Calculating TimeIntegral Quantities in Depletion Calculations
A method referred to as tally nuclides is presented for accurately and efficiently calculating the timestep 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 stepaverage 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 endofstep 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 constantpower burnup calculation during the calculation without a need for a reference solution.
 Authors:

^{[1]}
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Aalto Univ., Otaniemi (Finland)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Nuclear Science and Engineering
 Additional Journal Information:
 Journal Volume: 183; Journal Issue: 3; Journal ID: ISSN 00295639
 Publisher:
 American Nuclear Society  Taylor & Francis
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE Office of Nuclear Energy (NE)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; depletion; tally nuclides; CRAM
 OSTI Identifier:
 1362197
Isotalo, Aarno. Calculating TimeIntegral Quantities in Depletion Calculations. United States: N. p.,
Web. doi:10.13182/NSE15119.
Isotalo, Aarno. Calculating TimeIntegral Quantities in Depletion Calculations. United States. doi:10.13182/NSE15119.
Isotalo, Aarno. 2016.
"Calculating TimeIntegral Quantities in Depletion Calculations". United States.
doi:10.13182/NSE15119. https://www.osti.gov/servlets/purl/1362197.
@article{osti_1362197,
title = {Calculating TimeIntegral Quantities in Depletion Calculations},
author = {Isotalo, Aarno},
abstractNote = {A method referred to as tally nuclides is presented for accurately and efficiently calculating the timestep 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 stepaverage 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 endofstep 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 constantpower burnup calculation during the calculation without a need for a reference solution.},
doi = {10.13182/NSE15119},
journal = {Nuclear Science and Engineering},
number = 3,
volume = 183,
place = {United States},
year = {2016},
month = {6}
}