Research On The Boundary Flow Response Matrix Method In Nuclear Reactor Physics Calculation

The flux-volume weighting method is usually used as the conventional cell-wisehomogenization calculation method in nuclear reactor physics calculation. It maintainsthe flux and reaction rates conservation of each group under reflective boundaryconditions, but there is a considerable error for the simulation results when the incidentflow varies obviously. Based on the response matrix (RM) theory, an improved methodfor the homogenization calculation taking advantage of the response of incident flowand exit flow instead of the conservation of mean flux is proposed in this thesis. In thenew method the conservation of response of exit flow to incident flow and reaction ratesis maintained. Almost little calculation amount is added in the new methodcomparatively. The verifications on a slab problem with reflector and the2-DC5G7MOX benchmark problem indicate that the new method can improve thesimulation accuracy of the eigenvalue and pin power distribution.Based on the RM method, this thesis also investigates the equivalent method forassemblies and whole core iteration method in consideration of the existence of manyrepetition structures in nuclear reactor cores. The basic idea of this method is using theresponse relationship of incident flow and exit flow on the surface of assemblies tocarry out the equivalent calculation, instead of transforming assemblies intohomogenized ones. In order to make the relationship between the incident flow and theexit flow of the assembly boundary a linear one, the fission cross sections are dividedby the keff, thus transforming the eigen-value problem into a fixed source problem. As aresult, the coupling correlations of incident flow and exit flow can be decided by thelinear coupling coefficients. Through iteration calculation in the reactor core, the keffofthe reactor core and the boundary flows of every assembly can be worked out, as well asthe flux distribution. A calculation code is finished based on the above theory and the2-D C5G7MOX benchmark and some other test problems are used as testing problems.The results show that both high efficiency and good precision can be achieved.Compared with other transport calculation methods, such as Sn, the calculationspeed of RM method is improved by at least two orders. The calculation time neededfor different numbers of grids using the RM method is also investigated, which proves the advantage of this method in term of calculation speed. The approximation in theexpansion of assembly boundary flow leads to the sacrifice in the precision of pinpower distribution. In order to improve pin power precision, the shape factor correctionmethod and the Characteristic Response Matrix method (CRM) are introduced. Theshape factor correction method can improve the pin power precision partly, while theCRM method based on reflective boundary conditions is more potential in furtherresearch.