Polynomial approach method to solve the neutron point kinetics equations with use of the analytic continuation
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Abstract
In 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.
Kurzfassung
In dieser Arbeit wird über die Lösung punktkinetischer Gleichungen durch Anwendung polynomgestützter Methoden berichtet. Der Hauptgedanke dabei ist die Entwicklung der Neutronendichte und der Vorläufer verzögerter Neutronen als Potenzreihe unter Betrachtung der Reaktivität als eine beliebige Funktion der Zeit in einem relativ kurzen Zeitintervall um einen gewöhnlichen Punkt. Im ersten Intervall werden die Anfangsbedingungen und die analytische Fortsetzung zur Bestimmung der Lösungen des nächsten Intervalls verwendet. Auf der Basis des Rest-Theorems wurde eine Methode zur Fehlervermeidung entwickelt. Zur Veranschaulichung werden Simulationen verschiedener Ansätze (linear, quadratisch und kubisch) beschrieben. Die durch numerische Simulationen erhaltenen Ergebnisse werden mit Ergebnissen aus der Literatur verglichen.
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© 2016, Carl Hanser Verlag, München
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Articles in the same Issue
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Use of molybdenum as a structural material of fuel elements for improving nuclear reactors safety
- Effect of ultra high temperature ceramics as fuel cladding materials on the nuclear reactor performance by SERPENT Monte Carlo code
- Spatial distribution of nanoparticles in PWR nanofluid coolant subjected to local nucleate boiling
- Impact of mesh points number on the accuracy of deterministic calculations of control rods worth for Tehran research reactor
- Dependence of neutron rate production with accelerator beam profile and energy range in an ADS-TRIGA RC1 reactor
- Effects of the wallpaper fuel design on the neutronic behavior of the HTR-10
- Loss of flow Accident (LOFA) analyses using LabView-based NRR simulator
- Basket criticality design of a dual purpose cask for VVER 1000 spent fuel assemblies
- Simulation of polycarbonate-CNT nanocomposite dosimeter based on electrical characteristics
- Thermoluminescence properties of micro and nano structure hydroxyapatite after gamma irradiation
- Equilibrium based analytical model for estimation of pressure magnification during deflagration of hydrogen air mixtures
- Polynomial approach method to solve the neutron point kinetics equations with use of the analytic continuation
- The slab albedo problem for the triplet scattering kernel with modified FN method
- Calculation of the fuel composition and the deterministic reloading pattern in the second cycle of the BUSHEHR VVER-1000 reactor using the weighting factor method