Calculation And Application Of Coarse Mesh Equivalent Homogenization Parameters With Non-Reflective Boundary Condition

Because of the existing deficiency in the theory and computational method for LWR core physics analysis and the increasingly aggressive core design, the Next Generation Method (NGM, the 3rd generation) for numerical analysis of LWR cores is under extensive development worldwide. The approach to NGM generally adopted is to completely abandon the currently used methods, which are based on the process of assembly transport calculation, assembly homogenization calculation and full-core three-dimensional diffusion calculation, and to replace it with direct full core three-dimensional transport calculation. Therefore, the resources invested and the experiences accumulated over the years in methods and computational codes for LWR core physics analysis will be abandoned as well. For this reason, an innovation idea was proposed as a cooperation project between SJTU and the Westinghouse Electric Company, the objective of which is to meet the future requirements by improving current methods. The study in this paper focuses on improving assembly homogenization method, numerical computation of assembly homogenization parameters, and the development of a multi-group pin power reconstruction method.In this thesis, the Colorset model is used to perform assembly homogenization calculation instead of the reflective single assembly model, so that the transport effect and spectral interaction on assembly interfaces can be accurately accounted. In Colorset homogenization calculation, assembly quad homogenization with non-reflective boundary condition must be performed. The calculation method used in assembly quad homogenization with non-reflective boundary condition must be consistent with that in the subsequent full-core diffusion calculation. The assembly discontinuity factors are calculated by solving two one-dimensional boundary value problems. The approximations used in solving the one-dimensional boundary value problems, such as diffusion coefficients of homogenized assembly,mesh size, flux expansion and transverse leakage approximation, must be identical to those used in solving the full-core diffusion equation. Imposing conservation of surface average net current, nodal average flux and keff, one-dimensional flux distribution in a homogenized node can be calculated, from which surface average flux and discontinuity factors can be obtained. The equivalent homogenization parameters so obtained can effectively account for discrepancy caused by assembly homogenization and the approximations in subsequent full-core diffusion calculations.Two multigroup pin power reconstruction methods are developed in this thesis. In the first method, the flux distribution inside a node is expanded by semi-analytic base functions (polynomials and plane wave functions). The coefficients of polynomials are determined by fission and scattering source expansion. Surface average fluxes and corner fluxes are used to determine the coefficients of plane wave functions. The source expansion is then updated with least square fitting. The corner fluxes are iteratively calculated via a whole-core sweeping process, which applies the source free and flux continuity condition at each corner to relate the corner flux to all other corner fluxes and surface-average fluxes in the neighboring nodes. The second method also expands the flux distribution inside a node by the same semi-analytic base functions. Constraints on the flux expansion are the node average flux, surface average fluxes, surface average net currents and corner point net currents, which can be determined from the quadratic transverse leakage profile. A least square method is then applied to require the transversely integrated intra-nodal flux to best fit the corresponding one-dimensional intra-nodal flux obtained from the global nodal solution. The Lagrange multiplier method is used to determine the coefficients of flux expansion. The two methods are programmed in computer codes. Both the pin power reconstruction methods have been tested with several benchmark problems. They can predict pin power distribution with accuracy comparable to that of detailed pin-by-pin models.Computer code using the above improved assembly homogenization method has been applied to the C5G7-MOX 2D/3D benchmark problem. The results show accuracy comparable to that of full core heterogeneous transport calculation. Energy group collapse is investigated in this thesis using the C5G7-MOX 2D/3D benchmark problem. The 7G cross-sections are collapsed to 2G, and a leakage correction method is used to correct for the Colorset spectrum difference from the full core spectrum. The accuracy of the 2G results is also comparable to that of full core heterogeneous transport method. The feasibility of the method in this thesis is therefore confirmed by these results.The improved assembly homogenization method is a natural evolution of the current method for LWR core physics analysis. The improvement of the calculation model and process is the key to the method. It has significant academic value and application value as well.