Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been anal...Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been analyzed. The efficiency of the proposed higher-order approximation scheme has been discussed in the results section. The solutions of SPKEs in the presence of Newtonian temperature feedback have also been provided to further discuss the physical behavior of the fractional model.展开更多
The exact calculation of point kinetic parameters is very important in nuclear reactor safety assessment, and most sophisticated safety codes such as RELAP5, PARCS,DYN3D, and PARET are using these parameters in their ...The exact calculation of point kinetic parameters is very important in nuclear reactor safety assessment, and most sophisticated safety codes such as RELAP5, PARCS,DYN3D, and PARET are using these parameters in their dynamic models. These parameters include effective delayed neutron fractions as well as mean generation time.These parameters are adjoint-weighted, and adjoint flux is employed as a weighting function in their evaluation.Adjoint flux calculation is an easy task for most of deterministic codes, but its evaluation is cumbersome for Monte Carlo codes. However, in recent years, some sophisticated techniques have been proposed for Monte Carlo-based point kinetic parameters calculation without any need of adjoint flux. The most straightforward scheme is known as the ‘‘prompt method'' and has been used widely in literature. The main objective of this article is dedicated to point kinetic parameters calculation in Tehran research reactor(TRR) using deterministic as well as probabilistic techniques. WIMS-D5B and CITATION codes have been used in deterministic calculation of forward and adjoint fluxes in the TRR core. On the other hand, the MCNP Monte Carlo code has been employed in the ‘‘prompt method''scheme for effective delayed neutron fraction evaluation.Deterministic results have been cross-checked with probabilistic ones and validated with SAR and experimental data. In comparison with experimental results, the relativedifferences of deterministic as well as probabilistic methods are 7.6 and 3.2%, respectively. These quantities are10.7 and 6.4%, respectively, in comparison with SAR report.展开更多
The present work aims to achieve a fast and accurate analytical solution of the point kinetics equations applied to subcritical reactors such as ADS (Accelerator-Driven System), assuming a linear reactivity and extern...The present work aims to achieve a fast and accurate analytical solution of the point kinetics equations applied to subcritical reactors such as ADS (Accelerator-Driven System), assuming a linear reactivity and external source variation. It was used a new set of point kinetics equations for subcritical systems based on the model proposed by Gandini & Salvatores. In this work it was employed the integrating factor method. The analytical solution for the case of interest was obtained by using only an approximation which consists of disregarding the term of the second derivative for neutron density in relation to time when compared with the other terms of the equation. And also, it is proposed an approximation for the upper incomplete gamma function found in the solution in order to make the computational processing faster. In addition, for purposes of validation and comparison a numerical solution was obtained by the finite differences method. Finally, it can be concluded that the obtained solution is accurate and has fast numerical processing time, especially when compared with the results of numerical solution by finite difference. One can also observe that the gamma approximation used achieve a high accuracy for the usual parameters. Thus we got satisfactory results when the solution is applied to practical situations, such as a reactor startup.展开更多
A molten salt reactor(MSR) is one of the six advanced reactor concepts selected by the generation Ⅳ international forum because of its advantages of inherent safety, and the promising capabilities of Th-U breeding an...A molten salt reactor(MSR) is one of the six advanced reactor concepts selected by the generation Ⅳ international forum because of its advantages of inherent safety, and the promising capabilities of Th-U breeding and transuranics transmutation. A dynamics model for the channel-type MSR is developed in this work based on a three-dimensional thermal–hydraulic model(3DTH) and a point reactor model. The 3DTH couples a three-dimensional heat conduction model and a one-dimensional single-phase flow model that can accurately consider the heat conduction between different assemblies. The 3DTH is validated by the RELAP5 code in terms of the temperature and mass flow distribution calculation. A point reactor model considering the drift of delayed neutron precursors is adopted in the dynamics model. To verify the dynamics model, three experiments from the molten salt reactor experiment are simulated. The agreement of the experimental data and simulation results was excellent.With the aid of this model, the unprotected step reactivity addition and unprotected loss of flow of the 2 MWt experimental MSR are modeled, and the reactor power and temperature evolution are analyzed.展开更多
The point-reactor model with power reactivity feedback becomes a nonlinear system. Its dynamic characteristic shows great complexity. According to the mathematic definition of stability in differential equa- tion qual...The point-reactor model with power reactivity feedback becomes a nonlinear system. Its dynamic characteristic shows great complexity. According to the mathematic definition of stability in differential equa- tion qualitative theory, the model of a reactor with power reactivity feedback is judged unstable. The equilibrium point is a saddle-node point. A portion of the trajectory in the neighborhood of the equilibrium point is parabolic fan curve, and the other is hyperbolic fan curve. Based on phase locus near the equilibrium point, it is pointed out that the model is still stable within physical limits. The difference between stabilities in the mathematical sense and in the physical sense is indicated.展开更多
The system of point kinetics equations describes the time behaviour of a nuclear reactor, assuming that, during the transient, the spatial form of the flux of neutrons varies very little. This system has been largely ...The system of point kinetics equations describes the time behaviour of a nuclear reactor, assuming that, during the transient, the spatial form of the flux of neutrons varies very little. This system has been largely used in the analysis of transients, where the numerical solutions of the equations are limited by the stiffness problem that results from the different time scales of the instantaneous and delayed neutrons. Its derivation can be done directly from the neutron transport equation, from the neutron diffusion equation or through a heuristics procedure. All of them lead to the same functional form of the system of differential equations for point kinetics, but with different coefficients. However, the solution of the neutron transport equation is of little practical use as it requires the change of the existent core design systems, as used to calculate the design of the cores of nuclear reactors for different operating cycles. Several approximations can be made for the said derivation. One of them consists of disregarding the time derivative for neutron density in comparison with the remaining terms of the equation resulting from the P1 approximation of the transport equation. In this paper, we consider that the time derivative for neutron current density is not negligible in the P1 equation. Thus being, we obtained a new system of equations of point kinetics that we named as modified. The innovation of the method presented in the manuscript consists in adopting arising from the P1 equations, without neglecting the derivative of the current neutrons, to derive the modified point kinetics equations instead of adopting the Fick’s law which results in the classic point kinetics equations. The results of the comparison between the point kinetics equations, modified and classical, indicate that the time derivative for the neutron current density should not be disregarded in several of transient analysis situations.展开更多
A design for instantaneous neutron flux signal acquisition system is being carried out for reactivity measurement of the nuclear research reactor. It is a computer-based digital data acquisition system that can perfor...A design for instantaneous neutron flux signal acquisition system is being carried out for reactivity measurement of the nuclear research reactor. It is a computer-based digital data acquisition system that can perform continuous monitor and measurement of reactivity inserted into or removed from the research reactor. The acquisition system accomplishes with two major parts. The first part is an interfacing PCI based data acquisition card and the corresponding driver software intending to on-line acquisition of neutron flux signals from plant instrumentation channel. The second part incorporates the high-level Visual Basic real time program, indigenously developed for computation of reactivity by the solution of neutron point kinetic equations and other relevant functional modules like input file logging, reactivity calculation, graphics demonstration etc.展开更多
This paper presents findings on the sliding mode controller for a nuclear reactor. One of the important operations in nuclear power plants is load following. In this paper, a sliding mode control system, which is a ro...This paper presents findings on the sliding mode controller for a nuclear reactor. One of the important operations in nuclear power plants is load following. In this paper, a sliding mode control system, which is a robust nonlinear controller, is designed to control the pressurizedwater reactor power. The reactor core is simulated based on the point kinetics equations and six delayed neutron groups. Considering neutron absorber poisons and regarding the limitations of the xenon concentration measurement, a sliding mode observer is designed to estimate its value, and finally, a sliding mode control based on the sliding mode observer is presented to control the core power of reactor. The stability analysis is given by means Lyapunov approach; thus, the control system is guaranteed to be stable within a large range. The employed method is easy to implement in practical applications, and moreover,the sliding mode control exhibits the desired dynamic properties during the entire output-tracking process independent of perturbations. Simulation results are presented to demonstrate the effectiveness of the proposed observerbased controller in terms of performance, robustness and stability.展开更多
A phase one design of a new free energy nano reactor is presented. The design is based on a basically topological interpretation of the Casimir effect as a natural intrinsic property of the geometrical topological str...A phase one design of a new free energy nano reactor is presented. The design is based on a basically topological interpretation of the Casimir effect as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. In particular we view dark energy, Hawking negative energy, Unruh temperature and zero point vacuum energy as being different sides of the same multi-dimensional coin. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so-called missing dark energy density of the cosmos. We start with a general outline of the theoretical principle and basic design concepts of a proposed Casimir dark energy nano reactor. In a nutshell the theory and consequently the actual design depend crucially upon the equivalence between the dark energy density of the cosmos and the faint local Casimir effect produced by two sides boundary condition quantum waves. This Casimir effect is then colossally amplified as a one internal quantum wave representing a Hartle-Hawking state vector of the universe pushing from the inside against the boundary of the universe with nothing balancing it from the non-existent outside. This strange situation becomes completely natural and logical when we remember that the boundary of the universe is a one sided Möbius like manifold. In view of the present theory, this is essentially what leads to the observed accelerated expansion of the cosmos. As in any reactor, the basic principle in the present design is to produce a gradient so that the excess energy on one side flows to the other side. Thus in principle we will restructure the local topology of space using material nanoscience technology to create an artificial local high dimensionality with a Dvoretzky theorem like 96 percent volume measure concentration. Without going into the intricate nonlinear dynamics and technological detail, it is fair to say that this would lead us to pure, clean, free energy obtained directly from the topology of spacetime via an artificial singularity. Needless to say, the entire design is based completely on the theory of quantum wave dark energy proposed by the present author for the first time in 2011 in a conference held in the Bibliotheca Alexandrina, Egypt and a little later in Shanghai, Republic of China. The quintessence of the present theory is easily explained as the Φ3 intrinsic Casimir topological energy where Φ=?(√5-1)/2 is produced from the zero set Φ of the quantum particle when we extract the empty set quantum wave Φ2 from it and find Φ-Φ2=Φ3 by restructuring space via conducting but uncharged plates similar to that of the classical Casimir experiments. Our proposed preliminary design of this Casimir-spacetime artificial singularity reactor follows in a natural way from the above.展开更多
文摘Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been analyzed. The efficiency of the proposed higher-order approximation scheme has been discussed in the results section. The solutions of SPKEs in the presence of Newtonian temperature feedback have also been provided to further discuss the physical behavior of the fractional model.
文摘The exact calculation of point kinetic parameters is very important in nuclear reactor safety assessment, and most sophisticated safety codes such as RELAP5, PARCS,DYN3D, and PARET are using these parameters in their dynamic models. These parameters include effective delayed neutron fractions as well as mean generation time.These parameters are adjoint-weighted, and adjoint flux is employed as a weighting function in their evaluation.Adjoint flux calculation is an easy task for most of deterministic codes, but its evaluation is cumbersome for Monte Carlo codes. However, in recent years, some sophisticated techniques have been proposed for Monte Carlo-based point kinetic parameters calculation without any need of adjoint flux. The most straightforward scheme is known as the ‘‘prompt method'' and has been used widely in literature. The main objective of this article is dedicated to point kinetic parameters calculation in Tehran research reactor(TRR) using deterministic as well as probabilistic techniques. WIMS-D5B and CITATION codes have been used in deterministic calculation of forward and adjoint fluxes in the TRR core. On the other hand, the MCNP Monte Carlo code has been employed in the ‘‘prompt method''scheme for effective delayed neutron fraction evaluation.Deterministic results have been cross-checked with probabilistic ones and validated with SAR and experimental data. In comparison with experimental results, the relativedifferences of deterministic as well as probabilistic methods are 7.6 and 3.2%, respectively. These quantities are10.7 and 6.4%, respectively, in comparison with SAR report.
文摘The present work aims to achieve a fast and accurate analytical solution of the point kinetics equations applied to subcritical reactors such as ADS (Accelerator-Driven System), assuming a linear reactivity and external source variation. It was used a new set of point kinetics equations for subcritical systems based on the model proposed by Gandini & Salvatores. In this work it was employed the integrating factor method. The analytical solution for the case of interest was obtained by using only an approximation which consists of disregarding the term of the second derivative for neutron density in relation to time when compared with the other terms of the equation. And also, it is proposed an approximation for the upper incomplete gamma function found in the solution in order to make the computational processing faster. In addition, for purposes of validation and comparison a numerical solution was obtained by the finite differences method. Finally, it can be concluded that the obtained solution is accurate and has fast numerical processing time, especially when compared with the results of numerical solution by finite difference. One can also observe that the gamma approximation used achieve a high accuracy for the usual parameters. Thus we got satisfactory results when the solution is applied to practical situations, such as a reactor startup.
基金supported by the Chinese TMSR Strategic Pioneer Science and Technology Project(No.XDA02010000)the Frontier Science Key Program of the Chinese Academy of Sciences(No.QYZDY-SSW-JSC016)the National Natural Science Foundation of China Key Program(No.91326201)
文摘A molten salt reactor(MSR) is one of the six advanced reactor concepts selected by the generation Ⅳ international forum because of its advantages of inherent safety, and the promising capabilities of Th-U breeding and transuranics transmutation. A dynamics model for the channel-type MSR is developed in this work based on a three-dimensional thermal–hydraulic model(3DTH) and a point reactor model. The 3DTH couples a three-dimensional heat conduction model and a one-dimensional single-phase flow model that can accurately consider the heat conduction between different assemblies. The 3DTH is validated by the RELAP5 code in terms of the temperature and mass flow distribution calculation. A point reactor model considering the drift of delayed neutron precursors is adopted in the dynamics model. To verify the dynamics model, three experiments from the molten salt reactor experiment are simulated. The agreement of the experimental data and simulation results was excellent.With the aid of this model, the unprotected step reactivity addition and unprotected loss of flow of the 2 MWt experimental MSR are modeled, and the reactor power and temperature evolution are analyzed.
基金Supported by Natural Science Foundation of Hubei Province (Grant No: 2007ABA360)
文摘The point-reactor model with power reactivity feedback becomes a nonlinear system. Its dynamic characteristic shows great complexity. According to the mathematic definition of stability in differential equa- tion qualitative theory, the model of a reactor with power reactivity feedback is judged unstable. The equilibrium point is a saddle-node point. A portion of the trajectory in the neighborhood of the equilibrium point is parabolic fan curve, and the other is hyperbolic fan curve. Based on phase locus near the equilibrium point, it is pointed out that the model is still stable within physical limits. The difference between stabilities in the mathematical sense and in the physical sense is indicated.
文摘The system of point kinetics equations describes the time behaviour of a nuclear reactor, assuming that, during the transient, the spatial form of the flux of neutrons varies very little. This system has been largely used in the analysis of transients, where the numerical solutions of the equations are limited by the stiffness problem that results from the different time scales of the instantaneous and delayed neutrons. Its derivation can be done directly from the neutron transport equation, from the neutron diffusion equation or through a heuristics procedure. All of them lead to the same functional form of the system of differential equations for point kinetics, but with different coefficients. However, the solution of the neutron transport equation is of little practical use as it requires the change of the existent core design systems, as used to calculate the design of the cores of nuclear reactors for different operating cycles. Several approximations can be made for the said derivation. One of them consists of disregarding the time derivative for neutron density in comparison with the remaining terms of the equation resulting from the P1 approximation of the transport equation. In this paper, we consider that the time derivative for neutron current density is not negligible in the P1 equation. Thus being, we obtained a new system of equations of point kinetics that we named as modified. The innovation of the method presented in the manuscript consists in adopting arising from the P1 equations, without neglecting the derivative of the current neutrons, to derive the modified point kinetics equations instead of adopting the Fick’s law which results in the classic point kinetics equations. The results of the comparison between the point kinetics equations, modified and classical, indicate that the time derivative for the neutron current density should not be disregarded in several of transient analysis situations.
文摘A design for instantaneous neutron flux signal acquisition system is being carried out for reactivity measurement of the nuclear research reactor. It is a computer-based digital data acquisition system that can perform continuous monitor and measurement of reactivity inserted into or removed from the research reactor. The acquisition system accomplishes with two major parts. The first part is an interfacing PCI based data acquisition card and the corresponding driver software intending to on-line acquisition of neutron flux signals from plant instrumentation channel. The second part incorporates the high-level Visual Basic real time program, indigenously developed for computation of reactivity by the solution of neutron point kinetic equations and other relevant functional modules like input file logging, reactivity calculation, graphics demonstration etc.
文摘This paper presents findings on the sliding mode controller for a nuclear reactor. One of the important operations in nuclear power plants is load following. In this paper, a sliding mode control system, which is a robust nonlinear controller, is designed to control the pressurizedwater reactor power. The reactor core is simulated based on the point kinetics equations and six delayed neutron groups. Considering neutron absorber poisons and regarding the limitations of the xenon concentration measurement, a sliding mode observer is designed to estimate its value, and finally, a sliding mode control based on the sliding mode observer is presented to control the core power of reactor. The stability analysis is given by means Lyapunov approach; thus, the control system is guaranteed to be stable within a large range. The employed method is easy to implement in practical applications, and moreover,the sliding mode control exhibits the desired dynamic properties during the entire output-tracking process independent of perturbations. Simulation results are presented to demonstrate the effectiveness of the proposed observerbased controller in terms of performance, robustness and stability.
文摘A phase one design of a new free energy nano reactor is presented. The design is based on a basically topological interpretation of the Casimir effect as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. In particular we view dark energy, Hawking negative energy, Unruh temperature and zero point vacuum energy as being different sides of the same multi-dimensional coin. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so-called missing dark energy density of the cosmos. We start with a general outline of the theoretical principle and basic design concepts of a proposed Casimir dark energy nano reactor. In a nutshell the theory and consequently the actual design depend crucially upon the equivalence between the dark energy density of the cosmos and the faint local Casimir effect produced by two sides boundary condition quantum waves. This Casimir effect is then colossally amplified as a one internal quantum wave representing a Hartle-Hawking state vector of the universe pushing from the inside against the boundary of the universe with nothing balancing it from the non-existent outside. This strange situation becomes completely natural and logical when we remember that the boundary of the universe is a one sided Möbius like manifold. In view of the present theory, this is essentially what leads to the observed accelerated expansion of the cosmos. As in any reactor, the basic principle in the present design is to produce a gradient so that the excess energy on one side flows to the other side. Thus in principle we will restructure the local topology of space using material nanoscience technology to create an artificial local high dimensionality with a Dvoretzky theorem like 96 percent volume measure concentration. Without going into the intricate nonlinear dynamics and technological detail, it is fair to say that this would lead us to pure, clean, free energy obtained directly from the topology of spacetime via an artificial singularity. Needless to say, the entire design is based completely on the theory of quantum wave dark energy proposed by the present author for the first time in 2011 in a conference held in the Bibliotheca Alexandrina, Egypt and a little later in Shanghai, Republic of China. The quintessence of the present theory is easily explained as the Φ3 intrinsic Casimir topological energy where Φ=?(√5-1)/2 is produced from the zero set Φ of the quantum particle when we extract the empty set quantum wave Φ2 from it and find Φ-Φ2=Φ3 by restructuring space via conducting but uncharged plates similar to that of the classical Casimir experiments. Our proposed preliminary design of this Casimir-spacetime artificial singularity reactor follows in a natural way from the above.
