Position-dependent delayed-neutron fractions for IQS calculations and application to PHWR kinetics calculations

The core of a Pressurized Heavy-Water Reactor (PHWR) contains fuel bundles with burnups varying between zero and the discharge burnup. Because the delayed-neutron fraction varies (decreases) with burnup, the spatial variation of the fuel burnup causes the delayed-neutron fraction to also depend on position. High-fidelity kinetics calculations need to account for such spatial dependence of the delayed-neutron fraction. This work documents the implementation of the capability to model position-dependent delayed-neutron fractions in the multi-group diffusion code DONJON which performs kinetics calculations using the Improved Quasi-Static (IQS) method. Consistent with the IQS method, the effect of the spatial variation of the delayed-neutron fraction is accounted for both in the overall effective delayed neutron fraction and in the spatial dependence of the delayed-neutron source. Consequently, both the amplitude and the shape of the neutron flux are impacted by the position-dependence of the delayed-neutron fraction. The functionality of the newly-implemented capability is tested for a stylized coolant-voiding transient in a PHWR core and differences in reactor power and core neutron flux shape are shown to exist between the results of calculations that use position-dependent delayed-neutron fractions and those that only use spatially uniform ones.