New basis functions for reactor core calculations using the nodal expansion method

2022 ◽  
Vol 166 ◽  
pp. 108714
Author(s):  
Sérgio B. Paixão ◽  
Fernando C. Silva
Keyword(s):  
Reactor Core ◽  
Expansion Method ◽  
Basis Functions ◽  
Nodal Expansion Method

Nodal Expansion and its Application in AP1000 Nuclear Reactor Core Monitoring System

2013 ◽  
Vol 448-453 ◽  
pp. 1907-1911
Author(s):  
Wei Zhi Jia ◽  
Rui Wang ◽  
Yun Zhou
Keyword(s):  
Monitoring System ◽  
Nuclear Reactor ◽  
Reactor Core ◽  
Expansion Method ◽  
The Core ◽  
Nodal Model ◽  
Nuclear Reactor Core ◽  
Nodal Expansion Method ◽  
Full Core

As the core monitoring system of AP1000, BEACON always uses a full-core nodal model for core monitoring based on the ANC-NEM nodal model. The theory behind the nodal expansion method is discussed, and the application of the method in BEACON is described. Finally, an ANC-NEM calculation simulation is proposed.

scholarly journals Three-dimensional time-dependent neutron diffusion simulation using average current nodal expansion method

2020 ◽  
Vol 35 (3) ◽  
pp. 189-200
Author(s):  
Kambiz Valavi ◽  
Ali Pazirandeh ◽  
Gholamreza Jahanfarnia
Keyword(s):  
Three Dimensional ◽  
Reactor Core ◽  
Expansion Method ◽  
Steady State Solution ◽  
Time Dependent ◽  
Test Case ◽  
Neutron Diffusion ◽  
Average Current ◽  
Coarse Meshes ◽  
Nodal Expansion Method

In this work, the average current nodal expansion method was developed for the time-dependent neutronic simulation of transients in a nuclear reactor's core. For this purpose, an adopted iterative algorithm was proposed for solving the 3-D time-dependent neutron diffusion equation. In the average current nodal expansion method, the domain of the reactor core can be modeled by coarse meshes for neutronic calculation associated with reasonable precision of results. The discretization of time differential terms in the time-dependent equations was fulfilled, according to the implicit scheme. The proposed strategy was implemented in some kinetic problems including an infinite slab reactor, TWIGL 2-D seed-blanket reactor, and 3-D LMW LWR. At first, the steady-state solution was carried out for each test case, and then, the dynamic neutronic calculation was performed during the time for a specified transient scenario. Obtained results of static and dynamic solutions were verified in comparison with well-known references. Results can indicate the ability of the developed calculator to simulate transients in a nuclear reactor's core.

Improved nodal expansion method for solving neutron diffusion equation in cylindrical geometry

2010 ◽  
Vol 240 (8) ◽  
pp. 1997-2004 ◽  
Author(s):  
Dengying Wang ◽  
Fu Li ◽  
Jiong Guo ◽  
Jinfeng Wei ◽  
Jingyu Zhang ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Expansion Method ◽  
Cylindrical Geometry ◽  
Neutron Diffusion ◽  
Nodal Expansion Method ◽  
Neutron Diffusion Equation

scholarly journals COMPARISON OF A GENERAL SERIES EXPANSION METHOD AND THE HOMOTOPY ANALYSIS METHOD

2010 ◽  
Vol 24 (15) ◽  
pp. 1699-1706 ◽  
Author(s):  
CHENG-SHI LIU ◽  
YANG LIU
Keyword(s):  
Series Expansion ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Expansion Method ◽  
Basis Functions ◽  
Analysis Method ◽  
Convergence Region ◽  
General Series ◽  
Homotopy Analysis ◽  
Series Expansion Method

A simple analytic tool, namely the general series expansion method, is proposed to find the solutions for nonlinear differential equations. A set of suitable basis functions [Formula: see text] is chosen such that the solution to the equation can be expressed by [Formula: see text]. In general, t0 can control and adjust the convergence region of the series solution such that our method has the same effect as the homotopy analysis method proposed by Liao, but our method is simpler and clearer. As a result, we show that the secret parameter h in the homotopy analysis methods can be explained by using our parameter t0. Therefore, our method reveals a key secret in the homotopy analysis method. For the purpose of comparison with the homotopy analysis method, a typical example is studied in detail.

Depletion Calculation for a Nodal Reactor Physics Code

2010 ◽  
Author(s):  
Antonio Carlos Marques Alvim ◽  
Fernando Carvalho da Silva ◽  
Aquilino Senra Martinez
Keyword(s):  
Diffusion Equation ◽  
Nuclear Reactor ◽  
Reactor Core ◽  
Expansion Method ◽  
Design System ◽  
Pressurized Water Reactor ◽  
Reactor Physics ◽  
Pressurized Water ◽  
Nodal Method ◽  
Orthogonal Polynomial Expansion

This paper deals with an alternative numerical method for calculating depletion and production chains of the main isotopes found in a pressurized water reactor. It is based on the use of the exponentiation procedure coupled to orthogonal polynomial expansion to compute the transition matrix associated with the solution of the differential equations describing isotope concentrations in the nuclear reactor. Actually, the method was implemented in an automated nuclear reactor core design system that uses a quick and accurate 3D nodal method, the Nodal Expansion Method (NEM), aiming at solving the diffusion equation describing the spatial neutron distribution in the reactor. This computational system, besides solving the diffusion equation, also solves the depletion equations governing the gradual changes in material compositions of the core due to fuel depletion. The depletion calculation is the most time-consuming aspect of the nuclear reactor design code, and has to be done in a very precise way in order to obtain a correct evaluation of the economic performance of the nuclear reactor. In this sense, the proposed method was applied to estimate the critical boron concentration at the end of the cycle. Results were compared to measured values and confirm the effectiveness of the method for practical purposes.

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