Discontinuity factors in SP3 theory

Abstract

The SP3 theory is a better approximation than diffusion theory when modeling a nuclear reactor, but the properties of homogenization and discontinuity factors are not known. This master thesis, at Studsvik Scandpower, has been done to investigate the usage of discontinuity factors in the SP3 theory and compare the results with the traditional diffusion theory. The discontinuity factors should have the property to conserve the reaction rates and interface currents. Four different methods were tested to create discontinuity factors for SP3 theory, one analytical and three numerical. Two methods (the analytical one and one of the numerical methods) where able to conserve both the currents and reaction rates but at different costs. The analytical method has the problem of possible numerical instabilities, and the numerical method the problem of no unique solution. Good approximations are also found with minimal errors in flux and the effective multiplication factor keff . The thesis has shown that it is possible to use discontinuity factors in SP3 theory, either by recreating the solution completely, or use good approximations. For more reliable results and numerical stabilities some future improvements are needed. As a good approximation found was to use the traditional discontinuity factors with the change that the discontinuity factors for the second moment flux is set to unity.