DOI QR코드

DOI QR Code

On the use of spectral algorithms for the prediction of short-lived volatile fission product release: Methodology for bounding numerical error

  • Zullo, G. (Politecnico di Milano, Department of Energy, Nuclear Engineering Division) ;
  • Pizzocri, D. (Politecnico di Milano, Department of Energy, Nuclear Engineering Division) ;
  • Luzzi, L. (Politecnico di Milano, Department of Energy, Nuclear Engineering Division)
  • Received : 2021.05.07
  • Accepted : 2021.10.19
  • Published : 2022.04.25

Abstract

Recent developments on spectral diffusion algorithms, i.e., algorithms which exploit the projection of the solution on the eigenfunctions of the Laplacian operator, demonstrated their effective applicability in fast transient conditions. Nevertheless, the numerical error introduced by these algorithms, together with the uncertainties associated with model parameters, may impact the reliability of the predictions on short-lived volatile fission product release from nuclear fuel. In this work, we provide an upper bound on the numerical error introduced by the presented spectral diffusion algorithm, in both constant and time-varying conditions, depending on the number of modes and on the time discretization. The definition of this upper bound allows introducing a methodology to a priori bound the numerical error on short-lived volatile fission product retention.

Keywords

References

  1. J.A. Turnbull, C.E. Beyer, Background and Derivation of ANS-5.4 Standard Fission Product Release Model, United States Nuclear Regulatory Commision, 2010, p. 11.
  2. F. D'Auria, C. Camargo, O. Mazzantini, The Best Estimate Plus Uncertainty (BEPU) approach in licensing of current nuclear reactors, Nucl. Eng. Des. 248 (Jul. 2012) 317-328, https://doi.org/10.1016/j.nucengdes.2012.04.002.
  3. L.G. Williams, Overview of international nuclear safety regulation and licensing, in: Reference Module in Earth Systems and Environmental Sciences,, Elsevier, 2020, https://doi.org/10.1016/b978-0-12-409548-9.12380-2.
  4. M.S. Veshchunov, V.D. Ozrin, V.E. Shestak, V.I. Tarasov, R. Dubourg, G. Nicaise, Development of the mechanistic code MFPR for modelling fission-product release from irradiated UO2 fuel, Nucl. Eng. Des. 236 (2) (2006) 179-200, https://doi.org/10.1016/j.nucengdes.2005.08.006.
  5. K. Lassmann, TRANSURANUS: A Fuel Rod Analysis Code Ready for Use, in: Nuclear Materials for Fission Reactors, 1992, pp. 295-302, https://doi.org/10.1016/b978-0-444-89571-4.50046-3.
  6. R.L. Williamson, et al., Validating the BISON fuel performance code to integral LWR experiments, Nucl. Eng. Des. 301 (May 2016) 232-244, https://doi.org/10.1016/j.nucengdes.2016.02.020.
  7. G. Pastore, D. Pizzocri, C. Rabiti, T. Barani, P. van Uffelen, L. Luzzi, An effective numerical algorithm for intra-granular fission gas release during non-equilibrium trapping and resolution, J. Nucl. Mater. 509 (2018) 687-699, https://doi.org/10.1016/j.jnucmat.2018.07.030.
  8. D. Pizzocri, C. Rabiti, L. Luzzi, T. Barani, P. Van Uffelen, G. Pastore, PolyPole-1: an accurate numerical algorithm for intra-granular fission gas release, J. Nucl. Mater. 478 (2016) 333-342, https://doi.org/10.1016/j.jnucmat.2016.06.028.
  9. V. Georgenthum, et al., SCANAIR-BISON Benchmark on CIP0-1 RIA Test, 2017.
  10. D. Pizzocri, T. Barani, L. Luzzi, SCIANTIX: a new open source multi-scale code for fission gas behaviour modelling designed for nuclear fuel performance codes, J. Nucl. Mater. 532 (2020) 152042, https://doi.org/10.1016/j.jnucmat.2020.152042.
  11. P. Hermansson, A.R. Massih, An effective method for calculation of diffusive flow in spherical grains, J. Nucl. Mater. 304 (2-3) (2002) 204-211, https://doi.org/10.1016/S0022-3115(02)00873-5.
  12. K. Forsberg, A.R. Massih, Fission gas release under time-varying conditions, J. Nucl. Mater. 127 (2-3) (1985), https://doi.org/10.1016/0022-3115(85)90348-4.
  13. K. Forsberg, A.R. Massih, Diffusion theory of fission gas migration in irradiated nuclear fuel UO2, J. Nucl. Mater. 135 (2-3) (1985), https://doi.org/10.1016/0022-3115(85)90071-6.
  14. A.H. Booth, A Method of Calculating Fission Gas Diffusion from UO2 Fuel and its Application to the X-2-F Loop Test, Atomic Energy of Canada Limited, 1957.
  15. D.R. Olander, Fundamental Aspects of Nuclear Reactor Fuel Elements, Technical lnformation Center Energy Research and Development Administration, 1976.
  16. R.J. White, M.O. Tucker, A new fission-gas release model, J. Nucl. Mater. 118 (1) (1983) 1-38, https://doi.org/10.1016/0022-3115(83)90176-9.
  17. P. Van Uffelen, R.J.M. Konings, C. Vitanza, J. Tulenko, Analysis of Reactor Fuel Rod Behavior, in: D.G. Cacuci (Ed.), Handbook of Nuclear Engineering, first ed., Springer, US, 2010.
  18. J. Rest, M.W.D. Cooper, J. Spino, J.A. Turnbull, P. Van Uffelen, C.T. Walker, Fission gas release from UO2 nuclear fuel: a review, J. Nucl. Mater. 513 (2019) 310-345, https://doi.org/10.1016/j.jnucmat.2018.08.019.
  19. J.A. Turnbull, C.A. Friskney, J.R. Findlay, F.A. Johnson, A.J. Walter, The diffusion coefficients of gaseous and volatile species during the irradiation of uranium dioxide, J. Nucl. Mater. 107 (2-3) (1982) 168-184, https://doi.org/10.1016/0022-3115(82)90419-6.
  20. K. Lassmann, H. Benk, Numerical algorithms for intragranular fission gas release, J. Nucl. Mater. 280 (2) (2000) 127-135, https://doi.org/10.1016/S0022-3115(00)00044-1.
  21. W.N. Rausch, F.E. Panisko, ANS54: a Computer Subroutine for Predicting Fission Gas Release, Pacific Northwest Laboratory, USA, 1979.
  22. S. Sengupta, T.K. Sengupta, J.K. Puttam, K.S. Vajjala, Global spectral analysis for convection-diffusion-reaction equation in one and two-dimensions: effects of numerical anti-diffusion and dispersion, J. Comput. Phys. 408 (2020) 109310, https://doi.org/10.1016/j.jcp.2020.109310.
  23. V.K. Suman, T.K. Sengupta, C. Jyothi Durga Prasad, K. Surya Mohan, D. Sanwalia, Spectral analysis of finite difference schemes for convection diffusion equation, Comput. Fluid 150 (2017) 95-114, https://doi.org/10.1016/j.compfluid.2017.04.009.
  24. T.K. Sengupta, A. Dipankar, P. Sagaut, Error dynamics: beyond von Neumann analysis, J. Comput. Phys. 226 (2) (2007) 1211-1218, https://doi.org/10.1016/j.jcp.2007.06.001.
  25. R. Hamlet, "Random Testing," in Encyclopedia of Software Engineering, John Wiley & Sons, Inc., Hoboken, NJ, USA, 2002, https://doi.org/10.1002/0471028959.sof268.
  26. P. Tramontana, D. Amalfitano, N. Amatucci, A. Memon, A.R. Fasolino, Developing and evaluating objective termination criteria for random testing, ACM Trans. Software Eng. Methodol. 28 (3) (Jun. 2019), https://doi.org/10.1145/3339836.
  27. C. Baker, The fission gas bubbles distribution in uranium dioxide from high temperature irradiated SGHWR fuel pins, J. Nucl. Mater. 66 (1977) 283-291. https://doi.org/10.1016/0022-3115(77)90117-9
  28. G. Ducros, P.P. Malgouyres, M. Kissane, D. Boulaud, M. Durin, Fission product release under severe accidental conditions: general presentation of the program and synthesis of VERCORS 1-6 results, Nucl. Eng. Des. 208 (2) (2001) 191-203, https://doi.org/10.1016/S0029-5493(01)00376-4.
  29. G. Ducros, Y. Pontillon, P.P. Malgouyres, Synthesis of the VERCORS experimental programme: separate-effect experiments on Fission Product release, in support of the PHEBUS-FP programme, Ann. Nucl. Energy 61 (2013) 75-87, https://doi.org/10.1016/j.anucene.2013.02.033.
  30. Y. Pontillon, G. Ducros, Behaviour of fission products under severe PWR accident conditions: the VERCORS experimental programme - Part 2: release and transport of fission gases and volatile fission products, Nucl. Eng. Des. 240 (7) (2010) 1853-1866, https://doi.org/10.1016/j.nucengdes.2009.06.024.
  31. J.B. Ainscough, B.W. Oldfield, J.O. Ware, Isothermal grain growth kinetics in sintered UO2 pellets, J. Nucl. Mater. 49 (2) (1973) 117-128, https://doi.org/10.1016/0022-3115(73)90001-9.
  32. NEA/CSNI/R(2010)1, Nuclear Fuel Behaviour under Reactivity-Initiated Accident (RIA) Conditions, 2010.
  33. M. Ishikawa, S. Shiozawa, A study of fuel behavior under reactivity initiated accident conditions d review, J. Nucl. Mater. 95 (1-2) (1980) 1-30. https://doi.org/10.1016/0022-3115(80)90076-8