Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Development of the S3-HACNEM simulator program in order to solving the Forward and Adjoint neutron diffusion equation for rectangular geometry reactor cores

Document Type : Research Paper

Authors

A. Kolali,
D. Naghavi Dizaji
N. Vosoughi

Department of Energy Engineering, Sharif University of Technology, P.O.BOX: 14565-1114, Tehran - Iran

https://doi.org/10.24200/nst.2023.469.1319
Abstract
 
In nuclear reactor calculations, such as burn-up and fuel management, transient analysis, and pin power reconstruction, methods are being developed that are optimal, and are both cost-efficient and time-efficient. In this paper, the discretization of the neutron diffusion equation with a high-order average current nodal expansion method is shown, which can calculate in optimum time and with acceptable accuracy. The discretization of the Forward and Adjoint neutron diffusion equation is performed for two-dimensional rectangular geometry in two energy groups and then the S3-HACNEM reactor core simulator is developed. To verify, the calculations for the BIBLIS-2D reactor core are performed and compared with valid references. It results that the computational error improves from 9.67% to 0.58% by increasing the flux expansion order from quadratic polynomials to fourth-degree polynomials.

Highlights

  1. Bell G.I, Glasstone S, Nuclear reactor theory. US Atomic Energy Commission. Washington. DC (United States). (1970).
  2. Hosseini S.A, Vosoughi N, Neutron noise simulation by GFEM and unstructured triangle elements. Nuclear Engineering and Design. 2012;253:238-258.
  3. Hosseini S.A, Vosoughi N, Vosoughi J. Neutron noise simulation using ACNEM in the hexagonal geometry. Annals of Nuclear Energy. 2018;113:246-255.
  4. Poursalehi N, Zolfaghari A, Minuchehr A. Performance comparison of zeroth order nodal expansion methods in 3D rectangular geometry. Nuclear Engineering and Design. 2012;252:248-266.
  5. Lawrence R.D. DIF3D nodal neutronics option for two-and three-dimensional diffusion theory calculations in hexagonal geometry. [LMFBR], Argonne National Lab. IL (USA). 1983.
  6. Finnemann H. A consistent Nodal Method for the Analysis of Space-Time Effects in large LWR's. 1975.
  7. Hall S. The Development of a Nodal Method for the Analysis of PWR Cores with Advanced Fuels. 2013.
  8. Sims R.N. A coarse-mesh nodal diffusion method based on response matrix considerations. Massachusetts Institute of Technology. 1977.
  9. De Abreu M.P, Da Silva F.C, Alvim A.C.M. Transverse net leakage into the second-order Nodal Expansion Method. Annals of Nuclear Energy. 1995;22:85-95.
  10. Putney J.M. Nodal methods for solving the diffusion equation for fast reactor analysis. 1984.
  11. Smith K.S. An analytic nodal method for solving the two-group, multidimensional, static and transient neutron diffusion equations. Massachusetts Institute of Technology. 1979.
  12. Kolali A, Naghavi D, Vosoughi N. Development of the SH3-ACNEM Simulator Program in order to Solving the Forward and Adjoint Neutron Diffusion Equation for Hexagonal Geometry Reactor Cores. Journal of Nuclear Science and Technology. 2019 [In Persian]. available at: http://jonsat.sinaweb. net/article_994_dcc90d037bdf9ecc554bfc78a98b4c1b.pdf

Keywords

Simulator
Adjoint calculation
Diffusion equation
Rectangular geometry
ACNEM
  1. Bell G.I, Glasstone S, Nuclear reactor theory. US Atomic Energy Commission. Washington. DC (United States). (1970).
  2. Hosseini S.A, Vosoughi N, Neutron noise simulation by GFEM and unstructured triangle elements. Nuclear Engineering and Design. 2012;253:238-258.
  3. Hosseini S.A, Vosoughi N, Vosoughi J. Neutron noise simulation using ACNEM in the hexagonal geometry. Annals of Nuclear Energy. 2018;113:246-255.
  4. Poursalehi N, Zolfaghari A, Minuchehr A. Performance comparison of zeroth order nodal expansion methods in 3D rectangular geometry. Nuclear Engineering and Design. 2012;252:248-266.
  5. Lawrence R.D. DIF3D nodal neutronics option for two-and three-dimensional diffusion theory calculations in hexagonal geometry. [LMFBR], Argonne National Lab. IL (USA). 1983.
  6. Finnemann H. A consistent Nodal Method for the Analysis of Space-Time Effects in large LWR's. 1975.
  7. Hall S. The Development of a Nodal Method for the Analysis of PWR Cores with Advanced Fuels. 2013.
  8. Sims R.N. A coarse-mesh nodal diffusion method based on response matrix considerations. Massachusetts Institute of Technology. 1977.
  9. De Abreu M.P, Da Silva F.C, Alvim A.C.M. Transverse net leakage into the second-order Nodal Expansion Method. Annals of Nuclear Energy. 1995;22:85-95.
  10. Putney J.M. Nodal methods for solving the diffusion equation for fast reactor analysis. 1984.
  11. Smith K.S. An analytic nodal method for solving the two-group, multidimensional, static and transient neutron diffusion equations. Massachusetts Institute of Technology. 1979.
  12. Kolali A, Naghavi D, Vosoughi N. Development of the SH3-ACNEM Simulator Program in order to Solving the Forward and Adjoint Neutron Diffusion Equation for Hexagonal Geometry Reactor Cores. Journal of Nuclear Science and Technology. 2019 [In Persian]. available at: http://jonsat.sinaweb. net/article_994_dcc90d037bdf9ecc554bfc78a98b4c1b.pdf

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