Exact solution for the non-linear two point kinetic model of reflected reactors

Aboanber, Ahmed E.

doi:10.1016/j.pnucene.2009.03.003

Cited by 13 publications

(6 citation statements)

References 20 publications

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“…To test the validity of the proposed stochastic model, the zero-power research reactor PROTEUS, which consists of a relatively small core surrounded by a thick graphite reflector, is taken into consideration [8,9]. For the different reactivity insertion scenarios such as step reactivity, ramp reactivity, and ramp reactivity insertion in presence of the Newtonian temperature feedback effect the mean response of the stochastic model is compared with the results of the deterministic numerical methods.…”

Section: Computational Resultsmentioning

confidence: 99%

“…By using the adiabatic model, the Newtonian temperature reactivity feedback due to the fuel temperature is expressed as follows [9,10]:…”

Section: =1mentioning

confidence: 99%

“…Different type of numerical and analytical solution methods such as fundamental matrix method, analytical exponential method, analytical inversion method, and exact solution methods were used to solve either linear or non-linear two-point reactor kinetics equations [8,9,[11][12][13].…”

Section: =1mentioning

confidence: 99%

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Yansıtıcılı reaktörlerin stokastik iki-nokta reaktör kinetik denklemlerinin sayısal simülasyonu

Maleki

2020

Nevşehir Bilim Ve Teknoloji Dergisi

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Deterministic numerical solutions of point reactor kinetic equations give us the mean values of the neutron population and delayed neutron precursor concentrations, whereas the actual dynamical process is stochastic. The neutron population and precursor concentrations fluctuate randomly with time.In the present study, a novel stochastic model for two-point reactor kinetics equations is developed and used to analyze the dynamical behavior of the source-free strongly reflected reactors with six groups of delayed neutron precursors. To derive the Itô stochastic differential equations system corresponding to this model, the two-point reactor kinetics equations are separated into three terms: prompt neutrons, delayed neutrons, and reflected neutrons. In the case of different perturbation scenarios, both with and without the Newtonian temperature reactivity feedback effects, this system of stochastic differential equations is solved using the Euler-Murayama numerical method. It is observed that the mean response of the system is comparable with the results of other deterministic numerical methods.

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Section: Computational Resultsmentioning

confidence: 99%

“…By using the adiabatic model, the Newtonian temperature reactivity feedback due to the fuel temperature is expressed as follows [9,10]:…”

Section: =1mentioning

confidence: 99%

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Yansıtıcılı reaktörlerin stokastik iki-nokta reaktör kinetik denklemlerinin sayısal simülasyonu

Maleki

2020

Nevşehir Bilim Ve Teknoloji Dergisi

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Silva

Alvim

Vilhena

et al. 2014

IJNEST

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An analytical solution of the point kinetics equations to calculate time-dependent reactivity by the decomposition method has recently appeared in the literature. In this paper, we consider the neutron point kinetics equations together with temperature feedback effects. To this end, point kinetics is perturbed by a temperature equation that depends on the neutron density, obtaining a second-order non-linear ordinary differential equation. This equation is then solved by the decomposition method by expanding the neutron density in a series and expressing the non-linear terms by Adomian polynomials. Upon substituting these expansions into the non-linear ordinary equation, we construct a recursive set of linear problems that can be solved and resulting in an exact analytical representation for the solution. We also report numerical simulations and comparison against literature results.

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“…Using the resulting Green's functions, the time-dependent neutron population and precursor concentrations are obtained from the following integrals:In the nuclear reactors, prompt neutron average lifetime changes from 10 −7 to 10 −5 whereas the delayed neutron precursor average lifetime varies from 10 −2 to 10 +2 . The effective lifetime of the neutrons is given in Equation(16) where the average lifetime of delayed neutron is roughly taken equal to precursor lifetime. ) conditions the prompt neutrons alone make the reactor supercritical and due to small lifetime of the prompt neutrons the reactor control with mechanical equipment becomes almost impossible.…”

mentioning

confidence: 99%

Solution of two-point reactor kinetic equations for source-driven reﬂected reactors using the Green's function generation method

Maleki

2020

Sinop Üniversitesi Fen Bilimleri Dergisi

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The transient analysis of nuclear reactors is a very important issue from the safety point of view. The point reactor kinetics equations are extensively used in the analysis of the transient behavior of the nuclear reactors. The experimental results confirm that the dynamical behavior of the strongly reflected reactors cannot be adequately characterized by the conventional onepoint reactor kinetics equations. In this study, a Green's function generation method is developed to solve the two-point reactor kinetics equations for a subcritical source-driven reflected reactor with one group of delayed neutron precursors during the reactor start-up. Moreover, the two-point reactor kinetics equations are solved using the prompt-jump approximation method and it is shown that the obtained results are in good agreement with the results obtained from the Green's function generation method. The validity of the given methodologies is also demonstrated through comparison with asymptotic solutions.

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Exact solution for the non-linear two point kinetic model of reflected reactors

Cited by 13 publications

References 20 publications

Yansıtıcılı reaktörlerin stokastik iki-nokta reaktör kinetik denklemlerinin sayısal simülasyonu

Yansıtıcılı reaktörlerin stokastik iki-nokta reaktör kinetik denklemlerinin sayısal simülasyonu

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

Solution of two-point reactor kinetic equations for source-driven reﬂected reactors using the Green's function generation method

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