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Integral Methods in Science and Engineering, Volume 1 pp 249–258Cite as

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Mono-Energetic Neutron Space-Kinetics in Full Cylinder Symmetry: Simulating Power Decrease

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Abstract

In the present work we discuss neutron space-kinetics in cylindrical geometry with a domain defined by two sectionally homogeneous cylinder cells, mono-energetic neutrons and one group of delayed neutron precursors. The solution is determined using variable separation and the associated complete spectra are analysed and truncated such as to allow a parametrized global solution. For the obtained solution we present numerical results for the scalar neutron flux and its time dependence for the case of power decrease.

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References

  1. Aboanber, A.E., Hamada, Y.M.: Generalized Runge-Kutta method for two- and three-dimensional space-time diffusion equations with a variable time step. Ann. Nucl. Energy 35(6), 1024–1040 (2008)

    Article  Google Scholar 

  2. Aboanber, A.E., Hamada, Y.M.: Computation accuracy and efficiency of a power series analytic method for two- and three-space-dependent transient problems. Prog. Nucl. Energy 51(3), 451–464 (2009)

    Article  Google Scholar 

  3. Aboanber, A.E., Nahla, A.A.: Solution of two-dimensional space-time multigroup reactor kinetics equations by generalized Padé and cut-product approximations. Ann. Nucl. Energy 33(3), 209–222 (2006)

    Article  Google Scholar 

  4. Aboanber, A.E., Nahla, A.A.: Adaptive matrix formation AMF method of space-time multigroup reactor kinetics equations in multidimensional model. Ann. Nucl. Energy 34(1–2), 103–119 (2007)

    Article  Google Scholar 

  5. Ceolin, C., Schramm, M., Vilhena, M.T., Bodmann, B.E.J.: On the neutron multi-group kinetic diffusion equation in a heterogeneous slab: an exact solution on a finite set of discrete points. Ann. Nucl. Energy 76, 271–282 (2015)

    Article  Google Scholar 

  6. Dahmani, M., Baudron, A.M., Lautard, J.J., Erradi, L.: A 3D nodal mixed dual method for nuclear reactor kinetics with improved quasistatic model and a semi-implicit scheme to solve the precursor equations. Ann. Nucl. Energy 28(8), 805–824 (2001)

    Article  Google Scholar 

  7. Grossman L.M., Hennart, J.P.: Nodal diffusion methods for space-time neutron kinetics. Prog. Nucl. Energy 49(3), 181–216 (2007)

    Article  Google Scholar 

  8. Gupta, A., Modak, R.S., Gupta, H.P., Kumar, V., Bhatt, K.: Parallelised Krylov subspace method for reactor kinetics by IQS approach. Ann. Nucl. Energy 32(15), 1693–1703 (2005)

    Article  Google Scholar 

  9. Hançerlioǧullari, A.: Neutronic calculations at uranium powered cylindrical reactor by using Bessel differential equation. In: Korkut, T. (ed.) Nuclear Science and Technology, pp. 15–24. Transworld Research Network, Kerala (2012)

    Google Scholar 

  10. Miró, R., Ginestar, D., Verdú, G., Hennig, D.: A nodal modal method for the neutron diffusion equation. Application to BWR instabilities analysis. Ann. Nucl. Energy 29(10), 1171–1194 (2002)

    Article  Google Scholar 

  11. Petersen, C.Z., Bodmann, B.E.J., Vilhena, M.T., Barros, R.C.: Recursive solutions for multi-group neutron kinetics diffusion equations in homogeneous three-dimensional rectangular domains with time dependent perturbations. Kerntechnik 79, 494–499 (2014)

    Article  Google Scholar 

  12. Quintero-Leyva, B.: The multi-group integro-differential equations of the neutron diffusion kinetics. Solutions with the progressive polynomial approximation in multi-slab geometry. Ann. Nucl. Energy 37(5), 766–770 (2010)

    Google Scholar 

  13. Seliverstov, V.V.: Kinetic diffusion equation in a one-dimensional cylindrical geometry. Atom. Energy 115, 319–327 (2014)

    Article  Google Scholar 

  14. Wang, D., Li, F., Guo, J., Wei, J., Zhang, J., Hao, C.: Improved nodal expansion method for solving neutron diffusion equation in cylindrical geometry. Nucl. Eng. Des. 240, 1997–2004 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Federal University of Rio Grande do Sul, Porto Alegre, RS, Brazil

    F. R. Oliveira, B. E. J. Bodmann & M. T. Vilhena

  2. Federal University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil

    F. Carvalho da Silva

Authors
  1. F. R. Oliveira
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  2. B. E. J. Bodmann
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  3. M. T. Vilhena
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  4. F. Carvalho da Silva
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Corresponding author

Correspondence to F. R. Oliveira .

Editor information

Editors and Affiliations

  1. Department of Mathematics, The University of Tulsa, Tulsa, Oklahoma, USA

    Christian Constanda

  2. Department of Mathematics, The University of Tulsa, Tulsa, Oklahoma, USA

    Matteo Dalla Riva

  3. Department of Mathematics, University of Padova, Padova, Italy

    Pier Domenico Lamberti

  4. Systems Analysis, Prognosis and Control, Fraunhofer Institute for Industrial Math, Kaiserslautern, Germany

    Paolo Musolino

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Oliveira, F.R., Bodmann, B.E.J., Vilhena, M.T., Carvalho da Silva, F. (2017). Mono-Energetic Neutron Space-Kinetics in Full Cylinder Symmetry: Simulating Power Decrease. In: Constanda, C., Dalla Riva, M., Lamberti, P., Musolino, P. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59384-5_22

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