Solution of the point kinetics equations in the presence of Newtonian temperature feedback by Pad  approximations via the analytical inversion method

An accurate solution of point kinetics equations of one-group delayed neutrons and an extraneous neutron source for step reactivity insertion

“…The Hermite polynomial, Gear, and Taylor polynomial methods are chosen for analysis. To obtain accurate solutions, the time steps of the Hermite polynomial and Taylor polynomial methods are chosen to be h = 0.0001 s and h = 0.001 s, respectively, which are generally used as solution benchmarks [17][18][19]. The results for step reactivity ρ = 0.0015 and ρ = 0.0032 are presented in Tables 1 and 2.…”

“…A small step results in a long computing time, and more importantly, there is large accumulated error due to *These authors contributed equally to this work †Corresponding author (email: Cwz2@21cn.com) the many computation steps. Many researchers have attempted to solve this problem and some relatively effective numerical methods have been proposed, such as the finite-difference method [5], finite-element method [6], Runge-Kutta procedure [7], quasistatic method [8,9], piecewise polynomial approach [10], singular perturbation method [11], stiffness confinement method [12], power series solution [13][14][15], and Padé approximation [16][17][18].…”

On a closed-form solution of the point kinetics equations with reactivity feedback of 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.…”

Solution of Point Reactor Neutron Kinetics Equations with Temperature Feedback by Singularly Perturbed Method

“…The analysis of variation of neutron density (or power) and reactivity with time under the different conditions is an important content of nuclear reactor physics or neutron kinetics [1][2][3][4][5][6][7]. Some important achievements on the supercritical transient with temperature feedback with big ( 0 > ) or small ( 0 < ) reactivity inserted have been approached through the effort of many scholars [7][8][9][10][11][12].…”

“…The analysis of variation of neutron density (or power) and reactivity with time under the different conditions is an important content of nuclear reactor physics or neutron kinetics [1][2][3][4][5][6][7]. Some important achievements on the supercritical transient with temperature feedback with big ( 0 > ) or small ( 0 < ) reactivity inserted have been approached through the effort of many scholars [7][8][9][10][11][12]. The studies on the delayed supercritical transient with small reactivity inserted and temperature feedback are introduced in the related literature [13][14][15], in which the explicit function of density (or power) and reactivity with respect to time is derived mainly with decoupling method, power prompt jump approximation, precursor prompt jump approximation, temperature prompt jump approximation [10,16], and so forth.…”