Position-Dependency of Fuel Assembly Homogenization in a Pressurized Water Reactor
2-step nuclear reactor core analysis has long been established as the conventional calculational procedure for the pressurized water reactor (PWR) due to its efficiency. This is because the procedure significantly avoids the potentially huge computational burden arising from an explicit geometrical modeling and consideration of over ∼ 500 energy groups. It instead approaches the problem with spatial homogenization and group condensation: a 2-D lattice transport calculation to homogenize the fuel assembly cross-sections and a 3-D whole core nodal diffusion. One notes that the few-group constant generation using deterministic method could be complicated due to its limited flexibilities in geometrical modeling and inherent drawbacks of the multi-group approximation. Furthermore, accuracy of the deterministic few-group constant generation can especially be compromised during the resonance treatment calculation. As such, an alternative lattice calculation using the Monte Carlo (MC) approach, in place of the deterministic fuel assembly homogenization (few-group constant generation), has previously been proposed. During the assembly homogenization, directions and magnitudes of the current at boundaries are unknowns. Therefore, zero net current boundary conditions (infinite lattice) are instead used as the assembly node. The assumption is quite reasonable considering heterogeneities inside the node are more dominant than heterogeneities due to nodal location in the core. In fact, this approximation has successfully been applied to many LWR core analyses to reasonable accuracy. It should nonetheless be noted that the net current zero boundary assumption effectively ignores position-dependency of the fuel assembly homogenization in the general 2-step method. As such, there are a number of well-known researches on the extended assembly homogenization techniques, which introduce correction factors to compensate effects of the assembly environment, such as Generalized Equivalence Theory (GET), Super-homogenization method (SPH), and color set calculation method. Even though the assembly environment effect has long been acknowledged, its effect has not properly been investigated due to the limited computing power in the past and due to the reasonable accuracy of the extended assembly homogenization techniques. Nonetheless, quantification of position-dependency of the assembly homogenization in the core could still potentially offer additional value in terms of calculation accuracy to the 2-step reactor analysis. It is upon this motivation that the paper is prepared. In this research, position-dependent few-group constants were calculated and compared against those of infinite lattices. All calculations were completed using the MC Serpent2 code with ENDF/B7.0 nuclear data library. In this study, position-dependency of the fuel assembly homogenized cross sections in a PWR core has been investigated through comparison of the conventional 2-step reactor analysis with the reference high fidelity Monte Carlo simulation. It was found that the homogenized two-group constants are clearly position-dependent as the discrepancies between infinite lattice and whole-core calculations are quite significant especially in a rodded assembly. As such, the corresponding correction required due to the assembly environment effect is not negligible compared to the correction required due to assembly heterogeneity itself. It is therefore quite clear that position-dependency of the group cross sections should be considered in the 2-step procedure for a more accurate PWR core analysis. (authors)