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

JOURNAL OF NUCLEAR MATERIALS

卷:509

Article

Pastore, G.^1,2  Pizzocri, D.³  Rabiti, C.¹  Barani, T.³  Van Uffelen, P.⁴  Luzzi, L.³ 

[1] Idaho Natl Lab, POB 1625, Idaho Falls, ID 83415 USA

[2] MIT, Dept Nucl Sci & Engn, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[3] Politecn Milan, Dept Energy, Nucl Engn Div, Via La Masa 34, I-20156 Milan, Italy

[4] European Commiss, Joint Res Ctr, Directorate Nucl Safety & Secur, POB 2340, D-76125 Karlsruhe, Germany

关键词: Fission gas;    Diffusion;    Trapping;    Resolution;    Nuclear fuel modeling;    Intra-granular fission gas release;    Quasi-stationary approximation;    Effective diffusion coefficient;    Numerical algorithms;    Modal methods;    PolyPole;   

DOI  :  10.1016/j.jnucmat.2018.07.030

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier B.V. All rights reserved.

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