Higher order methods for burnup calculations with Bateman solutions

Isotalo, Aarno; Aarnio, P.

doi:10.1016/j.anucene.2011.04.022

Cited by 54 publications

(16 citation statements)

References 4 publications

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“…It is important to note that γ ij and γ j are constant for a single solution of the Bateman equations in a single burnup step. However, more solutions are usually calculated for a single burnup step, by employing predictor-corrector methods [28]. Equation (2) can be written in matrix notation:…”

Section: Motivation Of the Methodologymentioning

confidence: 99%

Development of a Reduced Order Model for Fuel Burnup Analysis

Castagna

Aufiero²,

Lorenzi

et al. 2020

Energies

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Fuel burnup analysis requires a high computational cost for full core calculations, due to the amount of the information processed for the total reaction rates in many burnup regions. Indeed, they reach the order of millions or more by a subdivision into radial and axial regions in a pin-by-pin description. In addition, if multi-physics approaches are adopted to consider the effects of temperature and density fields on fuel consumption, the computational load grows further. In this way, the need to find a compromise between computational cost and solution accuracy is a crucial issue in burnup analysis. To overcome this problem, the present work aims to develop a methodological approach to implement a Reduced Order Model (ROM), based on Proper Orthogonal Decomposition (POD), in fuel burnup analysis. We verify the approach on 4 years of burnup of the TMI-1 unit cell benchmark, by reconstructing fuel materials and burnup matrices over time with different levels of approximation. The results show that the modeling approach is able to reproduce reactivity and nuclide densities over time, where the accuracy increases with the number of basis functions employed.

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Section: Motivation Of the Methodologymentioning

confidence: 99%

Development of a Reduced Order Model for Fuel Burnup Analysis

Castagna

Aufiero²,

Lorenzi

et al. 2020

Energies

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“…1. The Substep scheme for coupled MC codes was originally introduced by (Isotalo and Aarnio, 2011a). The method relied on dividing the depletion step into substeps and solving the depletion problem separately for each substep.…”

Section: Stochastic Semi-implicit Substep (Sie) Methodsmentioning

confidence: 99%

Stochastic semi-implicit substep method for coupled depletion Monte-Carlo codes

Kotlyar

Shwageraus

2016

Annals of Nuclear Energy

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Coupled Monte Carlo burnup codes aim to evaluate the time evolution of different parameters, such as nuclide densities, for accurate modeling of the different reactor designs and associated fuel cycles. Recently a major deficiency in numerical stability of existing Monte Carlo coupling schemes was identified. Alternative, stable coupling schemes were derived, implemented and verified. These methods are iterative and rely on either the end-or middle-of-step (MOS) reaction rates to evaluate the end-of-step (EOS) nuclide densities. Here, we demonstrate that applying the EOS methods for realistic problems may lead to highly inaccurate results. Considerable improvement can be made by adopting MOS method but the accuracy may still be insufficient. The solution proposed in this work relies on the substep method that allows reducing the time discretization errors. The proposed and tested substep method also assumes that the reaction rates are linear functions of the logarithm of the nuclide densities. The method was implemented in BGCore code and subsequently used to perform a series of test case calculations. The results demonstrate that better accuracy and hence efficiency can be achieved with negligible additional computational burden.

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“…Particularly, in Serpent2 were implemented some burnup routines that work through some advanced options for predictor-corrector calculation: they were tested higher order methods to solve the depletion solutions in burnup calculations [20]. However, in this comparison it was used a standard predictor-corrector routine based on CE/LI algorithm (CE: Constant Extrapolation for the predictor, LI: Linear Interpolation for the corrector) [21].…”

Section: Serpent2mentioning

confidence: 99%

Comparison Among Monte Carlo Based Burnup Codes Applied to the GFR Demonstrator ALLEGRO

Chersola

Lomonaco

Mazzini

2018

Glob. J. Energ. Technol. Res. Updat.

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This paper aims to compare three Monte Carlo (MC) burnup based codes, i.e. MCNP6, Monteburns and Serpent on a future prototype reactor, named ALLEGRO, based on Gas cooled Fast Reactor (GFR) technology. GFR reactors are one of the proposed Generation-IV fast reactors; ALLEGRO facility is scheduled to be built in Europe as a GFR demonstrator, so its deepened simulation can help in its future development. The present study follows other researches already performed and aims to exhibit the different approaches in burnup calculations applied to a gas cooled fast reactors, i.e. this paper would like to show and to compare some results concerning nuclear parameters as keff and flux spectra, as well as the mass inventories versus burnup for some nuclides evaluated with different Monte Carlo codes. From obtained results, it seems to exist some differences in evaluation of nuclear parameters, mainly in effective multiplication factor and in mass inventories. The remaining differences are mainly related to calculation time: indeed between the fastest, that is SERPENT, and the slowest, that are MCNP6 and MONTEBURNS, the differences are about one order of magnitude. As far as precision is concerned, it was considered the standard only for effective multiplication factor and it seems that all codes are in good agreement.

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Higher order methods for burnup calculations with Bateman solutions

Cited by 54 publications

References 4 publications

Development of a Reduced Order Model for Fuel Burnup Analysis

Development of a Reduced Order Model for Fuel Burnup Analysis

Stochastic semi-implicit substep method for coupled depletion Monte-Carlo codes

Comparison Among Monte Carlo Based Burnup Codes Applied to the GFR Demonstrator ALLEGRO

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