| Fusion energy is one of the ultimate solutions for future energy,and the research on fusion reactor is currently one of the frontier research hotspots of science.The fusion blanket,which is core component for fusion device,plays an important role in tritium breeding and energy conversion.Hence,ensuring its safe and efficient operation is pivotal to the effective use of fusion energy.Ceramic particles are usually used as tri-tium breeders(e.g.,Li4SiO4,Li2TiO3 particle)and neutron multipliers(e.g.,Be/Be12 particle)inside the blanket.The packing performance of the ceramic pebble bed can di-rectly affect tritium breeding and extraction,thermal hydraulics,and then affects struc-tural design of the blanket.Therefore,it is necessary to conduct an in-depth analysis of the packing performance of the pebble bed.At the same time,the granular material in the pebble bed usually faces a very complicated load environment,the stress condition inside the particle is complicated,it is inevitable that continuous crushing will occur.However,there is currently no universal theoretical framework for describing the crush-ing behavior of granular materials in the pebble bed,and there are significant limitations in both related experiments and numerical simulations.Hence,it is necessary to estab-lish corresponding theoretical models and numerical methods to describe and simulate the crushing behavior of granular materials in the pebble bed,which could provide the theoretical reference for the design and operation of the fusion blanket.Based on the above objectives,we have conducted the following research:Firstly,based on the nonlinear Hertz-Mindlin contact model,the effects of two key input parameters in the Discrete Element Method(DEM)simulation,namely the coefficient of friction and the coefficient of restitution,have been studied.The physi-cal mechanism of the friction and collision in the particle system were discussed.The results showed that the pebble bed particle assembly system transitions between the friction dominance and energy dissipation dominance states.For the packing system,friction will hinder the rearrangement process of particles,thus reduce the packing den-sity,while collision will promote the rearrangement of particles and increase bulk den-sity.At the same time,a left-shifted phenomenon of the peak value of contact force and coordination number distribution appearing as the coefficient of friction occurred.Secondly,the packing mechanical performance of the "J"-tube structure pebble bed,which is used in an optimized design of CFETR helium-cooled solid blanket has been investigated numerically by the Discrete Element Method.The packing structure,contact force distribution,radial and axial local packing factor and coordination number,etc.were simulated and analyzed.Studies have shown that the global packing factor of the pebble bed is 0.6212,and the packing factor of irregularly shaped part is smaller than that of the regular part.The difference in packing performance caused by geometric characteristics will be weakened as the aspect ratio increases.At the same time,the oscillation amplitude of the local packing factor in the radial direction is much larger than the oscillation amplitude in the axial direction,and the radial oscillation behavior is limited to the range of 5-7 particle diameters from the container wall.Then,based on the fractal theory and particle impact crushing experiment of glass particle,we established a theoretical model for decribing crushing behavior of the peb-ble bed pebble in fusion reactor,which integrates the fractal dimensions of particle crushing,the size effect of particle strength,and particle strength variation character-istics into one theoretical framework,thus obtained the particle crushing equation and the mathematical and physical relationship between the fractal dimension and Weibull distribution.By the theoretical analysis of single particles,the selection of principle of particle strength was determined.The fractal theory was used to describe the size distri-bution of particles after crushing.According to the deduced crushing fractal dimension,quantitative mathematics of the size effect of particle strength was performed,combined with the Weibull distribution to quantitatively describe the strength variation character-istics,and finally,the theoretical model was verified by the impact crushing test of the glass particles.The test results showed that the size distribution of the fragments after the crushing of the particles is presented with linear characteristics in the double loga-rithmic coordinate system,and with the impact energy increases,the fractured fractal dimension will reach a limit value.Finally,based on the established theoretical model.we developed a numerical method under the framework of the discrete element method,which is suitable for sim-ulating the crushing behavior of granular material in the pebble bed and based on this framework,the particle crushing behavior of the fusion reactor pebble bed under one-dimensional compression was analyzed.In addition,the evolution law of the mechan-ical properties of the Li4SiO4 ceramic pebble bed under different crushing conditions was explored.The calculation results showed that with the axial load increasing,the distribution of crushing particles is also influenced by the wall effects.In the case of small strain,the crushing particles mainly appear in the upper and middle position of the axial direction,and the distribution in the radial direction is not uniform.With strain increased,the distribution of crushing particles tends to be uniform in both the axial and radial directions.Particle crushing mainly affects the oscillation amplitude of the local packing factor nearby the wall,and has little effect on the oscillation width.The in-crease of the crushed particle will lead to the reduction of the pebble bed stress,which plays a positive role in improving the stress condition.The results also showed that there exists a critical crushing ratio,the positive effect increases rapidly after exceeding the critical point,thereby protecting the particles from further crushing Invalidate. |
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