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

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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.

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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

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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.

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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

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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.

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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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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 

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  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.

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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 

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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 

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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 

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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 

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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

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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.

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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.

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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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