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Ravindra Babu P, Pal U, Sen R, Karthikeyan R. Runge–Kutta type-2 method for solving reactor point kinetics equations and its validation by analysing thermal and fast reactor benchmarks. ANN NUCL ENERGY 2022. [DOI: 10.1016/j.anucene.2022.108979] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/01/2022]
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Rafiei M, Ansarifar G, Hadad K, Mohammadi M. Load-following control of a nuclear reactor using optimized FOPID controller based on the two-point fractional neutron kinetics model considering reactivity feedback effects. PROGRESS IN NUCLEAR ENERGY 2021. [DOI: 10.1016/j.pnucene.2021.103936] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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3
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Hui J, Yuan J. Disturbance observer based adaptive sliding mode control for power tracking of PWRs. NUCLEAR ENGINEERING AND TECHNOLOGY 2020. [DOI: 10.1016/j.net.2020.04.027] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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4
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Xiao Y, Gu Z, Zhang Q, Ge L, Zeng G, Li F. New semi-analytical algorithm for solving PKEs based on Euler-Maclaurin approximation. ANN NUCL ENERGY 2020. [DOI: 10.1016/j.anucene.2020.107308] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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5
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On the numerical solution of the point reactor kinetics equations. NUCLEAR ENGINEERING AND TECHNOLOGY 2020. [DOI: 10.1016/j.net.2019.11.034] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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6
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Polo-Labarrios M, Quezada-García S, Espinosa-Paredes G, Ortiz-Villafuerte J. Assessment of the fractional neutron point kinetic equation to simulate core transients with Newtonian temperature feedback. ANN NUCL ENERGY 2020. [DOI: 10.1016/j.anucene.2019.107197] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Roul P, Madduri H, Obaidurrahman K. An implicit finite difference method for solving the corrected fractional neutron point kinetics equations. PROGRESS IN NUCLEAR ENERGY 2019. [DOI: 10.1016/j.pnucene.2019.02.002] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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8
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A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems. SCIENCE AND TECHNOLOGY OF NUCLEAR INSTALLATIONS 2018. [DOI: 10.1155/2018/7105245] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
A new method based on shifted Chebyshev series of the first kind is introduced to solve stiff linear/nonlinear systems of the point kinetics equations. The total time interval is divided into equal step sizes to provide approximate solutions. The approximate solutions require determination of the series coefficients at each step. These coefficients can be determined by equating the high derivatives of the Chebyshev series with those obtained by the given system. A new recurrence relation is introduced to determine the series coefficients. A special transformation is applied on the independent variable to map the classical range of the Chebyshev series from [-1,1] to [0,h]. The method deals with the Chebyshev series as a finite difference method not as a spectral method. Stability of the method is discussed and it has proved that the method has an exponential rate of convergence. The method is applied to solve different problems of the point kinetics equations including step, ramp, and sinusoidal reactivities. Also, when the reactivity is dependent on the neutron density and step insertion with Newtonian temperature feedback reactivity and thermal hydraulics feedback are tested. Comparisons with the analytical and numerical methods confirm the validity and accuracy of the method.
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Yuferov A. Quadrature formulas for integral equations of kinetics and digital reactimeters. NUCLEAR ENERGY AND TECHNOLOGY 2017. [DOI: 10.1016/j.nucet.2017.08.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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12
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Parameter analysis of neutron point kinetics for nuclear reactors. NUCLEAR ENGINEERING AND DESIGN 2017. [DOI: 10.1016/j.nucengdes.2017.04.025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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13
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Analytical solution of the fractional point kinetics equations with multi-group of delayed neutrons during start-up of a nuclear reactor. ANN NUCL ENERGY 2017. [DOI: 10.1016/j.anucene.2016.08.030] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Tumelero F, Petersen CZ, Gonçalves GA, Schramm M. Polynomial approach method to solve the neutron point kinetics equations with use of the analytic continuation. KERNTECHNIK 2016. [DOI: 10.3139/124.110600] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
AbstractIn this work, we report a solution to solve the Neutron Point Kinetics Equations applying the Polynomial Approach Method. The main idea is to expand the neutron density and delayed neutron precursors as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions and the analytical continuation is used to determine the solutions of the next intervals. A genuine error control is developed based on an analogy with the Rest Theorem. For illustration, we also report simulations for different approaches types (linear, quadratic and cubic). The results obtained by numerical simulations for linear approximation are compared with results in the literature.
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Affiliation(s)
- F. Tumelero
- 1Universidade Federal de Pelotas, Programa de Pós Graduação em Modelagem Matemática, Campus Universitário Capão do Leão s/n, 96010-610 Capão do Leão, RS, Brazil, E-mail:
| | - C. Z. Petersen
- 2Universidade Federal de Pelotas, Programa de Pós Graduação em Modelagem Matemática, Campus Universitário Capão do Leão s/n, 96010-610 Capão do Leão, RS, Brazil, E-mail corresponding author:
| | - G. A. Gonçalves
- 3Universidade Federal de Pelotas, Programa de Pós Graduação em Modelagem Matemática, Campus Universitário Capão do Leão s/n, 96010-610 Capão do Leão, RS, Brazil, E-mail:
| | - M. Schramm
- 4Universidade Federal do Rio Grande do Sul, Programa de Pós-graduação em Engenharia Mecânica, Rua Sarmento Leite, 425, 90050-170 Porto Alegre, RS, Brazil, E-mail:
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Nahla AA. Numerical treatment for the point reactor kinetics equations using theta method, eigenvalues and eigenvectors. PROGRESS IN NUCLEAR ENERGY 2015. [DOI: 10.1016/j.pnucene.2015.09.008] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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17
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The modified exponential time differencing (ETD) method for solving the reactor point kinetics equations. ANN NUCL ENERGY 2015. [DOI: 10.1016/j.anucene.2014.09.020] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Nowak TK, Duzinkiewicz K, Piotrowski R. Numerical solution analysis of fractional point kinetics and heat exchange in nuclear reactor. NUCLEAR ENGINEERING AND DESIGN 2015. [DOI: 10.1016/j.nucengdes.2014.11.028] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Chen W, Xiao H, Li H, Chen L. Explicit appropriate basis function method for numerical solution of stiff systems. ANN NUCL ENERGY 2015. [DOI: 10.1016/j.anucene.2014.08.040] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Trigonometric Fourier-series solutions of the point reactor kinetics equations. NUCLEAR ENGINEERING AND DESIGN 2015. [DOI: 10.1016/j.nucengdes.2014.11.017] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Aboanber AE, Nahla AA, Al-Muhiameed ZI. A novel mathematical model for two-energy groups of the point kinetics reactor dynamics. PROGRESS IN NUCLEAR ENERGY 2014. [DOI: 10.1016/j.pnucene.2014.06.016] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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El_Tokhy MS, Mahmoud II. Parameter analysis of the neutron point kinetics equations with feedback temperature effects. ANN NUCL ENERGY 2014. [DOI: 10.1016/j.anucene.2014.01.020] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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A numerical approach based on Haar wavelet operational method to solve neutron point kinetics equation involving imposed reactivity insertions. ANN NUCL ENERGY 2014. [DOI: 10.1016/j.anucene.2014.01.008] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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A numerical solution to the point kinetic equations using Taylor–Lie series combined with a scaling and squaring technique. NUCLEAR ENGINEERING AND DESIGN 2014. [DOI: 10.1016/j.nucengdes.2013.12.066] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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25
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Stiffness treatment of differential equations for the point reactor dynamic systems. PROGRESS IN NUCLEAR ENERGY 2014. [DOI: 10.1016/j.pnucene.2013.12.004] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Bogado Leite SQ, Palma DA, de Vilhena MT, Bodmann BE. Analytical representation of the solution of the point reactor kinetics equations with adaptive time step. PROGRESS IN NUCLEAR ENERGY 2014. [DOI: 10.1016/j.pnucene.2013.07.008] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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27
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Time discretization of the point kinetic equations using matrix exponential method and First-Order Hold. ANN NUCL ENERGY 2013. [DOI: 10.1016/j.anucene.2013.06.022] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Hamada YM. Confirmation of accuracy of generalized power series method for the solution of point kinetics equations with feedback. ANN NUCL ENERGY 2013. [DOI: 10.1016/j.anucene.2012.12.013] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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An accurate solution of point reactor neutron kinetics equations of multi-group of delayed neutrons. ANN NUCL ENERGY 2013. [DOI: 10.1016/j.anucene.2012.10.024] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Solution of Point Reactor Neutron Kinetics Equations with Temperature Feedback by Singularly Perturbed Method. SCIENCE AND TECHNOLOGY OF NUCLEAR INSTALLATIONS 2013. [DOI: 10.1155/2013/261327] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
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.
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The development of natural circulation operation support program for ship nuclear power machinery. ANN NUCL ENERGY 2012. [DOI: 10.1016/j.anucene.2012.08.005] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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32
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An efficient technique for the point reactor kinetics equations with Newtonian temperature feedback effects. ANN NUCL ENERGY 2011. [DOI: 10.1016/j.anucene.2011.08.021] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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33
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Hamada YM. Generalized power series method with step size control for neutron kinetics equations. NUCLEAR ENGINEERING AND DESIGN 2011. [DOI: 10.1016/j.nucengdes.2011.05.006] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Nahla AA. Taylor’s series method for solving the nonlinear point kinetics equations. NUCLEAR ENGINEERING AND DESIGN 2011. [DOI: 10.1016/j.nucengdes.2011.02.016] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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An accurate solution of point kinetics equations of one-group delayed neutrons and an extraneous neutron source for step reactivity insertion. CHINESE SCIENCE BULLETIN-CHINESE 2010. [DOI: 10.1007/s11434-010-4220-2] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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37
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Inhomogeneous point kinetics equations and the source contribution. NUCLEAR ENGINEERING AND DESIGN 2010. [DOI: 10.1016/j.nucengdes.2010.09.036] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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38
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Analytical solution to solve the point reactor kinetics equations. NUCLEAR ENGINEERING AND DESIGN 2010. [DOI: 10.1016/j.nucengdes.2010.03.003] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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