Granule crushing pebble bed geometric modeling and heat and mass transfer characteristic calculation method

Abstract

The invention provides a geometric modeling and heat and mass transfer characteristic calculation method for a particle crushing pebble bed. The method comprises the steps of determining coordinates of particles in a complete pebble bed, carrying out a high-temperature pebble bed particle crushing and screening experiment, carrying out geometric modeling on the particle crushing pebble bed, constructing a thermal mass transfer numerical model of the particle crushing pebble bed, solving thermal mass transfer characteristics of the particle crushing pebble bed and the like. According to the method, the authenticity of particle gradation and space structure in the geometric modeling process of the particle crushing pebble bed is improved based on particle crushing and screening experimental data, and the potential uncertainty of the influence of particle crushing on the heat and mass transfer characteristics in the pebble bed can be systematically analyzed and evaluated.

Description

Technical Field

[0001] The present invention relates to the technical field of particle crushing ball bed simulation modeling, and in particular to a particle crushing ball bed geometric modeling and heat and mass transfer characteristic calculation method. Background Art

[0002] Studying the thermal and mass properties of particle-broken pebble beds has important engineering value for the safety analysis and optimized design of packed-bed reactor systems under high-temperature and complex operating conditions. In engineering applications such as nuclear reactor pebble-bed fuel elements and chemical fixed-bed reactors, granular materials can break under multiple factors, including thermal stress and mechanical loads, leading to the reconstruction of the internal pore structure and particle contact network. For example, in fusion reactor blankets, tritium breeder pebble beds are subjected to long-term combined high-temperature thermal loads and neutron irradiation. Particle breakage can cause structural distortion in the bed, affecting tritium retention and local temperature increases, ultimately reducing tritium breeding efficiency and threatening the safety of the blanket structure. Similar situations also exist in other fields, such as graphite sphere breakage in high-temperature gas-cooled reactors, which can cause coolant flow blockage, and catalyst particle breakage in chemical fixed-beds, which can alter the diffusion paths of reactants. Therefore, accurately predicting the impact of particle breakage on the thermal and mass transfer properties of pebble beds is a key scientific issue for ensuring the safe operation and optimized design of packed-bed reactor systems. However, the main challenge facing current technology is how to balance the complexity of the model while retaining the real characteristics of the crushed pebble bed as much as possible when modeling the particle crushing pebble bed geometry, and effectively apply it to numerical calculations to reveal the heat and mass transfer characteristics of the particle crushing pebble bed.

[0003] Under extreme working conditions, in-situ extraction of the particle crushing ball bed structure faces many challenges, and due to the irregularity of the crushed fragments, the structure requires a huge amount of calculation during the numerical simulation process, making it difficult to use directly for engineering calculations. Therefore, existing numerical studies on particle crushing ball beds all use small-sized spherical sub-particles instead of crushed fragments to simplify the calculation. However, existing methods for determining the particle size of sub-particles are mostly based on the theoretical assumption of a single size or fractal distribution. Although this method has certain conveniences in mathematical modeling, it is often difficult to accurately reflect the actual grading characteristics after particle crushing in actual engineering applications. Since the particle crushing process is affected by many factors, such as material properties, stress distribution, crushing mechanism and external environmental conditions, a single size or fractal distribution model is difficult to cover the distribution characteristics of crushed fragments of different sizes after particle crushing. In addition, in the existing particle crushing ball bed simulation modeling process, the crushed sub-particles are usually randomly inserted into the ball bed, but this random filling method cannot truly reflect the spatial aggregation characteristics of the sub-particles at the crushing site. These limitations of geometric modeling not only affect the authenticity of particle grading data, but may also lead to large deviations between numerical simulation results and experiments or engineering practices, thereby restricting the in-depth understanding and analysis of the particle crushing process and its heat and mass transfer characteristics.

[0004] At the same time, current research on particle crushing pebble beds mainly focuses on examining the mechanical properties of pebble beds or single particles, such as particle crushing strength and crushing rate, while there is less research on the effect of particle crushing on the heat and mass transfer characteristics of pebble beds. Pebble beds in industrial systems often involve a multi-physics coupling process of flow-heat transfer-mass transfer: the flow state of the fluid directly affects the efficiency of heat and material transfer, and temperature changes react to the flow state by changing fluid properties such as density and viscosity, while also affecting the diffusion coefficient of the material, forming a complex nonlinear interaction. In addition, changes in the local pore channel structure of the pebble bed caused by particle crushing will also directly affect the heat and mass transfer process within it. However, the specific laws governing the effect of particle crushing on the flow, heat transfer, and mass transfer characteristics within the pebble bed are still unclear.

[0005] Therefore, in order to reveal the heat and mass transfer characteristics under the coupling of multiple physical fields, it is urgent to establish a numerical model of the particle crushing ball bed and construct a corresponding heat and mass transfer characteristics calculation method. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for geometric modeling of a particle crushing ball bed and calculation of heat and mass transfer characteristics to solve the problems existing in the prior art.

[0007] The technical solution employed to achieve the objectives of the present invention is a method for geometric modeling and heat and mass transfer calculation of a particle crushing bed. High-temperature particle crushing and screening experiments were conducted on the bed to determine the bed's crushing rate and the particle size probability distribution of the sub-particles within the bed under the combined effects of high temperature and load. Based on the experimentally obtained sub-particle size probability distribution, a geometric and numerical model of the bed was constructed. A multi-physics coupling solver was used to mesh and numerically solve the geometric model of the bed, determining the heat and mass transfer characteristics of the bed after particle crushing.

[0008] Further, the following steps are included:

[0009] S1. Determine the coordinates of the particles within the complete pebble bed. Using the discrete element method, the complete particles are randomly distributed within the pebble bed. The coordinates of the particles are adjusted by the elastic forces between the particles until the elastic potential energy of the particle system drops below a preset threshold. The particle coordinates at this point are then recorded.

[0010] S2. Conduct a high-temperature pebble bed particle crushing and screening experiment. This experiment consists of two parts: uniaxial compression of the high-temperature pebble bed and screening of the crushed sub-particles. This experiment determines the pebble bed crushing rate and the particle size probability distribution of the sub-particles within the crushed pebble bed under the combined effects of high temperature and load.

[0011] S3. Geometric modeling of the particle crushing bed. Based on the experimentally obtained probability distribution of sub-particle sizes, and while maintaining mass conservation, the sizes of the crushed sub-particles are calculated and randomly inserted into the corresponding original crushed particle regions. The particle coordinates are then adjusted using the discrete element method until the elastic potential energy of the crushed sub-particle system falls below a preset threshold. Finally, the sub-particle coordinates are recorded and the modeling is completed.

[0012] S4. Construct a numerical model of heat and mass transfer in a pellet crushing bed. Establish the multi-physics governing equations for the flow, heat, and mass transfer processes in the pellet crushing bed, and define the boundary conditions and physical parameters of the equations.

[0013] S5. Solve the heat and mass transfer characteristics of the particle crushing pebble bed. Use a multiphysics coupling solver to mesh and numerically solve the geometric model of the particle crushing pebble bed. Calculate and analyze the flow, temperature, and concentration fields within the particle crushing pebble bed, and evaluate the internal resistance pressure drop, convective heat transfer, and convective mass transfer characteristics.

[0014] Furthermore, in step S2, a pressure testing machine is used to apply a load to the ball bed sample under a high temperature environment for uniaxial compression, and then the crushed particle fragments are screened through a screen, and the ball bed crushing rate and fragment size distribution are statistically calculated. The pressure testing machine includes a transmission rod, a pressure head, a ball bed container, a base, a support rod, a pressure sensor, a fixed pin and a high-temperature environmental box arranged in sequence from top to bottom. The upper end of the ball bed container is open and has a cylindrical cavity. The ball bed container is fixed on the base. The ball bed container contains the ball bed sample inside to restrict the lateral movement of the particles. The transmission rod and the pressure head are connected by a fixed pin. The base and the support rod are connected by a fixed pin. The pressure sensor is arranged on the transmission rod to measure the axial pressure applied during the loading process in real time. The lower end of the pressure head extends into the ball bed container to directly contact the ball bed sample, and the force of the transmission rod is evenly applied to the ball bed sample. The high-temperature environmental box covers the experimental area and provides a controllable high-temperature environment. The pressure head, the pebble bed sample, the pebble bed container, the base, the fixing pins, part of the transmission rod and part of the support rod are located in a high temperature environment box.

[0015] Furthermore, in step S2, the crushed particle fragments are screened through a screen, and the ball bed crushing rate and fragment size distribution are calculated. The screen includes multiple screen layers. The screen hole diameter gradually decreases from top to bottom. After screening, the intact particles are located above the screen, and the crushed sub-particles are distributed along the screen with a particle size gradually decreasing from top to bottom. By calculating the percentage of fragments of different sizes, the particle size d of the sub-particles after crushing can be used as the particle size d of the sub-particles after crushing. s The probability distribution P(d s ), thereby characterizing the crushing characteristics of a real pebble bed under typical high temperature and load.

[0016] Furthermore, step S3 specifically includes the following sub-steps:

[0017] S3.1. Calculate the number of broken particles to be replaced based on the breakage rate obtained in step S2. in is the breakage rate.

[0018] S3.2, randomly select N from the complete granular bed generated in step S1. c The particles are regarded as broken particles and deleted from the complete ball bed. The space where these particles originally reside is recorded as the set {Ω i |i=1,2,…,M c}.

[0019] S3.3. Generate a probability distribution P(d s ) and mass conservation constraint ∑m ij =M i The set of broken particles, where m ijis the mass of the jth sub-particle generated by the i-th broken particle, M i is the mass of the original crushed particles.

[0020] S3.4. Randomly distribute the sub-particles to the Ω corresponding to the original broken particles. i region, thus considering the spatial aggregation effect of broken fragments at the broken site. Assuming that the breakage of a small number of particles does not affect the contact network of other unbroken particles, the discrete element method of step S1 is used to iteratively adjust the position of the sub-particles until the elastic potential energy of the system converges. Finally, the geometric parameterized model of the particle crushing ball bed is output and modeled using 3D modeling software. At the same time, in order to reduce the inlet and outlet effects, the inlet and outlet areas of the ball bed are extended by ≥10d. p Length of the inlet and outlet sections, where d p The complete particle size.

[0021] Furthermore, the control equations of step S4 are composed of the following conservation equations:

[0022] A. Mass Conservation Equation: Continuity Equation

[0023]

[0024] B. Momentum conservation equation: Navier-Stokes equation

[0025]

[0026] C. Energy conservation equation: Heat transfer equation

[0027]

[0028] D. Component Conservation Equation: Mass Transfer Equation

[0029]

[0030] Where ρ is density, t is time, and u is velocity. is the Laplace operator, p is pressure, μ is dynamic viscosity, F is volume force, T is temperature, λ is thermal conductivity, C p is the constant pressure specific heat capacity, Φ is the internal heat source intensity, c is the concentration, D is the diffusion coefficient, and S is the mass source intensity. The boundary conditions of the pebble bed can be set using Dirichlet conditions to apply velocity, temperature, and concentration distribution as the inlet boundary. Set the pressure distribution as the outlet boundary. The flow at the wall is set to the no-slip condition u=0, the heat transfer can be set to constant temperature, constant heat flow, or convection boundary, and the mass transfer can be set to Neumann boundary conditions.

[0031] Furthermore, the flow field, temperature field, and concentration field in the pebble bed are directly calculated using a multi-physics coupling solver. The heat and mass transfer characteristics of the pebble bed are evaluated by calculating the resistance pressure drop coefficient f, convective heat transfer coefficient h, and convective mass transfer coefficient k based on the definition formula:

[0032] Resistance pressure drop coefficient f:

[0033] Convective heat transfer coefficient h:

[0034] Convective mass transfer coefficient k:

[0035] Where ε is the porosity of the pebble bed, u in is the fluid velocity at the pebble bed inlet, subscript in represents the pebble bed inlet, V s is the total volume of particles in the pebble bed, subscript s represents solid particles, A s is the total surface area of ​​the solid particles in the pebble bed, and are the average temperatures of the particle surface and fluid domain in the pebble bed, and are the average concentrations on the particle surface and in the fluid domain within the pebble bed, respectively.

[0036] The present invention also discloses an application of the method according to any one of the above items for evaluating the effect of particle breakage on heat and mass transfer characteristics within a tritium breeder pebble bed in a fusion reactor blanket.

[0037] Furthermore, the tritium breeder particles are made of lithium silicate with a particle size of 0.8 to 1.2 mm. The randomly packed cylindrical pebble bed is 40 mm tall and 50 mm in diameter. Based on the operating environment of a real fusion reactor blanket, the high-temperature environmental chamber temperature is maintained at 400°C, and the pressure loads are set at 4 MPa and 6 MPa, respectively, to account for the pebble bed's breakage under extreme operating conditions.

[0038] Furthermore, the COMSOL Multiphysics multi-physics coupling solver was used to calculate the helium flow rate and pressure, the pebble bed temperature, and the tritium concentration distribution in the pebble bed. Then, the resistance pressure drop coefficient f, the convective heat transfer coefficient h, and the convective mass transfer coefficient k in the pebble bed were calculated using the definition formula to evaluate its heat and mass transfer characteristics.

[0039] The technical effects of the present invention are unquestionable:

[0040] A. Data obtained from high-temperature pebble bed particle crushing and screening experiments can more realistically reflect the actual gradation characteristics of sub-particles of different sizes after particle crushing under extreme conditions. Furthermore, through optimized modeling, the spatial aggregation effect of crushed fragments at the crushing site is considered, thereby improving the authenticity of particle gradation and spatial structure, and providing a more reliable geometric model for subsequent numerical simulations of heat and mass transfer processes in particle crushing pebble beds.

[0041] B. A multi-physics numerical model covering the interaction between flow, heat transfer, and mass transfer processes was established. This model can systematically analyze and evaluate the potential uncertainties in the effects of particle crushing on the heat and mass transfer characteristics within the pebble bed. This provides an effective way to gain a deeper understanding of the performance changes of the particle crushing pebble bed under complex working conditions, and is therefore of great value to the safety analysis and optimal design of industrial pebble bed reactors and heat exchange equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is the overall flow chart;

[0043] Figure 2 Schematic diagram of the high-temperature ball bed uniaxial compression experimental device;

[0044] Figure 3 This is a schematic diagram of the crusher particle screening experimental device;

[0045] Figure 4 This is the experimental result diagram of the mass and quantity percentage distribution of crushed particles;

[0046] Figure 5 The geometric models of the intact particle bed and the crushed particle bed;

[0047] Figure 6 This is the calculation result of the resistance pressure drop coefficient of the tritium breeder particle crushing ball bed;

[0048] Figure 7 This is the calculation result of the convective heat transfer coefficient of the tritium breeder particle crushing ball bed;

[0049] Figure 8 This is the calculation result of the convective mass transfer coefficient of the tritium breeder particle crushing ball bed.

[0050] In the figure: pressure sensor 1, transmission rod 2, pressure head 3, ball bed 4, ball bed container 5, base 6, support rod 7, fixing pin 8, high temperature environment box 9, intact particles 10, crushed particles 11, and screen 12. DETAILED DESCRIPTION

[0051] The present invention will be further described below with reference to the following examples, but it should not be understood that the scope of the present invention is limited to the following examples. Without departing from the above technical ideas of the present invention, various substitutions and modifications can be made according to common technical knowledge and customary means in the art, and all of these should be included in the scope of protection of the present invention.

[0052] Example 1:

[0053] This embodiment provides a method for geometric modeling and heat and mass transfer characteristic calculation of a particle crushing ball bed, conducts a high-temperature ball bed particle crushing and screening experiment, obtains the ball bed crushing rate and the particle size probability distribution of sub-particles in the particle crushing ball bed under the combined action of high temperature and load; constructs a geometric and numerical model of the particle crushing ball bed based on the sub-particle size probability distribution obtained in the experiment; uses a multi-physics field coupling solver to mesh and numerically solve the geometric model of the particle crushing ball bed, and obtains the heat and mass transfer characteristics of the ball bed after particle crushing.

[0054] See also Figure 1 A method for geometric modeling and heat and mass transfer characteristic calculation of a particle crushing ball bed comprises the following steps:

[0055] S1. Determine the coordinates of the particles within the complete pebble bed. Using the discrete element method, the complete particles are randomly distributed within the pebble bed. The coordinates of the particles are adjusted by the elastic forces between the particles until the elastic potential energy of the particle system drops below a preset threshold. The particle coordinates at this point are then recorded.

[0056] S2. Conduct a high-temperature pebble bed particle crushing and screening experiment. This experiment consists of two parts: uniaxial compression of the high-temperature pebble bed and screening of the crushed sub-particles. This experiment determines the pebble bed crushing rate and the particle size probability distribution of the sub-particles within the crushed pebble bed under the combined effects of high temperature and load.

[0057] See also Figure 2A pressure testing machine was used to apply a load to a pebble bed sample 4 under high temperature conditions for uniaxial compression. The crushed particle fragments were then screened using a sieve, and the pebble bed crushing rate and fragment size distribution were calculated. The pressure testing machine comprises, arranged from top to bottom, a transmission rod 2, a pressure head 3, a pebble bed container 5, a base 6, a support rod 7, a pressure sensor 1, a fixed pin 8, and a high-temperature environmental chamber 9. The pebble bed container 5 has an open top and a cylindrical cavity. The pebble bed container 5 is fixed to the base 6. The pebble bed container 5 houses the pebble bed sample 4, restricting lateral movement of the particles. The transmission rod 2 and the pressure head 3 are connected by a fixed pin 8. The base 6 and the support rod 7 are connected by a fixed pin 8. The pressure sensor 1 is mounted on the transmission rod 2 and measures the axial pressure applied during loading in real time. The lower end of the pressure head 3 extends into the pebble bed container 5, directly contacting the pebble bed sample 4 and evenly applying the transmission rod's force to the pebble bed sample 4. The high-temperature environmental chamber 9 encloses the test area, providing a controllable high-temperature environment. The pressure head 3 , the pebble bed sample 4 , the pebble bed container 5 , the base 6 , the fixing pin 8 , and part of the transmission rod 2 and part of the support rod 7 are located in a high temperature environment box 9 .

[0058] See also Figure 3 The crushed particle fragments are screened through the screen 12, and the ball bed crushing rate and fragment size distribution are calculated. The screen 12 includes multiple screen layers. The screen hole diameter gradually decreases from top to bottom. After screening, the complete particles 10 are located above the screen, and the crushed sub-particles 11 are distributed along the screen from top to bottom with a particle size gradually decreasing. By calculating the percentage of fragments of different sizes, the particle size d of the crushed sub-particles can be used as the particle size d of the crushed sub-particles. s The probability distribution P(d s ), thereby characterizing the crushing characteristics of a real pebble bed under typical high temperature and load.

[0059] S3. Geometric modeling of the particle crushing bed. Based on the experimentally obtained probability distribution of the sub-particle size, and while maintaining mass conservation, the particle size of the crushed sub-particles is calculated and randomly inserted into the corresponding original crushed particle area. The particle coordinates are then adjusted using the discrete element method until the elastic potential energy of the crushed sub-particle system drops below a preset threshold. Finally, the coordinates of the sub-particles are recorded and the modeling is completed. Step S3 specifically includes the following sub-steps:

[0060] S3.1. Calculate the number of broken particles to be replaced based on the breakage rate obtained in step S2. in is the breakage rate.

[0061] S3.2, randomly select n from the complete granular bed generated in step S1. c The particles are regarded as broken particles and deleted from the complete ball bed. The space where these particles originally reside is recorded as the set {Ωi |i=1,2,…,N c}.

[0062] S3.3. Generate a probability distribution P(d s ) and mass conservation constraint ∑m ij =M i The set of broken particles, where m ij is the mass of the jth sub-particle generated by the i-th broken particle, M i is the mass of the original crushed particles.

[0063] S3.4. Randomly distribute the sub-particles to the Ω corresponding to the original broken particles. i region, thus considering the spatial aggregation effect of broken fragments at the broken site. Assuming that the breakage of a small number of particles does not affect the contact network of other unbroken particles, the discrete element method of step S1 is used to iteratively adjust the position of the sub-particles until the elastic potential energy of the system converges. Finally, the geometric parameterized model of the particle crushing ball bed is output and modeled using 3D modeling software. At the same time, in order to reduce the inlet and outlet effects, the inlet and outlet areas of the ball bed are extended by ≥10d. p Length of the inlet and outlet sections, where d p The complete particle size.

[0064] S4. Construct a numerical model of heat and mass transfer in a pellet crushing bed. Establish the multi-physics governing equations for the flow, heat, and mass transfer processes in the pellet crushing bed, and define the boundary conditions and physical parameters of the equations. The governing equations for step S4 consist of the following conservation equations:

[0065] A. Mass Conservation Equation: Continuity Equation

[0066]

[0067] B. Momentum conservation equation: Navier-Stokes equation

[0068]

[0069] C. Energy conservation equation: Heat transfer equation

[0070]

[0071] D. Component Conservation Equation: Mass Transfer Equation

[0072]

[0073] Where ρ is density, t is time, and u is velocity. is the Laplace operator, p is pressure, μ is dynamic viscosity, F is volume force, T is temperature, λ is thermal conductivity, Cp is the constant pressure specific heat capacity, Φ is the internal heat source intensity, c is the concentration, D is the diffusion coefficient, and S is the mass source intensity. The boundary conditions of the pebble bed can be set using Dirichlet conditions to apply velocity, temperature, and concentration distribution as the inlet boundary. Set the pressure distribution as the outlet boundary. The flow at the wall is set to the no-slip condition u=0, the heat transfer can be set to constant temperature, constant heat flow, or convection boundary, and the mass transfer can be set to Neumann boundary conditions.

[0074] S5. Solve the heat and mass transfer characteristics of the particle crushing ball bed. Use a multi-physics coupling solver to mesh and numerically solve the geometric model of the particle crushing ball bed, calculate and analyze the flow field, temperature field and concentration field in the particle crushing ball bed, and evaluate its internal resistance pressure drop, convective heat transfer and convective mass transfer characteristics. Step S5 directly calculates the flow field, temperature field and concentration field in the ball bed through the multi-physics coupling solver, and calculates the resistance pressure drop coefficient f, convective heat transfer coefficient h and convective mass transfer coefficient k in the ball bed based on the definition formula to evaluate its heat and mass transfer characteristics:

[0075] Resistance pressure drop coefficient f:

[0076] Convective heat transfer coefficient h:

[0077] Convective mass transfer coefficient k:

[0078] Where ε is the porosity of the pebble bed, u in is the fluid velocity at the pebble bed inlet, subscript in represents the pebble bed inlet, V s is the total volume of particles in the pebble bed, subscript s represents solid particles, A s is the total surface area of ​​the solid particles in the pebble bed, and are the average temperatures of the particle surface and fluid domain in the pebble bed, and are the average concentrations on the particle surface and in the fluid domain within the pebble bed, respectively.

[0079] Example 2:

[0080] This embodiment provides an application of the method described in Example 1 to evaluate the impact of particle breakage on the heat and mass transfer characteristics within a tritium breeder pebble bed in a fusion reactor blanket. The tritium breeder pebble bed in a fusion reactor blanket is a core component for tritium breeding and energy conversion. The heat and mass transfer phenomena within it include helium flow, heat transfer, and tritium transport, involving a complex multi-physics coupling process involving flow, heat transfer, and mass transfer. Under extreme service environments such as high temperature and load, the breeder particles may break, thereby changing the pebble bed structure and affecting its internal heat and mass transfer characteristics.

[0081] The tritium breeder granular material used in the experiment is lithium silicate with a particle size of 0.8 to 1.2 mm. The randomly filled and stacked cylindrical ball bed has a height of 40 mm and a bottom diameter of 50 mm. According to the working environment of the real fusion reactor blanket, the temperature of the high-temperature environmental box is stabilized at 400 ° C, and the pressure load is taken as 4 MPa and 6 MPa respectively, which is used to consider the crushing of the ball bed under extreme working conditions. After compression and crushing, standard sieves (with apertures of 1 mm, 0.8 mm, 0.6 mm, 0.4 mm and 0.2 mm, respectively) are stacked from top to bottom in order from large to small aperture, and the particle crushed ball bed sample is evenly spread on the top sieve for screening. Since the total mass of sub-particles below 0.2 mm accounts for only 2% to 3%, in order to reduce grid resources and computational complexity, and considering that these small-sized powder particles may migrate out of the pebble bed channel under the action of helium purge, the influence of these fragments is reasonably ignored in the subsequent discussion and modeling calculation process, and the particle size range of the crushed sub-particles is limited to between 0.2 and 0.8 mm.

[0082] Under a high temperature environment of 400℃, after testing with a load of 4MPa and 6MPa, the obtained pebble bed breakage rates were 9.36% and 13.2% respectively, indicating that under complex working conditions, the local breakage rate of the actual cladding pebble bed may exceed 10%. Figure 4 The percentage distribution of the number of sub-particles is shown in the figure. It is found that the probability distribution of the sub-particle size P(d s ) are essentially the same, indicating that the load conditions have little effect on the particle size distribution of the sub-particles. Therefore, the average crushing sub-particle size probability distribution under the two working conditions was selected as the typical crushing characteristics of lithium silicate particles under extreme high temperature conditions, and this was used as the basis for constructing a particle crushing ball bed model.

[0083] According to steps S1 to S3, the geometric models of the intact ball bed of tritium breeder particles and the broken ball bed of particles with a breakage rate of 5%, 10% and 15% are established as follows: Figure 5 The boundary conditions of the pebble bed are shown in Table 1, and the physical properties of the materials are shown in Table 2. According to steps S4 to S5, the COMSOL Multiphysics multi-physics coupling solver is used to calculate the helium flow rate and pressure, the pebble bed temperature, and the tritium concentration distribution in the pebble bed. Then, the resistance pressure drop coefficient f, the convective heat transfer coefficient h, and the convective mass transfer coefficient k in the pebble bed are calculated using the definition formula to evaluate its heat and mass transfer characteristics. Figures 6 to 8The resistance pressure drop, convective heat transfer, and convective mass transfer coefficients within the pebble bed are compared under different inlet flow rates and breakup rates. It can be seen that particle breakage significantly affects the heat and mass transfer characteristics within the tritium breeder pebble bed. As the breakup rate increases, the resistance pressure drop coefficient within the pebble bed increases, indicating that particle breakage increases the pebble bed's resistance to helium flow. The convective heat transfer coefficient and convective mass transfer coefficient within the pebble bed first increase and then decrease with increasing breakup rate. This is because in the early stages of particle breakage (breakage rates of 5% and 10%), the heat and mass transfer processes are enhanced by increasing the particle surface area and improving the fluid flow state. However, when the breakage rate continues to increase to 15%, the flow resistance in the broken area increases, and the reduced airflow velocity in the local broken area actually inhibits the heat and mass transfer processes. Therefore, given the significant impact of particle breakage on the heat and mass transfer characteristics within the pebble bed, the technical solution provided by the present invention can be used to assess the potential uncertainties in the impact of particle breakage on pebble bed performance, and is of great value for the safety analysis and optimized design of industrial pebble bed reactors and heat exchange equipment.

[0084] Table 1 Boundary conditions of tritium breeder pebble bed

[0085]

[0086] Table 2 Physical properties of materials in tritium breeder pebble bed

[0087]

[0088]

Claims

1. A method for geometric modeling and heat and mass transfer characteristics calculation of a particle crushing ball bed, characterized by: A high-temperature pebble bed particle crushing and screening experiment was conducted to obtain the pebble bed crushing rate and the particle size probability distribution of sub-particles in the particle crushing pebble bed under the combined action of high temperature and load; based on the sub-particle size probability distribution obtained from the experiment, a geometric and numerical model of the particle crushing pebble bed was constructed; the geometric model of the particle crushing pebble bed was meshed and numerically solved using a multi-physics field coupling solver to obtain the heat and mass transfer characteristics of the pebble bed after particle crushing.

2. The method for geometric modeling and heat and mass transfer characteristic calculation of a particle crushing ball bed according to claim 1 is characterized in that: The following steps are involved: S1. Determine the coordinates of the particles in the complete pebble bed. Based on the discrete element method, the complete particles are randomly distributed in the pebble bed space, and the coordinates of the particles are adjusted by the elastic forces between the particles until the elastic potential energy of the particle system drops below a preset threshold. Finally, the particle coordinates at this time are recorded. S2. Conduct a high-temperature pebble bed particle crushing and screening experiment. The experiment includes two parts: uniaxial compression of the high-temperature pebble bed and screening of the crushed sub-particles. Through the experiment, the crushing rate of the pebble bed under the combined effects of high temperature and load and the probability distribution of particle size of the sub-particles in the particle crushing pebble bed are obtained. S3. Geometric modeling of the particle crushing bed is performed. Based on the experimentally obtained probability distribution of the sub-particle size, the particle size of the crushed sub-particles is calculated while ensuring mass conservation. The particle size is randomly inserted into the corresponding original crushed particle area. The particle coordinates are then adjusted using the discrete element method until the elastic potential energy of the crushed sub-particle system drops below a preset threshold. Finally, the coordinates of the sub-particles are recorded and the modeling is completed. S4. Construct a numerical model of heat and mass transfer in a pellet crushing bed; establish the multi-physics field governing equations for the flow, heat and mass transfer processes in the pellet crushing bed, and clarify the boundary conditions and physical parameters of the equations; S5. Solve the heat and mass transfer characteristics of the particle crushing ball bed; use a multi-physics field coupling solver to mesh and numerically solve the geometric model of the particle crushing ball bed, calculate and analyze the flow field, temperature field and concentration field in the particle crushing ball bed, and evaluate its internal resistance pressure drop, convective heat transfer and convective mass transfer characteristics.

3. The method for geometric modeling and heat and mass transfer characteristic calculation of a particle crushing ball bed according to claim 2 is characterized by: In step S2, a pressure testing machine is used to apply a load to the ball bed sample (4) under a high temperature environment for uniaxial compression, and then the crushed particle fragments are screened through a screen, and the ball bed crushing rate and fragment size distribution are counted; the pressure testing machine includes a transmission rod (2), a pressure head (3), a ball bed container (5), a base (6), a support rod (7), a pressure sensor (1), a fixing pin (8) and a high temperature environment box (9) arranged in sequence from top to bottom; the ball bed container (5) is open at the top and has a cylindrical cavity; the ball bed container (5) is fixed on the base (6); the ball bed container (5) contains the ball bed sample (4) inside to constrain the lateral movement of the particles; the transmission rod (2) and the pressure head (3) are connected by a fixed pin (8); the base (6) and the support rod (7) are connected by a fixed pin (8); the pressure sensor (1) is arranged on the transmission rod (2) to measure the axial pressure applied during the loading process in real time; the lower end of the pressure head (3) extends into the ball bed container (5) to directly contact the ball bed sample (4), and evenly applies the force of the transmission rod to the ball bed sample (4); the high-temperature environmental box (9) covers the experimental area and provides a controllable high-temperature environment; the pressure head (3), the ball bed sample (4), the ball bed container (5), the base (6), the fixed pin (8), and part of the transmission rod (2) and part of the support rod (7) are located in the high-temperature environmental box (9).

4. The method for geometric modeling and heat and mass transfer characteristic calculation of a particle crushing ball bed according to claim 2 is characterized by: In step S2, the crushed particle fragments are screened by a screen (12), and the ball bed crushing rate and fragment size distribution are calculated; the screen (12) includes multiple screen layers; the screen hole diameter of the screen gradually decreases from top to bottom; after screening, the complete particles (10) are located above the screen, and the crushed sub-particles (11) are distributed along the screen from top to bottom with a particle size gradually decreasing; by calculating the percentage of the number of fragments of different sizes, the particle size d of the sub-particles after crushing can be used as the particle size d of the sub-particles after crushing. s The probability distribution P(d s ), thereby characterizing the crushing characteristics of a real pebble bed under typical high temperature and load.

5. The method for geometric modeling and heat and mass transfer characteristic calculation of a particle crushing ball bed according to claim 2 is characterized in that: Step S3 specifically includes the following sub-steps: S3.

1. Calculate the number of broken particles to be replaced based on the breakage rate obtained in step S2. in is the crushing rate; S3.2, randomly select N from the complete pebble bed generated in step S1. c The particles are regarded as broken particles and deleted from the complete particle bed. The space where these particles originally reside is recorded as the set {Ω i |i=1,2,…,N c }; S3.

3. Generate a probability distribution P(d s ) and mass conservation constraint ∑m ij =M i The set of broken particles, where m ij is the mass of the jth sub-particle generated by the i-th broken particle, M i is the mass of the original crushed particles; S3.

4. Randomly distribute the sub-particles to the Ω corresponding to the original broken particles. i region, thus considering the spatial aggregation effect of broken fragments at the broken site. Assuming that the breakage of a small number of particles does not affect the contact network of other unbroken particles, the discrete element method of step S1 is used to iteratively adjust the position of the sub-particles until the elastic potential energy of the system converges. Finally, the geometric parameterized model of the particle crushing ball bed is output and modeled using 3D modeling software. At the same time, in order to reduce the inlet and outlet effects, the inlet and outlet areas of the ball bed are extended by ≥10d. p Length of the inlet and outlet sections, where d p The complete particle size.

6. The method for geometric modeling and heat and mass transfer characteristic calculation of a particle crushing ball bed according to claim 2 is characterized in that: The control equations of step S4 are composed of the following conservation equations: A. Mass Conservation Equation: Continuity Equation B. Momentum conservation equation: Navier-Stokes equation C. Energy conservation equation: Heat transfer equation D. Component Conservation Equation: Mass Transfer Equation Where ρ is density, t is time, and u is velocity. is the Laplace operator, p is pressure, μ is dynamic viscosity, F is volume force, T is temperature, λ is thermal conductivity, C p is the constant pressure specific heat capacity, Φ is the internal heat source intensity, c is the concentration, D is the diffusion coefficient, and S is the mass source intensity. The boundary conditions of the pebble bed can use Dirichlet conditions to impose velocity, temperature, and concentration distributions as the inlet boundary; set the pressure distribution as the outlet boundary; set the flow at the wall to the no-slip condition u = 0, heat transfer can be set to constant temperature, constant heat flow, or convection boundary, and mass transfer can be set to Neumann boundary conditions.

7. The method for geometric modeling and heat and mass transfer characteristic calculation of a particle crushing ball bed according to claim 2, characterized in that: Step S5 directly calculates the flow field, temperature field, and concentration field in the pebble bed through the multi-physics coupling solver, and calculates the resistance pressure drop coefficient f, convective heat transfer coefficient h, and convective mass transfer coefficient k in the pebble bed based on the definition formula to evaluate its heat and mass transfer characteristics: Resistance pressure drop coefficient f: Convective heat transfer coefficient h: Convective mass transfer coefficient k: Where ε is the porosity of the pebble bed, u in is the fluid velocity at the pebble bed inlet, subscript in represents the pebble bed inlet, V s is the total volume of particles in the pebble bed, subscript s represents solid particles, A s is the total surface area of ​​the solid particles in the pebble bed, and are the average temperatures of the particle surface and fluid domain in the pebble bed, and are the average concentrations on the particle surface and in the fluid domain within the pebble bed, respectively.

8. Use of the method according to any one of claims 1 to 7, characterized in that: Used to evaluate the effect of particle breakage on the heat and mass transfer characteristics within the tritium breeder pebble bed in the blanket of a fusion reactor.

9. The method for geometric modeling and heat and mass transfer characteristic calculation of a particle crushing ball bed according to claim 8, characterized in that: The tritium breeder particle material is lithium silicate with a particle size of 0.8 to 1.2 mm; the randomly filled and stacked cylindrical ball bed has a height of 40 mm and a bottom diameter of 50 mm; based on the working environment of the actual fusion reactor blanket, the temperature of the high-temperature environmental box is stabilized at 400°C, and the pressure loads are 4 MPa and 6 MPa respectively to consider the breakage of the ball bed under extreme working conditions.

10. The method for geometric modeling and heat and mass transfer characteristic calculation of a particle crushing ball bed according to claim 8, characterized in that: The COMSOL Multiphysics multi-physics coupling solver was used to calculate the helium flow rate and pressure, the pebble bed temperature, and the tritium concentration distribution in the pebble bed. Then, the resistance pressure drop coefficient f, the convective heat transfer coefficient h, and the convective mass transfer coefficient k in the pebble bed were calculated using the definition formula to evaluate its heat and mass transfer characteristics.

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