Residence Time Theory Applied to Circulating Fuel Reactors: Zero-Power Analysis

Circulating-fuel reactors (CFRs) lose reactivity when delayed-neutron precursors (DNPs) drift out of the core and may regain part of it when the fuel re-enters the core. This paper formulates a physics-based description of both effects by combining DNP transport with residence-time theory. Then, treating the core and ex-core regions as two mixing volumes in series, closed-form expressions for (i) the static reactivity loss due to precursor drift and (ii) the zero-power transfer function that governs linearised dynamics are derived. When the gamma residence-time distributions are used, the new framework is shown to reduce to the plug-flow and Continuous-Stirred-Tank-Reactor limits as special cases, while generalising to intermediate mixing regimes via a single parameter: the degree of mixing. Performed parameter studies show that DNP recirculation has the highest impact when core and ex-core residence times are comparable and the product of the DNP decay constant and the in-core residence time is small. Benchmarks against the Molten-Salt Reactor Experiment are able to reproduce the measured static loss ($k_0 \approx 0.32$ \$) and its frequency response, with $\approx$20% of the steady-state DNP worth arising from recirculation. Additionally, for the EVOL reference Molten-Salt Fast Reactor the model is shown to agree well with the results of high-fidelity Serpent-2 calculations coupled with Computational Fluid Dynamics. Overall, the residence-time approach offers a computationally light yet versatile tool for sensitivity studies and generation of physical intuition for the behaviour of CFRs. Foundation for extensions to importance weighting of DNPs and application of the framework to time-domain analysis is also briefly sketched.