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Unclassified NEA/CSNI/R(2009)13 Organisation de Coopération et de Développement Économiques Organisation for Economic Co-operation and Development 21-Dec-2009
___________________________________________________________________________________________
_____________ English text only NUCLEAR ENERGY AGENCY
COMMITTEE ON THE SAFETY OF NUCLEAR INSTALLATIONS
BEMUSE PROGRAMME
Best-Estimate Methods
Uncertainty and Sensitivity Evaluation
BEMUSE Phase V Report
Uncertainty and Sensitivity Analysis of a LB-LOCA in ZION Nuclear Power Plant
JT03276446
Document complet disponible sur OLIS dans son format d'origine
Complete document available on OLIS in its original format
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Coordinators: F. Reventós, L. Batet, M. Pérez
Participating Organisations and Authors:
AEKI, Hungary A. Guba, I.Tóth
CEA, France T.Mieusset, P.Bazin, A.de Crécy
EDO-GIDROPRESS, Russia S.Borisov
GRS, Germany T.Skorek, H.Glaeser
IRSN, France J.Joucla, P.Probst
JNES, Japan A.Ui
KAERI, South Korea B.D.Chung
KINS, South Korea D.Y.Oh
NRI1, Czech Republic R.Pernica, M.Kyncl
NRI2, Czech Republic J.Macek
PSI, Switzerland A.Manera, J.Freixa
UNIPI1, Italy A.Petruzzi, F.D'Auria
UNIPI2, Italy A.Del Nevo, F.D'Auria
UPC, Spain M.Pérez, F.Reventós, L.Batet
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TABLE OF CONTENTS
GLOSSARY AND ACRONYMS ................................................................................................................... 7
EXECUTIVE SUMMARY ............................................................................................................................. 9
1. INTRODUCTION .................................................................................................................................. 13
1.1 Framework ...................................................................................................................................... 13 1.2 Content of the document ................................................................................................................. 13 1.3 Description of the BEMUSE programme ....................................................................................... 14 1.4 Participating organisations .............................................................................................................. 14 1.5 Specification for the BEMUSE Phase V ......................................................................................... 15 1.6 ZION and LB-LOCA brief description ........................................................................................... 16 1.7 Requirements for Phase V ............................................................................................................... 16 1.8 Uncertainty methodologies ............................................................................................................. 17
2. PART 1. LIST AND UNCERTAINTIES OF THE INPUT UNCERTAIN PARAMETERS ............... 19
2.1 Step 1: General sources of uncertainties ......................................................................................... 19 2.2 Step 2: Selection of parameters associated with uncertainty .......................................................... 24 2.3 Step 3: Quantification of uncertainty .............................................................................................. 26 2.4 Step 4: Synthesis ............................................................................................................................. 26
2.4.1 Synthesis table ........................................................................................................................... 26 2.4.2 Comparison of the considered phenomena ................................................................................ 33 2.4.3 Ranges of variation for the input parameters ............................................................................. 36
2.5 First conclusions on input parameters. Comparison with Phase III ................................................ 37
3. PART 2: UNCERTAINTY ANALYSIS RESULTS ............................................................................. 43
3.1 Steps 5 and 6: Main features of the methods .................................................................................. 43 3.1.1 Common features ....................................................................................................................... 43 3.1.2 Differences ................................................................................................................................ 43
3.2 Step 7: Uncertainty results .............................................................................................................. 46 3.2.1 Scalar quantities ......................................................................................................................... 46 3.2.2 Maximum cladding temperature ................................................................................................ 52 3.2.3 Upper plenum pressure .............................................................................................................. 56 3.2.4 First conclusions on uncertainty analysis results ....................................................................... 59
4. PART 3: SENSITIVITY ANALYSIS RESULTS ................................................................................. 61
4.1 General definitions: sensitivity and influence, global and local sensitivities .................................. 61 4.2 Ranking of the phenomena and parameters according to their influence ....................................... 61
4.2.1 Method of ranking ..................................................................................................................... 61 4.2.2 Ranking of the parameters ......................................................................................................... 62 4.2.3 Ranking of the phenomena ........................................................................................................ 66
CONCLUSIONS AND RECOMMENDATIONS ........................................................................................ 75
REFERENCES .............................................................................................................................................. 79
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APPENDIX A ............................................................................................................................................. 81
1. Introduction ........................................................................................................................................ 81 2. Parameters, ranges and pdfs to be included in Phase V specification ................................................ 82
2.1 General aspects .......................................................................................................................... 82 2.2 Ranges and pdfs ......................................................................................................................... 83 2.3 Physical models ......................................................................................................................... 84 2.4 Other parameters ....................................................................................................................... 85
3. Output specification, steps and files ................................................................................................... 85 3.1 Definition of the output uncertain parameters ........................................................................... 85
3.2 Step by step requirements ............................................................................................................... 85 Step 1: List the general sources of uncertainties considered for the Phase V of BEMUSE ................... 86 Step 2: How is the list of input uncertain parameters established? ........................................................ 86 Step 3: How are the uncertainties of the input uncertain parameters quantified? .................................. 86 Step 4: List the input uncertain parameters and quantify their uncertainties: the synthesis ................... 86 Step 5: Sampling for the probabilistic approach .................................................................................... 86 Step 6: Running the code ....................................................................................................................... 86 Step 7: First uncertainty analysis results ................................................................................................ 87 Step 8: Sensitivity analysis ..................................................................................................................... 87 3.3 Files to submit ........................................................................................................................... 88
4. References .......................................................................................................................................... 88
ANNEX 1. Considerations on the Uncertainty of the Upper-Head Temperature. ........................................ 89
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GLOSSARY AND ACRONYMS
AEKI Hungarian Academy of Sciences KFKI Atomic Energy Research Institute
BEMUSE Best Estimate Methods Uncertainty and Sensitivity Evaluation
BCL Broken Cold Leg
BHL Broken Hot Leg
BL Broken Loop
CCFL Counter Current Flow Limitation
CHF Critical Heat Flux
CIAU Code with the Capability for Internal Assessment of Uncertainty
CIPSU Common Input Parameters associated with a Specific Uncertainty
CEA Comissariat à l‟Energie Atomique
DWR Downcomer
EDO Gidropress Experimental Design Office
EPRI Electric Power Research Institute
GRS Gesselschaft für Anlagen und Reaktorsicherheit mbH
HPIS High Pressure Injection System
HS Heat Structures
HTC Heat Transfer Coefficient
ICL Intact Cold Leg
IL Intact Loop
IRSN Institut de Radioprotection et de Sûreté Nucléaire
JNES Japan Nuclear Energy Safety
KAERI Korea Atomic Energy Research Institute
KINS Korean Institute of Nuclear Safety
LB-LOCA Large Break Loss of Coolant Accident
LN Log Normal
LPIS Low Pressure Injection System
LUB Lower Uncertainty Bound
MCT Maximum Cladding Temperature
MPCT Maximum Peak Cladding Temperature
N Normal
NRI Nuclear Research Institute Rez
PCC Partial Correlation Coefficient
PCT Peak Cladding Temperature
pdf Probability Density Function
PIRT Phenomena Identification and Ranking Table
PSI Paul Scherrer Institute
PWR Pressurized Water Reactor
PZR Pressurizer
QF Quench Front
RC Reference Case
SCC Spearman Correlation Coefficient
SPDF Subjective Probability Density Function
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SRRC Standardized Rank Regression Coefficient
SRS Simple Random Sampling
U Uniform
UH Upper-head
UNIPI Università di Pisa
UP Upper Plenum
UPB Upper Uncertainty Bound
UPC Universitat Politècnica de Catalunya
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EXECUTIVE SUMMARY
Background
Since nuclear energy was first used to produce electricity in the 1950s, the evaluation of nuclear power
plant performance during accidental transient conditions has been the main issue in thermal-hydraulic
safety research worldwide.
Different computer codes such as ATHLET, CATHARE, RELAP, TRAC and TRACE have been
developed since those days for this purpose and are currently widely used in the nuclear community. These
codes are very sophisticated and can predict time trends of safety-related quantity of interest during
transients of a LWR. Data recorded in scaled facilities is used to assess the capabilities of the codes.
Today, the amount of available experimental data obtained in very simple loops (like Basic Test Facilities
or Separate Effect Test Facilities) or in very complex Integral Test Facilities is huge. The use of a code to
predict a real NPP situation depends on two conditions: (1) the experimental data selected for qualifying a
code has to be able to reproduce the phenomena expected in the plant and (2) codes have to be able to
qualitatively and quantitatively reproduce those data on scaled facilities. The calculation of the plant
transient using best-estimate computer codes should include an additional analysis evaluating the
uncertainties of the obtained results. This analysis can be also completed by a sensitivity analysis, which
provides additional information.
The BEMUSE (Best Estimate Methods - Uncertainty and Sensitivity Evaluation, see Ref.[10])
programme-promoted by the working Group on Accident Management and Analysis (GAMA) and
endorsed by the Committee on the Safety of Nuclear Installations (CSNI) - represents in this context an
important step towards reliable application of high-quality best-estimate and uncertainty and sensitivity
evaluation methods. The application of these methods to a Large-Break Loss of Coolant Accident
(LB-LOCA) constitutes the main activity of the programme, structured into two main stages:
Step 1: Best-estimate and uncertainty and sensitivity evaluations of the LOFT L2-5 test (Phases II
and III). LOFT is the only Integral Test Facility with a nuclear core where thermal-hydraulic safety
experiments have been performed.
Step 2: Best-estimate and uncertainty and sensitivity evaluations of a nuclear power plant (Phases IV
and V).
A presentation of the uncertainty methodologies to be used by the participants (Phase I) is included in the
first step. The final phase (Phase VI) consists of the synthesis conclusions and recommendations.
Objective of the work
The BEMUSE programme is focused on the application of uncertainty methodologies to LB-LOCA
scenarios. The main goals of the programme are:
To evaluate the practicability, quality and reliability of Best Estimate methods including uncertainty
evaluations in applications relevant to nuclear reactor safety
To develop a common understanding in this domain
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To promote/facilitate the use of these methods by the regulatory bodies and the industry
The scope of Phase V of the BEMUSE programme is the uncertainty analysis of a LB-LOCA based on a
Phase IV reference calculation. The LB-LOCA scenario takes place in ZION plant which is a generic 4
loop PWR reactor.
The objectives of the activity are:
To obtain uncertainty bands for the maximum cladding temperature (evolution plotted against time),
upper plenum pressure (evolution plotted against time), maximum peak cladding temperature (scalar
value), 1st peak cladding temperature (scalar value), 2nd peak cladding temperature (scalar value),
time of accumulator injection (scalar value), time of complete core quenching (scalar value).
When using a probabilistic approach methodology: to evaluate the influence of the selected
parameters on the maximum cladding temperature (evolution plotted against time) and the upper
plenum pressure (evolution plotted against time).
To compare procedures with the experience gained in previous Phase III.
Task specification
Phase V deals with a generic plant without any detailed information concerning the plant‟s initial and
boundary conditions, fuel properties, etc... A similar situation was also present in Phase IV, where the lack
of data needed for both modelling the reactor and performing the uncertainty analysis led to a spread of
results for the reference calculation. To solve this situation and diminish the spread, it was agreed to
provide common information about geometry and modelling. Considering the experience gained in Phase
IV, a list of common input parameters concerning uncertainties of the nuclear power plant was prepared by
CEA, GRS and UPC teams. These parameters were strongly recommended to be included in the
uncertainty analysis when a probabilistic approach was followed. The list contains the selected parameters,
the uncertainty distribution type and its range.
The rest of the activity followed the example of Phase III and only a new scalar quantity was included in
the exercise: the maximum peak cladding temperature as a scalar parameter.
Used methods
Two types of methodologies have been applied in BEMUSE Phase V exercise to obtain the uncertainty
bands: “propagation of input uncertainty” type (twelve participants out of the total fourteen), and
“propagation of output accuracy” type (two participants).
The method based upon "extrapolation of output uncertainties", the so called CIAU, derives automatically
the uncertainty of the simulated scenario using a database of qualified experimental data and qualified
system code calculation results. The applications based on the CIAU method have been performed with
two different thermal-hydraulic codes, RELAP5/mod3.2 (UNIPI1) and CATHARE2V2.5_1 (UNIPI2), and
two independent uncertainty databases have been used for uncertainty quantification.
The “propagation of input uncertainty” type, the so called probabilistic approach, is based on the selection
of a set of input parameters for which a range of variation (uncertainty) is associated, the use of Wilks‟
formula to determine the number of code runs needed, and finally the statistical treatment of the results to
build the uncertainty bands.
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The common features of the methodologies were: the Simple Random Sampling (SRS) technique used, no
dependency considered among the uncertain input parameters, and the form of the uncertainty results: two
unilateral tolerance intervals, giving respectively an estimation of the 5% and the 95% quantiles, with a
confidence level at least of 95% for both quantiles.
The differences were: Wilks‟ order (from 2 to 9) the set of input uncertain parameters, the laws used to
associate uncertainty and the treatment of failed calculations.
The two types of methodology have advantages and drawbacks. The main drawback of the probabilistic
approach is the need of engineering judgment for limiting the number of input uncertain parameters and, in
some cases, for the process of associating the uncertainty. For the “output extrapolation accuracy”
approach, the main drawbacks are that it depends on the availability of “relevant” experimental data
(therefore it is not applicable when no relevant experimental information is available) and that the process
of combining errors is not based upon fundamental principles and requires detailed validation. This second
approach seeks to avoid engineering judgement as much as possible.
Main Results and conclusions
The main results can be summarised as follows:
All participants managed to obtain the requested uncertainty bands with reasonable values.
A database, including comparative tables and plots, has been produced.
Concerning the results for the cladding temperature-type output parameters, the uncertainty bands for both
the 1st and the 2nd Peak Cladding Temperatures (PCTs), show nearly no overlap. However, when
comparing results for the “maximum peak cladding temperature”, the dispersion of the band width is
significantly reduced for the probabilistic approach, and there is a region of overlap of about 15K. The
missing overlap can be explained by quite different best-estimate calculations combined with rather narrow
uncertainty bands. For the pressure-type output parameters the estimation of the uncertainty bands
(accumulator injection time and time trend for primary pressure) is very different depending upon the
approach used. The CIAU approach obtains a width larger than the width found by other methods, which is
almost negligible.
Although the overall results are clearly a step forward towards the consolidation of the different methods,
the uncertainty bands for the scalar output parameters, which do not show a clear agreement among the
probabilistic approach users, may point out that for this approach, the uncertainty analyses have been not
so well mastered by some participants.
Despite it was not a main goal of the exercise, it is worth mentioning that the upper limit estimations
(95/95) for maximum values of PCT predicted by participants do not exceed the safety criterion.
Sensitivity analysis has been successfully performed by all participants using the probabilistic method. A
comparison has been carried out about the influence ranking of the uncertain parameters. Users of the
CIAU methodology presented sensitivity results evaluating the effect of the nodalization which can be
found in their own contribution document.
The influence ranking has been estimated for two macro responses: cladding temperature and primary
pressure. The sensitivity coefficients used by participants are Pearson and Spearman correlation
coefficient, standardised rank regression coefficients, Pearson and Spearman partial correlation coefficients
and SOBOL indices.
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The sensitivity results allowed defining several parameters as influential by the 12 participants using the
probabilistic method. These quantities are:
From the set of common parameters: “Power after scram” (12 participants out of 12) and “UO2
conductivity” (11/12) for the cladding temperature, “Containment pressure” (10/12), “Initial ILCL
temperature” (9/10) and “Initial UH temperature” (6/8) for the primary pressure.
From the other parameters: “Film boiling” (6/8) and “Critical heat flux” (7/9)
The present document also contains a comparison with Phase III, although final conclusions will be
provided in the following Phase VI document.
Phase V results are a step forward that contributes to the general goals of the BEMUSE project.
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1. INTRODUCTION
1.1 Framework
The BEMUSE (Best Estimate Methods – Uncertainty and Sensitivity Evaluation) Programme has been
promoted by the Working Group on Accident Management and Analysis (WGAMA) and endorsed by the
Committee on the Safety of Nuclear Installations (CSNI).
The high-level objectives of the work are:
To evaluate the practicability, quality and reliability of Best-Estimate (BE) methods including
uncertainty and sensitivity evaluation in applications relevant to nuclear reactor safety
To develop a common understanding in this domain
To promote and facilitate their use by the regulatory bodies and the industry
Operational objectives include an assessment of the applicability of best-estimate and uncertainty and
sensitivity methods to integral tests and their use in reactor applications.
The scope of the programme is to perform Large Break Loss-Of-Coolant Accident (LB-LOCA) analyses
making reference to experimental data and to a Nuclear Power Plant (NPP) to address the issue of “the
capabilities of computational tools” including scaling and uncertainty analysis.
This report is focused on BEMUSE Phase V activities and results. In Phase I the methodologies were
discussed, in Phase II the Best-Estimate calculation of a test was performed, in Phase III the uncertainties
and sensitivities were analyzed for the previous test and finally, in Phase IV, the Best Estimate calculation
for a NPP was developed. All these previous phases constitute the background which is intended to be used
in the present phase in order to produce final uncertainty results. Nowadays, Best Estimate Plus
Uncertainty Methods are broadly used worldwide, directly for licensing purposes (USA, Netherlands,
Brazil, etc.) or linked to future use for licensing (Canada, Czech Republic, France, etc.). The results
presented in this report conclude on the computational aspects of the comparative exercise as they are a
necessary step for future uses of these methods for licensing purposes.
1.2 Content of the document
This document is organised in 3 different parts together with a brief introduction and a final summary of
the main conclusions. In the introduction a summary overview of the starting point of this Phase of the
BEMUSE programme is presented. After some basic comments on framework and contents a brief
description of the whole BEMUSE programme is given along with the list of participating organisations.
The specification of this Phase V is cited and the requirements are summarised. The Zion plant and the
scenario are briefly introduced and the methodologies are also cited.
Part 1 is devoted to the uncertainties of the input parameters. The different sequence of steps established in
Phase III are slightly adapted here in Phase V as the subjects as “General sources of uncertainty”
“Selection of uncertainty parameters” and “Quantification” are introduced. A synthesis section and some
conclusions on input parameters are also given in Part 1.
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Part 2 is devoted to uncertainty analysis results. It also has the structure of steps. After reviewing the main
features of the methods used by participants, it explains the main results of the uncertainty analysis using
figures and tables to show uncertainty bands of the selected output parameters.
Part 3 is devoted to sensitivity analysis results and has also a step structure. The general definitions needed
in sensitivity analysis (influence, global and local sensitivities…) are given in this section along with the
ranking of phenomena. A brief comparison with Phase III is also added.
The document ends with a summarizing “Conclusions and Recommendations” section.
A list of references is introduced after the conclusions and Appendix A contains the full text of the Phase
specification.
1.3 Description of the BEMUSE programme
BEMUSE programme consists of 6 Phases separated into two steps. The first step aimed at analysing the
experiment L2-5 carried out in the LOFT facility whereas the second one is focused on the study of a
hypothetical LB-LOCA in a commercial Nuclear Power Plant (more precisely, a four loop PWR
Westinghouse).
The six Phases of BEMUSE are:
Phase I: Description of the uncertainty methodology to be used by participants. This phase was
coordinated by IRSN (see Ref.[1]).
Phase II: Best-estimate calculation of the ISP-13: LOFT L2-5. It was to be the reference case for the
following phase. Some sensitivity calculations were proposed in the specifications document and
performed by the participants. This phase was coordinated by UNIPI (see Ref.[3]).
Phase III: Uncertainty and Sensitivity analysis of LOFT L2-5, first conclusions on the
methodologies and suggestions for improvement. This phase was coordinated by CEA (see Ref.[4]).
Phase IV: Best-estimate calculations of a LB-LOCA in ZION nuclear power plant. Analogous to
Phase II but without experimental data. Reference case for next phase. Some sensitivity calculations
were proposed on Phase II basis. This phase was coordinated by UPC (see Ref.[5]).
Phase V: Uncertainty and Sensitivity analysis of a LB-LOCA scenario in ZION nuclear power plant.
Analogous to previous Phase III. This phase has been coordinated by UPC.
Phase VI: Status report on the area, classification of the methods, conclusions and recommendations.
This phase is being coordinated by GRS.
The present document compiles and compares the work performed by participants in Phase V of BEMUSE
programme.
1.4 Participating organisations
Fourteen groups from twelve organisations and ten countries have participated in the exercise.
Six thermal-hydraulic system codes have been used, sometimes in different versions:
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ATHLET: 3 participants.
CATHARE: 3 participants.
MARS: 1 participant.
RELAP5: 4 participants.
TECH-M-97: 1 participant.
TRACE: 2 participants.
The list of the organisations participating in BEMUSE Phase V is given in
Table 1: List of participants in BEMUSE Phase V
Numb. Organisation Country Name E-mail Code
1 AEKI Hungary A.Guba
I.Tóth
I. Trosztel
ATHLET 2.0A
2 CEA France T.Mieusset
P.Bazin
A.de Crécy
CATHARE2
V2.5_1 (r5_567)
3 EDO Russia S.Borisov [email protected] TECH-M-97
4 GRS Germany T.Skorek
H.Glaeser [email protected]
ATHLET 2.1B
5 IRSN France J.Joucla
P.Probst [email protected]
CATHARE2
V2.5_1 mod6.1
6 JNES Japan A.Ui [email protected] TRACE ver4.05
7 KAERI South Korea B.D.Chung [email protected] MARS 3.1
8 KINS South Korea D.Y.Oh [email protected] RELAP5/mod3.3
9 NRI-1 Czech Republic R.Pernica
M.Kyncl [email protected]
RELAP5/mod3.3
10 NRI-2 Czech Republic Jiri Macek [email protected] ATHLET 2.1 A
11 PSI Switzerland A.Manera
J.Freixa
TRACE5rc3
12 UNIPI-1 Italy A.Petruzzi
F.d‟Auria [email protected]
RELAP5/mod3.2
13 UNIPI-2 Italy A.Del Nevo
F.d‟Auria [email protected]
CATHARE2
V2.5_1 mod6.1
14 UPC Spain M.Pérez
F.Reventós
L.Batet
RELAP5/mod3.3
1.5 Specification for the BEMUSE Phase V
UPC, acting as coordinator of the present Phase V, prepared a specifications document and, in close
collaboration with CEA and GRS, a list of common input uncertainty parameters to be used by those
participants using a probabilistic methodology (all except UNIPI). The full text of the specification is
included as APPENDIX A.
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1.6 ZION and LB-LOCA brief description
Extended information on the simulated nuclear power plant and scenario features can be found in the
report of previous Phase IV (see Ref.[5]).
Zion Unit 1 was operated and owned by the Commonwealth Edison network. Its main features are:
Location: Zion, Illinois.
4 loops PWR.
Westinghouse design.
Net output: 1040 MWe.
Thermal power: 3250 MWth.
Status: permanently shut down.
Date started: June 1973.
Date closed: January 1998.
The scenario simulated is a cold leg LB-LOCA without HPIS actuation.
1.7 Requirements for Phase V
Following Phase III procedures, six output parameters are considered for uncertainty analysis: four scalar
quantities and two time trends (see Table 2). A new scalar quantity was included in the exercise, the
maximum peak cladding temperature as a scalar parameter.
Table 2: Output parameters for uncertainty and sensitivity analysis
Type Definition Criterion
Time trend Maximum cladding temperature: MCT See comment below
Pressure in the upper plenum: Pup No criterion
Scalar
quantities
1st PCT (blowdown Phase) MCT and t < tinj
2nd PCT (~ reflood Phase) MCT and t > tinj
Time of accumulator injection: tinj Time of beginning of injection
Time of complete core quenching: tque Tclad ≤ Tsat + 30K
Maximum peak cladding temperature: MPCT See comment below
Where:
Tclad: cladding temperature.
Tsat: saturation temperature.
The maximum cladding temperature (MCT) is defined as in previous phases: maximum cladding
temperature at each time step without location dependency (neither axial nor radial).
The maximum peak cladding temperature (MPCT) is a scalar quantity defined as the maximum temperature
value reached on the cladding surface during the whole transient, independently of its location (axial or radial).
Also following Phase III development, the specifications document for Phase V (see 0) required a number
of steps to describe the work performed by each participant:
Part 1. Input parameters and associated uncertainties.
Step 1. General sources of uncertainties considered for BEMUSE Phase V.
Step 2. Selection of uncertain parameters.
Step 3. Quantification of uncertainty.
Step 4. Synthesis: selected parameters and their associated ranges of uncertainty.
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Part 2. Uncertainty analysis.
Step 5. Sampling (for the probabilistic approach).
Step 6. Running the code.
Step 7. First uncertainty results.
Part 3. Sensitivity analysis.
Step 8. Sensitivity analysis.
1.8 Uncertainty methodologies
Uncertainty methodologies used by participants have been described in Phase I and Phase III reports (see
Ref.[1] and Ref.[4]).
Except for UNIPI groups that analysed uncertainties with the CIAU method, the rest of participants used a
fully probabilistic approach, based on the use of Wilks‟ formula (see Ref.[7]).
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2. PART 1. LIST AND UNCERTAINTIES OF THE INPUT
UNCERTAIN PARAMETERS
2.1 Step 1: General sources of uncertainties
The UPC team, in collaboration with CEA and GRS, elaborated a list of input parameters with proposed
uncertainty ranges, which were strongly recommended to be taken into account by participants using a
probabilistic methodology (see 0). The reason of preparing such list of “Common Input Parameters
associated with a Specific Uncertainty” (CIPSU) is connected with the results of Phase IV showing for the
reference case of the different participants quite an important dispersion. Another reason was that a number
of data were not available for the Zion plant and participants would have taken different assumptions. In
order to minimize further dispersion it was agreed that participants – while following their own
methodology – should take into account to the extent possible the proposed list of CIPSU. Table 3 gives
types of distribution functions and ranges for the above mentioned parameters:
Material properties
Initial and boundary conditions
Friction form loss factors.
Table 3: Common input parameters associated with a specific uncertainty, range of variation and type of
probability density function.
Phenomenon Parameter Imposed range of
variation
Type of pdf Comments
Flow rate at
the break Containment
pressure
[0.85, 1.15], see
Table 4 in
Appendix A
Uniform Multiplier.
Fuel thermal
behaviour Initial core
power
[0.98; 1.02] Normal Multiplier affecting both nominal
power and the power after scram.
Peaking factor
(power of the hot
rod)
[0.95; 1.05] Normal Multiplier.
Hot gap size
(whole core
except hot rod)
[0.8; 1.2]
Normal Multiplier. Includes uncertainty on
gap and cladding conductivities.
Hot gap size (hot
rod)
[0.8; 1.2]
Normal Multiplier. Includes uncertainty on
gap and cladding conductivities.
Power after
scram
[0.92; 1.08] Normal Multiplier
UO2
conductivity
[0.9, 1.1]
(Tfuel <2000 K )
[0.8,1.2]
(Tfuel >2000 K)
Normal Multiplier. Uncertainty depends on
temperature.
UO2 specific
heat
[0.98, 1.02]
(Tfuel <1800 K )
[0.87,1.13]
(Tfuel >1800 K)
Normal Multiplier. Uncertainty depends on
temperature.
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Phenomenon Parameter Imposed range of
variation
Type of pdf Comments
Pump
behaviour Rotation speed
after break for
intact loops
[0.98; 1..02] Normal Multiplier.
Rotation speed
after break for
broken loop
[0.9; 1.1] Normal Multiplier.
Data related
to injections Initial
accumulator
pressure
[-0.2; +0.2] MPa Normal
Friction form
loss in the
accumulator line
[0.5; 2] Log-normal Multiplier.
Accumulators
initial liquid
temperature
[-10; +10] °C Normal
Flow
characteristic of
LPIS
[0.95 ; 1.05] Normal Multiplier.
Pressurizer Initial level [-10; +10] cm Normal
Initial pressure [-0.1; +0.1] MPa Normal
Friction form
loss in the surge
line
[0.5; 2] Log-normal Multiplier.
Initial
conditions:
primary
system
Initial intact loop
mass flow rate
[0.96; 1.04] Normal Multiplier. This parameter can be
changed through the pump speed or
through pressure losses in the
system...
Initial intact loop
cold leg
temperature
[-2; +2] K Normal This parameter can be changed
through the secondary pressure, heat
transfer coefficient or area in the U-
tubes...
Initial upper-
head mean
temperature
[Tcold ;
Tcold + 10 K]
Uniform This parameter refers to the “mean
temperature” of the volumes of the
upper plenum (see Annex 1 in
Appendix A)
Table 4 summarises the sources of uncertainties taken into account by the participants. The table includes
UNIPI1 and UNIPI2 despite they are not considering directly input uncertainties. Three participants
considered only, and when possible, the set of parameters suggested in the specifications document:
EDO did not include the following parameters: initial upper head temperature, initial accumulator
liquid temperature and hot gap size (zones 1, 2, 3, 4)
JNES only used the 20 CIPSU
PSI did not consider the upper-head mean temperature parameter of the CIPSU due to the use of a
3D vessel nodalization used, but considered CCFL at the upper tie plate with the uncertainty
distribution specified in the specifications document
Participants using a 3D vessel nodalization (CEA, JNES, KAERI and PSI) could not implement directly
the “upper-head mean temperature” uncertainty. Two participants, KAERI (using MARS) and PSI (using
TRACE) could not associate uncertainty to the specified temperature. Among the other two, CEA group
NEA/CSNI/R(2009)13
21
specified in its contribution the way utilised for this purpose. JNES did not give any specific explanation
for this parameter.
Two participants (AEKI, KINS) applied a unique multiplier for all temperatures when dealing with UO2
properties instead of splitting the temperature range into two as specified in the documentation for phase V.
Three participants (IRSN, NRI2 and UPC) used two different multipliers, one for each range. The rest of
the participants used a unique multiplier and re-scaled it depending upon the temperature falling within the
lower or the upper temperature range as specified in the basis document for phase V.
Participants gave details on the way the uncertainty of the CIPSU was applied when the general guidelines
given in the specifications document (see CD with the appendices to BEMUSE Phase V Report) were not
followed.
Figure 1 to Figure 5 show the reference case results for maximum cladding temperature and primary
pressure obtained by all participants. The figures for these time trend quantities are included because
AEKI, CEA, GRS, IRSN, KINS and PSI groups have used in Phase V a different reference case
calculation than the one submitted in Phase IV (Ref.[5]). The detailed information on changes can be found
in each participant‟s contribution. Participant‟s results are grouped according to the code used. The KAERI
results (MARS code), are included in RELAP5 graphs because of the similarity between the codes.
The KAERI reference calculation of Phase IV could not be updated in the last version of Phase IV
document; therefore the results here presented for KAERI group differ from those from the report of Phase
IV.
General comments related to reference calculations and to code and user effects are written in “Appendix
G” and in “Appendix C” of the Phase IV report document (see Ref.[5]).
NEA/CSNI/R(2009)13
22
Table 4: Input parameters with uncertainty considered by the participants
NEA/CSNI/R(2009)13
23
Figure 1: Reference calculation. ATHLET code
Maximum cladding temperature
400
500
600
700
800
900
1000
1100
1200
1300
1400
-50 0 50 100 150 200 250 300 350 400 450 500
Time (s)
Te
mp
era
ture
(K
)
AEKI GRS NRI2
Upper plenum pressure
0
2
4
6
8
10
12
14
16
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ss
ure
(M
Pa
)
AEKI GRS NRI2
Figure 2: Reference calculation. CATHARE code.
Maximum cladding temperature
400
500
600
700
800
900
1000
1100
1200
1300
1400
-50 0 50 100 150 200 250 300 350 400 450 500
Time (s)
Te
mp
era
ture
(K
)
CEA IRSN UNIPI2
Upper plenum pressure
0
2
4
6
8
10
12
14
16
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ss
ure
(M
Pa
)
CEA IRSN UNIPI2
Figure 3: Reference calculation. RELAP5 code.
Maximum cladding temperature
400
500
600
700
800
900
1000
1100
1200
1300
1400
-50 0 50 100 150 200 250 300 350 400 450 500
Time (s)
Te
mp
era
ture
(K
)
KINS NRI1 UNIPI1 UPC KAERI (MARS code)
Upper plenum pressure
0
2
4
6
8
10
12
14
16
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ss
ure
(M
Pa
)
KINS NRI1 UNIPI1 UPC KAERI (MARS code)
NEA/CSNI/R(2009)13
24
Figure 4: Reference calculation. TRACE code
Maximum cladding temperature
400
500
600
700
800
900
1000
1100
1200
1300
1400
-50 0 50 100 150 200 250 300 350 400 450 500
Time (s)
Te
mp
era
ture
(K
)
JNES PSI
Upper plenum pressure
0
2
4
6
8
10
12
14
16
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ss
ure
(M
Pa
)
JNES PSI
Figure 5: Reference calculation. TECH-M-97 code.
Maximum cladding temperature
400
500
600
700
800
900
1000
1100
1200
1300
1400
-50 0 50 100 150 200 250 300 350 400 450 500
Time (s)
Te
mp
era
ture
(K
)
EDO
Upper plenum pressure
0
2
4
6
8
10
12
14
16
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ss
ure
(M
Pa
)
EDO
2.2 Step 2: Selection of parameters associated with uncertainty
Only participants following a probabilistic approach are concerned by this step.
The Phase III report distinguished two kinds of approaches to select the uncertain parameters.
In the first approach (KAERI, KINS, and UPC), a PIRT process was used. In Phase III, participants using
the PIRT approach obtained a lower number of uncertain input parameters than other participants.
Participants of both Phase III and V have increased in the present phase the number of uncertain input
parameters with respect to Phase III. The increase is, in the first place, a direct consequence of the
agreement on a minimal “nominal” set of parameters (the 20 CIPSU). As it can be seen in Table 5 three
participants (KAERI, KINS and UPC) considered less than 20 uncertain parameters in Phase III (AEKI
and EDO did not contribute to Phase III). Other reasons for the enlargement of the number of parameters
are related to the recommendations given in Phase III and to the experience gained by participants. For
example: some parameters that were established as relevant from the sensitivity analysis of Phase III (see
Ref.[3]) are included in Phase V.
Participants using the second approach (CEA, GRS, IRSN, NRI1 and NRI2) obtain a higher number of
parameters since they consider all the potentially influential parameters. In Phase V, the three possible
NEA/CSNI/R(2009)13
25
change options occurred in relation to Phase III: increasing the number of input uncertain parameters
(IRSN and GRS), decreasing it (CEA and NRI2), and approximately keeping the same number (NRI1).
In this phase some participants did not follow any of the previous two approaches. Three participants
(EDO, JNES and PSI) considered only the 20 CIPSU and therefore did not take into account the
uncertainties related to code physical models.
Table 5 compares the number of parameters used in Phases III and V by participants in Phase V. Generally
speaking, the mean number of uncertain input parameters considered is roughly the same but its dispersion
among participants has decreased. When considering only the participants that do not apply only the
minimum 20 CIPSU the mean number of the selected parameters obviously increases (since there‟s no
limit for the number of parameters) to almost 39 and the dispersion between participants diminishes to 11.
When comparing these values with previous Phase III the mean number increases by almost six parameters
and the standard deviation decreases of seven parameters.
Table 5: Number of input parameters. Comparison with Phase III (Table 9 in Ref.[4])
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
Mea
n
Sta
ndar
d
dev
iati
on
Phase III - 53 - 49 42 27 14 13 31 64 24 14 33.1 18.1
Phase V 36 44 17 55 54 20 25 24 33 44 20 32 33.7 13.2
Phase V (*)
36 44 - 55 54 - 25 24 33 44 - 32 38.6 11.4 (*)
Only participants considering more parameters than the ones proposed in the
specifications document.
Table 6: Order of Wilks' application. Comparison with Phase III (Table 9 in Ref.[4])
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
Phase III - 2 (100) - 2 (100) 1 (59) 1(100) 2 (100) 1 (59) 1 (59) 1 (60) 3 (150) 2 (100)
Phase V 3
(130)
5 (200) 2 (93) 4 (153) 9 (300) 2 (110) 3 (200) 3 (124) 5 (200) 2 (93) 2 (120) 3 (124)
The comparison of Wilks‟ order used in both phases (for Phase III data see Table 9 in Ref.[4]) is shown in
Table 6 where the number in the parenthesis indicates the number of code calculations performed,
including failed code runs. It is interesting to compare them since there were no recommendations on this
issue in the specifications document.
One recommendation provided in the phase III report (see Ref.[3]) was to increase the number of
calculations to about 150 to 200 when the upper tolerance limit approaches regulatory acceptance
criteria. Table 17 describes the results for the Maximum peak cladding temperature. Some remarks to
this table are:
The minimum order for Wilks‟s method in Phase V is two, while in phase III it was one.
NEA/CSNI/R(2009)13
26
The general tendency among the participants has been to increase at least one order with respect to
Phase III.
Only one participant (PSI) decreased the number of code runs and the order of application.
4 participants used 2nd order (EDO, JNES, NRI2 and PSI).
4 participants used 3rd order (AEKI, KAERI, KINS and UPC).
4 participants used higher orders than third (GRS used 4th order, CEA and NRI1 used 5
th order, and
IRSN used 9th order)
Some participants performed additional analysis by increasing the number of runs and, thus, the order of
Wilks‟ formula application. Detailed performance of these analyses can be found in the CD of participant
contributions (see Ref[13]).
2.3 Step 3: Quantification of uncertainty
Only participants following a probabilistic approach are concerned by this step.
For the CIPSU specified in 0, all the participants used the recommended type of uncertainty and range. The
methods to quantify the uncertainty of the other input parameters are: literature review such as code
manuals (e.g. R5 code manual, see Ref.[8]), fitting of experimental data, previous studies such as CSAU
(see Ref.[12]) or UMS (see Ref.[9]), and expert judgement.
2.4 Step 4: Synthesis
2.4.1 Synthesis table
Table 7 summarises the input parameters used by each participant (that followed a probabilistic
approach) with its associated uncertainty. Table 7 is constructed following the same procedure as in
the Phase III report (Ref.[4]). The indication “Y” (yes) means that the parameter has been considered
by the participant and, when necessary, comments have been added in parenthesis. When a number is
written, it indicates the number of multipliers (or added quantities) used for that parameter. Parameters
are associated, if possible, with certain phenomena or, if not, they are classified by the type of
physical law.
Common input parameters written in specifications document (0) are shaded in grey.
NEA/CSNI/R(2009)13
27
Table 7: Input parameters considered by the participants (using a probabilistic approach). Associated
phenomena or physical law
Participant
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
Number of input parameters 36 44 17 55 54 20 25 24 33 44 20 32
Phenomenon Parameter
Flow rates repartition in the
circuit/ pressure
drops
Form loss coef. – active core
Y Y
Form loss coef.
– core bypass Y
Form loss coef. – DWR & core
cross
connections
Y
Form loss coef. – lower core
plate
Y
Form loss coef. – ICL
Y
Form loss coef.
– BCL Y
Y
(DW
R-BCL)
Form loss coef.
– BHL Y
Form loss coef. – all legs
Y
Darcy-
Weisbach friction factor
in loops and
HA connection pipe
Y
Darcy-
Weisbach friction factor
in reactor vessel
Y
Momentum
term approximation
(yes or no)
Y Y
Wall friction Wall friction
factor, primary system
Y
Two-Phase
multiplier of
pressure drop in vertical pipe
(Martinelli-
Nelson correlation)
Y Y
Two-Phase
multiplier of pressure drop in
horizontal pipe
(Martinelli-Nelson
correlation)
Y Y
NEA/CSNI/R(2009)13
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Participant
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
Number of input parameters 36 44 17 55 54 20 25 24 33 44 20 32
Phenomenon Parameter
Void fraction
dependent correction
coefficient for
fraction of water and steam
in total wall
friction
Y
Liquid-wall
friction Y (2)
Vapour-wall
friction Y (2)
Flow rate at the break
Energy (heat) transfer at
liquid-vapour
interface due to flashing
Y Y
Flashing delay Y
Turbulence
factor in critical break flow
model
Y Y
Wall friction
factor Y Y Y
Momentum
term
approximation at the break
(yes or no)
Y Y
Break discharge coefficient
Y Y(2) Y(2)
Fuel thermal behaviour
Initial core power
Y Y Y Y Y Y Y Y Y Y Y Y
Peaking factor Y Y Y Y Y Y Y Y Y Y Y Y
Hot gap size
(whole core except rod #5)
Y Y Y Y Y Y*1 Y Y Y Y Y
Hot gap size
(hot rod #5) Y Y Y Y Y Y Y*1 Y Y Y Y Y
Power after scram
Y Y Y Y Y Y Y Y Y Y Y Y
UO2
conductivity Y*2 Y Y Y Y(2) Y Y Y*2 Y
Y(2
) Y
Y(
2)
UO2 specific heat
Y*2 Y Y Y Y(2) Y Y Y*2 Y Y(2
) Y
Y(2)
Boundary
conditions
Containment
pressure Y Y Y Y Y Y Y Y Y Y Y Y
Pump rotational
speed (IL) Y Y Y Y Y Y Y Y Y Y Y Y
Pump rotational
speed (BL) Y Y Y Y Y Y Y Y Y Y Y Y
Two-Phase pump head
degradation
(IL)
Y
Two-Phase pump head
degradation
(BL)
Y
NEA/CSNI/R(2009)13
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Participant
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
Number of input parameters 36 44 17 55 54 20 25 24 33 44 20 32
Phenomenon Parameter
Global heat
transfer
Complex of
heat transfer models: heat
transfer fouling
factor
Y
Structure heat
transfer
surfaces: heat transfer fouling
factor
Y
Heat transfer in
the rewetted
zone
Forced
convection to
liquid
Y Y Y(2) Y Y Y
Natural
convection to
liquid
Y
Nucleate boiling
Y Y Y Y Y Y Y(2)
Heat transfer in
the dry zone
Forced
convection to
vapour
Y Y Y Y Y Y
Natural convection to
vapour
Y Y
Vapour-interface energy
transfer
Y
Alternative models - forced
convection to
vapour
Y (Dittus-Boelter or
Mc
Eligot)
Y (Dittus-Boelter or
Mc
Eligot)
Film boiling
Y Y
Y(2) (all
Phases /
reflood)
Y Y Y Y(
2)
Alternative
models – film
boiling.
Y
(Dougall-
Rohsenow / Condie-
Bengtson)
Y
(Dougall-
Rohsenow / Condie-
Bengtson)
Y
Minimum of
stable film temperature
(Tmfs)
Y Y Y Y
Transition boliling
Y Y Y
Pool film
boiling for
natural
convection
Y Y
Alternative
models – pool film boiling
Y
Critical heat
flux
Critical heat
flux Y Y Y Y Y Y Y Y
Alternative
models – critical heat
flux
Y
NEA/CSNI/R(2009)13
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Participant
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
Number of input parameters 36 44 17 55 54 20 25 24 33 44 20 32
Phenomenon Parameter
Interfacial
friction
*Blowdown:
interfacial friction (ILHL,
UP and core)
Y
*Refill and reflood:
Interfacial
friction in dispersed flow
(core,
downstream from the
quench front
and UP)
Y
*Refill and reflood: Steen-
Wallis velocity
for onset of entrainment
IHL
Y
Interfacial friction
downstream QF
Y
Interfacial friction (core,
upstream from
the QF)
Y
Velocity of transition from
non-dispersed
to dispersed droplet flow in
vertical bundle
Y
Critical velocity of transition
from non-
dispersed to dispersed
droplet flow in
vertical pipe and downcomer
Y
Interfacial shear
in dispersed
vertical droplet pipe flow
Y Y
Interfacial
friction for annular flows
Y
Interfacial
friction (churn-bubblle flows)
in pipe
geometry
Y Y
Interfacial friction (churn-
bubblle flows)
in assembly geometry
Y Y
NEA/CSNI/R(2009)13
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Participant
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
Number of input parameters 36 44 17 55 54 20 25 24 33 44 20 32
Phenomenon Parameter
Interfacial
friction (churn-bubblle flows)
in annular
geometry
Y Y Y
Alternative
models – two-
Phase flow interfacial drag
model: EPRI or
Bestion
Y
Alternative models: liquid
entrainment
model in the downcomer
Y
Interfacial
friction in bubbly-slug
flow
(downcomer)
Y
Interfacial shear in stratified and
wavy horizontal pipe flow
Y Y Y Y
Interfacial shear
in bubbly, slug
and churn turbulent
horizontal pipe
flow
Y Y
Critical velocity
of transition
from stratified to slug flow in
horizontal pipes
Y Y
Velocity of
transition from non-dispersed
to dispersed
droplet flow in horizontal pipes
Y Y
Interfacial shear
in dispersed horizontal
droplet pipe
flow
Y Y
CCFL CCFL in the
upper core
plate: c of
Wallis correlation
Y Y Y Y
Condensation Direct condenstion
due to energy
transfer at liquid-vapour
interface
Y Y Y
NEA/CSNI/R(2009)13
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Participant
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
Number of input parameters 36 44 17 55 54 20 25 24 33 44 20 32
Phenomenon Parameter
Liquid-interface
heat transfer: Shah
correlation
Y
Liquid-interface heat transfer:
stratified flows
Y
Liquid-interface
heat transfer: turbulences
induced by
injection
Y
Liquid-interface
heat transfer:
droplet flows
Y
Liquid-interface heat transfer
during reflood:
droplet flows
Y
Vapour
interface heat
transfer in condensation
Y (2)
Fraction of wall
condensation heat flow
Y
Condensation
by injection of
under-saturated
water
Y
Evaporation Vapour-
interface heat
transfer in evaporation
Y (2)
Droplet
diameter (core) Y
Number of bubbles per unit
volume
Y Y
Number of
droplets per unit volume
Y Y
Limiting of
vapour specific volume for
evaporation rate
at low pressure
Y Y
Data related to
injections
Accumulator
pressure Y Y Y Y Y Y Y Y Y Y Y Y
Accumulator
line form loss
coefficient
Y Y Y Y Y Y Y Y Y Y Y Y
Accumulator:
liqud
temperature
Y Y Y Y Y Y Y Y Y Y Y
LPIS: Flow characteristic of
liquid injection
Y Y Y Y Y Y Y Y Y Y Y Y
NEA/CSNI/R(2009)13
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Participant
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
Number of input parameters 36 44 17 55 54 20 25 24 33 44 20 32
Phenomenon Parameter
Data related to
pressurizer
Form loss
coeffcient in the surge line
Y Y Y Y Y Y Y Y Y Y Y Y
Pressurizer
initial pressure Y Y Y Y Y Y Y Y Y Y Y
Pressurizer level
Y Y Y Y Y Y Y Y Y Y
Data specific to
0D module
Droplets fall
velocity Y
Bubbles rise
velocity Y
Reflood (if not quoted in heat
transfer in the
dry zone)
Fluid-wall heat transfer (2D
conduction near
QF)
Y Y
Interface-wall heat transfer
downstream QF
Y
Rewetted side HTC: upper QF
Y Y
Rewetted side
HTC: lower QF Y Y
Global HTC (core,
downstream
from the QF)
Y
Initial conditions:
primary system
Initial intact loop mass flow
rate
Y Y Y Y Y Y Y Y Y Y
Initial intact
loop cold leg temperature
Y Y Y
Y (upper
plenum temperatu
re)
Y Y Y Y Y Y
Initial upper-head mean
temperature Y
Y (recirculat
ing mass
flow at UP and
UH)
Y Y Y Y Y
Numerical
parameters
Convergence
criterion Y
Checking sensitivities Y *1 In this code only cold gap size can be modified. *2 A unique multiplier was applied to the whole temperature range.
2.4.2 Comparison of the considered phenomena
In Table 8 the number of parameters associated to each phenomenon or physical law is listed for the
different participants. Those phenomena included in the specification‟s document (0) are shaded in grey;
the number of parameters included in the specifications document is written in parenthesis.
Comments on Table 8:
Participants who have only considered the parameters set in the specifications document are not taken into
account for the following considerations. Nine participants have included all relevant parameters in the
uncertainty analysis.
NEA/CSNI/R(2009)13
34
9 out of 9 (9/9) participants considered the phenomenon of:
o Critical heat flux.
8/9 participants considered the phenomenon of:
o Heat transfer in the dry zone.
7/9 participants considered the phenomenon of:
o Heat transfer in the rewetted zone.
Global heat transfer was considered by one more participant not included in previous classifications,
therefore it may be stated that heat transfer was considered by 9/9 participants.
5/9 participants considered the following phenomena:
o Flow rates repartition / pressure drops,
o Interfacial friction.
o Condensation (ATHLET and CATHARE users),
o Evaporation (ATHLET and CATHARE users).
4/9 participants considered the phenomenon of:
o Reflood (ATHLET and CATHARE users, except NRI2)
3/9 participants considered the phenomenon of:
o Wall friction.
When looking at codes and kind of phenomena treated, TRACE and TECH-M-97 cannot be included in
general comments since the participants using them, mainly considered only the set of 20 CIPSU of the
specifications document. Only ATHLET and CATHARE users considered condensation and evaporation
phenomena, while for CCFL, all RELAP users and PSI (using TRACE) considered it. CCFL was
considered by ATHLET indirectly as the interfacial friction factor for vertical flows was developed on the
basis of CCFL correlation and considers counter-current flow limitations.
Table 8: Number of input parameters considered for each phenomenon by participants using a
probabilistic approach
Phenomenon Code Name/Version
Total Number of Par
AEKI CEA EDO GRS IRSN JNES KAERI KINS NRI1 NRI2 PSI UPC
A20 C25 T97 A21B C25 T4 M31 R5 R5 A21A T4 R5
36 44 17 55 54 20 25 24 33 44 20 32
Flow rates
repartition/pressure
drops
6 3 0 2 0 0 0 0 2 0 0 1
Wall friction 0 0 0 3 4 0 0 0 1 2 0 0
Flow rate at the break 2 3 0 3 1 0 0 1 2 0 0 2
Fuel thermal behaviour
(7) 7 7 6 7 9 7 7 7 7 9 7 9
Boundary conditions (3) 3 3 3 3 3 3 3 3 5 3 3 3
Global heat transfer 0 0 0 0 0 0 0 0 2 0 0 0
Heat transfer in the
rewetted zone 0 2 0 3 3 0 2 2 0 2 0 2
Heat transfer in the dry zone
3 4 0 6 5 0 3 3 0 6 0 3
Critical heat flux 1 1 0 1 1 0 1 1 1 1 0 1
NEA/CSNI/R(2009)13
35
Phenomenon Code Name/Version
Total Number of Par
AEKI CEA EDO GRS IRSN JNES KAERI KINS NRI1 NRI2 PSI UPC
A20 C25 T97 A21B C25 T4 M31 R5 R5 A21A T4 R5
36 44 17 55 54 20 25 24 33 44 20 32
Interfacial friction 0 6 0 11 6 0 0 0 2 5 0 0
CCFL 0 0 0 0 0 0 0 1 1 0 1 1
Condensation 1 1 0 1 8 0 0 0 0 1 0 0
Evaporation 2 1 0 3 2 0 0 0 0 1 0 0
Data related to injections (4)
4 4 3 4 4 4 4 4 4 4 4 4
Data related to
pressurizer (3) 3 3 3 3 1 3 3 2 3 3 3 3
Data specific to 0D module
0 0 0 0 2 0 0 0 0 0 0 0
Reflood (if not quoted in
heat transfer in the dry zone)
2 2 0 2 2 0 0 0 0 0 0 0
Initial conditions (3) 1 3 2 2 3 3 2 0 3 2 2 3
Numerical parameters 1 0 0 0 0 0 0 0 0 0 0 0
Others 0 1 0 0 0 0 0 0 0 0 0 0
Other than the phenomena in the specification‟s document, some other phenomena like Heat Transfer in the Dry
Zone and Heat Transfer in the Rewetted Zone have been considered by most of the participants. Table 9 and
Table 10 contain the parameters considered by participants regarding these two phenomena, respectively.
Table 9: Parameters related to HT in the dry zone and critical heat flux, considered by participants using a
probabilistic approach
HT in the dry zone
Code name/version
Total num par
AEKI CEA GRS IRSN KAERI KINS NRI1 NRI2 UPC
A20 C25 A21B C25 M31 R5 R5 A21A R5
4 5 7 6 4 4 1 7 4
Forced convection to vapour Y Y Y Y Y Y
Natural convection to vapour Y Y
Vapour-interface energy transfer Y
Alternative models - forced
convection to vapour Y (Dittus-Boelter
or Mc Eligot)
Y (Dittus-
Boelter or Mc
Eligot)
Film boiling Y Y
Y(2) (Berenson/
Bryce)
Y Y Y Y(2)
Alternative models – film boiling Y Y (Dougall-
Rohsenow /
Condie-Bengsont)
Y (Dougall-
Rohsenow / Condie-
Bengsont)
Y
Minimum of stable film temperature
Y Y Y Y
Transition boliling Y Y Y
Pool film boiling for natural
convection Y Y
Alternative modles – pool film boiling
Y
Critical heat flux Y Y Y Y Y Y Y Y
Alternative models – critical heat flux
Y
Table 10: Parameters related to the HT in the rewetted zone by the participants using a probabilistic
approach
HT in the rewetted zone
Code name/version
Total num par
AEKI CEA GRS IRSN KAERI KINS NRI1 NRI2 UPC
A20 C25 A21B C25 M31 R5 R5 A21A R5
0 2 3 3 2 2 0 2 2
Forced convection to liquid Y Y Y(2) Y Y Y
Natural convection to liquid Y
Nucleate boiling Y Y Y Y Y Y Y(2)
NEA/CSNI/R(2009)13
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2.4.3 Ranges of variation for the input parameters
Figure 6 shows the uncertainty ranges (~4σ in case of normal laws) for heat transfer related parameters. As
it is briefly commented below, differences among methods and also user effect will appear in this section.
Ranges for “forced convection to liquid” show regular widths except for CEA (using expert
judgement in this case), which has a rather large range.
Ranges for “nucleate boiling”, “film boiling” and “forced convection to vapour” are divided in two
groups depending upon the used correlation. UPC uses a larger range for the multiplier of subcooled
nucleate boiling than other participants do for saturated nucleate boiling. The fact that RELAP5
users apply different ranges and distributions to the same correlations is another example of user
effect, since the same code manual is differently understood depending on the participant.
Ranges for “critical heat flux” show two tendencies depending upon the code used: CATHARE and
ATHLET users apply similar ranges, and MARS and RELAP5 users apply similar larger ranges.
UPC multiplier is rather small compared to MARS and RELAP5 widths.
Ranges for “transition boiling” are only applied by RELAP5 and MARS users. The range for the
multiplier is quite different for the four participants, so this is an example of unsatisfactory state of
knowledge concerning model uncertainty.
NRI1 used a global heat transfer parameter that represents the uncertainty of all heat transfer
parameters (the value of the global heat transfer multiplier is used for all heat transfer multipliers) so
for all heat transfer regimes the same value has been depicted for NRI1 contribution.
As stated in Phase III report (see Ref.[4]), differences related to correlations are code and model
dependent. When users of the same code apply different uncertainty ranges for a correlation, the origin of
the discrepancy can be found in the source of information (code manuals, expert judgement, and
experimental database), its interpretation, and/or in the specific way the multiplier is applied.
Figure 6: Comparison of the uncertainty ranges for heat transfer multipliers
Forced convection to liquid
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
AEKI CEA EDO GRS IRSN JNES KAERI KINS NRI1 NRI2 PSI UPC
Nucleate boiling
0
0.5
1
1.5
2
2.5
AEKI CEA EDO GRS IRSN JNES KAERI KINS NRI1 NRI2 PSI UPC
UPC: Saturated
UPC: Subcooled
NEA/CSNI/R(2009)13
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Transition boiling
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
AEKI CEA EDO GRS IRSN JNES KAERI KINS NRI1 NRI2 PSI UPC
Film boiling
0
1
2
3
4
5
6
7
8
AEKI CEA EDO GRS IRSN JNES KAERI KINS NRI1 NRI2 PSI UPC
GRS: Dougall-Rohsenow
GRS: Condie-Bengston IV
IRSN: All phases
IRSN: Reflood
UPC: Conduction term
UPC: Convection term
Forced convection to vapour
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
AEKI CEA EDO GRS IRSN JNES KAERI KINS NRI1 NRI2 PSI UPC
GRS: Dittus-Boelter II
GRS: Mc Eligot
Critical heat flux
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
AEKI CEA EDO GRS IRSN JNES KAERI KINS NRI1 NRI2 PSI UPC
2.5 First conclusions on input parameters. Comparison with Phase III
Some preliminary conclusions can be drawn for this part of the Phase V:
Firstly Table 5 shows that in comparison with Phase III and even though the participants are considering
the same number of parameters, the dispersion has decreased.
Secondly as Phase V deals with a generic plant, there is no documentation available concerning the state of
the plant as initial and boundary conditions, fuel properties, etc... Therefore, in the specifications, a
common set uncertain parameters with their ranges of variation (CIPSU) has been proposed (other
parameters were not considered uncertain because the phenomenon was already covered by the CIPSU)
which has reduced not only the dispersion in its numerical value, but also the dispersion in their ranges.
Nevertheless, the dispersion in the ranges of the parameters related to code correlations is still large. In
addition, and regarding specifications, not all the participants have considered the CIPSU. In some cases,
the ranges specified have not been used in the same way as proposed.
In Table 11, parameters which appeared influential on cladding temperature and primary pressure in Phase
III (see Table 12 and Table 13 in Ref.[4]) are compared with parameters considered in Phase V. The aim of
this table is to evaluate the use among participants of the synthesis tables for sensitivities produced in
Phase III as a tool to select the uncertainty parameters for Phase V. It is important to remind, as stated in
Phase III report, that the synthesis tables produced in Phase III are not entirely valid for a LBLOCA
scenario in a typical PWR due to the specificity of both the L2-5 transient and LOFT facility. AEKI is
included in Table 11 even though they did not participate in Phase III. Table 11 compares parameters taken
into account by participants in Phase V with parameters found influential in Phase III – irrespective of
which group identified them as influential and of the magnitude of the influence.
NEA/CSNI/R(2009)13
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The following regrouping/renaming changes have been performed in order to facilitate comparison with
Phase V:
With regards to influential parameters on the cladding temperature (Table 12 in Ref.[4]):
“Critical flow sub cooled” and “Critical flow two-phase” are included in “Break discharge
coefficient”.
“Complex of heat transfer models” is included once in “Global heat transfer” phenomenon (in phase
III it was written in “heat transfer in the dry zone” and “heat transfer in the rewetted zone”)
“Break area” is not considered directly (but through “Break discharge coefficient”).
“Gap size” has been considered through “Gap conductivity” parameter according to the
specifications document.
“Conduction term of the wall to fluid HT in the film boiling regime” is included in film boiling
regime.
Related to CCFL only Wallis correlation has been used among participants.
With regards to influential parameters on the primary pressure (Table 13 in Ref.[4]):
“Jet temperature for injection of sub cooled liquid” corresponds in Phase V to “Condensation by
injection of under-saturated water”.
“Initial accumulator pressure” and “Accumulator pressure set-point” from Phase III are brought
together under “Initial accumulator pressure”.
For parameters quoted in their table of relevant parameters, a ranking (from 0 to 3) of relevance is
introduced for both macro-responses, see also section 4.2.3:
0: the parameter is considered by the participant but never appear as relevant
1: for the less relevant quoted parameter
2: for medium relevance parameter
3: for the highest level of relevance
The total ranking of a parameter cannot exceed 3 for one participant, even if
it is found as being relevant for several outputs making up a macro-response.
The following parameters have not been included in Table 11 because no participants in Phase V took
them into account compared to Phase III:
“Phase distribution coefficients at junctions” - was considered by 1 participant and for the primary
pressure the ranking was 1 in Phase III.
“Reflood activation model” - was considered by 1 participant and for the primary pressure the
ranking was 1.
“Structure heat transfer surfaces” - was considered by 1 participant and for the primary pressure the
ranking was 2.
NEA/CSNI/R(2009)13
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“Form loss in broken loop HL, in DC/CL at branch” - was considered by 1 participant and for both
the primary pressure and the cladding temperature the ranking was 3.
A more detailed explanation of some of the entries in Table 11 follows:
The row “Input parameters (Phase V)” includes the number of parameters used by each participant
in Phase V.
“Common: Ph.III and not Ph.V-Specs” row lists the number of parameters considered by the
participant that can be found in the influence ranking table of cladding temperature or of primary
pressure in Phase III (no matter which participant found them influential), that are not specified in
the specifications of Phase V.
“Common: Ph.III and Ph.V-Specs.” row lists the number of parameters considered by the participant
that can be found in the influence ranking table of cladding temperature or of primary pressure in
Phase III (no matter which participant found them influential), that are specified in the specifications
of Phase V.
In “Total common” row there is the total number of parameters common to Phase V and that appear
in the influence ranking tables of Phase III.
Table 11: Input parameter selection. Comparison with influential parameters in Phase III
Participant
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
Input parameters (phase V) 36 44 17 55 54 20 25 24 33 44 20 32
Common: Ph.III and not Ph.V-
Specs. 3 10 - 17 15+5 - 6 8 9+1 12 - 7+3
Common: Ph.III and Ph.V-Specs. 11 11 10 11 9+2 11 11 9 11 10 11 11+2
Total common 14 21 10 28 24+7 11 17 17 20+1 22 11 18+5
Phenomenon Parameter
Flow rates
repartition in the circuit/
pressure drops
Form loss coef. –
active core Y Y
Form loss coef. –
BHL Y
Wall friction Void fraction
dependent correction coefficient for
fraction of water and steam in total wall
friction
Y
Liquid-wall friction Y (2)
Vapour-wall friction Y (2)
Flow rate at
the break Break discharge
coefficient Y Y(2) Y(2)
Fuel thermal behaviour
Initial core power Y Y Y Y Y Y Y Y Y Y Y Y
Peaking factor Y Y Y Y Y Y Y Y Y Y Y Y
Hot gap size (whole
core except rod #5) Y Y Y Y Y Y*1 Y Y Y Y Y
Hot gap size (hot rod
#5) Y Y Y Y Y Y Y*1 Y Y Y Y Y
Power after scram Y Y Y Y Y Y Y Y Y Y Y Y
UO2 conductivity Y*2 Y Y*2 Y Y(2) Y Y Y*2 Y Y(2) Y Y(2)
UO2 specific heat Y*2 Y Y*2 Y Y(2) Y Y Y*2 Y Y(2) Y Y(2)
NEA/CSNI/R(2009)13
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Participant
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
Boundary
conditions
Two-Phase pump
head degradation (IL) Y
Two-Phase pump head degradation
(BL)
Y
Global heat
transfer
Complex of heat
transfer models Y
Heat transfer
in the rewetted zone
Forced convection to
liquid Y Y Y(2) Y Y Y
Nucleate boiling Y Y Y Y Y Y Y(2)
Heat transfer in the dry
zone
Forced convection to vapour
Y Y Y Y Y Y
Film boiling
Y Y
Y(2)
(all Phases
/refloo
d)
Y Y Y Y(2)
Minimum of stable film temperature
(Tmfs)
Y Y Y Y
Transition boliling Y Y Y
Pool film boiling for natural convection
Y Y
Critical heat
flux
Critical heat flux Y Y Y Y Y Y Y Y
Alternative models –
critical heat flux Y
Interfacial
friction
Interfacial shear in
dispersed vertical droplet pipe flow
Y Y
Interfacial friction
(churn-bubblle flows)
in pipe geometry
Y Y
Interfacial friction
(churn-bubblle flows)
in assembly geometry
Y Y
Interfacial friction
(churn-bubblle flows)
in annular geometry
Y Y Y
Alternative models – two-Phase flow
interfacial drag
model: EPRI or Bestion
Y
Alternative models:
liquid entrainment model in the
downcomer
Y
Interfacial shear in
stratified and wavy horizontal pipe flow
Y Y Y
Critical velocity of
transition from stratified to slug flow
in horizontal pipes
Y Y
CCFL CCFL in the upper
core plate: c of Wallis correlation
Y Y Y Y
Condensation Direct condensation due to energy transfer
at liquid-vapour
interface
Y Y Y
NEA/CSNI/R(2009)13
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Participant
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
Liquid-interface heat transfer: Shah
correlation
Y
Condensation by
injection of under-saturated water
Y
Evaporation Vapour-interface heat
transfer in evaporation
Y (2)
Number of bubbles
per unit volume Y Y
Data related
to injections
Accumulator:pressure Y Y Y Y Y Y Y Y Y Y Y Y
Data related
to pressurizer
Pressurizer initial
pressure Y Y Y Y Y Y Y Y Y Y Y
Pressurizer level Y Y Y Y Y Y Y Y Y Y
Data specific to 0D module
Bubbles rise velocity Y
Reflood (if
not quoted in heat transfer
in the dry
zone)
Rewetted side HTC:
upper QF Y Y
Global HTC (core, downstream from the
QF)
Y
Initial conditions:
primary
system
Initial intact loop cold leg temperature
Y Y Y
Y (upper
plenu
m tempe
rature
)
Y Y Y Y Y Y
*1 In this code only cold gap size can be modified. *2 A unique multiplier was applied to the whole temperature range.
Table 11 summarises the comparison of the selected input parameters with those found influential in Phase
III. This table complements the information given in the sensitivity studies section (Part 3 of this report).
NEA/CSNI/R(2009)13
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NEA/CSNI/R(2009)13
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3. PART 2: UNCERTAINTY ANALYSIS RESULTS
3.1 Steps 5 and 6: Main features of the methods
Except for UNIPI1 and UNIPI2 (using CIAU methodology), all the participants obtained the uncertainty
bands by performing a probabilistic approach with propagation of the input uncertainties and using Wilks‟
formula. Table 12 summarises the main features of the probabilistic methodologies.
3.1.1 Common features
Sampling: Simple Random Sampling (SRS) as recommended when using Wilks‟ formula.
Input parameters correlations: no dependency.
Two unilateral tolerance intervals, giving respectively an estimation of the 5% and the 95%
quantiles, with a confidence level at least of 95% for both quantiles.
3.1.2 Differences
Wilks‟ order
Treatment of failed calculations
No code failures (EDO, NRI1, NRI2)
Code failures, but they are all corrected (AEKI, CEA, KINS and UPC)
Code failure, run repeated on another computer (GRS)
Code failures, not used (IRSN, JNES, KAERI, PSI).
The pdf laws used were:
Uniform
Log-uniform
Normal
Log-normal
Triangular
Log-triangular
Discrete
Histogram
Polygonal
NEA/CSNI/R(2009)13
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Table 12: Main features of the probabilistic methods used for the uncertainty analysis
NEA/CSNI/R(2009)13
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For a proper use of the Wilks‟ formula all code runs have to be successful or corrected in case of any
failure. The main reason of this is that no information is available on the failed code runs: they might
correspond with the highest values of the considered output parameter (for an upper tolerance limit) That is
also the reason why, however, a relatively low number of failures can be treated in a conservative way by
assuming that the nf failed runs produced the nf most adverse values of the parameter of interest (e.g.
PCT). If the number of overall calculations was high enough to use the Wilks 95%/95% formula at the
order k, then the k-1 most adverse results can be discarded, which means that nf≤k-1. For example, for a
second order application, requiring 93 code runs for α = β = 95%, at least 92 successful code runs (93-1)
are needed, in other words only one failure is admitted. The failure is discarded and the maximum value
among the successful runs is taken as the 95%/95% estimation.
As an example, let us consider the case of PSI, which has performed 120 code runs with 4 code failures. As
explained above, it is not correct to consider that the 116 successful code runs are sufficient to apply Wilks
at the order 2, based on the argument that at this order and for α = β = 95%, only 93 code runs are needed.
The correct approach is to assume that the 4 failed code runs might correspond with the highest values of
the key variable, if they had been successful. Considering the highest value among the 116 successful code
runs as the 95%/95% estimation is equivalent to apply the Wilks‟ formula at the order 5. However, to
apply the Wilks‟ formula at the order 5 with α = β = 95%, 181 code runs are needed, and not 120. With
120 code runs and always for α = 95% and β > 95%, the Wilks‟ formula can be applied at the order 2,
which allows for a single failed run.
It is, however, possible to check the evolution of the parameter values of interest in the failed runs. If, until
the code failure occurs, these values are within the band of the successful runs, then one can consider that
the failed runs do not correspond with extreme values of the output and consequently it is not necessary to
eliminate them.
The following approach was used among the participants who discarded code run failures:
IRSN, applying Wilks‟ formula at 9th order, obtained a single run failure. Following Phase III
recommendations (see page 75 in Ref.[4]), according to the order applied they could have discarded
up to 8 code runs (above the upper bound when looking at the estimation of the maximum value).
They used the conservative method, assuming, e.g. for PCT, that the single failed calculation led to
highest temperatures among all calculations and therefore only discarded seven code runs. Their
procedure agrees with Phase III recommendations when code failures cannot be corrected.
PSI, applying Wilks‟ formula at 2nd
order, obtained four run failures. Although – as discussed in the
example above – for second order only one code run can be discarded, PSI results can be
nevertheless considered as correct for the parameter PCT, because they checked that results of the
failed runs were within the band of the successful simulations up to the time when the failure
occurred (that was well beyond time of PCT).
KAERI obtained a rather large number of code run failures and commented it in the following way:
During the analysis, ratio of the failed code runs was 14 %. The root causes of failures were not
clear, but the direct reason would be a fault of automatic time step control of semi-implicit
numerical scheme in violent thermal-hydraulic process during reflood phase. It was found that many
failures can be overcome by restarting with adjusted time step size. However the corrective actions
rely heavily on the human decision, which should not be a part of code calculation. Since the human
factor was not taken into account in the quantification process, the failed calculations were simply
discarded by KAERI. Another option would have been to consider these code runs with modified
time step as corrected and consequently as successful.
Considering the option retained by KAERI, the same kind of checking as the one used by PSI was
performed: As the failures seem to be related to the reflood process, the uncertainty bands for the
NEA/CSNI/R(2009)13
46
maximum cladding temperature shouldn‟t be affected by not considering the failed runs, if it was
checked that the maximum cladding temperature of the failed cases are within the band of the
successful ones.
JNES, applying Wilks‟ formula at 2nd
order obtained 9 code runs failures. Treatment of the failed
runs was similar to the procedure used by PSI. Each code run was checked, whether the cladding
was quenched or not. If a calculation stopped before quench time, the case was regarded as failed.
All failed cases stopped during the reflood phase (after PCT but before quench). The time-trends of
cladding temperature of the failed runs were compared with the successful ones and it was found
that PCT values of the failed cases were within the range of upper and lower bounds.
3.2 Step 7: Uncertainty results
3.2.1 Scalar quantities
In addition to the four scalar quantities requested in the specifications document, a new one – Maximum
Peak Cladding Temperature (MPCT) – was been added. This new parameter is defined as the maximum
temperature value reached in the fuel cladding, independently of the axial or radial location in the active
core during the whole transient.. The reason of including it is because it is the main parameter which is
compared with its design safety limit in LOCA licensing analyses. This scalar parameter is called
“Maximum Peak Cladding Temperature” in order to avoid misunderstandings with the time trend called
“Maximum Cladding Temperature” and other two scalars called “First Peak Cladding Temperature” and
“Second Peak Cladding Temperature”. For comparison purposes it was agreed to submit the 5/95 and
95/95 estimations of the one-sided tolerance limits, that is, to determine the tolerance limits with a 95%
confidence level – and not greater. Table 13, Table 14, Table 15, Table 16, Table 17 and Figure 7, resume
these results.
Participants having computed a higher number of calculations than the required by Wilks‟ formula (see
Table 6) have computed as well the estimations of the tolerance limits with the corresponding confidence
level (higher than 95%). These results can be found in their contributions (and not in the comparison
report).
The “Mean” and “Standard deviation” rows of the tables are aimed only to allow a comparison of the
obtained estimation of the limits. They do not represent any physical concept.
Some comments:
There is one participant (KAERI – MARS code) who does not obtain complete core quench in the
upper bound case of the uncertainty band. The reason given is the low CHF.
Two participants (EDO – TECH-M-97 code, NRI2 – ATHLET code) find an upper bound for the
maximum peak temperature close to (difference less than 30 K) 1477 K – the acceptance criterion
for the fuel cladding.
Participants using CIAU methodology (UNIPI1 – RELAP5 code, UNIPI2 – CATHARE code)
obtain accumulator injection time band width larger than the other participants, which is originated
by the fact that CIAU is the only method where the time error is explicitly considered..
The two approaches to quantify uncertainties, the probabilistic and UNIPI CIAU methods, give very
different estimations for the uncertainty bands of the accumulator injection time. This is a direct
consequence of the primary pressure “uncertainty width” obtained by the CIAU users.
NEA/CSNI/R(2009)13
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Table 13: Uncertainty results. 1st PCT – Scalar quantities
1st PCT LUB (K) RC (K) UUB (K) UUB – LUB (K) UUB-RC (K)
AEKI 1139 1216 1295 156 79
CEA 1168 1252 1326 159 75
EDO 1212 1306 1382 170 76
GRS 1190 1293 1393 203 100
IRSN 1142 1218 1379 237 161
JNES 1075 1185 1234 159 49
KAERI 1129 1187 1237 108 50
KINS 1178 1244 1375 196 131
NRI1 1046 1191 1299 253 108
NRI2 1080 1189 1374 294 185
PSI 1131 1178 1237 106 59
UNIPI1 991 1054 1116 125 63
UNIPI2 1156 1204 1252 96 48
UPC 1069 1187 1324 256 137
Mean 1089 1207 1318 232 109
Std Dev 117 60 70 121 46
Table 14: Uncertainty results. 2nd PCT – Scalar quantities
2nd
PCT LUB (K) RC (K) UUB (K) UUB – LUB (K) UUB – RC (K)
AEKI 1130 1200 1362 232 162
CEA 1045 1127 1373 336 246
EDO 1216 1326 1450 234 124
GRS 1112 1251 1365 253 114
IRSN 960 1149 1308 348 159
JNES 998 1076 1132 134 56
KAERI 1174 1247 1336 162 89
KINS 1213 1291 1435 222 144
NRI1 1090 1220 1298 208 78
NRI2 1075 1219 1459 384 240
PSI 1164 1208 1313 149 105
UNIPI1 979 1198 1418 439 220
UNIPI2 1093 1218 1342 249 124
UPC 1114 1189 1342 228 153
Mean 1080 1208 1360 275 143
Std Dev 104 64 88 120 60
NEA/CSNI/R(2009)13
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Table 15: Uncertainty results. Accumulator injection – Scalar quantities
Accumulator
injection time LUB (s) RC (s) UUB (s) UUB – LUB (s) UUB – RC (s)
AEKI 14.3 15.2 15.7 1.3 0.5
CEA 12.6 12.9 13.8 1.2 0.9
EDO 11.5 11.8 12.1 0.6 0.3
GRS 13.3 14.0 14.4 1.1 0.4
IRSN 14.5 14.9 15.7 1.2 0.9
JNES 11.4 11.8 12.2 0.8 0.4
KAERI 22.9 23.1 23.5 0.6 0.4
KINS 15.0 15.1 15.1 0.1 0.0
NRI1 14.4 15.7 17.3 2.9 1.6
NRI2 19.6 20.1 20.5 0.9 0.4
PSI 12.8 12.8 13.1 0.4 0.3
UNIPI1 5.8 16.2 27.2 21.4 11.0
UNIPI2 5.0 15.1 25.0 20.0 9.9
UPC 14.5 15.5 16.5 2.0 1.0
Mean 13.4 15.3 17.3 4.1 2.1
Std Dev 4.6 3.1 4.9 7.4 3.7
Table 16: Uncertainty results. Complete core quenching time - Scalar quantities
Complete core
quench LUB (s) RC (s) UUB (s) UUB – LUB (s) UUB-RC (s)
AEKI 112.3 259.0 334.6 222.3 75.6
CEA 247.3 370.3 583.5 336.2 213.2
EDO 124.1 136.1 379.3 255.2 243.2
GRS 179.4 273.1 423.8 244.4 150.7
IRSN 248.7 430.8 616.5 367.8 185.8
JNES 230.0 332.0 395.0 165.0 63.0
KAERI 152.1 209.8 < 1000.0 - -
KINS 145.7 194.7 286.4 140.7 91.7
NRI1 125.0 162.8 197.8 72.8 35.0
NRI2 158.9 192.4 214.0 55.1 21.6
PSI 178.7 199.5 263.1 84.4 63.6
UNIPI1 172.0 264.0 356.0 184.0 92.0
UNIPI2 228.0 324.0 420.0 192.0 96.0
UPC 151.0 205.0 265.0 114.0 60.0
Mean 175.2 253.8 364.2 184.3 109.6
Std Dev 46.2 84.6 128.1 100.8 72.0
NEA/CSNI/R(2009)13
49
Table 17: Uncertainty results. Maximum peak cladding temperature - Scalar quantities
Maximum peak
cladding
temperature
LUB (K) RC (K) UUB (K) UUB – LUB (K) UUB – RC (K)
AEKI 1216 1139 1362 146 223
CEA 1172 1252 1381 209 129
EDO 1221 1326 1450 229 124
GRS 1198 1293 1402 204 109
IRSN 1142 1218 1392 250 174
JNES 1089 1185 1238 150 53
KAERI 1174 1247 1336 162 89
KINS 1213 1291 1435 222 144
NRI1 1090 1220 1304 215 85
NRI2 1092 1221 1459 367 239
PSI 1164 1206 1313 149 107
UNIPI1 979 1198 1418 439 220
UNIPI2 1093 1218 1342 249 124
UPC 1119 1189 1342 223 153
Mean 1140 1229 1370 236 135
Std Dev 68 49 62 83 52
According to recommendation stated in Phase III report, the number of code runs may be increased to
some 150-200 when the upper tolerance limit approaches regulatory acceptance criteria (e.g. 1477.6 K). As
stated above, two participants (EDO and NRI2) obtain an estimate for the MPCT upper tolerance limit
close to the acceptance criterion for fuel cladding. These contributions used 93 calculations – 2nd
Wilks
order, the lowest number of code runs.
Figure 7 plots the scalar results ordered by increasing value of Upper limit minus Reference case.
When comparing results for the MPCT, there is an overlap region of, roughly, 15K (between 1221K and
1238K); however this region is rather too small. For 1st and 2
nd PCT the uncertainty bands of all
participants show no overlap, although when not considering participants with extreme values of the
uncertainty bands, it is possible to obtain overlap regions for the other two peak cladding quantities. In this
case for the 1st PCT there is an overlap region of roughly 20K when not taking into account UNIPI1 (with
the lower upper bound) and EDO (with the highest lower bound) results, and for the 2nd
PCT the overlap
exists when not considering JNES results with the lowest upper bound. Concerning the participants out of
the overlap region, JNES and EDO were two (out of the three) groups that considered only the minimum
number of 20 CIPSU and did not include the physical models, while for UNIPI1 group the reason seems to
be that comparing to the other participants, they obtained a rather low value for the reference calculation
and a narrow band for the 95%/95% values.
Uncertainty bands for “Accumulator injection time” (only for the probabilistic estimations) and “Complete
core quenching time” have no overlap. For accumulator related quantity the reasons are the too narrow
uncertainty bands for the probabilistic methods and also the spread of the reference case results, while for
the CIAU users the results seem to have a good agreement. For the “Complete core quenching time” the
NEA/CSNI/R(2009)13
50
reasons are similarly a combination of too narrow bands for some participants with the spread of reference
calculation values.
Figure 7: Uncertainty bands. Scalar quantities
1st PCT
700
800
900
1000
1100
1200
1300
1400
1500
UNIPI2 JNES KAERI PSI UNIPI1 CEA EDO AEKI GRS NRI1 KINS UPC IRSN NRI2
Participant
Te
mp
era
ture
(K
)
Lower limit 5/95 Reference case Upper limit 95/95
2nd
PCT
700
800
900
1000
1100
1200
1300
1400
1500
JNES NRI1 KAERI PSI GRS EDO UNIPI2 KINS UPC IRSN AEKI UNIPI1 NRI2 CEA
Participant
Tem
pera
ture
(K
)
Lower limit 5/95 Reference case Upper limit 95/95
Accumulator injection time
0
5
10
15
20
25
30
KINS EDO PSI GRS KAERI NRI2 JNES AEKI IRSN CEA UPC NRI1 UNIPI2 UNIPI1
Participant
Tim
e (
s)
Lower limit 5/95 Reference case Upper limit 95/95
Complete core quenching time
100
200
300
400
500
600
700
NRI2 NRI1 UPC JNES PSI AEKI KINS UNIPI1 UNIPI2 GRS IRSN CEA EDO KAERI
Participant
Tim
e (
s)
Lower limit 5/95 Reference case Upper limit 95/95
Maximum peak cladding temperature
700
800
900
1000
1100
1200
1300
1400
1500
JNES NRI1 KAERI PSI GRS EDO UNIPI2 CEA KINS UPC IRSN UNIPI1 AEKI NRI2
Participant
Te
mp
era
ture
(K
)
Lower limit 5/95 Reference case Upper limit 95/95
The following considerations must be taken into account when discussing the CIAU uncertainty bands:
CIAU is a method that takes explicitly into account and propagates consistently the time error: this
implies a „larger error‟ (and a larger band width) when gradients are steep.
Three definitions of uncertainty values are adopted in CIAU (see Figure 8):
NEA/CSNI/R(2009)13
51
Quantity Uncertainty (QU): uncertainty (with 95% of probability) characterising the quantity
value at a certain time instant;
Time Uncertainty (TU): uncertainty (with 95% of probability) characterising the time of
occurrence of any points during the transient;
Total Quantity Uncertainty (TQU): uncertainty (with more than 95% of probability) deriving
from the geometric combination of QU and TU.
It is worthwhile to note the time uncertainty of a point A may influence the total quantity uncertainty of a
point B, with tA < tB. See Figure 8.
The CIAU uncertainty bands (derived from TQU) provide more than the 95% percentile. If the 95%
percentile value for maximum and minimum values of the uncertainty bands are considered (for
comparison purposes with the request of BEMUSE Phase 5 specification), smaller band widths are
generated by CIAU through the consideration of QU only (see Table 18).
Table 18: QU point values (in parenthesis the TQU values)
OUTPUT UNCERTAIN PARAMETERS
LOWER
UNCERTAINTY
BAND
REFERENCE
CALCULATION
UPPER
UNCERTAINTY
BAND
1st PCT (RELAP5) (K) 991.3
(905.7) 1053.5
1115.7
(1175.9)
2nd PCT (RELAP5) (K) 978.6
(848.2) 1198.4
1418
(1418)
1st PCT (CATHARE2-V2.5) (K) 1156
(792) 1204
1252
(1368)
2nd PCT (CATHARE252-V2.5) (K) 1093
(994) 1218
1342
(1342)
NEA/CSNI/R(2009)13
52
Figure 8: Definitions of Time Uncertainty (TU), Quantity Uncertainty (QU) and
Total Quantity Uncertainty (TQU)
More detail on CIAU can be found in UNIPI‟s contribution in Phase I (see [1]) and in the appended
documents of UNIPI1 and UNIPI2 contribution (see CD with the appendices to BEMUSE Phase V
Report).
3.2.2 Maximum cladding temperature
For time trend quantities – maximum cladding temperature and upper plenum pressure – results with
confidence levels derived from the number of computations used for the analysis, are used.
Figure 9 and Figure 10 show the uncertainty band widths obtained by all participants for MCT.
Figure 11 shows the difference between the upper bound and the reference case value for MCT time
trends.
(TQU)A-
(TQU)A+
B
A
100 t
Q
tA tB
RC
UB
LB (TU)A
(TU)B
(QU)A
(QU)B
(TQU)B-
(TQU)B+
LB: Lower Band
UB: Upper Band
RC: Reference Calculation
QU: Quantity Uncertainty
TU: Time Uncertainty
TQU+: Total Quantity Uncertainty respect to
UB and LB respectively
ΔtAB = 1 sec if t < 100 sec
(TU)A (TQU)B
(TU)B (TQU)A
NEA/CSNI/R(2009)13
53
Figure 9: Maximum cladding temperature: upper minus lower bound
0
100
200
300
400
500
600
700
800
900
1000
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Te
mp
era
ture
(K
)
AEKI CEA EDO GRS IRSN JNES KAERI
KINS NRI1 NRI2 PSI UNIPI1 UNIPI2 UPC
Figure 10: Maximum cladding temperature: upper minus lower bound. Zoom
0
100
200
300
400
500
600
-5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
Time (s)
Tem
pera
ture
(K
)
AEKI CEA EDO GRS IRSN JNES KAERI
KINS NRI1 NRI2 PSI UNIPI1 UNIPI2 UPC
NEA/CSNI/R(2009)13
54
Figure 11: Maximum cladding temperature: upper bound minus reference calculation
0
100
200
300
400
500
600
700
800
900
1000
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Tem
pera
ture
(K
)
AEKI CEA EDO GRS IRSN JNES KAERI
KINS NRI1 NRI2 PSI UNIPI1 UNIPI2 UPC
In Figure 12 uncertainty bands for MCT time trend are depicted. Some participants did not obtain the
complete core quenching in the 500 seconds simulation: CEA, IRSN, KAERI.
Figure 12: Uncertainty results for maximum cladding temperature
AEKI – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Tem
pera
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
CEA – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Tem
pera
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
NEA/CSNI/R(2009)13
55
EDO – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Te
mp
era
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
GRS – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Te
mp
era
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
IRSN – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600 625 650
Time (s)
Tem
pera
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
JNES – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Tem
pera
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
KAERI – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Tem
pera
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
KINS – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Tem
pera
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
NEA/CSNI/R(2009)13
56
NRI1 – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Tem
pera
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
NRI2 – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Tem
pera
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
PSI – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Tem
pera
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
UNIPI1 – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Tem
pera
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
UNIPI2 – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Tem
pera
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
UPC – Maximum cladding temperature
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
-25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Time (s)
Tem
pera
ture
(K
)
Lower uncertainty bound Reference case Upper uncertianty bound
3.2.3 Upper plenum pressure
Figure 13 shows the uncertainty band width for upper plenum pressure time trend.
Figure 14 shows the uncertainty bands obtained by each participant for upper plenum pressure time trend.
NEA/CSNI/R(2009)13
57
Figure 13: Upper plenum pressure: upper minus lower bound
0
1
2
3
4
5
6
7
8
9
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ssu
re (
MP
a)
AEKI CEA EDO GRS IRSN JNES KAERI
KINS NRI1 NRI2 PSI UNIPI1 UNIPI2 UPC
Figure 14: Uncertainty results for upper plenum pressure
AEKI – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ssu
re (
MP
a)
Lower uncertainty bound Reference case Upper uncertainty bound
CEA – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ssu
re (
MP
a)
Lower uncertainty bound Reference case Upper uncertainty bound
NEA/CSNI/R(2009)13
58
EDO – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ss
ure
(M
Pa)
Lower uncertainty bound Reference case Upper uncertainty bound
GRS – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ss
ure
(M
Pa
)
Lower uncertainty bound Reference case Upper uncertainty bound
IRSN – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ssu
re (
MP
a)
Lower uncertainty bound Reference case Upper uncertainty bound
JNES – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ssu
re (
MP
a)
Lower uncertainty bound Reference case Upper uncertainty bound
KAERI – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ssu
re (
MP
a)
Lower uncertainty bound Reference case Upper uncertainty bound
KINS – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ssu
re (
MP
a)
Lower uncertainty bound Reference case Upper uncertainty bound
NEA/CSNI/R(2009)13
59
NRI1 – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ss
ure
(M
Pa)
Lower uncertainty bound Reference case Upper uncertainty bound
NRI2 – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ss
ure
(M
Pa)
Lower uncertainty bound Reference case Upper uncertainty bound
PSI – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ssu
re (
MP
a)
Lower uncertainty bound Reference case Upper uncertainty bound
UNIPI1 – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ssu
re (
MP
a)
Lower uncertainty bound Reference case Upper uncertainty bound
UNIPI2 – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ssu
re (
MP
a)
Lower uncertainty bound Reference case Upper uncertainty bound
UPC – Upper plenum pressure
0
2
4
6
8
10
12
14
16
18
-5 0 5 10 15 20 25 30 35 40 45 50
Time (s)
Pre
ssu
re (
MP
a)
Lower uncertainty bound Reference case Upper uncertainty bound
3.2.4 First conclusions on uncertainty analysis results
From the uncertainty analysis results the following comments can be made:
There is a nearly empty intersection of the uncertainty bands for all the scalar outputs except for the
“Maximum peak cladding temperature”, for which there is a narrow overlap region of about 15 K. It
is worth to remind that this scalar is in direct relation with the primary safety criterion for a LB-
LOCA.
NEA/CSNI/R(2009)13
60
As a general statement, the uncertainty bands found by the probabilistic methodologies for the
“Accumulator injection time” and the “Upper plenum pressure” (“primary pressure” macro
response) are narrower than those obtained using the method based upon extrapolation of output
uncertainties.
For the “cladding temperature” macro response, the dispersion of the uncertainty results could derive
from the rather large differences among the reference calculations.
For the “primary pressure” macro response the reasons could be explained as a combination of the
spread of the reference calculation results and the narrow bands obtained by the participants using a
probabilistic approach.
Although the overall results are clearly a step forward towards the consolidation of the different methods,
they also show that some probabilistic methods are not so well mastered by a number of participants, as the
not so good best-estimate calculations should be expected to be corrected by quite large uncertainty bands.
NEA/CSNI/R(2009)13
61
4. PART 3: SENSITIVITY ANALYSIS RESULTS
4.1 General definitions: sensitivity and influence, global and local sensitivities
General definitions are given in Phase III report (pages 51 and 52 in Ref.[4]).
Table 19 resumes the types of sensitivity and influence measures used by each participant.
Comparison has been performed among influence results.
Table 19: Summary of the influence and sensitivity measures used by participants using a probabilistic
approach
Organisation AEKI CEA EDO GRS IRSN JNES KAERI KINS NRI1 NRI2 PSI UPC
Numb. of
code runs 105 200 93 153 300 110 200 124 200 93 116 124
Influence SCC SRRC SCC SCC SOBOL
indices
SCC
PCC
SRC
Pearson Pearson SCC SCC
Pearson
PearsonPCC
SCC
SpearmanPCC
SRRC
Sensitivity
Linear
regression
– first
order
response
surface
PCC: Partial Correlation Coefficient
SCC: Spearman Correlation Coefficient
SRRC: Standardised Rank Regression Coefficient
4.2 Ranking of the phenomena and parameters according to their influence
4.2.1 Method of ranking
Following the method proposed in BEMUSE Phase III report (see Ref.[4]), the output parameters required
for sensitivity ranking are separated into two groups: one related to cladding temperature and another
related to the primary pressure:
Output parameters related to the core cladding temperatures:
1st PCT
2nd PCT
MPCT
Time of complete core quenching
Maximum cladding temperature as a function of time
Output parameters related to the primary pressure behaviour:
Time of accumulator injection
Upper plenum pressure as a function of time.
NEA/CSNI/R(2009)13
62
4.2.2 Ranking of the parameters
For participants using CIAU method, ranking and selection of parameters steps are not requested. Despite,
UNIPI1 has performed sensitivity calculations related to nodalization to support the results of the
uncertainty evaluation. Such results can be found in their contribution document.
For the participants using a probabilistic approach, Table 20 and Table 21 summarise the obtained ranking
for the considered “macro” responses: the maximum cladding temperature and the primary pressure,
respectively. The ranking is provided by each participant and values are given for the most relevant (rank =
3), second most relevant (rank = 2), third most relevant (rank = 1) and not relevant but considered (rank=0)
parameters. According to BEMUSE Phase III procedures, the total ranking for a parameter cannot exceed 3
for the same participant. In the similar way: when a parameter is ranked as influential more than once for
the same “macro” response, only the maximum ranking is considered. When both alternative models and a
multiplier for the correlation have been rank as influent, the total ranking has been computed as a sum of
the two contributions. Black boxes indicate that those parameters were not considered, although they are
part of the common proposed set. Fugure 15 and Figure 16 depict the total ranking and use colour legend
for the number of participants.
For the maximum cladding temperature 18 out of the 20 common uncertain parameters were considered
influential at some level.
For the primary pressure 19 out of the 20 common uncertain parameters were considered influential at
some level.
Table 20: Ranking per participant of the influence on the cladding temperature of the input parameters
(for the participants using a probabilistic approach)
Phenomenon Parameter
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
To
tal
Nu
mb
. O
f P
art.
Flow rates
repartition in
the circuit/ pressure drops
Form loss coef. – BCL
0 3 3 1
Wall friction Two-Phase multiplier of pressure drop in
vertical pipe
(Martinelli-Nelson correlation)
0 1 1 1
Liquid-wall friction 3 3 1
Flow rate at
the break Energy (heat) transfer
at liquid-vapour interface due to
flashing
0 2 2 1
Break discharge
coefficient 0 3 3 6 2
Wall friction factor 0 2 2 1
Fuel thermal behaviour
Initial core power 2 1 1 2 1 1 1 1 10 8
Peaking factor 2 3 3 3 2 1 14 6
Hot gap size (whole
core except rod #5) 1 3 1 5 3
Hot gap size (hot rod #5)
2 2 3 2 9 4
Power after scram 3 1 3 1 1 2 1 1 3 3 2 1 22 12
UO2 conductivity 3 *2 3 3 *2 1 3 3 2 *2 3 1 3 2 27 11
NEA/CSNI/R(2009)13
63
Phenomenon Parameter
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
To
tal
Nu
mb
. O
f P
art.
UO2 specific heat 1 1 1
Boundary conditions
Containment pressure 3 2 3 1 3 3 3 3 2 23 9
Pump rotational speed
(IL) 1 1 1
Pump rotational speed
(BL) 2 2 1
Global heat transfer
Complex of heat transfer models: heat
transfer fouling factor
2 2 1
Heat transfer
in the
rewetted zone
Forced convection to
liquid 2 2 1
Nucleate boiling 1 3 4 2
Heat transfer
in the dry zone
Forced convection to
vapour 2 2 1 0 0 0
8 4 Alternative models -
forced convection to
vapour
3 0
Film boiling 3 1 3 3 3 0 0
18 6 Alternative models –
film boiling. 3 3 0
Transition boliling 2 3 0 5 2
Critical heat
flux
Critical heat flux 2 3 0 3 3 2 0 2
18 7 Alternative models –
critical heat flux 3
Interfacial
friction Interfacial friction
downstream QF 2 2 1
Interfacial friction
(core, upstream from
the QF)
1 1 1
Velocity of transition from non-dispersed to
dispersed droplet flow
in vertical bundle
2 2 1
Interfacial shear in
dispersed vertical
droplet pipe flow
0 1 1 1
Interfacial friction (chrn-bubble flows) in
assembly geometry
3 0 3 1
Alternative models – two-Phase flow
interfacial drag model:
EPRI or Bestion
1 1 1
Alternative models: liquid entrainment
model in the
downcomer
3 3 1
Interfacial friction in
bubbly-slug flow
(downcomer)
3 3 1
Interfacial shear in stratified and wavy
horizontal pipe flow
0 0 0 1 1 1
Interfacial shear in dispersed horizontal
droplet pipe flow
0 2 2 1
CCFL CCFL in the upper core
plate: c of Wallis correlation
0 2 1 0 3 2
NEA/CSNI/R(2009)13
64
Phenomenon Parameter
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
To
tal
Nu
mb
. O
f P
art.
Condensation Direct condensation due to energy transfer
at liquid-vapour
interface
0 0 1 1 1
Liquid-interface heat transfer: turbulences
induced by injection
2 2 1
Evaporation Number of droplets per
unit volume 2 1 3 1
Data related
to injections
Accumulator:pressure 1 1 1
Accumulator line form loss coefficient
2 2 4 2
Accumulator: liqud
temperature 1 2 3 2
LPIS: Flow characteristic of liquid
injection
1 1 2 2
Data related
to pressurizer
Pressurizer initial
pressure 1 1 2 2
Data specific
to 0D module
Bubbles rise velocity 0 1 1 1
Reflood (if
not quoted in heat transfer
in the dry
zone)
Fluid-wall heat transfer
(2D conduction near QF) 3 3 6 2
Rewetted side HTC:
lower QF 0 1 1 1
Global HTC (core, downstream from the
QF)
3 3 1
Initial
conditions:
primary system
Initial intact loop mass
flow rate 1 1 2 4 3
Initial intact loop cold leg temperature
1 3 4 2
Initial upper-head mean
temperature 3 3 6 2
*1 In this code only cold gap size can be modified. *2 A unique multiplier was applied to the whole temperature range.
NEA/CSNI/R(2009)13
65
Table 21: Ranking per participant of the influence on the primary pressure of the input parameters (for
participants using a probabilistic approach)
Phenomenon Parameter
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
To
tal
Nu
mb
. O
f P
art.
Flow rates repartition in
the circuit/
pressure drops
Form loss coef. – BCL 0 3 3 1
Form loss coef. – all
legs 1 1 1
Momentum term
approximation (yes or
no)
3 0 3 1
Wall friction Liquid-wall friction 2 2 1
Vapour-wall friction 3 3 1
Flow rate at
the break
Energy (heat) transfer
at liquid-vapour
interface due to flashing
1 1 2 2
Wall friction factor 0 3 1 4 2
Turbulence factor in
critical break flow model
2 2 1
Momentum term
approximation at the
break (yes or no)
3 0 3 1
Break discharge
coefficient 0 3 3 6 2
Fuel thermal
behaviour
Initial core power 3 3 1
Peaking factor 3 3 1
Hot gap size (whole
core except rod #5) 3 3 1
Hot gap size (hot rod #5)
1 1 1
Power after scram 2 3 2 7 3
UO2 conductivity 2 2 4 2
Boundary
conditions
Containment pressure 3 3 3 1 3 3 3 3 3 3 28 10
Pump rotational speed
(IL) 1 3 1 5 3
Pump rotational speed
(BL) 1 2 3 2
Heat transfer
in the
rewetted zone
Nucleate boiling
0 0 0 2 0 0 0 2 1
Heat transfer in the dry
zone
Film boiling 3 0 2 0 0 0 0 5 2
Minimum of stable film temperature (Tmfs)
3 3 1
Transition boliling 0 2 0 2 1
Pool film boiling for
natural convection 0 2 2 1
Critical heat flux
Critical heat flux 0 0 0 0 3 0 0 0 3 1
Interfacial friction
*Blowdown: interfacial friction (ILHL, UP and
core)
1 1 1
*Refill and reflood: Steen-Wallis velocity
for onset of
entrainment IHL
1 1 1
Interfacial friction
downstream QF 1 1 1
NEA/CSNI/R(2009)13
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Phenomenon Parameter
AE
KI
CE
A
ED
O
GR
S
IRS
N
JNE
S
KA
ER
I
KIN
S
NR
I1
NR
I2
PS
I
UP
C
To
tal
Nu
mb
. O
f P
art.
Velocity of transition from non-dispersed to
dispersed droplet flow
in vertical bundle
1 1 1
Interfacial friction (churn-bubble flows) in
assembly geometry
3 3 1
Interfacial friction (chrun-bubble flows) in
annular geometry
2 0 2 1
Alternative models:
liquid entrainment model in the
downcomer
3 3 1
Interfacial shear in stratified and wavy
horizontal pipe flow
0 0 0 1 1 1
Condensation Direct condensation
due to energy trasnfer
at liquid-vapour interface
0 3 1 4 2
Liquid-interface heat
transfer: droplet flows 2 2 1
Data related
to injections
Accumulator:pressure 3 3 3 3 2 3 2 19 7
Accumulator line form loss coefficient
1 2 1 2 3 1 2 2 14 8
Accumulator: liqud
temperature 2 1 1 3 3 1 11 6
LPIS: Flow
characteristic of liquid
injection
3 3 1
Data related
to pressurizer
Form loss coeffcient in
the surge line 3 2 3 1 1 1 11 6
Pressurizer initial
pressure 3 2 2 3 10 4
Pressurizer level 1 1 1
Initial conditions:
primary
system
Initial intact loop mass flow rate
3 1 2 1 2 2 11 6
Initial intact loop cold
leg temperature 3 3 3 3 3 3 3 2 3 1 27 10
Initial upper-head mean temperature
1 1 2 3 1 1 9 6
*1 In this code only cold gap size can be modified. *2 A unique multiplier was applied to the whole temperature range.
4.2.3 Ranking of the phenomena
The total influence ranking per phenomenon is shown in Figure 17.
NEA/CSNI/R(2009)13
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Figure 15: Total ranking of the influence on the cladding temperature per parameter
02468
10
12
14
16
18
20
22
24
26
28
Form loss coef. (BCL)
Two-Phase multiplier of pressure drop in
Liquid-wall friction
Heat transfer flashing
Break discharge coefficient
Initial core power
Peaking factor
Hot gap size (whole core except rod #5)
Hot gap size (hot rod #5)
Power after scram
UO2 conductivity
UO2 specific heat
Containment pressure
Pump rotational speed (IL)
Pump rotational speed (BL)
Complex of heat transfer models: heat
Forced convection to liquid
Nucleate boiling
Forced convection to vapour
Film boiling
Transition boliling
Critical heat flux
*Blowdown: interfacial friction (ILHL, UP and
*Refill and reflood: Interfacial friction in
*Refill and reflood: Steen-Wallis velocity for
Interfacial friction downstream QF
Interfacial shear in non-dispersed vertical
Interfacial shear in non-dispersed vertical
Velocity of transition from non-dispersed to
Critical velocity of transition from non-
Interfacial friction for annular flows
Alternative models – two-Phase flow
Alternative models: liquid entrainment model
Interfacial friction in bubbly-slug flow (DWR)
Interfacial shear in stratified and wavy
Interfacial shear in dispersed horizontal
CCFL in the upper core plate: c of Wallis
Direct condensation
Liquid-interface heat transfer: turbulences
Number of droplets per unit volume
Accumulator:pressure
Accumulator line form loss coefficient
Accumulator: liqud temperature
LPIS: Flow characteristic of liquid injection
Pressurizer initial pressure
Bubbles rise velocity
Fluid-wall heat transfer (2D conduction near
Rewetted side HTC: lower QF
Interfacial friction (core, upstream from the
Global HTC (core, downstream from the
Initial intact loop mass flow rate
Initial intact loop cold leg temperature
Initial upper header mean temperature
Pa
ram
ete
r
Total rankingk = 1
1 < k < 7
k ≥ 7
k = number of participants
k =
1
1<
k <
7
k ≥
7
k=
num
ber
of
par
tici
pan
ts.
NEA/CSNI/R(2009)13
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Figure 16: Total ranking of the influence on the primary pressure per parameter
02468
10
12
14
16
18
20
22
24
26
28
30
Form loss coef. – BCL
Form loss coef. – all legs
Momentum term approximation (yes or no)
Liquid-wall friction
Vapour-wall friction
Energy (heat) transfer at liquid-vapour
Wall friction factor
Turbulence factor in critical break flow model
Momentum term approximation at the break
Break discharge coefficient
Initial core power
Peaking factor
Hot gap size (whole core except rod #5)
Hot gap size (hot rod #5)
Power after scram
UO2 conductivity
Containment pressure
Pump rotational speed (IL)
Pump rotational speed (BL)
Nucleate boiling
Film boiling
Minimum of stable film temperature (Tmfs)
Transition boliling
Pool film boiling for natural convection
Critical heat flux
*Blowdown: interfacial friction (ILHL, UP and
*Refill and reflood: Steen-Wallis velocity for
Interfacial friction downstream QF
Interfacial shear in non-dispersed vertical
Interfacial shear in non-dispersed vertical
Velocity of transition from non-dispersed to
Alternative models: liquid entrainment model
Interfacial shear in stratified and wavy
Direct condensation
Liquid-interface heat transfer: droplet flows
Accumulator:pressure
Accumulator line form loss coefficient
Accumulator: liqud temperature
LPIS: Flow characteristic of liquid injection
Form loss coeffcient in the surge line
Pressurizer initial pressure
Pressurizer level
Initial intact loop mass flow rate
Initial intact loop cold leg temperature
Initial upper header mean temperature
Pa
ram
ete
rs
Total ranking
k = 1
1< k < 7
k ≥ 7
k= number of participants.
310
=
k
k =
1
1<
k <
7
k ≥
7
k=
num
ber
of
par
tici
pan
ts.
NEA/CSNI/R(2009)13
69
Figure 17: Total influence ranking per phenomenon
0
10
20
30
40
50
60
70
80
90
10
0
Flow rates repartition
wall friction
Flow rate at the break
Fuel thermal behaviour
Boundary conditions
Global heat transfer
Heat transfer in the
rewetted zone
Heat transfer in the dry
zone
Critical heat flux
Interfacial friction
CCFL
Condensation
Evaporation
Data related to
injections
Data related to
pressurizer
Data specific to 0D
module
Reflood
Initial conditions:
primary system
Ph
en
om
en
on
Total influence ranking
Ma
xim
um
cla
dd
ing
te
mp
era
ture
Prim
ary
pre
ssu
re
NEA/CSNI/R(2009)13
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4.2.4 First conclusions on sensitivity analysis results
The conclusions refer firstly to the set of common parameters and secondly to the rest of parameters which
appeared to have an influence to the selected macro responses: the cladding temperature and the primary
pressure.
4.2.4.1 Influence on the cladding temperature
For the set of parameters proposed in the specifications, 18 (out of 20) were found, by at least one
participant, to have some influence on the cladding temperature. Only two parameters related to the
pressurizer (level and form loss coefficients in the surge line) did not show any influence for the sensitivity
analysis performed. The list that follows groups them according to the number of participants that have
ranked them and orders them according the total ranking obtained (in parenthesis after the parameter):
12 or 11 participants:
UO2 conductivity (27)
Power after scram (22)
7 to 10 participants:
Containment pressure (23)
Initial core power (10)
Between 1 and 6 participants:
Peaking factor (14)
Hot gap size (hot rod#5) (9)
Hot gap size (whole core except rod#5) (7)
Initial upper-head mean temperature (6)
Accumulator line form loss coefficient(4)
Initial intact loop mass flow rate (4)
Initial intact loop cold leg temperature (4)
Accumulator liquid temperature (3)
LPIS flow characteristic of liquid injection, Pressurizer initial pressure (2)
1 participant:
Pump rotational speed (BL) after break (2)
UO2 specific heat (1)
Pump rotational speed (IL) after break (1)
Accumulator pressure (1)
From the list can be concluded that, for the set of proposed parameters, the most influent ones are related to
the fuel thermal behaviour and the containment pressure, of medium importance are the primary circuit
initial conditions, while parameters related to injections and pumps performance show the smallest
influence among the total group. Pressuriser related ones have influence to the cladding temperature (the
pressuriser pressure could be re-written as initial primary system pressure). Nonetheless only “Power after
NEA/CSNI/R(2009)13
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scram” and “UO2 conductivity” parameters were ranked, at some level, by all the twelve participants, and
by eleven participants, respectively. The other parameters, even for those having high total rankings, were
not identified by all participants or by similar ranking levels.
As for the rest of parameters, Table 22 resumes the results for the parameters found as influential by more
than three participants. When uncertainty has been treated in different ways (alternative models or
multiplier to the correlation coefficient) the ranking values have been added up, except for the case that the
same participant has associated uncertainty in both ways in which case only the highest value is taken into
account.
It has to be noted that for the majority of the parameters not quoted in the common list, only groups of one
participant found them influential. A possible explanation is that a high number of parameters were
considered in the uncertainty analysis by only that one participant.
Table 22: Most influential parameters among parameters not quoted in the common list
Parameter Total ranking Numb. of Participants
Forced convection to vapor 8 4
Film boiling 18 6
Critical heat flux 18 7
Figure 18 compares parameters listed in Table 22 in terms of both, the range of variation and the influence
ranking for the participants.
Some comments on Figure 18:
For the “film boiling heat transfer” 6 participants found some influence after performing the
sensitivity analysis.
Uncertainty ranges for CATHARE users are much larger than the rest of the participants. This
difference may be explained by the differences among the codes.
AEKI and GRS considered selection of alternative models and GRS additionally multiplier for both
correlations.. For AEKI no uncertainty range is depicted. For GRS the ranking of the parameter is
higher than 3, as it considers influences from both the use of alternative model and the correlation
multiplier.
Not all participants having considered this input parameter found it as influent, although the
rankings obtained are high. For all participants ranking it as high, the uncertainty associated was a
multiplier to the correlation except for GRS, who obtained, see Table 20, the highest ranking (3)
when analysing the influence of the model and not the influence of the multiplier to the correlation
(ranked as 1).
For the MARS and RELAP5 users the discrepancies are noticeable: KAERI and KINS ranked as
maximum the parameter while NRI1 and UPC did not even ranked it.
The distribution range of this parameter is in the case of CEA, IRSN, KAERI and KINS larger than
in the case of GRS, UPC and NRI1. Additionally, KAERI and KINS consider relatively low number
of uncertain input parameters, what increases the probability that an influential parameter obtains
higher ranking.
NEA/CSNI/R(2009)13
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For the “single vapour phase heat transfer“, not all participants having considered it have ranked as
influent. The rankings vary from the lowest influence to the maximum. AEKI obtained the
maximum ranking by analysing the effect of the use of alternative models. GRS considers selection
of alternative modes as well as correlation multiplication factor and obtains as result large influence
of correlation selection and no influence due to multiplication factor. The rest of the participants
associated a multiplier to the correlation. Only CATHARE and ATHLET users ranked the parameter
as influent but they defined larger uncertainty of this parameter (GRS and AEKI ranking is due to
correlation selection).
For the CHF all groups considering it, except for IRSN, ranked the parameter of high influence
(rankings of 2 and 3). The ranking obtained is high despite the spread of the ranges is significantly
large. The range of parameter variation is similar for IRSN and UPC, but IRSN defined also
uncertainty of the quench front model (one parameter with ranking 3), what can decrease the
influence of the CHF correlation in the reflood phase.
Figure 18: Ranges of variation and influence to cladding temperature for some input parameters
Film boiling heat transfer
0
1
2
3
4
5
6
7
8
9
10
AEKI CEA EDO GRS IRSN JNES KAERI KINS NRI1 NRI2 PSI UPC
Participant
Ra
ng
e w
idth
0
1
2
3
4
5
Ra
nkin
g v
alu
e
Range width Ranking value
GRS: Dougall-Rohsenow
GRS: Condie-Bengston IV
IRSN: All phases
IRSN: Reflood
UPC: Conduction term
UPC: Convection term
Forced convection to vapour
0
0.5
1
1.5
2
AEKI CEA EDO GRS IRSN JNES KAERI KINS NRI1 NRI2 PSI UPC
Participant
Ra
ng
e w
idth
0
1
2
3
4
Ra
nkin
g v
alu
e
Range width Ranking value
GRS: Dougall-Rohsenow
GRS: Condie-Bengston IV
Critical heat flux
0
0.5
1
1.5
2
AEKI CEA EDO GRS IRSN JNES KAERI KINS NRI1 NRI2 PSI UPC
Participant
Ra
ng
e w
idth
0
1
2
3
4
Ra
nk
ing
va
lue
Range width Ranking value
4.2.4.2 Influence on the primary pressure
For the set of parameters proposed in the specifications, 19 (out of 20) were found, by at least one
participant, only the specific heat of the fuel was not identified for the sensitivity analysis to be of
influence for the primary pressure.
NEA/CSNI/R(2009)13
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12 or 11 participants:
None
Between 7 and 10 participants:
Containment pressure (28)
Initial intact loop cold leg temperature (24)
Accumulator pressure (19)
Accumulator line form loss coefficient (14)
Between 1 and 6 participants:
Accumulator liquid temperature (11)
Form loss coefficient in the surge line (11)
Initial intact loop mass flow rate (11)
Pressurizer initial pressure (10)
Initial upper-head mean temperature (9)
Power after scram (7)
Pump rotational speed (BL) after break (5)
UO2 conductivity (4)
Pump rotational speed (BL) after break (3)
1 participant:
Initial core power (3)
Peaking factor (3)
Hot gap size (whole core except rod#5) (3)
LPIS flow characteristics of liquid injection (3)
Hot gap size (rod#5), pressuriser level (1)
Underlined quantities are the ones that have been considered and ranked by nine or ten participants out of
twelve.
From the list can be concluded that, for the set of proposed parameters, the most influential ones to the
primary pressure are related to boundary conditions in the break, initial conditions in the primary circuit
and accumulator settings.
For the analysis of the rest of parameters all of them were found to have influence by only one participant
except for “break discharge coefficients” and “direct condensation” by two participants and therefore no
further comparison has been performed.
For maximum cladding temperature as well as for primary pressure the “containment pressure” is important at
the late phase of the transient after equalisation of pressure between primary circuit and containment and
practically after reflood of the core. At that time no important phenomena occur. Therefore this parameter is not
really relevant for the uncertainty of the important phase of calculated LB LOCA.
Those parameters considering power plant uncertainty were defined commonly and were used by all
participants. The model parameters were defined individually and considered by only few participants with
NEA/CSNI/R(2009)13
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exception of some heat transfer correlations. Even when, some of these additional parameters have been
found important, their overall ranking was, in general, low.
NEA/CSNI/R(2009)13
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CONCLUSIONS AND RECOMMENDATIONS
This report includes the summary of the contributions of the fourteen participants collaborating in
BEMUSE Phase V exercise: Uncertainty and Sensitivity Analysis of a LB-LOCA in ZION Nuclear Power
Plant.
Phase V is analogous to Phase III in the application of the methodologies (described in Phase I except for
AEKI, not taking part in the first step of BEMUSE) to a LB-LOCA scenario. The main difference is the
application to a plant in which the transient is simulated:
In Phase III the scenario was the former ISP-13 case, a simulation of a LB-LOCA carried out in LOFT
facility, therefore the analysis of both the reference case (Phase II) and the uncertainty bands (Phase III)
could be compared against experimental data.
In Phase V the scenario is a LB-LOCA in ZION plant as a generic 4 loops PWR reactor since no detailed
information was available. The simulation of a fictitious reactor supposed a lack of data needed for both
modelling and performance of uncertainty analysis. This fact caused a spread of results for the reference
calculations in the first stage of Phase IV and, to decrease the size of the spread, it was agreed collect a
specification document including the geometry and modelling as a common basis. A similar procedure was
carried out for the uncertainty analysis exercise, by proposing a common list of input parameters associated
with density functions, strongly recommended to be used by participants using a probabilistic
methodology. The set of common input parameters contains material properties, initial conditions,
boundary conditions and friction form loss factors. This document, addressed only to probabilistic
methodologies, was prepared in collaboration with CEA, GRS and UPC. The use of this set of selected
parameters was agreed and all participants applying a probabilistic approach included them, or when not
possible, specified the reason.
Two main directions have been given for this phase: on the one hand the recommendations of BEMUSE
Phase III and, on the other hand, the information and requirements provided to the participants for Phase
V.
In a similar way than in Phase III, different parts were defined for Phase V:
1) List and uncertainties of the input uncertain parameters
2) Uncertainty analysis results
3) Sensitivity analysis results
5% and 95% percentiles were provided for 7 output parameters, which were of two kinds:
Scalar output parameters
First peak cladding temperature
Second peak cladding temperature
Maximum peak cladding temperature
Time of accumulator injection
NEA/CSNI/R(2009)13
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Time of complete quenching
Time trends output parameters
Maximum cladding temperature
Upper plenum pressure
With respect to Phase III parameters, a new scalar quantity was included in the exercise, the maximum
peak cladding temperature which represents the maximum temperature value reached in the cladding for
any location at any time during the transient.
The main lessons learned from Phase V of the BEMUSE programme (often connected to recommendations
of Phase III) are:
For uncertainty analysis, all the participants used a probabilistic method associated with the use of
Wilks‟ formula, except UNIPI with its CIAU method (Code with the Capability of Internal
Assessment of Uncertainty). Both methods have been successfully applied.
The task of selecting the uncertain parameters to be used has been successfully performed generally
following the recommendations given at the end of Phase III. Three participants, however,
considered only the agreed common set of proposed parameters without uncertainties of code
models. Most participants made use of the lessons learned in Phase III and came up with a suitable
list of parameters adapted to the scenario. Nevertheless, for ranges and distribution functions for
code model parameters, there are still differences even among users of the same code, which can be
explained by the fact that these were primarily established by engineering judgement.
Users of the probabilistic methodologies applied the Simple Random Sampling technique, as
recommended in Phase III.
When treating code failures different procedures were followed. Most of the participants corrected
all failed runs. Nevertheless Phase III recommendations were not followed by all the participants.
The main recommendation of Phase III was to have a conservative approach in case of few failures:
if n code runs are performed allowing to apply Wilks‟ formula at the k order, the maximum of
authorized code failures among the n code runs is (k-1). If there are exactly (k-1) code failures,
Wilks‟ formula must be applied at the first order with the remaining successful code runs, if there
are (k-2) code failures, Wilks‟ formula is applied at the order 2, etc. In some cases more code runs
were discarded than recommended in this procedure.
For the cladding temperature-type output parameters, all participants managed to obtain the
requested uncertainty bands with reasonable values. The uncertainty bands for both the 1st and the
2nd
PCTs, show no overlap. However, when comparing results for the “Maximum peak cladding
temperature” (scalar value), the dispersion of the band width is significantly reduced for the
probabilistic approach, and there is a region of overlap of about 15K. The missing overlap can be
explained by quite different best-estimate calculations combined with rather narrow uncertainty
bands.
For the pressure-type output parameters the estimation of the uncertainty bands (accumulator
injection time and time trend for primary pressure) is very different depending upon the approach
used. The CIAU approach obtains a width larger than the width found by other methods, which is
almost negligible.
Even though it was not an objective of the exercise, upper limit estimations (95/95) for maximum
values of MPCT predicted by participants do not exceed the safety criterion.
NEA/CSNI/R(2009)13
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Although the overall results are clearly a step forward towards the consolidation of the different
methods, the uncertainty bands for the scalar output parameters (which do not show a clear
agreement among the probabilistic approach users) may point out that, for the this probabilistic
approach, the uncertainty analyses have been not so well mastered by some participants.
A database, including comparative tables and plots has been produced.
Sensitivity analysis has been successfully performed by all participants using the probabilistic
method. A comparison has been carried out about the influence ranking of the uncertain parameters.
Users of the CIAU methodology presented sensitivity results evaluating the effect of the
nodalization which can be found in their own contribution
The influence of ranking has been estimated for two macro responses: cladding temperature and
primary pressure. The sensitivity coefficients used by participants are Pearson and Spearman
correlation coefficient, standardised rank regression coefficients, Pearson and Spearman partial
correlation coefficients and SOBOL indices.
The sensitivity results have shown that several parameters were ranked as influential by the majority
of the 12 participants. These quantities are:
o From the set of common parameters: “Power after scram” (12 participants out of 12 – 12/12) and
“UO2 conductivity” (11/12) for the cladding temperature, “Containment pressure” (10/12),
“Initial ILCL temperature” (9/10) and “Initial UH temperature” (6/8) for the primary pressure.
o From the other parameters: “Film boiling” (6/8) and “Critical heat flux” (7/9)
A first comparison with Phase III has been performed. This comparison is shown in each section of
this document (e.g. when comparing uncertain parameters used by participants).
Regarding the task of selecting input uncertain parameters, Phase V results show that, in comparison with
Phase III, there is less difference between participants in the number of uncertain parameters considered. In
average, participants are considering the same number of parameters in both phases. The reason is that
common uncertain parameters with their ranges of variation have been proposed, and besides that, some
other parameters have not been considered uncertain because the phenomenon was already covered by any
of the proposed ones. That has reduced not only the differences in their number, but also the dispersion in
their ranges. Common uncertain parameters were related only to quantities such as initial and boundary
conditions, and material properties. Uncertainties of code models could not be fixed in a general way due
to differences among codes. The dispersion in the ranges of these code related parameters has been found
to be still large, in some cases even when comparing to users of the same code. The list of the inputs and
quantification of their uncertainty requires a large effort in using probabilistic methods.
BEMUSE Phase V has helped clarifying the treatment of failed calculations and its relation with the
number of runs for participants using statistical methods to provide 95%/95% statements. All participants
managed to follow the recommendation stated in Phase III to increase the number of code runs in the case
of failed runs.
The initiative of studying uncertainty bands for a new scalar quantity (MPCT) turned out to be interesting
due to two main reasons: on the one hand the quantity, as directly related to safety criterion helps
understanding the global qualitative importance of the exercise, and on the other hand MPCT shows a quite
limited dispersion in participant results.
Finally, sensitivity analysis is only possible using the probabilistic method and results have demonstrated
to be consistent in ranking parameters as influential and confirming decisions made in the uncertainty
evaluation step.
NEA/CSNI/R(2009)13
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BEMUSE Phase V has fulfilled its particular goals in the context of BEMUSE general objectives.
Some comparative aspects as well as some questions having arisen during Phase V, have been intentionally
left for Phase VI, among them: deeper comparison among methods or considerations on acceptance
criteria.
NEA/CSNI/R(2009)13
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REFERENCES
[1] M. J. Lewis, R. Pochard, F. D‟Auria et al., “Thermohydraulics of emergency core cooling in light
water reactors – a state of the art report”, OECD/NEA, Paris, France, October 1989.
[2] “BEMUSE: Phase I Report: Presentation a priori of the uncertainty evaluation methodology to be
used by the participants.”
[3] “BEMUSE Phase II Report: Re-Analysis of the ISP-13 Exercise, Post Test Analysis of the Loft
L2-5 Test Calculation.” NEA/CSNI/R(2006)2, Jun 2006.
[4] “BEMUSE Phase III Report: Uncertainty and Sensitivity Analysis of the LOFT L2-5 Test.”
NEA/CSNI/R(2007)4, Oct 2007.
[5] “BEMUSE Phase IV Report: Simulation of a LB-LOCA in ZION Nuclear Power Plant.” April 2008.
[6] “Requirements for phase 5 of BEMUSE”, Rev0, January 2008. L.Batet, M.Pérez, F.Reventós,
P.Bazin, A. de Crécy, T.Skorek. UPC.
[7] “Statistical prediction with special reference to the problem of tolerance limits”. S.S Wilks. Paper
presented at the American Mathematical Society. September 1942
[8] “RELAP/MOD3.3 Code Manual”, Vol.1 – Vol.8, ISL, NUREG/CR-5535/Rev1, December 2001.
[9] “Report on the Uncertainty Methods Study2, Vol.1 and Vol.2, NEA/CSNI R(97) 35, June 1998.
[10] “Best-Estimate Methods (Including Uncertainty Methods and Evaluation) Qualification and
Application. First Meeting of the Programme Committee”, NEA/SEN/SIN/AMA(2003)8,
Issy-les-Moulineaux, France, February 12-13, 2003.
[11] “Quantifying Reactor Safety Margins, Part 2: Characterization of Important Contributors to
Uncertianty”, Nuclear Engineering and Design 119, pg17-31, G.E. Wilson, et al., 1990.
[12] “Quantifying Reactor Safety Margins, Part 3: Assessment and Ranging of Parameters”, Nuclear
Engineering and Design 119, pg33-65, G.E. Wilson, et al., 1990
[13] Appendices to BEMUSE Phase V Report (CD). OECD Nuclear Energy Agency.
NEA/CSNI/R(2009)13
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NEA/CSNI/R(2009)13
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APPENDIX A
Requirements for Phase V of BEMUSE
Revision 0, January 2008
Coordinators: L. Batet, M. Pérez and F. Reventós (UPC)
Also Contributors: P. Bazin and A. De Crécy (CEA) and T. Skorek (GRS)
1. Introduction
The present document specifies the requirements needed to develop Bemuse Phase V and is organised in 3
different parts:
o Introduction
o Considerations on parameters, ranges and pdfs
o Output specification and steps
The introduction starts with some background considerations that are fundamental to understand the
general scope of this Phase‟s comparative exercise. After the introduction, and mainly due to background
considerations, significant details on the fundamental parameters are presented. Finally, the third part
specifies how the results have to be produced and organized in order to allow the comparative analysis.
Bemuse Phase V is the uncertainty evaluation of a Large Break LOCA scenario in an actual plant. The
reference plant is Zion and the reference case has been analyzed by participants during Bemuse Phase-IV.
Most of the participants have also been involved in Phase III in which the uncertainty evaluation has been
performed for L2-5 LOFT test. Connection of Phase V with both Phase III and IV has to be ensured.
As a first general statement, the definitions given in Part I of Bemuse Phase III specification are adopted.
Three different aspects of the present document help ensuring the connection with Phase III:
Cooperation between coordinator teams
Output structure
Lessons learned
For the first aspect, the main part of this document is already known by participants because it has been
prepared after some interchange of opinions among CEA, GRS and UPC and distributed in October 2007. In the
preparation of such information most of the decisions made have been carefully approved by consensus.
For the second aspect the structure of the results to be sent to the coordinator team are almost identical in
both Phases.
Lessons learned from previous Phases (and mainly from Phase III) have been included when would affect
the content of the present specification. Most of these lessons learned are part of section 2 like
NEA/CSNI/R(2009)13
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considerations on input parameters (type and number). Some others are pieces of advice explained in the
appropriate section depending on the subject they are related to. The most general ones are:
1. There is an important consideration related to connection with Phase IV. Zion is not properly an
“actual plant” but, it is known by all participants, that Zion was the only available option to develop
Bemuse Phases IV and V. In a real “actual plant”, information about parameters related to the plant
(areas, losses, initial conditions, boundary conditions...) would normally be available to the analysts.
In BEMUSE step 2 (Phases IV and V), some information has not been directly available. This lack
on information has been partially solved in the past (Phase IV) by making the most suitable
assumption when needed. Participants are encouraged to take this constriction into account and to
communicate with coordinators as soon as they are confronted with parameters or phenomena
needed of any additional assumption. These assumptions are necessary due to the fact that a detailed
description of the plant is not available. It is obvious that this coordination on basic aspects leaves
the participants freedom to apply their own techniques and make the needed methodological
assumptions following their own methods.
2. There are also important considerations related to lessons learned in Phase III. To begin with,
sensitivity analysis performed for Phase III has lead to synthesis figures (denoted as Figures 19 and
20 in the final synthesis report) with the list of the potentially influential parameters for each kind of
output: cladding temperature and primary pressure. As it has been experienced through discussions
carried out in Phase III for example, theoretically all these parameters must be considered for Phase
V. If a parameter is eliminated, it is clear that justifying its elimination becomes extremely useful for
methodology consolidation. Based on this practice, participants are required to provide such
explanations.
3. There is also another piece of advice that comes as a consequence of performing Phase III which is
related to the number of code runs. If your methodology allows it, it is recommended to increase the
number of runs when we compare it with that of Phase III. Phase III proved that increasing the
number of code runs (obviously successful code runs) comes up with reducing dispersion and
improving reliability of sensitivity results. Again based on this practice, participants are required to
take into account this recommendation in the framework of the applied methodology.
4. Finally, related to the sensitivity analysis, and taking advantage of the advice from the Phase III
coordinators ( see Ref.[A1]), there is the issue of the form of the sensitivity measures to be gathered
and compared. The sensitivity measures must include the range of variation of the inputs Xi
(influences), and dimensionless influence values are preferable, i.e. )/)·(/( YXXY ii like
values. Only those sensitivities which are really meaningful (from physical or statistical point of
view) must be indicated.
2. Parameters, ranges and pdfs to be included in Phase V specification
2.1 General aspects
This section specifies the range of variation of some of the parameters that participants in BEMUSE Phase
V should consider as fundamental in this particular uncertainty analysis. Ranges and probability density
functions (pdfs) are strongly recommended and any participant using other value or distribution must
provide an explanation for it.
In order to have specifications as clear and as simple as possible, which are easy to implement by the
participants, few in number and reasonable enough to minimise the foreseeable disagreements, the
following considerations have been done:
NEA/CSNI/R(2009)13
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1. It is considered that the fuel is fresh.
2. When a parameter has been deemed non-influential it has not been included in the list. Besides,
when a phenomenon is influenced by either one or several parameters, only one of them has been
taken into account (This is desirable for the sensitivity analysis wherein, especially in case of
regression coefficients, the number of uncertain input parameters must be low with respect to the
number of code runs).
3. The range of variation and pdfs are imposed only for two kinds of parameters: those describing the
state of the plant and for material properties. It has not been possible to avoid parameters which are
the result of the calculations (e.g. the initial temperatures obtained during the steady state), but they
can be sampled using other non calculated parameters (e.g. secondary pressure...). No uncertainties
due to scenario are considered; as a consequence, the LPIS start-up pressure set-point and the size of
the break are to be taken as fixed.
4. Whenever possible, the range of variation is given in the form of a dimensionless multiplicative
factor.
2.2 Ranges and pdfs
Table 1 contains the proposed range of variation and probability distribution functions for those parameters
to be included in the uncertainty analysis.
Except for some parameters, normal probability densities have been preferred. For these parameters the
indicated ranges of variation correspond to 2.5% and 97.5% percentiles ( 1.96 ). These percentiles are
given to specify the density functions, and must not be considered as a requirement for their truncation
during the propagation step: participants can truncate as they want, for example at 3.09.
In Table 1, units are systematically indicated for input parameters that are not of the type “multiplicative
factors”.
The following clarifications are provided for those parameters in Table 1 that deserve an additional
explanation.
Containment pressure. A range of 15% is proposed. A best estimate containment program can
obtain pressure accuracy of 10% in containment during a LB LOCA (see Table 4 in addition to
Table 1).
Initial power. A range of 2% is proposed. An increment of 2% in the total power is used as
conservative in the Safety Analysis Report (SAR).
Peaking factor (power of the hot rod #5). The range of variation for this parameter (5% with
respect to the reference case value) has been chosen to avoid having the hot rod colder than hot FA.
Hot gap size. A quite large range of variation of the gap thickness (20% with respect to the
reference case value) has been chosen. It includes the uncertainty on the gap conductivity (a priori
quite well known if the fill gas is only helium). It has been deemed of interest to consider two
different parameters in order to capture two distinct effects: one for the hot rod #5 alone (thermal
effect for the PCT), the other one for the whole core except rod #5 (global effect). The same range
of variation is to be considered for both parameters (so that if one parameter results more relevant
than the other one, for example on the 1st PCT, it will be the consequence of a higher sensitivity and
not of a different range of variation).
UO2 conductivity. According to researches performed by NRI during BEMUSE Phase II (see
Appendix C in Ref.[A2]), and supported by GRS and CEA experts, uncertainty of thermal
NEA/CSNI/R(2009)13
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conductivity for very low or not-irradiated UO2 can be estimated as 10% for temperatures below
2000 K and 20% for temperatures above 2000 K. Participants must explain the way these ranges
are implemented and any simplification of the ranges (for instance, using a temperature independent
value of 15%) is also to be explained.
UO2 specific heat capacity. According to researches performed by NRI during BEMUSE Phase II
(see Appendix C in Ref.[A2]), and supported by GRS and CEA experts, uncertainty range has been
estimated as 2% for temperatures below 1800K and 13% for temperatures above 1800K.
Participants must explain the way these ranges are implemented and any simplification of the ranges
(for instance, using a temperature independent value of 8%) is also to be explained.
Initial pressure in pressurizer. The uncertainty in the pressure is related only to the measurement
of the pressure which can be taken as 1 bar.
Upper-head temperature. See Annex 1.
Table 2 contains the parameters that are not to be included in the uncertainty analysis because (1) the effect
of their uncertainty on a phenomenon has been taken into account by other parameter, or (2) they are part
of the defined scenario and are considered “fixed”. An example of the first case is the gap conductivity
(uncertainty in gap conductance is accounted by the gap size); an example of the second is the time of start
of LPIS, which is defined and fixed in the scenario.
The following clarifications are provided for those parameters in Table 2 that deserve an additional
explanation.
Gap conductivity. The proposal is to consider only the gap size as uncertain parameter to describe
the heat transfer through the gap. Besides, if the fuel is fresh, there is only helium in the gap and the
conductivity of which is quite well known.
Cladding conductivity. Total cladding thermal resistance is much smaller than the uncertainty of
the gap thermal resistance or thermal resistance due to heat transfer to coolant. Therefore there is no
need to add this parameter to the input uncertainties.
Cladding heat capacity. Total cladding heat capacity is far below uncertainty of the fuel heat
capacity. Therefore there is no need to add this parameter to the input uncertainties.
2.3 Physical models
Although in some cases it can be desirable that participants using the same models in the same code apply
the same pdfs, there are reasons for not including this type of uncertain parameters in a compulsory list. A
first reason may be that the determination of the pdfs can be part of the participant own method and
secondly, finding a consensus among the participants for the pdf of the physical models may be very long
and difficult.
It has been therefore decided not to include this kind of parameters in the list. Nevertheless, it is
encouraged that participants using the same code try to use the same range and pdfs for uncertain
parameters whenever possible.
In this way, it is suggested that RELAP5 users dealing with 1D models be guided by Table 3 with respect
to CCFL. It is reminded that there is only one uncertain parameter, which concerns the upper core plate.
The same hydraulic diameter has to be considered (13.23 mm, see page 13 in Ref.[A3]).
NEA/CSNI/R(2009)13
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All the participants are to supply information of the model uncertainties in order to detect unrealistic
variations and obtain explanation for possible inconsistencies as it will be very useful for the quality of
analysis and final comparison.
2.4 Other parameters
Even though if in an actual plant, the information about parameters related to the transient (areas, head
losses, initial conditions, boundary conditions...) would normally be available to the analysts, in BEMUSE
step 2, some information may not be directly available. So, for the missing parameters participants are
asked to follow their own methodology while taking into account the general comment given in the
introduction related to the hierarchy of the needed assumptions. However, the intention is not to define as
uncertain those parameters which are unknown in this particular exercise but usually would be available in
the case of an operating NPP.
3. Output specification, steps and files
3.1 Definition of the output uncertain parameters
Output uncertain parameters are the same that those considered for the Phase III. Two time trends and four
single valued output parameters are finally considered and are defined on Table 5. The time trends are:
o Maximum clad temperature
o Pressure in the upper plenum
The single value output parameters are:
o First PCT (blowdown Phase)
o Second PCT (reflood Phase)
o Time of accumulator injection
o Time of complete quenching
Definitions and criteria are given in Table 5. Some helpful comments are given below.
The maximum cladding temperature (Max_TC) is defined as the maximum value (envelop value) of all the
rod surface temperatures irrespective of the location (assembly or elevation) and the power level. This
definition can be applied either to the 1-D or 3-D modelling of the core.
3.2 Step by step requirements
The steps specified in this section are very similar to their equivalent of Phase III. They can be considered
as a guideline for both developing Phase V and preparing participants individual report. Steps 1, 2 and 3
are general considerations about the sources of uncertainties and how they are considered via the input
uncertain parameters. Step 4 is the list of the participant‟s input uncertain parameters. In steps 5 and 6 the
participants will provide information about the way they use their method. Step 7 is devoted to the results
of the uncertainty method and step 8 those of sensitivity evaluation. Steps 9 and 10 of Phase III are not
required in Phase V.
As in Phase III these requirements are only devoted to homogenize the different contributions. They must
be completed in few words. Below, one can find a summary of each step definition. The contents of this
section are intended to be as close as possible to that of Phase III. Consequently some details are omitted as
Phase III specification can be looked up for clarification.
NEA/CSNI/R(2009)13
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Step 1: List the general sources of uncertainties considered for the Phase V of BEMUSE
Among the different sources of uncertainties listed below, specify those considered for the Phase V of
BEMUSE:
Physical models
Boundary and initial conditions
Material properties
Geometrical modelling
Alternative models
Maximum allowed time step, convergence criteria, etc.
Phenomena not taken into account by the code. Specify how they are treated (bias to be added to the
output parameters?)
Scaling effect
User‟s effect
Step 2: How is the list of input uncertain parameters established?
This chapter deals with all the input parameters, nevertheless a special attention is paid to those concerning
the physical models of the used code. The goal of this step is to describe in few words the adopted
approach to establish the list of the input uncertain parameters. The list itself will be given in step 4, with
the associated uncertainties.
Step 3: How are the uncertainties of the input uncertain parameters quantified?
This part is equivalent to part 2, but in this case for the quantification of the uncertainties of the input
uncertain parameters. Briefly specify the origin of the uncertainty given for the input parameters (of
course, this origin can depend on the parameter).
If a specific method has been developed for the estimation of the uncertainties some explanation has to be
provided.
Step 4: List the input uncertain parameters and quantify their uncertainties: the synthesis
A table like the Table 6 must be completed, including the number of each parameter. This table is given
with five examples of input parameters, the first two parameters concerning physical models.
Step 5: Sampling for the probabilistic approach
Specify the type of sampling: SRS, LHS, etc. and justify it.
Are intervals of variation of input parameters truncated, for example in case of normal or log-normal
SPDF?
Are dependencies between parameters considered?
For Wilks‟ formula: Is the use of several samples planned (in other words, is the effect of the
generated sample of the input parameters studied?)
Step 6: Running the code
General information about the calculations is to be given by the participant. In few words:
Mean CPU cost per calculation.
Ratio of the failed calculations to the total number of performed calculations.
NEA/CSNI/R(2009)13
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Specify the processing adopted for failed calculations:
Step 7: First uncertainty analysis results
The form of the uncertainty of the output parameters is chosen by the participant among the following
ones, given by decreasing order of preference:
A SPDF (for scalar parameters)
Two unilateral tolerance intervals, giving respectively an estimation of the 5% and the 95%
quantiles, with a confidence level of 95% for both quantiles.
5 % and 95% quantiles (corresponding to a 90% variation interval)
Mean value and standard deviation, associated to a hypothesis about the form of the SPDF (for
scalar parameters) followed by the output parameter (e.g. a normal law), allowing to have an
estimation of the 5% and 95% quantiles.
It is apparent that, whatever the form chosen for the uncertainty of the output parameters, it is possible to
define a lower and an upper uncertainty bound for each output parameter (corresponding to theoretical or
empirical 5% and 95% quantiles). Consequently, in order to homogenize the results, the following
presentation is requested:
For the single-value output parameters: Complete Table 7.
If the method allows to plot an empirical histogram, because a large enough number of calculations has
been performed, all the values found for each output parameter must be given on one column in the sheet
“UA: single-valued output parameters” of the “excel” file: “results_BEMUSE_5”.
For the time trend output parameters:
The sheets “UA: Max_TC” and “UA: Pressure_upper_plenum” of the “excel” file: “results_BEMUSE_5”
must be completed.
Step 8: Sensitivity analysis
The participant must define his measure of sensitivity.
Sensitivities should be of type “global sensitivity”, i.e. including the uncertainty range (Xi) of
the input uncertain parameters. They can be obtained with different coefficients, which have to
be specified (e.g. standard regression coefficients, partial correlation coefficients, spearman
correlation coefficients, etc.). The dimensionless forms are strongly preferable, i.e.
)/)·(/( YXXY ii like values
Indicate if other methods are used, and describe them precisely.
As far as allowed by their method, participants must complete the “excel” file:
“results_BEMUSE_5” as follows:
For the single-valued output parameters:
Fill the sheet: “SA: single-valued output parameters”. Only 11 parameters are indicated in the
sheet, but the values of the sensitivity coefficients must be given for all the uncertain input
parameters.
For the time trend output parameters:
NEA/CSNI/R(2009)13
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Fill the sheets: “SA: Max_TC” and “SA: Pressure_upper_plenum”. Specify the unit, depending
on the type of sensitivity method considered (for example, dimensionless, %, K, MPa). In order
to make the figures easily readable, one sheet must correspond with 10 parameters.
Consequently, if more than 10 parameters are considered, there will be more than one sheet for
each output parameter. Write the calculated values of sensitivity coefficient for chosen time
points.
Each participant has also to give the final ranking of the input parameters with a table like the Table
8. In this table, the list of the significantly influential parameters as well as their influence measure
must be indicated. To find these influential parameters, at least for the scalar outputs, participants are
encouraged to use statistic tests, more precisely to test the “null” hypothesis with a significance level
equal to 5%. It means to test for the correlation coefficients the hypothesis “there is zero correlation
between the output and the input”, and for the regression coefficient the hypothesis „the regression
coefficient is equal to 0”. Indications of times are given for time trend output parameters, because
the relevant parameters are not necessarily the same ones during the whole transient.
3.3 Files to submit
Participants have to submit their results providing 2 different files:
A Word file named “PhaseV-Participant.doc” with explanations and answers to questions posed in
section 3.2 “Step by step requirements”
An Excel file named “PhaseV-Participant.xls” filled starting from the supplied template.
4. References
[A1] “Summary Record of the 5th Meeting of the BEMUSE Programme Group”.
NEA/SEN/SIN/AMA(2007)9. June 26-28, 2007 at the NEA offices in Issy-les-Moulineaux.
[A2] “Input and Output Specifications for the LOFT L2-5 Experiment. Phase 2 of BEMUSE
Program-rev3”, A. Petruzzi, F. D‟Auria, DIMNP NT 517(05), University of Pisa, June 2005.
[A3] “Phase 4 of BEMUSE Programme: Simulation of a LB-LOCA in ZION Nuclear Power Plant.
Input and Output Specifications” Rev. 3. M. Pérez, F. Reventós, Ll. Batet. Barcelona, July 2007
NEA/CSNI/R(2009)13
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ANNEX 1. Considerations on the Uncertainty of the Upper-Head Temperature
In this annex a justification of the uncertainty of the mean upper-head temperature is provided.
It must be recalled that the value for that temperature was arbitrarily chosen having into account the
limitations of the simplified 1D models. In those models, the upper plenum and lower part of the
upper-head have a nominal temperature of 571K (equal to that of the downcomer), while the temperature
of the main body of upper-head is 590 K. It is, indeed, a virtual distribution of temperatures; the objective
was to obtain an energy content in the water above fuel somewhere in between cold and hot values.
In a configuration like that of the RELAP input supplied (see next figure), that temperature distribution is
obtained because of the flow paths established along the upper parts of the vessel.
It is not a drawback if a particular code cannot obtain this distribution, as the goal is having a similar
“energy content” in the water (equivalent to a mean temperature of 576 K). Maybe the value chosen is not
the best one, but it is a sound value (lying somewhere in between cold and hot temperatures)
Now, if we have to change the mean temperature of the water above fuel, we realize that we can only
reduce it in 5 K (cold temp is 571 K). If the range is to be symmetric, this leads to 5 K. To avoid
asymmetry when sampling the cold leg temperature, the proposal is to use, as a mean upper-head
temperature a value in the range:
[Tcold , Tcold +10 K]
Flow
restriction
310
355
350
356
Dead end
volume
“Warm” Water
“Cold” Water
Inlet Outlet
Cold water
Steady flow
of 22 kg/s
NEA/CSNI/R(2009)13
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Table 1: Input parameters, range of variation and type of probability density function
Phenomenon Parameter Quoted in Imposed range of
variation
Type of pdf Comments
Flow rate at
the break Containment
pressure
Phase III
report
Table 4
[0.85, 1.15], see
Table 4 below
Uniform Values in the table for
the reference case
(except initial one) are
to be affected by the
multiplier.
Fuel thermal
behaviour Initial core
power
Phase III
report
Tables 12
or 13
[0.98; 1.02] Normal This multiplier affects
both the nominal
(initial) power and the
power after scram,
which is entered as a
fraction affected as
well by an uncertainty
–see below.
Peaking
factor (power
of the hot rod
#5)
Phase III
report
Tables 12
or 13
[0.95; 1.05] Normal This peaking factor
should be applied at all
the elevations of the
hot rod of the hot
assembly (rod #5),
although it leads to a
(very) slight
increase/decrease of
the total power.
Hot gap size
(whole core
except rod #5)
Phase III
report
Tables 12
or 13
[0.8; 1.2]
Normal The large range of this
parameter includes the
uncertainty on the gap
conductivity and on the
cladding conductivity.
Hot gap size
(hot rod #5)
Phase III
report
Tables 12
or 13
[0.8; 1.2]
Normal The large range of this
parameter includes the
uncertainty on the gap
conductivity and on the
cladding conductivity.
Power after
scram
Phase III
report
Tables 12
or 13
[0.92; 1.08] Normal Values for the
reference case (which
are a fraction of initial
power) are to be
affected by the
multiplier. This is only
to affect values for t ≥
0.3 s. A proper
implementation has to
be done so that Value
= MAX (multiplier ·
Reference Value,
1.00).
UO2
conductivity
Phase III
report
Tables 12
or 13
[0.9, 1.1]
(Tfuel <2000 K )
[0.8,1.2]
(Tfuel >2000 K)
Normal Uncertainty depends
on temperature.
NEA/CSNI/R(2009)13
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Phenomenon Parameter Quoted in Imposed range of
variation
Type of pdf Comments
UO2 specific
heat
Phase III
report
Tables 12
or 13
[0.98, 1.02]
(Tfuel <1800 K )
[0.87,1.13] (Tfuel
>1800 K)
Normal Uncertainty depends
on temperature.
Pump
behaviour Rotation
speed after
break for
intact loops
Phase III
report
Tables 12
or 13
[0.98; 1..02] Normal Values in the table for
the reference case
(except initial one) are
to be affected by the
multiplier.
Rotation
speed after
break for
broken loop
Phase III
report
Tables 12
or 13
[0.9; 1.1] Normal Values in the table for
the reference case
(except initial one) are
to be affected by the
multiplier.
Data related to
injections Initial
accumulator
pressure
Phase III
report
Tables 12
or 13
[-0.2; +0.2] MPa Normal ±0.2 MPa is deduced
from the nominal value
for a CP1 reactor,
which is 4.2 MPa, and
the conventional use of
considering 4 MPa
when a conservative
calculation is
performed.
Friction form
loss in the
accumulator
line
Phase III
report
Table 4
[0.5; 2] Log-normal Multiplicative factor
(y) to be applied to the
coefficient equal to
8.65 found in the
specifications (xls file).
ln(y) distributes as a
normal with mean= 0
and = ln(2)/1,96
Accumulators
initial liquid
temperature
Phase III
report
Table 4
[-10; +10] °C Normal The range tries to take
into account the fact
that this temperature is
not as well measured
as in the LOFT L2-5
case, where the
experimental
uncertainty was ± 6.1
°C (NRI-2
contribution).
Flow
characteristic
of LPIS
Phase III
report
Table 4
[0.95 ; 1.05] Normal Flow values in the
table (flow vs.
pressure) for the
reference case are to be
affected by the
multiplier
Pressurizer Initial level Phase III
report
Tables 12
or 13
[-10; +10] cm Normal Expert judgement.
NEA/CSNI/R(2009)13
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Phenomenon Parameter Quoted in Imposed range of
variation
Type of pdf Comments
Initial
pressure
Phase III
report
Tables 12
or 13
[-0.1; +0.1] MPa Normal Expert judgement.
Friction form
loss in the
surge line
Phase III
report
Table 4
[0.5; 2] Log-normal Multiplicative factor
(y) to be applied to the
coefficient equal to 1
found in the
specifications (xls file).
ln(y) distributes as a
normal with mean= 0
and = ln(2)/1,96
Initial
conditions:
primary
system
Initial intact
loop mass
flow rate
Phase III
report
Table 4
[0.96; 1.04] Normal This parameter can be
changed through the
pump speed or through
pressure losses in the
system...
Initial intact
loop cold leg
temperature
Phase III
report
Table 4
[-2; +2] K Normal This parameter can be
changed through the
secondary pressure,
heat transfer
coefficient or area in
the U-tubes...
Initial upper-
head mean
temperature
Summary
record 5th
BEMUSE
meeting
[Tcold ;
Tcold + 10 K]
Uniform This parameter refers
to the “mean
temperature” of the
volumes of the upper
plenum.
Table 2: Parameters not to be included in the uncertainty analysis
Phenomenon Parameter Quoted in Comments
Flow rate at the
break Break area Phase III
report Table
4
It has been decided not to introduce uncertainties
related to the definition of the scenario.
Fuel thermal
behaviour Gap conductivity Phase III
report Tables
12 or 13
See “hot gap size” in Table 1
Cladding
conductivity
Phase III
report Table
4
See “hot gap size” in Table 1
Cladding heat
capacity
Phase III
report Table
4
UO2 specific heat uncertainty is quite larger than
cladding specific heat.
LPIS LPIS delay Phase IV It has been decided not to introduce uncertainties
related to the definition of the scenario.
NEA/CSNI/R(2009)13
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Table 3: Parameters specific for RELAP5 users with 1D models
Phenomenon Parameter Quoted in Imposed range of
variation
Type of
Comments
CCFL at
upper core tie
plate
Gas intercept
(parameter c) in
Wallis
correlation.
Phase III report
Tables 12 or 13 c 0.69;1.03
5 Ref. value =
0.8625
Uniform Only for RELAP5
participants using a
1D description of the
vessel
Expert judgement
(From NRI-1
contribution to Phase
III, pag.11).
Table 4: Minimum, nominal and maximum value for the containment pressure
Time after
scram (s)
Minimum value
(MPa)
Nominal value
(MPa)
Maximum value
(MPa)
0.0 0.100 0.10 0.100
12.5 0.2975 0.35 0.4025
50.0 0.2125 0.25 0.2875
200.0 0.17 0.20 0.23
1.e5 0.17 0.20 0.23
Table 5: Definition of the output parameters
Type Definition Criterion
Time trend Max_TC See comment below
Pressure in the upper plenum: Pup No criterion
Single valued
parameter
1st PCT (blowdown Phase) Max_TC and t < tinj
2nd
PCT ( ~ reflood) Max_TC and t > tinj
Time of accumulator
injection: tinj
Time of beginning of
injection
Time of complete
quenching: tque
Tsat + 30 K
Table 6: Template for the summary of the features of the input uncertain parameters
1 2 3 4 5 6 7 8
No.
Parameter
Phase Component Phenomenon Parameter
description
Uncertainty Method
used to
determine
the
uncertainty
Experiments
used to
determine
the
uncertainty
1 Blowdown
Phase
Core Heat
transfers in
dry zone
Heat transfer
coefficient in
film boiling
[0.15 ; 7]
log-normal
law
Fitting of
data (cf.
step 3)
Winfrith, Inel
2 Refill and
reflood
Phases
Intact cold
leg
Oscillations
upstream of
the ECCS
injection
point
Liquid-
interface
heat transfer
in
condensation
[1 ; 10]
log-normal
law
Expert
judgement
None
3 t = 0 s Fuel rods Thermal Initial power [34.8 ; 37.2] Literature: None
NEA/CSNI/R(2009)13
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behaviour (in MW) normal law LOFT
documentati
on
4 t = 0 s Accumulator Liquid
injection
from the
accumulator
Available
liquid
volume
1.82 0.11
m3
uniform law
Literature :
LOFT
documentati
on and
expert
judgement
None
5 Every
Phases
Fuel rods Thermal
behaviour
UO2
conductivity 20%
normal law
Expert
judgement
None
Table 7: First results of uncertainty analysis for single-valued output parameters
Output uncertain
parameter
Lower
uncertainty
bound
Reference
calculation
value
Upper
uncertainty
bound
1st PCT (blowdown
Phase)
2nd
PCT ( ~ reflood
Phase)
Time of
accumulator
injection: tinj
Time of complete
quenching: tque
Table 8: Ranking of the most relevant parameters, following sensitivity analysis results
Parameter
number
Sensitivity
value
Parameter
description
Associated
phenomenon
1st PCT (blowdown Phase)
2nd
PCT (~ reflood Phase)
Time of accumulator injection: tinj
Time of complete quenching: tque
…..
Max_TC Time <
tinj
Time >
tinj
Pressure_upper_plenum Time <
tinj
…..
Time >
tinj
…..