A unified generic theory on discontinuity factors in diffusion, SP3 and transport calculations. (January 2015) - Yu, Lulin; Chao, Yung-An
Highlights: Theory for calculation of discontinuity factors. Generally applied in transport, SP3 and diffusion. Works well even with serious heterogeneity. Definition of boundary DF of assemblies is discussed. Produced DF is compared with SPH. Abstract: A theory is presented that unifies the calculation of discontinuity factors in diffusion, SP3 and transport calculations. The idea of Even Parity Discontinuity Factor (EPDF) was recently introduced for transport calculation using homogenized pin cells. In this paper a rigorous method is worked out to numerically calculate and implement the angular dependent EPDF while using angular flux without parity decomposition. This is made possible by converting EPDF forth and back to an equivalent Angular Flux Discontinuity Factor (AFDF) during the transport calculation. In order to save the required data storage to make the method practical, the angular independent EPDF is also introduced that can still preserve the cell reaction rate but greatly simplifies the calculation. The angular independent EPDF can be uniquely determined by using only the reference value of the cell surface net current without the need of knowing the reference value of the surface flux. The EPDF so determined is called the Prime EPDF. The EPDF can be renormalized by demanding a certain surface quantity to match its reference value after EPDF application. If the EPDF is generated with a single assembly model, the Prime EPDF and the Renormalized EPDF will have identical effect on the cell interface boundary conditions except for that on the assembly boundary surface when the assembly is placed in a core model. The EPDF theory suggests that the normalization target should be the sum of the incoming and outgoing partial currents on each surface. This angular independent EPDF theory can be easily applied to SP3 and diffusion calculation as special cases. Here the EPDF can be applied directly without the need of the supporting AFDF. Both the Prime EPDF and the Renormalized EPDF options apply to these special cases. For SP3 calculation the theory shows that both the zeroth order and the second order flux moments in SP3 should share the same EPDF, thus removing the fundamental ambiguity of how to define and calculate the SP3 discontinuity factors. For diffusion calculation the theory gives an EPDF defined differently from the conventionally adopted discontinuity factor. The theory has been tested to work well on a series of mini-core benchmark problems with severe heterogeneity. The tests are made for the Method of Characteristics (MOC) transport calculation, the SP3 calculation and the diffusion calculation. Both pin-cell homogenization and assembly homogenization cases are covered in the tests. Comparison is made on the results using the Prime EPDF, the Renormalized EPDF, the conventional discontinuity factor and the SPH (super homogenization) factor. Generally speaking, for cases with homogenized pin cells the Prime EPDF gives the best accuracy while for cases with homogenized assemblies the Renormalized EPDF gives the best accuracy.