Monte Carlo and thermal hydraulic coupling using low-order nonlinear diffusion acceleration

Abstract

Monte Carlo (MC) methods for reactor analysis are most often employed as a benchmark tool for other transport and diffusion methods. In this work, we identify and resolve a few of the issues associated with using MC as a reactor design tool. It is widely thought that MC tallies converge at an ideal rate proportional to the inverse of the square root of the number of tally batches. This is true only if tally batches are independent from one another. For a high dominance ratio light water reactor such as the BEAVRS model, significant correlation is present and the convergence rate was much slower. This work developed a means for analytically predicting tally convergence rates when batches are correlated. Analyses supported these findings and confirmed less than ideal convergence rates. For highly correlated problems, it is recommended to reduce error by running additional independent simulations, rather than increasing the number of neutrons in each individual simulation through additional batches. Before tallies can be accumulated, the fission source must be stationary. For the BEAVRS model, this took approximately 200 fission source generations. This process can be accelerated by using coarse mesh finite difference (CMFD), a nonlinear diffusion acceleration method. CMFD was implemented in the continuous-energy MC code OpenMC. When employing this technique, the number of inactive generations was reduced by a factor of 10. Realistic reactor calculations also require thermal hydraulic (TH) feedback which was integrated into the source convergence process. The use of CMFD in addition to TH reduced the number of fission source generations by a factor of 3. Further reduction was achieved by performing nonlinear iterations between the low-order CMFD operator and TH model. Support vector regression, a machine learning algorithm, was used to construct coolant density and fuel temperature dependencies of diffusion parameters between each TH update using MC tallies. A framework was introduced to obtain relative pin power distributions with 95% confidence intervals to 1% with continuous-energy Monte Carlo coupled to thermal hydraulics using low-order CMFD iterations.