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Nuclear Reactor Theory - Nuclear Reactor Analysis -
FRM-II
The Neutron Flux ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Neutron Flux ,[object Object],[object Object],[object Object],[object Object],[object Object]
The Neutron Flux ,[object Object],Ref.: http://www.tpub.com/content/doe/h1019v1/css/h1019v1_138.htm
FRM-II
The Diffusion Approximation: Fick´s Law ,[object Object],[object Object],[object Object],[object Object],[object Object],Neutron Current Density Vector x  (x) J x Gradient of Flux
The Equation of Continuity ,[object Object],[object Object],[object Object],V r
The Equation of Continuity ,[object Object],[object Object],[object Object],Surface J x J z J y
The Diffusion Equation ,[object Object],[object Object],Fick´s Law Diffusion Length The integrands must satisfy The integration is over the same volume V
The Diffusion Equation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],A B n d  x)  d)=0
The Diffusion Equation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Low  A High A Reflectors have LOW  A
One-group Reactor Equation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
One-group Reactor Equation ,[object Object],[object Object],[object Object],[object Object],[object Object]
One-group Reactor Equation ,[object Object],[object Object],[object Object],[object Object],Material Buckling Geometric Buckling
Criticality of a Bare Reactor ,[object Object],[object Object],[object Object],[object Object],[object Object],k eff   accounts also for the leakage Material Properties
One-group Critical Reactor Equation ,[object Object],Power Energy per fission The Solution for the Flux is: Buckling Spherical Critical Reactor The flux is a function only of the radius  r Homogeneous Reactor The power is given by the integral There are many possible values of  B that will satisfy the boundary conditions , but the geometrical buckling  is the  FIRST  eigenvalue  B 1 r R
One-group Critical Reactor Equation ,[object Object],Finite Cylindrical Critical Reactor The flux is a function of the radius  r  and  z Two Functions: The solution: Homogeneous Reactor z r H/2 H/2 R
One-group Critical Reactor Equation ,[object Object],[object Object],[object Object],[object Object],[object Object],Too large for a real reactor. Real reactors have  FLATTER  Flux distributions by using reflectors and distributing the fuel.
Multi-group Reactor Equation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],g 1 g 2 g N …… .. Discretization of the Neutron Energy for Multi-group Calculations
Multi-group Reactor Equation ,[object Object],[object Object],[object Object],[object Object],[object Object],Group 1 ( g 1 ) Group 2 ( g 1 ) Group n-1 ( g n-1 ) Group N ( g N ) … . Energy Increasing Energy Groups for a N-Group Diffusion Calculation Transfer out of  g Transfer into  g
Multigroup Diffusion Core Analysis Codes ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
State-of-the-Art Nodal Methods Ref.: www.fz-juelich.de/ ief/ief-6/2/htr2-flu.html Node  i,j,k Ref.: http://www.polymtl.ca/nucleaire/en/GAN/GAN.php The Multi-group equations are solved for each node i,j,k in which the reactor is divided. The nodes “homogenize” the heterogeneous reactor.
Neutron Transport ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Neutron Transport ,[object Object],Fission Source Scattering External Neutron Source Time variation and removal of neutrons Angular Flux and Neutron Density z x y dV dA

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Arn 02-0-reactor theory

  • 1. Nuclear Reactor Theory - Nuclear Reactor Analysis -
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  • 23. State-of-the-Art Nodal Methods Ref.: www.fz-juelich.de/ ief/ief-6/2/htr2-flu.html Node i,j,k Ref.: http://www.polymtl.ca/nucleaire/en/GAN/GAN.php The Multi-group equations are solved for each node i,j,k in which the reactor is divided. The nodes “homogenize” the heterogeneous reactor.
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