Numerical analysis of startup PWR with fractional neutron point kinetic equation

In this paper we present the numerical analysis of the neutron density behavior when the nuclear reactor power is increased during startup of a PWR. The fractional neutron point kinetic (FNPK) equation with one-group delayed neutron precursor and external neutron source was used for this analysis. It is considered that there is a relaxation time associated with a rapid variation in the neutron flux and this effect is considered with the FNPK which have a physical interpretation of the fractional order is related with the sub-diffusive process, i.e., non-Fickian effects from the neutron diffusion equation point of view. In order to study the relaxation time effects during start-up of a PWR, a numerical analysis with FNPK is carried out, which it is assumed that during the ith step of control rod withdrawal the way of reactivity insertion is step to step, where the neutron source strength was defined as a constant in terms of a known initial stable sub-criticality and the neutron signal from a steady state condition. The results of the FNPK were compared with the classical neutron point kinetics (CNPK), for different values of the anomalous relaxation time.

► The behavior of neutron density when reactor starts up using fractional neutron point kinetics approximation is performed. ► Physical interpretation of the fractional order is related with non-Fickian effects. ► The effect of the anomalous diffusion coefficient and the relaxation time is analyze. ► There are sub-diffusive processes which are considered by FNPK and they cannot be negligible.