Nuclear Safety
NEA/CSNI/R(2020)10
October 2022
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Reactivity Initiated Accident
Benchmark Phase III ReportNEA/CSNI/R(2020)10  1
Nuclear Energy Agency

NEA/CSNI/R(2020)10
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14 October 2022

NUCLEAR ENERGY AGENCYCOMMITTEE ON THE SAFETY OF NUCLEAR INSTALLATIONS

Reactivity Initiated Accident Benchmark Phase III Report

This document is available in PDF format only.

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REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT
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2  NEA/CSNI/R(2020)10
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REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  3

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REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT4  NEA/CSNI/R(2020)10

Acknowledgements
This report was prepared by the reactivity-initiated accident (RIA) Benchmark Phase III
Task Group of the Working Group on Fuel Safety (WGFS).
Special gratitude is expressed to Jean Baccou, Vincent Georgenthum andNicolas Tregoures (IRSN, France) for drafting the report, as well as to Asko Arkoma (VTT,
Finland), Rolando Calabrese (ENEA, Italy), Charles Folsom (INL, United States),
Isabelle Guénot-Delahaie (CEA, France), Lars Olof Jernkvist (Quantum Technologies,
Sweden) and Jinzhao Zhang (TRACTEBEL, Belgium) for reviewing the report.
The following WGFS members and experts performed calculations and provided valuable
input to various chapters of the report:
Asko Arkoma

VTT, Finland

Jean Baccou

IRSN, France

Felix Boldt

GRS, Germany

Rolando Calabrese

ENEA, Italy

Marco Cherubini

NINE, Italy

Martin Dostal

ÚJV, Czech RepublicThomas Drieu

TRACTEBEL, Belgium

Charles Folsom

INL, United States

Vincent Georgenthum

IRSN, France

Isabelle Guénot-Delahaie

CEA, France

Hyedong Jeong

KINS, Korea

Lars Olof Jernkvist

Quantum Technologies, Sweden

Jan Klouzal

ÚJV, Czech Republic

Raoul Ngayan-Happy

PSI, Switzerland

Ian Porter

NRC, United States

Heinz Günther Sonnenburg

GRS, Germany

Yutaka Udagawa

JAEA, Japan

Jinzhao Zhang

TRACTEBEL, Belgium

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  5

Table of contents

Executive summary ............................................................................................................................... 8
RIA benchmark Phase III specifications.............................................................................................. 8
Participants and codes used ................................................................................................................. 9
Results and summary ........................................................................................................................... 9Conclusions and recommendations.................................................................................................... 10
List of abbreviations and acronyms ................................................................................................... 11
1. Background and introduction ........................................................................................................ 14
References.......................................................................................................................................... 15
2. Summary of the RIA benchmark Phase III specifications .......................................................... 16
2.1. Description of the CIP0-1 case ................................................................................................... 16
2.2. CIP0-1 initial state evaluation ..................................................................................................... 19
2.3. Methodology ............................................................................................................................... 20
2.4. Specification of uncertain input parameters................................................................................ 222.5. Output specification .................................................................................................................... 23
References.......................................................................................................................................... 25
3. Participants and codes used............................................................................................................ 26
4. Results summary and analysis ....................................................................................................... 28
4.1. Experimental results ................................................................................................................... 28
4.2. Methodology ............................................................................................................................... 29
4.3. Comparison with experimental results........................................................................................ 33
4.4. Additional analysis of uncertainty results ................................................................................... 40
4.5. Sensitivity analysis ..................................................................................................................... 51
References.......................................................................................................................................... 57
5. Conclusions and recommendations................................................................................................ 58
References.......................................................................................................................................... 60
Annex A. Description of the transient codes used ............................................................................ 61
A.1
ALCYONE (CEA) ............................................................................................................ 61
A.2
FALCON (PSI) .................................................................................................................. 62
A.3
FRAPTRAN (TRACTEBEL) ........................................................................................... 63
A.4
RANNS (JAEA) ................................................................................................................ 64
A.5
SCANAIR (IRSN, QT-SSM, VTT) .................................................................................. 66
A.6
TESPA-ROD (GRS) .......................................................................................................... 67
A.7
TRANSURANUS (ENEA, ÚJV) ...................................................................................... 69
References.......................................................................................................................................... 70
Annex B. Description of the codes used by the participants during the benchmark .................... 73
B.1

French Alternative Energies and Atomic Energy Commission (CEA) ............................. 73

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT6  NEA/CSNI/R(2020)10
B.2
National Agency for New Technologies, Energy and Sustainable Economic
Development (ENEA)........................................................................................................................ 73
B.3
Gesellschaft Für Anlagen- Und ReaktorSicherheit (GRS) ................................................ 74
B.4
IRSN .................................................................................................................................. 75
B.5
JAEA ................................................................................................................................. 76
B.6
Paul Scherrer Institute (PSI) .............................................................................................. 77
B.7
QT-SSM ............................................................................................................................ 78
B.8
TRACTEBEL .................................................................................................................... 79
B.9
ÚJV Řež (ÚJV).................................................................................................................. 79
B.10
VTT Technical Research Centre of Finland Ltd (VTT) .................................................... 80
References.......................................................................................................................................... 81

List of figures
Figure 2.1. CIP0-1 mother rod: Axial burn-up profile .......................................................................... 16
Figure 2.2. CIP0-1 clad zirconia thickness and diameter before the test .............................................. 17
Figure 2.3. Axial power profile (left), core power and injected energy during the CIP0-1
test (right) ............................................................................................................................ 18
Figure 2.4. Visual examination of the rod after the test (left), zirconia thickness (middle)
and clad diameter measurements (right).............................................................................. 18
Figure 2.5. Zirconia thickness measurements before and after the test (left), raw clad diametermeasurements before and after the test (middle) and corrected diameter (i.e. sound clad
diameter) measurements before and after the test (right) .................................................... 19
Figure 2.6. Examples of FRAPCON radial profile output at peak power node location ...................... 20
Figure 3.1. Intragranular and grain boundary gas radial distribution for different participants ............ 27
Figure 4.1 Experimental data for TNa1 (z=25cm/BFC)........................................................................ 28
Figure 4.2. Experimental data for TNa2 (z=47 cm/BFC)...................................................................... 29
Figure 4.3. Experimental data for clad total axial elongation and clad residual hoop strain ................. 29
Figure 4.4. Example of union of participants’ intervals ........................................................................ 30
Figure 4.5. Information modelling associated with a source ................................................................. 31
Figure 4.6. Computation of the informativeness (left) and calibration (right) indicators associatedto a given output. ................................................................................................................. 32
Figure 4.7. Sodium temperature TNa1 (z=25 cm/BFC) and TNa2 (z=47 cm/BFC) ............................. 33
Figure 4.8. Clad permanent hoop strain at the end of the transient as a function of axial location ....... 34
Figure 4.9. Clad elongation as a function of time ................................................................................. 34
Figure 4.10. Fission gas release calculation as a function of time and measurements after the test ..... 35
Figure 4.11 Uncertainty interval widths for sodium coolant temperatures TNa1 and TNa2 ................ 35
Figure 4.12. Position of the experimental value within the uncertainty band (rexp) for TNa1 (left)
and TNa2 (right) ................................................................................................................ 36
Figure 4.13. Clad residual hoop strain UUB (left) and LUB (right) for all participants as a functionof axial height .................................................................................................................... 36
Figure 4.14. rexp value for clad residual hoop strain as a function of axial height ................................. 37
Figure 4.15. UUB and LUB for all participants (left) and position of the experimental value within
the uncertainty band (rexp) (right) for clad total axial elongation ....................................... 37
Figure 4.16. Average calibration indicator value for each output ......................................................... 38
Figure 4.17. Comparison of participants’ contribution with experimental results based on aqualitative graphical comparison (left) and on the computation of information
evaluation indicators (right) ............................................................................................... 38

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  7

Figure 4.18. Enthalpy increase as a function of time: Reference calculations and uncertainty
interval widths for all participants ..................................................................................... 41
Figure 4.19. Clad inner and outer temperature calculations: Reference cases ...................................... 42
Figure 4.20. Fuel elongation reference calculations (left) – participants’ uncertainty interval
widths, global uncertainty width and reference calculation dispersion (right) .................. 42
Figure 4.21. Clad hoop stress reference calculations and uncertainty interval widths .......................... 42
Figure 4.22. Fuel-to-clad heat exchange coefficient reference calculations and uncertainty interval
widths ................................................................................................................................. 43
Figure 4.23. Gap width reference calculations and uncertainty interval widths.................................... 43
Figure 4.24. Clad failure prediction/reference calculations and uncertainty interval widths ................ 44
Figure 4.25. Relative uncertainty interval for each output .................................................................... 44
Figure 4.26. Relative uncertainty interval for each output in Phase II .................................................. 45
Figure 4.27. Relative dispersion of reference calculations vs. relative uncertainty width .................... 46
Figure 4.28. Uncertainty results and reference calculation values for fuel thermal outputs ................. 46
Figure 4.29. Uncertainty results and reference calculation values for the fuel-to-clad heatexchange and the fuel-clad gap .......................................................................................... 47
Figure 4.30. Uncertainty results and reference calculation values for clad and fluid thermal
outputs................................................................................................................................ 48
Figure 4.31. Uncertainty results and reference calculation values for fuel and clad mechanicaloutputs................................................................................................................................ 48
Figure 4.32. Uncertainty results and reference calculation values for the fuel-clad gap, fuel-to-cladheat exchange, fission gas release and clad failure prediction ........................................... 50

List of tables
Table 2.1. List of time/height-dependent output parameters to be provided ......................................... 23
Table 2.2. List of time/height-dependent output parameters to be provided ......................................... 24
Table 2.3. List of different times for sensitivity analysis scalar output ................................................. 24
Table 3.1. Benchmark collected contributions (code combinations used for Phase III) ....................... 26
Table 4.1. Influential input parameters with respect to the type of behaviour when focusing
on the beginning of power pulse .......................................................................................... 52
Table 4.2 Influential input parameters with respect to the type of behaviour when focusing
on the time of pulse maximum power .................................................................................. 53
Table 4.3. Influential input parameters with respect to the type of behaviour when focusing
on the end of power pulse .................................................................................................... 54
Table 4.4. Influential input parameters with respect to the type of behaviour when focusing
on the end of the calculation ................................................................................................ 55
Table 4.5. Influential input parameters with respect to the type of behaviour when focusing
on the maximum value of each output ................................................................................. 56
Table 4.6. Percentage of participants that have identified a given input parameter as influential
for the maximum value of each output of interest ............................................................... 57

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT8  NEA/CSNI/R(2020)10

Executive summary
Following the recommendations from the technical workshop on “Nuclear Fuel Behaviour
during Reactivity-Initiated Accidents” organised by the Nuclear Energy Agency (NEA) in
September 2009, a first benchmark of the RIA fuel codes was organised between 2010 and2013. A second phase of the benchmark was launched in 2014, and the reports resulting
from these activities were approved by the Committee on the Safety of Nuclear Installationsin 2015 and 2016. The main conclusions of the two phases were:

Regarding fast transient thermal-hydraulic post-DNB (departure from nucleateboiling) behaviour, there are major differences between the modelling approaches,
resulting in significant deviations between simulations. Unfortunately, there are
currently no simple and representative experimental results that allow the different
approaches to be validated.



The models of fuel and clad thermo-mechanical behaviour and the associatedmaterials properties should be improved and validated for RIA conditions.



The different influential input parameters were identified for fresh fuel. For
instance, injected energy, fuel enthalpy, parameters related to the rod geometry(fuel and clad roughness, cladding inside diameter), fuel thermal-expansion modeland full width at half maximum of the power pulse come out as influential regarding
the maximum value of each output parameter of interest. However, the mostinfluential parameters in the case of irradiated fuel could be different from those of
fresh fuel.



Uncertainties cannot fully explain the scatter observed during Phase I of thisbenchmark exercise.

One recommendation from Phase II of the benchmark was to launch a complementary
phase focused on uncertainty and sensitivity analyses on an irradiated case in order to
identify the corresponding influential input parameters. In particular, the impact of theinitial state and key models on the results of the transient needed to be investigated and asensitivity study needed to be performed in order to identify or confirm the most influential
input uncertainties.

RIA benchmark Phase III specifications
Considering the results obtained during the first two phases, mainly the large discrepancy
regarding RIA thermal-hydraulics modelling, it was decided to limit the exercise to thepellet-cladding mechanical interaction (PCMI) phase, for which data are available from inpile tests. It was proposed to use the CIP0-1 test for this exercise performed in the CABRI
reactor in the sodium loop (for which it would be easier to reach a consensus between thecodes in relation to cladding-coolant heat transfer).
The CIP0-1 rodlet was refabricated from an ENUSA fuel rod with UO2 high burn-up fuel(75 GWd/tU) and ZIRLO™ cladding irradiated in the pressurised water reactor Vandellos
2 in Spain. The clad oxidation was significant, varying between 50 µm and 110 µm overthe length of the sample. The test was performed in 2002, at 280°C and low pressure(~3 bar). The injected energy in the test rod at peak power node was 99 cal/g and the power

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  9pulse width at half maximum 32 ms. No boiling crisis nor failure of the fuel rod occurred
during the test.
The assessment of the uncertainty associated with the test prediction is affected by thesimulation of the base irradiation to predict the rodlet pre-test conditions. In order to focus
this activity on the RIA codes, the state of the rod at the end of the base irradiation, before
the transient, was evaluated with the FRAPCON code, whose input data and results were
distributed to every participant.
Twelve uncertain input parameters with their reference values and their probability density
functions were defined. The probabilistic input uncertainty propagation method wasselected and the sample size was set to 200 code runs. The statistical study included not
only input parameters already identified for fresh fuel, but also extra “irradiation
parameters” such as zirconia thickness, power profile and initial fuel-clad gap.
For the uncertainty analysis, participants provided the lower and upper bounds of anuncertainty interval for the 19 specified output parameters; for the sensitivity analysis, they
provided the partial rank correlation coefficients associated with each uncertain input foreach specified output parameter at each specified time, including the one for theirmaximum values.

Participants and codes used
Ten organisations representing nine countries participated in the RIA benchmark Phase III.
The range of computer codes used was large, as analyses were performed with ALCYONE,FALCON, FRAPTRAN, RANNS, SCANAIR, TESPA-ROD and TRANSURANUS.
Some participants fully initialised their CIP0-1 analyses with the output from the
FRAPCON results. For the other data not provided by FRAPCON and needed for RIA
calculations, hypotheses were made.
Those participants who could not fully initialise their CIP0-1 input data with FRAPCON
output used their own means of calculating the non-initialisable parameters, and tried tomatch as much as possible the FRAPCON results, notably for fission gas distribution.

Results and summary
The uncertainty analysis has led to the following main conclusions:

The experimental results (time/height trend and scalar values) were well captured
by most of the participants, except for the fission gas release.

The strongest agreement with the experimental measurements is associated withthe evaluation of clad hoop strain and clad elongation, then sodium temperatures.

The maximum (relative) uncertainty band width depends on the type of outputs. As
in Phase II, the narrowest intervals are obtained for fuel thermal outputs. The
uncertainty interval width increases slightly for clad thermal outputs, then moresignificantly for fuel and clad mechanical ones. Finally, a large uncertainty has been
observed for the new outputs (that were not considered in Phase II): gap size,
fuel-to-clad heat exchange, fission gas release and clad failure prediction.



The same magnitude was observed for the relative uncertainty width and forreference calculation dispersion for numerous outputs.

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT10  NEA/CSNI/R(2020)10


When comparing participants’ uncertainty results for outputs considered inPhase II, the coherence ranking is the same, i.e. the highest coherence is obtainedfor fuel thermal outputs and fuel and clad mechanical outputs.

The sensitivity analysis has led to the following conclusions:

The injected energy is the most influential input parameter during the wholetransient and on almost all output data.

Input data related to rod state after base irradiation (initial fuel-clad gap, zirconia
thickness, radial power profile, roughness) are also very influential. Initial fuel-clad
gap is the most influential one in terms of clad failure prediction.



Fuel physical properties (fuel thermal-expansion and thermal conductivity models)
have a significant impact on behaviour.

Regarding the fission gas release, except injected energy, participants did not
identify any common influential input parameters.



The clad failure prediction is challenging because it is sensitive to many input data(nine influential input parameters out of the 12 studied here).

The clad physical properties (thermal-expansion and yield stress) have an impact
on few, but major, outputs (clad stress and clad failure prediction).

Conclusions and recommendations
The specifications of the RIA benchmark Phase III decoupled steady-state and transient
simulations. Some codes have been developed to perform both base irradiation andtransient calculations, which makes it possible to ensure continuity between the two phases,
but makes it more difficult to perform the decoupling. Their users thus had difficulties
matching the pre-transient state defined in the specifications.
Phase III confirmed the conclusions of Phase II concerning the strong dependence of theuncertainty results on the type of behaviour (in terms of uncertainty band width andcoherence between participants). Moreover, it expanded the list of influential input
parameters, with some input parameters related to the irradiation period.
Based on the main outcomes of the analysis, recommendations for future work are:

Safety analysis studies can require uncertainty analysis on parameters associatedwith the state of the rod at the end of irradiation. However, for some RIA codes,
pulse irradiation and base irradiation are not considered separately. It could beinteresting to develop strategies to allow the propagation of uncertainties on input
parameters associated to irradiation behaviour.

Further developments are required with a view to validate fission gas release andclad failure prediction models. It first involves gathering more high-quality data.

Mechanical models need to be improved, including cladding failure criteria andcladding stress behaviour.

A first task to carry out before uncertainty and sensitivity analyses is the quantification of
input uncertainties, which was partly performed in this benchmark using expert judgement.
The recent SAPIUM guidance could be used for a transparent and rigorous model for input
uncertainty quantification in order to minimise the user effect.

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  11

List of abbreviations and acronyms
BFC

Bottom of fissile column

CABRI

Test reactor in France

CDF

Cumulative distribution function

CEA

Alternative Energies and Atomic Energy Commission(Commissariat à l’Énergie atomique et aux énergies alternatives,
France)CFP

Clad failure prediction

CSED

Critical strain energy density

CSNI

Committee on the Safety of Nuclear Installations (NEA)DHR

Variation of radial average enthalpy

DNB

Departure from nucleate boiling

ECT

Clad total axial elongation

ECTH

Clad total (thermal + elastic + plastic) hoop strain

EFT

Fuel column total axial elongation

ENEA

National Agency for New Technologies, Energy and Sustainable
Economic Development (Agenzia nazionale per le nuove
tecnologie, l’energia e lo sviluppo economico sostenibile, Italy)

EPRI

Electric Power Research Institute

ETZ

Clad residual hoop strain

FGR

Fission gas release

GRS

Gesellschaft für anlagen- und ReaktorSicherheit (Germany)

HBS

High burn-up structure

HFC

Fuel-to-clad heat exchange coefficient

INL

Idaho National Laboratory (United States)

IRSN

Institute for Radiological Protection and Nuclear Safety(Institut de Radioprotection et de Sûreté Nucléaire, France)

J

Rice integral

JAEA

Japan Atomic Energy Agency

KINS

Korean Institute of Nuclear Safety

LUB/UUB

Lower/upper uncertainty boundLUBmin/UUBmax

Minimum/maximum of the LUBs/UUBs provided by allparticipants

MOX

Mixed oxide fuel (U and Pu)

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT12  NEA/CSNI/R(2020)10
NEA

Nuclear Energy Agency

NINE

Nuclear and Industrial Engineering (Italy)

NRC

Nuclear Regulatory Commission (United States)

NSRR

Nuclear Safety Research Reactor (Japan)

OECD

Organisation for Economic Co-operation and Development

PCMI

Pellet-cladding mechanical interaction

PNNL

Pacific Northwest National Laboratory (United States)

PPN

Peak power node

PRCC

Partial rank correlation coefficient

PSI

Paul Scherrer Institute

PWR

Pressurised water reactor

q0

Uncertainty interval width

q1

Indicator of the position of the reference calculation within theuncertainty interval

QT

Quantum Technologies AB (Sweden)

RCC

Rank (Spearman’s) Correlation Coefficient

REF

Reference calculation

REFmin/REFmax

Minimum/maximum of the reference calculations provided by allparticipants

RFO

Fuel outer radius

RIA

Reactivity-initiated accident

SCC

Simple (Pearson’s) Correlation Coefficient

SCH

Clad hoop stress at outer part of the clad

SNL

Sandia National Laboratories

SSM

Swedish Radiation Safety Authority(Strålsäkerhetsmyndigheten)

SUNSET

Sensitivity and Uncertainty Statistical Evaluation ToolTC

Thermocouple

TCI

Temperature of clad inner surface

TCO

Temperature of clad outer surface

TFC

Temperature of fuel centreline

TFM

Maximum fuel temperature

TFO

Temperature of fuel outer surfaceÚJV

Nuclear Research Institute (ÚJV Řež, Czech Republic)

UUB

Upper uncertainty bounds

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  13

VTT

VTT Technical Research Centre of Finland Ltd(Teknologian Tutkimuskeskus VTT Oy)

WGFSWorking Group on Fuel Safety (NEA/CSNI)REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT14  NEA/CSNI/R(2020)10

1. Background and introduction

Following the recommendations from the technical workshop on “Nuclear Fuel Behaviour
during Reactivity-Initiated Accidents” organised by the Nuclear Energy Agency (NEA) in
September 2009, a first benchmark of the reactivity-initiated accident (RIA) fuel codes wasorganised within the activities of the Working Group on Fuel Safety. The final report of
the first benchmark (NEA, 2013) was approved by the Committee on the Safety of Nuclear
Installations (CSNI) in 2013. A second phase of the benchmark was launched in 2014, andthose reports were approved by the CSNI in 2015 (NEA, 2016) and 2016 (NEA, 2017).
The main conclusions of those two phases were:

Regarding fast transient thermal-hydraulic post-DNB (departure from nucleateboiling) behaviour, there are major differences between the modelling approaches,
resulting in significant deviations between simulations. Unfortunately, there are
currently no simple and representative experimental results that allow the different
approaches to be validated.



The models of fuel and clad thermo-mechanical behaviour and the associatedmaterials properties should be improved and validated for RIA conditions.



The different influential input parameters are identified for fresh fuel. For instance,
injected energy, fuel enthalpy, parameters related to the rod geometry (fuel and cladroughness, cladding inside diameter), fuel thermal-expansion model and full widthat half maximum of the power pulse come out as influential regarding the maximum
value of each output parameter of interest. However, the most influential
parameters in the case of irradiated fuel could be different than with fresh fuel.



Uncertainties cannot fully explain the scatter observed during Phase I of thisbenchmark exercise.

One recommendation from Phase II of the benchmark was to launch a complementary
phase focused on uncertainty and sensitivity analyses on an irradiated case in order to
identify the corresponding influential input parameters. In particular, uncertainties
regarding fission products distribution, fuel microstructure, clad corrosion state and gap
conductance should be investigated.
Considering the results obtained during the first two phases, mainly the large discrepancy
regarding RIA thermal-hydraulics modelling, it was decided to limit the exercise to the“PCMI phase”, for which data are available from in-pile tests. Therefore, it was proposed
to use the CIP0-1 test for this exercise. This test was performed in the CABRI reactor in
the sodium loop (for which it would be easier to reach a consensus between the codes inrelation to cladding-coolant heat transfer) on an irradiated ZIRLO™-clad UO2 fuel.
This phase was focused on the assessment of the uncertainty of the results. In particular,
the impact of the initial state and key models on the results of the transient were
investigated. In addition, a sensitivity study was performed to identify or confirm the mostinfluential input uncertainties.
The assessment of the uncertainty associated with the test prediction is affected by thesimulation of the base irradiation to predict the rodlet pre-test conditions. In order to focus
this activity on the RIA codes, the state of the rod at the end of the base irradiation, before

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  15

the transient, was evaluated with the FRAPCON code, whose input data and results were
distributed to every participant.
This report is organised as follows:

Chapter 2 briefly describes the specifications of the RIA benchmark Phase III;

Chapter 3 presents the participants and their adopted codes;



Chapter 4 discusses the main findings of this benchmark, which are illustrated by
selected plots comparing the solutions provided by the participants;

Chapter 5 gives the conclusions of this phase of the RIA benchmark and provides
some recommendations for follow-up activities.

References
NEA (2017), “Reactivity-Initiated Accident (RIA) Fuel-Codes Benchmark Phase II: Uncertainty andSensitivity Analyses, NEA/CSNI/R(2017)1, OECD Publishing, Paris, https://www.oecdnea.org/jcms/pl_19762.
NEA (2016), “Reactivity Initiated Accident (RIA) Fuel Codes Benchmark Phase II: Volume 1:
Simplified Cases Results – Summary and Analysis”, NEA/CSNI/R(2016)6/VOL1, OECD Publishing,Paris, https://www.oecd-nea.org/jcms/pl_19710.
NEA (2013), “RIA Fuel Codes Benchmark - Volume 1”, NEA/CSNI/R(2013)7, OECD Publishing, Paris,
https://www.oecd-nea.org/jcms/pl_19332.

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT16  NEA/CSNI/R(2020)10

2. Summary of the RIA benchmark Phase III specifications

2.1. Description of the CIP0-1 case
The CIP0-1 experiment was performed in 2002 with UO2 high burn-up fuel (75 GWd/tU)
with ZIRLO™ cladding in the CABRI sodium loop facility, at 280°C and low pressure(~3 bar). No boiling crisis nor failure of the fuel rod occurred during the test.

2.1.1. Characteristics of the CIP0-1 rodlet before the test
The CIP0-1 rodlet was refabricated from an ENUSA fuel rod irradiated in the pressurised
water reactor Vandellos 2 in Spain in the frame of a joint Japanese-Spanish R&D
programme aimed at studying the behaviour of UO2 fuel at high burn-up (Watanabe et al.,2005). The UO2 rod, with an initial uranium 235 enrichment of 4.5% and a ZIRLO™
cladding, had been irradiated for five cycles, from June 1994 to September 2000, until a
rod average burn-up of 68 GWd/tU. The burn-up distribution measured along the rod isrepresented in Figure 2.1.
The detailed characteristics of the rod and the irradiation history in the Vandellos reactor
are given in NEA (2013) and Watanabe et al. (2005).
Figure 2.1. CIP0-1 mother rod: Axial burn-up profile

Source: IRSN, 2019.

The examinations performed in the Swedish Studsvik laboratory on the mother rod after
irradiation have shown the following results (Petit et al., 2007; Georgenthum et al., 2017):


rod axial elongation of about 0.8%;

fissile column axial elongation of 0.93%;

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  17fission gas release in the free volume: 7.4% of the total fission gas created during
the irradiation;free volume: 12.26 cm3;



plenum pressure: 5.85 MPa at 0°C.

The CIP0-1 rodlet was refabricated from the fifth span of the rod. The rod refabrication andsome non-destructive examinations on the rodlet were performed in the Studsvik
laboratory. The length of the CIP0-1 test rod was 541 mm. Figure 2.2 represents themeasurements of diameter and zirconia thickness on the outer part of the clad. The cladoxidation was significant: the mean zirconia thickness was 80 µm, varying between 50 µm
and 110 µm over the length of the sample.
Figure 2.2. CIP0-1 clad zirconia thickness and diameter before the test

Source: IRSN, 2019.

The cladding was highly hydrided with a mean hydride concentration of about 1 000 ppm.
The hydrides were long and oriented in the circumferential direction. No hydride blisters
were found, but hydride rims with a thickness of 50 µm were present. On fuel examinations,
one can estimate the visible high burn-up structure width to be about 120 ± 30 µm(probably corresponding to a fully restructured high burn-up structure). It is also worth
noting the very tight bonding between the fuel and the inner zirconia layer. The inner
zirconia thickness is estimated to be roughly equal to 10 µm.

2.1.2. CIP0-1 test characteristics and results
The CABRI CIP0-1 test was performed in 2002 in the sodium loop of the CABRI facility
in Cadarache, France. The main characteristics of the power transient were (Petit et al.,2007; Georenthum et al., 2017) (see Figure 2.3):


maximum core power: Pmax = 3 692 ± 222 MW;core energy deposition: Ecore = 189.6 ± 11.4 MJ (1.2 s after the beginning of theenergy deposition);power pulse width at half maximum: 32.4 ± 0.5 ms;injected energy in the test rod at peak power node (PPN): 99 ± 6 cal/g (1.2 s after
the beginning of the energy deposition.

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT18  NEA/CSNI/R(2020)10
Figure 2.3. Axial power profile (left), core power and injected energy during the CIP0-1
test (right)
4000

P(MW)

E (cal/g)
120

3500

100

3000
80

2500
Core power
2000

60

Injected energy

1500

40

1000
20

500
0

0
0

0,5

1

1,5

t(s)

2

Source: Georgenthum et al., 2017.

According to the measurements performed during and after the test, the rod underwent thepower transient without clad failure.
Visual examinations confirmed the non-failure of the rod and showed the high oxide
spallation of the rod along all angular orientations with many spalled areas (seeFigure 2.4, left panel, white area) of large dimensions (several mm wide and often several
cm long). The oxide spalling phenomenon is also noticeable on the clad diameter andzirconia thickness measurements that were performed along four and eight azimuths,
respectively (see Figure 2.4, middle and right panels).
Direct comparison between raw clad diameter measurements before and after the test does
not allow the clad residual hoop strain to be estimated. The clad diameter measurements
have been corrected based on the zirconia thickness measurements before and after the test(see Figure 2.5) in order to calculate the sound clad diameter before and after the test andthus the clad residual hoop strain. The clad residual hoop strain ranges from 0% at both
extremities of the rod to 0.5 ± 0.1% at the PPN location. According to the rod puncturing,
the fission gas release was estimated to be 13-16% of the creation and the final free volume
pressure at 20°C was 29 ± 22.6 bar.
Figure 2.4. Visual examination of the rod after the test (left), zirconia thickness (middle)
and clad diameter measurements (right)
Clad diameter measurements

zirconia thickness measurements
120

9,65

100

9,6

D (mm)eZrO2 (µm)

80
60

9,55

9,5

40

0°
90°
180°
270°

20

45°
135°
225°
315°

0°
45°
90°
135°

9,45

9,4

0
0

100

200

300
z (mm/BFC)

400

500

0

100

200

300

400

500

z (mm/BFC)

Source: Georgenthum et al., 2017.

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  19

Figure 2.5. Zirconia thickness measurements before and after the test (left),raw clad diameter measurements before and after the test (middle) and corrected diameter(i.e. sound clad diameter) measurements before and after the test (right)
100

70
D (mm)

60
50
40
30

Before test

20

After test

10

Mean sound clad diameter before and after test
9,47
9,46

Before test
9,44

9,52
9,51
9,5
9,49
9,48
9,47

0

100

200

300
z (mm/BFC)

400

500

9,43
9,42
9,41

After test

9,4

Before test

9,39

9,46
9,45
9,44

0

After test

9,45

9,58
9,57
9,56
9,55
9,54
9,53

D (mm)

80
e ZrO2 (µm)

Raw clad diameter before and after test

9,62
9,61
9,6
9,59

90

9,38
0

50

100

150

200

250

300

350

400

450

500

0

50

z (mm/BFC)

100

150

200

250

300

350

400

z (mm/BFC)

Source: Georgenthum et al., 2017.

2.2. CIP0-1 initial state evaluation
As stated in the introduction, the initial state of the rod, after base irradiation, was evaluatedwith the FRAPCON V4.0 P1 code.
FRAPCON calculations were done considering 18 axial meshes, 16 radial meshes in thefuel for the thermo-mechanical calculations, 45 radial meshes and a FRAPFGR model forthe gas calculations. Some end-of-base irradiation data mandatory for the reactivityinitiated accident (RIA) test calculation were extracted from the axial meshes 12, 13 and14, corresponding to the span five of the rod.
The corresponding FRAPCON input and output data files were given to the participants.
The following extracted data were also given to the participants (some examples areillustrated in Figure 2.6):
Rod geometry after cooling down (at 20°C): fuel outer, clad inner and outer radiiin each axial mesh.

In the fuel, as a function of radial and axial meshes or nodes:‒

plutonium content at the nodes (%);‒

local burn-up at the nodes (at% or GWd/tU);‒

end-of-life temperature (before cooling phase) at the nodes;‒

radial power profile at the nodes;‒

fuel density in each mesh (cm3/g);‒

porosity at the nodes;‒

stoichiometry in each mesh;‒grain radius: in each mesh (µm);‒

total gas retained in the meshes (cm3STP/g) (STP: standard temperature andpressure, 0°C and one bar);‒

intragranular gas in the meshes (cm3STP/g).

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT

450

500

20  NEA/CSNI/R(2020)10
Figure 2.6. Examples of FRAPCON radial profile output at peak power node location

Source: IRSN, 2019.

2.3. Methodology
2.3.1. Uncertainty analysis methodology
Among all the available uncertainty analysis methods, the probabilistic input uncertainty
propagation method is so far the most widely used in nuclear safety analysis (Glaeser,2008). With this method, the fuel codes are treated as “black boxes” and the input
uncertainties are propagated to the simulation model output uncertainties via the code
calculations, with sampled data from known or assumed distributions for key input
parameters (Zhang, Segurado and Schneidesch, 2011). The input parameters of interest
may also include uncertain material properties, model parameters, etc.
The method consists of the following steps:
Specification of the problem: all relevant code outputs and corresponding uncertain
parameters for the codes, plant modelling schemes, and plant operating conditions
are identified.



Uncertainty modelling: the uncertainty of each uncertain parameter is quantified bya probability density function based on engineering judgement and experience
feedback from code applications to separate tests, integral tests and to full plant
simulation. If dependencies between uncertain parameters are known and judged to
be potentially important, they can be quantified by correlation coefficients.



Uncertainty propagation through the computer code: the propagation is represented
by Monte-Carlo simulations (Gentle, 1985). In Monte-Carlo simulations, the

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  21

computer code is run repeatedly, each time using different values for each of theuncertain parameters. These values are drawn from the probability distributions anddependencies chosen in the previous step. In this way, one value for each uncertain
parameter is sampled simultaneously in each repetition of the simulation. The
results of a Monte-Carlo simulation lead to a sample of the same size for each
output quantity.


Statistical analysis of the results: the output sample is used to get any typicalstatistics of the code response, such as mean or variance, and to determine thecumulative distribution function (CDF). The CDF makes it possible to derive thepercentiles of the distribution.

A simple way to get information on percentiles is to use order statistics (Conover, 1999),
which is a well-established and shared methodology in the nuclear community, and hence
recommended for this activity.
The principle of order statistics is to derive results from the ranked values of a sample. If(X1,…,XN) denotes a sample of any random variable, X, and (X(1),…,X(N)) the
corresponding ranked one, order statistics first provide an estimation of the percentile ofinterest since the α-percentile can be estimated by X(αN). Moreover, it turns out that the
CDF of X(k), FX(X(k)), follows the beta law β(k,N-k+1), which does not depend on the
distribution of X. This key result allows quantifying the probability that any ranked value
is smaller than any percentile by the following formula:P(X(k) ≤ Xα) = Fβ(k,N-k+1)()where Fβ(k,N-k+1) denotes the CDF of the beta law β(k,N-k+1).
This equation can then be used to derive:
1. Lower and upper bounds of a percentile of interest, given the sample size N andthe confidence level γ that controls the probability that X(k) ≤ Xα. For this purpose,
it is necessary to solve the equation Fβ(k,N-k+1)()= γ.
2. The minimal sample size (and therefore the minimal number of code runs) toperform in order to obtain a lower or upper bound of a given percentile with a given
confidence level. It leads to the so-called Wilks’ formula (Wilks, 1941):
N = ln(1-γ)/ln()and Guba’s estimate in case of multiple output parameters in Guba, Makai and Pal (2003).
Order statistics are widely used since no information is needed on the distribution of therandom variable. Moreover, this method is very simple to implement, which makes it
extremely interesting for licensing applications to nuclear safety analyses.
The probabilistic input uncertainty propagation method was selected due to its simplicity,robustness and transparency. The highly recommended sample size is set to 200(i.e. 200 code runs must be performed). Strong justifications should be given if a lower
number of code runs is performed. The sample is constructed according to the selected
probability density functions coming from the uncertainty modelling step and assuming
independence between input parameters following a simple random sampling.
We focus on the estimation of a lower (or upper) bound of the 5% (or respectively 95%),
percentiles () at confidence level (γ) higher than 95%.

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT22  NEA/CSNI/R(2020)10
For N = 200 and = 0.05 or 0.95, the previous equations lead to:P(X(5) ≤ X5%) = 0.97
P(X(196) > X95%) = 0.97
the lower (or upper) bound is defined in this benchmark by X(5) (or respectively X(196)).
They are denoted LUB and UUB respectively in this document. Note that a one-sided
approach is used here, i.e. we focus on percentiles and not on interval and that the bounds
are estimated separately.

2.3.2. Sensitivity analysis methodology
In addition to the uncertainty analysis, a complementary study was performed to gain
qualitative insight on the most influential input parameters.
This work was done based on a sensitivity analysis using the 200 code runs previously
obtained. More precisely, if Y denotes the response of interest and {X i}i=1,…,p the set of p
uncertain input parameters (also called regressors), it is recommended to compute
Spearman-type correlation coefficients.
The Spearman’s rank correlation coefficient (RCC) is similar to the classical linear simple
correlation coefficient (i.e.  i 

Cov (Y , X i ) XY), but replaces input and output values by

their respective ranks. Working with ranks allows one to extend the previous underlying
linear regression model to a monotonic non-linear one. In the presence of non-linear but
monotonic relationships between the response and each of the p regressors, use of the rank
transform can substantially improve the resolution of sensitivity analysis results (McKay,
1988).
The partial rank correlation coefficient (PRCC) provides an improved measure of themonotonic relation between the response and one of the p regressors by removing trends
associated with other variables.
Based on this information (RCC or PRCC), the most influential uncertain input parameters
can be identified.

2.4. Specification of uncertain input parameters
In the RIA benchmark Phase II, the influence of 19 uncertain input parameters was studied
on the results of a fresh fuel RIA test in pressurised water reactor conditions. The input
parameters were classified into four categories:parameters associated with the fuel rod design, bounded by allowable
manufacturing tolerances;

thermal-hydraulics boundary conditions;core power boundary conditions;

physical properties/key models.

End-of-life fuel state parameters were added in the present study; on the other hand,parameters associated with the fuel rod design and the thermal-hydraulic boundary
conditions were not considered.

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  23

Table 2.1 provides the specified input parameters as well as the information related to theiruncertainty. In most cases, a normal distribution has been assigned to input parameters for
simplicity’s sake. Their standard deviation has been taken as half of the maximum of theabsolute value of the difference between their nominal value and their upper or lower
bound. In order to avoid unphysical numerical values, the sampling is performed(i.e. truncated) between the upper and lower bounds.
Note that some uncertainties on input parameters displayed by Table 2.1 have been fixedby expert judgement. The question of the influence of the uncertainty modelling and moregenerally of the quantification process to derive input uncertainties is beyond the scope of
this benchmark. This topic could be studied in further work.
Finally, although the dependency between the pulse width and the injected energy waswell known, it was not considered.
Depending on the code used, it might be difficult to modify some recommended input
parameters. In this case, the parameters could be discarded, but this information had to beclearly mentioned in the participants’ contributions.
Table 2.1. List of time/height-dependent output parameters to be provided
Input parameter uncertainty
Reference/mean value
1. End-of-life fuel state
Fuel-clad radial gap (at 20°C) (µm)
Cladding roughness (µm)
Fuel roughness (µm)
Zirconia thickness (multiplying
coefficient C)
2. Core power boundary conditions
Injected energy in the rod at peak
power node location (cal/g)
Radial power profile (“peaking factor”)
Pulse width (ms)
3. Physical properties/key models
Fuel thermal conductivity model(multiplying coefficient)
Fuel thermal-expansion model(multiplying coefficient)
Fuel enthalpy/heat capacity(multiplying coefficient)
Clad thermal-expansion model(multiplying coefficient)
Clad yield stress(multiplying coefficient)Standard
deviation

10.
0.1
0.1
Half of the upper
value (C =1/2)

Distribution
Type
Lower boundUpper boundUniform
Uniform
Uniform
Uniform

0.1
10-6
10-6
Total spalling
(C=0)

20
2.
2.
Before test
measurement
(C=1)

99

3

Normal93

105

FRAPCON
results (i.e. 0)
Measurement
32

0.125

Normal

-0.25

0.25

0.75

Normal

30.5

33.5

1.00

5%

Normal

0.90

1.10

1.00

5%

Normal

0.90

1.10

1.00

1.5%

Normal

0.97

1.03

1.00

5%

Normal

0.90

1.10

0.9

5%

Normal0.81

0.99

2.5. Output specification
After input uncertainty propagation, each participant gave lower and upper bounds
associated with all time/height trended output parameters listed in Table 2.2.

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT24  NEA/CSNI/R(2020)10
In addition, the results of the calculation with the nominal value of the input parameters,also called reference calculation, were provided.
Among the outputs of interest, the clad failure prediction parameter (CFP) had to be definedby each participant as a function of time. This parameter should be a continuous function
such that: if CFP < 1 no failure is predicted, if CFP ≥1 a failure is predicted (example: J/Jc,
SED/CSED, ECTH/ECTHc, with respectively Jc, CSED and ECTHc the critical values ofJ, SED and ECTH).
Moreover, the reference, lower and upper bound values for the maximum of each output
parameter in Table 2.2 had to be given.
Table 2.2. List of time/height-dependent output parameters to be provided
Parameter
EINJ
DHR

Unit
cal/g
cal/g

TFC
TFM
TFO
TCI
TCO
TNa1
TNa2
ECTH

°C
°C
°C
°C
°C
°C
°C
%

ECT
EFT
SCH
RFO
GAP
HFC
ETZ

mm
mm
MPa
mm
µm
W/m²/K
%

FGR
CFP

mm3
()

Description (function of time/height parameter)
Injected energy (radial averaged) as a function of time (at z= peak power node)
Variation of radial average enthalpy with respect to initial conditions of the transient in therodlet as a function of time (at z=peak power node) (please note that DHR(t=0)=0)
Temperature of fuel centreline as a function of time (at z= peak power node)
Maximum fuel temperature as function time (at z= peak power node)Temperature of fuel outer surface as a function of time (at z= peak power node)Temperature of clad inner surface as a function of time (at z= peak power node)Temperature of clad outer surface as a function of time (at z= peak power node)Temperature of Na coolant as a function of time (at z=25 cm/BFC)
Temperature of Na coolant as a function of time (at z=47 cm/BFC)
Clad total (thermal + elastic + plastic) hoop strain at the outer part of the sound clad as afunction of time (at z= peak power node)
Clad total axial elongation as a function of time
Fuel column total axial elongation as a function of time
Clad hoop stress at outer part of the clad as a function of time (at z= peak power node)
Fuel outer radius as a function of time (at z= peak power node)
Fuel-clad gap width as a function of time (at z= peak power node)
Fuel-to-clad heat exchange coefficient as a function of time (at z= peak power node)
Clad permanent hoop strain at the end of transient at the metal/oxide interface at end of thetransient as a function of height
Fission gas volume release as a function of time, at one bar and 0°C
Clad failure prediction as a function of time

Finally, regarding the sensitivity analysis, participants evaluated the partial rank correlation
coefficients (or Spearman’s if the PRCC was not available) associated to each uncertain
input parameter and for each output of interest, at the times defined in Table 2.3. It wasalso requested to perform the same analysis for the maximum (with respect to time orheight) of each output parameter.
Table 2.3. List of different times for sensitivity analysis scalar output
Time parameters
Definition
Value

t1
Beginning of power
pulse
0.0s

t2
Time of pulse
maximum power
0.437st3
End of power pulse
1.2s

t4
End of calculation
50s

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  25

References
Conover, W. (1999), Practical Non-parametric Statistics, Wiley, New York, NY.
Gentle, E. (1985), “Monte-Carlo methods”, Encyclopaedia of Statistics, Vol. 5, pp. 612-617, John Wileyand Sons, New York, NY.
Georgenthum, V., C. Folsom, A. Moal, O. Marchand, R. Williamson, H. Ban and D. Wachs (2017),“SCANAIR-BISON Benchmark on CIP0-1 RIA Test”, 2017 Water Reactor Fuel Performance
Meeting, 10-14 September 2017, Jeju Island, Korea, www.osti.gov/biblio/1409689.
Glaeser, H. (2008), “GRS method for uncertainty and sensitivity evaluation of code results andapplications”, Science and Technology of Nuclear Installations, Vol. 2008,
http://dx.doi.org/10.1155/2008/798901.
Guba, A., M. Makai and L. Pal (2003), “Statistical aspects of best-estimate method-I”, Reliability
Engineering & System Safety, Vol. 80/3, pp. 217-232, https://doi.org/10.1016/S0951-8320(03)00022X.
McKay, M.D. (1988), “Sensitivity and uncertainty analysis using a statistical sample of input values”,
Chapter 4 in: Ronen, Y. (ed.), Uncertainty Analysis, CRC Press, FL.
NEA (2013), “RIA Fuel Codes Benchmark - Volume 1”, NEA/CSNI/R(2013)7, OECD Publishing, Paris,
https://www.oecd-nea.org/jcms/pl_19332.
Petit, M., V. Georgenthum, J. Desquines, T. Sugiyama and M. Quecedo (2007), “A comparative analysis
of CABRI CIP0-1 and NSRR VA-2 reactivity initiated accident”, EUROSAFE 2007: Towards
convergence of technical nuclear safety practices in Europe, Berlin, Germany, 5-6 November 2007.
Watanabe, S., S. Abeta, J. Serna, J. Alonso, T. Sendo and P. Gonzalez (2005), “Post-irradiation
examinations on 67-75 GWd/t rods for confirmation of the integrity and appropriate performance ofthe claddings for future”, Proceedings of the 2005 Water Reactor Fuel Performance Meeting, Kyoto,
Japan, 2-6 October 2005.
Wilks, S.S. (1941), “Determination of sample sizes for setting tolerance limits”, The Annals of
Mathematical Statistics, Vol. 12/1, pp. 91-96, https://www.jstor.org/stable/2235627.
Zhang, J., J. Segurado and C. Schneidesch (2011), “Towards an industrial application of statisticaluncertainty analysis methods to multi-physical modelling and safety analyses”, Proceedings of the
OECD/CSNI Workshop on Best-Estimate Methods and Uncertainty Evaluations, Barcelona, Spain,
16-18 November 2011.

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT26  NEA/CSNI/R(2020)10

3. Participants and codes used

The participants of the RIA benchmark Phase III, which represented nine countries, were:

TRACTEBEL (ENGIE) from Belgium;ÚJV Řež (ÚJV) from the Czech Republic;Institute for Radiological Protection and Nuclear Safety (IRSN) and Alternative
Energies and Atomic Energy Commission (CEA) from France;

VTT Technical Research Centre of Finland Ltd (VTT) from Finland;

Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) GmbH from Germany;

Italian National Agency for New Technologies, Energy and Sustainable Economic
Development (ENEA) from Italy;

Japan Atomic Energy Agency (JAEA) from Japan;



Swedish Radiation Safety Authority (SSM) represented by Quantum Technologies
from Sweden (QT);Paul Scherrer Institut (PSI) from Switzerland.

As can be seen, research institutions, utilities, technical safety organisations and safety
authorities were all well represented. Ten participants contributed to the study. They arelisted in Table 3.1 along with the codes they used for base irradiation, transient simulationand sensitivity/uncertainty analyses.
In terms of computer fuel rod codes used, the spectrum was also large for base irradiationand transient simulations. Brief descriptions of the computer codes are given in Annexes A
and B.
Table 3.1. Benchmark collected contributions (code combinations used for Phase III)
Organisation
CEA
ENEA

Base irradiation
ALCYONE V1.4
TRANSURANUS

GRS
IRSN
JAEA
PSI
QT-SSM
TRACTEBELÚJVGiven FRAPCON results
FRAPCON 4.0 P1
FEMAXI-8
FALCON
Given FRAPCON results
FRAPCON 4.0P1
TRANSURANUS

VTTGiven FRAPCON results

Codes
Transient simulation
ALCYONE V1.4
TRANSURANUS, Version 2018TESPA-ROD_20.3.1
SCANAIR V_7_8
RANNS 8.1.102f
FALCON v1.4.1, GRSW-A 3.02
SCANAIR V_7_8
FRAPTRAN 2.1
TRANSURANUS
v1m3j12modCEZ18SCANAIR V_7_8

Statistical analysis
URANIE V4.1
TRANSURANUS(TuStat)
SUSA 4.1
SUNSET V2.1
DAKOTA 6.5
Python internal tool
SUNSET V2.1
DAKOTA 6.2
ROOT
Python internal tool

Source: IRSN, 2019.

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Some participants fully initialised their CIP0-1 analyses with the output from the
FRAPCON results. For other data needed for the RIA calculations but not provided by
FRAPCON, hypotheses were formulated.
Those participants who could not fully initialise their CIP0-1 input data with FRAPCON
output used their own means of calculating the non-initialisable parameters, and tried tomatch the FRAPCON results as much as possible, notably fission gas distribution.
As an illustration, the intragranular and grain boundary gas distributions, as given by theparticipants, are plotted in Figure 3.1 and compared to the FRAPCON output data. While
the grain boundary gas distributions are quite similar for all participants and consistent with
FRAPCON output, this is not the case for intragranular gas distributions.
Figure 3.1. Intragranular and grain boundary gas radial distribution for different
participants

Source: IRSN, 2019.

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4. Results summary and analysis

This chapter is devoted to the synthesis of the RIA benchmark Phase III results. The firsttwo sections focus on the available experimental results that are used in the analysis ofparticipants’ contributions and on the methodology to perform the analysis. They arefollowed by a summary of the main points.

4.1. Experimental results
Among the outputs listed in Table 2.2, experimental information is available for the Na
coolant temperature (TNa1, TNa2), clad elongation (ECT), clad residual hoop strain (ETZ)
and fission gas release (FGR).
Figures 4.1-4.3 display the experimental time trends associated to TNa1, TNa2, ECT and
ETZ. They correspond to measurements and associated uncertainty defined according toan internal experimental report. More precisely:TNa1, TNa2 (Figures 4.1 and 4.2): the left panel provides the time trends given by
three sensors. The right panel includes the average temperature of the three sensors
as well as the experimental uncertainty. This last quantity is defined, for each time
considered, as the interval [TNamin – 3°C; TNamax + 3°C] where TNamin, (orrespectively TNamax), is the minimum (or respectively the maximum), of thetemperature measured by the three sensors.

ECT (Figure 4.3, left panel): the three time trends correspond to the raw
measurements (exp) and to the uncertainty defined for each considered time as[exp – 2 mm; exp + 2 mm]. The uncertainty was set to zero before the transient.

ETZ (Figure 4.3, right panel): the three times trends correspond to a smoothing of
the measurements computed by (quadratic) regression and to an uncertainty of 22.

Finally, the experimental value for the FGR is the final value of the experimental timetrend. It is equal to 88 298 mm3 with an uncertainty of 6.3%.
Figure 4.1 Experimental data for TNa1 (z=25cm/BFC)

Source: IRSN, 2019.

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Figure 4.2. Experimental data for TNa2 (z=47 cm/BFC)

Source: IRSN, 2019.

Figure 4.3. Experimental data for clad total axial elongation and clad residual hoop strain

Note: ECT: clad total axial elongation; ETZ: clad residual hoop strain.
Source: IRSN, 2019.

4.2. Methodology
This section provides an overview of the methods and tools that were used to analyse theparticipants’ results.

4.2.1. Uncertainty analysis
A first study is performed on the time/height trend outputs. The focus then moves to theresults associated with scalar outputs.
Time/height trend outputs
For each output, the analysis is focused on the uncertainty interval ([LUB, UUB]). Moreprecisely, three kinds of synthesis have been performed.

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They are based on the evolution with respect to the time of:the union of all participants’ intervals, i.e. [LUBmin, UUBmax] with LUBmin(respectively UUBmax) defined as the minimum (respectively maximum) of all
lower uncertainty bounds (LUBs) and upper uncertainty bounds (UUBs) (Figure
4.4);



the uncertainty interval (or band) width of each participant:q0  UUB  LUB


for sodium temperature, ECT and ETZ, the position of the experimental value
within the uncertainty band and computed for each participant as:

𝑈𝑈𝐵 − 𝐸𝑋𝑃
𝑈𝑈𝐵 − 𝐿𝑈𝐵
By construction, if this last quantity varies between zero and one, the experimental value
is inside the uncertainty band. Otherwise, it is outside.
𝑟𝑒𝑥𝑝 =

Figure 4.4. Example of union of participants’ intervals

Participant 1
Participant 2

Participant 3

LUBmin

UUBmax

Source: NEA, 2018

Scalar outputs
The maximal values (as a function of time or height) are considered for each output.
A first synthesis relies on the aggregation of all participants’ results: it is based on two
different treatments. The relative uncertainty interval is first computed. For each scalar
output, the interval bounds are defined respectively by LUBmin and UUBmax divided by theaverage of all of the reference calculations. The relative uncertainty width is then the
difference between these bounds.
Moreover, it is also interesting to analyse each participant’s uncertainty result separately
and to compare them to reference data when experimental information is available. Thiscan be achieved with the formal approach of information synthesis developed by the IRSN
(Baccou and Chojnacki, 2014). This approach was introduced in Destercke and Chojnacki(2008) and already applied during the PREMIUM benchmark (NEA, 2017a). It is
composed of three steps, which are fully described in Baccou and Chojnacki (2014).

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For the purpose of this study, we only focus on:information modelling;

information evaluation.

The two steps are briefly recalled in the sequel starting from participants’ contributions,i.e. uncertainty interval ( [ LUB ,UUB ] ) and reference value ( REF ) and from LUBmin(respectively UUBmax) defined as the minimum (respectively maximum) of all LUBs
(respectively UUBs).
Information modelling - A triangular model as displayed in Figure 4.5 is associated witheach output of interest and each contribution. For a source s (i.e. a contribution) and an
output variable v, its parameterisation is denoted  s , v (t ) and defined by:1 REF  LUB (t  LUB ), if t  [ LUB , REF ],(1)
 s ,v (t )  1(t  UUB ), if t  [ REF , UUB ] REF  UUB
Figure 4.5. Information modelling associated with a source

1

LUB

REF

UUB

Source: NEA, 2018.

Information evaluation - It is achieved by computing the two following quantities:


Informativeness: this indicator measures the precision of the information. It does
not require any experimental information. It is related to the ratio between the areaof the triangle (A(T)) and the area associated to the uniform possibility defined on[LUBmin,UUBmax] (A(U)) (Figure 4.6, left panel) and that represents the complete
ignorance:
𝐼𝑣 = 1 −𝐴(𝑇)𝑈𝑈𝐵 − 𝐿𝑈𝐵
=1−
𝐴(𝑈)
2(𝑈𝑈𝐵𝑚𝑎𝑥 − 𝐿𝑈𝐵min⁡)A value close to one (respectively zero point five) therefore means that the uncertainty
range is narrow (respectively large).
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Figure 4.6. Computation of the informativeness (left) and calibration (right) indicators
associated to a given output.

1

1

LUBmin LUB

RV

UUB

π1

πexp

UUBmaxNote:𝐼𝑣 = 1 − 𝑟⁡ where r is the ratio between the area in brown and the sum of the area in brown andred, Cv is the ratio between the red triangle (intersection between participant and experimental
results) and green one (experimental result).
Source: IRSN, 2019.



Calibration: This indicator measures the agreement between information provided
by the source and experimental information (experimental value, EXP andexperimental uncertainty [LUBexp,UUBexp] in our case). Similarly to eachparticipant’s contribution, this experimental information can be represented by atriangle function of type (1) (denoted Texp) where REF, LUB and UUB are replacedby EXP, LUBexp, UUBexp respectively. The calibration indicator is then defined by
the ratio between the area of the intersection between the source and experimental
results and the area of the experimental result (Figure 4.6, right panel):𝐶𝑣 =𝐴(𝑇 ∩ 𝑇𝑒𝑥𝑝 )𝐴(𝑇𝑒𝑥𝑝 )A value close to one (respectively zero) therefore represents a high (respectively low)coherence with the experimental results.

4.2.2. Sensitivity analysis
Several approaches are available to perform sensitivity analysis (Iooss and Lemaitre, 2015).
However, their mathematical treatment follows the same steps as for uncertainty analysis:
input sampling, propagation through the evaluation model and analysis of the results
leading to qualitative insight on the most influential input parameters.
In this benchmark, the input sample comes from the random sample constructed after
uncertainty analysis and the analysis step consists of evaluating correlation coefficients.
As mentioned in the specifications, the sensitivity analyses are based on Spearman rankcorrelation coefficients (rank [Spearman’s] correlation coefficient – RCC; or partial rankcorrelation coefficient – PRCC). The most influential input parameters have been identified
for each participant, based on their calculated correlation coefficients and using a fixedsignificance threshold (to be exceeded) of 0.25.
The synthesis is achieved by averaging, for each output, the number of participants thatconsider a given parameter as influential. This short calculation has been repeated for the

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four fixed times (see Table 2.3) when the correlation coefficients were evaluated and for
maximum values, as required in the specifications. Moreover, in order to draw conclusions,for practical issues, the results have been summarised with respect to groups of outputs
corresponding to one type of behaviour (fuel thermal and mechanical behaviour, clad
thermal and mechanical behaviour, gap size, fuel-to-clad heat exchange, fission gas releaseand clad failure), following the rule that if an input parameter is influential for an output
associated with a given behaviour, it is considered as influential for the whole group.

4.3. Comparison with experimental results
This analysis is focused on the outputs for which experimental information is available.

4.3.1. Reference case vs. experimental measurements
The coolant temperature calculations and measurements during the transient are
represented in Figure 4.7 for the two axial locations (TNa1 and TNa2).
Figure 4.7. Sodium temperature TNa1 (z=25 cm/BFC) and TNa2 (z=47 cm/BFC)

Source: IRSN, 2019.

The experimental measurement general trend was well caught by all of the participants.
The coolant temperature increase was nevertheless too quick and too large for a majorityof the participants.
The dispersion of reference calculations at the beginning of the transient and on the peaktemperature (~90°C) is large, especially for TNa2, which is measured at a higher axial
location: the forced convection in sodium coolant is probably not correctly computed forsome codes. In the second phase (time >1 s), the dispersion is rather low (< 20°C).
As shown in Figure 4.8, there is some dispersion of the clad permanent hoop strain
calculations with a ratio of two between the highest (~0.5%) and the lowest values(~0.25%). Nevertheless, even if participants’ calculations slightly underestimated themeasurements, the calculations are consistent and close to the lower bound of themeasurements.

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Figure 4.8. Clad permanent hoop strain at the end of the transient as a function of axial
location

Source: IRSN, 2019.

There is a good agreement between calculations and measurements for the clad elongation(Figure 4.9): the calculations are rather dispersed, but remain in the uncertainty band forall participants almost all along the transient.
Figure 4.9. Clad elongation as a function of time

Source: IRSN, 2019.

As already observed in Phase I, the fission gas release calculations are strongly dispersed,
with one order of magnitude between the highest and the lowest evaluations (Figure 4.10).
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Only one of the participants calculated a final FGR inside the experimental uncertainty
band.
Figure 4.10. Fission gas release calculation as a function of time and measurements after thetest

Source: IRSN, 2019.

4.3.1. Uncertainty results vs. experimental measurements
This section is devoted to a comparison of the participants’ contributions, taking into
account the uncertainties on input data. See above for a description of the synthesis method.
Time/height trend output
The uncertainty interval width calculated by every participant for TNa1 and TNa2 isrepresented in Figure 4.11.
Except for one participant, the uncertainty interval widths are very similar for allparticipants and very low after 1.5 s.
Figure 4.11 Uncertainty interval widths for sodium coolant temperatures TNa1 and TNa2

Source: IRSN, 2019.

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The position of the average experimental measurement in the uncertainty band (r exp) ispresented in Figure 4.12 for sodium temperature at the two axial locations (TNa1 andTNa2) between 0.4 s (beginning of power pulse) and 1.5 s. We recall that the value of rexp
is between zero and one when the measurement is inside the uncertainty band. Even with
the input data uncertainty propagation, participants had difficulties to catch the very
beginning of the sodium heat-up; nevertheless, after 0.5 s, the agreement between
calculations and measurements is good (rexp between or very close to [0;1] interval).
Figure 4.12. Position of the experimental value within the uncertainty band (r exp) for TNa1
(left) and TNa2 (right)

Source: IRSN, 2019.

The impact of input data uncertainty on the clad hoop strain as a function of axial height(ETZ) is illustrated in Figure 4.13.
Figure 4.13. Clad residual hoop strain UUB (left) and LUB (right) for all participants as afunction of axial height

Note: ETZ: clad residual hoop strain; UUB: upper uncertainty bound; LUB: lower uncertainty bound.
Source: IRSN, 2019.

The average measurement is bounded by the LUB and the UUB, i.e. rexp is between [0;1],
for almost all participants along the entire axial height, as illustrated in Figure 4.14.

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Figure 4.14. rexp value for clad residual hoop strain as a function of axial heightSource: IRSN, 2019.

The effect on uncertainty of input data on clad elongation (ECT) is shown in Figure 4.15.
Figure 4.15. UUB and LUB for all participants (left) and position of the experimental value
within the uncertainty band (rexp) (right) for clad total axial elongation

Source: IRSN, 2019.

Globally, considering the uncertainty around input data for the calculations and theexperimental measurement uncertainties, there is a good agreement between thecalculations and the measurements.
Scalar output
Figure 4.16 displays the average of participants’ calibration indicator value for each output(maximal value of TNa1, TNa2, ECT and ETZ). It can first be noticed that this indicator isstrictly positive, meaning that, on average, the intersection between simulation andexperimental results is not empty. However, the agreement depends on the output. The
strongest one is associated to clad hoop strain evaluation, then to the group (TNa1, TNa2,
ECT) and finally, the lowest one corresponds to the FGR.

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Figure 4.16. Average calibration indicator value for each output

Note: ECT: clad total axial elongation; ETZ: clad residual hoop strain; FGR: fission gas release.
Source: IRSN, 2019.

It is also interesting to analyse each participant’s contribution separately. Figure 4.17
provides two types of graphical representation for each scalar output.
Figure 4.17. Comparison of participants’ contribution with experimental results
based on a qualitative graphical comparison (left) and on thecomputation of information evaluation indicators (right)

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Figure 4.17. Comparison of participants’ contribution with experimental results
based on a qualitative graphical comparison (left) and on thecomputation of information evaluation indicators (right) (Continued)

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Figure 4.17. Comparison of participants’ contribution with experimental results
based on a qualitative graphical comparison (left) and on thecomputation of information evaluation indicators (right) (Continued)

Note: ECT: clad total axial elongation; ETZ: clad residual hoop strain; FGR: fission gas release.
Source: IRSN, 2019.

Concerning sodium temperatures, a dispersion between reference calculations is noticeable(~ 50°C for TNa1 and ~ 90°C for TNa2). As a result, at most half of the participants’reference calculation falls inside the experimental interval for these outputs. Taking into
account uncertainty makes it possible to improve the results with a non-empty intersection
for a majority of the participants. However, the uncertainty interval widths are also
dispersed (from 0.01°C to 50°C for TNa1 and from 10°C to 70°C for TNa2), which leads
to the low average calibration indicator value already noticed on Figure 4.16.
When focusing on clad mechanical behaviour, ECT and ETZ, all clad elongation reference
calculations are encompassed by the experimental uncertainty interval while less than 50%
are for residual hoop strain reference calculations. When adding the uncertainty result, theintersection with the experimental interval is non-empty for both outputs, leading to ahigher coherence between participants’ contributions compared to sodium temperatures.
However, it is important to mention that, contrary to ETZ, the uncertainty interval widthfor ECT is always smaller than the width of the experimental one. As a result, ETZ results
are better calibrated on average than ECT ones.
Figure 4.17 also shows that, for sodium temperatures, the highest calibration is not obtained
for the lowest informativeness (i.e. the largest uncertainty bands). It is not the case for ECT
and ETZ, where a negative trend between calibration and informativeness is noticeable,
indicating that a large uncertainty band (low informativeness) is more likely to encompass
the experimental value (high calibration).
Finally, there is a very low coherence for the FGR. This can be explained by the dispersionof reference calculations and narrow uncertainty intervals for a majority of the participants.

4.4. Additional analysis of uncertainty results
This section is devoted to the analysis without taking account of experimental results. It
therefore concerns all of the outputs.

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4.4.1. Time trend outputs
Some time trend outputs are presented in Figures 4.18-4.24.
As in the RIA benchmark Phase II, the fuel thermal outputs (DHR, temperature of fuelcentreline [TFC], maximum fuel temperature as function time [TFM] and temperature offuel outer surface [TFO]) are consistent for all participants during the transient. As an
example, the reference calculations for enthalpy variation (DHR) are represented in
Figure 4.18. The dispersion on maximal enthalpy increase is about five cal/g. Except for
one participant, there is also a good consistency on the uncertainty interval widths.
Figure 4.18. Enthalpy increase as a function of time: Reference calculations and uncertainty
interval widths for all participants

Source: IRSN, 2019.

Regarding the cladding thermal behaviour (Figure 4.19), the clad inner temperature (TCI)
is more consistent between participants than the clad outer temperature (TCO). Thisbehaviour is probably explained by clad-to-coolant heat exchange. The modelling of thisquantity is different between the codes.
Figure 4.20 gathers the reference calculations, the uncertainty interval widths and thereference calculation dispersion for the fuel elongation (EFT). Contrary to the DHR, thereis quite a large dispersion of the reference calculations and uncertainty interval widths forthis output. It is worth noting that there is already a discrepancy on the initial fuel elongation
before the transient. This difference between the codes is greater than for the fresh fuel casestudied during Phase II.
As illustrated in Figure 4.20 (right panel), the reference calculation dispersion is close to
the total uncertainty width and larger than any uncertainty band width provided by allparticipants. The code effect is very significant for this output.

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Figure 4.19. Clad inner and outer temperature calculations: Reference cases

Source: IRSN, 2019.

Figure 4.20. Fuel elongation reference calculations (left) – participants’ uncertainty interval
widths, global uncertainty width and reference calculation dispersion (right)

Source: IRSN, 2019.

The clad hoop stress reference calculations and interval widths have the same time trend
for all participants, but with significantly different maximal values, in particular for theuncertainty band width (Figure 4.21). This difference on the maximum value has been
identified as a result of different yield stress models in the codes.
Figure 4.21. Clad hoop stress reference calculations and uncertainty interval widths

Source: IRSN, 2019.

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Regarding the fuel-to-clad heat exchange coefficient, both the reference calculations andthe uncertainty band widths are really dispersed with different time trends (Figure 4.22).
This result is probably partially linked to the gap width evolutions that are also significantly
dispersed between the participants (Figure 4.23).
Figure 4.22. Fuel-to-clad heat exchange coefficient reference calculations
and uncertainty interval widths

Source: IRSN, 2019.

Figure 4.23. Gap width reference calculations and uncertainty interval widths

Source: IRSN, 2019.

Only six participants provided a clad failure prediction. As shown in Figure 4.24, thedispersion on reference calculations and on uncertainty interval widths is very large.

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Figure 4.24. Clad failure prediction/reference calculations and uncertainty interval widths

Source: IRSN, 2019.

4.4.1. Scalar output
Figure 4.25 displays the relative uncertainty interval for each output.
Figure 4.25. Relative uncertainty interval for each output

Source: IRSN, 2019.

The results show that the relative uncertainty width depends on the type of parameter
observed. More precisely, the narrowest intervals are obtained for fuel and fluid thermal
behaviour outputs (DHR, TFC, TFM, TNa1, TNa2 and TFO to a lesser extent). The
uncertainty width increases slightly for clad thermal outputs (TCI, TCO), then moresignificantly for fuel and clad mechanical ones (EFT, fuel outer radius [RFO], ECT, ECTH,
clad hoop stress at outer part of the clad [SCH]). Among clad mechanical outputs, a large
relative uncertainty width can be observed for the ETZ and a similar conclusion also holds
for the fuel-clad gap width (GAP), the FGR, the fuel-to-clad heat exchange coefficient(HFC) and the clad failure prediction (CFP).

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The relative uncertainty interval was also studied in Phase II (see Figure 4.26 extracted
from the Phase II report). Even if some outputs are different, it appears that, as for fresh
fuel, the relative uncertainty width is lower for fuel thermal outputs. Moreover, there areglobally larger relative uncertainties for irradiated fuels.
To continue the analysis of the relative uncertainty, Figure 4.27 plots the relative dispersionof reference calculations, which is defined as the difference between the maximum and theminimum of all reference calculations divided by the average of all reference calculations
versus the relative uncertainty width (difference between maximal and minimal relative
uncertainty bounds). The same magnitude is observed for the relative uncertainty widthand for the relative reference calculation dispersion. Moreover, the results are clusteredwith respect to the type of behaviour considered. The smallest relative uncertainty widthand relative dispersion are associated with thermal outputs. They then increase whenmoving to mechanical outputs.
Figure 4.26. Relative uncertainty interval for each output in Phase II

Note: DHR: variation of radial average enthalpy: TFC: temperature of fuel centreline: TFO: temperature of fuelouter surface; TCO: temperature of clad outer surface; ECTH: clad total (thermal + elastic + plastic) hoop strain;
SCH: clad hoop stress at outer part of the clad; EFT: fuel column total axial elongation; ECT: clad total axial
elongation; RFO: fuel outer radius.
Source: IRSN, 2019.

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Figure 4.27. Relative dispersion of reference calculations vs. relative uncertainty width

Note: CFP: clad failure prediction; DHR: variation of radial average enthalpy: ECT: clad total axial elongation;
ECTH: clad total (thermal + elastic + plastic) hoop strain; EFT: fuel column total axial elongation; EINJ:
injected energy (radial averaged); ETZ: clad residual hoop strain; FGR: fission gas release; GAP: fuel-clad gap
width; HFC: fuel-to-clad heat exchange coefficient RFO: fuel outer radius; TCI: temperature of clad innersurface; TCO: temperature of clad outer surface; TFC: temperature of fuel centreline; TFM: maximum fueltemperature; TFO: temperature of fuel outer surface; SCH: clad hoop stress at outer part of the clad.
Source: IRSN, 2019.

It is also interesting to analyse the coherence between participants’ contributions for each
output. Figures 4.28-4.32 provide uncertainty interval and reference calculation values foreach participant with respect to the type of outputs.
Figure 4.28. Uncertainty results and reference calculation values for fuel thermal outputs

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Figure 4.28. Uncertainty results and reference calculation values for fuel thermal outputs(Continued)

Note: DHR: variation of radial average enthalpy: TFC: temperature of fuel centreline: TFM: maximum fueltemperature; TFO: temperature of fuel outer surface.
Source: IRSN, 2019.

As already observed, there is a quite good consistency between participants both onreference calculation value and uncertainty interval width for the fuel thermal output,
except for the fuel outer temperature. This last value is linked to the fuel thermal behaviour,
but also to the HFC.
Figure 4.29. Uncertainty results and reference calculation values for the fuel-to-clad heatexchange and the fuel-clad gap

Note: HFC: fuel-to-clad heat exchange coefficient; GAP: fuel-clad gap width.
Source: IRSN, 2019.

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Figure 4.30. Uncertainty results and reference calculation values for clad and fluid thermal
outputs

Note: TCI: temperature of clad inner surface; TCO: temperature of clad outer surface.
Source: IRSN, 2019.

Figure 4.31. Uncertainty results and reference calculation values for fuel and cladmechanical outputs

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Figure 4.31. Uncertainty results and reference calculation values for fuel and cladmechanical outputs (Continued)

Note: EFT: fuel column total axial elongation; RFO: fuel outer radius; ECT: clad total axial elongation; ECTH:
clad total (thermal + elastic + plastic) hoop strain; ETZ: clad residual hoop strain; SCH: clad hoop stress atouter part of the clad.
Source: IRSN, 2019.

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Figure 4.32. Uncertainty results and reference calculation values for the fuel-clad gap,
fuel-to-clad heat exchange, fission gas release and clad failure prediction

Note: GAP: fuel-clad gap width; HFC: fuel-to-clad heat exchange coefficient; FGR: fission gas release; CFP:
clad failure prediction.
Source: IRSN, 2019.

It appears that the results are highly conflicting if all participants’ contributions are taken
into account (i.e. empty intersection of all uncertainty intervals) except for the DHR, theTFM and the ETZ. However, an empty intersection can be due to a single contribution andfurther qualitative analysis is required. A closer look at the previous figures reveals that thecoherence between participants depends on the type of outputs. This point had already been
observed in the RIA benchmark Phase II. More precisely, the uncertainty results exhibit
four main levels of coherence:High coherence: includes participants’ results that are, for a large majority, inagreement as regards to the uncertainty interval width and reference calculation. It
corresponds to fuel thermal behaviour outputs, except the TFO.



Medium coherence: concerns participants’ results exhibiting coherent uncertainty
interval width for a large majority, but with dispersion in the reference calculations
due to a few participants’ contributions. This is the case for fuel and cladmechanical behaviour output except for the SCH.

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

Low coherence: corresponds to participants’ results exhibiting dispersion for bothreference calculation and uncertainty interval width. This is the case for the TFO,
the SCH, GAP as well as for clad and fluid thermal outputs.



No coherence: this last level is associated with large dispersion for both reference
calculation and uncertainty interval width. It includes the remaining outputs: theHFC, the FGR and the CFP.

Only three levels of coherence were introduced in the Phase II report. In Phase III, fourlevels are defined in order to take account of the results associated with the extra outputs
HFC, FGR and CFP that exhibit strong disagreement. However, for the outputs consideredin both phases, the same coherence ranking has been found.

4.5. Sensitivity analysis
The most influential input parameters have been identified for each participant, based on
the correlation coefficients they calculated and using a fixed significance threshold of 0.25.
The synthesis methodology was recalled above.
Tables 4.1-4.5 summarise the results in terms of percentage of participants with respect togroups of outputs corresponding to a type of behaviour. We recall the followed rule: if an
input parameter is found to be influential for an output associated with a given behaviour,
it is considered as influential for the whole group. A dark blue cell in the tables means that
more than 50% of the participants identified the corresponding input parameter as
influential for the type of behaviour.
At the beginning of power pulse (t1):

Before the transient, there is a strong agreement on influential parameters (very high orvery low percentage). The state of the rod, before the energy injection, depends only on a
few input parameters, mainly the initial fuel-to-clad radial gap, the fuel and clad thermalexpansion (Table 4.1).

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT52  NEA/CSNI/R(2020)10
Table 4.1. Influential input parameters with respect to the type of behaviour when focusing
on the beginning of power pulse

Fuel-to-clad radial
gap
Cladding roughness
Fuel roughness
Zirconia thickness
Injected energy in therod
Radial power profile
Power pulse width
Fuel thermal
conductivity model
Fuel thermalexpansion model
Fuel enthalpy
Clad thermalexpansion
Clad yield stress

Fuel thermal(DHR, TFC,
TFM, TFO)

Cladthermal(TCI, TCO)

Fluid thermal(TNa1, TNa2)

Fuelmechanical(EFT, RFO)

GAP

HFC

FGR

CFP

37.5%

Clad
mechanical(ECT, ECTH,
SCH)
87.5%

37.5%

12.5%

14.3%

87.5%

62.5%

28.6%

60.0%

30.0%
0.0%
25.0%
30.0%

10.0%
0.0%
33.3%
20.0%

11.1%
0.0%
25.0%
11.1%

0.0%
0.0%
0.0%
0.0%

10.0%
0.0%
66.7%
0.0%

10.0%
0.0%
0.0%
0.0%

60.0%
50.0%
0.0%
0.0%

0.0%
0.0%
0.0%
0.0%

16.7%
0.0%
0.0%
0.0%

25.0%
66.7%
60.0%

12.5%
55.6%
10.0%

14.3%
37.5%
11.1%

0.0%
37.5%
10.0%

0.0%
44.4%
10.0%

0.0%
0.0%
10.0%

0.0%
0.0%
10.0%

0.0%
0.0%
0.0%

0.0%
20.0%
0.0%

30.0%

10.0%

0.0%

80.0%

50.0%

90.0%

70.0%

0.0%

33.3%

11.1%
0.0%

0.0%
0.0%

0.0%
0.0%

0.0%
10.0%

10.0%
50.0%

0.0%
60.0%

10.0%
50.0%

0.0%
0.0%

0.0%
33.3%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

Notes: DHR: variation of radial average enthalpy; TFC: temperature of fuel centreline; TFM: maximum fueltemperature; TFO: temperature of fuel outer surface; TCI: temperature of clad inner surface; TCO: temperatureof clad outer surface; EFT: fuel column total axial elongation; RFO: fuel outer radius; ECT: clad total axial
elongation; ECTH: clad total (thermal + elastic + plastic) hoop strain; SCH: clad hoop stress at outer part of theclad; GAP: fuel-to-clad gap width; HFC: fuel-to-clad heat exchange coefficient; FGR: fission gas release; CFP:
clad failure prediction.
A dark blue cell in the tables means that more than 50% of the participants have identified the corresponding
input parameter as influential for the type of behaviour.

At the time of pulse maximum power (t2):There is less agreement among participants at the pulse maximum power time than before
the pulse. Injected energy and initial gap are identified as influential for most of the outputs.
Fuel enthalpy and thermal-expansion models, zirconia thickness, fuel and clad roughness,
power profile and pulse width are also influential for several thermal and mechanicaloutputs. These last outcomes are consistent with what was reported by the RIA benchmark
Phase II.
As in Phase II, at time t2, the fuel thermal conductivity has a low impact on fuel thermal
behaviour because the fuel behaviour is close to adiabaticity during the power pulse firstpart.
The GAP output has no influential input parameters because at the time of pulse maximal
power the gap is closed, whatever the case. Consequently, the sole influential parameterson the fuel-to-clad heat exchange are the fuel and clad roughness.

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  53

Table 4.2 Influential input parameters with respect to the type of behaviour when focusing
on the time of pulse maximum power

Fuel-clad radial
gap
Claddingroughness
Fuel roughness
Zirconia thickness
Injected energy inthe rod
Radial power
profilePower pulse width
Fuel thermal
conductivity model
Fuel thermalexpansion model
Fuel enthalpy
Clad thermalexpansion
Clad yield stress

Fuel thermal(DHR, TFC,
TFM, TFO)

Cladthermal(TCI, TCO)

Fluid thermal(TNa1, TNa2)

Fuelmechanical(EFT, RFO)

GAP

HFC

FGR

CFP

85.7%

Clad
mechanical(ECT, ECTH,
SCH)
87.5%

50.0%

62.5%

57.1%

28.6%

37.5%

37.5%

100.0%

60.0%

60.0%

44.4%

11.1%

20.0%

11.1%

60.0%

20.0%

33.3%

50.0%
11.1%
100.0%

50.0%
77.8%
80.0%

37.5%
75.0%
66.7%

12.5%
0.0%
80.0%

12.5%
44.4%
80.0%

0.0%
0.0%
0.0%

50.0%
11.1%
40.0%

12.5%
0.0%
50.0%

0.0%
50.0%
66.7%

75.0%

75.0%

85.7%

25.0%

37.5%

0.0%

37.5%

37.5%

0.0%

66.7%
30.0%

66.7%
40.0%

75.0%
11.1%

50.0%
11.1%

44.4%
10.0%

12.5%
0.0%

22.2%
20.0%

44.4%
0.0%

20.0%
0.0%

0.0%

20.0%

22.2%

100.0%

100.0%

11.1%

10.0%

10.0%

83.3%

90.0%
0.0%

20.0%
0.0%

0.0%
0.0%

66.7%
33.3%

50.0%
40.0%

0.0%
11.1%

0.0%
0.0%

40.0%
0.0%

50.0%
33.3%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

Notes: DHR: variation of radial average enthalpy; TFC: temperature of fuel centreline; TFM: maximum fueltemperature; TFO: temperature of fuel outer surface; TCI: temperature of clad inner surface; TCO: temperatureof clad outer surface; EFT: fuel column total axial elongation; RFO: fuel outer radius; ECT: clad total axial
elongation; ECTH: clad total (thermal + elastic + plastic) hoop strain; SCH: clad hoop stress at outer part of theclad; GAP: fuel-clad gap width; HFC: fuel-to-clad heat exchange coefficient; FGR: fission gas release; CFP:
clad failure prediction.
A dark blue cell in the tables means that more than 50% of the participants have identified the corresponding
input parameter as influential for the type of behaviour.

At the end of power pulse (t3):At the end of the power pulse, injected energy is still identified as a very influential input.
The initial zirconia thickness and radial power profile and the fuel enthalpy are also very
influential parameters.
The fuel thermal conductivity model is now identified as influential for fuel and clad outer
temperature and clad stress. The fuel-to-clad initial gap has a strong influence on the fueland clad mechanical behaviour and clad failure prediction.

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT54  NEA/CSNI/R(2020)10
Table 4.3. Influential input parameters with respect to the type of behaviour when focusing
on the end of power pulse

Fuel-clad radial
gap
Claddingroughness
Fuel roughness
Zirconia
thickness
Injected energy
in the rod
Radial power
profilePower pulse
width
Fuel thermal
conductivity
model
Fuel thermalexpansion model
Fuel enthalpy
Clad thermalexpansion
Clad yield stress

Fuel thermal(DHR, TFC,
TFM, TFO)

Cladthermal(TCI, TCO)

Fluid thermal(TNa1, TNa2)

Fuelmechanical(EFT, RFO)

GAP

HFC

FGR

CFP

71.4%

Clad
mechanical(ECT, ECTH,
SCH)
87.5%

12.5%

25.0%

14.3%

14.3%

37.5%

37.5%

60.0%

60.0%

50.0%

44.4%

30.0%

40.0%

11.1%

60.0%

10.0%

33.3%

50.0%
77.8%

37.5%
77.8%

37.5%
37.5%

12.5%
75.0%

25.0%
66.7%

0.0%
0.0%

50.0%
55.6%

12.5%
22.2%

0.0%
83.3%

100.0%

80.0%

88.9%

100.0%

90.0%

11.1%

30.0%

80.0%

50.0%

75.0%

62.5%

85.7%

57.1%

62.5%

0.0%

12.5%

25.0%

60.0%

33.3%

33.3%

50.0%

22.2%

33.3%

0.0%

22.2%

44.4%

0.0%

80.0%

80.0%

100.0%

50.0%

60.0%

0.0%

30.0%

20.0%

33.3%

0.0%

0.0%

10.0%

100.0%

100.0%

0.0%

20.0%

50.0%

50.0%

100.0%
0.0%

50.0%
0.0%

60.0%
0.0%

80.0%
11.1%

70.0%
20.0%

0.0%
0.0%

30.0%
0.0%

60.0%
0.0%

66.7%
16.7%

11.1%

0.0%

0.0%

55.6%

66.7%

0.0%

22.2%

11.1%

20.0%

Notes: DHR: variation of radial average enthalpy; TFC: temperature of fuel centreline; TFM: maximum fueltemperature; TFO: temperature of fuel outer surface; TCI: temperature of clad inner surface; TCO: temperatureof clad outer surface; EFT: fuel column total axial elongation; RFO: fuel outer radius; ECT: clad total axial
elongation; ECTH: clad total (thermal + elastic + plastic) hoop strain; SCH: clad hoop stress at outer part of theclad; GAP: fuel-clad gap width; HFC: fuel-to-clad heat exchange coefficient; FGR: fission gas release; CFP:
clad failure prediction.
A dark blue cell in the tables means that more than 50% of the participants have identified the corresponding
input parameter as influential for the type of behaviour.

At the end of calculation (t4):Similar to the time t3, the injected energy is still influential (for a large majority ofparticipants) for every output. It is also important to point out that the fuel properties(enthalpy, conductivity and thermal-expansion model) have some effects on the final stateof the rod (clad hoop strain, fuel and clad elongation).

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  55

Table 4.4. Influential input parameters with respect to the type of behaviour when focusing
on the end of the calculation

Fuel-clad radial
gap
Claddingroughness
Fuel roughness
Zirconia thickness
Injected energy inthe rod
Radial power
profilePower pulse width
Fuel thermal
conductivity model
Fuel thermalexpansion model
Fuel enthalpy
Clad thermalexpansion
Clad yield stress

Fuel thermal(DHR, TFC,
TFM, TFO)

Cladthermal(TCI, TCO)

Fluid thermal(TNa1, TNa2)

Fuelmechanical(EFT, RFO)

GAP

HFC

FGR

CFP

62.5%

Clad
mechanical(ECT, ECTH,
SCH)
87.5%

25.0%

12.5%

25.0%

12.5%

25.0%

25.0%

60.0%

40.0%

30.0%

30.0%

30.0%

10.0%

10.0%

20.0%

10.0%

33.3%

37.5%
55.6%
90.0%

25.0%
66.7%
80.0%

25.0%
50.0%
77.8%

12.5%
50.0%
80.0%

12.5%
55.6%
90.0%

0.0%
66.7%
100.0%

37.5%
55.6%
90.0%

12.5%
22.2%
80.0%

0.0%
50.0%
83.3%

37.5%

12.5%

14.3%

50.0%

25.0%

25.0%

37.5%

37.5%

40.0%

44.4%
60.0%

33.3%
40.0%

44.4%
55.6%

22.2%
40.0%

44.4%
10.0%

22.2%
0.0%

33.3%
0.0%

44.4%
30.0%

20.0%
33.3%

70.0%

50.0%

55.6%

90.0%

100.0%

100.0%

80.0%

40.0%

66.7%

30.0%
10.0%

20.0%
0.0%

22.2%
0.0%

40.0%
11.1%

70.0%
30.0%

70.0%
30.0%

50.0%
10.0%

40.0%
0.0%

50.0%
33.3%

33.3%

11.1%

11.1%

22.2%

55.6%

44.4%

44.4%

0.0%

0.0%

Notes: DHR: variation of radial average enthalpy; TFC: temperature of fuel centreline; TFM: maximum fueltemperature; TFO: temperature of fuel outer surface; TCI: temperature of clad inner surface; TCO: temperatureof clad outer surface; EFT: fuel column total axial elongation; RFO: fuel outer radius; ECT: clad total axial
elongation; ECTH: clad total (thermal + elastic + plastic) hoop strain; SCH: clad hoop stress at outer part of theclad; GAP: fuel-clad gap width; HFC: fuel-to-clad heat exchange coefficient; FGR: fission gas release; CFP:
clad failure prediction.
A dark blue cell in the tables means that more than 50% of the participants have identified the corresponding
input parameter as influential for the type of behaviour.



For the maximum value of each output of interest

As regards the maximum value of every output, the most influential input parameters havebeen identified not only with respect to the type of behaviour considered, as gathered inTable 4.5, but also on each individual output, as gathered in Table 4.6. Table 4.6 is to becompared with Table 4.9 of the Phase II report (NEA, 2017).

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT56  NEA/CSNI/R(2020)10
Table 4.5. Influential input parameters with respect to the type of behaviour when focusing
on the maximum value of each output

Fuel-clad radial
gap
Claddingroughness
Fuel roughness
Zirconia
thickness
Injected energy
in the rod
Radial power
profilePower pulse
width
Fuel thermal
conductivity
model
Fuel thermalexpansion model
Fuel enthalpy
Clad thermalexpansion
Clad yield stress

Fuel thermal(DHR, TFC,
TFM, TFO)

Cladthermal(TCI, TCO)

Fluid thermal(TNa1, TNa2)

Fuelmechanical(EFT, RFO)

GAP

HFC

FGR

CFP

71.4%

Clad
mechanical(ECT, ECTH,
SCH)
87.5%

37.5%

25.0%

14.3%

25.0%

50.0%

25.0%

100.0%

60.0%

60.0%

55.6%

30.0%

30.0%

10.0%

60.0%

10.0%

50.0%

50.0%
55.6%

50.0%
77.8%

50.0%
75.0%

12.5%
62.5%

12.5%
88.9%

0.0%
66.7%

50.0%
11.1%

12.5%
22.2%

25.0%
50.0%

100.0%

100.0%

88.9%

100.0%

90.0%

100.0%

10.0%

80.0%

83.3%

87.5%

75.0%

85.7%

71.4%

37.5%

25.0%

25.0%

37.5%

60.0%

77.8%

44.4%

50.0%

33.3%

33.3%

11.1%

11.1%

44.4%

20.0%

70.0%

70.0%

88.9%

10.0%

20.0%

0.0%

10.0%

30.0%

66.7%

0.0%

0.0%

0.0%

100.0%

100.0%

100.0%

30.0%

30.0%

83.3%

100.0%
0.0%

40.0%
0.0%

50.0%
0.0%

80.0%
11.1%

80.0%
30.0%

70.0%
40.0%

0.0%
10.0%

50.0%
0.0%

83.3%
50.0%

0.0%

0.0%

0.0%

33.3%

66.7%

44.4%

0.0%

0.0%

40.0%

Notes: DHR: variation of radial average enthalpy; TFC: temperature of fuel centreline; TFM: maximum fueltemperature; TFO: temperature of fuel outer surface; TCI: temperature of clad inner surface; TCO: temperatureof clad outer surface; EFT: fuel column total axial elongation; RFO: fuel outer radius; ECT: clad total axial
elongation; ECTH: clad total (thermal + elastic + plastic) hoop strain; SCH: clad hoop stress at outer part of theclad; GAP: fuel-clad gap width; HFC: fuel-to-clad heat exchange coefficient; FGR: fission gas release; CFP:
clad failure prediction.
A dark blue cell in the tables means that more than 50% of the participants have identified the corresponding
input parameter as influential for the type of behaviour.

An analysis of these two tables allows the following conclusions to be drawn:

The injected energy is the most influential input parameter: it is considered
influential by a large majority of participants for 16 out of the 17 outputs.

Input data related to the end-of-life state (zirconia thickness, radial power profile,
gap size, roughness) are also very influential.

Fuel physical properties, thermal-expansion and thermal conductivity models havea significant impact on the rod mechanical and thermal behaviours.

Regarding the fission gas release, except for injected energy, participants did not
identify any common influential input parameter.



The clad failure evaluation is the most sensitive output data (9 influential input
parameters out of the 12 studied here).

The clad physical properties (thermal-expansion and yield stress) have little impact
on the outputs.



It is worth noting that some outputs classified under the same behaviour type do
not always have the same influential parameters (for instance, DHR and TFC).
REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORTNEA/CSNI/R(2020)10  57

Table 4.6. Percentage of participants that have identified a given input parameter as
influential for the maximum value of each output of interest
DHR TFC TFM TFO TCI TCO TNa1 TNa2 ECTH ECT EFT SCH RFO GAP HFC
Fuel-clad radial
13% 0% 13% 38% 13% 25% 13% 14% 88% 88% 71% 88% 50% 25% 50%
gap
Cladding
50% 10% 30% 60% 60% 60% 50% 56% 30% 10% 0% 30% 30% 10% 60%
roughness
Fuel roughness 38% 0% 25% 50% 50% 50% 50% 38% 13% 13% 13% 13% 13% 0% 50%
Zirconia
56% 0% 33% 33% 78% 78% 67% 75% 33% 56% 63% 89% 22% 67% 11%
thickness
Injected energy
100% 100% 100% 90% 100% 80% 80% 89% 90% 90% 89% 50% 100% 100% 10%
in the rod
Radial power
88% 75% 63% 75% 75% 75% 75% 86% 25% 38% 71% 38% 25% 25% 25%
profilePower pulse
78% 33% 78% 56% 44% 44% 44% 50% 33% 33% 13% 22% 33% 11% 11%
widthFuel thermal
conductivity
50% 10% 70% 30% 50% 70% 80% 89% 10% 20% 0% 10% 10% 0% 10%
model
Fuel thermalexpansion
0% 0% 0% 0% 0% 0% 0% 0% 90% 100% 100% 100% 100% 100% 30%
model
Fuel enthalpy
40% 100% 80% 50% 40% 40% 50% 44% 80% 70% 78% 40% 80% 70% 0%
Clad thermal0% 0% 0% 0% 0% 0% 0% 0% 20% 30% 11% 10% 0% 40% 10%
expansion
Clad yield
0% 0% 0% 0% 0% 0% 0% 0% 0% 33% 33% 67% 0% 44% 0%
stressFGR CFP
25% 100%
10% 50%13% 25%22% 50%80% 83%
38% 60%44% 20%30% 67%

30% 83%
50% 83%
0%

50%

0%

40%

The darker blue is associated with a percentage greater than 50%, lighter blue with a percentage between 0% and 50%
and white with 0%.

References
Baccou, J. and E. Chojnacki (2014), “A practical methodology for information fusion in presence of
uncertainty: Application to the analysis of a nuclear benchmark”, Environment Systems andDecisions, Vol. 34/2, pp. 237-248, https://doi.org/10.1007/s10669-014-9496-3.
Destercke, S. and E. Chojnacki (2008), “Methods for the evaluation and synthesis of multiple sources of
information applied to nuclear computer codes”, Nuclear Engineering and Design, Vol. 238/9,
pp. 2484-2493, https://doi.org/10.1016/j.nucengdes.2008.02.003.
Iooss, B. and P. Lemaitre (2015), “A review on global sensitivity analysis methods”, in Meloni, C. and
G. Dellino (eds.), Uncertainty Management in Simulation-Optimisation of Complex Systems:
Algorithms and Applications, Springer.
NEA (2017a), “Reactivity-Initiated Accident (RIA) Fuel-Codes Benchmark Phase II: Uncertainty andSensitivity Analyses”, NEA/CSNI/R(2017)1, OECD Publishing, Paris, https://www.oecdnea.org/jcms/pl_19762.
NEA (2017b), “Post-BEMUSE Reflood Model Input Uncertainty Methods (PREMIUM) Benchmark:Final Report”, NEA/CNSI/R(2016)18, OECD Publishing, Paris, www.oecd-nea.org/jcms/pl_19752.

REACTIVITY INITIATED ACCIDENT BENCHMARK PHASE III REPORT58  NEA/CSNI/R(2020)10

5. Conclusions and recommendations

The third phase of the WGFS RIA fuel codes benchmark focused on the uncertainty
assessment of the calculation results for the irradiated case CIP0-1. The objective was toevaluate the impacts of the initial state and key models on the results during and after thetransient in order to study the influence of the transient code, not the modelling of the baseirradiation code. In addition, a sensitivity study was performed to identify or confirm themost influential input parameters.
Ten organisations representing nine countries participated in the RIA benchmark Phase III.
For the uncertainty analysis, they provided the lower and upper bounds associated withspecified output parameters; for the sensitivity analysis, they provided the partial rankcorrelation coefficients associated with each uncertain input for each specified output
parameter at each specified time, including for their maximum values.
In terms of transient computer codes used, the spectrum was large as analyses were
performed with ALCYONE, FALCON, FRAPTRAN, RANNS, SCANAIR, TESPA-ROD
and TRANSURANUS.
The specifications of the RIA benchmark Phase III decoupled steady-state and transient
simulations. Some codes have been developed to perform both base irradiation andtransient calculations, which can ensure continuity between the two phases but makes it
more difficult to perform the decoupling. Their users therefore had difficulty matching the
pre-transient state defined in the specifications. More precisely, participants that usually do
not use FRAPCON to evaluate the rod state after base irradiation had difficulty initialising
their transient calculations according to FRAPCON outcomes, which somewhat biased thecomparison among all the participants’ results.
The statistical study included not only input parameters already identified for fresh fuel,but also extra “irradiation parameters” such as zirconia thickness, power profile, initialfuel-to-clad gap.
The uncertainty analysis has led to the following main conclusions:

The experimental results (time/height trend and scalar values) were well caught by
most of the participants, except for fission gas release.

The strongest agreement with experimental measurements was associated to theevaluation of clad hoop strain and clad elongation, then sodium temperatures.

The maximum (relative) uncertainty band width depends on the type of outputs. As
in Phase II, the narrowest intervals are obtained for fuel thermal outputs. The
uncertainty interval width increases slightly for clad thermal outputs, then moresignificantly for fuel and clad mechanical ones. Finally, a large uncertainty wasobserved for the new outputs (that were not considered in Phase II) fuel-clad gap
width, fission gas release, fuel-to-clad heat exchange coefficient and clad failure
prediction.



The same magnitude was observed for the relative uncertainty width and forreference calculation dispersion for numerous outputs.

When comparing participants’ uncertainty results for outputs considered inPhase II, the coherence ranking is the same. These are, from the highest coherence

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to the lowest: 1) fuel thermal outputs (except temperature of fuel outer surface);2) fuel and clad mechanical outputs (except clad hoop stress at the outer part of theclad); 3) temperature of fuel outer surface, clad hoop stress at outer part of the clad,
fuel-clad gap width, clad and fluid thermal outputs; and 4) fuel-to-clad heatexchange coefficient, fission gas release and clad failure prediction.
The sensitivity analysis led to the following conclusions:

The injected energy is the most influential input parameter during the wholetransient and on almost all output data.

Input data related to rod state after base irradiation (initial fuel-to-clad gap, zirconia
thickness, radial power profile, roughness) are also very influential. Initial fuel-toclad gap is the most influential one in terms of clad failure prediction.



Fuel physical properties (fuel thermal-expansion and thermal conductivity models)
have a significant impact on the behaviour.

With the exception of injected energy, participants did not identify any common
influential input parameters for the fission gas release.



The clad failure prediction is challenging because it is sensitive to many input data
(9 influential input parameters out of the 12 studied here).

The clad physical properties (thermal-expansion and yield stress) have an impact
on few, but major, outputs (clad stress and clad failure prediction).

Phase III confirmed the conclusions of Phase II concerning the strong dependence of theuncertainty results on the type of behaviour (in terms of uncertainty band width andcoherence between participants). Moreover, it allowed enlargement of the list of influential
input parameters with some due to the irradiation period.
Based on the main outcomes of the analysis, the recommendations for further work are:

Safety analysis studies can require uncertainty analysis on parameters associatedwith the state of the rod at the end of irradiation. However, for some RIA codes,
the pulse-irradiation and base irradiation are not considered apart. It could beinteresting to develop strategies to allow the propagation of uncertainties on input
parameters associated with irradiation behaviour.

Further developments are required with a view to validated fission gas release andclad failure prediction models. It first involves gathering more high-quality data.

Mechanical models need to be improved, including cladding failure criteria andcladding stress behaviour.

A first task before uncertainty and sensitivity analyses is the quantification of input
uncertainties, which was partly performed in this benchmark by expert judgement.
The recent SAPIUM guidance (Baccou et al., 2020; NEA, forthcoming) could be
used to create a transparent and rigorous model for input uncertainty quantificationin order to minimise the user effect.

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References
Baccou, J. et al. (2020), “SAPIUM: A Generic Framework for a Practical and Transparent Quantificationof Thermal-Hydraulic Code Model Input Uncertainty”, Nuclear Science and Engineering, 194, pp.
721-736. https://doi.org/10.1080/00295639.2020.1759310.
NEA (forthcoming), “SAPIUM: Development of a Systematic Approach for Input Uncertainty
quantification of the physical Models in thermal-hydraulic codes Good Practices Guidance Report”,
OECD Publishing, Paris.

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Annex A. Description of the transient codes used

A.1

ALCYONE (CEA)
ALCYONE is a multidimensional pressurised water reactor (PWR) fuel performance codedeveloped at the French Alternative Energies and Atomic Energy Commission (CEA) in
Cadarache (France) within the PLEIADES software environment (Michel et al., 2013).
ALCYONE release 1.4 contains four schemes (Sercombe et al., 2013): 1) a standard 1.5D
description of the fuel rod; 2) a 3D scheme dealing with one-quarter of a pellet fragment
and associated cladding; 3) a 2D(r,θ) scheme describing the behaviour of the mid-pellet
plane of a 3D pellet fragment (Sercombe et al., 2012); and 4) a 3D multipellet fragment
scheme where part or the complete fuel rod can be simulated.
The different schemes use the same finite-element code CAST3M to solve the thermomechanical pellet – gap – cladding problem and share the same physical material models
at each node or integration point of the finite-element mesh. This makes comparison ofsimulated results from one scheme to another possible with no dependency on theconstitutive models.
ALCYONE was originally developed for the modelling of fuel rod behaviour during
normal (base irradiation) and off-normal (power ramp) loading sequences. The following(main) phenomena are included in the fuel performance code (Michel et al., 2012): power
deposition; heat conduction in the fuel pellet and cladding; creep and fragmentation of thepellet; generation and diffusion of fission gases in the fuel microstructure; fission
gas-induced swelling; fission gas release (FGR); pellet densification; high burn-up
structure; heat convection at the clad – coolant and clad – pellet interface; irradiation creep;
thermal creep and plasticity of the cladding; external clad corrosion; unilateral contact withfriction at the clad-pellet interface (2D, 3D); clad – pellet axial locking after contact.
In ALCYONE, the pre-RIA transient state has been assessed by comparison to an extensive
database of post-irradiation examinations of base-irradiated and ramp-tested
UO2-Zircaloy-4, UO2-M5® and MOX-Zircaloy-4 rods with burnups up to 80 GWd/tM(Struzik et al., 2012). The experimental measures include clad profilometry, zirconia
thickness, rod elongation, radial concentration profiles of fission gas and fission gas bubble
size, FGR, and internal pressure in the rod. The 3D scheme allows one to more precisely
assess the local behaviour of the fuel rod by comparing the following experimental andcalculated data: clad ridge heights at pellet – pellet interface and mid-pellet level, dishfilling and number of radial-axial cracks in the pellets (Sercombe et al., 2013).
In the last ten years, ALCYONE’s capabilities have been extended to accident conditions(RIA [Sercombe et al., 2010] and loss-of-coolant accident [Struzik et al., 2014]) with a very
limited amount of new developments. In this way, the continuity between nominal andtransient conditions has been ensured. Extension of the fuel code schemes topulse-irradiation required the following improvements: solving of the transient thermalheat balance equation for the pellet – gap – cladding system, incorporation of material laws
for irradiated Zircaloy-4 and M5® suitable for the large temperature and strain rate ranges
encountered in reactivity-initiated accident (RIA) conditions (Le Saux et al., 2008;
Hellouin de Menibus et al., 2014), incorporation of a material law describing the creep,
plasticity and grain boundary cracking of irradiated fuel for the large temperature and strain
rate ranges encountered in RIA conditions (Salvo et al., 2015), solving of the thermal and

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mass balance equations for sodium or water coolant in transient conditions, implementationof the clad-water coolant heat exchange correlations proposed by Bessiron for PWR
conditions (Bessiron, 2007) and stagnant liquid water (Bessiron et al., 2007). Simulationsof RIA transients in ALCYONE have so far been focused on the CABRI REP-Na(Sercombe et al., 2010; Guénot-Delahaie et al., 2018), CIP tests and NSRR tests(Guénot-Delahaie et al., 2018) (UO2-Zircaloy-4, UO2-M5® and MOX-Zircaloy-4). The
assessment of the code predictions is based on the numerous measures available: online
clad elongation, online sodium coolant temperatures at different axial positions, online clad
temperatures, residual clad diameters and ridge heights, radial-axial cracking of the pellets,and dish filling. Rod failure assessment during RIA transients relies on 2D simulations,where the brittle cracking of hydride blisters in the cladding and the subsequent strain
localisation in a shear band are explicitly taken into account (Sercombe et al., 2016).

A.2

FALCON (PSI)
FALCON is a light water reactor fuel rod analysis programme developed under the
auspices of the Electric Power Research Institute (EPRI) in the United States (Rashid et al.,2004). Outside the EPRI, the programme is in use by a few research organisations
worldwide, nuclear power utilities and the ANATECH Corporation, who developed thecode for the EPRI. The programme originates from the ESCORE and FREY codes, whichwere earlier used by the EPRI to model fuel rod performance under steady-state operationand transients, respectively. These two codes have been merged into FALCON, which isapplicable to a wide range of fuel operating regimes, from normal steady-state operation to
fast transients. In 2012, the EPRI released the first version of a so-called redesigned versionof the code, FALCON V1 (EPRI, 2014) with the source code being updated to FORTRAN
95 and providing a graphical user interface for input and post-processing based on thehierarchical data format. The current version is FALCON V1.4, which includes amechanistic model, GRSW-A, for FGR and fuel swelling during base irradiation andthermal transients. The GRSW-A model was implemented and verified at the Paul Scherrer
Institut (PSI) in Switzerland as part of a research, legacy version of the code, FALCON
MOD01 (Khvostov et al., 2011).
FALCON comprises best-estimate models for the involved physical phenomena, and uses
a 2D finite-element method to solve the coupled equations of heat conduction andmechanical equilibrium. The fuel rod can be modelled in either axisymmetric orcross-sectional geometry. Pellet-clad mechanical interaction can in both geometries bemodelled with the Amontons-Coulomb law of friction for the tangential contact forces. The
deformation mechanisms considered by FALCON for the cladding tube arethermoelasticity, plasticity, creep and irradiation growth. For the fuel pellets, FALCON
considers thermal-expansion, solid- and gaseous-bubble swelling, elastoplasticity,
cracking, and creep.
The GRSW-A model, as integrated into the FALCON code, predicts macroscopic variablesof fuel state, such as FGR and pellet swelling, based on the analysis of meso- andmicroscopic processes in each integration point of the pellet mesh. A special option ofanalysis restart was developed for FALCON with the GRSW-A model in order to accountfor the fuel pre-irradiation and, eventually, refabrication before a simulated transient.
Furthermore, the FALCON code has been recently extended by special models that are
expected to have a considerable effect on fuel behaviour during the RIA, viz.: a model
simulating the pellet-cladding bonding assisted trapping of the released fission gases during
the base irradiation; a model that describes the so-called “burst” release during the thermal

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transients, such as RIA, of the fission gases retained by the grain boundaries and trappedby bonding after the base irradiation; and a model for specific features of intragranular gas
behaviour, such as inhibited bubble coalescence and enhanced intragranular gas release to
the grain boundaries during fast thermal transients. Detailed description of the new models
integrated into the FALCON code and dedicated to fuel behaviour during an RIA ispresented in available open literature (Khvostov, 2018; Khvostov, 2022). In addition, asemi-empirical model for burst release of fission product gases, caused by grain boundary
decohesion, is available in FALCON. This model is intended particularly for analyses of
MOX fuel under RIAs.
The cladding failure criterion for RIA in FALCON is based on the concept of a criticalstrain energy density, meaning that failure is assumed as soon as the strain energy density
in the material reaches a critical value (Rashid et al., 2000). The critical strain energy
density (CSED) is a measure of clad ductility. In FALCON, the CSED is correlated tocladding oxide thickness and pre-transient temperature, and the correlation is based onmechanical property tests performed on irradiated Zircaloy-4 cladding (Rashid et al., 2000).
It should be noted that the CSED is not a true material property. As with total elongation,i.e. the plastic strain to failure, the CSED depends on the stress state and loading path up to
failure. The CSED applied in clad tube failure criteria should therefore be determined fromtests performed with a similar biaxial stress state as expected under a RIA. The correlation
for the CSED used in FALCON has been determined from clad tube burst tests, ring tension
tests and uniaxial tensile tests, using penalty factors to compensate for the non-prototypicalstress states in the tests.

A.3

FRAPTRAN (TRACTEBEL)FRAPTRAN is a computer code for analysing the thermal-mechanical behaviour of lightwater reactor fuel rods under transients and accidents, such as loss-of-coolant accidents and
RIAs (Cunningham et al., 2001). The code originates from FRAP-T6, a fuel rod code fortransient thermal-mechanical analysis from the 1970s. Compared to its ancestor,
FRAPTRAN has extended capability for modelling high burn-up fuel rods. The code isbased on best-estimate models, but comprises some conservative optional models, intended
for licensing analyses.
FRAPTRAN is closely linked to FRAPCON-3, which is a fuel performance code foranalysis of steady-state operating conditions (Berna et al., 1997). The necessary initialconditions for a transient analysis with FRAPTRAN can be generated with FRAPCON-3,
whereby data for a selected burn-up step are streamlined from the output deck of
FRAPCON-3 to the input deck of FRAPTRAN. Both codes were developed for the US
Nuclear Regulatory Commission, and are maintained by the Pacific Northwest National
Laboratory (PNNL) in the United States. The codes are used worldwide, and the user
community contributes to the development and testing of new models.
FRAPTRAN uses an axisymmetric representation of the fuel rod geometry, but a modelaccounting for local non-axisymmetric cladding deformation (ballooning) can be used inanalyses of loss-of-coolant accidents. The code is 1D in nature, and governing equations
are solved with respect to the radial co-ordinate direction in a number of disjointed axial
segments. Interaction between the axial segments of the rod is confined to calculations of
coolant axial flow and rod internal gas pressure.
FRAPTRAN uses a thin shell model for the cladding. The temperature, material properties,stresses and strains are thus assumed to be uniform across the cladding thickness. This is a

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definite drawback in analyses of RIAs, in which large radial gradients in temperature andstress arise in the cladding.
The pellets are assumed to deform only by thermal-expansion under the transient, whereas
the cladding is assumed to deform by thermoelasticity, plasticity and creep. Pellet-cladmechanical interaction is treated in each axial segment separately. This local approach issomewhat simplistic, since axial contact forces induced in the cladding are not transferred
to axial segments below the region of pellet-clad contact. Moreover, complete sticking isassumed, i.e. axial slip between the contacting pellet and cladding is precluded.
FRAPTRAN-2.0 has a model for transient fission gas release in RIA conditions, andcomprises a model for axial flow of gas in the pellet-clad gap. This model is of importanceto clad ballooning.
Cladding failure under RIA is predicted by use of a strain-based failure criterion. The
calculated plastic strain in the hoop direction is in each time step compared with a thresholdvalue, which is correlated to the temperature and hydride content of the cladding material.
The failure strain correlation is based on uniform elongation data from burst tests anduniaxial ring tensile tests on irradiated Zircaloy-2 and Zircaloy-4 cladding. This makes thefailure criterion conservative, since observed failure strains under RIA fall somewhere
between data for uniform elongation and total elongation. The advantage of using uniform
elongation as a basis for the failure criterion is that uniform elongation is not much affectedby stress state and loading path. It can therefore be viewed as a material property, in contrast
to the total elongation.

A.4

RANNS (JAEA)The RANNS code (Suzuki et al., 2006) was developed to analyse thermal and mechanicalbehaviours of a single fuel rod in RIA conditions. The code was originally based on thelight water reactor fuel analysis code FEMAXI-7 (Suzuki et al., 2011), which wasdeveloped for normal operation conditions and anticipated transient conditions, andcurrently implemented on the latest version of FEMAXI: FEMAXI-8.
The same analytical geometry is applied to both codes: a single rod can be divided into amaximum of 40 axial segments in a cylindrical co-ordinate, and thermal analysis and FEM
mechanical analysis are performed at each axial segment in which, in the default calculationmode, the pellet stack is divided into 36 iso-volumetric ring elements and cladding is
divided into eight iso-thickness ring elements in the metal part, one oxide element at the
inner surface and two oxide elements at the outer surface. The mesh configuration is more
flexible in the latest version of the programme. In analyses of high burn-up fuels, rodconditions during their base irradiation in commercial reactors are analysed with the
FEMAXI-8 code along power histories from BOL to EOL. The results of
FEMAXI-8 calculations are then fed into the RANNS code calculation.
The code adopts, with some modifications, MATPRO models for material properties likepellet and cladding thermal-expansion coefficients (Hagrman and Reymann,1979), Ohira’s model and MATPRO-09 models for thermal conductivities, MATPRO-11
for specific heat, Ross and Stout’s model for pellet-cladding gap conductance withconsideration of bonding effect, MATPRO-11 for Young’s moduli with consideration ofpellet cracking effects, Tachibana’s model for pellet plasticity (Tachibana et al.,1976), and the MATPRO model for cladding plasticity.
The RANNS code shares the basic framework and major part of its modules with the
FEMAXI-8 code, but has its own specific models for transient fuel behaviour: a transient
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FGR model, a cladding surface heat transfer model and a pellet-cladding mechanicalinteraction (PCMI) failure model.
A transient FGR model is implemented to simulate the grain separation and burst releaseof gas from grain boundary inventory in the rapidly heated pellet in RIA conditions. It is
assumed that the grain separation occurs when the expanding force from gas bubbles
exceeds the compressive force from its surroundings. This compressive force is a sum ofgrain boundary combining force, thermal stress and reactive force from cladding due to
PCMI. RANNS calculates the compressive force from temperature, gas amount, bubble
size, etc., and determines if the grain separation condition is fulfilled or not at each ringelement, at each axial node and at each time step. In a ring element in which grain
separation occurs, it is assumed that the whole grain boundary gas inventory is
instantaneously released. On grain separation, the present model assumes that the swelling
contribution of the original gas bubbles disappears, while rod internal pressure rise occurs
due to released gas. The gas pressure inside a fuel element, in which grain separation
occurs, is assumed to be in balance with the external force. Namely, the total gas volume
increases as a result of grain separation, because gas bubble pressure decreases to be equal
to the external pressure. The pellet internal stress state (deformation) and PCMI isrecalculated within the time step by taking account of this gas pressure change.
The latest cladding surface heat transfer model for water coolant conditions in RANNS isbased on the vapourisation model proposed by Bessiron et al. (2007) and a classical heattransfer coefficient approach. Four heat transfer phases are considered: 1) in Phase I, thecladding surface heat transfer coefficient hSURF is calculated by Dittus-Boelter’s correlation
when TSURF is below TSAT and by Chen’s correlation when TSURF is above TSAT. Here, TSURF
is the cladding surface temperature and TSAT is the saturation temperature of water coolant.
Once TSURF reaches the critical temperature TCRIT, heat transfer moves to Phase II.
In Phase II, TSURF is imposed to remain at TCRIT. Water vapourisation is assumed at the
cladding surface and the thickness of generated vapour film, δ, is estimated considering
heat unbalance between the conductive heat fluxes in the cladding wall and in the coolant
water, which is induced by fixing TSURF. During Phase II, effective hSURF is proportional to
the temperature gradient in the cladding wall in the vicinity of the cladding surface. A
boiling crisis is assumed to be triggered and the heat transfer phase moves to Phase III
when δ exceeds its critical value δC, which is one of the model parameters. The criticalheat flux ΦCRIT is defined as the cladding surface heat flux at the occurrence of boiling
crisis.
In Phase III, hSURF is determined so that the cladding surface heat flux at TSURF, Φ(TSURF),
satisfies the relation: Φ(TSURF) =ΦCRITf1 (TSURF) + ΦMINf2(TSURF), where f1(TCRIT) = f2(TMIN)= 1.0, f1(TMIN) = f2(TCRIT) = 0.0, f1(TSURF) = (TSURF – TMIN)2 / (TCRIT – TMIN)2, f2(TSURF) = 1.0– f1(TSURF), and ΦMIN is the cladding surface heat flux at TMIN, calculated by the modified
Bromley’s correlation described below. Once TSURF reaches the temperature TMIN, which isone of the model parameters, heat transfer phase moves to Phase IV.
In Phase IV, hSURF is calculated by modified Bromley’s film boiling correlation as hBRM =C1 [kG3 ρG (ρL –ρG) hfg g]0.25 / [μG L ΔT SUP]0.25, and hSURF = hBRM [ 1.0 + C2 ΔT SUB ], wherekG is vapour thermal conductivity, ρG is vapour density, ρL is saturated liquid density, hfg islatent heat, g is acceleration of gravity, μG is vapour viscosity, L is fuel stack length, ΔT SUP
is cladding surface superheat, ΔT SUB is liquid subcooling, and C1 and C2 are model
parameters. TMIN is used as quenching temperature, at which heat transfer moves to Phase I.

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The aforementioned model parameters were fitted to the thermocouples (TCs)measurement data from RIA-simulation experiments with low flow conditions. Future
development of the model will involve: solving a numerical instability problem which isseen in Phase III when TMIN or δC is relatively large; further validation of the model,
especially for the irradiated fuel test conditions after removing the limitations in tuning
TMIN and δC by solving the numerical instability; implementation and validation of film
boiling models for high flow conditions.
The latest PCMI failure model in RANNS is based on the fracture mechanics approach
proposed by Georgenthum et al. (2008). The J-integral, a fracture mechanics parameter thatis applicable to crack tip stress and strain fields under both elastic and plastic deformation
condition, is calculated at each axial node by a subroutine named “J_interpolation”. The
calculated J-integral is compared with critical J-integral values derived from high burn-up
PWR fuel tests conducted in the NSRR reactor. If the calculated J-integral exceeds thecritical J-integral, the code assumes that the cladding has failed at the axial node.

A.5

SCANAIR (IRSN, QT-SSM, VTT)The French Institute for Radiological Protection and Nuclear Safety (IRSN) initiated thedevelopment of the SCANAIR computer code in parallel with the CABRI REP-Na test
programme on RIA (Moal et al., 2014; Georgenthum et al., 2014). The code is used by the
IRSN and by organisations participating in the CABRI REP-Na and the CABRI
international programmes. SCANAIR is specifically designed for analyses of RIAs. It
distinguishes itself by having models that link fission gas behaviour to fuel pellet
deformation.
The fuel rod state before the transient is defined as input, and is usually generated bysimulation of normal steady-state operation by a separate fuel performance code, such as
FRAPCON. Developments are underway at the IRSN to extend the application domain of
SCANAIR to normal operating conditions in order to improve the initialisation of the fuelrod state.
SCANAIR comprises three main modules dealing with thermal dynamics (including
thermal hydraulics in the coolant channel), structural mechanics and gas behaviour. These
modules communicate with each other through a database.
SCANAIR uses an axisymmetric representation of the fuel rod geometry, and the code isconsidered as 1.5D in makeup. All fundamental equations are solved with respect to theradial co-ordinate direction, treating each axial segment of the rod separately. However,the segments are collectively treated in calculations of coolant axial flow, rod internal gas
pressure and transfer of axial forces from pellet-clad mechanical interaction. The axial
contact forces are calculated by assuming perfect sticking of the two objects: when pellet
and cladding come into contact anywhere along the rod, the code postulates zero relative
axial motion between fuel and cladding, not only in the segment where contact occurs, butalso in the segments below the contact point.
The fuel pellets are assumed to deform by thermoelasticity, plasticity, viscoplasticity,transient expansion of gaseous fission products and fuel cracking. Deformations due to fueldensification, irradiation creep and solid fission product swelling are not modelled in
SCANAIR during RIA, since the code is intended for analysis of short-term transients. As
fuel creep is significant at high temperature, according to experiments, transient fuel creep
models are available in the code. The cladding tube is assumed to deform by
thermoelasticity, plasticity and transient creep. The equations of mechanical equilibrium
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are discretised in the radial direction and solved by using a finite-element method, both forthe fuel pellet and the cladding tube. Hence, the cladding tube can be divided into several
annuli, and the variation of temperature, hydrogen concentration and material properties
across the cladding thickness can be considered in analyses. Different kinds of fuels (UO2or (U,Pu)O2) and cladding materials (Zircaloy-2, Zircaloy-4, ZIRLO™, M5®, E110) canbe modelled, thanks to a large set of correlations for thermo-physical and thermomechanical properties (Moal et al., 2014; Cazalis et al., 2007).
Three populations of pressurised cavities are modelled inside the fuel: intragranular
bubbles, intergranular bubbles and pores. The transient FGR model does not account forthe migration of individual gas atoms in the fuel, since all fission product gases are assumed
to be collected in pores and bubbles. Hence, the slow diffusion of gas atoms in the fuel is
not modelled, but the transport of intragranular gas bubbles into the grain boundaries andthe formation of intergranular bubbles are modelled. Also, the release of intergranular
bubble gas into large pores, through which it can be conveyed to the rod free volume, isconsidered. Release of fission gas takes place by rupture (overpressurisation or saturation)of grain boundaries and/or pores. Two models can be used to simulate the gas flow in thefree volumes. The first one only considers the radial flow of fission gases through the open
pores and assumes instantaneous equilibrium of pressure in the free volumes. The second
one takes into account the mixture of gaseous species (fission gases, helium, argon, air)and simulates radial and axial flow with possible local overpressure in the pellet-clad gap.
The coolant is modelled as a single-phase fluid with heat transfer coefficients on the walls(Bessiron, 2007). The solution of the mass and energy conservation equations provides thecoolant temperature and flowrate. The pressure is imposed in the channel. Heat exchanges
between the coolant and the clad are modelled by use of heat transfer coefficients,
following the successive boiling regimes (convection/conduction, nucleate boiling,transition boiling and film boiling). The specific boiling curve takes into account that thecritical heat flux and film boiling phenomena involved in fast transient conditions are
significantly different from steady-state conditions.
A cladding failure criterion to be used for the PCMI phase in analyses of RIA withSCANAIR is proposed by the IRSN (Georgenthum et al., 2008). Elastoplastic fracture
mechanics is applied to calculate a critical initial crack length for cladding failure under theconsidered RIA. Cladding failure is assumed to occur if there are pre-transient defects or
flaws at the cladding outer surface which are deeper than the calculated critical crack
length. Moreover, for corroded cladding tubes, it is assumed that the depth of the surface
defects is equal to the thickness of the densely hydrided rim at the cladding outer surface.

A.6

TESPA-ROD (GRS)TESPA-ROD – TEmperature, Stress and Pressure Analysis of a Fuel ROD – is a transientcomputer code for fuel rod simulation in design basis accidents, operational transients andlong-term spent fuel storage conditions.1 TESPA-ROD models the fuel rod behaviour in
1.5D spatial resolution. It provides the transient radial temperature distribution in across-sectional area of a fuel rod, while the axial temperature distribution is approximatedfrom an axial power factor which is user input. The rod can be divided into axial zones forthe simulation axial distribution of hoop strain and fuel rod elongation in case of PCMI.
Characteristic fuel rod volumes like fuel rod plena or gap volume are described with1.

https://www.grs.de/en/simulation-codes/tespa-rod.

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designated volumes. Perfect fission gas communication among these volumes is assumed.
The code provides models for UO2, MOX and gadolinium fuel.
The visco-plastic hoop stress/strain model in TESPA-ROD provides no radial stressresolution within the cladding. The effect of radially localised yielding in the cladding is
considered in TESPA-ROD with the ratio of yield stress to burst stress. This ratio is
deduced from the analytical solution of the 3D visco-plastic stress/strain relation for
thick-walled cylinders. According to this analysis, the location of the elastic-plastictransition occurs at the inner cladding surface first, which is associated with yield stress.
Finally, the location of the elastic-plastic transition reaches the outer surface, which is
associated with both the plastic collapse of the cladding and the burst stress. For ductile
cladding behaviour, the stress ratio depends on the cladding inner diameter and outer
diameter. For brittle cladding behaviour, the stress ratio is close to unity with 0.985. In the
TESPA-ROD code, the cladding is considered either brittle or ductile, depending on the
average hydrogen pick-up in the cladding.
A pressure difference across the cladding, as well as the expansion of a pellet, may induce
tensile hoop stresses in the cladding. These stresses may lead to cladding creep and/or
cladding plastic deformation. Both effects on the cladding deformation are modelled in
TESPA-ROD. While plastic deformation affects evenly the circumferential hoop strain, thecreep strain can be circumferentially localised, depending on the eccentricity parameter
provided by user input. All hoop strains result in cladding thinning, according to plastic
flow rule. The irreversible deformation contributes to an additional heat-up of the cladding.
If the hoop stress exceeds the hoop burst stress, burst of cladding is assumed. The burst
stress in TESPA-ROD is determined based on the correlation developed at KfK Karlsruhe
for Zircaloy-4 in the early 1980s. The EDGAR tests showed that this approach is still valid
with some modification. Cladding creep models of the Norton type are available for Zry-4,
Zry-2, Duplex, ZIRLO™, E110 and M5®. These high temperature creep models also take
into account both the hydrogen and oxygen content. While increased hydrogen content
increases the creep strain rate, the oxygen content reduces the creep strain rate.
Furthermore, the creep rate strongly depends on the α-β phase transformation.
The gap between the pellet outer surface and the cladding inner surface contains helium
and to some extent fission gas. The gap heat transfer model in TESPA-ROD is similar tothat used in the fuel rod code SCANAIR.
TESPA-ROD provides an empirical FGR model for the operational fission gas releasedepending on the fuel rod average burn-up level only. If complex power histories need tobe considered, a coupled code version TESPA-ROD/FRAPCON can be applied optionally.
The transitional FGR in TESPA-ROD is modelled based on both a gas diffusion model for
mid-term transients (in the time range of minutes) and a power density model for shortterm transients (in the time range of milliseconds). The short-term transient model
considers the transitional FGR from intergranular pellet location. This FGR rate is
proportional to the fission gas content at grain boundaries. The fission gas release rate isvalidated with rod internal pressure data of NSRR test LS1.
In high power transients like RIA transients, the pellet expansion is controlled by both thethermal-expansion of the pellet and the power density related expansion. The second
contribution is a result of a partial amorphous state of the fuel, due to the large atomic
displacement rate at high power densities. Although the UO2 crystal cannot reach apermanent amorphous state, a transitional amorphous state can be achieved. Under normal
operation, the damage accumulation in UO2 crystals becomes saturated at ten dpa without
reaching a permanent amorphous state, but a transitional amorphous state is achievable
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beyond that of ten dpa with a displacement rate of about ten dpa/s, e.g. during peak powerof RIA transients. The additional fuel expansion associated with the transitional amorphousstate is predicted in TESPA-ROD. Fresh fuel (fuel with less than ten dpa) has no damage
accumulation in the crystal lattice and therefore the power density related expansion
vanishes. Fission gas bubble expansion in the fuel is not considered in the TESPA-ROD
code because of an almost complete loss of fission gas at intergranular locations during theearly period of RIA transients predicted by TESPA-ROD.
Heat transfer between cladding and coolant can be provided as user input to the code. For
RIA transients in water coolant, an extra heat transfer model is optionally available. This
heat transfer model predicts departure from nucleate boiling (DNB) if the cladding surface
temperature exceeds the DNB temperature deduced from the thermal-mechanicalnon-equilibrium (Schroeder-Richter, 1996). The film boiling heat transfer is modelled as amultiple of radiation heat transfer. The multiplier (~9.0) reflects the enhanced heat transfer
due to the wavy steam/water interface. The cladding surface temperature must fall below
the Leidenfrost temperature in order to re-establish both nucleate boiling heat transfer anda cladding surface that is wetted by liquid coolant. Before wetting occurs, a pre-cooling
effect takes place, which is modelled by quadratic interpolation between film boiling heattransfer and nucleate boiling heat transfer. This interpolation starts if the cladding surface
temperature approaches 25% of the Leidenfrost temperature after passing the peak cladding
surface temperature.

A.7

TRANSURANUS (ENEA, ÚJV)TRANSURANUS is a computer programme for the thermal and mechanical analysis offuel rods in nuclear reactors. The code is owned by the European Commission and used byresearch centres, nuclear safety authorities, universities and industrial partners (Lassmann,
1992). The development of TRANSURANUS is carried out by a team of scientists working
at the JRC/ITU Karlsruhe (Germany). In TRANSURANUS, the equations of the radial heattransfer are solved and the radial strain and stress distribution determined in both the fueland the cladding. The analysis is based on the assumptions that the geometric modelling offuel pin is 1D, plane and axisymmetric. A second assumption considers that
Young’s modulus of elasticity and Poisson’s ratio are constant and isotropic within acylindrical ring; finally, the constitutive equations take into account elastic and non-elasticstrains.
The most important phenomena occurring under irradiation are modelled. Calculations
account for: thermal and irradiation induced densification of fuel, swelling due to solid andgaseous fission products, creep, plasticity, pellet cracking and relocation, oxygen andplutonium redistribution, volume changes during phase transitions, formation and closureof a central void. The axial friction forces are evaluated when the gap between fuel andcladding is closed. Fuel restructuring, actinide redistribution, grain growth and, formationof high burn-up structure are tracked during a TRANSURANUS run.
The code accounts for the creation of fission gas in the fuel matrix, the diffusion of fission
gas atoms to grain boundaries and its release to the rod free volume. This event occurs
when the saturation concentration at the grain boundaries has been reached. Beside theconventional FGR model, a physics-based model has been recently developed andimplemented in the code. This approach extends the description of fission gas diffusion
taking into account the gas atoms trapped in bubbles. Bubble coalescence and microcracking are also modelled. Fuel swelling is estimated from bubble volumes.

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The axial and radial geometrical mesh of both fuel column and cladding are flexible. Oncethe behaviour of fuel is solved in each slice, solutions are coupled by means of friction
forces, axial deformation and pin inner pressure. Therefore, TRANSURANUS is a 1.5D
fuel performance code, while 2D (3D) codes solve the equations simultaneously in two(three) dimensions. The TRANSURANUS code consists of a clearly defined mechanical–
mathematical framework into which physical models can easily be introduced. The code
has a comprehensive set of materials including: oxide, mixed oxide, carbide and nitride
fuels; zircaloy and steel claddings; and several different types of coolant. It can be
employed in two different versions: as a deterministic and as a statistical code. Besides its
flexibility for fuel rod design, the TRANSURANUS code can deal with a wide range ofdifferent situations, as given in experiments under normal, off-normal and accident
conditions. Furthermore, the code is used for boiling water reactors, pressurised water
reactors and water-water energetic reactors. The code is capable of analysing problems withtime scales spanning from milliseconds to years. Hence, complex irradiation experiments
can be simulated where instrumented refabricated fuel rods are irradiated under different
operating conditions.

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Cunningham, M.E. et al. (2001), “FRAPTRAN: A computer code for the transient analysis of oxide fuelrods”, NUREG/CR-6739, Vol. 1, US Nuclear Regulatory Commission, Washington, DC,
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Georgenthum, V. et al. (2008), “Fracture mechanics approach for failure mode analysis in CABRI and
NSRR RIA tests”, in: Proceedings of the 2008 Water Reactor Fuel Performance Meeting, 1923 October 2008, Seoul.
Guénot-Delahaie, I. et al. (2018), “Simulation of reactivity-initiated accident transients on UO2-M5 fuelrods with ALCYONE V1.4 fuel performance code”, Nuclear Engineering and Technology, Vol. 50/2,
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for use in the analysis of light water reactor fuel rod behaviour”, NUREG/CR-0497, US Nuclear
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Hellouin de Menibus, A. et al. (2014), “Thermo-mechanical loading applied on the cladding tube during
the pellet-cladding mechanical interaction phase of a rapid reactivity-initiated accident”, Journal of
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Khvostov, G. (2022), “Modelling effects of transient FGR in LWR fuel rods during a LOCA”, Journal of
Nuclear Materials, 559, 153446 (26 pp.). https://doi.org/10.1016/j.jnucmat.2021.153446.
Khvostov, G. (2018), “Models for numerical simulation of burst FGR in fuel rods under the conditions ofRIA”, Nuclear Engineering and Design, Vol. 328, pp. 36-57,
https://doi.org/10.1016/j.nucengdes.2017.12.028.
Khvostov, G. et al. (2011), “A model for fission gas release and gaseous swelling of the uranium dioxide
fuel coupled with the FALCON code”, Nuclear Engineering and Design, Vol. 241/8, pp. 2983-3007,
https://doi.org/10.1016/j.nucengdes.2011.06.020.
Lassmann, K. (1992), “TRANSURANUS: A fuel rod analysis code ready for use”, Journal of Nuclear
Materials, Vol. 188, pp. 295-302, https://doi.org/10.1016/0022-3115(92)90487-6.
Le Saux, M. et al. (2008), “A model to describe the anisotropic behaviour of fresh and irradiatedZircaloy-4 fuel claddings under RIA loading conditions”, Journal of Nuclear Materials, Vol. 378/1,
pp. 60-69, https://doi.org/10.1016/j.jnucmat.2008.04.017.
Michel, B. et al. (2017), “Simulation of pellet-cladding interaction within the PLEIADES fuelperformance software environment”, Nuclear Technology, Vol. 182/2, pp. 124-137,
https://doi.org/10.13182/NT13-A16424.
Michel, B., et al. (2012), “3.22 – Modelling of pellet-cladding interaction”, in Comprehensive Nuclear
Materials, pp. 677-712, http://dx.doi.org/10.1016/B978-0-08-056033-5.00074-4.
Moal, A. et al. (2014), “SCANAIR: A transient fuel performance code – Part one: General modelling
description”, Nuclear Engineering and Design, Vol. 280, pp. 150-171,
https://doi.org/10.1016/j.nucengdes.2014.03.055.
Rashid, Y.R. et al. (2004), “Fuel analysis and licensing code: FALCON MOD01: Volume 1: Theoreticaland numerical bases”, TR-1011307, EPRI, Palo Alto, CA,
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Rashid, Y.R. et al. (2000), “A cladding failure model for fuel rods subjected to operational and accident
transients”, in: Nuclear Fuel Behaviour Modelling at High-Burn-up and Its Experimental Support,
IAEA-TECDOC-1233, International Atomic Energy Agency, Vienna, https://wwwpub.iaea.org/MTCD/Publications/PDF/te_1233_prn.pdf.
Salvo, M. et al. (2015), “Experimental characterization and modelling of UO2 grain boundary cracking athigh temperatures and high strain rates”, Journal of Nuclear Materials, Vol. 460, pp. 184-199,
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Schroeder-Richter, D. (1996), “Analytical modelling of complete Nukiyama curves corresponding to
expected low void fraction at high subcooling and flow rate”, Fusion Technology, Vol. 29/4, pp. 468486, https://doi.org/10.13182/FST96-A30691.
Sercombe, J. et al. (2016), “2D simulation of hydride blister cracking during a RIA transient with the fuelcode ALCYONE”, EPJ Nuclear Science and Technology, Vol. 2/22,
https://doi.org/10.1051/epjn/2016016.
Sercombe, J. et al. (2013), “3D modelling of strain concentration due to PCI within the fuel code
ALCYONE”, in: LWR Fuel Performance Meeting TopFuel 2013.

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Sercombe, J. et al. (2012), “Power ramped cladding stresses and strains in 3D simulations with burn-updependent pellet – clad friction”, Nuclear Engineering and Design, Vol. 242, pp. 164-181,
https://doi.org/10.1016/j.nucengdes.2011.08.069.
Sercombe, J. et al. (2010), “1D and 3D modelling of PCMI during a RIA with ALCYONE V1.1”, inProceedings of the 2010 LWR Fuel Performance Meeting/Top Fuel/WRFPM, American Nuclear
Society.
Struzik, C. et al. (2014), “LOCA tests IFA 650 analysis through the fuel state at the end-of-baseirradiation and its thermo-mechanical behaviour during the experiment”, EHPG, Norway.
Struzik, C. et al. (2012), “Validation of fuel performance CEA code ALCYONE, scheme 1D, on
extensive database”, in Proceedings of Top Fuel Conference, Manchester, United Kingdom.
Suzuki, M. et al. (2011), “Light water reactor fuel analysis code FEMAXI-7: Model and structure”,
JAEA-Data/Code 2010-035, Japan Atomic Energy Agency, Tokai-mura, Japan.
Suzuki, M. et al. (2006), “Analysis on pellet-clad mechanical interaction process of high-burn-up PWR
fuel rods by RANNS code in reactivity-initiated accident conditions”, Nuclear Technology,
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https://doi.org/10.1080/18811248.1976.9734063

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Annex B. Description of the codes used by the participants during thebenchmarkB.1

French Alternative Energies and Atomic Energy Commission (CEA)
The same fuel performance code, namely ALCYONE, was used by the CEA forbase-irradiation and transient calculations, complemented by the URANIE platform(Gaudier, 2010) tools as regards the uncertainty quantification and sensitivity analysis.
ALCYONE pulse-irradiation simulations clearly take advantage of starting from the baseirradiation conditions that the code itself computes. Among the important phenomena for
UO2 and MOX fuels, the fission gas model deals with fission gas creation and evolution at
the grain scale. With no need for any user-dependent specific initialisation of the variablesprior to pulse-irradiation simulations, the precise and relevant description of the initial fuelrod state and spatial distribution of fission gases in each phase – inter- or intragranular, inbubbles or dissolved, with partial to total restructuration (high burn-up structure) – isautomatically ensured.
The URANIE platform developed by the CEA is based on the ROOT data analysis
framework (http://root.cern.ch). This open source project (available at:
http://sourceforge.net/projects/uranie) offers various possibilities and methods in terms ofdefinition of the uncertain variables and sampling from their characteristics,
to-be-interfaced code launching, uncertainty propagation and sensitivity analysis between
the inputs and the outputs of the code, as well as optimisation for automatic calibration ofcodes, and reliability considerations.
Within the scope of the RIA benchmark Phase III, only the 1.5D scheme of ALCYONE
release 1.4 was used. The fuel porosity radial profile at the end-of-base irradiation given
by ALCYONE fission gas model was found to differ significantly from the specified
FRAPCON profile. As any modification in the fission gas model parameters could have
led to non‐negligible and non-physical impacts on gas inventory, clad strain, fission gas
release (FGR), etc., CEA calculations were thus based on the fuel porosity radial profile
given by the ALCYONE fission gas model.
All uncertain parameters were treated with URANIE release 4.1 as requested through a
200-run design of experiment generated by Latin hypercube sampling.

B.2

National Agency for New Technologies, Energy and Sustainable Economic
Development (ENEA)
Results provided by the ENEA were obtained by means of the TRANSURANUS fuelperformance code (version v1m1j18) (Lassmann, 1992). TRANSURANUS has themodelling capabilities and a built-in Monte-Carlo technique (random number generator,
probability density functions, up to 70 random input variables) required to accomplish theobjectives of the benchmark. The type of TRANSURANUS run employed for thebenchmark is a combination of deterministic (base irradiation) and statistical restart run(transient test). A TRANSURANUS tool (RSTRTM) was used to take into account therefabrication of CIP0-1. The output variables indicated in the specifications were written
to the statistic file during each statistical run. Results were then extracted to the Excel
templates distributed to the participants. This step was performed by means of a purpose-

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developed code in FORTRAN95. In addition, this tool calculates the Spearman’s rankcorrelation coefficients for the analysis of sensitivity.
The ENEA’s results are based on the analysis of nine uncertain inputs instead of 12, as
indicated in the specifications. This choice was mainly due to lack of time. The random
input variables not accounted for are: the radial power profile, pulse width and gap size.
Most of the uncertain inputs considered in the analysis of uncertainties and sensitivity areavailable in the code version distributed to the users. Three uncertain inputs wereintroduced in the code for the purpose: fuel and cladding roughness and zirconia thickness.
All the output variables considered in the benchmark were calculated during a
TRANSURANUS run. The clad failure prediction parameter was defined according to theoverstress criterion adopted in the calculations.
With regard to the cladding material, a complete set of ZIRLO™ correlations is notavailable in TRANSURANUS. For this reason, the generic Zircaloy correlations wereapplied. The yield stress used in calculations is based on the Zr1%Nb correlation multipliedby an empirical factor. The development of ZIRLO™ correlations is underway.

B.3

Gesellschaft Für Anlagen- Und ReaktorSicherheit (GRS)
1. Base irradiation:
The base irradiation results of FRAPCON 4 provided by the IRSN were used to match
specifications adequately.
2. RIA transient:
The GRS fuel rod code TESPA-ROD version 20.3 was used for the transient calculations.
Some parameters were adapted from the FRAPCON 4 code provided by the IRSN.
2.1 The code used nine axial zones
The following parameters were separated into nine values:

rod relative power during transient: 0.801, 0.927, 1.022, 1.095, 1.143, 1.135, 1.090,
0.991, 0.808;

averaged outer oxide layer (three taken from FRAPCON, the other six wereinterpolated and extrapolated close to measurements: 62, 63, 67, 75, 80, 83, 85, 87,
88 [µm]).

The following parameters were distributed on three axial nodes (three each):pellet outer radius (FRAPCON);

clad outer diameter: based on pellet diameter, gap size cladding thickness: 9.553,
9.560, 9.540 mm;

density of fuel (FRAPCON).

The following parameters were equal to all zones:

design cladding thickness;burn-up of 76.6 MWd/kg (radial pellet averaged);

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radial power profile: pellet divided in ten equidistant rings - ring 10 power shift of+37.9 %, rings 1-9 power shift of -8.9%. Values derived from the FRAPCON 4
power profile.

3. Uncertainty and sensitivity analysis:
The GRS code SUSA 4.1 was used.
All uncertain parameters have been considered except for:B.4



Yield strength uncertainty and reduction in reference case are not considered (thehigh hydrogen content effects the fracture limits).



One value for fuel roughness as cladding roughness (sum of both).

Fuel gap and roughness may lead to geometrical overlap of cladding and fuel(roughness > gap). Adjustment of gap to prevent overlap.

All samples start with full zirconia thickness at the beginning of the transient.
Spallation model leads to X% of spallation as specified in uncertainty of zirconia
thickness. Spallation occurs at transient hoops strains of 0.5%.

All cases with burst of cladding (CFP = 1) are included in the uncertainty andsensitivity analysis.

IRSN
Base irradiation
The rod state at the end of the base irradiation was evaluated through the code FRAPCON
V4.0 Patch1 using the FRAPCON input file given in the specifications.
SCANAIR input data deck
An interface tool named FRAPSCAN was used to read the results coming from FRAPCON
to create most of the SCANAIR input data deck. In order to complete the data deck,
hypotheses were made for the end of state data not given by the FRAPCON code and for
SCANAIR calculations:

rod initial state hypotheses:‒gas repartition between intra and inter pore, intra and inter bubble size (radial
distribution), grain size in the high burn-up structure: deduced fromexaminations on other fuels;‒

fuel-clad roughness: only one roughness can be taken into account in
SCANAIR calculations; the value of the global roughness ranged from 0.1 µm
to 4.0 µm.

SCANAIR calculation hypotheses:‒

Failure evaluation: CLARIS approach was used. This approach is based on the
hypothesis that the pellet-cladding mechanical interaction failure may result
from the propagation in the outer part of the cladding of an existing incipient
crack (due to the presence of brittle area with dense hydride). An initial
incipient crack of 50 µm was evaluated on metallographic examinations
performed before the tests.

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Fuel and clad mechanical modelling: perfectly elastoplastic behaviour with theCanon’s yield stress law for UO2 fuel and the so-called Crocodile visco-plastic
model based on the Lemaitre formulation for ZIRLO™ cladding.

‒

Fuel failure limit (for grain boundary FGR): the limit was set at 120 MPa.

Statistical analysis
SUNSET (Sensitivity and Uncertainty Statistical Evaluation Tool) software was used toperform this analysis. It is a statistical tool providing a collection of methods for
information treatment in risk analysis studies. It includes statistical tools to perform aprobabilistic assessment of uncertainties, where the uncertainty sources are modelled using
random variables. To be able to handle both aleatory and epistemic uncertainties,
techniques based on the Dempster-Shafer evidence framework are also available, but were
not exploited during this benchmark. SUNSET can be used for sensitivity analyses to
identify the variables which have the largest contributions to the overall model response
uncertainty. The methods are based on algebraic and statistical tools combining design ofexperiment theory and regression techniques.
A more exhaustive description of the software can be found at:
www.irsn.fr/en/research/scientific-tools/computer-codes/pages/sunset.aspx. This software
can be downloaded for free at: https://gforge.irsn.fr/gf/project/sunset.

B.5

JAEA
Base irradiation
The EOL fuel-rod state was computed by the code FEMAXI-8 (version 8.1.102f). The
model set adopted for the present benchmark is identified as 00018lq6dIC8R. Differencesfrom the “reference” model, whose detailed description can be found in a recent publication(model-ID:00015ix3c [569]), are enumerated below; they were introduced mainly to follow
the benchmark specification.


FGR model further tuned to match the FRAPCON calculation;

mesh configuration changed so that the number of cladding radial meshes formechanical calculation is eight;

fuel cracking model inactivated;

HBS swelling model activated;

more rigid behaviour of fuel pellet: higher yield stress of fuel pellet so that thecalculated cladding elongation agrees better with the measurement in CIP0-1.

RIA transient
The transient fuel behaviour during CIP0-1 was computed by the RANNS code. The code
version and model set are common with the FEMAXI-8 calculation for its base irradiation.
Additional or RIA-specific models adopted in the present benchmark are described in
Annex A. RANNS read the result coming from the base irradiation calculation by
FEMAXI-8 to initialise fuel states for the transient simulation. The following special
options were introduced to satisfy requirements in the benchmark:a restart option which forces the clad inner radius to some different values from
EOL(FEMAXI) state was added to treat fuel-clad gap as an input uncertainty
parameter;
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a restart option which forces force clad oxide thickness to some different
values/distribution from EOL(FEMAXI) state was added to treat zirconia thickness
as an input uncertainty parameter;a restart option which scales history input in the time-axis direction and keeping
time-integrated power constant was added to treat pulse width as an input
uncertainty parameter.

Statistical analysis
The uncertainty and sensitivity analyses were performed with Dakota 6.5 developed andprovided by the Sandia National Laboratories (SNL). Dakota read the regressor (uncertain
input parameters) information through its input file, generated sampled input parameters
within given uncertain range and associated RANNS input files, launched RANNS
calculations, read the outputs, and computed statistical measures required in thebenchmark.

B.6

Paul Scherrer Institute (PSI)
The current analyses of base irradiation and RIA transients were carried out using
FALCON v1.4.1 and the GRSW-A 3.02 model for FGR and swelling. FALCON utilised afully 2D thermo-mechanical calculation of an axisymmetric fuel rod. The rod geometry ispresented in the R-Z co-ordinate system.
For the full-length mother rods, the radial mesh is formed using three element-columns in
the pellets and three columns in the cladding. Nine element-rows were used to form theaxial mesh in the active part of the full-length mother rod for the tests.
The standard FALCON-based methodology was used for calculation of the thermaltransients in refabricated rodlets, including the advanced restart procedure. It writes thewhole array of the integrated microscopic and macroscopic variables for each calculation
node and time step of the base irradiation analysis into a binary file. When the following
calculation of the thermal transient starts, the variable arrays are “plugged out” from thebinary file for the predetermined lifetime – when the transient starts – and an interpolation
technique is applied to determine the array variables in the nodes of the new finite-element
mesh, which now corresponds to the new rod refabricated from the “mother” rod after thebase irradiation (Ribeiro and Khvostov, 2015).
As regards the uncertainty quantification and sensitivity analysis, all studies were
performed using an in-house Pythontool, for which an interface with FALCON wasdeveloped to manage data I/O, job executions on clusters and data extraction in the scopeof benchmark specifications. The Latin hypercube sampling was used to generate thematrix of uncertain parameters. Sensitivity analysis was based on the computation of
Spearman rank correlation coefficients.
The PSI’s results are based on an analysis of 11 of the 12 uncertain variables, as the radial
power profile was not included, since this property is not available in FALCON as an input
parameter. For the fuel-clad radial gap, in order not to change the fuel and clad geometries(as requested in the specifications), FALCON uses a relocation model with a parameterthat sets the gap as the ratio of the cold gap to the as-manufactured gap. This was used as
input, the reference value of 10 μm corresponding to a ratio of approximately 0.12 of thecold gap (0.0825 mm). A uniform thickness of 43.5 μm (C=1/2) was considered as areference for the zirconia thickness because an axial distribution cannot be given as input
in FALCON (as requested in the specifications).

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B.7

QT-SSM
Base irradiation
The calculated results from the FRAPCON-4.0P1 computer programme, which were
provided together with the benchmark specifications, were used to define the state of thefuel rod at the end-of-base irradiation. All FRAPCON results provided with thespecifications were used, except for the calculated partitioning of retained fission gas. The
reason for this exception is that FRAPCON-4.0P1 calculates an intragranular gas
concentration in the outermost part of the HBS (rim zone) that is several times higher thanwhat is typically observed in measurements on fully restructured HBS material. For thisreason, the gas partitioning was calculated as a function of axial and radial position, basedon the assumed spatial variation of fuel microstructure (see below).
SCANAIR input data deck
The input data deck to SCANAIR V_7_8 was prepared by combining the aforementioned
FRAPCON results for the rodlet pre-test conditions with the CABRI test parameters
defined in the specifications. The following hypotheses and assumptions were made forparameters not defined in the specifications:

Rod pre-test state:‒

Axial-radial distributions of fuel microstructural properties, viz. grain size andsize of intra- and intergranular fission gas bubbles, were deduced from results
reported from examinations of similar fuel. These results were adapted to theassumed extension of the restructured rim zone, as defined by the porosity
distribution calculated with FRAPCON-4.0P1.

‒

The partitioning of retained fission gas between intragranular bubbles,intergranular bubbles and larger scales pores was calculated as a function of
axial and radial position by models in SCANAIR V_7_8, based on the assumed
distributions for totally retained gas, porosity and the microstructural properties
mentioned above.

‒

The effective fuel-clad roughness was taken as the sum of the fuel and cladding
roughnesses, which were assumed to be independent, uniformly distributed
parameters. The effective fuel-clad roughness used in the calculations withSCANAIR V_7_8 therefore followed an Irwin-Hall distribution. This is a majordifference from the calculations done by the IRSN and the VTT, with a large
impact on the calculated results.

SCANAIR calculations:‒

SCANAIR V_7_8 was used with recommended models and settings, except forthe cladding failure criterion. More precisely, the “strain” option was used,which invokes a strain-based failure criterion that had earlier been used for RIA
analyses in Sweden (Jernkvist, 2006). The ZIRLO™ cladding was modelled asa perfectly elasto-plastic material, with the yield strength given by thecorrelation defined in the benchmark specifications.

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Statistical analysis
The SUNSET software was used for statistical analyses; see Section B.4.

B.8

TRACTEBELThe simulation of the base irradiation was performed with the input file provided by thetask leaders, with the last production version of the FRAPCON code (FRAPCON 4.0 P1).
The rod state at the end of the base irradiation was communicated to FRAPTRAN throughthe use of a restart file.
The transient modelling was performed with a beta version of FRAPTRAN 2.1 containing
the sodium correlations and provided by the US NRC specifically for this task. Except for
the use of the sodium correlations, the default models selected by the code were used.
The uncertainty and sensitivity analyses were performed with Dakota 6.2. The sampledparameters were automatically implemented in the FRAPTRAN input file and the
FRAPCON restart file before running the calculations.

B.9ÚJV Řež (ÚJV)
TRANSURANUS code version V1M3J12modCEZ was used for the simulation. Only a
few modifications regarding the time step control were made in the code to improve theapplicability in RIA conditions. Scripts written in ROOT were used to generate and process
the statistical results. This set of computational tools is used for the core reload and safety
analysis of the Czech nuclear power plants at ÚJV.
The CIP0-1 experiment modelling was done in three steps:whole rod calculation of base irradiation with nominal parameters;modelling of the CIP0-1 segment base irradiation, where the coolant properties andfree volume were tuned to obtain the same results as in the whole rod calculation;

statistical calculations of CIP0-1 – only the segment with the tuned base irradiation
input was modelled.

Free volume and rod internal pressure were adjusted during the restart according to required
input data.
The porosity profile and gap size prior to CIP0-1 test would be difficult to adjust since they
are integrally calculated by TRANSURANUS during the base irradiation. These were notvaried independently of the other models.
Uncertainties in code models were applied already for the base irradiation and thepellet-cladding gap variation was achieved by this approach. Therefore, the initial pelletcladding gap is strongly correlated with code models multipliers and the pellet-cladding
gap was therefore not taken into account in sensitivity analyses.
The radial power profile during the base irradiation was modelled according to the
TRANSURANUS “TuBrnp” model. For the CIP0-1 test, benchmark specifications were
followed.
The porosity profile is linked to the base irradiation modelling and was not varied
independently.

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Pulse width was varied according to the specifications (not in TRANSURANUS itself but
by the pre-processing script).
A cladding corrosion layer was assumed to be present for thermal analysis, but spalled fora mechanical one (modelling of spallation during the test is not possible in the
TRANSURANUS code without further modifications).
Fission gas release during CIP0-1 was modelled by simple correlation based on the
FRAPTRAN model – temperature threshold for grain boundary (1 100°C) and HBS(800°C) release (activated by user for transient only).

B.10

VTT Technical Research Centre of Finland Ltd (VTT)
Base irradiation
Steady-state irradiation parameters generated by the IRSN with FRAPCON V4.0 Patch1
were used.
SCANAIR input data deck
An in-house Python script was used to generate the SCANAIR inputs for the uncertainty
analysis. Not all of the necessary input parameters are provided by FRAPCON, andtherefore some hypotheses had to be made:

Rod initial state hypotheses:‒

In SCANAIR input, the total amount of gas taken from FRAPCON
initialisation is given radially for each axial segment. SCANAIR then divides
the gas into intergranular and intragranular and porosity gas. For this partition,
SCANAIR needs the fuel end-of-life temperature distribution and porositypressure. Grain size distribution and intragranular and intergranular bubble size
distributions also affect the partition. An arbitrary constant value of 15.7 MPa
is here used for the porosity pressure, and VTT-ENIGMA fuel performancecode results from RIA benchmark Phase 1 were applied as end-of-life radial
temperature profiles in fuel. A grain size of 0.1 μm was used for the outmost
radial nodes. Arbitrary values were given for intergranular and intragranular
bubbles sizes, ranging between 10 and 500 Å, depending on the radial location.

‒

Fuel-clad roughness: Only one roughness can be taken into account in
SCANAIR calculations. In the specifications, fuel and cladding roughnesses
are given separately, and therefore the single roughness value given in the input
is taken as the sum of these two (sampled) roughnesses.

SCANAIR calculation hypotheses:‒

ZIRLO™ cladding material property models are not included in the SCANAIR
version delivered to the VTT, therefore Zircaloy-4 properties were used forcladding thermal conductivity, Young modulus, thermal-expansion, enthalpy
and visco-plastic behaviour.

‒

No visco-plastic model was applied for the fuel. A high temperature viscoplastic model developed for Zircaloy-4 in slow transient conditions was used
for the cladding.

‒

Chamfers or dishings were not taken into account (high burn-up fuel).
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Inner oxide layer is defined in the specifications to be about 10 μm, but it cannot
be taken into account in SCANAIR.

‒

Channel wall calculation and by-pass modelling were enabled. The material
properties of the channel wall and by-pass are taken from CABRI sodium loop
example inputs delivered with the SCANAIR code.

‒

Rupture stress limit for grain boundary fission gas release: 50 MPa.

‒

Cladding failure prediction was done with SCANAIR’s fracture mechanics
approach called CLARIS. As the cladding hydride rim thickness given in thespecifications was 50 μm, this value was used as the outer brittle zone depth
needed in the fracture mechanical approach.

References
Gaudier, F. (2010), “URANIE: The CEA/DEN uncertainty and sensitivity platform”, Procedia: Social
and Behavioral Sciences, Vol. 2/6, pp. 7660-7661, https://doi.org/10.1016/j.sbspro.2010.05.166.
Jernkvist, L.O. (2006), “Computational assessment of burnup-dependent fuel failure thresholds forreactivity initiated accidents”, Journal of Nuclear Science and Technology, Vol. 43/5, pp. 546-561.
https://doi.org/10.1080/18811248.2006.9711133
Lassmann, K. (1992), “TRANSURANUS: A fuel rod analysis code ready for use”, Journal of Nuclear
Materials, Vol. 188, pp. 295-302, https://doi.org/10.1016/0022-3115(92)90487-6.
Ribeiro, F. and Khvostov, G. (2015), “Multi-scale approach to advanced fuel modelling for enhanced
safety’, Progress in Nuclear Energy, 84, 24-35. https://doi.org/10.1016/j.pnucene.2015.03.022.

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