Development of Transient Analysis Capability of PROTEUS-MOC for Micro-reactor Applications

Abstract

Micro-reactors are gaining increasing interest from the industry, and various micro-reactors are being developed. These micro-reactors typically have a complex core configuration, and thus neutronics analysis are usually performed with Monte Carlo codes. However, the application of Monte Carlo method to transient analysis is not practical yet. Motivated by the need for accurate and efficient deterministic tool which supports irregular geometry problems, transient analysis capabilities and associate acceleration schemes have been developed and implemented into the PROTEUS-MOC code of Argonne National Laboratory (ANL), which has an arbitrary geometry modeling capability through unstructured finite element meshes. To improve the computational performance of PROTEUS-MOC prototype for practical reactor problem applications, coarse mesh finite difference (CMFD) acceleration methods were developed and implemented in PROTEUS-MOC to speed up both the steady state and transient calculations. The original GMRES iteration method for solving the within-group transport equations was replaced with a nonlinear fixed-point iteration method. The conditionally stable CMFD acceleration method was replaced with the two-level partial current CMFD formulation (pCMFD), which is unconditionally stable and more efficient. More importantly, an unstructured CMFD method (uCMFD) was developed for the application to irregular complex geometry problems. Verification tests with the C5G7 benchmark, a TREAT experiment, and the EMPIRE micro-reactor design showed that the two-level CMFD results in a speed-up of ~20 times and the uCMFD yields a speed-up of more than 10 times. Three new pin-resolved transient solvers were developed into PROTEUS-MOC. Using the direct time integration method, a new transient fixed-source problem (TFSP) solver was developed without relying on the isotropic approximation of the angular flux time derivative. A moving axial mesh scheme was implemented to model the control rod movement without the control rod cusping problem. To model the rotational movement of control drums in micro-reactors, an approximating flux weighting method was also developed to calculate the effective cross sections of the control drum meshes of which azimuthal boundaries are not lined up with the absorber tips. In order to reduce the computational time further without a significant loss of accuracy, two quasi-static solvers were also developed: an improved quasi-static method (IQM) and a predictor-corrector quasi-static method (PCQM) solver. Verification tests were performed using the C5G7 time-dependent benchmark (C5G7-TD). The test results showed that the three transient solvers yield accurate kinetics solutions. Furthermore, it was found that the isotropic approximation of angular flux time derivative could yield non-negligible local power errors and that the kinetics parameters in the quasi-static calculations should be weighted with the adjoint angular flux instead of the adjoint scalar flux, which is used in most of the current pin-resolved transport codes. As an integral test, a heat pipe-cooled micro-reactor proposed by Los Alamos National Laboratory (LANL) was analyzed using a one-sixth core model. Multigroup cross sections were generated using the SERPENT-2 Monte Carlo code. Steady state calculations were performed for two control drum configurations: absorber-in and -out configurations. For both configurations, the eigenvalue and pin power distribution of PROTEUS-MOC agreed very well with the SERPENT-2 Monte Carlo solutions. A reactivity insertion transient without thermal feedback was also analyzed by rotating a control drum 32 degrees. This simulation demonstrated that practical micro-reactor transient problems can be solved with PROTEUS-MOC.