Block Meshless Method To Solve The Neutron Transport Equation

As the development of new reactors,such as space uranium block reactors,small reactors and other special reactor types,the design of nuclear power system needs further in-depth study.The simulation of nuclear power system plays an important role in the design,development and safety verification of nuclear power system.The calculation of the neutron flux dens ity distribution in the nuclear power system is the precondition to obtain the radiation source and heat source of the system,and to design the shielding and heat transfer of the system.The degree of freedom of node selection of meshless method is high a nd independent of the geometric dimension.It is easy to solve complex structure problems.However,the development of meshless method is not enough,and the global meshless method has high calculation accuracy,but its coefficient matrix is full,which leads to too much calculation;the local meshless method can reduce the calculation amount to a certain extent,but the accuracy is not high due to the defects of its approximate method.On this basis,the main work of this thesis can be divided into the following aspects:First of all,based on the existing global meshless method and local meshless method,combined with the physical structure of typical nuclear reactor core,a new block meshless method is proposed to optimize and improve the numerical calculation method,so as to improve the numerical accuracy and calculation efficiency.Next,the new block meshless method is applied to solve the neutron transport problem.On this basis,several transient,steady state and critical neutron transport problems are solved in different spatial dimensions.The numerical accuracy of block meshless method applied to solve the neutron transport problem in the core of nuclear reactor is investigated.The calculation parameters such as radial basis function,shape factor,discrete node quantity and physical parameters such as absorption cross section and scattering cross section are studied.In order to further improve the calculated node quantity of block meshless method,to simulate the neutron transport problems in the nuclear reactor core structure with higher geometric complexity and more freedoms,this paper also uses the diffusion approximation method to approximate the neutron transport equation to the neutron diffusion equation,and solves several nuclear reactor core problems with complex geometry.Then,the block meshless method is used to solve the coupled problems of neutron transport and heat transfer.On the basis of coupled calculation,the structure of nuclear power system is optimized.Genetic algorithm i s used to optimize the shielding layers of a spent fuel transportation tank,and response surface analysis method is used to optimize a three-dimensional pressurized water reactor.After optimization,better results are gained.Neutron transport equation is a high-dimensional equation including angle,energy group and one to three-dimensional space dimensions.In order to further shorten the calculation time and improve the calculation efficiency,based on the Open MP parallel method,this paper has carried out segmentation and parallel calculation in the angle,space and energy group dimensions respectively,in order to reduce the calculation time of using block meshless method to solve the neutron transport equation.Finally,the physical modeling software and computing software of block meshless method are developed.For the physical modeling process,BRBFCM-geo3 D code and BRBFCM-geo2 D code are developed to describe the geometric structure of the problems to be solved,to divide the models into blocks and to collocate the nodes.For the calculation process,the BRBFCM code is developed,which improves the usability of block meshless method.