Modeling Of Heat Transfer In Particle Scale For The Pebble Bed Of High Temperature Gas-cooled Reactor

For high temperature gas-cooled reactors,the core is a dense pebble bed filled with large quantities of fuel elements of random packing.The pebble bed is operated in high temperature and cooled by helium gas under high pressure.In this work,the numerical models of the heat transfer in particle scale for the pebble beds are developed,which include particle conduction,thermal radiation and the heat convection with the fluid phase.For the particle motion,the effects of size ratio and region width on the mixing and dispersion of pebbles in the two-region pebble bed are studied by discrete element method(DEM).The particle-scale mixing index and mixing entropy are used to quantify the particle mixing process.It is shown that the size ratio has greater effects on the mixing and dispersion of pebble than the region ratio and the stagnant region will decrease greatly when large size particles flow in the central region.The particle thermal radiation in pebble bed increases significantly at high temper-ature and it becomes an important part of the heat transfer processes.Three radiation models under different spatial scales are developed and analyzed with reference to exist-ing correlations.The long-range model takes into account all possible radiation between surrounding spheres and only Voronoi neighboring pairs are considered in short-range radiation model.It is found that when solid conductivity is much greater than the effective thermal conductivity of radiation,long-range model is strictly valid for the pebble bed.However,when the conductivities are in same order,the effect of solid conductivity on the particle radiation is canceled out in general by cutting off the long-range radiation parts,short-range radiation model provides good results in predicting the radiative heat exchange.From the design aspect and accident analysis of the pebble beds,it is a fundamental task to model effective thermal conductivity of thermal radiation.Based on the effective heat transfer cells of structured packing,the short-range radiation model and the sub-cell radiation model are applied to obtain analytical expressions of the effective thermal conductivity.It is shown that the short-range radiation model is slightly higher than empirical correlations when temperature exceeds 1200?.However,the sub-cell radiation model is a generic theoretical approach and it is still applicable at very high temperature ranges(over 1500?).In this work,a complete CFD-DEM method coupled with particle-scale thermal ra-diation is discussed for pebble beds,considering particle motion,fluid flow,particle-fluid interactions and heat convection,conduction in contact and particle radiation.When the cell size is close to or even less than the particle diameter,CFD-DEM model with the void fraction of the divided finite volume method is rather difficult to converge and it will be no longer applicable for the CFD-DEM simulations.In this case,the smoothed void fraction method(SVFM)is suggested in the CFD-DEM simulations of fluid-particle systems on sub-particle scale mesh.The diffusion function in SVFM is obtained analytically as the spatial distribution function,which converges to the step-function-type distribution of particle volume in the sub-particle-scale divided finite volume method when the smoothing degree goes to 0.The CFD-DEM simulation using the void fraction method on sub-particle scale meshes is performed for the HTR-10 benchmark problem,the numerical results are in good agreement with the empirical code of THERMIX.In addition,the discussion indicates that the smoothing degree is recommended to be 0.5~0.7 according to the void fraction distribution of Voronoi-tessellation.