random finite element modeling of thermomechanical behavior of agr bricks jose david arregui mena,...
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Random Finite Element Modeling of thermomechanical behavior of AGR bricks
Jose David Arregui Mena, Louise Lever, Graham Hall, Lee Margetts, Paul Mummery
Introduction• AGR Reactors
• Random Finite Element Method -Young’s Modulus Random Field
• Compression Tests
• Preliminary Results Random Thermoelastic Analysis
AGR Graphite Moderated Reactors
Fast Neutron Damage• Neutron
bombardment of graphite
Radiolytic Oxidation• Chemical reaction
between irradiated CO2 and graphite
ionization radiation *2CO CO O
*2CO O CO
Damage in nuclear reactors
*O C CO
Safety Requirements
Requirements during normal and fault conditions:• Unimpeded loading and
unloading of control rods and fuel rods
• An adequate flow of coolant gas• Provide neutron moderation
and thermal inertia
Hypothesis
• Initial, pre-operation spatial variation in the values of the material properties of nuclear graphite have an effect on stress and strain distribution in graphite bricks, which in turn determines the safe operation of a nuclear graphite core
Random Finite Element Methodand Nuclear Graphite
The Finite Element Method
• Numerical technique to solve differential equations• Transforms differential equations to a set of
algebraic equations
{ } { }F K U
External forces
Materialproperties
and geometry
Displacements
s
Probability of failure
Young’s ModulusRandom Field
Top-Down Approach, Local Average Method ProcessAdapted from (Vanmarcke, 1983)
2D Local Average Method Process
Scale of fluctuation
10 mm
10 mm
1 mm
1 mm
The average of a portionof the random field of1x1 mm will return the mean value of the Young’s Modulus μ
1 mm
1 mmμ
Scale of fluctuationof 1 mm
Random Fields for Young’s Modulus
+Young’s Modulus
-Young’s Modulus
Mean Value
Correlation length 0.1 Correlation length 1.0 Correlation length 100.0
Calibration of the random fieldGrey Scale
Density and Young’s
Modulus
CT X-Ray Tomography
Porosity
3D Random Fields from2D Images
Young’s Modulus
Porosity
Compression Tests
Boundary Conditions for Axial Compression tests
Fixed in x,y,z Fixed in zUniform axial
Displacement of 4.2 mm
DeterministicRealization
Random Simulation with a scale of fluctuation (100, 100, 100)
Maximum Value – 82.495
Maximum Value – 64.324
Random Simulation with a scale of fluctuation (500, 500, 500)
Maximum Value – 70.894
Random Simulation with a scale of fluctuation (1000, 1000, 1000)
Preliminary Results Random
Thermoelastic Analysis
Preliminary Thermoelastic Analysis
• Octant of an AGR brick• Free to expand
0fT T Thermal strains
α – Coefficient of Thermal expansionTf – Final temperatureT0 – Reference temperature
Temperature profile for the simulations - ΔT
Random Material Properties for Young’s ModulusRandom PropertiesDeterministic Properties
DisplacementsRandom simulationDeterministic simulation
Random simulationDeterministic simulationStress analysis
Road Map
Compression test
Calibration of theRandom fields and
Creation of a randomField for CTE
ThermomechanicalAnalysis
Creep
Acknowledgements
Thank you!