Adjoint Sensitivity Analysis of a 1D Stationary Neutronics-Thermohydraulics Coupled Molten Salt Reactor Model

Molten Salt Reactors (MSRs) are a promising technology for the future of nuclear energy. The complex multi-physics of MSRs requires the development of advanced neutronic and thermal-hydraulic coupling models. Sensitivity analysis is a powerful tool to study the impact of input parameters on the system’s responses. Among several possible sensitivity methods, adjoint are the most efficient for complex systems with many input parameters and few output responses, methods such as reactor physics problems. This work presents the mathematical adjoint sensitivity framework for a 1D model of the stationary neutronics - thermohydraulics coupled MSR, using the Lagrangian formalism. The specific case of a response function dependent only on the effective multiplication factor k_eff is treated. The model is implemented numerically in Python and some results are discussed using the Molten Salt Fast Reactor (MSFR) data. The adjoint sensitivities calculated are in good agreement with finite differences, showing the potential of adjoint methods for the multi-physics of MSRs. The numerical challenges of the adjoint problem are also discussed.