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

3D Computational Code for Calculation of Kineric Parameters Based on Galerkin Finite Element Method

Document Type : Research Paper

Author

S. A Hosseini
Abstract
In the present paper, development of the Galerkin Finite Element Method-Kinetic-3 Dimentional (GFEM-KIN-3D) computational code for the calculation of the kinetic parameters is reported. To this end, the static neutron diffusion and corresponding adjoint equations are solved using Galerkin Finite element method in the 3 dimensional geometry. Then, the calculated neutron and adjoint flux distributions are used in the perturbation theory to calculate the effective delayed neutron fraction and mean generation time of the neutrons. There is no benchmark problem that includes the information such as the delayed neutron fraction, prompt and delayed neutron spectrum. Therefore, some problems were designed by the author and the kinetic parameters were calculated for the considered problem. Since the neutron diffusion solver was previously validated against the well-known benchmark problems and the equations of perturbation theory is available, we conclude that if the required information is known, the kinetic parameters will be calculated with high accuracy. The developed GFEM-KIN-3D is applicable to the core calculation of the both hexagonal and rectangular reactor cores.

Highlights

[1] E. Villarino, MTR_PC V2. 6, a neutronic, thermalhydraulic and shielding calculations of MTR-type reactors on personal computers. Nuclear Engineering Division, INVAP SE, San Carlos de Bariloche, Argentina (1995).

 

[2] M. Zaker, Effective delayed neutron fraction and prompt neutron lifetime of Tehran research reactor, Ann. Nucl. Energy. 30 (2003) 1591-1596.

 

[3] A. Lashkari, H. Khalafi, H. Kazeminejad, Effective delayed neutron fraction and prompt neutron lifetime of Tehran research reactor mixed-core, Ann. Nucl. Energy. 55 (2013) 265-271.

 

[4] J.S. Hendricks, G.W. McKinney, M.L. Fensin, M.R. James, R.C, Johns, J.W. Durkee, MCNPX 2.6.0 Extensions, Los Alamos National Laboratory (2008).

 

[5] M. Arkani, M. Hassanzadeh, S. Khakshournia, Calculation of six-group importance weighted delayed neutron fractions and prompt neutron lifetime of MTR research reactors based on Monte Carlo method, Prog. Nucl. Energy. 88 2016) 352-363.

 

[6] S.A. Hosseini, one dimensional neutron diffusion solver based on the Galerkin Finite Element Method, ANCC, (2008), ANC-RPT-DES-FG-100-Rev.01 (In Persian).

 

[7] S.A. Hosseini, Two dimensional neutron diffusion solver based on the Galerkin Finite Element Method, ANCC, (2008), ANC-RPT-DES-FG-200-Rev.01 (In Persian).

 

[8] J.J. Duderstadt, L.J. Hamilton, Nuclear reactor analysis, Wiley New York, 1 (1976).

 

[9] Taylor RL, Zhu JZ. The finite element method: its basis and fundamentals. Elsevier Butterworth-Heinemann (2005).

 

[10] J.R. Lamarsh, Nuclear Reactor Theory, Addison-Wesley (1966).

 

 

 

 

 

[11] S.A. Hosseini, N. Vosoughi, M.B. Ghofrani, M. Gharib, Calculation, measurement and sensitivity analysis of kinetic parameters of Tehran Research Reactor, Ann. Nucl. Energy. 37 (2010) 463-470.

 

[12] S.A. Hosseini, N. Vosoughi, Uncertainty evaluation of calculated and measured kinetics parameters of Tehran Research Reactor. Nucl.  Eng. and Des. 240 (2010) 2761-2767.

 

 

 

 

 

[13] S.A. Hosseini, N. Vosoughi, M. Hosseini, Monte Carlo simulation of Feynman-α and Rossi-α techniques for calculation of kinetic parameters of Tehran Research Reactor, Ann. Nucl. Energy. 38 (2011) 2140-2145.

 

[14] G. Schulz, Solutions of a 3D VVER-1000 Benchmark, Proc. 6-th symposium of AER on VVER reactor physics and safety, Kirkkonummi, Finland (1996).

 

Keywords

Neutron Flux
Adjoint Flux
Tetrahedral Elements
Effective Delayed Neutron Fraction
Mean Generation Time of the Neutrons
[1] E. Villarino, MTR_PC V2. 6, a neutronic, thermalhydraulic and shielding calculations of MTR-type reactors on personal computers. Nuclear Engineering Division, INVAP SE, San Carlos de Bariloche, Argentina (1995).
 
[2] M. Zaker, Effective delayed neutron fraction and prompt neutron lifetime of Tehran research reactor, Ann. Nucl. Energy. 30 (2003) 1591-1596.
 
[3] A. Lashkari, H. Khalafi, H. Kazeminejad, Effective delayed neutron fraction and prompt neutron lifetime of Tehran research reactor mixed-core, Ann. Nucl. Energy. 55 (2013) 265-271.
 
[4] J.S. Hendricks, G.W. McKinney, M.L. Fensin, M.R. James, R.C, Johns, J.W. Durkee, MCNPX 2.6.0 Extensions, Los Alamos National Laboratory (2008).
 
[5] M. Arkani, M. Hassanzadeh, S. Khakshournia, Calculation of six-group importance weighted delayed neutron fractions and prompt neutron lifetime of MTR research reactors based on Monte Carlo method, Prog. Nucl. Energy. 88 2016) 352-363.
 
[6] S.A. Hosseini, one dimensional neutron diffusion solver based on the Galerkin Finite Element Method, ANCC, (2008), ANC-RPT-DES-FG-100-Rev.01 (In Persian).
 
[7] S.A. Hosseini, Two dimensional neutron diffusion solver based on the Galerkin Finite Element Method, ANCC, (2008), ANC-RPT-DES-FG-200-Rev.01 (In Persian).
 
[8] J.J. Duderstadt, L.J. Hamilton, Nuclear reactor analysis, Wiley New York, 1 (1976).
 
[9] Taylor RL, Zhu JZ. The finite element method: its basis and fundamentals. Elsevier Butterworth-Heinemann (2005).
 
[10] J.R. Lamarsh, Nuclear Reactor Theory, Addison-Wesley (1966).
 
 
 
 
 
[11] S.A. Hosseini, N. Vosoughi, M.B. Ghofrani, M. Gharib, Calculation, measurement and sensitivity analysis of kinetic parameters of Tehran Research Reactor, Ann. Nucl. Energy. 37 (2010) 463-470.
 
[12] S.A. Hosseini, N. Vosoughi, Uncertainty evaluation of calculated and measured kinetics parameters of Tehran Research Reactor. Nucl.  Eng. and Des. 240 (2010) 2761-2767.
 
 
 
 
 
[13] S.A. Hosseini, N. Vosoughi, M. Hosseini, Monte Carlo simulation of Feynman-α and Rossi-α techniques for calculation of kinetic parameters of Tehran Research Reactor, Ann. Nucl. Energy. 38 (2011) 2140-2145.
 
[14] G. Schulz, Solutions of a 3D VVER-1000 Benchmark, Proc. 6-th symposium of AER on VVER reactor physics and safety, Kirkkonummi, Finland (1996).
 

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