likely to lead to particle aggregation rather than breakage and dispersion, thus resulting in… As the volume fraction increases, the probability of particle collisions decreases in the low volume fraction region, and the particles maintain higher kinetic energy. At this point, particles tend to collide at higher speeds, and the collision behavior is more inclined towards particle breakup and separation than aggregation, thus leading to… The decrease in volume fraction is consistent with the observation in the experiment that high volume fraction regions (i.e., regions with more particle aggregation) exhibit larger aggregate movement. On the other hand, a comparison between the gas phase velocity contour map and the particle phase diameter contour map ( Figure 15 At point e), the apparent air velocity and The conclusion is inversely proportional: higher air velocities and turbulent behavior make collisions between secondary aggregates more prone to high-speed collisions. These collisions are more likely to cause particle breakage, resulting in the disintegration of particles into several smaller aggregates and individual particles. This phenomenon is directly reflected in the LDAP model as follows: In low-velocity regions, particles gain limited kinetic energy, and collisions between particles tend to be low-speed collisions. This collision behavior is more likely to lead to particle aggregation. Improvements were made. The rationality of the LDAP model was verified, and the characterization of the diameter of microscopic local aggregates has greater application value for reactive fluidized beds.

[0161] like Figure 16-18 As shown, Model, A comparison of the flow fields of the three models: the LDAP model, the IDE model, and the IDE model. Figure 16 middle The model exhibits a relatively uniform particle phase distribution. The model exhibits more pronounced bubbles in low-volume-fraction regions and more high-volume-fraction regions; the LDAP model falls somewhere in between. Figure 17 middle The gas in the model exhibits a more uniform trajectory during its ascent, with a more pronounced flow field dispersion in the middle and later stages and weaker vortex characteristics. The model exhibits a large-scale airflow circulation motion with a concentration of high-velocity regions; the LDAP model shows that the gas trajectory during the ascent is characterized by an overall meandering upward motion, with relatively concentrated high-speed regions, and the significance of vortices and the maximum velocity are between the former two. Figure 18 middle The model particle trajectory is highly similar to the airflow trajectory, and there is an inconspicuous vortex distribution in the main gas flow region; The particle trajectories in the model are similar to those of gas and circulate within a large region; the particle motion in the LDAP model exhibits a certain degree of stratification, that is, there are more vortex paths at different heights.

[0162] The model exhibits significantly higher flow field uniformity than the other two models. Bubble phenomena and bubble volume are both reduced. This is because the model only considers the influence of drag on bed height, without taking into account the reduced particle phase viscosity caused by the actual particle size being too low. This suppresses the formation of bubbles and vortices, resulting in a more uniform and stable particle distribution. The phenomena of gas vortex and particle turbulence are also significantly reduced.

[0163] Under the model and the LDAP model, the influence of granular phase shear stress on the flow field is more clearly demonstrated, and significant vortices are generated. Among them, The diameter of the model particles is a constant. Regulation can only rely on volume fraction and cannot be controlled by utilizing differences in particle phase diameter variations using methods similar to the LDAP model. , The model further reduces the volume fraction in the low volume fraction region, leading to an increase in the proportion of the high volume fraction region. This results in a higher local gas velocity, implying a higher local shear rate. The high volume fraction region accounts for 47.03% of the mass and 15.6% of the volume. At this point, the local high-speed airflow tends to form local jets, causing particulate matter to circulate globally. The LDAP model, by introducing variations in aggregate diameter locally, shows smaller particle diameters and lower shear rates in the high-velocity, low-volume-fraction region. The proportion of high volume fraction regions has decreased, and the proportion of high volume fraction regions ( The region with a mass percentage of >28% (35.54% by mass and 12% by volume) exhibits more turbulence, manifesting as more localized small vortices in the particle phase motion trajectory. The number of vortices increases from one (e.g., Figure 18 The number of zones in the central A area has been increased to four (e.g., Zone A). Figure 18 (Areas B, C, D, and E in the text).

[0164] Therefore, the LDAP model provides a more comprehensive gas-particle multiphase flow dynamics system by more precisely describing the impact of viscosity changes caused by agglomeration. Furthermore, the LDAP model more accurately describes the changes in gas and particle phase velocities, as well as the increase or decrease in local particle diameter due to collision factors, thus more accurately reflecting the drag differences caused by agglomeration. This results in a smaller particle diameter in the low volume fraction region and a smoother boundary in the high volume fraction region. This suppresses particle turbulence behavior in the high volume fraction region over a larger area, making it more likely to occur in smaller local areas, thereby increasing the vortex region and correspondingly reducing the bubble volume, which is closer to the actual behavior of fluidized beds.

[0165] Figure 19 The model (LDAP model) established by this method to account for particle aggregation and reduce the density of aggregated particles is compared with... A comparison of the variations in bed height and average particle size between the model and experimental results under different apparent gas velocities. Firstly, both models show high consistency with the experimental results for bed height at an apparent gas velocity of 0.248 m / s. However, as the gas velocity increases... The deviation between the model and experimental values ​​gradually increased, while the LDAP model showed better consistency. As the apparent gas velocity increased, the error between the LDAP model's bed height performance and the experimental values ​​remained within 3%, while... The model's error regarding bed height gradually increased from 2.07% at an apparent gas velocity of 0.248 m / s to 29.39% at an apparent gas velocity of 0.424 m / s. Secondly, the error was calculated using Formula 17. Figure 19 The mass-average particle size curve of the LDAP model was obtained by calculating the equilibrium particle aggregation diameter at different apparent gas velocities using the Xu-Zhu model. Figure 19 In the global aggregation size model, the particle size curves show that the equilibrium aggregate diameter obtained by the LDAP model under low gas velocity conditions is larger than that of the two curves. In the model, as apparent gas velocity increases, the difference between the two gradually decreases until, after crossover, the LDAP model is greater than... The particle phase diameter calculated by the model; in addition, Figure 19 Region A shows a situation where the two models predict similar bed heights, but their equilibrium aggregate sizes differ significantly. Region B shows a situation where the two models have similar equilibrium aggregate sizes, but significant differences in bed height. This trend indicates that the two models produce some differences in prediction results under different gas velocities, but overall remain relatively consistent.

[0166] Region B represents the bed height difference when both have the same mass-average particle size. This indicates that under conditions of local particle size differences, although larger particles increase the difficulty of fluidization, the more prominent effect is that smaller agglomerated particle phase diameters make fluidization easier, leading to a higher bed height. Similarly, in Region A, under the same bed height, the LDAP model exhibits a larger average agglomerated particle phase diameter. The differences between these two regions suggest that, compared to the global particle size model, the improved model (LDAP model) introduced local particle size variations, resulting in lower particle size regions that exhibit easier fluidization, leading to higher bed heights, or, under the same bed height, a more relaxed requirement for the average particle size; thus, it achieves more accurate bed height prediction and characterization capabilities.

[0167] Figure 20 In both the experimental results and the LDAP model, the pressure drop decreases with increasing apparent gas velocity. In contrast, The pressure drop trend in the model is relatively slow. The bed pressure drop trend obtained from the LDAP model at different apparent gas velocities is close to the experimental results. As the apparent gas velocity increases, the pressure drop performance of the LDAP model consistently maintains an error of less than 0.5% compared to the experimental values. The model's error in terms of pressure drop gradually increased from 0.6% at an apparent gas velocity of 0.248 m / s to 6.74% at an apparent gas velocity of 0.424 m / s. Therefore, the LDAP model significantly improves the accuracy of numerical simulation and has good predictive performance.

[0168] By analyzing fluidization behavior, particle phase diameter, fluidized flow field, bed height, and pressure drop, the LDAP model establishes the process of C-type particle agglomeration. , Understanding the changing relationships allows for the correction of particle phase pressure in type C particles during fluidization, enabling adaptive changes in particle size. This results in a more accurate expression of viscosity relationships. Therefore, the numerical simulation results of the LDAP model show a high correlation with experimental values, and its performance in predicting bed conditions is more consistent with experiments compared to traditional methods. Applying this model to the bi-Euler model can provide a solution for large-scale, complex flow field numerical simulations in industrial applications that balances computational efficiency and accuracy, and can provide more detailed information on local dynamic particle phase diameters.

[0169] The invention points of this method are as follows: 1. A secondary agglomeration theoretical model is proposed, clarifying the scheme of using the agglomeration particle size as the numerical simulation particle size. This model clarifies the key parameters. , , The relationship under agglomeration conditions effectively explains the characteristics of difficult fluidization and wide compressibility range of Class C particles, creating a foundation for the reasonable description of the flow field drag relationship and particle phase viscosity relationship by the mass conservation and momentum conservation equations. 2. By introducing a local grid, the relative velocity of the gas particles within the grid region is used as an evaluation of the local motion collision intensity, and the apparent gas velocity is used as an evaluation of the collision intensity between grid regions. A local dynamic diameter model is established. This model, together with the secondary agglomeration theory model, constitutes a local dynamic agglomeration particle model, realizing the dynamic characterization of the local particle size of Class C particles based on the double Euler model.

[0170] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the invention. All equivalent changes made based on the description and drawings of the present invention are included within the scope of the present invention.

Claims

1. A CAE simulation method for C-type particle flow based on a double Euler model, characterized in that, Includes the following steps: S1: Based on the aggregation mechanism of C-type particles from initial aggregation to secondary aggregation, a secondary aggregation theoretical model is established and the model parameters under the secondary aggregation theoretical model conditions are defined. The model parameters include: particle phase diameter, particle phase density, particle phase volume fraction, and the relationship between particle phase shear viscosity and particle phase volume fraction under the secondary aggregation theoretical model conditions. S2: Based on the principle of particle energy balance, a local dynamic diameter model is established. Then, based on the principle of energy balance, the relationship between the agglomerate diameter and the particle phase density, material properties, and flow field parameters is obtained. S3: Based on the basic information of the gas-particle multiphase flow device, a geometric model of the gas-particle multiphase flow field is established using modeling software, thereby obtaining a simulation model of the gas-particle multiphase flow field; the simulation model of the gas-particle multiphase flow field is meshed to form a multiphase flow mesh model and imported into a computational fluid dynamics solver; S4: In the computational fluid dynamics solver, set the corresponding material for the C-type particles involved and define the physical properties of the material; S5: Set up the Euler multiphase flow model and phase interaction in the computational fluid dynamics solver. At the same time, set the boundary conditions of the Euler multiphase flow model, the model parameters under the secondary agglomeration theory model conditions, and the physical properties of the material. Import the local dynamic diameter model into the Euler multiphase flow model to enable the Euler multiphase flow model to obtain the dynamic characterization capability of particle diameter. This will result in a local dynamic agglomeration particle model for flow simulation of C-type particles, namely the LDAP model, and obtain the simulation results. S6: Multiphase flow calibration experiments were conducted on C-type particles, and the experimental results were obtained; S7: Compare the simulation results with the experimental results. If the simulation results do not meet expectations, adjust the parameters in the agglomerate diameter relationship in the local dynamic diameter model and continue the simulation. If the simulation results meet expectations, use the LDAP model for subsequent simulation and analyze the variation law of the local dynamic particle phase diameter of C-type particles in post-processing.

2. The CAE simulation method for C-type particle flow based on the double Euler model according to claim 1, characterized in that: Step S1 specifically includes: S101: According to the C-type particle agglomeration process, as the particle diameter decreases, the surface energy relatively increases. Individual particles first form small agglomerates, and then form larger secondary agglomerates through secondary agglomeration. This phenomenon leads to porosity between the particles in the formed agglomerates, and its state differs from the physical meaning of the double Euler model; therefore, in the LDAP model, the particle phase diameter... The value does not take the particle diameter. And take the diameter of the aggregate ; Particle phase density The value is not taken as the true density value of the particles. And take the aggregation density of the particles Correspondingly, the volume fraction of the particulate phase The value is taken as the volume fraction under the condition of agglomerated particles; S102: Determine the aggregation density under particle aggregation conditions based on the morphology and packing model of type C particles. ; S103: Based on consolidation and compression experiments above 100 kPa, determine the approximate value of the closest packing model for type C particles, and obtain the true density of type C particles. Volume fraction of type C particles in contact with each other under certain conditions and ; S104: Based on true density With aggregation density Mapping ratio coefficient and volume fraction Calculate the minimum volume fraction of the activation frictional pressure of the aggregates. When the volume fraction of the particulate phase Less than or equal to the minimum volume fraction At that time, the particle phase shear viscosity in the LDAP model From collision viscosity Dynamic viscosity Composition; when the volume fraction of the particulate phase Greater than the minimum volume fraction At that time, the particle phase shear viscosity in the LDAP model From collision viscosity Dynamic viscosity and friction viscosity It consists of three parts; S105: Obtain the bulk volume fraction of agglomerated particles under various consolidation pressure conditions in the consolidation compression experiment, and fit the consolidation compression curve to obtain the particle phase volume fraction. The relationship between frictional pressure and particles.

3. The CAE simulation method for C-type particle flow based on the double Euler model according to claim 1, characterized in that: Based on the principle of energy balance, the relationship between the agglomerate diameter and the particle phase density and material properties is obtained as follows: In the formula, The diameter of the aggregate. The porosity of the aggregates. Hamek's constant, The viscosity is the gas phase viscosity. For gas phase density, The original diameter of the particle. This represents the initial distance between the two aggregates. For particle aggregation density, It is a dimensionless constant used to evaluate the relative collision velocity of particles. It needs to be obtained through fluidized bed calibration or particle cohesion-related experiments, including avalanche angle test or particle direct shear test. The average apparent gas velocity corresponding to the operating gas volume. The macroscopic minimum fluidization velocity was obtained experimentally. For gas phase velocity, For particle phase velocity; The definition of is: in, The true density of C-type particles; Accordingly, the parameters in the agglomerate diameter relationship in the local dynamic diameter model are adjusted to adjust the dimensionless constants used to evaluate the relative collision velocities of particles. .

4. The CAE simulation method for C-type particle flow based on the double Euler model according to claim 2, characterized in that: Collision viscosity The calculation formula is as follows: in, This is the collision recovery coefficient, with a value of 0.

05. The particle temperature is solved using the Algebraic model in the solver, which achieves interphase coupling. It is a radial distribution function; in, is the volume fraction of closely packed particles, and is the volume fraction when the particles reach the packing limit. Dynamic viscosity The Gidaspow model is used; The bulk viscosity of the particulate phase was determined using the Lun model. Frictional viscosity The Schaeffer model was adopted. in, Frictional pressure, It is the internal friction angle. This is the second invariant of the deviatoric stress tensor; The parameters in the formulas are all obtained directly from the physical properties of the basic materials or automatically obtained from the computational fluid dynamics solver.

5. The CAE simulation method for C-type particle flow based on the double Euler model according to claim 4, characterized in that: Volume fraction of particulate phase in S105 The relationship between frictional pressure and particle pressure, based on the Johnson & Jackson semi-empirical formula, is expressed as follows: In the formula, Fr, n, and m are constants that are related to the particle properties and are obtained by fitting the consolidation compression curve in S105. This represents the volume fraction of the particulate phase. To activate the minimum volume fraction of frictional pressure, This represents the packing limit of the particles. and Based on the density change under agglomeration conditions, the results were obtained from the consolidation and compression experiments of C-type particles in S103 and S104.

6. The CAE simulation method for C-type particle flow based on the double Euler model according to claim 1, characterized in that: In S3, the mesh generation process includes: S301: Use preprocessing software to perform polyhedral mesh generation on the gas-particle multiphase flow field simulation model, and perform physical property labeling and naming conventions on the flow field domain boundary. The flow field domain boundary includes the inlet, outlet and wall. S302: After determining the optimal mesh size distribution through mesh independence verification, import the optimized mesh model into the computational fluid dynamics solver.

7. The CAE simulation method for C-type particle flow based on the double Euler model according to claim 4, characterized in that: In step S3, the physical properties of the material include at least the gas phase density. True density Gas phase viscosity Particulate phase viscosity .

8. The CAE simulation method for C-type particle flow based on the double Euler model according to claim 7, characterized in that: In S4, the first phase of the Euler multiphase flow model is the gas phase, and the second phase is the particle phase. The gas-particle two-phase equilibrium equations include the mass conservation equation and the momentum conservation equation. In the conservation of momentum, momentum exchange mainly depends on the drag coefficient, for which the Gidaspow drag model is used; when the gas volume fraction The Wen-Yu expression is used when the gas phase volume fraction is... When using Ergun expressions, the expression is employed. in, Represents the Reynolds number, This represents the gas phase volume fraction.

9. The CAE simulation method for C-type particle flow based on the double Euler model according to claim 8, characterized in that: Momentum exchange in the conservation of momentum also depends on the viscous stress tensor of the gas phase. Adhesive stress tensor of particles ; ； ； in, For the deviatoric stress tensor, This refers to the gas phase bulk viscosity. The bulk viscosity of the particulate phase. This refers to the gas phase shear viscosity. Particulate phase shear viscosity; gas phase shear viscosity Vapor volume viscosity All equal to gas phase viscosity .

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