Application of Spring Method-based Thermal Expansion Feedback Method to Deterministic Neutron Transport Core Calculation

With the evolution of reactor core design, the impact of thermal expansion effects on reactivity has become increasingly significant and cannot be overlooked. There are many researches focusing on the coupled calculation of neutronics-thermal-mechanics based on the finite element method and Monte Carlo method, aiming at high fidelity and thorough simulation of coupling. However, the physics analysis used in core design calculation phase based on deterministic method could also use the coupled calculation in order to better consider the expansion feedback effect, given a viable methodology. Consequently, it is necessary to develop a neutronics-thermal-mechanical coupling methodology based on the nodal neutron transport method to efficiently and accurately account for this effect in core nuclear design calculations. Such a method is essential to explicitly and reliably account for the deformation-induced changes in material densities and geometries during steady-state and transient calculations. In this work, the classical spring mechanics model was introduced in SARAX-LAVENDER code to describe radially non-uniform thermal expansion without altering the original neutron transport mesh topology. The expansion of material was first described as the expansion of mesh, and then transformed into the expansion of spring. The state of the spring system after applying expansion was described as the minimal energy state, and the energy minimization problem of the spring system was solved using the L-BFGS method, thereby obtaining the expanded core mesh. The geometry was then updated and the material distribution, macro cross-section could be calculated afterwards. The SARAX-LAVENDER was applied to a hypothetical case of non-uniform thermal expansion in a cylindrical bare reactor, in order to demonstrate the viability and liability of the expansion calculation method, as well as the coupling method with neutronics calculation. The UO₂ fuel in this reactor was manually divided into three different layer zones. The fuel in the middle layer was applied a significant high temperature while the fuel in the inner and outer layer was not, so that a non-uniform expansion in the radial direction was simulated with decent feedback effect on neutronics calculation. The same problem was modeled also in the commercial software COMSOL, and the expansion results calculated by SARAX-LAVENDER show good agreement with those obtained from COMSOL’s mechanical simulation module. The Monte Carlo code SERPENT was used and the reactivity feedback based on the reference geometry given by COMSOL, as well as on the geometry given by SARAX-LAVENDER’s expansion module, was calculated. The comparison of eigenvalue calculation between SERPENT and SARAX-LAVENDER indicates that for a total introduced reactivity of approximately 120 pcm, the calculation deviation in eigenvalues is about 5 pcm. This demonstrates that the SARAX-LAVENDER achieves good accuracy in calculating radially non-uniform thermal expansion and its feedback effect on neutronics calculation for core physics analysis.