Lattice Boltzmann Modeling Of Neutron Transport Process And Its Complex Mesh Technique

The processes of generation,propagation,absorption,scattering and leakage for neutron particles in fuel rod,moderator and coolant within the nuclear reactor can be described by the neutron transport equation.For different applications,the neutron transport equation show different formats,including steady-state,transient,fixed source and eigen-value schemes.In recent decades,there are many numerical techniques for solving the neutron transport problem in academia and engineering.These methods have their own advantages and disadvantages as well as suitable for different applications.An excellent numerical technique shall meet several requirements for numerical computation,including high accuracy,low memory cost,high efficiency,complex geometry adaptability,parallel computation,coupling computing of neutronic and thermal-hydrodynamic and the computational simplicity and feasibility.The lattice Boltzmann method,based on the relationship between lattice Boltzmann equation and macroscopic conservation equation,is a novel numerical technique for solving the macroscopic physical problem.Compared with the conventional technique,this method shows clearly physical background,computational simplicity and feasibility,parallel computation and suitable for coupling computation.The development of classical lattice Boltzmann method,namely the finite-volume lattice Boltzmann method,can effectively adapt the irregular complex geometric,which improve the drawback of standard lattice Boltzmann method for irregular complex geometric.This paper extended the lattice Boltzmann method into the neutron transport problem.In these works,the lattice Boltzmann model for transient neutron transport problem,the neutron transport finite-volume lattice Boltzmann method in unstructured mesh,the neutron diffusion lattice Boltzmann for large reactor physical calculation and the adaptive-mesh-refinement technique for proposed lattice Boltzmann method were established.This paper introduced the neutron transport theory and the details of lattice Boltzmann method for solving the numerical problem.Besides,the implementation of lattice Boltzmann method and its typical boundary treatments were described.Based on the transient neutron transport equation,we adopted the discrete-ordinate SN scheme to establish the discrete-ordinate neutron transport equation and discussed the treatments of typical boundary conditions.The relationship between the neutron transport equation and standard lattice Boltzmann equation was analyzed,and the multi-dimensional neutron transport lattice Boltzmann model in Cartesian coordinates based on standard lattice Boltzmann equation was established.Through the Chapman-Enskog expansion,the relationship between the lattice Boltzmann equation and the transient neutron transport equation is established as well as the correspondences for different parameters are analyzed.By adding a external time derivation term in the right hand side of lattice Boltzmann equation,the rigorous multi-scale expand and recovered relations between the lattice Boltzmann equation and neutron transport equation were ensured.The transient radiative effect of one-and multi-dimensional absorbing and scattering medium is analysis while the transient evolution of transient neutron transfer process was studied.The differences of neutron transport processes within strongly absorbing medium,half-scattering medium and the strongly scattering medium and their influent factor were studied.The lattice Boltzmann method’s results agreed well with those obtained from the literatures,which testified that the proposed lattice Boltzmann model can be adopted to simulate the transient neutron transport process efficiently.The neutron transport finite-volume lattice Boltzmann method in triangular(2D)and quadrilateral(3D)mesh were established.Through a series of numerical transformations,the neutron transport equation was converted into the discrete velocity Boltzmann scheme.By integrating the discrete velocity Boltzmann equation over the control volume,the neutron transport finite-volume lattice Boltzmann model was established.Through the Chapman-Enskog expansion,the relationship between the neutron discrete velocity Boltzmann equation and neutron diffusion equation was studied.The computational efficiency of proposed finite-volume lattice Boltzmann method and traditional numerical technique for neutron transport problem were analyzed.The transient neutron transport process of irregular complex geometry and the applicable of proposed finite-volume lattice Boltzmann method in unstructured mesh were studied.The finite-volume lattice Boltzmann method’s solutions agreed well with those obtained from the literatures,which testified that the proposed finite-volume lattice Boltzmann model can be adopted to simulate the neutron transport process in irregular complex geometry efficiently.The lattice Boltzmann method for neutron diffusion problem was established and the relationship between neutron diffusion equation and lattice Boltzmann equation was analyzed.The adaptive-mesh-refinement technique for lattice Boltzmann method was established and the information communication between different mesh was studied.The relationship between grid distribution and neutron distribution was studied while the accuracy and efficiency of neutron diffusion lattice Boltzmann equation in different condition were analyzed.The resource saving of adaptive-mesh-refinement technique in neutron transport problem was studied.The lattice Boltzmann method’s solutions agree well with those from the literatures and the adaptive-mesh-refinement technique can reduce the computational cost effectively,which can be applied to the large engineering calculation.