Solution of the nonlinear point nuclear reactor kinetics equations

On a closed-form solution of the point kinetics equations with reactivity feedback of temperature

“…The obtained results coincide almost perfectly with those from Nahla and Zayed (2010) in the time interval used in that paper.…”

“…The model used in this study starts from the point kinetics equations and one group precursors as reported in Nahla and Zayed (2010), where n(t) is the time-dependent neutron population, C(t) is the concentration of delayed neutrons precursors, T(t) is the time-dependent temperature of the core, ρ(T) is the temperature-dependent reactivity, β is the delayed neutron fraction, L is the prompt neutron generation time and λ is the average decay constant of the precursors:…”

“…The grey shaded areas in the same figures are a measure for the difference of our Semi-analytical Solution (SA) to the Numerical Findings (NF) of Nahla and Zayed (2010). The difference in percentage is given by an asymmetry, defined by   SA NF 100 SA NF     , which applies to the solutions for the power and the temperature.…”

“…Computing solutions of the point kinetics equations provide information on the dynamics of nuclear reactor operation and are useful for an understanding of power fluctuations experienced especially during start-up or shutdown, when the control rods are adjusted. Recently, a large number of kinetics studies have been reported, which modelled the time-dependent behaviour of a nuclear reactor using point kinetics equations (see for instance Aboanber, 2009;Aboanber andHamada, 2002, 2003;Aboanber and Nahla, 2002;Chen et al, 2007;Kinard and Allen, 2004;Nahla and Zayed, 2010;Nahla, 2010;Peinetti, et al, 2009;Saha Ray and Patra, 2013;Tashakor et al, 2010). In a review article (Espinosa-Paredes et al, 2011) where primarily a fractional neutron point kinetics equation for nuclear reactor dynamics is discussed, temperature feedback is also considered and its earlier approaches by adiabatic feedback models are addressed.…”

“…Note that in the present work we focus on the same problem as discussed in Nahla and Zayed (2010) and Abdallah and Nahla (2011), i.e. the point reactor kinetics equations with Newtonian temperature feedback effects.…”