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NEUTRON DIFFUSION ANALYSIS OF A FUEL PEBBLE WITH VOLUME AVERAGING METHOD

Volume 23, Issue 4, 2020, pp. 363-381
DOI: 10.1615/JPorMedia.2020027522
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ABSTRACT

The nuclear reactor is a highly heterogeneous system where the nuclear and heat transfer processes take place at multiple scales. With the volume-averaged method, a nuclear reactor can be upscaled. However, with this methodology one integro-differential mathematical model is obtained containing more unknown variables, i.e., dependent variables with respect to the nonaveraged model. Thus, in order to obtain one upscaled and closed neutron diffusion equation, we present the closure problems that were numerically solved to compute the effective coefficients. These closure problems are defined as integro-differential boundary-value problems at microscale. In order to demonstrate the applicability of the theory, we solved the closure problems and computed effective coefficients for a Generation IV nuclear reactor containing pebble bed nuclear fuel. The results obtained with the volume-averaged model agree well with those from the classic diffusion theory and Boltzmann's equation.

REFERENCES
  1. Aggelopoulos, C.A. and Tsakiroglou, C.D., The Longitudinal Dispersion Coefficient of Soils as Related to the Variability of Local Permeability, Water Air Soil Poll, vol. 185, pp. 223-237,2007.

  2. Auwerda, G.J., Kloosterman, J.L., Lathouwers, D., and Van der Hagen, T.H.J.J., Effects of Random Pebble Distribution on the Multiplication Factor in HTR Pebble Bed Reactors, Ann. Nucl. Energy, vol. 37, pp. 1056-1066,2010.

  3. Banki, R. Hoteit, H., and Firoozabadi, A., Mathematical Formulation and Numerical Modeling of Wax Deposition in Pipelines from Enthalpy-Porosity Approach and Irreversible Thermodynamics, Int. J. Heat Mass Transf., vol. 51, pp. 3387-3398,2008.

  4. Behar, C., et al., Technology Roadmap Update for Generation IV Nuclear Energy Systems, OECD Nuclear Energy Agency for he Generation IVInternational Forum, Paris, January 2014.

  5. Berman, Y., An Improved Homogenization Technique for Pin-by-Pin Diffusion Calculations, Ann. Nucl. Energy, vol. 53, pp. 238-243,2013.

  6. Bozsak, F., Chomaz, J.M., and Barakat, A.I., Modeling the Transport of Drugs Eluted from Stents: Physical Phenomena Driving Drug Distribution in the Arterial Wall, Biomech. Model. Mech., vol. 13, pp. 327-347,2014.

  7. Capriste, G.H., Rotstein, E., and Whitaker, S., A General Closure Scheme for the Method of Volume Averaging, Chem. Eng. Sci., vol. 41, pp. 227-235,1986.

  8. Civan, F., Modeling Transport in Porous Media by Control Volume Analysis, J. Porous Media, vol. 13, pp. 855-873,2010.

  9. de Anna, P., Jimenez-Martinez, J., Tabuteau, H., Turuban, R., Le Borgne, T., Derrien, M., and Melheust, Y., Mixing and Reaction Kinetics in Porous Media: An Experimental Pore Scale Quantification, Environ. Sci. Technol., vol., 48, pp. 508-516,2013.

  10. Druska, C., Kasselmann, S., and Lauer, A., Investigations of Space-Dependent Safety-Related Parameters of a PBMR-Like HTR in Transient Operating Conditions Applying a Multi-Group Diffusion Code, Nucl. Eng. Design, vol. 239, pp. 508-520,2009.

  11. Duderstadt, J.J. and Hamilton, L.J., Nuclear Reactor Analysis, Hoboken, NJ: John Wiley & Sons, pp. 133-138,1976.

  12. Espinosa-Paredes, G. and Aguilar-Madera, C.G., Scaled Neutron Point Kinetics (SUNPK) Equations for Nuclear Reactor Dynamics: 2D Approximation, Ann. Nucl. Energy, vol. 115, pp. 377-386,2018.

  13. Espinosa-Paredes, G., Castillo-Jimenez, V., Herranz-Puebla, L.E., and Vazquez-Rodriguez, R., Surface Energy Equation for Heat Transfer Process in a Pebble Fuel, Nucl. Eng. Design, vol. 280, pp. 269-284,2014.

  14. Espinosa-Paredes, G. and Vazquez-Rodriguez, R., Nuclear Reactor Physics: A Conceptual Approach, Barcelona: OmniaScience, pp. 63-64,2015. (in Spanish).

  15. Golfier, F., Lasseux, D., and Quintard, M., Investigation of the Effective Permeability of Vuggy or Fractured Porous Media from a Darcy-Brinkman Approach, Comput. Geosci., vol. 19, pp. 63-78,2015.

  16. Golfier, F., Quintard, M., and Whitaker, S., Heat and Mass Transfer in Tubes: An Analysis Using the Method of Volume Averaging, J. Porous Media, vol. 5, pp. 1-18,2002.

  17. Gurau, V. and Mann Jr., J.A., A Critical Overview of Computational Fluid Dynamics Multiphase Models for Proton Exchange Membrane Fuel Cells, SIAMJ. Appl. Math, vol. 70, pp. 410-454,2009.

  18. Heizler, S.I., Asymptotic Telegrapher's Equation (P1) Approximation for the Transport Equation, Nucl. Sci. Eng., vol. 166, no. 1, pp. 17-35,2010.

  19. Helmig, R., Flemisch, B., Wolff, M., Ebigbo, A., and Class, H., Model Coupling for Multiphase Flow in Porous Media, Adv. Water Resour., vol. 51, pp. 52-66,2013.

  20. Ho, H.Q., Honda, Y., Goto, M., and Takada, S., Investigation of Uncertainty Caused by Random Arrangement of Coated Fuel Particles in HTTR Criticality Calculations, Ann. Nucl. Energy, vol. 112, pp. 42-47,2018.

  21. Howes, F.A. and Whitaker, S., The Spatial Averaging Theorem Revisited, Chem. Eng. Sci., vol. 40, pp. 1387-1392,1985.

  22. Kapellos, G.E., Alexiou, T.S., and Payatakes, A.C., A Multiscale Theoretical Model for Diffusive Mass Transfer in Cellular Biological Media, Math. Biosci, vol. 210, pp. 177-237,2007.

  23. Kim, H.C., Kim, S.H., and Kim, J.K., A New Strategy to Simulate a Random Geometry in a Pebble-Bed Core with the Monte Carlo CodeMCNP, Ann. Nucl. Energy, vol. 38, pp. 1877-1883,2011.

  24. Klann, M. and Koeppl, H., Spatial Simulations in Systems Biology: From Molecules to Cells, Int. J. Mol. Sci., vol. 13, pp. 7798-7827,2012.

  25. Lahey, R.T. and Moody, F.J., The Thermal-Hydraulics of a Boiling Water Nuclear Reactor, Second Edition, La Grange Park, IL: American Nuclear Society, pp. 3-14,1993.

  26. Latifi, M.S., Setayeshi, S., Starace, G., and Fiorentino, M., A Numerical Investigation on the Influence of Porosity on the Steady-State and Transient Thermal-Hydraulic Behavior of the PBMR, J. Heat Transf., vol. 138, no. 10, pp. 102003:1-9,2016.

  27. Lillington, J.N., The Future of Nuclear Power, Amsterdam: Elsevier, 2004.

  28. Pilehvar, A.F., Aghaie, M., Esteki, M.H., Zolfaghari, A., Minuchehr, A., Daryabak, A., and Safavi, A., Evaluation of Compressible Flow in Spherical Fueled Reactors Using the Porous Media Model, Ann. Nucl. Energy, vol. 57, pp. 185-194,2013.

  29. Porta, G.M., Riva, M., and Guadagnini, A., Upscaling Solute Transport in Porous Media in the Presence of an Irreversible Bi-molecular Reaction, Adv. Water Resour., vol. 35, pp. 151-162,2012.

  30. Powers, J.J. and Wirth, B.D., A Review of TRISO Fuel Performance Models, J. Nucl. Mater-, vol. 405, pp. 74-82,2010.

  31. Price, M.S.T., The Dragon Project Origins, Achievements and Legacies, Nucl. Eng. Design, vol. 251, pp. 60-68,2012.

  32. Prieto-Guerrero, G. and Espinosa-Paredes, G., Linear and Non-Linear Stability Analysis in Boiling Water Reactors: The Design of Real-Time Stability Monitors, London: Elsevier, pp. 25-55,2019.

  33. PRIS, Power Reactor Information System, accessed February 21,2019, from https://pris.iaea.org/PRIS/home.aspx/, 2019.

  34. Quintard, M. and Whitaker, S., Transport in Ordered and Disordered Porous Media I: The Cellular Average and the Use of Weighting Functions, Transp. Porous Media, vol. 14, pp. 163-177,1994.

  35. Reitsma, F., Strydom, G., De Haas, J.B.M., Ivanov, K., Tyobeka, B., Mphahlele, R., and Sikik, U.E., The PBMR Steady-State and Coupled Kinetics Core Thermal-Hydraulics Benchmark Test Problems, Nucl. Eng. Design, vol. 236, pp. 657-668,2006.

  36. Sanchez, R., Assembly Homogenization Techniques for Core Calculations, Prog;. Nucl. Energy, vol. 51, pp. 14-31,2009.

  37. Smith, K.S., Assembly Homogenization Techniques for Light Water Reactor Analysis, Prog. Nucl. Energy, vol. 17, pp. 303-335, 1986.

  38. Stacey, W.M., Nuclear Reactor Physics, Weinheim, Germany: Wiley-VCH, 2004.

  39. Strydom, G., Xenon-Induced Axial Power Oscillations in the 400 MW PBMR, Nucl. Eng. Design, vol. 238, pp. 2960-2975,2008.

  40. Tilton, N., Daniel, D., and Riaz, A., The Initial Transient Period of Gravitationally Unstable Diffusive Boundary Layers Developing in Porous Media, Phys. Fluids, vol. 25, pp. 1-19,2013.

  41. Todreas, N.E. and Kazimi M.S., Nuclear Systems I. Thermal Hydraulic Fundamentals, Second Edition, Abingdon, UK: Taylor & Francis, 2011.

  42. Valdes-Parada, F.J., Aguilar-Madera, C.G., and J. Alvarez-Ramirez, J., On Diffusion, Dispersion and Reaction in Porous Media, Chem. Eng. Sci., vol. 66, pp. 2177-2190,2011.

  43. Valdes-Parada, F.J. and Espinosa-Paredes, G., Darcy's Law for Immiscible Two-Phase Flow: A Theoretical Development, J. Porous Media, vol., 8, pp. 557-567,2005.

  44. Verfondern, K., Nabielek, H., Kania, M.J., and Allelein, H.J., High-Quality Thorium TRISO Fuel Performance in HTGRs, Deutschen: Forschungszentrum Julich GmbH Zentralbibliothek, pp. 9-16,2013.

  45. Wang, M.J., Sheu, R.J., Peir, J.J., and Liang, J.H., Criticality Calculations of the HTR-10 Pebble-Bed Reactor with SCALE6/CSAS6 and MCNP5, Ann. Nucl. Energy, vol. 64, pp. 1-7,2014a.

  46. Wang, X.H., Jia, J.T., Liu, Z.F., and Jin, L.D., Derivation of the Darcy-Scale Filtration Equation for Power-Law Fluids with the Volume Averaging Method, J. Porous Media, vol. 17, pp. 741-750,2014b.

  47. Whitaker, S., The Method of Volume Averaging, Dordrecht, Netherlands: Kluwer Academic Publishers, 1999.

  48. Yamamoto, A., Kitamura, Y., and Yamane, Y., Cell Homogenization Methods for Pin-by-Pin Core Calculations Tested in Slab Geometry, Ann. Nucl. Energy, vol. 31, pp. 825-847,2004.

  49. Zhang, B., Wu, H., Li, Y., Cao, L., and Shen, W., Evaluation of Pin-Cell Homogenization Techniques for PWR. Pin-by-Pin Calculation, Nucl. Sci. Eng., vol. 186, pp. 134-146,2017.

  50. Zhou, F., Hansen, N.E., Geb, D.J., and Catton, I., Obtaining Closure for Fin-and-Tube Heat Exchanger Modeling based on Volume Averaging Theory (VAT), J. Heat Transf., vol. 133,pp. 1-19,2011.

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