In liquid-fueled molten salt reactors (MSRs), the nuclear fuel is dissolved in a molten salt mixture that circulates through the primary loop. For system-scale simulations of MSRs, a point kinetics model (PKM) is commonly employed to describe the core neutronic behavior. In this model, flow-related terms are added to the delayed neutron precursor (DNP) balance equation by simplifying the reactor system into two lumped regions - a reactor core and an external loop. This simplified approach is, however, inadequate for a realistic MSR system with complex flow paths. To overcome this limitation, a DNP transport equation can be incorporated into the PKM in place of the DNP balance equation, enabling a more accurate representation of the DNP distribution throughout the reactor system.
In this study, a one-dimensional thermal-hydraulic model is assumed for MSR system simulations, and the axial power distribution in the reactor core is considered to be either uniform or sinusoidal. Analytical solutions to the steady-state DNP transport equation are then derived to obtain one-dimensional DNP profiles in the core and the corresponding effective delayed neutron fraction. These analytical results can serve as reference solutions for verifying thermal-hydraulic system codes developed for MSRs.
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