Development and analysis of some versions of the fractional-order point reactor kinetics model for a nuclear reactor with slab geometry

摘要

In this paper, we report the development and analysis of some novel versions and approximations of the fractional-order (FO) point reactor kinetics model for a nuclear reactor with slab geometry. A systematic development of the FO Inhour equation, Inverse FO point reactor kinetics model, and fractional-order versions of the constant delayed neutron rate approximation model and prompt jump approximation model is presented for the first time (for both one delayed group and six delayed groups). These models evolve from the FO point reactor kinetics model, which has been derived from the FO Neutron Telegraph Equation for the neutron transport considering the subdiffusive neutron transport. Various observations and the analysis results are reported and the corresponding justifications are addressed using the subdiffusive framework for the neutron transport. The FO Inhour equation is found out to be a pseudo-polynomial with its degree depending on the order of the fractional derivative in the FO model. The inverse FO point reactor kinetics model is derived and used to find the reactivity variation required to achieve exponential and sinusoidal power variation in the core. The situation of sudden insertion of negative reactivity is analyzed using the FO constant delayed neutron rate approximation. Use of FO model for representing the prompt jump in reactor power is advocated on the basis of sub-diffusion. Comparison with the respective integer-order models is carried out for the practical data. Also, it has been shown analytically that integer-order models are a special case of FO models when the order of time-derivative is one. Development of these FO models plays a crucial role in reactor theory and operation as it is the first step towards achieving the FO control-oriented model for a nuclear reactor. The results presented here form an important step in the efforts to establish a step-by-step and systematic theory for the FO modeling of a nuclear reactor.