Development of Advanced Leakage Feedback Method for Two-step Core Analyses

Abstract

In reactor core analyses, Direct Whole Core (DWC) calculations employing no essential approximations are now feasible owing to the continued advance in computer performance. Nonetheless, the conventional two-step (2S) core calculation procedure has indispensable merits due to its far lower cost than DWC calculations. Since two-step core analyses employing B1 critical leakage correction provides acceptable accuracy, it has been adopted as the standard procedure for reactor design analyses in the nuclear industry for a long period of time. However, it has not drawn sufficient attention that the neighbor-irrelevant correction of B1 induces biased reactivity errors and checkerboard-like power distribution errors. In this work, it is demonstrated the drawbacks of the B1 method need to be overcome by better leakage correction to improve the accuracy of the two-step core analyses.<br/> Previously, Palmtag devised the Spectral Correction Method which assumes that the difference in few-group constants (GCs) between zero leakage and non-zero leakage cases is proportional to the leakage-to-removal ratio. However, as the method adopted the B1 method to simulate leakage conditions, it was impossible to properly reflect the leakage effects in actual cores. In this regard, an advanced leakage correction method named Leakage Feedback Method (LFM) is devised here which uses checkerboard colorsets as better representations of the actual core conditions. One novelty of the new method is to use both fast and thermal leakage fractions as the functionalization parameters based on the observation that the fast group cross-sections show strong dependency on thermal leakage as well. Another uniqueness of the method is the special treatment for peripheral assemblies which have quite different leakage characteristics than the interior assemblies due to the presence of the reflector. The Peripheral Assembly Treatment (PAT) scheme devised here employs spectral index (SI) shift as a measure of the shift in the fast-to-thermal flux ratio as an additional functionalization parameter.<br/> LFM with PAT is implemented in the nTRACER-RENUS two-step core analysis system. The performance of the advanced two-step method is evaluated through a series of assessments for various problems including the BEAVRS and the VERA benchmark cores, AP1000 and APR1400 core, and also a small modular reactor core. Especially for the APR1400 core model, thermal feedback, depletion, and control rod insertion cases are additionally analyzed. Through all the cases, it is verified that RENUS augmented with the new leakage feedback method renders reactivity errors less than 50 pcm and assembly-wise power RMS errors less than 0.8 % when compared against the nTRACER direct whole core calculation results. It is noted that the corresponding values of the conventional approach are 150 pcm and 1.5 %, respectively.<br/> Considering the advantage of the low cost of the transport calculations for two-dimensional checkerboard problems needed for the generation of the leakage correction functions and the simple concept and implementation procedure of the LFM method, it is possible to effectively enhance the accuracy of a two-step procedure. As a transitional method between the assembly-wise two-step method and the DWC method, the pin-wise two-step calculation methods are being developed these days for the next-generation practical core analysis codes. The concepts of LFM and PAT can be adapted to the pin based two-step procedure. Meanwhile, some of the DWC codes achieved execution times less than 5 minutes for a single state core calculation on massively parallel cluster machines. But it might take at least a decade to make it possible to utilize that kind of huge machines for routine design calculations. Thus, this advanced two-step method will remain effective in the industry for a sufficiently long time.<br/> <br/> Keywords: <br/> Two-step Core Analysis<br/> Homogenized Group Constants<br/> Leakage Feedback Correction<br/> Peripheral Assembly Treatment<br/> <br/> Student Number: 2012-21001<br/>