Power series solution method for solving point kinetics equations with lumped model temperature and feedback

Sathiyasheela, T.

doi:10.1016/j.anucene.2008.11.005

Cited by 28 publications

(8 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Chen¹,

Hao²,

Chen³

2013

Science and Technology of Nuclear Installations

View full text Add to dashboard Cite

The singularly perturbed method (SPM) is proposed to obtain the analytical solution for the delayed supercritical process of nuclear reactor with temperature feedback and small step reactivity inserted. The relation between the reactivity and time is derived. Also, the neutron density (or power) and the average density of delayed neutron precursors as the function of reactivity are presented. The variations of neutron density (or power) and temperature with time are calculated and plotted and compared with those by accurate solution and other analytical methods. It is shown that the results by the SPM are valid and accurate in the large range and the SPM is simpler than those in the previous literature.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Chen¹,

Hao²,

Chen³

2013

Science and Technology of Nuclear Installations

View full text Add to dashboard Cite

show abstract

“…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].…”

mentioning

confidence: 99%

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

Xue-Li

Chen

2010

Chin. Sci. Bull.

View full text Add to dashboard Cite

The continuous indication of the neutron density and its rate of change are important for the safe startup and operation of reactors. The best way to achieve this is to obtain analytical solutions of the neutron kinetics equations because none of the developed numerical methods can well satisfy the need for real-time or even super-time computation for the safe startup and operation of reactors in practice. In this paper, an accurate analytical solution of point kinetics equations with one-group delayed neutrons and an extraneous neutron source is proposed to calculate the change in neutron density, where the whole process from the subcritical stage to critical and supercritical stages is considered for step reactivity insertions. The accurate analytical solution can also be used as a benchmark of all numerical methods employed to solve stiff neutron kinetics equations. neutron kinetics, accurate solution, extraneous neutron source, step reactivity Citation:Li H F, Shang X L, Chen W Z. An accurate solution of point kinetics equations of one-group delayed neutrons and an extraneous neutron source for step reactivity insertion.Equations of point reactor neutron kinetics describe variations in the densities of neutrons and delayed neutron precursors, and are coupled but stiff equations. Huge disparities between the life-spans of the prompt neutron and delayed neutron lead to time constants with different orders of magnitude for the solutions of fast and slow components. It is well accepted that analytical solutions can be obtained only under simplified conditions, such as there being no extraneous neutron source, there being a prompt jump [1-3], and there being a constant neutron source [4]. These analytical solutions can only be used for qualitative rather than quantitative computation. For the latter, researchers have to turn to a numerical method. However, a very small step size has to be adopted for stability when applying a general numerical method such as the Euler, Runge-Kutta, or Adams method. 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 [13-15], and Padé approximation [16-18]. Other methods [19] are being proposed and discussed.However, none of these methods can satisfy the need for real-time or even super-time computation in the safe operation of a reactor in practice. With so many numerical methods available, which should we choose? Can we in fact obtain an accurate analytical solution to the equations of point reactor neutron kinetics for step reactivity inse...

show abstract

“…Calculations of these parameters are concerned with the reactor dynamics. The neutron density is one of the most important parameters in reactor dynamics [5][6][7]. According to the importance of neutron density in the cold start-up stage, the external neutron source makes a significant contribution to the reactor power [8].…”

Section: Introductionmentioning

confidence: 99%

Generalization of the analytical solution of neutron point kinetics equations with time-dependent external source

2014

View full text Add to dashboard Cite

Point reactor kinetics equations with one group of delayed neutrons in the presence of the time-dependent external neutron source are solved analytically during the start-up of a nuclear reactor. Our model incorporates the random nature of the source and linear reactivity variation. We establish a general relationship between the expectation values of source intensity and the expectation values of neutron density of the sub-critical reactor by ignoring the term of the second derivative for neutron density in neutron point kinetics equations. The results of the analytical solution are in good agreement with the results obtained with numerical solution.

show abstract

Power series solution method for solving point kinetics equations with lumped model temperature and feedback

Cited by 28 publications

References 3 publications

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

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

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

Generalization of the analytical solution of neutron point kinetics equations with time-dependent external source

Contact Info

Product

Resources

About