TY - JOUR
T1 - Fractional neutron point kinetics equations for nuclear reactor dynamics
AU - Espinosa-Paredes, Gilberto
AU - Polo-Labarrios, Marco A.
AU - Espinosa-Martínez, Erick G.
AU - Valle-Gallegos, Edmundo Del
N1 - Funding Information:
The authors are grateful for the referee’s comments on this work, which allowed to establish with more clarity the physical interpretation of the new paradigm presented in this work. Special thanks to Dr. Rodolfo Vazquez-Rodriguez and Dr. Francisco Valdes-Parada for their personal comments related with the fractional constitutive law and its implications. Finally, the first author wishes to thank the Safeguard and Nuclear Security National Commission (CNSNS by its Spanish acronym) of México due to their financial support along the last ten years through different grants for research projects.
PY - 2011/2
Y1 - 2011/2
N2 - The fractional point-neutron kinetics model for the dynamic behavior in a nuclear reactor is derived and analyzed in this paper. The fractional model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional order, acting as exponent of the relaxation time, to obtain the best representation of a nuclear reactor dynamics. The physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. The numerical approximation to the solution of the fractional neutron point kinetics model, which can be represented as a multi-term high-order linear fractional differential equation, is calculated by reducing the problem to a system of ordinary and fractional differential equations. The numerical stability of the fractional scheme is investigated in this work. Results for neutron dynamic behavior for both positive and negative reactivity and for different values of fractional order are shown and compared with the classic neutron point kinetic equations. Additionally, a related review with the neutron point kinetics equations is presented, which encompasses papers written in English about this research topic (as well as some books and technical reports) published since 1940 up to 2010.
AB - The fractional point-neutron kinetics model for the dynamic behavior in a nuclear reactor is derived and analyzed in this paper. The fractional model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional order, acting as exponent of the relaxation time, to obtain the best representation of a nuclear reactor dynamics. The physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. The numerical approximation to the solution of the fractional neutron point kinetics model, which can be represented as a multi-term high-order linear fractional differential equation, is calculated by reducing the problem to a system of ordinary and fractional differential equations. The numerical stability of the fractional scheme is investigated in this work. Results for neutron dynamic behavior for both positive and negative reactivity and for different values of fractional order are shown and compared with the classic neutron point kinetic equations. Additionally, a related review with the neutron point kinetics equations is presented, which encompasses papers written in English about this research topic (as well as some books and technical reports) published since 1940 up to 2010.
KW - Diffusion equation
KW - Neutron point kinetics
KW - Non-Fickian approximation
KW - Reactivity changes
KW - Stability analysis
UR - http://www.scopus.com/inward/record.url?scp=78751626779&partnerID=8YFLogxK
U2 - 10.1016/j.anucene.2010.10.012
DO - 10.1016/j.anucene.2010.10.012
M3 - Artículo
SN - 0306-4549
VL - 38
SP - 307
EP - 330
JO - Annals of Nuclear Energy
JF - Annals of Nuclear Energy
IS - 2-3
ER -