PolyPole1: An accurate numerical algorithm for intragranular fission gas release
Abstract
This paper describes the development of a new numerical algorithm (called PolyPole1) to efficiently solve the equation for intragranular fission gas release in nuclear fuel. The work was carried out in collaboration with Politecnico di Milano and Institute for Transuranium Elements. The PolyPole1 algorithms is being implemented in INL's fuels code BISON code as part of BISON's fission gas release model. The transport of fission gas from within the fuel grains to the grain boundaries (intragranular fission gas release) is a fundamental controlling mechanism of fission gas release and gaseous swelling in nuclear fuel. Hence, accurate numerical solution of the corresponding mathematical problem needs to be included in fission gas behaviour models used in fuel performance codes. Under the assumption of equilibrium between trapping and resolution, the process can be described mathematically by a single diffusion equation for the gas atom concentration in a grain. In this work, we propose a new numerical algorithm (PolyPole1) to efficiently solve the fission gas diffusion equation in timevarying conditions. The PolyPole1 algorithm is based on the analytic modal solution of the diffusion equation for constant conditions, with the addition of polynomial corrective terms that embody the information on the deviation from constant conditions.more »
 Authors:
 Publication Date:
 Research Org.:
 Idaho National Lab. (INL), Idaho Falls, ID (United States)
 Sponsoring Org.:
 USDOE Office of Nuclear Energy (NE)
 OSTI Identifier:
 1361421
 Report Number(s):
 INL/JOU1638537
Journal ID: ISSN 00223115; PII: S0022311516302793
 DOE Contract Number:
 DEAC0705ID14517
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Nuclear Materials; Journal Volume: 478; Journal Issue: C
 Country of Publication:
 United States
 Language:
 English
 Subject:
 11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS; Diffusion; Fission gas release; Fuel modeling; Numerical algorithms; PolyPole
Citation Formats
Pizzocri, D., Rabiti, C., Luzzi, L., Barani, T., Van Uffelen, P., and Pastore, G. PolyPole1: An accurate numerical algorithm for intragranular fission gas release. United States: N. p., 2016.
Web. doi:10.1016/j.jnucmat.2016.06.028.
Pizzocri, D., Rabiti, C., Luzzi, L., Barani, T., Van Uffelen, P., & Pastore, G. PolyPole1: An accurate numerical algorithm for intragranular fission gas release. United States. doi:10.1016/j.jnucmat.2016.06.028.
Pizzocri, D., Rabiti, C., Luzzi, L., Barani, T., Van Uffelen, P., and Pastore, G. 2016.
"PolyPole1: An accurate numerical algorithm for intragranular fission gas release". United States.
doi:10.1016/j.jnucmat.2016.06.028. https://www.osti.gov/servlets/purl/1361421.
@article{osti_1361421,
title = {PolyPole1: An accurate numerical algorithm for intragranular fission gas release},
author = {Pizzocri, D. and Rabiti, C. and Luzzi, L. and Barani, T. and Van Uffelen, P. and Pastore, G.},
abstractNote = {This paper describes the development of a new numerical algorithm (called PolyPole1) to efficiently solve the equation for intragranular fission gas release in nuclear fuel. The work was carried out in collaboration with Politecnico di Milano and Institute for Transuranium Elements. The PolyPole1 algorithms is being implemented in INL's fuels code BISON code as part of BISON's fission gas release model. The transport of fission gas from within the fuel grains to the grain boundaries (intragranular fission gas release) is a fundamental controlling mechanism of fission gas release and gaseous swelling in nuclear fuel. Hence, accurate numerical solution of the corresponding mathematical problem needs to be included in fission gas behaviour models used in fuel performance codes. Under the assumption of equilibrium between trapping and resolution, the process can be described mathematically by a single diffusion equation for the gas atom concentration in a grain. In this work, we propose a new numerical algorithm (PolyPole1) to efficiently solve the fission gas diffusion equation in timevarying conditions. The PolyPole1 algorithm is based on the analytic modal solution of the diffusion equation for constant conditions, with the addition of polynomial corrective terms that embody the information on the deviation from constant conditions. The new algorithm is verified by comparing the results to a finite difference solution over a large number of randomly generated operation histories. Furthermore, comparison to stateoftheart algorithms used in fuel performance codes demonstrates that the accuracy of the PolyPole1 solution is superior to other algorithms, with similar computational effort. Finally, the concept of PolyPole1 may be extended to the solution of the general problem of intragranular fission gas diffusion during nonequilibrium trapping and resolution, which will be the subject of future work.},
doi = {10.1016/j.jnucmat.2016.06.028},
journal = {Journal of Nuclear Materials},
number = C,
volume = 478,
place = {United States},
year = 2016,
month = 9
}

Polypole Program For The Calculation Of Intragranular Fission Gas Release
PolyPole is a numerical algorithm for the calculation of intragranular fission gas release. In particular, the algorithm solves the gas diffusion problem in a fuel grain in timevarying conditions. The program has been extensively tested. PolyPole combines a high accuracy with a high computational efficiency and is ideally suited for application in fuel performance codes. 
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