Methods for reconstruction of the density distribution of nuclear power

In analytical reconstruction method (ARM), the two-dimensional (2D) neutron diffusion equation is analytically solved for two energy groups (2G) and homogeneous nodes with dimensions of a fuel assembly (FA). The solution employs a 2D fourth-order expansion for the axial leakage term. The Nodal Expansion Method (NEM) provides the solution average values as the four average partial currents on the surfaces of the node, the average flux in the node and the multiplying factor of the problem. The expansion coefficients for the axial leakage are determined directly from NEM method or can be determined in the reconstruction method. A new polynomial reconstruction method (PRM) is implemented based on the 2D expansion for the axial leakage term. The ARM method use the four average currents on the surfaces of the node and four average fluxes in corners of the node as boundary conditions and the average flux in the node as a consistency condition. To determine the average fluxes in corners of the node an analytical solution is employed. This analytical solution uses the average fluxes on the surfaces of the node as boundary conditions and discontinuities in corners are incorporated. The polynomial and analytical solutions to the PRM and ARM methods, respectively, represent the homogeneous flux distributions. The detailed distributions inside a FA are estimated by product of homogeneous distribution by local heterogeneous form function. Moreover, the form functions of power are used. The results show that the methods have good accuracy when compared with reference values and the ARM method is more accurate than the PRM method. The largest errors are in the peripheries of FAs, near the reflector, reinforcing the fact that these errors are associated with the homogenization process.