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Implementation of the time dependent neutron transport algorithm in 2D utilizing modular ray tracing by method of characteristic framework

Document Type : Research Paper

Authors

1 School of Mechanical Engineering, Shiraz University, P.O.Box: 7193616548, Shiraz - Iran

2 Reactor and Nuclear Safety Research School, Nuclear Science and Technology Research Institute, AEOI, P.O.Box: 14155-1339, Tehran - Iran

3 Security Research Center, Shiraz University, Postalcode: 7193616548, Shiraz - Iran

Abstract

This paper discusses the implementation of an algorithm for solving 2D time-dependent neutron transport equations in heterogeneous media. A novel modular ray tracing algorithm where neutrons are allowed to travel a longer path before being removed from the structure, is adopted for the transient calculation. The time derivative of angular flux is considered as a major source of challenges in implementing the neutron transport equation, in which two cases for the time derivative of angular flux are included, first, the angular dependency of the time derivative is preserved and second mode, isotropic scalar flux approximation is applied to the time derivative. Sensitivity analysis on time step size has been investigated as an effective parameter on both computational accuracy and cost. Investigating the compatibility of the proposed numerical algorithm as well as considering the substantial role of delayed neutrons in transient processes, three multigroup mathematical models for delayed neutrons are evaluated along with the neutron transport equation. For the implementation of the verification algorithm, the well-known TWIGL benchmark is modeled and the results are compared with MPACT and DeCART codes.

Highlights

  1. G.R. Keepin, Physics of nuclear kinetics, Addison-Wesley Publishing Company (1965).

 

  1. D.L. Hetrick, Dynamics of Nuclear Reactors, (1971).

 

  1. G.I. Bell, S. Glasstone, Nuclear reactor theory, US Atomic Energy Commission, Washington, DC (United States) (1970).

 

  1. J.B. Taylor, A.J. Baratta, A time-dependent method of characteristics for 3D nuclear reactor kinetics applications, (2009).

 

  1. A. Talamo, Numerical solution of the time dependent neutron transport equation by the method of the characteristics, Journal of Computational Physics, 240, 248-267 (2013).

 

  1. K. Tsujita, et al., Higher order treatment on temporal derivative of angular flux for time-dependent MOC, in Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering-M and C 2013, (2013).

 

  1. B. Carlson, G. Bell, Solution of the transport equation by the Sn method, Los Alamos Scientific Lab., N. Mex (1958).

 

  1. P.M. Keller, J.C. Lee, A time-dependent collision probability method for one-dimensional space-time nuclear reactor kinetics, Nuclear Science and Engineering, 129(2), 124-148 (1998).

 

  1. J. Cho, et al., Transient capability of the DeCART code, Korea Atomic Energy Research Institute (2005).

 

  1. D.G. Cacuci, Handbook of Nuclear Engineering: Vol. 1: Nuclear Engineering Fundamentals; Vol. 2: Reactor Design; Vol. 3: Reactor Analysis; Vol. 4: Reactors of Generations III and IV; Vol. 5: Fuel Cycles, Decommissioning, Waste Disposal and Safeguards, Vol. 1. (2010): Springer Science & Business Media (2010).

 

  1. M. Hursin, Full core, heterogeneous, time dependent neutron transport calculations with the 3D code DeCART, UC Berkeley (2010).

 

  1. B. Collins, B. Kochunas, S. Stimpson, Consortium for Advanced Simulation of LWRs, (2019).

 

  1. M. Porhemmat, K. Hadad, M. Mahzoon, Modular ray tracing in 2D whole core transport with MOC, Progress in Nuclear Energy, 99, 103-109 (2017).

 

  1. B. Collins, B. Kochunas, T. Downar, Assessment of the 2D MOC solver in MPACT: Michigan parallel characteristics transport code, American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL (2013).

 

  1. B.M. Kochunas, A Hybrid Parallel Algorithm for the 3-D Method of Characteristics Solution of the Boltzmann Transport Equation on High Performance Compute Clusters, (2013).

 

  1. T. Downar, et al., Theory manual for the PARCS kinetics core simulator module. Department of Nuclear Engineering and Radiological Sciences University of Michigan, USA, (2009).

 

  1. A. Zhu, et al., Transient methods for pin-resolved whole core transport using the 2D-1D methodology in MPACT, Proc. M&C 2015, 19-23 (2015).

 

  1. B. Kochunas, M. Hursin, T. Downar, DeCART-v2. 05 Theory Manual, University of Michigan, (2009).

 

  1. S.C. Shaner, Transient method of characteristics via the Adiabatic, Theta, and Multigrid Amplitude Function methods, Massachusetts Institute of Technology (2014).

 

  1. M. Porhemmat, et al., Improved memory management for solving neutron transport via a novel Modular Ray Tracing (MRT) approach embedded in parallel method of characteristic (MOC) framework, Progress in Nuclear Energy, 132, 103590 (2021).

Keywords

References
  1. G.R. Keepin, Physics of nuclear kinetics, Addison-Wesley Publishing Company (1965).

 

  1. D.L. Hetrick, Dynamics of Nuclear Reactors, (1971).

 

  1. G.I. Bell, S. Glasstone, Nuclear reactor theory, US Atomic Energy Commission, Washington, DC (United States) (1970).

 

  1. J.B. Taylor, A.J. Baratta, A time-dependent method of characteristics for 3D nuclear reactor kinetics applications, (2009).

 

  1. A. Talamo, Numerical solution of the time dependent neutron transport equation by the method of the characteristics, Journal of Computational Physics, 240, 248-267 (2013).

 

  1. K. Tsujita, et al., Higher order treatment on temporal derivative of angular flux for time-dependent MOC, in Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering-M and C 2013, (2013).

 

  1. B. Carlson, G. Bell, Solution of the transport equation by the Sn method, Los Alamos Scientific Lab., N. Mex (1958).

 

  1. P.M. Keller, J.C. Lee, A time-dependent collision probability method for one-dimensional space-time nuclear reactor kinetics, Nuclear Science and Engineering, 129(2), 124-148 (1998).

 

  1. J. Cho, et al., Transient capability of the DeCART code, Korea Atomic Energy Research Institute (2005).

 

  1. D.G. Cacuci, Handbook of Nuclear Engineering: Vol. 1: Nuclear Engineering Fundamentals; Vol. 2: Reactor Design; Vol. 3: Reactor Analysis; Vol. 4: Reactors of Generations III and IV; Vol. 5: Fuel Cycles, Decommissioning, Waste Disposal and Safeguards, Vol. 1. (2010): Springer Science & Business Media (2010).

 

  1. M. Hursin, Full core, heterogeneous, time dependent neutron transport calculations with the 3D code DeCART, UC Berkeley (2010).

 

  1. B. Collins, B. Kochunas, S. Stimpson, Consortium for Advanced Simulation of LWRs, (2019).

 

  1. M. Porhemmat, K. Hadad, M. Mahzoon, Modular ray tracing in 2D whole core transport with MOC, Progress in Nuclear Energy, 99, 103-109 (2017).

 

  1. B. Collins, B. Kochunas, T. Downar, Assessment of the 2D MOC solver in MPACT: Michigan parallel characteristics transport code, American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL (2013).

 

  1. B.M. Kochunas, A Hybrid Parallel Algorithm for the 3-D Method of Characteristics Solution of the Boltzmann Transport Equation on High Performance Compute Clusters, (2013).

 

  1. T. Downar, et al., Theory manual for the PARCS kinetics core simulator module. Department of Nuclear Engineering and Radiological Sciences University of Michigan, USA, (2009).

 

  1. A. Zhu, et al., Transient methods for pin-resolved whole core transport using the 2D-1D methodology in MPACT, Proc. M&C 2015, 19-23 (2015).

 

  1. B. Kochunas, M. Hursin, T. Downar, DeCART-v2. 05 Theory Manual, University of Michigan, (2009).

 

  1. S.C. Shaner, Transient method of characteristics via the Adiabatic, Theta, and Multigrid Amplitude Function methods, Massachusetts Institute of Technology (2014).

 

  1. M. Porhemmat, et al., Improved memory management for solving neutron transport via a novel Modular Ray Tracing (MRT) approach embedded in parallel method of characteristic (MOC) framework, Progress in Nuclear Energy, 132, 103590 (2021).
Journal of Nuclear Science, Engineering and Technology (JONSAT)
Volume 44, Issue 4 - Serial Number 106
December 2024
Pages 46-54
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