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

Neutron density study in sub-critical state with pulsed neutron source

Authors

Rasoul Khodabakhsh
Sohrab Behina
Masoud Seyedi
Abstract
 During the cold start-up, the reactor is in sub-critical state. Therefore, the external neutron source cannot be neglected. In this research paper, the analytical solution of neutron point kinetics equations with a group of delayed neutrons in the presence of the pulsed neutron source in a pressurized-water reactor with 235U as a fuel is presented. The analytical solution is based on the expansion of the neutron density in powers of the prompt neutrons generation time. The point kinetics equations with this method are solvable for step and ramp reactivity and lead to better results compared with other analytical works, but are not solvable for sinusoidal reactivity. So, the neutron density response to sinusoidal reactivity is analyzed by using the fixed point and Lyapunov exponents method.
 

Keywords

Pulsed neutron source
Prompt neutrons generation time
Lyapunov exponent
Neutron density
[1] G.R. Keepin, Physics of reactor kinetics, Addison-Wesley Publishing Company, INC (1965).
[2] W.M. Stacey, Nuclear reactor physics, John Wiley and Sons, Inc., New York, United States of America, (2001).
[3] A.A. Nahla, Analytical solution to solve the point reactor kinetics equations, Nuclear Engineering and Design, 240 (2010)
1622-1629.
[4] A.E. Aboanber, Y.M. Hamada, Power series solution (PWS) of nuclear reactor dynamics with Newtonian temperature feedback, Annals of Nuclear Energy, 30 (2003a) 1111-1122.
[5] A.A. Nahla, Taylor’s series method for solving the nonlinear point kinetics equations, Nuclear Engineering and Design, 241 (2011)
1592-1595.
[6] A.E. Aboanber, A.M. El Mhlawy, Solution of two-point kinetics equations for reflected reactors using Analytical Inversion Method (AIM), Progress in Nuclear Energy, 51 (2009) 155-162.
[7] A.A. Nahla, Generalization of the analytical exponential model to solve the point kinetics equations of Be- and D2O-moderated reactors, Nuclear Engineering and Design, 238 (2008) 2648-2653.
[8] T. Sathiyasheela, Sub-critical reactor kinetics analysis using incomplete gamma functions and binomial expansions, Annals of Nuclear Energy, 37 (2010) 1248-1253.
[9] F. Zhang, W.Z. Chen, X.W. Gui, Analytic method study of point-reactor kinetic equation when cold start-up, Annals of Nuclear Energy 35 (2008) 746-749.
[10] D.A.P. Palma, A.S. Martinez, A.C. Gonçalves, Analytical solution of point kinetics equations for linear reactivity variation during the start-up of a nuclear reactor, Annals of Nuclear Energy, 36 (2009) 1469-1471.
[11] H. Li, W. Chen, L. Luo, Q. Zhu, A new integral method for solving the point reactor neutron kinetics equations, Annals of Nuclear Energy, 36 (2009) 427-432.
[12] A.A. Nahla, An analytical solution for the point reactor kinetics equations with one group of delayed neutrons and the adiabatic feedback model, Progress in Nuclear Energy, 51 (2009) 124-128.
[13] S.D. Hamieh, M. Saidinezhad, Analytical solution of the point reactor kinetics equations with temperature feedback, Annals of Nuclear Energy, 42 (2012) 148-152.
[14] R. Hilborn, Chaos and nonlinear dynamics, Oxford University Press, (2000).
[15] J.L. Munoz-Cobo, G. Verdu, C. Pereira, Dynamic reconstruction and Lyapunov exponents from time series data in boiling water reactors application to BWR stability analysis, Annals of Nuclear Energy, 19 (1992) 223-235.
[16] G.V. Durga Prased, M. Pandey, Stability analysis and nonlinear dynamics of natural circulation boiling water reactor, Nuclear Engineering and Design, 238 (2008) 229-240.
[17] C. Lange, D. Hennig, M. Schulze, A. Hurtado, Complex BWR dynamics from the bifurcation theory point of view, Annals of Nuclear Energy, 67 (2013) 91-108.
[18] C. Lange, D. Hennig, M. Schulze, A. Hurtado, Comments on the application of bifurcation analysis in BWR stability analysis, Progress in Nuclear Energy, 68 (2013) 1-15.
[19] E. Ott, Chaos in dynamical system, Cambridge University Press, Canada, (1993).
[20] J.R. Dorfman, An Introduction to Chaos in Nonequilibrium Statistical Mechanics, Cambridge University Press, Cambridge, (1999).
[21] S.T. Strogatz, Nonlinear dynamics and chaos, Perseus Books Publishing, L.L.C (1994).
[22] R. Della, E. Alhassan, N.A. Adoo, C.Y. Bansah, B.J.B. Nyarko, E.H.K. Akaho, Stability analysis of the Ghana Research Reactor-1 (GHARR-1), Energy Conversion and Management, 74 (2013) 587-593.
[23] H. Shibata, Fluctuation of mean Lyapunov exponent for turbulence, Physica A, 292 (2001) 175-181.
[24] H. Shibata, Physica A, Fluctuation of mean Lyapunov exponent for a coupled map lattice model, 284 (2000) 124-130.
[25] A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Determining Lyapunov exponents from a time series, Physica D, 16 (1985) 285-317.
[26] D.L. Hetrick, Dynamics of nuclear reactors, American Nuclear Society, La Grange Park, (1993).

Home