Calculating Time-Integral Quantities in Depletion Calculations

Isotalo, Aarno

doi:10.13182/NSE15-119

Title: Calculating Time-Integral Quantities in Depletion Calculations

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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. Some examples of the 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. Furthermore, 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. Here, 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.

Authors:

Isotalo, Aarno ^[1]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Aalto Univ., Otaniemi (Finland)

Publication Date:: 2016-06-02

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE Office of Nuclear Energy (NE)

OSTI Identifier:: 1362197

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Nuclear Science and Engineering

Additional Journal Information:: Journal Volume: 183; Journal Issue: 3; Journal ID: ISSN 0029-5639

Publisher:: American Nuclear Society - Taylor & Francis

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; depletion; tally nuclides; CRAM

Citation Formats


                    Isotalo, Aarno. Calculating Time-Integral Quantities in Depletion Calculations.  United States: N. p., 2016. 
Web.  doi:10.13182/NSE15-119.

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                    Isotalo, Aarno. Calculating Time-Integral Quantities in Depletion Calculations.  United States.  https://doi.org/10.13182/NSE15-119

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                    Isotalo, Aarno. Thu .  
"Calculating Time-Integral Quantities in Depletion Calculations".  United States.  https://doi.org/10.13182/NSE15-119.  https://www.osti.gov/servlets/purl/1362197.

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@article{osti_1362197,

  title        = {Calculating Time-Integral Quantities in Depletion Calculations},

  author       = {Isotalo, Aarno},

  abstractNote = {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. Some examples of the 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. Furthermore, 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. Here, 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.},

  doi          = {10.13182/NSE15-119},

  journal      = {Nuclear Science and Engineering},

  number       = 3,

  volume       = 183,

  place        = {United States},

  year         = {2016},

  month        = {6}

}

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