The liquid-fueled molten salt reactor (MSR) is one of the candidate reactors for the Generation IV advanced nuclear power systems, which utilizes flowing liquid molten salt as both fuel and coolant. In transients of liquid-fueled MSRs, the distribution change in the delayed neutron precursors (DNPs) in the primary loop has an important impact on system safety analysis. In order to analyze and evaluate this effect, the RELAP5-TMSR code with a 1-D DNP transport model was used to model the Molten Salt Breeder Reactor (MSBR), and several representative transient scenarios, including the loss of primary flow, increase in primary flow, loss of secondary flow, reactivity perturbation, and load change, were simulated and analyzed. The results show that the DNP distribution changes obviously during primary flow transients, especially during the loss of primary flow. Besides, the power response trends at different power levels during the loss of primary flow are different. The analysis results reveal the steady-state and dynamic characteristics of the DNP distribution, indicating that the DNP distribution, temperature feedback, and reactor power are strongly coupled, which has significant implications for the design and safety analysis of liquid-fueled MSRs.

The high-dimensional integral–differential nature of the neutron transport equation and the complexity of nuclear reactors result in high computational costs. A set of reduced-order modeling frameworks based on Proper Orthogonal Decomposition (POD) is developed to improve the computational efficiency for neutron diffusion calculations while maintaining accuracy, especially for small samples. For modal coefficient calculations, three methods—Galerkin, radial basis function (RBF), and Deep Neural Network (DNN)—are introduced and analyzed for molten salt reactors. The results show that all three reduced-order models achieve sufficient accuracy, with neutron flux L₂ errors below 1% and delayed neutron precursor (DNP) L₂ errors below 2.4%, while the acceleration ratios exceed 800. Among these, the POD–Galerkin model demonstrates superior performance, achieving average L₂ errors of less than 0.00658% for neutron flux and 1.01% for DNP concentration, with an acceleration ratio of approximately 1800 and excellent extrapolation ability. The POD–Galerkin reduced-order model significantly enhances the computational efficiency for solving neutron multi-group diffusion equations and DNP conservation equations in molten salt reactors while preserving the solution accuracy, making it ideal for a liquid fuel molten salt reactor in the case of small samples.

The transmutation of transuranic (TRU) elements produced by pressurized water reactors (PWRs) can effectively reduce their radioactive hazards. The molten chloride salt fast reactor (MCSFR) is a type of liquid-fueled molten salt reactor (MSR) using fuel in the form of molten chloride salts. The MCSFR utilizing a fast neutron spectrum and high actinide fraction is considered to be a potential reactor type for TRU transmutation. An online refueling and reprocessing scenario is the unique feature of liquid-fueled MSRs. On account of this characteristic, a new fuel management code named ThorNEMFM with a nodal expansion method (NEM) was developed and validated with the molten salt breeder reactor (MSBR) and the molten salt fast reactor (MSFR) benchmarks. Then, the transmutation and breeding performances of the MCSFR were simulated and analyzed with the ThorNEMFM code. The MCSFR adopts TRU elements as initial fissile loads and online feeding fissile materials. The results show that the transmutation ratio of TRU elements in the MCSFR can reach 50%, and the breeding ratio can reach 1.359. Moreover, the MCSFR has low radiotoxicity due to lower buildup of fission products (FPs).

To provide reliable safety margins in reactor design and safety analysis, the best estimate plus uncertainty (BEPU) analysis, which is recommended by the International Atomic Energy Agency (IAEA), has drawn increasing attention worldwide. In order to systematically evaluate the sensitivity and uncertainty in the design and safety analysis of molten salt reactors (MSRs), a sensitivity and uncertainty analysis framework has been developed by integrating the reactor system safety analysis code RELAP5-TMSR with the data analysis code RAVEN. The framework is tested using the transient scenarios of the molten salt reactor experiment (MSRE): reactivity insertion accident (RIA) and station blackout (SBO). The testing results demonstrate that the proposed framework effectively conducts sensitivity and uncertainty analysis. Sensitivity analyses identify key input parameters, including the primary exchanger parameters, air radiator parameters, initial temperatures, delayed neutron parameters and volumetric heat capacity of the INOR-8 alloy. Uncertainty quantification provides 95% confidence intervals for the figures of merit (FOMs) and the steady-state and RIA scenarios remained within safety limits. The developed framework enables automated, efficient, and high-capacity sensitivity and uncertainty analysis across multiple parameters and transient scenarios. The systematic analysis provides sensitivity indicators and uncertainty distributions, offering quantitative insights into the safety margins and supporting the design and safety analysis of MSRs.