effect of agr fuel-brick end-face features on stress

Content contained within this presentation must not be copied or distributed without

consent from The University of Manchester.

Nuclear Graphite Research Group

University of Manchester, UK

Effect of AGR Fuel-Brick End-Face Features on Stress Predictions

Muhammad Fahada , Emma Tanb , Nick Warrenb , Abbie Jonesa , Graham Halla

b HSE Science and Research Centre, UK

a

INGSM-2019 - September 16-19, 2019

Content contained within this presentation must not be copied or distributed without consent from The University of Manchester.

Brick Cracking Network (BCN)

• Independent advice and consultancy:• Support to the Office for Nuclear Regulation (ONR) in the area

of nuclear graphite core degradation.

• University of Manchester (UoM)• Finite element modelling

• HSE Science and Research Centre• Statistical analysis

• University of Birmingham• Material properties and testing

Note:This presentation and the work it describes were funded by the Office of Nuclear Regulation (ONR). Its contents, including any opinions and/or conclusions expressed, are those of the presenter alone and do not necessarily reflect ONR policy.


Introduction

• Advanced Gas Cooled Reactors• Majority of the AGRs operating in the world are in UK.

• Licence – EDF Energy UK

• In operation since 1976 (Hinkley Point ‘B’ and Hunterston‘B’)

• Electricity 20% from nuclear power plants


AGR core and fuel bricks

• An AGR core can be considered as a

cylinder of graphite components

• Components of AGRs core• Fuel channels

• Control rod channels

• Channels for coolant gas

• Moderator

• Bricks in layers: 12 (320 channels)

• Cylindrical – 8 sided


Fuel bricks

• Peripheral boundaries of a fuel brick aredesigned in such a way as to accommodatekeying system (for interlocking of fuel bricks).

• The end-faces features accommodate the non-uniform deformation during the life of a reactor.


Core layout

• Fuel bricks in AGRs are designed with differentend-face orientations to accommodate theoverall non-uniform deformation of the core.

• End-face features are important; however theymay act as stress concentrators.

• Recently the pattern of cracking has beenobserved to vary by end-face featuresorientation.


Three different end-face orientation of fuel bricks

0° 45° 22.5°


Our work

• Single brick FE modelling with different orientations.

• Design matrix using Latin Hypercube (design).• 36 parameters varied in ManUMAT

• ManUMAT: User defined material subroutine includes thetemporal constitutive relationship for irradiated Young’sModulus, dimensional change, creep and coefficient ofthermal expansion.

• These material properties are function of neutron dose,irradiation temperature and weight loss.

• Due to semi-anisotropic behaviour of Gilso-carbongraphite, material properties relationships were specifiedwith and against grain).

• Irradiation-induced creep is based on UKAEA creep law(Kelly and Brocklehurst, 1977).


Our work

• A sensitivity analysis is carried out to determine theparameters that are influential in determining stressand the effects of those parameters over time.

• The ultimate aim of this work is to use the results of theFE analysis in a probabilistic stress analysis via MonteCarlo simulation, to take account of the variability anduncertainty in the graphite material and field variables,and how these influence stresses.

• These stress predictions may then be comparedagainst the predicted strength of the graphite bricks topredict the timing of keyway root cracking.


Our work

• Carried out a variance-based sensitivity analysis to identify which inputparameters are most influential in determining the Maximum in-planeprincipal stresses (MIPS).

• Used GEM-SA software (Gaussian emulation machine for sensitivityanalysis). The software builds a Gaussian process emulator from a set ofinputs and a set of outputs, which is then used to carry out a sensitivityanalysis.

• A design matrix of input parameter values and the MIPS output associatedwith each design point, are fed into the software (150 design points).

• Software outputs the proportion of the total variation in MIPS that isexplained by each parameter (total 100%). The higher the proportion, themore influential the parameter is in determining MIPS.

.


Single brick FE modelling with different orientation Three different finite element models were developed (0º, 45º

and 22.5º) for HNB.

Some fine features were ignored.

Methane holes were not taken into consideration.

• Mesh density for all three models was kept as close aspossible.

• Same number of nodes were seeded along keyway roots.


Interstitial keyway

Loose keyway


FE mesh

0° 45° 22.5°


Stresses at baseline parameters


Sensitivity analysis

• Ran 150 simulations for each layer i.e. between 4 and 6, for two orientations (0° and 45°).

• Maximum MIPS along keyway roots; At interstitial and loose keyways.


Maximum in-plane principal stresses: Design matrix results


Zero degrees 45 degrees

Power SD Power SD

Dose 7.1 7.2 7.9 6.9

A4 WG 34.2 12.1 31.7 11.1

A4 AG 5.2 2.5 6.3 2.8

z 28.8 12.4 34.6 12.0

C2 0.5 46.8 0.3 47.8


Power SD Power SD

Dose 7.6 5.9 9.1 8.3

A4 WG 25.3 5.3 24.8 8.7

A4 AG 11.8 2.6 4.5 1.5

z 31.7 7.0 36.3 10.4

C2 0.4 60.6 0.3 48.4

Interstitial keyway at 24 fpy Loose keyway at 24 fpy



Power SD Power SD

Dose 6.6 4.9 6.8 3.0

A4 WG 29.3 15.8 29.4 9.7

A4 AG 7.3 1.8 7.8 1.0

z 15.5 6.6 15.8 2.8

C1 0.0 7.5 0.0 11.7

C2 0.1 41.1 0.1 48.2

SCC 9.2 3.2 8.6 2.0

SC k 8.9 3.2 8.6 1.8


Power SD Power SD

Dose 8.4 5.0 6.9 3.2

A4 WG 32.0 12.4 27.1 9.9

A4 AG 8.3 2.1 8.7 1.0

z 19.8 6.2 15.1 3.1

C1 0.0 7.0 0.0 12.6

C2 0.2 48.5 0.1 48.5

SCC 5.5 1.4 9.1 1.8

SC k 5.9 1.7 9.1 1.8

Sensitivity analysis: Layer 4



Power SD Power SD

Dose 7.2 6.7 7.6 7.1

A4 WG 34.4 11.7 30.9 10.9

A4 AG 3.9 2.1 5.1 2.2

z 28.5 11.3 35.7 12.3

C2 0.5 48.4 0.3 45.6


Power SD Power SD

Dose 7.2 6.5 7.9 7.1

A4 WG 25.2 6.3 30.5 11.3

A4 AG 9.9 2.5 7.2 2.6

z 32.0 7.9 34.1 11.3

C2 0.3 57.0 0.2 48.7

Loose keyway at 24 fpyInterstitial keyway at 24 fpy


Power SD Power SD

Dose 6.8 4.5 6.7 2.8

A4 WG 31.0 13.8 31.2 9.3

A4 AG 5.7 1.3 7.1 0.7

z 15.2 5.3 17.4 3.3

C1 0.0 9.6 0.0 12.2

C2 0.1 44.3 0.1 49.2

SCC 8.4 2.9 7.4 1.6

SC k 8.3 2.8 7.5 1.4


Power SD Power SD

Dose 7.4 3.1 7.0 3.5

A4 WG 21.7 6.1 27.8 10.3

A4 AG 11.8 0.6 8.2 1.0

z 15.5 2.0 15.2 3.9

C1 0.0 15.2 0.0 11.1

C2 0.1 57.7 0.1 48.3

SCC 10.0 1.0 9.0 1.8

SC k 9.3 1.5 9.1 2.4





Power SD Power SD

Dose 7.3 6.5 9.1 8.0

A4 WG 34.0 11.7 20.3 8.2

A4 AG 4.0 2.2 2.3 0.3

z 28.1 11.0 36.6 10.4

C2 0.5 46.6 0.5 41.7


Power SD Power SD

Dose 7.9 6.5 8.0 7.1

A4 WG 27.6 8.6 30.0 10.7

A4 AG 8.6 2.3 7.0 2.8

z 31.9 9.2 34.5 11.4

C2 0.1 51.4 0.2 47.9

Interstitial keyway at 24 fpy



Power SD Power SD

Dose 7.8 5.4 8.6 5.2

A4 WG 42.9 20.2 33.2 14.7

A4 AG 1.8 1.0 7.1 2.4

z 22.7 9.8 25.4 8.6

C1 0.0 5.5 0.0 8.3

C2 0.0 38.8 0.2 44.4

SCC 2.3 1.1 2.1 0.1

SC k 3.2 1.3 3.6 0.6


Power SD Power SD

Dose 7.7 5.7 6.9 3.2

A4 WG 43.1 21.6 27.1 9.9

A4 AG 1.9 1.0 8.7 1.0

z 21.9 9.7 15.1 3.1

C1 0.0 5.0 0.0 12.6

C2 0.0 38.2 0.1 48.5

SCC 2.5 1.2 9.1 1.8

SC k 3.5 1.4 9.1 1.8

Loose keyway at 24 fpy



Summary of results

24 fpy

• Power: Most influential parameters are A4 (with grain) and z. These parametersare dimensional parameters. They are much less influential at shutdown than atpower.

• Shutdown: Most influential parameter is C2 (CTE parameter). Not influential atpower.

32 fpy

• Power: Most influential parameter is A4 (with grain). However some of thesecondary creep parameters (secondary creep coefficient, and secondary creepYoung’s modulus fitting constant k) become more influential at 32 fpy than atearlier time points.

• Shutdown: Most influential parameter is C2 (CTE parameter). A4 (with grain)parameter becomes more influential at shutdown at 32 fpy than at earlier timepoints.


Summary of results and future work

• Little effect of orientation, layer or keyway on theinfluential parameters. The condition (power orshutdown) and time do affect which parameters areinfluential.

• Ultimate aim of this work is to use probabilistic stressanalysis via Monte Carlo simulation

• Need to account for variability and uncertainty in theparameters that go into the Monte Carlo simulution; thesensitivity analysis has highlighted the parameterswhere characterisation of uncertainty and variability isimportant and where calibration or further materialproperty analysis may be beneficial.


Thank youDisclaimer:This presentation and the work it describes were funded bythe Office of Nuclear Regulation (ONR). Its contents, includingany opinions and/or conclusions expressed, are those of thepresenter alone and do not necessarily reflect ONR policy.


References

• Kelly, BT. and Brocklehurst, JE., (1977),UKAEA reactor group studies of irradiationinduced creep in graphite, Journal of NuclearMaterials, 65 (1), 79-85.

Content contained within this presentation must not be copied or distributed without

consent from The University of Manchester.

Nuclear Graphite Research Group

University of Manchester, UK

Effect of AGR Fuel-Brick End-Face Features on Stress [email protected]

effect of agr fuel-brick end-face features on stress

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