Direct Discrete Method for Neutronic Calculations

2002 ◽  
Author(s):  
Naser Vosoughi ◽  
Majid Shahriari ◽  
Ali Akbar Salehi
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Balance Equation ◽  
Physical Meaning ◽  
Neutron Transport ◽  
Direct Method ◽  
Cylindrical Shape ◽  
Neutron Transport Equation ◽  
Discrete Method ◽  
Discrete Equations

The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for a cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution.

scholarly journals Direct discrete method and its application to neutron transport problems

2003 ◽  
Vol 18 (2) ◽  
pp. 12-23 ◽  
Author(s):  
Naser Vosoughi ◽  
Akbar Salehi ◽  
Majid Shahriari ◽  
Enzo Tonti
Keyword(s):  
Neutron Transport ◽  
Direct Method ◽  
External Boundary ◽  
Discrete Equation ◽  
Cylindrical Shape ◽  
Neutron Transport Equation ◽  
Discrete Method ◽  
Pass Through ◽  
Set Up ◽  
Transport Problems

The objective of this paper is to introduce a new direct method for neutronic calculations. This method, called direct discrete method, is simpler than the application of the neutron transport equation and more compatible with the physical meanings of the problem. The method, based on the physics of the problem, initially runs through meshing of the desired geometry. Next, the balance equation for each mesh interval is written. Considering the connection between the mesh intervals, the final discrete equation series are directly obtained without the need to pass through the set up of the neutron transport differential equation first. In this paper, one and multigroup neutron transport discrete equation has been produced for a cylindrical shape fuel element with and without the associated clad and the coolant regions each with two different external boundary conditions. The validity of the results from this new method is tested against the results obtained by the MCNP-4B and the ANISN codes.

Behavior of a Sequence of Geometric Transformations for a Truncated Ellipsoid Geometry in Transport Theory

2009 ◽  
Author(s):  
Rube´n Panta Pazos
Keyword(s):  
Boundary Conditions ◽  
Symmetry Axis ◽  
Transport Theory ◽  
Neutron Transport ◽  
Complex Function ◽  
Computational Techniques ◽  
Neutron Transport Equation ◽  
Geometric Transformations ◽  
The Right ◽  
Transport Problems

The neutron transport equation has been studied from different approaches, in order to solve different situations. The number of methods and computational techniques has increased recently. In this work we present the behavior of a sequence of geometric transformations evolving different transport problems in order to obtain solve a transport problem in a truncated ellipsoid geometry and subject to known boundary conditions. This scheme was depicted in 8, but now is solved for the different steps. First, it is considered a rectangle domain that consists of three regions, source, void and shield regions 5. Horseshoe domain: for that it is used the complex function: f:D→C,definedasf(z)=12ez+1ezwhereD=z∈C−0.5≤Re(z)≤0.5,−12π≤Im(z)≤12π(0.1) The geometry obtained is such that the source is at the focus of an ellipse, and the target coincides with the other focus. The boundary conditions are reflective in the left boundary and vacuum in the right boundary. Indeed, if the eccentricity is a number between 0,95 and 0,99, the distance between the source and the target ranges from 20 to 100 length units. The rotation around the symmetry axis of the horseshoe domain generates a truncated ellipsoid, such that a focus coincides with the source. In this work it is analyzed the flux in each step, giving numerical results obtained in a computer algebraic system. Applications: in nuclear medicine and others.

scholarly journals Regularity of Milne problem with geometric correction in 3D

2017 ◽  
Vol 27 (03) ◽  
pp. 453-524 ◽  
Author(s):  
Yan Guo ◽  
Lei Wu
Keyword(s):  
Boundary Conditions ◽  
Transport Equation ◽  
Convex Domain ◽  
Neutron Transport ◽  
Geometric Correction ◽  
Neutron Transport Equation ◽  
Milne Problem ◽  
Diffusive Boundary

Consider the Milne problem with geometric correction in a 3D convex domain. Via bootstrapping arguments, we establish [Formula: see text]-regularity for its solutions. Combined with a uniform [Formula: see text]-estimate, such regularity leads to the validity of diffusive expansion for the neutron transport equation with diffusive boundary conditions.

scholarly journals The Pij matrix and flux calculation of one-dimensional neutron transport in the slab geometry of nuclear fuel cell using collision probability method

2018 ◽  
Vol 197 ◽  
pp. 02006 ◽  
Author(s):  
Mohammad Ali Shafii ◽  
Jakaria Usman ◽  
Seni H. J. Tongkukut ◽  
Ade Gafar Abdullah
Keyword(s):  
Fuel Cell ◽  
Boundary Conditions ◽  
Neutron Flux ◽  
Nuclear Fuel ◽  
Neutron Transport ◽  
Collision Probability ◽  
Probability Method ◽  
Neutron Transport Equation ◽  
Slab Geometry ◽  
One Dimensional

Calculation of Pij matrix of one-dimensional neutron transport in the slab geometry of the nuclear fuel cell using Collision Probability (CP) method has been done. Pij matrix is one of important parameters within the distribution of neutron flux in the nuclear fuel cell. The CP method is the most efficient methods to solve the neutron transport equation in the reactor core. The study is focused on neutron interaction with nuclear fuel cell of U-235 and U-238 for homogeneous condition. The parameters to calculate the Pij matrix are the cross section of nuclear fuel, width of the region and number of regions. A lattice of slabs have been constructed using void boundary conditions for model of finite system to calculate the collision probabilities. If the Pij matrix has been calculated then neutron flux can be determined. The results show that total value of Pij matrix using CP method for U-235 and U-238 is less than one, respectively. This is in accordance with the definition of void boundary conditions for finite slab geometry. Along with Pij matrix, neutron flux is also appropriate with the reference.

The Powerful MOC Module in Advanced Neutronics Lattice Code GALAXY

2016 ◽  
Author(s):  
Xiaoming Chai ◽  
Xiaolan Tu ◽  
Wei Lu
Keyword(s):  
Boundary Conditions ◽  
Nuclear Power ◽  
Method Of Characteristics ◽  
Neutron Transport ◽  
Computation Time ◽  
Neutron Transport Equation ◽  
Lattice Codes ◽  
Geometrical Shapes ◽  
The Galaxy ◽  
Complicated Geometry

Due to powerful geometry treatment capability, Method Of Characteristics (MOC) becomes the most popular method to solve neutron transport equation. However, boundary conditions always restrict the MOC method’s widely application. Most of the current neutronics lattice codes based on MOC can only be used to solve one or two specific geometrical shapes. In this paper, we developed a powerful MOC module, which can treat different geometrical shapes with two methods. For special geometrical shapes, such as rectangle, 1/8 of square, hexagon, 1/3 of hexagon, 1/6 of hexagon, the MOC module adopts special trajectory layout and angle quadrature set, which can reduce the computation time. For other general geometrical shapes, the MOC module use ray prolongation method, which can treat arbitrary geometry shapes and boundary conditions but need much computation time. This MOC module was incorporated into advanced neutronics lattice code GALAXY, which developed by Nuclear Power Institute of China. The numerical results show that the GALAXY code can be used to calculate 2D neutronics problems with rectangle, hexagon, and other complicated geometry shapes accurately. In future, the GALAXY code will gradually become the main neutroncis lattice code in NPIC.

On the stochastic nonlinear neutron transport equation

1992 ◽  
Vol 121 (3-4) ◽  
pp. 253-272 ◽  
Author(s):  
Mustapha Mokhtar-Kharroubi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Transport Equation ◽  
Nuclear Reactor ◽  
Neutron Transport ◽  
Neutron Transport Equation ◽  
Chain Reaction ◽  
Partial Differential ◽  
Model Case

SynopsisThe probability that a neutron leads to a divergent chain reaction in a nuclear reactor is governed by a nonlinear integro-partial-differential equation [1]. A model case of this equation was completely analysed by Pazy and Rabinowitz [2,3]. The purpose of this paper is to extend their results to the general case and to tackle some related topics.

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