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Input Calibration, Code Validation and
Surrogate Model Development for
Analysis of Two-phase Circulation Instability
and Core Relocation Phenomena
VIET-ANH PHUNG
Doctoral Thesis
KTH Royal Institute of Technology School of Engineering Sciences
Department of Physics Division of Nuclear Power Safety
Stockholm, Sweden 2017
TRITA-FYS 2017:03 ISSN 0280-316X ISRN KTH/FYS/--17:03-SE ISBN: 978-91-7729-265-4
KTH, AlbaNova University Center Roslagstullsbacken 21, D5 SE-106 91 Stockholm SWEDEN
Akademisk avhandling som med tillstånd av Kungliga Tekniska högskolan i Stockholm framlägges till offentlig granskning för avläggande av teknologie doktorexamen i fysik den 17 februari 2017, FA32, Albanova Universitetcentrum, Roslagstullsbacken 21, Stockholm.
© Viet-Anh Phung, February 2017
III
Abstract Code validation and uncertainty quantification are important tasks in nuclear reactor safety analysis. Code users have to deal with large number of uncertain parameters, complex multi-physics, multi-dimensional and multi-scale phenomena. In order to make results of analysis more robust, it is important to develop and employ procedures for guiding user choices in quantification of the uncertainties. The work aims to further develop approaches and procedures for system analysis code validation and application to practical problems of safety analysis. The work is divided into two parts. The first part presents validation of two reactor system thermal-hydraulic (STH) codes RELAP5 and TRACE for prediction of two-phase circulation flow instability. The goals of the first part are to: (a) develop and apply efficient methods for input calibration and STH code validation against unsteady flow experiments with two-phase circulation flow instability, and (b) examine the codes capability to predict instantaneous thermal hydraulic parameters and flow regimes during the transients. Two approaches have been developed: a non-automated procedure based on separate treatment of uncertain input parameters (UIPs) and an automated method using genetic algorithm. Multiple measured parameters and system response quantities (SRQs) are employed in both calibration of uncertain parameters in the code input deck and validation of RELAP5 and TRACE codes. The effect of improvement in RELAP5 flow regime identification on code prediction of thermal-hydraulic parameters has been studied. Result of the code validations demonstrates that RELAP5 and TRACE can reproduce qualitative behaviour of two-phase flow instability. However, both codes misidentified instantaneous flow regimes, and it was not possible to predict simultaneously experimental values of oscillation period and maximum inlet flow rate. The outcome suggests importance of
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simultaneous consideration of multiple SRQs and different test regimes for quantitative code validation. The second part of this work addresses core degradation and relocation to the lower head of a boiling water reactor (BWR). Properties of the debris in the lower head provide initial conditions for vessel failure, melt release and ex-vessel accident progression. The goals of the second part are to: (a) obtain a representative database of MELCOR solutions for characteristics of debris in the reactor lower plenum for different accident scenarios, and (b) develop a computationally efficient surrogate model (SM) that can be used in extensive uncertainty analysis for prediction of the debris bed characteristics. MELCOR code coupled with genetic algorithm, random and grid sampling methods was used to generate a database of the full model solutions and to investigate in-vessel corium debris relocation in a Nordic BWR. Artificial neural networks (ANNs) with classification (grouping) of scenarios have been used for development of the SM in order to address the issue of chaotic response of the full model especially in the transition region. The core relocation analysis shows that there are two main groups of scenarios: with relatively small (<20 tons) and large (>100 tons) amounts of total relocated debris in the reactor lower plenum. The domains are separated by transition regions, in which small variation of the input can result in large changes in the final mass of debris. SMs using multiple ANNs with/without weighting between different groups effectively filter out the noise and provide a better prediction of the output cumulative distribution function, but increase the mean squared error compared to a single ANN. Keywords Reactor system code, input calibration, code validation, surrogate model, two-phase circulation flow instability, in-vessel core relocation, genetic algorithm, artificial neural network.
V
To Dad and Mom
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VII
Sammanfattning
Validering av datorkoder och kvantifiering av osäkerhetsfaktorer är viktiga delar vid säkerhetsanalys av kärnkraftsreaktorer. Datorkodanvändaren måste hantera ett stort antal osäkra parametrar vid beskrivningen av fysikaliska fenomen i flera dimensioner från mikro- till makroskala. För att göra analysresultaten mer robusta, är det viktigt att utveckla och tillämpa rutiner för att vägleda användaren vid kvantifiering av osäkerheter. Detta arbete syftar till att vidareutveckla metoder och förfaranden för validering av systemkoder och deras tillämpning på praktiska problem i säkerhetsanalysen. Arbetet delas in i två delar. Första delen presenterar validering av de termohydrauliska systemkoderna (STH) RELAP5 och TRACE vid analys av tvåfasinstabilitet i cirkulationsflödet. Målen för den första delen är att: (a) utveckla och tillämpa effektiva metoder för kalibrering av indatafiler och validering av STH mot flödesexperiment med tvåfas cirkulationsflödeinstabilitet och (b) granska datorkodernas förmåga att förutsäga momentana termohydrauliska parametrar och flödesregimer under transienta förlopp. Två metoder har utvecklats: en icke-automatisk procedur baserad på separat hantering av osäkra indataparametrar (UIPs) och en automatiserad metod som använder genetisk algoritm. Ett flertal uppmätta parametrar och systemresponser (SRQs) används i både kalibrering av osäkra parametrar i indatafilen och validering av RELAP5 och TRACE. Resultatet av modifikationer i hur RELAP5 identifierar olika flödesregimer, och särskilt hur detta påverkar datorkodens prediktioner av termohydrauliska parametrar, har studerats. Resultatet av valideringen visar att RELAP5 och TRACE kan återge det kvalitativa beteende av två-fas flödets instabilitet. Däremot kan ingen av koderna korrekt identifiera den momentana flödesregimen, det var därför ej möjligt att förutsäga experimentella värden på svängningsperiod och maximal inloppsflödeshastighet samtidigt. Resultatet belyser betydelsen
VIII
av samtidig behandling av flera SRQs liksom olika experimentella flödesregimer för kvantitativ kodvalidering. Den andra delen av detta arbete behandlar härdnedbrytning och omfördelning till reaktortankens nedre plenumdel i en kokarvatten reaktor (BWR). Egenskaper hos härdrester i nedre plenum ger inledande förutsättningar för reaktortanksgenomsmältning, hur smältan rinner ut ur reaktortanken och händelseförloppet i reaktorinneslutningen. Målen i den andra delen är att: (a) erhålla en representativ databas över koden MELCOR:s analysresultat för egenskaperna hos härdrester i nedre plenum under olika händelseförlopp, och (b) utveckla en beräkningseffektiv surrogatsmodell som kan användas i omfattande osäkerhetsanalyser för att förutsäga partikelbäddsegenskaper. MELCOR, kopplad till en genetisk algoritm med slumpmässigt urval användes för att generera en databas av analysresultat med tillämpning på smältans omfördelning i reaktortanken i en Nordisk BWR. Analysen av hur härden omfördelas visar att det finns två huvudgrupper av scenarier: med relativt liten (<20 ton) och stor (> 100 ton) total mängd omfördelade härdrester i nedre plenum. Dessa domäner är åtskilda av övergångsregioner, där små variationer i indata kan resultera i stora ändringar i den slutliga partikelmassan. Flergrupps artificiella neurala nätverk med klassificering av händelseförloppet har använts för utvecklingen av en surrogatmodell för att hantera problemet med kaotiska resultat av den fullständiga modellen, särskilt i övergångsregionen. Nyckelord Reaktorsystemkod, indata kalibrering, kodvalidering, surrogatmodell, två-fas cirkulationsflöde, instabilitet, härdrelokering i reaktortanken, genetisk algoritm, artificiella neurala nätverk.
IX
Acknowledgement
First I would like to express deep gratitude to my supervisor Associate
Professor Pavel Kudinov for positively motivating and guiding me
through countless long discussions. I have a great privilege to be in a
team specializing in different topics of reactor safety, in which members
help and learn a lot from each other.
I am very grateful to Professor Truc-Nam Dinh for crucial supports so I
could have the opportunity to work at the Division of Nuclear Power
Safety (NPS), Royal Institute of Technology - KTH. Without his advices
and inspirations, I could not have had an engineering mentality as I have
today.
I would like to thank Professor Bal Raj Seghal, Professor Sevostian
Bechta, Professor Tomas Lefvert for supports and for setting up great
research directions at the division.
I want to thank Dr. Dmitry Grishchenko for many valuable reviews
regarding my research, Dr. Tomasz Kozlowski for help when I started
with RELAP5 and TRACE, Assoc. Prof. Weimin Ma, Dr.
Walter Villanueva and Dr. Chi Thanh Tran for advices on MELCOR and
severe accident analysis.
Thanks to Sergey Galushin, Kaspar Kööp and Sebastian Raub for fruitful
collaboration on MELCOR analysis, GA-IDPSA and interesting
discussions about life. I would like to thank Dr. Martin Rohde and
colleagues at Delft University of Technology for helps with CIRCUS
experiments.
The NPS has become my second home for years. And I want to thank
Alexander, Simone, Marti, Sean, Aram, Andrei, Ignacio, Sachin, Huimin,
Hua, Joanna, Roberta, Ivan, colleagues at the NPS, the Department of
Physics and others which I cannot name them all here for creating a great
X
atmosphere. Thanks Sofia, Kajsa and the administration group for taking a good care of us.
I thank my friends, Minh Tuan, Bich Ngoc, Tuan Viet, Phuong Dung, Minh Nguyet, Julien, Thu Hien, Christoffer, Thanh Duc, Hans-Christian,
the Unity Nighters, chi Le Ngoc, chi Lan Huong, anh Quang Minh chi
Thanh Nga, friends at Nguoi Viet Stockholm and others for sharing with
me moments in life.
Last but not least, I need to thank my family, my dad Phung Van Duan,
my mom Nguyen Thanh Hanh, my sister Viet Ha and brother Huy Duc for love and all time support. My dad has taught me through his deeds
how one should never stop learning enthusiastically. It has been a tough
journey for me, yet I know I made them proud. But pride cannot be
compared to their unconditional support for my long absence from home. I am very grateful for that!
Projects and Sponsors
The work was done with financial support from Swedish Center for
Nuclear Technology (SKC), Swedish Nuclear Power Inspectorate (SKI) and power utility companies in Sweden - Accident Phenomena of Risk
Importance Project (APRI). I would like to express my gratitude to all
sponsors and their representatives, Prof. Jan Blomgren, Prof. Henrik Nylén, Dr. Farid Alavyoon, Dr. Anders Andrén, Dr. Claes Halldin, Dr.
Ayalette Walter and others.
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Preface
This dissertation is an original intellectual product of the author, V.-A. Phung. The presented work was carried out by the author at the Division
of Nuclear Power Safety, Department of Physics, Royal Institute of
Technology - Kungliga Tekniska högskolan, Sweden.
The dissertation summarizes the work on (i) validation of system
thermal-hydraulic codes RELAP5 and TRACE against two-phase
circulation flow instability, (ii) prediction of in-vessel corium debris relocation using severe accident code MELCOR and surrogate model.
Details of the results are presented in five archival publications included
in the appendix. CIRCUS-IV experimental facility is a property of the Delft University of Technology, the Netherlands. The tests were proposed
and carried out by the author.
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List of Publications
Journal publications included in the dissertation
Paper 1:
Phung, V. -A., Kudinov, P., Grishchenko, D., Rohde, M., Input Calibration and Validation of RELAP5 Against CIRCUS-IV Single
Channel Tests On Natural Circulation Two-Phase Flow Instability,
Journal of Science and Technology of Nuclear Installations, Volume 2015, Article ID 130741.
Paper 2:
Phung, V. -A., Kööp, K., Grishchenko, D., Vorobyev, Y., Kudinov, P., Automation of RELAP5 Input Calibration and Code Validation Using
Genetic Algorithm, Journal of Nuclear Engineering and Design, Volume
300, 2016, p. 210–221.
Paper 3:
Phung, V. -A., Kudinov, P., Prediction of Flow Regimes and Thermal
Hydraulic Parameters in Two-Phase Natural Circulation by RELAP5 and TRACE Codes, Journal of Science and Technology of Nuclear
Installations, Volume 2015, Article ID 296317.
Paper 4:
Phung, V. -A., Galushin, S., Raub, S., Goronovski, A., Villanueva, W.,
Kööp, K., Grishchenko, D., Kudinov, P., Characteristics of Debris in the
Lower Head of a BWR in Different Severe Accident Scenarios, Journal of Nuclear Engineering and Design, Volume 305, 2016, p. 359–370.
Paper 5: Phung, V. -A., Grishchenko, D., Galushin, S., Kudinov, P., Prediction of
In-Vessel Debris Bed Properties in BWR Severe Accident Scenarios using
MELCOR and Neural Networks, Journal of Annals of Nuclear Energy,
submitted January 2017.
XIV
Publications not included
Phung, V. -A., Galushin, S., Raub, S., Goronovski, A., Villanueva, W., Kööp, K., Grishchenko, D., Kudinov, P., Prediction of Corium Debris
Characteristics in Lower Plenum of a Nordic BWR in Different Accident
Scenarios Using MELCOR Code, Proceedings of The International
Congress on Advances in Nuclear Power Plants 2015 (ICAPP-2015), Paper 15367, May 03-06, 2015, Nice, France.
Kudinov, P., Galushin, S., Villanueva, W., Phung, V. -A., Grishchenko, D., & Dinh, N. (2014a). A Framework for Assessment of Severe Accident
Management Effectiveness in Nordic BWR Plants. 12th International
Probabilistic Safety Assessment and Management Conference, PSAM
2014, Honolulu, United States, 22 June 2014 - 27 June 2014.
Kudinov, P., Galushin, S., Raub, S., Phung, V. -A., Kööp, K., Karanta, I.,
Sunnevik, K., Feasibility Study for Connection Between IDPSA and conventional PSA Approach to Analysis of Nordic type BWR's. NKS-315,
ISBN 978-87-7893-394-2, 2014c.
Kozlowski T.; Peltonen J.; Gajev I.; Phung V. -A.; Roshan S., Predicting Actual Reactor Conditions: Why Time-Domain Simulation is Necessary
for BWR stability, Int. J. of Nuclear Energy Science and Technology, 2013
Vol.7, No.4, pp.319 – 342.
Phung, V. -A., Kudinov, P., Identification of Two-Phase Flow Regimes
in Unstable Natural Circulation Using TRACE and RELAP5, The 9th
International Topical Meeting on Nuclear Thermal-Hydraulics, Operation and Safety (NUTHOS-9), paper N9P0062, Kaohsiung, Taiwan,
September 9-13, 2012.
Phung, V. -A., Kudinov, P., Rohde, M., Validation of RELAP5 with
Sensitivity Analysis for Uncertainty Assessment for Natural Circulation
Two-Phase Flow Instability, The 13th International Topical Meeting on
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Nuclear Reactor Thermal Hydraulics (NURETH-13), paper N13P1248, Kanazawa City, Ishikawa Prefecture, Japan, September 27-October 2,
2009.
Phung V. -A., Kudinov P., Relaxation Time Concept for Flow Regime
Transition in Two-Phase Flow Simulations, American Nuclear Society
Transactions, vol 101, 2009.
Author Contribution to Publications
The first author was involved in drawing the main ideas and
methodologies, carrying out most calculations, experiments, analysis and
writing the papers. The main supervisor was involved in problem formulation, critical discussion of ideas, analysis and review of the
papers. Other co-authors were involved in discussions, work formulation
and assisting in calculations.
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XVII
Contents
Abstract ................................................................................................... III
Sammanfattning .................................................................................... VII
Acknowledgement .................................................................................. IX
Preface ..................................................................................................... XI
List of Publications .............................................................................. XIII
Contents .............................................................................................. XVII
List of Figures ...................................................................................... XXI
List of Tables ...................................................................................... XXV
List of Acronyms .............................................................................. XXVII
Summary of Individual Contributions and Technical Achievements
............................................................................................................. XXIX
INTRODUCTION ............................................................................... 1 1
STATE OF THE ART REVIEW ......................................................... 3 2
Two-phase circulation flow instability ........................................ 3 2.1
In-vessel core relocation ............................................................ 5 2.2
Uncertainty in code prediction ................................................... 7 2.3
Machine learning ....................................................................... 9 2.4
Genetic algorithm ................................................................... 9 2.4.1
Artificial neural network ........................................................ 11 2.4.2
MOTIVATION, GOAL, APPROACHES AND TASKS .................... 13 3
Validation of system codes against two-phase circulation flow 3.1
instability .............................................................................................. 13
XVIII
Motivation ............................................................................. 13 3.1.1
Goals .................................................................................... 14 3.1.2
Approaches .......................................................................... 15 3.1.3
Tasks .................................................................................... 16 3.1.4
Prediction of in-vessel corium debris relocation ...................... 18 3.2
Motivation ............................................................................. 18 3.2.1
Goals .................................................................................... 20 3.2.2
Approaches .......................................................................... 20 3.2.3
Tasks .................................................................................... 21 3.2.4
VALIDATION OF SYSTEM CODES AGAINST TWO-PHASE 4
CIRCULATION FLOW INSTABILITY ..................................................... 25
CIRCUS-IV single channel tests ............................................. 25 4.1
Experiment ........................................................................... 25 4.1.1
Main characteristics of two-phase circulation flow instability .... 4.1.2
.............................................................................................. 28
RELAP5 and TRACE models ............................................... 30 4.1.3
Input calibration and code validation based on separate 4.2
consideration of UIPs .......................................................................... 30
Procedure ............................................................................. 30 4.2.1
Summary of results and main findings ................................. 32 4.2.2
Automated input calibration and code validation using genetic 4.3
algorithm .............................................................................................. 34
Methodology ......................................................................... 34 4.3.1
Summary of results and main findings ................................. 35 4.3.2
Codes prediction of flow regimes ............................................ 41 4.4
PREDICTION OF IN-VESSEL CORIUM DEBRIS RELOCATION . 47 5
Nordic BWRs ........................................................................... 47 5.1
Accident scenario ................................................................. 47 5.1.1
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Characteristics of in-vessel core relocation .......................... 48 5.1.2
MELCOR model ................................................................... 48 5.1.3
Summary of MELCOR results ................................................. 49 5.2
Surrogate model using artificial neural networks..................... 57 5.3
Methodology ......................................................................... 57 5.3.1
Summary of results and main findings ................................. 61 5.3.2
CONCLUSIONS .............................................................................. 71 6
REFERENCES ........................................................................................ 75
Appendix A (Paper 1)
Validation of RELAP5 Against CIRCUS-IV Single Channel Tests On Natural Circulation Two-Phase Flow Instability.
Appendix B (Paper 2)
Automation of RELAP5 Input Calibration and Code Validation Using
Genetic Algorithm.
Appendix C (Paper 3)
Prediction of Flow Regimes and Thermal Hydraulic Parameters in Two-
Phase Natural Circulation by RELAP5 and TRACE Codes.
Appendix D (Paper 4)
Characteristics of Debris in the Lower Head of a BWR in Different Severe
Accident Scenarios.
Appendix E (Paper 5)
Prediction of In-Vessel Debris Bed Properties in BWR Severe Accident
Scenarios using MELCOR and Neural Networks.
XX
XXI
List of Figures
Figure 1. Two-phase flow regimes (a), vertical flow regime map in 5 cm
diameter tube (b) (Taitel, Bornea, & Dukler, 1980). .................................. 4
Figure 2. In-vessel core relocation in Nordic BWRs. ................................ 6
Figure 3. GA-IDPSA coupled with reactor code RELAP5 or MELCOR. .. 10
Figure 4. Typical model of a) an artificial neural node, b) a 2-layer feed-
forward ANN. ............................................................................................. 12
Figure 5. Risk assessment framework for severe accident in Nordic
BWRs. ......................................................................................................... 19
Figure 6. CIRCUS-IV a) test facility and b) uncovered riser section for flow observation. ....................................................................................... 26
Figure 7. Inlet flow rate in the CIRCUS-IV single channel tests. ............. 29
Figure 8. RELAP5 and TRACE nodalization of the CIRCUS-IV single
channel tests. ............................................................................................. 29
Figure 9. Procedure for manual input calibration and code validation. ... 31
Figure 10. Inlet flow rate from the calibrated inputs and the experiment. ................................................................................................................... 33
Figure 11. RELAP5 calculated and experimental values of a) inlet flow rate and b) oscillation period. .......................................................................... 33
Figure 12. Fitness values obtained with different calibrated inputs. ....... 37
Figure 13. Inlet flow rate: experimental data and prediction obtained with
different calibrated inputs. ....................................................................... 37
Figure 14. Upper and lower bounds of GA predicted uncertainties
normalized to experimental bounds. ........................................................ 39
Figure 15. Maximum inlet flow rate and oscillation period. .................... 40
XXII
Figure 16. Test I-2 - Riser flow regime (FR) and void fraction (VF) in the section for visual observation. .................................................................. 42
Figure 17. Test I-2 - Flow regime in the riser observation section: experimental data and predicted by RELAP5 using different flow regime
transition boundaries. ............................................................................... 43
Figure 18. Test I.2 - Inlet flow rate: experimental data and predicted by
RELAP5 using different flow regime transition boundaries. ................... 44
Figure 19. Total mass of debris bed in the lower plenum as a function of scenario parameters (tADS, tECCS, AECCS). ..................................................... 51
Figure 20. Total mass of debris bed in the lower plenum (a) and mass of UO2 (b). ..................................................................................................... 53
Figure 21. Ratio of oxide to metal debris masses in the lower plenum. ... 53
Figure 22. Cumulative distribution functions of total mass of debris bed
(a) and ratio of oxide to metal debris masses (b) in the lower plenum at
different time moments after scram. ........................................................ 54
Figure 23. Cumulative distribution function of mass of UO2 debris in
different axial layers in the lower plenum. ............................................... 55
Figure 24. Total debris mass in the lower plenum (a), mass of intact UO2
in the core (b). ........................................................................................... 56
Figure 25. Maximum cladding temperature in the core........................... 56
Figure 26. Total mass of debris bed as a function of scenario parameters -
MELCOR result. ........................................................................................ 58
Figure 27. Flow diagram of ANNs training and SM prediction of in-vessel core relocation. .......................................................................................... 60
Figure 28. Normalized mean squared error of results of prediction ANNs and SMs - Total mass of debris bed. MSE of prediction networks are in
case the scenarios were correctly classified. Errors are from the SM
testing process. .......................................................................................... 62
Figure 29. SM prediction (output) compared to MELCOR solutions
(target) - Total mass of debris bed. a) Training set, b) testing set, c)
random data set* (*: excluding scenarios on the diagonal plane)............. 65
XXIII
Figure 30. Cumulative distribution function for total mass of debris bed. ................................................................................................................... 66
Figure 31. Total mass of debris bed predicted by the SMs using different number of scenario groups, at full capacity of ECCS (AECCS = 1).............. 67
Figure 32. Total mass of debris bed as a function of scenario parameters predicted by the SM using (a) 4 scenario groups, (b) 4 groups with
weighted classification (unit: kg). ............................................................. 68
XXIV
XXV
List of Tables Table 1. Test conditions and regimes. ....................................................... 27
Table 2. Experimental uncertainties - Tests I-1, I-2. ................................ 27
Table 3. Ranges of predicted SRQs normalized to respective nominal
experimental values. ................................................................................. 38
Table 4. Number of calculated scenarios with different mass of debris
bed. ............................................................................................................ 49
XXVI
XXVII
List of Acronyms
ADS Automatic depressurization system
ANN Artificial neural network
BWR Boiling water reactor
CDF Cumulative distribution function
ECCS Emergency core cooling system
FM Full model
GA Genetic algorithm
MSE Mean squared error
SA Severe accident
SBO Station black out
SM Surrogate model
SRQ System response quantity
STH System thermal-hydraulic
UIP Uncertain input parameter
XXVIII
XXIX
Summary of Individual Contributions and
Technical Achievements
Chapter
4
Validation of system codes against two-phase
flow instability
4.2.1
Appx.A
Pre-test analysis was done in order to define
experiment procedure to obtain data suitable for code validation. Dynamics of the flow instability was found to
be sensitive to the steam dome conditions. A new test
procedure was suggested and carried out in which steam
dome pressure fluctuations were avoided.
A non-automated procedure for calibration of
uncertain parameters in code input and validation of STH codes was proposed. The procedure can be applied if the
facility can be split into sub-systems and respective UIPs
can be considered separately. The most influential UIPs
are identified and used for the code validation.
Such divide-and-conquer strategy helps to identify
physically meaningful combination of calibrated values of
the UIPs.
4.2.2
Appx.A,
Appx.C
RELAP5 and TRACE were validated against two-phase circulation flow instability experiments in CIRCUS-
IV facility. Calculation results overlap experimental values when the system response quantities (SRQs) were
considered individually.
XXX
4.3.1
Appx.B
An automated approach using genetic algorithm (GA) for input calibration and STH code validation was
developed for the case when the number of calibrated
input parameters and SRQs is large and dependencies
between them are complex.
Multiple SRQs are used for the calibration and
validation. GA is used for the input calibration in order to identify optimal combinations and ranges of UIPs by
minimizing the discrepancy between experimental and
simulation data. GA is used for the code validation in
order to identify maximum deviation of code prediction results from the experimental data for the obtained ranges
of UIPs.
The approach reduces the user effect on the outcomes of the input calibration and code validation and
increases computational efficiency in comparison to
random sampling.
4.3.2
Appx.B
The automated approach was applied for RELAP5 input calibration and code validation against data of two-
phase circulation flow instability. For individual SRQs,
ranges of uncertainty in the prediction generally overlap with experimental uncertainty ranges.
The study shows the importance of considering simultaneously multiple SRQs and different test regimes
for quantitative code validation. For instance, the code
was not able to predict simultaneously the oscillation
period and maximum inlet flow rate. This means that predicted and experimental system response surfaces do
not overlap. It is suggested that one of the possible
reasons can be the use of steady state flow regime map in RELAP5.
XXXI
4.4
Appx.C
High speed video acquisition was used in order to obtain data on instantaneous flow regimes.
RELAP5 and TRACE capabilities in prediction of
instantaneous flow regimes during the instability were examined.
It is found that both codes could not identify correctly flow regimes in the transients. One of the
reasons is the small diameter pipe model in RELAP5 flow
regime map and the combined bubbly-slug flow regime in
TRACE.
Flow regime transition boundaries in RELAP5 were
modified in order to improve the flow regime identification. The effect on code predictions of other
thermal-hydraulic parameters was assessed.
With the modified flow regime transition boundaries in RELAP5, a better match to the experimental flow
regimes was obtained, however prediction quality of the
other flow parameters deteriorated.
5
Prediction of in-vessel corium debris relocation
5.2
Appx.D
Station blackout scenario with delayed power
recovery in a Nordic BWR was considered using MELCOR code. Genetic algorithm, random and grid sampling
methods were used in order to identify the influence of
scenario’s recovery timing and capacity of ADS and ECCS
on properties of debris in the reactor lower plenum.
The MELCOR results show that most of the scenarios
end up with either small (< 20 tons) or large (> 100 tons) mass of relocated debris. In transition regions that
separate these two domains, results are sensitive to small
XXXII
variation of the input parameters.
Large relocation of core debris can be prevented if ADS is activated before 5000 s after scram and ECCS is
activated with at least 25% of the design capacity within
1000 s after ADS activation.
The onset of large debris relocation is around 7000 s
in most of the scenarios.
The bottom most layer of the bed often has a
relatively small fraction of UO2 and large fraction of metal,
which results in very small decay heat and high mass averaged thermal conductivity of the debris material that
can affect vessel failure modes.
5.3.1
Appx.E
A surrogate model (SM) has been developed using
artificial neural networks (ANNs). The model provides computationally efficient prediction of main
characteristics of debris bed (i.e., total mass of debris,
ratio of oxide to metal debris masses and onset of large debris relocation) in the reactor vessel lower plenum.
The ANNs were trained with the obtained database of
MELCOR solutions. The effect of the noisy data in the full model database was addressed by introducing scenario
classification (grouping) according to the ranges of the
output parameters.
5.3.2
Appx.E
The SMs were validated against the MELCOR solutions. SMs using different number of scenario groups
with/without weighting between predictions of different
ANNs and a distance based interpolation model were compared.
The study shows that a single ANN provides smaller mean squared error (MSE) but large deviation with
respect to the cumulative distribution function (CDF) of
the response. Multiple-group SMs effectively filter out the
XXXIII
noise and provide a better prediction of the output CDF,
but increase the MSE value due to a larger number of misclassified scenarios. There are likely two main reasons
for the scenario misclassification: noisy data of MELCOR
solutions and small number of scenarios in some groups.
Weighted classification between different groups reduces the error of misclassification, however, the issue could not
be resolved completely due to the noise in the original
database.
For network training using a biased database,
accuracy of a SM improves when increasing the weight for
scenarios in sparsely sampled regions.
The SMs based on ANNs provide better overall
results than the interpolation model. The obtained SM can be used for failure domain and failure probability analysis
in the risk assessment framework for Nordic BWRs.
XXXIV
1
INTRODUCTION 1
Nuclear reactors involve interacting physical phenomena with multi-
dimensional, multi-scale and multi-phase nature. Dedicated computer codes have been developed for many decades in order to calculate
processes in nuclear reactors. These codes often rely on correlations
derived from experiments and mechanistic models with large number of input parameters. In most cases exact values of these parameters are not
known and users have to rely on recommended ranges and calibration
data.
Thus during calculation of complex phenomena, code users have to deal
with numerous uncertainties. In order to assess code predictive capability
during validation or effect of code uncertainty on decision making during safety analysis, the code uncertainty has to be quantified. Uncertainty
quantification is a comprehensive and computationally expensive task. It
is necessary to further develop and apply approaches for uncertainty
quantification in the context of code validation and application.
In this work, I apply advanced machine learning techniques such as
genetic algorithm and artificial neural network to aid solving practical problems for system code
- input calibration;
- validation and uncertainty quantification;
- application (including surrogate model development).
The demonstration of approaches is based on computational analysis of
phenomena relevant to boiling water reactors (BWRs) safety: (i) two-phase circulation flow instability and (ii) in-vessel corium debris
relocation.
2
In the analysis of the two-phase flow instability, I demonstrate the process of input calibration and code validation, starting from the pre-
test analysis for the development of the experimental procedure, to
application of the non-automated procedure and the automated method
using genetic algorithm to assess predictive capabilities of the thermal hydraulic codes (RELAP5 and TRACE), and finishing with examining the
effect of improvement in code (RELAP5) flow regime identification on
code prediction.
In the analysis of in-vessel corium debris relocation, a severe accident
code MELCOR with genetic algorithm, random and grid sampling
methods were used first to investigate the phenomenon and obtain a database of code solutions. Then a surrogate model was developed using
artificial neural networks trained against the database of the full model
solutions.
3
STATE OF THE ART REVIEW 2
Two-phase circulation flow instability 2.1
Two-phase flow instability is an important issue affecting both
performance and safety of BWRs (D'Auria, et al., 1997) (Duncan, 1988). The instability can occur during reactor operation or beyond design basis
accidents. The phenomenon results in oscillations of thermal-hydraulic
parameters (e.g., flow rate, temperature, pressure, void fraction) and possibly also neutronic parameters. It may cause problems in reactor
control as well as failures due to thermal fatigue, mechanical vibrations,
premature burn-out. The failures may decrease significantly life span of
the systems.
There are different types of two-phase flow instability. This work
concerns flashing instability in natural circulation systems which belongs to density wave instability type (Fukuda & Kobori, 1979) (Nayak &
Vijayan, 2008), the most important and widely studied type in nuclear
systems. In natural circulation loops, fluid is heated from below and
cooled from above. Density gradient of the fluid creates driving force for the circulation flow. Flashing instability may take place in a boiling
system at low pressure due to strong interactions and delayed feedbacks
between inertia of the flow and compressibility of the two-phase mixture. The instability depends on the perturbed pressure drop in the two-phase
and single-phase regions of the system and the propagation time delay of
the void fraction in the system.
Thermal hydraulics of two-phase natural circulation flow instability has
been investigated extensively both experimentally and analytically for
decades. Sophisticated test facilities have been used. For example, Wissler et al. (1956), Boure et al. (1973), Aritomi et al. (1993), Chiang
et al. (1993) studied instability in natural circulation (NC) loops and NC
4
BWRs. Furuya et al. (2005a) (2005b) investigated mechanism of flashing induced instability. Stability map of NC BWR was studied by De Kruijf et
al. (2003) (2004), Zboray et al. (2004), Rohde et al. (2008). Ishii et al.
(1996) and Kuran et al. (2006) investigated the phenomena in a large
scale facility. At the CIRCUS facility, Manera and van der Hagen (2003), Marcel et al. (2005) carried out studies on the instability during NC BWR
startup.
Analytical studies resulted in the development of models for two-phase
flow instability that could be implemented in system codes (Paniagua,
Rohatgi , & Prasad, 1999) (Inada., Furuya, & Yasuo, 2000). Two-phase
flow instability was investigated using system thermal-hydraulic (STH) codes for example in the works of Kolev (2006), Shiralkar et al. (1993),
Rohde et al. (2008). Flashing induced instability was studied by Schäfer
and Manera using ATHLET (2004), Kozmenkov et. al using RELAP5 (2012).
a) b)
Figure 1. Two-phase flow regimes (a), vertical flow regime map in 5 cm
diameter tube (b) (Taitel, Bornea, & Dukler, 1980).
System thermal-hydraulic (STH) codes are widely used in analysis of
nuclear reactor behaviour during normal operation, incidents and accidents. The codes such as RELAP5 (Reactor Excursion and Leak Analysis Program) (Ransom, 1983) (USNRC & ISL, 2001), TRACE
5
(TRAC/RELAP Advanced Computational Engine) (USNRC, 2008), CATHARE and ATHLET were originally designed to calculate large and
small break loss of coolant accidents and other design basis accidents.
For two-phase flow calculations, the codes are based on two-fluid six-equation models. The rates of exchange of mass, energy and momentum
between vapor and liquid phases are sensitive to the topology of the
vapor-liquid interface, or flow regime. Flow regimes (Figure 1a) have been extensively studied experimentally and presented as flow regime
maps (for example, see Figure 1b) (Taitel, Bornea, & Dukler, 1980). In the
codes, the flow regimes influence simulation results through the closures
specific for each flow regime.
In-vessel core relocation 2.2
Severe accident in nuclear reactors involves complex physical processes
and phenomena. Severe accident management strategy in Nordic BWRs employs ex-vessel corium debris coolability. The mode of corium melt
ejection from the vessel determines conditions for ex-vessel accident
progression and threats to containment integrity, e.g., formation of a
non-coolable debris bed or energetic steam explosion (Kudinov, et al., 2014a). Melt interactions with the vessel structures, vessel failure and
melt ejection mode are affected by properties of corium debris bed in the
vessel lower plenum such as mass, composition, thermal properties, timing of relocation, spatial configuration and decay heat (Goronovski,
Villanueva, Tran, & Kudinov, 2013) (Goronovski, Villanueva, Kudinov, &
Tran, 2015). These properties are determined by in-vessel core
degradation and relocation. Characteristics of the accident scenario events, such as timing of failure and recovery and capacity of the
recovered systems, affect core relocation and result in different properties
of debris in the lower plenum.
Core relocation involves multi-phase flows and complex interplay
between thermal, chemical processes, and mechanical interactions
between fuel material with water and in-vessel structure (Figure 2).
6
Decay heat of the core is usually removed by water evaporation. During accidents if water injected into the reactor vessel is not sufficient, the core
becomes uncovered, degradations of Zirconium fuel cladding and control
rods start. Oxidation of Zirconium generates heat that accelerates the
melt down of fuel cladding and stainless steel structures in the core region. As soon as the cladding fails, fuel relocation starts. Debris cooling
by remaining water leads to quenching and formation of debris bed on
the core support plate. Usually, a small amount of debris relocates to the vessel lower plenum first. Later, larger masses of debris can relocate.
Figure 2. In-vessel core relocation in Nordic BWRs.
Core degradation and relocation phenomena have been studied
experimentally in the past, e.g., XR2-1 (Gauntt & Humphries, 1997), Phebus FP (March & Simondi-Teisseire, 2013), PBF-SFD (Spencer,
Jensen, & McCardell, 1982), LOFT-FP2 (Cronenberg, 1992), RASPLAV
(Asmolov V. , 1999), MASCA (Asmolov & Tsurikov, 2004), CORA (Hofmann, Hagen, Noack, Schanz, & Sepold, 1997), FLHT (Lombardo,
Lanning, Panisko, & Richard, 1992). The experiments are limited in
number. The data from the experiments has been used mostly for
development and validation of the models and computer codes.
Core degradation (T, M, C)
Large and droplet core relocation (M)
Boiling (T)
Debris spreading (T, M, C) Debris bed
Water
Core
Core support plate
Debris quenching (T, C)
Core support plate failure (T, M)
Processes
(T: thermal, M: mechanical, C: chemical)
Reactor vessel
7
In order to calculate progression of severe accidents, codes such as
MELCOR (Methods for Estimation of Leakages and Consequences of
Releases) (Summers, et al., 1991) (US NRC, et al., 2005) and MAAP
(Modular Accident Analysis Program) (Gabor & Henry, 1983) are used. The codes can model a broad spectrum of physical phenomena including:
thermal-hydraulics; core heatup, degradation, and relocation; molten
core-concrete interactions; hydrogen production; fission product release and transport. Phenomena are calculated in the codes based on
mechanistic models or correlations obtained from experiments.
Assumptions in the models are used due to incomplete knowledge of
underlying physics of complex multi-scale phenomena.
Uncertainty in code prediction 2.3
Uncertainty can potentially affect code prediction as well as experimental
results. It can originate from numerous sources (Petruzzi & D'Auria, 2008a), which can be classified as:
‐ modelling uncertainties: in physical laws, models, correlations in
codes,
‐ experimental uncertainties: measurement errors,
‐ numerical uncertainties: in spatial/temporal discretization,
machine accuracy,
‐ input parameter uncertainties: in boundary, initial conditions in
experimental or reactor conditions,
‐ and other user effects.
Uncertainties can also be categorized into epistemic uncertainties and
aleatory uncertainties (Helton, Johnson, Oberkampf, & Sallaberry, 2010). Epistemic uncertainties come from lack of knowledge about appropriate
values of parameters that are assumed to have known values. Aleatory
uncertainties come from inherent randomness of the system behaviour.
According to IAEA, (2006) definition:
8
‐ “System code validation is assessment of the accuracy of values predicted by the system code against relevant experimental data
for the important phenomena expected to occur.”
‐ “Model calibration is the process whereby model predictions are compared with field observations and/or experimental
measurements from the system being modelled, and the model
adjusted if necessary to achieve a best fit to the measured and/or observed data.”
Validation of system codes including system TH codes is an important
step in application of the codes to reactor safety analysis. The goal of the
validation process is to determine how well a code can represent physical
reality. This is achieved by comparing system response quantities (SRQs) taking into account both experimental and modelling uncertainties. Code
input development is the first step in the process of validation. One of the
sources of uncertainties is input parameters that are not measured directly in the experiment. Quantification of such parameters is often
called input calibration. Sufficient number of constrains should be
provided in the experimental data in order to enable inference of the
input parameters. The purpose of input calibration is to find a combination of values of the uncertain input parameters which provide
prediction closest to the experimental data.
In depth assessment of the uncertainties is an essential part of code
validation and reactor safety analysis (Oberkampf & Trucano, 2002)
(Oberkampf & Smith, 2014) (Petruzzi & D'Auria, 2008a). Uncertainty
quantification can be carried out using different methods such as propagation of code input uncertainty (Cacuci, 2003) (Glaeser, 2008),
propagation of code output uncertainty (Petruzzi & D'Auria, 2008a). To
compare multiple predicted and experimental SRQs for code validation, methodologies such as fast Fourier transform based method (FFTBM)
have been developed (D'Auria, Leonardi, & Pochard, 1994) (Kovtonyuk,
Petruzzi, & D'Auria, 2015). Random sampling methods are often
employed for quantifying uncertainties in probabilistic terms. Other advanced sampling techniques have been developed in order to assess the
effect of uncertainty in timing of stochastic events on the accident
progression (Hakobyan, et al., 2008), (Kloos & Peschke , 2006),
9
(Vorobyev & Dinh, 2008), (Vorobyev & Kudinov, 2012), (Vorobyev, Kudinov, Jeltsov, Kööp, & Nhat, 2014), (Kudinov, et al., 2014b).
Machine learning 2.4
Machine learning (Minsky, 1961) algorithms can autonomously learn
from and make predictions on data. The algorithms have great potential in approximating response of complex models and have been successfully
used in nuclear power applications (Uhrig & Tsoukalas, 1999). Genetic
algorithm and artificial neural networks are among the most commonly applied methods.
Genetic algorithm 2.4.1 Genetic Algorithm (GA) (Friedberg, 1958) (Friedberg, Dunham, & North,
1959) is a heuristic method which mimics the process of natural selection
in order to find the global optimum of a fitness function. Each candidate
state or candidate solution has (i) a set of values of the input parameters which can vary within their pre-determined ranges, and (ii) a fitness
function determined by a set of the output parameters. The process of
selection of the candidate states is guided by the GA towards the global optimum of the fitness function as follows:
1) Generate a population of candidate states (inputs) by random
selection of the uncertain input parameters within their ranges.
2) Run code and calculate value of the fitness function for each candidate state (input).
3) Select the best fitted candidate states based on evaluation of the
respective values of the fitness function. 4) Create a new population of candidate states from the selected
ones using a combination of GA operators: (i) genetic crossover,
which combines information from the parent states, and
(ii) random mutation of the states. 5) Go to step #2 and repeat the process in order to produce a pre-
determined number of generations which evolve towards the
optimum solution.
10
GA can be more computationally efficient than traditional sampling
methods when searching for specific scenarios or regimes in multi-
dimensional input parameter space (de Weck, 2004). Traditional
methods such as random sampling (Monte-Carlo), Latin hypercube or importance sampling do not receive guidance on the sampling process
from the output. A disadvantage of GA is that sampling is biased.
Figure 3. GA-IDPSA coupled with reactor code RELAP5 or MELCOR.
Defining Fitness Function
Defining Input Parameter Domain
GA‐IDPSA
Starting Code Calculations
GA‐IDPSA
Generating Code Inputs
GA‐IDPSA/MATLAB
Calculating Fitness Value
GA‐IDPSA Selecting the best fitted
candidate states
End of generation
Optimum Solution
Yes
No
Code outputs
Final generation No
Yes
Code inputs
11
GA-IDPSA code
Genetic Algorithm-based Integrated Deterministic Probabilistic Safety
Analysis (GA-IDPSA) code coupled with RELAP5 or MELCOR was used
in this work (Figure 3) (Vorobyev & Dinh, 2008) (Vorobyev, Kudinov, Jeltsov, Kööp, & Nhat, 2014). The system analysis code is considered by
GA-IDPSA as a “black box” model. GA-IDPSA code selects values of the
input parameters, generates code input decks and schedules multiple code runs on a parallel computational architecture. For calculation of
fitness functions, GA-IDPSA can use external tools such as MATLAB.
Artificial neural network 2.4.2
Artificial neural network (ANN) (McCulloch & Pitts, 1943) method is inspired by a hypothesis of learning in biological process, in which the
brain activity consists of primarily of electrochemical activity in networks
of cells called neurons. ANNs are used to approximate functions which
depend on uncertain input parameters. They can find solution for problems such as classification, regression and structured prediction
(Fausett, 1994).
An ANN consists of interconnected “neuron” nodes. Each node has input
connections, input function (often being the summation), activation
function and output connections (Figure 4a). Each input connection has a numeric weight associated with it, which can be improved by automatic
learning from examples. The learning process depends on main factors:
component of the network to be improved, prior knowledge of the system, representation used for the data, and the nodes and feedback
available to learn from.
There are different types of ANNs which are categorized mostly based on the activation functions and on how the nodes are connected. In this
work, feed-forward networks also known as multi-layer perceptrons were
used. A two-layer feed forward network with multiple inputs and outputs is illustrated in Figure 4b. The input layer consists of the inputs to the
12
network. Then follows a hidden layer, which consists of a number of hidden nodes (z1,…,zq) placed in parallel. Each node performs a weighted
summation of the inputs, which then passes a nonlinear activation
function (a sigmoid function in this case). The output layer is formed by
another weighted summation of the outputs of the hidden nodes. The networks can use different learning techniques, for instance backward
propagation of errors.
a) b)
Figure 4. Typical model of a) an artificial neural node, b) a 2-layer feed-
forward ANN. ANNs are flexible and computationally efficient tools which can be used to approximate complex non-linear systems. Most of the computational
time for ANNs is often spend on learning the data. After the networks are
trained, their calculation time during applications is much shorter. ANN, however, is a “black box” learning approach which cannot interpret
relationship between input and output.
Activation Function
Output LinksInput Links
ai injw
i,j
g
aj=g(inj)
Node j
Input Output
z1
z2
z3
zq
x1
x2
x3
xn
1 1
Inputs Outputs
Input layer
Output layer
y1
y2
y3
ym
Neural nodes
W1 W2
Hidden layer
13
MOTIVATION, GOAL, APPROACHES 3
AND TASKS Quantifying uncertainties and code validation are important tasks in
nuclear reactor safety analysis. It is usually computationally expensive due to a large number of uncertain parameters and multi-physics, multi-
dimensional, multi-scale physical phenomena. This work addresses
computational analysis of (i) two-phase circulation flow instability and (ii) in-vessel corium debris relocation in the context of boiling water
reactor (BWR) safety.
Validation of system codes against two-3.1
phase circulation flow instability
Motivation 3.1.1
System thermal-hydraulic codes such as RELAP5 and TRACE use two-phase flow regime maps with criteria for transition between different
regimes based on results of fully developed, steady state experiments.
Instantaneous flow parameters are used in the codes for determining flow regimes with no regards to the flow history (e.g., acceleration or
deceleration of the flow). In reality, flow regime transitions need time to
develop (Lucas, Krepper, & Prasser, 2005). Transient flow regimes can be
different from steady state ones at the same instantaneous flow parameters (Prassinos & Liao, 1979). Rates of exchange of mass, energy
and momentum between the vapor and liquid phases depend on the flow
regime. As a consequence, there is a concern that the steady state flow regime maps in the codes may lead to significant errors for transients
with rapidly changing flow regimes. Such transients can be found during
two-phase flow instabilities.
14
In order to assess code capability to model two-phase flow instability,
code input calibration and code validation must be performed.
Quite often in engineering practice, input calibration and code validation
are carried out manually relying on engineering judgment about input
uncertainties. However, calibration and uncertainty quantification in code validation become challenging tasks when the number of uncertain
input parameters (UIPs) and system response quantities (SRQs) is large
and dependencies between them are complex. The outcomes of the whole process become prone to the so called “user effects” (when using the same
code different users obtain different results). For calibration of code
model parameters, advanced methods have been used such as genetic
algorithm (Marseguerra, Zio, & Canetta, 2004) (Tsai, Shih, & Wang, 2014), multidirectional search (Carlos, Ginestar, Marorell, & Serradell,
2003).
Furthermore, uncertainty quantification often employs random sampling
methods. However, such methods can become computationally
expensive, when it is necessary to quantify the tails of model output distribution especially in multi-dimensional scenario spaces. For
example, in order to achieve 99% confidence level that sampled model
output covers at least 0.99 fraction of its unknown distribution one will need to perform 662 calculations (Wilks, 1941).
A computationally efficient approach to code input calibration and code validation that can resolve the above issues is necessary.
Goals 3.1.2
The main goals of this part of the work are to:
(i) develop and apply efficient methods for input calibration and STH code validation against unsteady flow experiments with
two-phase circulation flow instability,
(ii) examine the codes capability to predict instantaneous thermal hydraulic parameters and flow regimes during the transients.
15
Approaches 3.1.3
Two approaches have been developed for code input calibration and code
validation: a non-automated “manual” procedure based on separate
consideration of UIPs during the calibration and an automated approach
that considers multiple parameters at once using genetic algorithm (GA).
The approaches were applied for calibration and validation of RELAP5
and TRACE models of two-phase circulation flow instability in CIRCUS-
IV facility.
In the first approach (Phung, Kudinov, Grishchenko, & Rohde, 2015a),
the facility was split into sub-systems and respective UIPs were
considered separately. The most influential UIPs were identified and used
during code validation. Such divide-and-conquer strategy helps to
identify physically meaningful combination of calibrated values of the
UIPs.
After applying the first approach, it is noticed that calibration and
validation becomes difficult when the number of calibrated input
parameters and SRQs is large. Specifically, criteria which take into
account simultaneously several SRQs are needed for better evaluation of
the code validity. Therefore, the second approach using GA has been
developed.
The automated method using GA (Phung, Kööp, Grishchenko, Vorobyev,
& Kudinov, 2016a) aims to reduce the user effect on the outcomes of the
input calibration and increase computational efficiency in comparison to
random sampling during code validation. GA enables to use multiple
SRQs during calibration and validation. During input calibration GA is
used to identify optimal combinations and ranges of UIPs by minimizing
the discrepancy between experimental and simulation data. During code
validation GA is used to identify maximum deviation of code prediction
results from the experimental data for the obtained ranges of UIPs. This
provides a conservative assessment of the code error in prediction.
16
RELAP5 and TRACE capabilities in prediction of instantaneous flow
regimes during the instability were examined (Phung & Kudinov, 2015b). Flow regime transition boundaries in RELAP5 were modified in order to
improve the flow regime identification and prediction of the other
thermal-hydraulic parameters.
Tasks 3.1.4 In order to achieve the goals, the following tasks have been completed:
Task 1.1: Design of experimental procedure and carrying
out CIRCUS-IV single channel tests (refer to Section 4.1 for more information).
Preliminary analysis of the CIRCUS-IV experiments was carried out
in order to define a new test procedure to produce data suitable for code validation.
Task 1.2: Develop input models and identify sources of uncertainties (refer to Section 4.1 for more information).
RELAP5 and TRACE input models were developed. The effect of spatial and temporal resolution of the numerical model was
investigated (Ferreri & Ambrosini, 2002) in order to demonstrate
that numerical uncertainties are not dominant.
The experimental data were analysed in order to identify code input,
and experimental measurement uncertainties. From measured
parameters, a set of representative SRQs was selected for input calibration and code validation.
Task 1.3: Develop and apply a procedure based on separate effect treatment of UIPs (refer to Sections 4.2.1 and 4.2.2 for
results and discussions).
17
The procedure employs a possibility to address uncertainty in different UIPs separately by modelling of different parts of the facility
(such as test section) and different flow regimes (single phase, two-
phase). Parametric studies were carried out in order to identify
possible ranges of the most influential UIPs and respective uncertainty in the code prediction.
Task 1.4: Develop and apply the automated approach to
input calibration and code validation using genetic algorithm (refer to Sections 4.3.1 and 4.3.2 for results and
discussions).
In the input calibration, multiple, normalized and weighted SRQs
were used in the target functions. GA is used in order to identify
optimal combinations and possible ranges of UIPs by minimizing the
discrepancy between experimental and simulation in the input calibration process. The user effect is reduced by selecting wide
ranges of the UIPs for the GA analysis. GA is used for the code
validation in order to identify maximum deviation of code prediction results from the experimental data for the obtained ranges or UIPs.
Task 1.5: Validate codes capabilities in prediction of flow regimes (refer to Section 4.4 for results and discussions).
High speed video acquisition on instantaneous flow regimes and thermal-hydraulic parameters from the CIRCUS-IV single channel
tests were used for the validation. Predicted flow regime was
compared with the test data. Flow regime map models in RELAP5
and TRACE were scrutinized in order to find explanations for discrepancies between the calculated and the experimental data.
Sensitivity of prediction of thermal-hydraulic parameters of
instability to variations in the flow regime transition boundaries of RELAP5 was studied. The analysis was not carried out for TRACE
due to lack of the source code.
18
Prediction of in-vessel corium debris 3.2
relocation
Motivation 3.2.1
This work belongs to the program on development of the risk assessment framework for severe accident in Nordic BWRs (Kudinov, et al., 2014a).
The program employs experience of Risk Oriented Accident Analysis
Methodology (ROAAM) that combines probabilistic and deterministic approaches (Theofanous, 1996). In order to assess the effect of
uncertainty in timing of stochastic events on the accident progression, the
methodology follows integrated deterministic-probabilistic safety analysis
(IDPSA) approaches (Hakobyan, et al., 2008), (Kloos & Peschke , 2006), (Vorobyev & Dinh, 2008), (Vorobyev & Kudinov, 2012), (Vorobyev,
Kudinov, Jeltsov, Kööp, & Nhat, 2014), (Kudinov, et al., 2014b). Artificial
neural networks have been successfully used in nuclear applications, for example for plant status or transient diagnosis (Bartlett & Uhrig, 1992)
(Uhrig & Tsoukalas, 1999) (Santosh, Srivastava, Sanyasi Rao, Gosh, &
Kushwaha, 2009) (Mo, Leo, & Seong , 2007), for prediction of outcomes
of different scenarios (Zio, Broggi, & Pedroni, 2009) (Na, et al., 2004) (Kim, Kim, Yoo, & Na, 2015). Recently fuzzy logic (Zadeh, 1965) based
approaches have gained considerable attention, for example in (Zio &
Baraldi, 2005) (Zio, Di Maio, & Stasi , 2007) (Guimarães & Lapa, 2007). Dozens or hundreds of full model (FM) simulations is often necessary for
development of a reliable surrogate model.
The ROAAM+ framework (Kudinov, et al., 2014a) is designed for comprehensive risk assessment and can be used for two main tasks: (i) to
characterize failure domains and (ii) to estimate failure probability in the
space of the accident scenario parameters. The framework is implemented using a set of coupled models for prediction of different
accident progression stages starting from core degradation and relocation
to the lower head, vessel failure, melt release and melt-coolant
interactions in the lower drywell (Figure 5).
19
In ROAAM+, surrogate (simplified) models are developed in order to approximate the response of complex and computationally expensive full
modes (such as MELCOR). The purpose of the surrogate models (SMs) is
to improve computational efficiency while maintaining acceptable
accuracy for extensive uncertainty analysis. For each accident stage, a representative database of FM solutions is obtained. Simplified modeling
approaches and data mining techniques are used in order to develop the
SMs.
Figure 5. Risk assessment framework for severe accident in Nordic BWRs.
(Kudinov, et al., 2014a)
In-vessel core degradation and relocation provide initial conditions for
further accident progression. Characteristics of the debris in the lower
plenum affect vessel failure and melt release conditions and therefore
containment failure probability. Outcomes of core relocation depend on the interplay between (i) accident scenarios (e.g. timing and
characteristics of failure and recovery of safety systems) and (ii) accident
phenomena. Uncertainty analysis is necessary for comprehensive risk assessment. However, computational efficiency of system analysis codes
such as MELCOR is one of the big obstacles. Another problem is that
code predictions can be quite sensitive to small variations of the input
parameters and numerical discretization, due to the highly non-linear feedbacks and discrete thresholds employed in the code models.
20
Goals 3.2.2
The main goals of this part are to:
(i) obtain a representative database of MELCOR solutions for characteristics of debris in the reactor lower plenum for
different accident scenarios,
(ii) develop a computationally efficient surrogate model for prediction of main characteristics of debris bed.
Approaches 3.2.3
MELCOR code is used as a full model (FM) for core relocation in Nordic
BWRs. Station blackout (SBO) with different possible delays of power recovery was considered. Genetic algorithm, random and grid sampling
methods were used (Phung, et al., 2016b) in order to identify the
influence of recovery timing and capacity (uncertain scenario parameters)
of automatic depressurization system (ADS) and emergency core cooling system (ECCS) on properties of debris in the reactor lower plenum.
Scenarios that result in similar characteristics of core degradation
transients were grouped; ranges and distributions of debris bed characteristics for each identified group of scenarios were determined.
The obtained database of MELCOR solutions was used to train artificial
neural networks (ANNs) in order to develop a computationally efficient core relocation surrogate model (SM) (Phung, Grishchenko , Galushin, &
Kudinov, 2017).
The FM database has considerable (physical and/or numerical) noise in
the response. Sampling was also biased towards regions of scenario
parameters of special interest for analysis of the further accident progression (i.e. small or large mass of relocated debris). The effect of the
noisy data in the FM database was addressed by introducing scenario
classification (grouping) according to the ranges of the output parameters. The SMs used different number of scenario groups
with/without weighting between predictions of different ANNs.
21
Tasks 3.2.4 The following tasks have been carried out:
Task 2.1: Select (i) relevant accident scenario, (ii) ranges of
uncertain input parameters, and (iii) characteristics of debris to be predicted by the model (refer to Section 5.1.1 and
5.1.2 for more information).
Station Blackout (SBO) was selected as the largest contributor to the core damage frequency. Timing of recovery and capacity of safety
systems were selected as uncertain scenario parameters. The ranges
of the parameters were selected based on preliminary analysis and data about accident progression phenomena relevant to the vessel
failure.
Debris bed mass, composition and timing of relocation to the reactor lower plenum have been shown important for vessel failure and melt
release modes in Nordic BWRs.
Task 2.2: Develop MELCOR input (refer to Section 5.1.3 for
more information).
MELCOR model of a Nordic BWR was developed using reference
plant data including safety systems and control logics. The effect of
spatial (number of radial rings in the core) and temporal resolution of the numerical model was investigated. Preliminary calculations
showed that variations in the numerical resolution can lead to
noticeable differences in predictions for individual cases. However, it
was still possible to identify general tendencies determined by the scenario parameters.
Task 2.3: Obtain a representative database of MELCOR solutions (refer to Sections 5.2 for results and discussions).
22
o Task 2.3.1: Run MELCOR calculations.
The database of MELCOR calculations included data from
random, grid and genetic algorithm samplings. Different fitness
functions for GA were used: 1) Total mass of relocated debris bed in the lower
plenum. Target value of the fitness function was set to 70
tons to identify transition region from small (less than 20 tons) to large relocation (more than 100 tons).
2) Mass of UO2 in the debris layer in contact with the
vessel. Maximum value was targeted in the analysis. The
thickness of the layer (17 cm) was chosen according to the height of the vessel penetration nozzle.
o Task 2.3.2: Classify scenarios according to ranges of debris bed characteristics.
The scenarios were grouped according to the total mass of
relocated debris. Ranges and distributions of debris bed characteristics were determined for each scenario group.
We found that most of the scenarios had relocated debris mass either above 100 tons or less than 20 tons. The results are
sensitive to small variation of the input parameters in the
transition region. Local phenomena and parameters were also
analysed for a small number of selected scenarios in order to gain better understanding of the system behaviour in such
conditions.
Task 2.4: Develop and validate the surrogate model (refer to
Sections 5.3.1 and 5.3.2 for results and discussions).
Inputs and outputs of the core relocation SM were selected based on
the requirements of the next SM in the framework, importance of
input parameters for the output parameters.
23
The database of MELCOR solutions obtained in the previous tasks was analyzed.
The SM was designed in order to address the noise in the FM
database and reproduce both local values and statistical characteristics of the database of FM solutions. The SMs with
different number of scenario groups and with/without weighted
classification based on scenarios in neighborhood were used.
The ANNs were trained, validated and tested using the MELCOR
database. In order to deal with the biased sampling in the database,
different weights were used for scenarios in regions with different density of the samples. The SMs were validated against the MELCOR
solutions. The SMs using ANNs were also compared with a distance
based interpolation model. Error of the predicted debris bed characteristics and cumulative distribution functions (CDFs) were
assessed.
The best SM was selected for application in the risk assessment framework.
24
25
VALIDATION OF SYSTEM CODES 4
AGAINST TWO-PHASE CIRCULATION
FLOW INSTABILITY This chapter briefly discusses main results on code validation against
two-phase circulation flow instability and examining the codes capability
to predict instantaneous flow regimes during the transients. For more
details, refer to Appendices A, B, C or Phung et al. (2015a), (2016a), (2015b).
CIRCUS-IV single channel tests 4.1
Experiment 4.1.1
The CIRCUS-IV (Marcel, Rohde, & van der Hagen, 2005) is a natural
circulation test loop facility at the Delft University of Technology. It was designed to investigate two-phase flow instability in natural circulation
BWRs at low pressure.
CIRCUS-IV thermal-hydraulic loop (Figure 6a) consists of a test section
with four parallel channels, a heat exchanger, a downcomer, two upper
buffer vessels with steam domes and a lower buffer vessel with preheater.
Each parallel channel consists of a heated section with a heated rod inside, a bypass channel, and a riser section. The temperature of the
water at the inlet of the test section is controlled by the preheater.
The main measurement system includes a volumetric magnetic flow-
meter (F), thermocouples (T), pressure sensors (P) (Figure 6a), and a
high-speed camera located in front of the uncovered riser section (Figure
6b.).
26
Figure 6. CIRCUS-IV a) test facility and b) uncovered riser section for flow
observation.
P
P
Upper
Buffer Vessel
T
T
T
T
T
T
TT
T
TT
F
PHeat Exchanger
Buffer Vessel
with Preheater
Downcomer
Riser
1 Active,
3 Inactive
Channels
Heated
Channel
and
Bypass
Channel
Upper
Buffer Vessel
High Speed Camera
a)
b)
27
Table 1. Test conditions and regimes.
Test
Pressure
(bar)
Power
(kW)
Inlet water
temperature
(°C)
Test regime
S-1 1 2.5 89.0 Single-phase steady state
I-1 1 2.5 92.8 Two-phase instability
I-2 1 2.5 99.8 Two-phase instability
Table 2. Experimental uncertainties - Tests I-1, I-2.
Parameter
Measurement error Repeatability uncertainty
Absolute Relative, % Absolute Relative, %
Inlet Channel Maximum Flow Rate ±0.0002 l/s ±0.07~0.09 ±0.003~0.007 l/s ±1~3
Inlet Channel Average Flow Rate ±0.0002 l/s ±0.1~0.3 ±0.001~0.006 l/s ±2~5
Inlet Channel Minimum Flow Rate ±0.0002 l/s ±0.5~0.8 ±0.005~0.006 l/s ±13~30
Oscillation Period ±0.025 s ±0.05~0.17 ±0.1 s ±0.2~0.7
Inlet All Channels Temperature ±1 °C ±1 ±0.05 oC ±0.05
Inlet Heated Channel Temperature ±1 °C ±1 ±0.05 oC ±0.05
Inlet Riser Temperature ±1 °C ±1 -1 to +0.1 oC -1 to +0.1
Middle Riser Temperature ±1 °C ±1 -0.3 to +0.1 oC -3 to +1
Outlet Riser Temperature ±1 °C ±1 ±0.3 oC ±0.3
Inlet Downcomer Temperature ±1 °C ±1 ±0.07 oC ±0.07
Inlet Pressure ±0.03 bar ±2 ±0.02 bar ±1.2
28
Preliminary analysis of the CIRCUS-IV experiments found that the data were not suitable for code validation. The main reason is that dynamics of
the flow instability is sensitive to the variations of the steam dome
pressure which was oscillating significantly in the original tests.
The author defined and participated in performing new experiments with
a single active channel in the test section in order to eliminate possible
effects of parallel channels, and the steam domes opened to the atmosphere to maintain constant steam dome pressure.
Three experiments were carried out, which were designated as S-1, I-1
and I-2 (see Table 1). Ranges of measurement and experimental uncertainties are summarized in Table 2.
Main characteristics of two-phase circulation flow 4.1.2
instability
A flashing instability period consists of an incubation stage and a flashing
(or boiling) stage. During the incubation, the flow in the system remains at subcooled conditions reaching the minimum inlet flow rate (Figure 7),
and the maximum inlet pressure. When water in the test section reaches
saturation point, boiling starts and the incubation period ends. During
the flashing, the system experiences a strong boiling in the test section, thus a peak in inlet flow rate (Figure 7) which determines the maximum
value of inlet flow rate, a reverse peak in inlet pressure which determines
the minimum inlet pressure, and a strong decrease in the riser water temperature from its maximum value to its minimum.
In this work, time-averaged, maximum and minimum values of the inlet
flow rate, water temperatures in different locations of the loop, inlet pressure and averaged period of the flow oscillations were used as the
main SRQs for code validation. The maximum flow rate was considered
as the SRQ of primary interest.
29
Figure 7. Inlet flow rate in the CIRCUS-IV single channel tests.
Figure 8. RELAP5 and TRACE nodalization of the CIRCUS-IV single
channel tests.
0
0.1
0.2
0.3
0.4
0 50 100 150Time (s)
Inle
t Flo
w R
ate
(l/s
)
S-1I-1I-2
30
RELAP5 and TRACE models 4.1.3 In this work RELAP5 Mod 3.3gl and TRACE version 5.0 pack 2 were used for the calculations. Nodalization of the test facility in the code inputs is
shown in Figure 8. The test section part which is from the start of the
heated channel to the end of the riser has finer nodes than other parts of the loop to calculate better two-phase flow. The node sizes were selected
based on code user guidelines and the code input spatial convergence
analysis.
Input calibration and code validation based 4.2
on separate consideration of UIPs
Procedure 4.2.1 Main steps of the procedure are shown in Figure 9. In the input
calibration stage, single-phase steady state test data were used.
Application of the steady state data for calibration is beneficial as it results in smaller uncertainty ranges for calibrated parameters. Test
section provided the most complete set of boundary conditions.
Therefore, first, calibration of uncertain parameters in the input was done
using data from the test section only. Then, input of the entire loop was calibrated. The calibrations followed the same procedure:
i) Initial input calculations (base cases) were run.
ii) Sensitivity calculations were carried out in order to understand the system response to changes of the
uncertain input parameters.
iii) The ranges for inputs were selected considering
importance, dependencies and respective physically meaningful combinations of values of different UIPs.
After the full loop calibration, the most influential UIPs were
identified and selected for the code validation.
In the code validation stage, we used two-phase flow instability tests:
31
i) Instability base cases were calculated for the full loop inputs which UIPs were calibrated based on the steady
state data.
ii) Sensitivity calculations were carried out on a selected set
of the most influential UIPs. iii) Uncertainty in code prediction was determined.
Figure 9. Procedure for manual input calibration and code validation.
32
Summary of results and main findings 4.2.2
Input calibration
Result shows that variation of each uncertain input parameter can lead to
changes in a number of output parameters. It was found that the most influential UIPs are the inlet water temperature and the riser heat losses.
In the base case input several UIPs had to be changed in order to match
different experimental flow parameters. A calibrated input case was
suggested with the following values of UIPs:
- The inlet water temperature had to be increased by 0.8 °C in
comparison to the measured value. This adjustment is within the
range of the measurement uncertainty ±1 °C.
- The heat losses in the riser had to be 0.2 kW.
- The inlet valve loss coefficient of 28 was obtained. In the single-phase case calibration, the discrepancy between RELAP5
and TRACE predictions was marginal.
Code validation
Differences between the experimental values and calculations including
uncertainties were analysed. In general, most of the RELAP5 and TRACE results (flow rate, temperature, pressure, oscillation period) are in
reasonable agreement with the experimental data of two-phase
circulation flow instability. RELAP5 provided more physically reasonable prediction by showing increase in the average, maximum, minimum
values of inlet flow rate and decrease in the oscillation period when the
inlet temperature was increased. TRACE results showed increase in the
average value of inlet flow rate and decrease in the oscillation period, but no significant change in the maximum inlet flow rate.
33
a) Test I-1 b) Test I-2
Figure 10. Inlet flow rate from the calibrated inputs and the experiment.
a) b)
Figure 11. RELAP5 calculated and experimental values of a) inlet
flow rate and b) oscillation period.
Test I-1 at ~93ºC, test I-2 at ~100ºC water temperature at the inlet.
The amplitude of instability was better predicted by RELAP5. The oscillation period was better captured by TRACE (Figure 10). Both codes
significantly overestimated the maximum inlet flow rate (up to 17% for
RELAP5, up to 59% for TRACE). It is found that the predicted system
response quantities (SRQs) are less sensitive to variations of the UIPs in high frequency oscillation regime (test I-2). Taking into account
uncertainties, calculation results overlap experimental values when the
34
SRQs were considered individually (Figure 11). Only for the high frequency oscillations regime, the maximum inlet flow rate was
overestimated (Figure 11a).
The presented approach does not require a large number of simulations and is more effective if the facility can be split into sub-systems. However,
it has certain limitations if the number of calibrated UIPs and SRQs is
large and dependencies between them are complex.
Automated input calibration and code 4.3
validation using genetic algorithm
Methodology 4.3.1 Fitness functions
In the calibration process, GA guides the search process to minimize the fitness function which represented overall quantitative difference between the simulation and experiment (see Eq.1).
∑ (1)
where is fitness function; and are respectively predicted and
experimental SRQs; and are normalization and weighting factors respectively. The function is designed such that the deviation in prediction of all important SRQs can be addressed simultaneously. Simultaneous comparison of multiple predicted and experimental SRQs using weighting factors is also used in the FFTBM (D'Auria, Leonardi, & Pochard, 1994) where the SRQs are transformed from time domain to frequency domain. For accurate transformation a sufficient number of data samples is required. Approach employed in this work does not require fine data sampling. Also different weights can be assigned to different characteristic values of a parameter, i.e., average, maximum and minimum values.
35
The set of parameters was selected to maximize the number of experimental data points and respective constrains for the calibration process. The relative errors in prediction can vary within wide ranges for different SRQs. In this study we chose normalization factors based on acceptable error ranges for nodalization qualification suggested in (Petruzzi & D'Auria, 2008b) for steady state calculations. The weighting factors were varied in order to assess sensitivity of the optimal values of the UIPs to the increase of relative importance of different SRQs in the fitness function. The aim of code validation in this work is to find maximum possible deviations between predicted and experimentally measured SRQs. The difference between experimental and predicted maximum inlet flow rate was used as the fitness function. Two GA calculations were carried out for each instability case to find maximum (positive) and minimum (negative) values of the fitness function. Ranges of uncertain input parameters
The ranges of the UIPs were different for the input calibration and for the code validation. Initially wider ranges were selected for calibration of the
input. Different sets of optimal values of the uncertain input parameters
were obtained from GA search for each matrix of weighting factors. These
values were used in order to define narrower ranges of the parameters for the validation process. Namely minimum and maximum values of the
optimal calibrated parameters were used to define the ranges of the non-
measured parameters (e.g., heat losses, void fraction, loss coefficient). For the measured parameters (e.g., temperatures), the ranges were
defined by maximum and minimum values of (i) the optimal calibrated
values and (ii) experimental values with measurement uncertainty.
Summary of results and main findings 4.3.2 The automated approach was applied for RELAP5 input calibration and
code validation against data of two-phase circulation flow instability.
36
Input calibration
For single-phase test calibration, errors in prediction of SRQs are
generally in acceptable range for prediction of steady state parameters
(Petruzzi & D'Auria, 2008b) taking into account measurement errors. All inputs calibrated with GA provide smaller values of the fitness function
than the calibration using the first manual approach based on separate
consideration of UIPs (see section 4.2.2). For two-phase instability tests calibration, main SRQs and fitness values obtained from the GA method with 6 different weighting factors were
compared with those from the first manual approach and the experiment.
The best inputs calibrated by GA (with weighting factors W1 and W6)
provided slightly better or “as good” results as those obtained with the manual calibration for the fitness value (see Figure 12) and most of the
SRQs. In the weighting matrix W1, all parameters were considered
equally important. In W6, the oscillation period was prioritized. For the I-2 test data, qualitatively incorrect patterns of oscillation (Figure 13b)
were predicted with the inputs which were obtained with weighting
factors other than W1 and W6.
The values of calibrated UIPs obtained in the best GA cases (W1, W6) and
using the first approach generally agree with each other. The largest
differences are between values of heat losses in different sections of the loop.
Obtained results of input calibration indicate:
(i) Importance of selection of the fitness function SRQs and the weighting factors. In general, selection of appropriate fitness function might require understanding of key physics in system behaviour. In case of a lack of knowledge, uniform weighting factors can be used first and then sensitivity of the results to variations in the weighting factors should be addressed.
(ii) Importance of correct prediction of the oscillation period for the natural circulation instability, which can be achieved by assigning relatively large weighting factor for the period in the fitness function.
37
(iii) A need for further improvement in the formulation of the SRQs and respective fitness function, which could detect prediction of wrong oscillation patterns.
a) I-1 b) I-2
Figure 12. Fitness values obtained with different calibrated inputs.
Values of the fitness function were re-calculated using all weighting factors equal to unity (W1).
a) I-1 b) I-2
Figure 13. Inlet flow rate: experimental data and prediction obtained with
different calibrated inputs.
Incorrect oscillation patterns
38
Code validation
Uncertainty ranges of predicted SRQs using the GA method were compared for tests I-1 and I-2 (Figure 14). The experimental and
predicted uncertainty ranges were mostly close to each other and were
completely or partially overlapping in both tests when the SRQs were
considered individually. Predicted ranges for the maximum inlet flow rate and the oscillation period were much larger than the experimental
uncertainty ranges (Figure 14).Table 3 presents validation data obtained
by GA and with the first manual validation approach (see section 4.2.2) on these two SRQs (with the largest predicted uncertainty ranges). The
results suggest that GA provides more comprehensive analysis for
identification of extreme deviations of predicted and measured
parameters.
Table 3. Ranges of predicted SRQs normalized to respective nominal experimental values.
No. SRQ I-1 I-2
GA Manual GA Manual
1 Maximum inlet flow rate ±50% ±50% ±50% 0 to +35%
2 Period of oscillations -23% to +100%
-4% to +50%
-20% to +170%
-17% to +2%
Individual SRQs (Figure 14) are most commonly used for comparison
between experiment and prediction in code validation. However, good
agreement for individual SQRs does not necessarily mean that the code is capable of predicting different SRQs simultaneously. Figure 15 clearly
shows that the maximum inlet flow rate and the oscillation period are not
predicted by the code simultaneously. While general qualitative tendency is captured by the code, there are quantitative deviations. Predicted
system response surface does not overlap with the experimental one
(Figure 15), despite the fact that the projections of the response surfaces
(i.e. predicted and experimental ranges of uncertainty for the individual SRQs) do overlap (Figure 14). It is instructive to note that different
oscillation patterns were predicted within the ranges of uncertain input
parameters for the test I-2 (Figure 15).
39
a)
Tes
t I-
1
b) T
est
I-2
Fig
ure
14.
Up
per
an
d lo
wer
bou
nd
s of
GA
pre
dic
ted
un
cert
ain
ties
nor
mal
ized
to
exp
erim
enta
l bou
nd
s.
All
exp
erim
enta
l un
cert
ain
ty r
ange
s w
ere
nor
mal
ized
into
[–
1;1]
inte
rval
.
40
Figure 15. Maximum inlet flow rate and oscillation period.
Results obtained with calibrated input (GA W6) are shown as “Calib. GA”. Blue and green symbols correspond to the maximum (positive) and
the minimum (negative) difference between experimental and predicted
values of the maximum flow rate respectively used as the GA target.
Presented results clearly demonstrate the importance of simultaneous
comparison of multiple SRQs and multiple test regimes in code
validation. Simultaneous comparison of multiple SRQs clarifies if predicted and experimental system response surfaces overlap with each
other, whereas comparison of multiple test regimes clarifies if the code
and experiment show the same system response tendencies to variation of the initial and boundary conditions, i.e. that important physical
phenomena are qualitatively captured by the code models.
The GA method is more computationally efficient than random sampling in identifying maximum deviation of code prediction results from the
experimental data (Figure 15). Random sampling, however, provides data
Saw-shape oscillations regime
Transitional regime
Saw-shape oscillation close to steady state
I-2 I-1
Calc. Random Calc. GA Exp. Calib. GA
41
which can be directly used for assessment of probabilistic characteristics and overall behaviour of the system response surface in a multi-
dimensional parameter space which is beyond the scope of this work.
Another important advantage of GA based approach is that it reduces the
effect of user judgment on the process of input calibration and code
validation, especially in cases with large number of UIPs and SRQs of
interest. Provided that initial ranges for input parameter calibration are selected with sufficient conservatism, the rest of the process is more or
less automated and can be guided with relatively simple and universal
best practice recommendations.
Codes prediction of flow regimes 4.4
RELAP5 and TRACE capabilities in prediction of instantaneous flow
regimes during the instability were examined. The effect of modification of flow regime transition boundaries on code predictions of other
thermal-hydraulic parameters was analysed.
Prediction with the original flow regime map
There are significant discrepancies between recorded video and predicted flow regimes and regime transition timing (Figure 16). Bubbly, slug and
periodically changing churn and annular flow regimes were observed in
test I-2 during each cycle of flashing. RELAP5 predicted only bubbly and
slug flow regimes. No changes in the flow regime were predicted by TRACE during the transient. It is instructive to note that TRACE uses
bubbly-slug as a combined flow regime, and both codes consider single
phase flow as a part of the bubbly flow regime.
It is remarkable that void fraction predicted by both codes qualitatively
follows transient behaviour of experimentally observed flow regimes
(Figure 16). RELAP5 predicted slightly lower void fraction in the riser upon the flashing in comparison to TRACE.
42
Figure 16. Test I-2 - Riser flow regime (FR) and void fraction (VF) in the
section for visual observation.
One of the reasons for the incorrect identification of the bubbly and slug
flow regimes is the small diameter pipe flow regime transition model in
RELAP5. The diameter of a CIRCUS-IV riser is 0.024 m, thus the code
identified the bubbly-to-slug flow regime transition boundary BS at
0.001 in the test condition (instead of 0.25 for pipes with diameter larger
than 0.055 m). This boundary resulted in the predicted moment of
transition from bubbly to slug flow occurred much earlier (~3-5 s), while the reverse transition from slug to bubbly flow happened later (~1-2 s)
than those events in the experiments (Figure 16). Therefore, the
preclusion of bubbly flow in small diameter pipe in the code does not correspond to the experimental observations of the actual flow regimes.
Absence of annular flow regime in code prediction can be due to the slug-
to-annular flow regime transition boundary SA. For the CIRCUS-IV test
conditions, SA is set at its maximum value of 0.9, which is apparently too
high. There is no churn flow regime for vertical flow models in both
RELAP5 and TRACE. Thus, it is impossible for the codes to identify
43
periodic transitions between annular and churn flow regimes in test I-2 (Figure 16) and short appearance of the annular flow regime in test I-1.
RELAP5 prediction with modified flow regime maps
There are practical limitations for flow regime map modification in the
codes. The work requires source code which is not always available. The
modification often result in code crashes and require good knowledge about implementation of codes numerical schemes. For these reason in
this work only bubbly-to-slug and slug-to-annular flow regime transition
boundaries (BS and SA) in RELAP5 were modified.
It is found that a better match to the experimental flow regime was
obtained, while prediction quality of the other thermal-hydraulic
parameters deteriorated.
Figure 17. Test I-2 - Flow regime in the riser observation section:
experimental data and predicted by RELAP5 using different flow regime
transition boundaries.
(BS – bubbly-slug; SA – slug-annular)
With BS = 0.25 and SA = 0.55, predicted flow regimes became
qualitatively closer to the experimental ones (Figure 17). However, results
of flow prediction with modified BS and SA gave worse oscillation period
44
and inlet flow rate (Figure 18). When increasing only BS from the
original value in order to delay the transition from bubbly to slug regime
according to experimental observation, the discrepancy between
predicted and experimental maximum amplitude and frequency of the instability increased, though characteristic shape of the oscillation was
preserved. When changing only SA, the maximum inlet flow rate slightly
decreased, significant distortion appeared in the shape of oscillation.
Changing BS and SA simultaneously resulted in both increase in the
maximum inlet flow rate and distortion in the shape of oscillation.
Figure 18. Test I.2 - Inlet flow rate: experimental data and predicted by
RELAP5 using different flow regime transition boundaries.
(BS – bubbly-slug; SA – slug-annular)
The codes were not originally designed to calculate either flow in small
pipes or dynamics of two-phase circulation flow instability. Given the differences between experimental and predicted flow regimes, the quality
of prediction of thermal hydraulics phenomena by RELAP5 and TRACE
is quite remarkable. In theory, a STH code must identify correctly two-
phase flow regime in order to select proper correlations for mass, energy and momentum transfer. The results suggest that the codes do not need
to predict the flow regime correctly in order to obtain reasonably good
0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50Time (s)
Flo
w R
ate
(l/s
)
Experiment RELAP5R5 - BS 0.25 R5 - SA 0.55R5 - BS 0.25, SA 0.55
45
agreement with experimental data. This can be explained if flow regime misidentification is compensated by the other models and closures.
The obtained results suggest that thermal-hydraulic parameters are sensitive to the flow regime identification by the code. Modification of the
steady state flow regime map in RELAP5 and possibly also in other STH
codes, in order to account flow relaxation in transient phenomena, would
require also corrections in correlations for heat, mass and momentum exchange between the phases.
46
47
PREDICTION OF IN-VESSEL CORIUM 5
DEBRIS RELOCATION
In this chapter, main results on prediction of corium debris relocation
using MELCOR and the development of surrogate model are discussed.
For more details, refer to Appendices D, E or Phung et al. (2016b), (2017).
Nordic BWRs 5.1
Accident scenario 5.1.1
A considered severe accident scenario is initiated at full power (3900
MWt) with a loss of offsite and onsite power supply, followed by a
delayed power recovery. The station blackout (SBO) scenarios are chosen for analysis in this work as the main contributors to the Nordic BWRs
(Kudinov, et al., 2014c) core damage frequency. The auxiliary feed water
and containment cooling systems are assumed to remain unavailable
during the whole transient. Timing of activation of the automatic depressurization system (ADS), the emergency core cooling system
(ECCS), and capacity of the ECCS were considered as uncertain
parameters of the scenario. These parameters are sampled in the analysis within the following ranges:
(i) ADS activation time tADS: 0 - 10000 s.
(ii) ECCS activation time tECCS: 0 - 10000 s.
(iii) ECCS capacity AECCS: 0 - 1.0 of the design capacity.
48
Recovery timing of ADS and ECCS are not completely independent from each other. The ECCS requires depressurization, thus timing of EECS
activation can be larger or equal to the activation of ADS (tECCS ≥ tADS).
Characteristics of in-vessel core relocation 5.1.2
For the MELCOR calculations, the following characteristics of debris bed in the lower plenum were analysed:
- Total mass of debris bed and its compositions (UO2, Zr, stainless steel, ZrO2, stainless steel oxide, control rod poison).
- Ratio of oxide to metal debris masses.
- Onset of large core relocation.
- Mass averaged temperature of particulate debris.
- Mass averaged thermal conductivity of the debris material.
- Mass of UO2 and mass averaged thermal conductivity in axial
layers of debris bed.
The current surrogate model predicts the main characteristics:
- Total mass of debris bed at the end of the transients.
- Ratio of oxide to metal debris masses at the end of the transients.
- Onset of large core relocation.
MELCOR model 5.1.3
The MELCOR code version 1.8.6 was used in this work. The reactor core
region was nodalized with 5 radial rings and 8 axial levels. The lower
plenum had 6 radial rings and 5 axial levels. The core and lower plenum are separated by the core support plate represented by 6 radial rings and
1 axial level.
Reactor vessel breach condition in the MELCOR input was disabled, thus
all relocated corium debris stayed in the lower plenum until the end of
the transients. This approach was used to provide input data for
49
prediction of vessel failure with a separate model. The calculated
transient time is from 0 (start of the SBO) to 40000 s. The focus was on
the scenarios with early core relocation. Time step refinement was
applied if MELCOR calculations crash before reaching the end of the
transient time.
Summary of MELCOR results 5.2
In this section, results obtained with different samplings are compared,
different domains of scenarios are identified, and characteristics of
relocated debris bed are discussed.
Sampling and identification of scenario domains
Table 4. Number of calculated scenarios with different mass of debris bed.
Set Target
Total number
of scenarios
Total mass of debris bed (ton)
0 to 20 20 to 100 >100
I Random sampling 299 23% 1% 76%
II Grid sampling 174 21% 2% 77%
III GA: 70 tons of total mass of
debris bed 336
46% 8% 46%
IV GA: Maximum UO2 mass at
the bottom of lower plenum 241
8% 2% 90%
Total 1050 27% 4% 69%
Results obtained with random and grid sampling methods (calculation
set I and II) and genetic algorithm with different fitness functions
(calculation set III and IV) are compared (see Table 4). About ~76% of
the randomly or grid sampled scenarios resulted in large mass of
relocated debris (>100 tons), ~23% of the scenarios lead to no or small
mass of relocated debris bed (<20 tons), and only ~1% with intermediate
mass (20 -100 tons) of debris bed (Table 4). Most of scenarios sampled
50
by GA also resulted in relocated debris mass that was either above 100 tons or below 2o tons (Table 4). In set III (target: 70 tons) only 8% cases
resulted in intermediate mass of debris. In set IV (target: maximum UO2
debris mass) 90% of cases result in large mass of debris. This suggests that scenarios with large mass of debris also more likely to have higher
concentration of UO2 near the vessel wall.
The result shows that random or grid sampling can provide good general
information on behaviour of the system, while GA is more economical for
searching targeted scenario domains. To identify different scenario domains, all calculated cases were analysed together (Figure 19). The result suggests that:
(i) The domains with small (blue color) and large (red color) mass
of relocated debris bed are considerably larger than the
domain with the intermediate mass (green color). (ii) The domains that contain groups of scenarios with different
masses of relocated debris bed have no clear boundaries and
partially overlap with each other. The size of these transition regions becomes smaller when ECCS capacity is increasing. In
the transition regions, small changes in the input can result in
large changes in the mass of relocated debris bed.
(iii) Massive relocation can be avoided if the ADS is activated before 5000 s and the ECCS is activated within ~1000 s after
the ADS. The maximum time delay (~5000 sec) for activation
of the ADS that can still avoid large mass of relocated debris does not depend on capacity of the recovered ECCS if it is
larger than 25%.
(iv) The time of onset of massive core relocation, when mass of
debris relocated to the lower plenum exceeds 20 tons, is ~7000 s in most cases. Early ADS recovery (~1500 s) often
results in earlier large core relocation. Large core relocation
can be delayed if the ADS is activated before 6000 s and the ECCS within ~3000 s after the ADS.
51
Figure 19. Total mass of debris bed in the lower plenum as a function of
scenario parameters (tADS, tECCS, AECCS).
Note that AECCS=0 for tADS>7200s.
Transition region 0 - 20 20 - 100 >100 tons debris bed mass
52
Debris bed characteristics
Total mass of relocated debris, its composition and thermal properties were analysed. In scenarios with small mass of relocated debris (blue
color), the debris beds are composed mostly of stainless steel (SS), Zr,
and have little UO2, ZrO2 (see Figure 20). It is because the core meltdown and relocation start with Zr cladding and SS structures. In
scenarios with large mass of debris bed (yellow, orange and brown
colors), there are large sudden increases in mass of relocated UO2 (Figure
20b) due to the collapse of core support plate rings that leads to massive relocation of debris. Mass of SS debris increases gradually with time.
Massive relocation usually starts earlier in scenarios with large total mass
of relocated debris than in scenarios with intermediate mass (green color) (Figure 20a).
The number of scenarios with mass of relocated debris larger than 100
tons increases from ~2% to ~58% between 5000 to 10000 s after scram (black and blue lines) (Figure 22a). The total relocated mass of debris is
below 20 tons in ~67% of scenarios and larger than 70 tons in ~30% of
scenarios (red line) at 7000 s after scram. The fraction of scenarios with relocated core mass less than 100 tones slowly decreases after 15000 s
while the number of scenarios with more than 200 tons increases from
~28% to ~59% between 15000 and 40000 seconds (Figure 22a). It is
instructive to note that the failure of the vessel can be expected between ~1.5 and ~5 hours after relocation of more than 100 tons of debris to the
lower head (Villanueva, Tran, & Kudinov, 2012), (Goronovski,
Villanueva, Kudinov, & Tran, 2015), (Goronovski, Villanueva, Tran, & Kudinov, 2013).
Mass fractions of the oxide and metal components can significantly affect
mass averaged thermal conductivity of the debris bed material. Ratio of oxide to metal debris masses (Figure 21) ranges between ~1.2 and 2.2 for
most of the scenarios with large debris bed mass. It is lower for debris
beds with intermediate mass (~1-1.7) and for small debris beds (~0-0.7).
53
a) b)
Figure 20. Total mass of debris bed in the lower plenum (a) and mass of
UO2 (b).
Figure 21. Ratio of oxide to metal debris masses in the lower plenum.
The ratio of oxide mass to the mass of metal in the debris bed can be less
than 1.2 in ~22-36% of the cases after 10000 seconds (Figure 22b). The ratio is less than 1.5 in ~50% of the cases. The number of scenarios with
the oxide to metal mass ratio larger than 2 is decreasing with time from
38% at 10000 s to ~3% at 40000 sec.
0 - 20 20 - 100 100 - 200 200 - 250 >250 tons debris bed mass
0 - 20 20 - 100 100 - 200 200 - 250 >250 tons debris bed mass
54
a) b)
Figure 22. Cumulative distribution functions of total mass of debris bed (a) and ratio of oxide to metal debris masses (b) in the lower plenum at
different time moments after scram.
For scenarios with large mass of debris bed, the average temperature of particulate debris can stabilize at ~800-2000 K or increase up to 3000 K.
For scenarios with intermediate debris bed mass, the average
temperature stabilizes at ~400-800 K. Thermal conductivity of large
debris beds is found in the range of ~7-20 W/(m*K), while the value for intermediate mass of debris is ~10-15 W/(m*K), for small debris beds is
~12-20 W/(m*K). Mass averaged thermal conductivity of debris material
in the lower plenum ranges in ~7-20 W/(m*K) in 90% of the scenarios, and in ~10-17 W/(m*K) in 80% of the scenarios.
The mass of UO2 in each horizontal layer of debris bed behaves non-
monotonically with height and the smallest amount of UO2 is observed in
the bottommost layer (Figure 23). The thermal conductivity of debris
layers is found also non-monotonic with respect to the vertical coordinate. The bottom layer in most scenarios has high effective thermal
conductivity ~15-25 W/(m*K). This is because this layer consists mostly
of Zr and SS. Small debris beds also often have very small concentration
of UO2 and high effective thermal conductivity. The lower concentration of UO2 and thus lower decay heat provides smaller local temperatures in
the region with the vessel penetrations. However, higher conductivity of
the debris increases heat flux to the vessel wall.
55
Figure 23. Cumulative distribution function of mass of UO2 debris in
different axial layers in the lower plenum.
Cliff-edge effect
Most of the sampled scenarios resulted in total relocated debris mass that
was either above 100 tons or less than 20 tons. There are transition
regions in which small changes in the input can result in large changes in
the mass of relocated debris bed (cliff-edge effect). Detailed analysis of the cases suggests that this is mainly due to the interplay between
(i) failure criteria for fuel and core support plate structures and (ii) finite
core nodalization. The failure is triggered when temperature or mechanical load of the component exceeds the threshold (US NRC, et al.,
2005). For instance, a core ring fails when cladding temperature of the
ring reaches a threshold. When a bottom core ring fails, all rings above
fail. When a core support plate ring (or its supporting structures) fails due to stress, all particulate debris in the rings on top of it and some
56
debris in adjacent rings relocate to the lower plenum. Thus it is expected that the total mass of relocated debris will change in a stepwise manner
with the steps determined by the masses of the fuel in each core ring.
a) b)
Figure 24. Total debris mass in the lower plenum (a), mass of intact UO2
in the core (b).
Figure 25. Maximum cladding temperature in the core.
(Failure threshold for the cladding is at 2227 oC (2500 K).)
Results of sensitivity calculations show that small changes in uncertain
input parameters can affect drastically the outcomes of core relocation.
Formation and relocation of Zr, ZrO2
particulate debris
core ring 2
Complete failure of core ring 1
First fuel failure
Beginning of core support plate failure
57
Here for the demonstration, two scenarios are considered: Small-db and Large-db. The scenarios have ~150 s difference in ADS, ECCS recovery
timing and the same ECCS capacity at 0.6. Small-db scenario has ADS
and ECCS recovery timing at 4950 s, 5170 s respectively after scram. Only ~1/8 of the core (mostly on top) degraded and relocated (Figure 24b); the
core support plate did not fail; the scenario resulted in 7.5 tons of total
debris bed in the lower plenum (Figure 24a). Large-db scenario has ADS
and ECCS recovery timing at 5100 s, 5320 s respectively. Complete failure happened to core ring 1 (the middle ring) and 2 (Figure 25); only
1/6 of the core remained intact (Figure 24b). Large mass of debris heated
up and later failed the core support plate, which created 225 tons of total relocated debris to the lower plenum (Figure 24a).
A preliminary parametric study was carried out, including calculations
with finer core nodalization (9 core rings) for a number of selected scenarios. It is found that the nodalization may affect the transient
characteristics of core relocation, e.g., slightly smoothen the cliff-edge
effect. However, the effect on the masses of debris obtained at the end of the transient is not so dramatic.
Surrogate model using artificial neural 5.3
networks
Methodology 5.3.1
The development of core relocation SM included the following main steps.
1) Selecting inputs and outputs of the SM
In this work, inputs of core relocation SM are the uncertain parameters
of accident scenario describing the plant damage state: ADS activation time (tADS), ECCS activation time (tECCS), and ECCS capacity (AECCS).
Outputs of the SM are determined by the inputs necessary for debris
58
formation, re-melting and vessel failure models. Selected outputs are main characteristics of debris bed in the reactor lower plenum: total
debris mass, ratio of oxide to metal debris masses, and onset (timing) of
large relocation. The outputs were calculated at the end of the transient (40000 s).
Figure 26. Total mass of debris bed as a function of scenario parameters -
MELCOR result.
(kg)
59
2) Analyzing the database of MELCOR solutions The sampling of scenarios was biased in the obtained database towards
the diagonal of the input parameter space (tADS = tECCS), while coverage of some other regions was coarser. It is found in (Phung, et al., 2016b) that:
(i) most of the scenarios result in either relatively small (< 20 tons) or
large (>100 tons) mass of relocated debris at the end of the transient (see Figure 26), (ii) the debris mass is sensitive to small variation of the
scenario parameters in the transition regions that separate the domains
with large and small masses of relocated debris (Figure 26), (iii)
characteristics of the debris bed vary non-linearly with the scenario parameters and their ranges depend on the total debris mass.
3) Designing the SM using neural networks (Figure 27)
The full model (FM) response had significant noise (Figure 26). At the
same time there were clear general trends visible in the database. When
single ANN was used, the SM was trying to approximate the whole data
at once. That leads to appearance of the noise in the SM response. In order to reduce the artificial noise in the SM response, an alternative
approach based on classification of scenarios was used. I.e. scenarios in
the FM database were classified (grouped) according to the ranges of the output (number of groups N = 2, 3, 4). Separate ANNs were trained using
data from the respective groups of scenarios. An additional ANN was
implemented for classification, i.e. to select which ANN should be used
for prediction of the output given the input. In order to decrease the effect of potential scenario misclassification (see section 5.3.2), scenario
classification in the 4-group SM was weighted based on cases in the
neighbourhood. Specifically, response for additional 6 cases located in the vertices of a cube in the vicinity of the central point (tADS; tECCS; AECCS)
was computed. The output was then estimated as a weighted average of
all cases with higher weighting factor for the central point.
60
Figure 27. Flow diagram of ANNs training and SM prediction of in-vessel core relocation.
4) Training and selecting the best networks (Figure 27)
The training, validation and testing of ANNs were carried out and the best classification and prediction networks were selected for each SM.
For the classification network the process used all scenarios in the
database, while for the prediction networks only scenarios from the respective groups were used. In order to reduce the effect of biased
sampling in the database, the process was carried out with different
weights for scenarios in regions which were differently (coarsely or
densely) sampled.
Classification ANN
Database of
MELCOR Solutions
Group 1
ANNs Training, Validation and Testing
SM Prediction
Prediction ANNs
Group 2
Group n
SM Inputs, Outputs
SM Inputs, Outputs
Classification ANN
Group 1
Prediction ANNs
Group 2
Group n
SM Outputs
SM Inputs
Weighted Classification
61
Networks with different number of nodes (from 1 to 80) were trained, validated and tested; and the process was randomly initiated 8 times. The
best (one classification and N prediction) networks were selected based
on the lowest mean squared errors (MSEs) of the testing data.
5) Validating the SM
Different criteria can be introduced to evaluate quality of a SM, e.g.: (i) Small mean square error (MSE) in approximation of full
model database.
(ii) Good approximation of the cumulative distribution function (CDF) of the full model response.
The first requirement is a standard criterion for a goodness of an ANN
approximation. The second requirement is important if the SM is
required to reproduce percentiles of different scenarios (grouped according to different ranges of the response) as in the FM database.
Summary of results and main findings 5.3.2
Total debris mass is used in this section for demonstration. Described
trends are quite similar for the ratio of oxide and metal debris masses and for the onset of large debris relocation.
Accuracy of the SM
For correctly classified scenarios, accuracy of the prediction networks
improves when the number of scenario groups increases (Figure 28a). However, MSE of the multi-group SM tends to increase (Figure 28b).
With the increasing number of scenario groups in the SM, the regression
value (R) decreases (Figure 29). The majority of scenarios get closer to the regression diagonal line (i.e., better predicted), while a small number
of outlier scenarios deviate further from the line (Figure 29).
62
a) Individual MSE for separate networks
b) MSE for surrogate models
Figure 28. Normalized mean squared error of results of prediction ANNs and SMs - Total mass of debris bed. MSE of prediction networks are in
case the scenarios were correctly classified. Errors are from the SM
testing process.
The outliers, which lead to deterioration in MSE and R, appear due to scenario misclassification. There are likely two main reasons that can lead to scenario misclassification: (i) chaotic behavior of the MELCOR response, especially in transition regions and on the diagonal plane (e.g. see Figure 26), and (ii) small number of scenarios in some groups (e.g. in
63
group 2 with total mass of debris between 20-100 ton). The chaotic behavior and respective noise in the data can have physical and/or numerical origin. Noise due to physical instabilities can appear in the transition regions due to the cliff edge effect. Numerical noise may come from spatial, temporal sources such as system nodalization, code calculation time step when modeling systems with physical thresholds, e.g. for failure criteria for fuel or core support plate structures in the code (US NRC, et al., 2005).
Most of the misclassified scenarios locate close to the boundaries
between domains of different scenario groups (transition regions). In
order to decrease the effect of scenario misclassification, weighted classification was used for the 4-group SM. The MSE and R values get
better than that of the original 4- group SM (Figure 28b and Figure 29).
However, while error from the misclassification is reduced, error in prediction of correctly classified scenarios in the vicinity of the domain
boundaries increases.
Application of genetic algorithm resulted in biased sampling with larger density of cases in the vicinity of the diagonal plane tADS = tECCS. In order
to address possible effect of the biased sampling, different weights for
scenarios in different regions were used for training of the networks in SMs with 1 and 4 groups. The result shows that accuracy of the SM
improves when the weight of non-diagonal scenarios is increased.
Removing scenarios in densely sampled region (on the diagonal plane)
reduces the accuracy. The SMs discussed in the next section were obtained using the database with doubling of the weights for non-
diagonal scenarios.
64
a1) b1) c1)
SM – 1G
a2) b2) c2)
SM – 2G
a3) b3) c3)
SM – 3G
65
a4) b4) c4)
SM – 4G
a5) b5) c5)
SM – 4G, weighted classification
b6)
Interpolation model
Figure 29. SM prediction (output) compared to MELCOR solutions
(target) - Total mass of debris bed. a) Training set, b) testing set, c) random data set* (*: excluding scenarios on the diagonal plane).
66
Predicted CDFs and response surfaces
Figure 30. Cumulative distribution function for total mass of debris bed.
The SM predictions using ANNs are compared to the MELCOR database
and results of the interpolation model. Cumulative distribution functions (CDFs) get closer to the MELCOR random data set (red color) when the
number of scenario groups increases (Figure 30). The single-group SM
(blue color) provides worst CDFs. With 2 groups (green color), CDFs considerably improved. The main reasons are: (i) there is a narrow
67
transition region between domains where most of scenarios have total mass of debris bed below and above 20 tons respectively, (ii) there are
scenarios that can be very close to each other but have significantly
different values of response. The single-group SM tries to approximate the whole FM database with a smooth response surface. Such
interpolation introduces intermediate values of the response, which are
not present in the original database, especially in the transition region.
Multi-group ANNs can resolve the sharp changes and “filter-out” the local noise in the response function. The 4-group SM with weighted
classification (magenta color) and the interpolation model (yellow color)
produce CDFs worse than the 3 or 4-group SMs, especially for the small total mass of debris bed (small ratio of oxide to metal debris masses and
small onset of large debris relocation). Weighted classification reduces
the error of misclassification, however, the misclassification issue could
not be resolved completely due to the noise in the original database. The 4-group SM (black color) provides the best CDFs.
Figure 31. Total mass of debris bed predicted by the SMs using different
number of scenario groups, at full capacity of ECCS (AECCS = 1).
a) 1-group SM b) 2-group SM c) 3-group SM
d) 4-group SM e) 4-group SM, weighted classification f) Interpolation Model
(kg)
68
a)
b)
Figure 32. Total mass of debris bed as a function of scenario parameters
predicted by the SM using (a) 4 scenario groups, (b) 4 groups with
weighted classification (unit: kg).
69
The response surface prediction by the single-group SM is clearly affected by the noise in the FM database (Figure 31a and Figure 26). SMs with larger number of groups effectively filter out the noise and provide smooth response surfaces in each subdomain separated by relatively narrow transition regions (Figure 31b, c, d and Figure 26). The 4-group SM with weighted classification and the interpolation model provide smoother transition between different sub-domains (Figure 31e, f).
Figure 32 shows response surfaces of the debris bed characteristics predicted by the SMs with 4 groups. The response seems physically reasonable and agrees in general with the trends in MELCOR results (Figure 26). The SMs, however, had difficulties in classifying and thus predicting correctly some local scenarios, especially in the transition regions.
The prediction of the ratio of oxide to metal debris masses and the onset
of large debris relocation agrees in general with that in the FM database.
In summary, selection of the SM takes into account:
There is no SM which is simultaneously best for all criteria (MSE, R, CDFs).
The SMs based on ANNs provide better overall results than the interpolation model. Although MSE for the interpolation model
can be slightly better than that from the 4-group ANNs.
Single-group SM has no scenario misclassification and provides a smaller MSE value. However, fitting of smooth response
surface to the noisy data results in introduction of intermediate
values of the response (not present in the original database) and respective failure to reproduce the CDFs of the original
data.
If the SM uses many groups, it reproduces better the CDFs and the response surfaces are less affected by the noise. However,
misclassification results in increased number of outliers and
larger MSE.
70
If the SM uses many groups and weighted classification based on scenarios in neighborhood, error from misclassification is
reduced and overall performance of the SM can be improved. However, the effect of misclassification could not be resolved
completely.
The optimum SM should be selected based on the purpose of the application. I.e. if it is more important to reduce the
number of outliers or if it is more important to reproduce the
CFD of the response.
71
CONCLUSIONS 6
A non-automated procedure based on “manual” separate consideration of
uncertain input parameters (UIPs) and an automated approach using genetic algorithm (GA) have been developed and applied for input
calibration and code validation against unsteady flows (two-phase
circulation flow instability). The “manual” procedure can be applied if the
facility can be split into subsystems and respective UIPs can be considered separately. Such divide-and-conquer strategy helps to identify
physically meaningful combination of calibrated values of the UIPs. The
automated approach using GA was developed for the case when the number of calibrated input parameters and SRQs is large and
dependencies between them are complex. The approach reduces the user
effect on the outcomes of input calibration and code validation and has
increased computational efficiency in comparison to random sampling.
RELAP5 and TRACE were validated against CIRCUS-IV single channel
experiments. Calculation results overlap experimental values when the SRQs were considered individually. However, it was not possible to
predict simultaneously the oscillation period and maximum inlet flow
rate. This means that predicted and experimental system response
surfaces do not overlap.
Both codes could not identify correctly flow regimes in the transients.
One of the reasons is the steady state flow regime map, particularly the small diameter pipe model in RELAP5 and the combined bubbly-slug
flow regime in TRACE.
72
Flow regime transition boundaries in RELAP5 were modified. A better match to the experimental flow regimes was obtained, however
prediction quality of the other flow parameters deteriorated.
Reasonable prediction of thermal-hydraulic parameters while
misidentifying the flow regime is remarkable. It is necessary to carry out
further investigations on effect of the flow regime maps on STH codes’
prediction of two-phase flow transients. This requires exclusively designed separate effect tests (Dinh, 2013). Modification of the steady
state flow regime maps in the codes, in order to account flow relaxation
in transient phenomena, would need also corrections in respective correlations for heat, mass and momentum exchange between liquid and
vapour phases.
In summary, the overall prediction quality of RELAP5 and TRACE is quite remarkable, considering that calculations rely on a steady state map
for transition between flow regimes. Uncertainty propagation suggests
that codes can predict reasonably well system response quantities (SRQs) when SRQs are compared separately. However, the codes might fail to
capture SRQs simultaneously. Conclusion on the validity of the STH
codes in predicting two-phase flow instability is therefore contingent on
the list of SRQs and acceptable level of uncertainty for specific application. Further analysis and possibly code modifications may be
necessary to improve quality of the code prediction.
Station blackout scenario with delayed power recovery in a Nordic BWR
was considered. MELCOR model of the Nordic BWR was developed.
Genetic algorithm (GA), random and grid sampling methods were used
in order to characterize the influence of recovery timings and capacity of ADS and ECCS on debris bed properties in the lower plenum.
A parametric study was carried out. It was found that plant configuration, reactor core region nodalization and code calculation time
step may affect the characteristics of core relocation. As a result,
numerical convergence with respect to the time step could not be
73
demonstrated. However, certain tendencies in response functions can be clearly identified despite the apparent noise in the output.
Most of the scenarios are found with either small (< 20 tons) or large (> 100 tons) mass of relocated debris bed. Large relocation of core debris
can be prevented if ADS is activated before 5000 s after scram and ECCS
is activated with at least 25% of the design capacity within 1000 s after
ADS activation. Results are sensitive to small variation of the input parameters in the transition region that separates the domains with large
and small masses of relocated debris bed. The onset of large debris
relocation is around 7000 s in most of the scenarios.
Range and distribution of the debris bed characteristics were calculated.
The bottom most layer of the bed, which is in direct contact with the
vessel wall and penetrations, often has a relatively small fraction of UO2 and large fraction of metal. This results in very small decay heat and high
mass averaged thermal conductivity of the debris material that can affect
vessel failure modes.
A surrogate model (SM) has been developed using artificial neural
networks (ANNs). The model provides computationally efficient
prediction of main characteristics of in-vessel debris bed. The effect of the noisy data in the full model database was addressed by introducing
scenario classification (grouping) according to the ranges of the output
parameters. Several ANNs were trained for each group of scenarios. Weighting between predictions of different ANNs was also used.
A single ANN provides smaller MSE but larger deviation with respect to
the CDF of the response. This is because single ANN interpolates sharp local changes and discontinuities and tries to approximate the noise in
the data. SMs using multiple ANNs with/without weighting between
different groups effectively filter out the noise and provide a better prediction of the output CDF, but increase the MSE value (compared to a
single ANN) due to a larger number of misclassified scenarios (outliers).
There are likely two main reasons for the scenario misclassification:
74
noisy data of MELCOR solutions and small number of scenarios in some groups. For network training using a biased database, accuracy of a SM
improves when increasing the weight for scenarios in sparsely sampled
regions.
The work on core degradation and relocation analysis contributed to the
development of the risk assessment framework for severe accident in
Nordic BWRs. The SM is necessary for extensive sensitivity, uncertainty, failure domain and failure probability analysis in the framework.
Capability of the SM can be extended to prediction of debris bed
characteristics at different time moments. Further developments including approaches to treatment of the noise in the full model database
can enhance prediction of the SM, especially for scenarios in the
transition regions.
In conclusion, advanced machine learning algorithms (genetic algorithm
and artificial neural network) are instrumental in uncertainty
quantification. Approaches to input calibration, code validation and surrogate modelling have been developed and applied to analysis of
(i) two-phase circulation flow instability and (ii) in-vessel corium debris
relocation. The study has provided insights into (i) physics of different
important phenomena relevant to reactor safety and (ii) capability of the system codes in predicting those phenomena.
75
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