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Artykuły w czasopismach na temat „POINT REACTOR KINETICS”

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Data publikacji: 11 września 2023

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1

Planchard, J. "On the point-reactor kinetics approximation." Progress in Nuclear Energy 26, no. 3 (1991): 207–16. http://dx.doi.org/10.1016/0149-1970(91)90035-n.

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2

Abramov, B. D., and Yu V. Matveev. "Some Inverse Problems for Reactor Point Kinetics." Transport Theory and Statistical Physics 37, no. 2-4 (2008): 327–43. http://dx.doi.org/10.1080/00411450802515973.

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3

Aboanber, Ahmed E. "Generalized and Stability Rational Functions for Dynamic Systems of Reactor Kinetics." International Journal of Nuclear Energy 2013 (August 13, 2013): 1–12. http://dx.doi.org/10.1155/2013/903904.

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The base of reactor kinetics dynamic systems is a set of coupled stiff ordinary differential equations known as the point reactor kinetics equations. These equations which express the time dependence of the neutron density and the decay of the delayed neutron precursors within a reactor are first order nonlinear and essentially describe the change in neutron density within the reactor due to a change in reactivity. Outstanding the particular structure of the point kinetic matrix, a semianalytical inversion is performed and generalized for each elementary step resulting eventually in substantial time saving. Also, the factorization techniques based on using temporarily the complex plane with the analytical inversion is applied. The theory is of general validity and involves no approximations. In addition, the stability of rational function approximations is discussed and applied to the solution of the point kinetics equations of nuclear reactor with different types of reactivity. From the results of various benchmark tests with different types of reactivity insertions, the developed generalized Padé approximation (GPA) method shows high accuracy, high efficiency, and stable character of the solution.

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4

Zhu, Wenzhang, and Qiang ZHAO. "ICONE19-43375 Solution of Point-Reactor Neutron Kinetics Equation by Gauss Precise Time-Integration Method." Proceedings of the International Conference on Nuclear Engineering (ICONE) 2011.19 (2011): _ICONE1943. http://dx.doi.org/10.1299/jsmeicone.2011.19._icone1943_160.

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5

Singh, Sudhansu, and Mohapatra Dinakrushna. "Solution of the reactor point kinetics equations by MATLAB computing." Nuclear Technology and Radiation Protection 30, no. 1 (2015): 11–17. http://dx.doi.org/10.2298/ntrp1501011s.

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The numerical solution of the point kinetics equations in the presence of Newtonian temperature feedback has been a challenging issue for analyzing the reactor transients. Reactor point kinetics equations are a system of stiff ordinary differential equations which need special numerical treatments. Although a plethora of numerical intricacies have been introduced to solve the point kinetics equations over the years, some of the simple and straightforward methods still work very efficiently with extraordinary accuracy. As an example, it has been shown recently that the fundamental backward Euler finite difference algorithm with its simplicity has proven to be one of the most effective legacy methods. Complementing the back-ward Euler finite difference scheme, the present work demonstrates the application of ordinary differential equation suite available in the MATLAB software package to solve the stiff reactor point kinetics equations with Newtonian temperature feedback effects very effectively by analyzing various classic benchmark cases. Fair accuracy of the results implies the efficient application of MATLAB ordinary differential equation suite for solving the reactor point kinetics equations as an alternate method for future applications.

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6

Hayes, J. G., and E. J. Allen. "Stochastic point-kinetics equations in nuclear reactor dynamics." Annals of Nuclear Energy 32, no. 6 (2005): 572–87. http://dx.doi.org/10.1016/j.anucene.2004.11.009.

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7

Obaidurrahman, Khalilurrahman, and Om Singh. "A comparative study of kinetics of nuclear reactors." Nuclear Technology and Radiation Protection 24, no. 3 (2009): 167–76. http://dx.doi.org/10.2298/ntrp0903167o.

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The paper deals with the study of reactivity initiated transients to investigate major differences in the kinetics behavior of various reactor systems under different operating conditions. The article also states guidelines to determine the safety limits on reactivity insertion rates. Three systems, light water reactors (pressurized water reactors), heavy water reactors (pressurized heavy water reactors), and fast breeder reactors are considered for the sake of analysis. The upper safe limits for reactivity insertion rate in these reactor systems are determined. The analyses of transients are performed by a point kinetics computer code, PKOK. A simple but accurate method for accounting total reactivity feedback in kinetics calculations is suggested and used. Parameters governing the kinetics behavior of the core are studied under different core states. A few guidelines are discussed to project the possible kinetics trends in the next generation reactors.

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8

Valocchi, G., J. Tommasi, and P. Ravetto. "Reduced order models in reactor kinetics: A comparison between point kinetics and multipoint kinetics." Annals of Nuclear Energy 147 (November 2020): 107702. http://dx.doi.org/10.1016/j.anucene.2020.107702.

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9

Kale, Vivek, Rakesh Kumar, K. Obaidurrahman, and Avinash Gaikwad. "Linear stability analysis of a nuclear reactor using the lumped model." Nuclear Technology and Radiation Protection 31, no. 3 (2016): 218–27. http://dx.doi.org/10.2298/ntrp1603218k.

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The stability analysis of a nuclear reactor is an important aspect in the design and operation of the reactor. A stable neutronic response to perturbations is essential from the safety point of view. In this paper, a general methodology has been developed for the linear stability analysis of nuclear reactors using the lumped reactor model. The reactor kinetics has been modelled using the point kinetics equations and the reactivity feedbacks from fuel, coolant and xenon have been modelled through the appropriate time dependent equations. These governing equations are linearized considering small perturbations in the reactor state around a steady operating point. The characteristic equation of the system is used to establish the stability zone of the reactor considering the reactivity coefficients as parameters. This methodology has been used to identify the stability region of a typical pressurized heavy water reactor. It is shown that the positive reactivity feedback from xenon narrows down the stability region. Further, it is observed that the neutron kinetics parameters (such as the number of delayed neutron precursor groups considered, the neutron generation time, the delayed neutron fractions, etc.) do not have a significant influence on the location of the stability boundary. The stability boundary is largely influenced by the parameters governing the evolution of the fuel and coolant temperature and xenon concentration.

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10

Nahla, Abdallah A., and Elsayed M. E. Zayed. "Solution of the nonlinear point nuclear reactor kinetics equations." Progress in Nuclear Energy 52, no. 8 (2010): 743–46. http://dx.doi.org/10.1016/j.pnucene.2010.06.001.

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11

Nahla, Abdallah A. "Analytical solution to solve the point reactor kinetics equations." Nuclear Engineering and Design 240, no. 6 (2010): 1622–29. http://dx.doi.org/10.1016/j.nucengdes.2010.03.003.

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12

Theler, Germán G., and Fabián J. Bonetto. "On the stability of the point reactor kinetics equations." Nuclear Engineering and Design 240, no. 6 (2010): 1443–49. http://dx.doi.org/10.1016/j.nucengdes.2010.03.007.

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13

Espinosa-Paredes, Gilberto, Marco-A. Polo-Labarrios, Erick-G. Espinosa-Martínez, and Edmundo del Valle-Gallegos. "Fractional neutron point kinetics equations for nuclear reactor dynamics." Annals of Nuclear Energy 38, no. 2-3 (2011): 307–30. http://dx.doi.org/10.1016/j.anucene.2010.10.012.

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14

Kulikov, Gennady G., Anatoly N. Shmelev, Vladimir A. Apse, and Evgeny G. Kulikov. "On a significant slowing-down of the kinetics of fast transient processes in a fast reactor." Nuclear Energy and Technology 6, no. 4 (2020): 295–98. http://dx.doi.org/10.3897/nucet.6.60379.

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The kinetics of nuclear reactors is determined by the average neutron lifetime. When the inserted reactivity is more than the effective delayed neutron fraction, the reactor kinetics becomes very rapid. It is possible to slow down the fast reactor kinetics by increasing the neutron lifetime. The authors consider the possibility of using the lead isotope, 208Pb, as a neutron reflector with specific properties in a lead-cooled fast reactor. To analyze the emerging effects in a reactor of this type, a point kinetics model was selected, which takes into account neutrons returning from the 208Pb reflector to the reactor core. Such specific properties of 208Pb as the high atomic weight and weak neutron absorption allow neutrons from the reactor core to penetrate deeply into the 208Pb reflector, slow down in it, and have a noticeable probability to return to the reactor core and affect the chain fission reaction. The neutrons coming back from the 208Pb reflector have a long ‘dead-time’, i.e., the sum of times when neutrons leave the reactor core, entering the 208Pb reflector, and then diffuse back into the reactor core. During the ‘dead-time’, these neutrons cannot affect the chain fission reaction. In terms of the delay time, the neutrons returning from the deep layers of the 208Pb reflector are close to the delayed neutrons. Moreover, the number of the neutrons coming back from the 208Pb reflector considerably exceeds the number of the delayed neutrons. As a result, the neutron lifetime formed by the prompt neutron lifetime and the ‘dead-time’ of the neutrons from the 208Pb reflector can be substantially increased. This will lead to a longer reactor acceleration period, which will mitigate the effects of prompt supercriticality. Thus, the use of 208Pb as a neutron reflector can significantly improve the fast reactor nuclear safety.

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15

Ruščák, Marek, and Guido Mazzini. "PARCS/TRACE COUPLING METHODOLOGY FOR ROD EJECTION ON VVER 1000 REACTOR." Acta Polytechnica CTU Proceedings 4 (December 16, 2016): 80. http://dx.doi.org/10.14311/ap.2016.4.0080.

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The rod ejection (RE) is a design basis accident in accordance with NUREG-0800 and usually studied using point kinetics. In this paper a methodology and a 3D kinetic model is prepared (PARCS), coupled with a thermal hydraulic system code (TRACE) for simulating this accident scenario for general VVER 1000 technology.

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16

Abramov, B. "CORRECTION OF INVERSE POINT KINETICS EQUATIONS FOR MEASUREMENT REACTIVITY IN THE PROMPT JUMP APPROXIMATION." PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. SERIES: NUCLEAR AND REACTOR CONSTANTS 2019, no. 2 (2019): 151–59. http://dx.doi.org/10.55176/2414-1038-2019-2-151-159.

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We consider methods for calculating the reactivity of a nuclear reactor from the measured dependence of the neutron flux in the reactor on time, based on the use of the inverse point kinetics equations, which relate the values of reactivity and neutron flux in the reactor. The main attention is paid to the correction of the equations of inverse point kinetics in the prompt-jump approximation (or in the theory of singular perturbations for equations with a small parameter with the highest derivative). The nonequivalence of the corresponding problems for the direct and inverse point kinetics equations in the prompt-jump approximation is noted, which consists in the fact that, contrary to expectations, the reactivity values appearing in these problems do not generally coincide with each other. The reasons for this non-equivalence are investigated and ways to eliminate it are considered. New inverse point kinetics equations are proposed in the prompt-jump approximation, devoid of the indicated disadvantage of the traditional equations. These equations are tested by substituting in them analytical solutions of the corresponding (direct) Cauchy problems for point kinetics equations using the apparatus of the theory of systems of ordinary differential equations, adapted to the problem in question. It is shown that the use of the equations proposed in the work leads to the correct determination of reactivity immediately after the instantaneous introduction of a disturbance into the reactor, and not in asymptotics, as is usually the case when applying traditional equations.

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17

Suescún-Díaz, D., and G. Espinosa-Paredes. "On the numerical solution of the point reactor kinetics equations." Nuclear Engineering and Technology 52, no. 6 (2020): 1340–46. http://dx.doi.org/10.1016/j.net.2019.11.034.

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18

Hamada, Yasser Mohamed. "Trigonometric Fourier-series solutions of the point reactor kinetics equations." Nuclear Engineering and Design 281 (January 2015): 142–53. http://dx.doi.org/10.1016/j.nucengdes.2014.11.017.

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19

Nahla, Abdallah A., and Mohammed F. Al-Ghamdi. "Generalization of the Analytical Exponential Model for Homogeneous Reactor Kinetics Equations." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/282367.

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Mathematical form for two energy groups of three-dimensional homogeneous reactor kinetics equations and average one group of the precursor concentration of delayed neutrons is presented. This mathematical form is called “two energy groups of the point kinetics equations.” We rewrite two energy groups of the point kinetics equations in the matrix form. Generalization of the analytical exponential model (GAEM) is developed for solving two energy groups of the point kinetics equations. The GAEM is based on the eigenvalues and the corresponding eigenvectors of the coefficient matrix. The eigenvalues of the coefficient matrix are calculated numerically using visual FORTRAN code, based on Laguerre’s method, to calculate the roots of an algebraic equation with real coefficients. The eigenvectors of the coefficient matrix are calculated analytically. The results of the GAEM are compared with the traditional methods. These comparisons substantiate the accuracy of the results of the GAEM. In addition, the GAEM is faster than the traditional methods.

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20

R. Maleki, Bahram, Mehmet Tombakoglu, and Sedat Goluoglu. "Simulation of two-point reactor kinetics model of reflected reactors with Newtonian reactivity feedback." Annals of Nuclear Energy 177 (November 2022): 109315. http://dx.doi.org/10.1016/j.anucene.2022.109315.

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21

Nowak, Tomasz Karol, Kazimierz Duzinkiewicz, and Robert Piotrowski. "Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor." Archives of Control Sciences 24, no. 2 (2014): 129–54. http://dx.doi.org/10.2478/acsc-2014-0009.

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Abstract This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model’s response was examined. The results for typical input were discussed and compared.

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22

Altahhan, Muhammad Ramzy, Ahmed E. Aboanber, Hanaa H. Abou-Gabal, and Mohamed S. Nagy. "Response of the point-reactor telegraph kinetics to time varying reactivities." Progress in Nuclear Energy 98 (July 2017): 109–22. http://dx.doi.org/10.1016/j.pnucene.2017.03.008.

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23

Aboanber, Ahmed E., and Abdallah A. Nahla. "Mathematical treatment for two-point reactor kinetics model of reflected systems." Progress in Nuclear Energy 105 (May 2018): 287–93. http://dx.doi.org/10.1016/j.pnucene.2018.02.015.

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24

Peinetti, F., C. Nicolino, and P. Ravetto. "Kinetics of a point reactor in the presence of reactivity oscillations." Annals of Nuclear Energy 33, no. 14-15 (2006): 1189–95. http://dx.doi.org/10.1016/j.anucene.2006.08.002.

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25

Hamieh, S. D., and M. Saidinezhad. "Analytical solution of the point reactor kinetics equations with temperature feedback." Annals of Nuclear Energy 42 (April 2012): 148–52. http://dx.doi.org/10.1016/j.anucene.2011.12.021.

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26

Luan, Xiuchun, and Pavel V. Tsvetkov. "Novel consistent approach in controllability evaluations of point reactor kinetics models." Annals of Nuclear Energy 131 (September 2019): 496–506. http://dx.doi.org/10.1016/j.anucene.2019.04.003.

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27

Espinosa-Paredes, G., and D. Suescún-Díaz. "Point reactor kinetics equations from P1 approximation of the transport equations." Annals of Nuclear Energy 144 (September 2020): 107592. http://dx.doi.org/10.1016/j.anucene.2020.107592.

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28

Zarei, Mohamad. "An enhanced formalism for the inverse reactor kinetics problem." Kerntechnik 87, no. 1 (2022): 66–71. http://dx.doi.org/10.1515/kern-2021-1008.

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Abstract The inverse kinetics problem in reactor physics is a standard formalism to unfold reactivity on the basis of registered power (flux) profile. The classical inverse point kinetics framework has been retrofitted herein to comprise thermal reactivity feedback effects. The instantaneous fuel and coolant temperatures are thus computed by way of the exponential time-differencing scheme and the corresponding thermal reactivity feedback is plugged into the inverse kinetics module. The core external reactivity is therefore unfolded employing only two consecutive time-steps of the power (flux) profile. A history independent yet straightforward numerical routine is accrued enjoying noticeable robustness with regards to the time-step resolution.

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29

Cabrera, María I., Carlos A. Martín, Orlando M. Alfano, and Alberto E. Cassano. "Photochemical decomposition of 2,4-dichlorophenoxy acetic acid (2,4-D) in aqueous solution. I. Kinetic study." Water Science and Technology 35, no. 4 (1997): 31–39. http://dx.doi.org/10.2166/wst.1997.0079.

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The intrinsic kinetics of the photochemical decomposition of 2,4-dichlorophenoxyacetic acid in aqueous solution has been studied using light of 253.7 nm. Experiments were carried out in a well stirred batch reactor irradiated from its bottom by means of a tubular lamp and a parabolic reflector. Results were analyzed in terms of a very simple kinetic expression. Absorbed radiation effects were duly quantified by means of a one-dimensional radiation field model. This approach incorporates a variable absorption coefficient that is a function of the 2,4-D conversion. The decomposition kinetics can be properly represented with a point valued equation of the following form: RD, λ = − ΦD,λ eλ(y).

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30

Yuferov, Anatoly G. "On the concept of “effective delayed neutron fraction”." Nuclear Energy and Technology 8, no. 4 (2022): 275–79. http://dx.doi.org/10.3897/nucet.8.96567.

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The article considers methodological issues related to the conceptual and terminological apparatus of the dynamics of nuclear reactors. Based on an elementary analysis of the standard point reactor kinetics equations, the author shows that it is necessary to clarify the physical meaning of the parameter β included in the equations, which is traditionally interpreted as the “effective delayed neutrons fraction” (EDNF). It follows directly from the kinetics equations that the parameter β, which appears in these equations as the EDNF, is, from the point of view of the neutron balance, the fraction of prompt neutrons consumed for the generation of delayed neutron precursors (DNPs), and, from the point of view of the DNP balance, the DNP yield per prompt neutron in a single fission event. With these interpretations taken into account, the role of the β parameter is considered in situations related with its adjustment by multiplying it by the “delayed neutron efficiency factor” and with the establishment of the actual fractions of prompt and delayed neutrons. In particular, it is shown that: the statement “if the delayed neutron fraction is β, then the prompt neutron fraction is equal to 1 – β”, used in the problems of analyzing the nuclear reactor dynamics as a starting position, cannot be considered applicable to any reactor conditions; an increase in the β parameter by multiplying it by the “delayed neutron efficiency factor” leads, contrary to traditional interpretations, not to an increase but to a decrease in neutron reproduction in a supercritical reactor. The proposed clarifications are appropriate both in terms of more adequate descriptions of processes in nuclear reactors and in relation to the formulations of nuclear safety requirements.

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31

Irkimbekov, Ruslan, Alexander Vurim, Galina Vityuk, Olzhas Zhanbolatov, Zamanbek Kozhabayev, and Artur Surayev. "Modeling of Dynamic Operation Modes of IVG.1M Reactor." Energies 16, no. 2 (2023): 932. http://dx.doi.org/10.3390/en16020932.

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This paper presents the results of a calculation code approach providing a solution to the point kinetics problem for the IVG.1M research reactor of the National Nuclear Center of the Republic of Kazakhstan and allowing the simulation of dynamic processes going on during reactor start-ups, including changes in the thermal state of all its elements, reactor regulator displacement, accumulation of absorbers in the fuel, and the beryllium reflector. A mathematical description of the IVG.1M point kinetics model is presented, which provides a calculation of the reactor neutron parameters, taking into account the dependence of reactivity effects on the temperature, changes in the isotopic composition of materials, and thermal expansion of core structural elements. An array of data values was formed of reactivity added by separate elements of the core when changing their thermal state and other reactor parameters, as well as an array of data with the parameters of heat exchange of coolant-based reactor structural elements. These are used in the process of solving the point kinetics problem to directly replace formal parameters, eliminating the need to calculate the values of these parameters at each calculation step. Preliminary calculations to form an array of values of reactivity effects was applied to the reactor by separate structural elements when their temperature changes were performed using the IVG.1M precision reactor calculation model. The model was validated by the reactor parameters in the critical state. Preliminary calculations to form an array of data with the parameters of heat exchange of coolant-based reactor structural elements were performed in ANSYS Fluent software using the calculation model that describes the IVG.1M reactor fuel element in detail. Validation of the developed calculation code based on the results of two start-ups of the IVG.1M reactor was performed and its applicability for the analysis of transient and emergency modes of reactor operation and evaluation of its safe operation limits was confirmed.

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32

Fan, Gen, and Wen Bin Liu. "An Integral Method for Solving the Point Reactor Neutron Kinetics Equations with Newtonian Temperature Feedback." Advanced Materials Research 732-733 (August 2013): 83–89. http://dx.doi.org/10.4028/www.scientific.net/amr.732-733.83.

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A numerical integral method to efficiently solve the point kinetics equations with Newtonian temperature feedback is described and investigated, which employs the better basis function (BBF) for the approximation of the neutron density in integral of one time step. The numerical evaluation is performed by the developed BBF code. The code can solve the general non-linear kinetics problems with six groups of delayed neutron. For the application purposes, the developed code and the method are tested by using a variety of problems, including ramp reactivity input with or without temperature feedback. The results are shown that the BBF method is clearly an effective and accurate numerical method for solving the point kinetics equations with Newtonian temperature feedback, and it can be used in real time power reactor forecasting in order to prevent the reactivity accidents.

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33

Leung, H. K. Y., and A. A. Harms. "Graph-theoretical basis of reactor point-kinetics / Graphentheoretische Grundlegung einer Reaktor-Punktkinetik." Kerntechnik 51, no. 3 (1987): 181–85. http://dx.doi.org/10.1515/kern-1987-510317.

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34

El-Genk, Mohamed S., and Jean-Michel P. Tournier. "A point kinetics model for dynamic simulations of next generation nuclear reactor." Progress in Nuclear Energy 92 (September 2016): 91–103. http://dx.doi.org/10.1016/j.pnucene.2016.07.007.

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35

Kinard, Matthew, and E. J. Allen. "Efficient numerical solution of the point kinetics equations in nuclear reactor dynamics." Annals of Nuclear Energy 31, no. 9 (2004): 1039–51. http://dx.doi.org/10.1016/j.anucene.2003.12.008.

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36

Li, Haofeng, Wenzhen Chen, Lei Luo, and Qian Zhu. "A new integral method for solving the point reactor neutron kinetics equations." Annals of Nuclear Energy 36, no. 4 (2009): 427–32. http://dx.doi.org/10.1016/j.anucene.2008.11.033.

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37

Nowak, Tomasz Karol, Kazimierz Duzinkiewicz, and Robert Piotrowski. "Fractional neutron point kinetics equations for nuclear reactor dynamics – Numerical solution investigations." Annals of Nuclear Energy 73 (November 2014): 317–29. http://dx.doi.org/10.1016/j.anucene.2014.07.001.

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38

Espinosa-Paredes, Gilberto. "Fractional-space neutron point kinetics (F-SNPK) equations for nuclear reactor dynamics." Annals of Nuclear Energy 107 (September 2017): 136–43. http://dx.doi.org/10.1016/j.anucene.2016.08.007.

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39

Espinosa-Paredes, Gilberto, and Carlos G. Aguilar-Madera. "Scaled neutron point kinetics (SUNPK) equations for nuclear reactor dynamics: 2D approximation." Annals of Nuclear Energy 115 (May 2018): 377–86. http://dx.doi.org/10.1016/j.anucene.2018.01.020.

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40

Giménez, Jaime, David Curcó, and Pilar Marco. "Reactor modelling in the photocatalytic oxidation of wastewater." Water Science and Technology 35, no. 4 (1997): 207–13. http://dx.doi.org/10.2166/wst.1997.0120.

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Two different experimental devices have been tested for the photocatalytic oxidation of phenol, by using TiO2 suspensions. At the laboratory level, experiments were carried out in microreactors with Xe lamps. At pilot plant scale, the experiments were done at the Plataforma Solar de Almería (PSA), Spain, by using a high concentrating radiation systems (Heliomans) and solar radiation. Both systems were characterized from the point of view of the radiation field. Kinetic experiments and radiation measurements showed that kinetics are first order with respect to the phenol concentration, and a linear dependence of the reaction rate on the square root of the photonic flow. Kinetic constants (k) were calculated for both systems considering only concentration-time data. Results indicate that k values obtained at the laboratory were ten times greater than these obtained at the PSA. However, results improve when the radiation entering and the radiation absorbed by the catalyst were considered. The fitting of concentration-radiation data drives to values of the kinetic constants more similar for both systems and for all the catalyst concentrations tested. Thus, these new constants can be useful for the change of scale.

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41

Schiassi, Enrico, Mario De Florio, Barry D. Ganapol, Paolo Picca, and Roberto Furfaro. "Physics-informed neural networks for the point kinetics equations for nuclear reactor dynamics." Annals of Nuclear Energy 167 (March 2022): 108833. http://dx.doi.org/10.1016/j.anucene.2021.108833.

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42

Kastanya, Doddy. "Evaluating the variations of point kinetics parameters in pressurized heavy water reactor analyses." Annals of Nuclear Energy 173 (August 2022): 109130. http://dx.doi.org/10.1016/j.anucene.2022.109130.

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Chen Wen-Zhen, Zhu Bo, and Li Hao-Feng. "The analytic solutions of point-reactor neutron-kinetics equation with small step reactivity." Acta Physica Sinica 53, no. 8 (2004): 2486. http://dx.doi.org/10.7498/aps.53.2486.

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Ganapol, Barry. "A refined way of solving reactor point kinetics equations for imposed reactivity insertions." Nuclear Technology and Radiation Protection 24, no. 3 (2009): 157–66. http://dx.doi.org/10.2298/ntrp0903157g.

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Streszczenie:

We apply the concept of convergence acceleration, also known as extrapolation, to find the solution of the reactor kinetics equations (RKEs). The method features simplicity in that an approximate finite difference formulation is constructed and converged to high accuracy from knowledge of the error term. Through the Romberg extrapolation, we demonstrate its high accuracy for a variety of imposed reactivity insertions found in the literature. The unique feature of the proposed algorithm, called RKE/R(omberg), is that no special attention is given to the stiffness of the RKEs. Finally, because of its simplicity and accuracy, the RKE/R algorithm is arguably the most efficient numerical solution of the RKEs developed to date.

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Diniz, Rodrigo Costa, Alessandro da Cruz Gonçalves, and Felipe Siqueira de Souza da Rosa. "Neutron point kinetics model with precursors’ shape function update for molten salt reactor." Nuclear Engineering and Design 360 (April 2020): 110466. http://dx.doi.org/10.1016/j.nucengdes.2019.110466.

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Nowak, Tomasz Karol, Kazimierz Duzinkiewicz, and Robert Piotrowski. "Numerical solution analysis of fractional point kinetics and heat exchange in nuclear reactor." Nuclear Engineering and Design 281 (January 2015): 121–30. http://dx.doi.org/10.1016/j.nucengdes.2014.11.028.

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Sosnovsky, Eugeny, and Benoit Forget. "Bond graph representation of nuclear reactor point kinetics and nearly incompressible thermal hydraulics." Annals of Nuclear Energy 68 (June 2014): 15–29. http://dx.doi.org/10.1016/j.anucene.2013.12.013.

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Altahhan, Muhammad Ramzy, Mohamed S. Nagy, Hanaa H. Abou-Gabal, and Ahmed E. Aboanber. "Formulation of a point reactor kinetics model based on the neutron telegraph equation." Annals of Nuclear Energy 91 (May 2016): 176–88. http://dx.doi.org/10.1016/j.anucene.2016.01.011.

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Ayyoubzadeh, Seyed Mohsen, and Naser Vosoughi. "On the limitations of linear power reactor noise analysis: A point kinetics approach." Annals of Nuclear Energy 102 (April 2017): 124–33. http://dx.doi.org/10.1016/j.anucene.2016.12.007.

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Behringer, K., and J. Piñeyro. "Concerning the stability parameter in point reactor kinetics driven by random reactivity noise." Annals of Nuclear Energy 21, no. 12 (1994): 787–91. http://dx.doi.org/10.1016/0306-4549(94)90025-6.

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