Subdiffusive processes in BWRs

Abstract

The objective of this work is the analysis of subdiffusive processes in BWR reactors. Nuclear reactors are highly heterogeneous systems where the phenomena at the reactor scale are not possible to describe with constitutive standard laws (normal diffusion) of energy, momentum, and mass. However, there are methods to achieve it such as the volumetric average to upscale the reactor and incorporate up-scaled constitutive laws. However, it can also be proposed constitutive laws of fractional order to consider anomalous diffusion. For the neutronic processes, the neutron diffusion theory is non-appropriated to the reactor scale, because this theory is applied to the homogeneous reactor. Given the heterogeneity of these systems in describing the dynamic behaviour of BWRs with point models, it represents a challenge to the incorporation of the heterogeneous effects whose main characteristic is that the transport phenomena are subdiffusive with relaxation times (i.e., non-instantaneous) by nature. The point models called reducer-order models are important for stability analysis and to develop control strategies. In linear or nonlinear stability analysis and system control, they are carried out with reduced order models that are zero dimension, i.e., point models that depend exclusively on time. This is because existing methodologies propose mathematical expressions in the time or frequency domain for stability analysis or to establish control strategies. The challenge is for ROM models to be able to consider subdiffusive effects on neutron motion. This is achieved by various routes from the P1 theory that includes the temporal term with relaxation effects (relaxation time) or by proposing a more general constitutive equation of fractional order for the neutron current vector, as is presented in this work. Moreover, the Fractional Order Models behavior must be as a transport theory based model, as well as in those nuclear and thermohydraulic codes which are very useful but complex, for which is sometimes it is impossible to obtain analytical expressions. To incorporate these effects in this work we consider point models of fractional order, which represent the subdiffusive phenomenon when the fractional order (known as anomalous diffusion coefficient) is greater than 0 and less than 1.