An effective numerical algorithm for intra-granular fission gas release during non-equilibrium trapping and resolution

Fission gas release and gaseous swelling in nuclear fuel are driven by the transport of fission gas from within the fuel grains to grain boundaries (intra-granular fission gas release). The process involves gas atom diffusion in conjunction with trapping in and resolution from intra-granular bubbles...

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Bibliographic Details
Published in:Journal of nuclear materials 2018-10, Vol.509 (C), p.687-699
Main Authors: Pastore, G., Pizzocri, D., Rabiti, C., Barani, T., Van Uffelen, P., Luzzi, L.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computer applications
Differential equations
Diffusion
Diffusion algorithm
Diffusion coefficient
Effective diffusion coefficient
Finite difference method
Fission gas
Fission gas release
Grain boundaries
High temperature
Intra-granular fission gas release
Modal methods
NUCLEAR FUEL CYCLE AND FUEL MATERIALS
Nuclear fuel modeling
Nuclear fuels
Numerical algorithms
Numerical analysis
Partial differential equations
PolyPole
Quasi-stationary approximation
Resolution
Trapping
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Summary:Fission gas release and gaseous swelling in nuclear fuel are driven by the transport of fission gas from within the fuel grains to grain boundaries (intra-granular fission gas release). The process involves gas atom diffusion in conjunction with trapping in and resolution from intra-granular bubbles, and is described mathematically by a system of two partial differential equations (PDE). Under the assumption of equilibrium between trapping and resolution (quasi-stationary approximation) the system can be reduced to a single diffusion equation with an effective diffusion coefficient. Numerical solutions used in engineering fuel performance calculations invariably rely on this simplification. First, we investigate the validity of the quasi-stationary approximation compared to the solution of the general system of PDEs. Results demonstrate that the approximation is valid under most conditions of practical interest, but is inadequate to describe intra-granular fission gas release during rapid transients to relatively high temperatures such as postulated reactivity-initiated accidents (RIA). Then, we develop a novel numerical algorithm for the solution of the general PDE system in time-varying conditions. We verify the PolyPole-2 algorithm against a reference finite difference solution for a large number of randomly generated operation histories including prototypical RIA transients. Results demonstrate that PolyPole-2 captures the solution of the general system with a high accuracy and a low computational cost. The PolyPole-2 algorithm overcomes the quasi-stationary approximation and the concept of an effective diffusion coefficient for the solution of the intra-granular fission gas release problem in nuclear fuel analysis. •The calculation of fission gas transport to grain boundaries in engineering nuclear fuel analysis is dealt with.•The validity of the quasi-stationary approximation and associated one-equation formulation of the problem are investigated.•An effective numerical algorithm for the general two-equation formulation is developed.•The new algorithm can be implemented in any fuel performance code.•The algorithm overcomes the concept of an effective diffusion coefficient in nuclear fuel analysis.
ISSN:0022-3115
1873-4820
DOI:10.1016/j.jnucmat.2018.07.030