Research on neutron diffusion equation and nuclear thermal coupling method based on gradient updating finite volume method

Abstract

To solve the problem that the neutron diffusion equation has infinite solutions when the deterministic method is used to calculate the neutron diffusion equation, this paper uses the power calculation equation as a supplementary equation to form a differential and integral equation groups with the neutron diffusion equation, and designs a numerical analysis and machine learning coupling algorithm based on the gradient updating finite volume method that can be used to solve the above differential and integral equation groups. The algorithm decouples the multigroup neutron diffusion equations by source iteration. Then the finite volume method is used to solve the one group neutron diffusion equation and the reactor core power. Based on the power difference calculated by two adjacent iterations, the neutron flux density is updated by the gradient descent method until it converges. Finally, the algorithm can be used to calculate the neutron flux density and volumetric heat release rate of each energy group under the specified power. Taking 5 × 5 rod bundle channel as an example, the feasibility of the algorithm is verified in Fluent 18.0 by writing the UDF script. In addition, the thermal–hydraulic parameters such as temperature and velocity in the reactor can be further calculated according to the volumetric heat release rate, and a same set of grids can also be used to achieve the nuclear thermal coupling calculation. This algorithm can provide a new calculation method for the neutron diffusion equation, and also provide a theoretical basis for the development of application algorithms in the field of reactor physics using deep learning.