On the Dynamical Behavior of the Two-Temperature Feedback Nuclear Reactor Model

1976 ◽  
Vol 30 (4) ◽  
pp. 675-686 ◽  
Author(s):  
A. B. Poore
Keyword(s):  
Nuclear Reactor ◽  
Dynamical Behavior ◽  
Reactor Model ◽  
Temperature Feedback ◽  
Two Temperature

scholarly journals A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Yasser Mohamed Hamada
Keyword(s):  
Nuclear Reactor ◽  
Approximate Solutions ◽  
Time Interval ◽  
Neutron Density ◽  
Chebyshev Series ◽  
System A ◽  
Temperature Feedback ◽  
Exponential Rate Of Convergence ◽  
Point Kinetics ◽  
The Given

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.

SPECTRAL PROPERTIES OF AN ELASTIC ROD-SPRING COUPLED SYSTEM IMMERSED IN A FLUID

1992 ◽  
Vol 02 (04) ◽  
pp. 441-460 ◽  
Author(s):  
J. SANCHEZ-HUBERT ◽  
S. BÉRÉTÉ ◽  
J. PLANCHARD
Keyword(s):  
Heat Exchangers ◽  
Spectral Properties ◽  
Nuclear Reactor ◽  
Dynamical Behavior ◽  
Coupled System ◽  
Elastic Tube ◽  
Elastic Rod ◽  
Resonance Frequencies ◽  
Continuous Material ◽  
Very High

The study of vibrations of elastic tube bundles immersed in a fluid is very important in Engineering, for example concerning the dynamical behavior of heat exchangers, nuclear reactor cores, etc. This paper is concerned with the investigation of the resonance frequencies when the number of rods is very high. That requires us to use the homogenization technique for modelling this coupled system by an equivalent continuous material. We then show that this equivalent system may have an essential spectrum.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Wenzhen Chen ◽  
Jianli Hao ◽  
Ling Chen ◽  
Haofeng Li
Keyword(s):  
Nuclear Reactor ◽  
Large Range ◽  
Accurate Solution ◽  
Average Density ◽  
Singularly Perturbed ◽  
Neutron Density ◽  
Delayed Neutron ◽  
Small Step ◽  
Neutron Kinetics ◽  
Temperature Feedback

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.

The dynamics of a nuclear reactor model

1997 ◽  
Vol 30 (6) ◽  
pp. 3409-3416 ◽  
Author(s):  
Hongwei Chen
Keyword(s):  
Nuclear Reactor ◽  
Reactor Model
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