Neutron kinetics equations for APOLLO3® code and application to noise problems = Neutron kinetics equations for APOLLO3® code and application to noise problems

A 2-D noise model is implemented in the deterministic reactor code APOLLO3® to simulate a periodic oscillation of a structural component. The Two/Three Dimensional Transport (TDT) solver, using the Method of Characteristics, is adopted for the calculation of the case studies, constituted by a detector and a control-rod assembly. The period is constructed by properly linking the geometries corresponding to the temporal positions. The calculation is entirely performed in the real time domain, without resorting to the traditional frequency approach. The periodicity allows to express the delayed fission source as a function of the flux values over time, instead of precursor concentrations. A dynamic eigenvalue is defined that takes into account the system average reactivity over a period. The algorithm is accelerated by combining the Wielandt shift scheme and the DPN synthetic method. For each cell of the domain, the time values of fission rates are analysed to determine the noise extent: for this purpose maximum variations relative to the mean value over the period are plotted.