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Linear Chain Method for Numerical Modelling of Burnup Systems

Author

Listed:
  • Jerzy Cetnar

    (AGH University of Science and Technology, Faculty of Energy and Fuels, al. Mickiewicza 30, 30-059 Krakow, Poland)

  • Przemysław Stanisz

    (AGH University of Science and Technology, Faculty of Energy and Fuels, al. Mickiewicza 30, 30-059 Krakow, Poland)

  • Mikołaj Oettingen

    (AGH University of Science and Technology, Faculty of Energy and Fuels, al. Mickiewicza 30, 30-059 Krakow, Poland)

Abstract

The theoretical aspects of the linear chain method for the numerical modelling of nuclear transmutation systems, and particularly regarding the transmutation trajectory analysis (TTA), are presented. The theoretical background of the TTA method, as an advanced version of the linear chain method, with the detailed description of the applied mathematical set-up and graphical visualisation of transformation chains, is shown. As the TTA method was initially developed at the AGH University of Science and Technology almost 25 years ago, several numerical implementations were introduced worldwide, yet the mathematical improvements or alternative forms of solutions and numerical algorithms were reported since then. The method was also implemented and tested by different research groups, also in confrontation with alternative approaches to the nuclear transformation problem known as the matrix method. The aim of the paper is to present the background of the developed method and its advantages, clarify misunderstandings in the method perception and suggest unexplored options in numerical algorithm implementation.

Suggested Citation

  • Jerzy Cetnar & Przemysław Stanisz & Mikołaj Oettingen, 2021. "Linear Chain Method for Numerical Modelling of Burnup Systems," Energies, MDPI, vol. 14(6), pages 1-19, March.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:6:p:1520-:d:514132
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    References listed on IDEAS

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    1. Christian Castagna & Manuele Aufiero & Stefano Lorenzi & Guglielmo Lomonaco & Antonio Cammi, 2020. "Development of a Reduced Order Model for Fuel Burnup Analysis," Energies, MDPI, vol. 13(4), pages 1-26, February.
    2. Ruixian Fang & Dan G. Cacuci, 2020. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: V. Computation of Mixed 2nd-Order Sensitivities Involvin," Energies, MDPI, vol. 13(10), pages 1-50, May.
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    Cited by:

    1. Mikołaj Oettingen & Juyoul Kim, 2023. "Detection of Numerical Power Shift Anomalies in Burnup Modeling of a PWR Reactor," Sustainability, MDPI, vol. 15(4), pages 1-20, February.
    2. Girma Tadesse Chala & Berihun Mamo Negash, 2022. "Artificial Neural Network and Regression Models for Predicting Intrusion of Non-Reacting Gases into Production Pipelines," Energies, MDPI, vol. 15(5), pages 1-14, February.
    3. Michał Górkiewicz & Jerzy Cetnar, 2021. "Flattening of the Power Distribution in the HTGR Core with Structured Control Rods," Energies, MDPI, vol. 14(21), pages 1-14, November.
    4. Mikołaj Oettingen, 2022. "The Application of Radiochemical Measurements of PWR Spent Fuel for the Validation of Burnup Codes," Energies, MDPI, vol. 15(9), pages 1-15, April.
    5. Przemysław Stanisz & Mikołaj Oettingen & Jerzy Cetnar, 2022. "Development of a Trajectory Period Folding Method for Burnup Calculations," Energies, MDPI, vol. 15(6), pages 1-15, March.
    6. Ruslan Irkimbekov & Alexander Vurim & Galina Vityuk & Olzhas Zhanbolatov & Zamanbek Kozhabayev & Artur Surayev, 2023. "Modeling of Dynamic Operation Modes of IVG.1M Reactor," Energies, MDPI, vol. 16(2), pages 1-20, January.
    7. Mikołaj Oettingen, 2021. "Assessment of the Radiotoxicity of Spent Nuclear Fuel from a Fleet of PWR Reactors," Energies, MDPI, vol. 14(11), pages 1-23, May.
    8. Yizhen Wang & Menglei Cui & Jiong Guo & Han Zhang & Yingjie Wu & Fu Li, 2023. "Decay Branch Ratio Sampling Method with Dirichlet Distribution," Energies, MDPI, vol. 16(4), pages 1-17, February.
    9. Minyu Peng & Yafen Liu & Yang Zou & Ye Dai, 2023. "Preliminary Design and Study of a Small Modular Chlorine Salt Fast Reactor Cooled by Supercritical Carbon Dioxide," Energies, MDPI, vol. 16(13), pages 1-18, June.

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    Keywords

    burnup; transmutation; decay;
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