P1 generalized equivalence theory for PWR-core pin-by-pin neutronics calculation

Abstract

The essence of steady-state neutronics analysis for a nuclear reactor core lies in solving the six-dimensional the Boltzmann neutron transport linear equation. Due to the expensive computational cost in direct solving schemes, the two-step procedure based on homogenization theory has been the workhorse for decades for core neutronics calculation. Among these methods, the pin-by-pin two-step procedure has recently emerged as the most attractive option. The current widely-used pin-by-pin two-step procedure is based on the Simplified P₃ (SP₃) theory. To further reduce computational cost, this work proposes a two-step approach based on P₁ theory. This work presents several key advancements in achieving efficient and accurate neutronics calculations. First, the P₁ equation is derived from the Boltzmann neutron transport equation through a first-order spherical harmonic expansion of the angular flux in the angle-space. It comprises the angular-dependent total cross-sections and the first-order anisotropic scattering cross-sections, thereby eliminating the approximation introduced by the traditional Fick’s Law. Second, a Generalized Equivalent Theory (GET) approach is established to generate the Pin-cell Discontinuity Factors (PDF), ensuring the conservations of key quantities during homogenization. Lastly, the pin-cell homogenized cross-sections and PDF can be used to solve the P₁ equation numerically. This work employs the Finite Difference Method (FDM) for spatial discretization. The proposed method and code implementation have been verified via a series of validation tests. The results demonstrate that this new methodology achieves the SP₃-level accuracy with computing cost comparable to neutron diffusion.