基于改进变分节块法的共轭中子通量密度计算技术

The adjoint neutron flux is of great significance for nuclear safety and detector calculation in pressurized water reactor (PWR). However, existing nodal methods would cause a big error due to heterogeneous nodes, including heterogeneous cross sections and discontinuity factors, which will appear frequently with the control rod moving. In this paper, an improved variational nodal method (VNM) is proposed to reduce the error. It determines the continuous conditions for adjoint nodal methods that are different from forward equation. Unlike traditional VNM, which establishes a functional method globally, this paper establishes a functional method for each node. It constructs a multiplier term with a heterogeneous discontinuity factor to explicitly deal with the adjoint neutron flux with surface discontinuity. Apart from the expansions of adjoint neutron flux, cross section and surface partial neutron current densities, the surface discontinuity factor (DF) is also expanded into pieces-wise orthogonal polynomials to construct the nodal response matrixes. The numerical results of the BEAVRS benchmark problem with heterogeneous nodes existing demonstrate that compared with the traditional VNM, the improved VNM can reduce the error by two orders of magnitude for the adjoint neutron flux in fuel area and the adjoint effective multiplication factor, which can help realize high accuracy calculation for the inner product of forward and adjoint neutron flux.