Comparison of depletion algorithms for large systems of nuclides

Isotalo, Aarno; Aarnio, P.

doi:10.1016/j.anucene.2010.10.019

Cited by 78 publications

(26 citation statements)

References 9 publications

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“…Large variety of computational methods for obtaining matrix exponent has been invented and successfully applied in different transmutation codes. It is useful to remind the most prominent methodology well explained by (Isotalo and Aarnio, 2011;Isotalo, 2013):…”

Section: Bðnþ/ðrþmentioning

confidence: 99%

Burnup instabilities in the full-core HTR model simulation

Kępisty

Cetnar

2015

Annals of Nuclear Energy

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Section: Bðnþ/ðrþmentioning

confidence: 99%

Burnup instabilities in the full-core HTR model simulation

Kępisty

Cetnar

2015

Annals of Nuclear Energy

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“…The set of Bateman equations can be solved using a variety of numerical methods optimized for this purpose and several of them are discussed in the work by [4]. For example MCB applies Transmutation Trajectory Analysis (TTA) and Chebyshev Rational Approximation Method (CRAM) is implemented in SERPENT.…”

Section: Methodsmentioning

confidence: 99%

Underestimation of nuclear fuel burnup – theory, demonstration and solution in numerical models

2016

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Abstract.Monte Carlo methodology provides reference statistical solution of neutron transport criticality problems of nuclear systems. Estimated reaction rates can be applied as an input to Bateman equations that govern isotopic evolution of reactor materials. Because statistical solution of Boltzmann equation is computationally expensive, it is in practice applied to time steps of limited length. In this paper we show that simple staircase step model leads to underprediction of numerical fuel burnup (Fissions per Initial Metal Atom -FIMA). Theoretical considerations indicates that this error is inversely proportional to the length of the time step and origins from the variation of heating per source neutron. The bias can be diminished by application of predictor-corrector step model. A set of burnup simulations with various step length and coupling schemes has been performed. SERPENT code version 1.17 has been applied to the model of a typical fuel assembly from Pressurized Water Reactor. In reference case FIMA reaches 6.24% that is equivalent to about 60 GWD/t HM of industrial burnup. The discrepancies up to 1% have been observed depending on time step model and theoretical predictions are consistent with numerical results. Conclusions presented in this paper are important for research and development concerning nuclear fuel cycle also in the context of Gen4 systems.

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“…Different numerical and analytical methods have been developed to compute the result; it is useful to mention the most prominent methodology currently used [5]: -Runge-Kutta-Gauss solution (RGK), -Transmutation trajectory analysis (TTA), -Chebyshew rational approximation method (CRAM). In general, quantities such as  and T are time dependent in nuclear system even in steady state.…”

Section: Aspects Of Burnup Calculation Theorymentioning

confidence: 99%

“…Notice, that such formulation assumes neutron fl ux and temperature fi eld to be constant. The formal solution of this system is called 'matrix exponential' [5]:…”

Section: Aspects Of Burnup Calculation Theorymentioning

confidence: 99%

Assesment of advanced step models for steady state Monte Carlo burnup calculations in application to prismatic HTGR

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2015

Nukleonika

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IntroductionThe concept of using continuous energy Monte Carlo simulations for critical systems as a precise tool for burnup calculations is well known in the fi eld of research and development of fuel cycle. The beginning-of-step approximation of neutron fl ux over the time-step is often applied by many burnup codes for its simplicity. This approach assumes constant fl ux/power profi le during entire step, which can cause problems such as spatial instability of reaction rates in the simulated system [1]. Spatial oscillations of fl ux and xenon concentration appear for relatively short steps, thus affecting the core's equilibrium. Regarding fuel cycle analysis of prismatic HTGR, the spatial fl ux distribution of the core varies strongly in the vicinity of compensation rods, which are being slowly withdrawn in order to compensate the reactivity loss. In order to handle this problem properly, a better fl ux normalization procedure -so-called bridge scheme -was developed and applied in the study of PuMA project [2]. An optimal model of time-step is necessary to account for the non-constant system's behavior as well as to provide stability of burnup. Abstract. In this paper, we compare the methodology of different time-step models in the context of Monte Carlo burnup calculations for nuclear reactors. We discuss the differences between staircase step model, slope model, bridge scheme and stochastic implicit Euler method proposed in literature. We focus on the spatial stability of depletion procedure and put additional emphasis on the problem of normalization of neutron source strength. Considered methodology has been implemented in our continuous energy Monte Carlo burnup code (MCB5). The burnup simulations have been performed using the simplifi ed high temperature gas-cooled reactor (HTGR) system with and without modeling of control rod withdrawal. Useful conclusions have been formulated on the basis of results.

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Comparison of depletion algorithms for large systems of nuclides

Cited by 78 publications

References 9 publications

Burnup instabilities in the full-core HTR model simulation

Burnup instabilities in the full-core HTR model simulation

Underestimation of nuclear fuel burnup – theory, demonstration and solution in numerical models

Assesment of advanced step models for steady state Monte Carlo burnup calculations in application to prismatic HTGR

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