Difference between revisions of "Unstable 3D pin-cell burnup problem"

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In certain burnup problems such as long, axially symmetric 3D assemblies or fuel rods or large symmetric core geometries traditional Monte Carlo burnup schemes may run into instabilities<ref name="DufekNSE09"/><ref name="DufekANE13a"/>.
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In certain burnup problems such as long, axially symmetric 3D assemblies or fuel rods or large symmetric core geometries traditional Monte Carlo burnup schemes may run into instabilities<ref name="DufekNSE09"/><ref name="DufekANE13a"/>. This page describes the simulation of one such case first using the traditional burnup schemes (to showcase the instability) and then using a stable burnup scheme.
  
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== Problem description ==
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<div class="toccolours mw-collapsible mw-collapsed" style="width:40em;">
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'''Base input for unstable 3D pin-cell problem'''
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<div class="mw-collapsible-content">
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<nowiki>/*****************
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** Run options **
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*****************/
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% --- 50k neutrons per cycle, 100 inactive cycles
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 +
set pop 20000 1000 200
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% --- 200 W/cm linear power
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 +
set power 60000
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/*************************
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** Geometry definition **
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*************************/
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% --- Fuel Pin definitions:
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pin p1
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fuel  0.47
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void  0.48
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clad  0.54
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cool
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% --- Lattice
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lat l1  1  0.0 0.0 1 1 1.5
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p1
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% --- Surrounding surfaces:
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% Boundary of geometry:
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surf 3 cuboid -0.75 0.75 -0.75 0.75 -160 160
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% Lower boundary of fuel
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surf 4 pz -150
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% Upper boundary of fuel
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surf 5 pz  150
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% --- Cell definitions:
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% Active fuel pin
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cell  3  0  fill l1  -3  4 -5
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% Coolant below active fuel (bottom reflector)
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cell  4  0  cool    -3 -4
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% Coolant above active fuel (top reflector)
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cell  5  0  cool    -3  5
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% outside world
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cell 99  0  outside  3    % Outside world
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% --- Reflective boundary conditions in XY, black in Z:
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set bc 3 3 1
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/**************************
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** Material definitions **
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**************************/
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% --- Fuel material (4.85 % enrichment):
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mat fuel    -10.283 vol 208.19 rgb 200 200 125
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92235.09c      0.016166667
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92238.09c      0.317166667
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8016.09c      0.666666667
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% --- Cladding (Zr-4)
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mat clad -6.56000E+00 rgb 180 180 180
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8016.06c    -1.19276E-03
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8017.06c    -4.82878E-07
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24050.06c    -4.16117E-05
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24052.06c    -8.34483E-04
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24053.06c    -9.64457E-05
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24054.06c    -2.44600E-05
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26054.06c    -1.12572E-04
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26056.06c    -1.83252E-03
 +
26057.06c    -4.30778E-05
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26058.06c    -5.83334E-06
 +
40090.06c    -4.97862E-01
 +
40091.06c    -1.09780E-01
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40092.06c    -1.69646E-01
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40094.06c    -1.75665E-01
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40096.06c    -2.89038E-02
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50112.06c    -1.27604E-04
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50114.06c    -8.83732E-05
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50115.06c    -4.59255E-05
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50116.06c    -1.98105E-03
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50117.06c    -1.05543E-03
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50118.06c    -3.35688E-03
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50119.06c    -1.20069E-03
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50120.06c    -4.59220E-03
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50122.06c    -6.63497E-04
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50124.06c    -8.43355E-04
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% --- Coolant:
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mat cool    -0.75 moder lwtr 1001 rgb 50 50 255
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1001.06c    0.666666667
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8016.06c    0.333333333
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% --- Thermal scattering data for light water:
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therm lwtr lwj3.11t</nowiki>
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</div>
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</div>
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The base input for the problem is given above. The input describes a 300 cm long fuel rod in infinite lattice geometry. Axially the fuel rod is reflected from top and bottom with 10 cm water layers after which a black boundary condition is applied. The radial geometry is shown here:
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[[File:Unstable3Dpin_geom1.png|frameless|200px|xy-plot of the pin-cell geometry.]]
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== Unstable solution using explicit Euler's method ==
  
 
== References ==
 
== References ==

Revision as of 11:56, 29 September 2017

In certain burnup problems such as long, axially symmetric 3D assemblies or fuel rods or large symmetric core geometries traditional Monte Carlo burnup schemes may run into instabilities[1][2]. This page describes the simulation of one such case first using the traditional burnup schemes (to showcase the instability) and then using a stable burnup scheme.

Problem description

Base input for unstable 3D pin-cell problem 

/*****************
 ** Run options **
 *****************/

% --- 50k neutrons per cycle, 100 inactive cycles

set pop 20000 1000 200 

% --- 200 W/cm linear power

set power 60000

/*************************
 ** Geometry definition **
 *************************/

% --- Fuel Pin definitions:

pin p1
fuel  0.47
void  0.48
clad  0.54
cool

% --- Lattice 

lat l1  1  0.0 0.0 1 1 1.5
p1

% --- Surrounding surfaces:

% Boundary of geometry:

surf 3 cuboid -0.75 0.75 -0.75 0.75 -160 160

% Lower boundary of fuel

surf 4 pz -150

% Upper boundary of fuel

surf 5 pz  150

% --- Cell definitions:

% Active fuel pin 

cell  3  0  fill l1  -3  4 -5

% Coolant below active fuel (bottom reflector)

cell  4  0  cool     -3 -4

% Coolant above active fuel (top reflector)

cell  5  0  cool     -3  5

% outside world 

cell 99  0  outside   3     % Outside world

% --- Reflective boundary conditions in XY, black in Z:

set bc 3 3 1

/**************************
 ** Material definitions **
 **************************/

% --- Fuel material (4.85 % enrichment):

mat fuel    -10.283 vol 208.19 rgb 200 200 125
92235.09c      0.016166667
92238.09c      0.317166667
8016.09c       0.666666667

% --- Cladding (Zr-4)

mat clad -6.56000E+00 rgb 180 180 180
 8016.06c     -1.19276E-03
 8017.06c     -4.82878E-07
24050.06c     -4.16117E-05
24052.06c     -8.34483E-04
24053.06c     -9.64457E-05
24054.06c     -2.44600E-05
26054.06c     -1.12572E-04
26056.06c     -1.83252E-03
26057.06c     -4.30778E-05
26058.06c     -5.83334E-06
40090.06c     -4.97862E-01
40091.06c     -1.09780E-01
40092.06c     -1.69646E-01
40094.06c     -1.75665E-01
40096.06c     -2.89038E-02
50112.06c     -1.27604E-04
50114.06c     -8.83732E-05
50115.06c     -4.59255E-05
50116.06c     -1.98105E-03
50117.06c     -1.05543E-03
50118.06c     -3.35688E-03
50119.06c     -1.20069E-03
50120.06c     -4.59220E-03
50122.06c     -6.63497E-04
50124.06c     -8.43355E-04

% --- Coolant:

mat cool     -0.75 moder lwtr 1001 rgb 50 50 255
 1001.06c    0.666666667
 8016.06c    0.333333333

% --- Thermal scattering data for light water:

therm lwtr lwj3.11t

The base input for the problem is given above. The input describes a 300 cm long fuel rod in infinite lattice geometry. Axially the fuel rod is reflected from top and bottom with 10 cm water layers after which a black boundary condition is applied. The radial geometry is shown here:

xy-plot of the pin-cell geometry.

Unstable solution using explicit Euler's method

References

  1. ^ Dufek, J. and Hoogenboom, E. "Numerical Stability of Existing Monte Carlo Burnup Codes in Cycle Calculations of Critical Reactors", Nucl. Sci. Eng., 162 (2009) 307-311
  2. ^ Dufek, J. et al. "Numerical stability of the predictor–corrector method in Monte Carlo burnup calculations of critical reactors", Ann. Nucl. Energy, 56 (2013) 34-38
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