Aarno Isotalo

Comparison of Neutronics-Depletion Coupling Schemes for Burnup Calculations

Abstract Four predictor-corrector schemes for coupling the neutronics and depletion in burnup calculations are compared in four assembly segment test cases with various step lengths. Three of the coupling schemes are established methods. The last one, LE/QI with substeps, is one of the higher-order methods presented in our earlier publications. The purpose of this paper is twofold. First, it serves as a further validation of LE/QI, as well as a demonstration of the advantage it provides over the prior methods. Second, it aims to shed some light on the relative performances of the three prior methods as only two of them appear to have been compared in the open literature. Determining the relative performances of the prior methods is a value in itself, but it also serves to complement the results of our earlier studies, which compared the higher-order methods to only one of the prior methods.

Comparison of Neutronics-Depletion Coupling Schemes for Burnup Calculations—Continued Study

Abstract Four schemes for coupling the neutronics and depletion in burnup calculations are compared in four assembly segment test cases with various step lengths. Three of the coupling schemes use only one transport solution per step. While none of the methods was superior in every test case or in every respect, there are significant differences that can make one or the other preferable in different applications. The fourth method included in the comparison is the one dubbed CE/CM in our previous study, which compares schemes that use two transport solutions per step. The methods using only one transport solution per step were found to be more accurate than CE/CM but less accurate than the newer LE/LI and LE/QI methods. In cases where desired output intervals, rather than accuracy, are the limiting factor for step lengths, methods using only one transport solution per step can still provide a major advantage even when compared to LE/LI and LE/QI. Significant differences were also observed in the propagation of the statistical uncertainty from Monte Carlo neutronics through the different methods. While this topic was not studied further, it seems that differences in error propagation may in some cases be as significant as those in accuracy.

Calculating Time-Integral Quantities in Depletion Calculations

Abstract A method referred to as tally nuclides is presented for accurately and efficiently calculating the time-step averages and integrals of any quantities that are weighted sums of atomic densities with constant weights during the step. The method allows all such quantities to be calculated simultaneously as a part of a single depletion solution with existing depletion algorithms. Examples of results that can be extracted include step-average atomic densities and macroscopic reaction rates, the total number of fissions during the step, and the amount of energy released during the step. The method should be applicable with several depletion algorithms, and the integrals or averages should be calculated with an accuracy comparable to that reached by the selected algorithm for end-of-step atomic densities. The accuracy of the method is demonstrated in depletion calculations using the Chebyshev rational approximation method. As an example of a possible use, we demonstrate how the ability to calculate energy release in depletion calculations can be used to determine the accuracy of the normalization in a constant-power burnup calculation during the calculation without a need for a reference solution.