Application of a system thermal-hydraulics code to ...1209171/...simulation methodology for analysis...
Transcript of Application of a system thermal-hydraulics code to ...1209171/...simulation methodology for analysis...
Application of a system
thermal-hydraulics code to
development of validation
process for coupled STH-CFD
codes
KASPAR KÖÖP
Doctoral thesis No. 10, June 2018 KTH Royal Institute of Technology Engineering Sciences Department of Physics Stockholm, Sweden
AlbaNova University Center Roslagstullsbacken 21 TRITA-SCI-FOU 2018:10 10691 Stockholm ISBN 978-91-7729-727-7 Sweden Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie doktorexamen i fysik den 7 juni 2018, FB52, AlbaNova universitetscentrum, Stockholm. © Kaspar Kööp, June 2018 Tryck: Universitetsservice US AB
I
ABSTRACT
Generation IV reactors are designed to provide sustainable energy generation,
minimize waste production and excel in safety. Due to lack of operational
experience, ever evolving design and stringent safety requirements, these novel
reactors have to rely heavily on simulations.
Best estimate one-dimensional (1D) system thermal-hydraulics (STH) codes,
originally intended for simulating water-cooled reactor systems with high coolant
mass flow rates, are unable to capture complex three-dimensional (3D) phenomena
in liquid metal cooled pool-type reactors. Computational fluid dynamics (CFD)
codes are capable of resolving the 3D effects, however applying these methods with
high resolution for the whole primary system results in prohibiting computational
cost.
At the same time, there are system components where flow can, with reasonable
accuracy, be approximated with 1D models (e.g. core channels, some heat
exchangers, etc.). One of the proposed solutions in order to achieve adequate
accuracy and affordable computational efficiency in modelling of a Generation IV
reactor is to divide the primary system into 1D and 3D regions and apply coupled
STH and CFD codes on the respective sub-domains.
Successful validation is a prerequisite for application of both, standalone and
coupled STH and CFD codes in design and safety analysis of Generation IV systems.
In this work we develop and apply different aspects of code validation methodology
with an emphasis on (i) STH code analysis in support of validation experiment
design (facility and test conditions), (ii) calibration of uncertain code input
parameters and validation of standalone STH code, (iii) development of an approach
to couple STH and CFD codes.
A considerable part of the thesis work is related to the development of a loop-type,
3 leg, liquid metal experimental facility TALL-3D for code validation. Particular
focus was on identification of test conditions featuring complex feedbacks between
1D-3D phenomena, which can be challenging for the codes. Standalone STH code
(RELAP5) was validated against experimental data. The domain of natural
circulation instabilities in TALL-3D operation parameters was discovered using a
validated STH code and global optimum search algorithms. Then existence of
growing natural circulation oscillations was experimentally confirmed. An
international benchmark was initiated in the framework of EU SESAME project
based on the obtained experimental data.
II
Simulations were performed to define dimensions and location of a new test section
for coolant solidification experiments that would also enhance possibilities for
studying natural circulation instabilities in the future tests.
An approach to automated input calibration and code validation is developed in
order to minimize possible “user effect” in case of multiple uncertain input
parameters (UIPs) and system response quantities (SRQs). These methods were
applied extensively in the development of RELAP5 input models and identification
of the natural circulation instability regions.
Domain overlapping approach to coupling of RELAP5 and Star-CCM+ codes was
proposed and resulted in considerable improvement of the predictive capabilities in
comparison to standalone RELAP5.
III
SAMMANFATTNING
Generation IV-reaktorer är utformade för att möjliggörahållbar energiproduktion,
minimera avfallsproduktion och utmärka sig i säkerhet. På grund av brist på
operativ erfarenhet, ständig utvecklaning av design och höga säkerhetskrav behöver
framtagning av dessa tekniska lösningar baseras på beräkningar och simulationer.
Best estimate termohydraulikkoder för endimensionella (1D) system, ursprungligen
avsedda för att simulera vattenkylda reaktorsystem med höga
kylvätskemassaflöden, kan inte beskriva komplexa tredimensionella (3D) fenomen
i flytande metallkylda bassäng-typ reaktorer.Beräkningsströmningsdynamikkoder
(CFD) kan hantera 3D-effekterna, men tillämpning av dessa metoder skulle
innebära beräkningar med hög upplösning för hela primärsystemet som i sin tur
resulterar i ogynnsamma beräkningskostnader.
Samtidigt finns det systemkomponenter där flöde med rimlig noggrannhet kan
approximeras med 1D-modeller (t ex kärnkanaler, vissa värmeväxlare, etc.). En av
de föreslagna lösningarna för att uppnå tillräcklig noggrannhet och kostnadseffektiv
beräkningseffektivitet vid modellering av en Generation IV-reaktor är att dela det
primära systemet i 1D- och 3D-regioner och tillämpa kopplade STH- och CFD-koder
på respektive deldomäner.
Framgångsrik validering är en förutsättning för tillämpning av både fristående och
kopplade STH- och CFD-koder i design och säkerhetsanalys av Generation IV-
system. I detta arbete utvecklar och tillämpar vi vidare aspekter av
kodvalideringsmetodik med inriktning på (i) STH-kodanalys till stöd för
utformningen av valideringsexperimentet (anläggnings- och testförhållanden), (ii)
kalibrering av kodinmatningsparametrar med osäkerheter, (iii) utveckling av
metoder för att koppla STH- och CFD-koder, iv) validering av fristående STH och
kopplade STH-CFD-koder.
En stor del av avhandlingsarbetet är kopplat till utvecklingen av en experimentell
slinga-typ 3-bens flytande metall anläggning TALL-3D för kodvalidering. Särskild
fokus har varit på identifiering av testförhållanden med komplexa återkopplingar
mellan 1D-3D-fenomen, vilket kan vara utmanande för koderna. Fristående STH-
kod (RELAP5) validerades mot experimentella data. Domänen för de instabiliteter
av naturlig cirkulation i TALL-3D-operationsparametrar upptäcktes med en
validerad STH-kod och globala optimala sökalgoritmer. Därpå bekräftades
experimentellt förekomsten av växande naturliga cirkulationsoscillationer. Ett
internationellt benchmark inleddes inom ramen för EU SESAME-projektet, baserat
på de erhållna experimentella uppgifterna.
IV
Simuleringar utfördes för att definiera dimensioner och plats för en ny provsektion
för experiment om stelning av kylmedel, som också skulle förbättra förutsättningar
för att studera naturliga instabiliteter i framtida provningar.
Ett tillvägagångssätt för automatisk inmatningskalibrering och kodvalidering är
utvecklad för att minimera möjlig "användareffekt" vid flertal osäkra
inmatningsparametrar (UIP) och systemresponsmängder (SRQs). Dessa metoder
användes i stor utsträckning vid utveckling av RELAP5 inmatningsmodellerna och
vid identifiering av de instabilitetsregionerna av naturliga cirkulation.
Domän-överlappande tillvägagångssätt för koppling av RELAP5 och Star-CCM +
koder föreslogs vilket resulterade i avsevärd förbättring av de prediktiva förmågorna
i jämförelse med fristående RELAP5.
V
LIST OF PUBLICATIONS
Included journal publications
I. V.-A. Phung, K. Kööp, D. Grishchenko, Y. Vorobyev, P. Kudinov “Automation
of RELAP5 input calibration and code validation using genetic algorithm”,
Published in Nuclear Engineering and Design, Volume 300, 15 April 2016. —
Contribution: Implementation of the genetic algorithm and RELAP5 input
modification, carried out GA-IDPSA calculations.
II. D. Grishchenko, M. Jeltsov, K. Kööp, A. Karbojian, W. Villanueva, and P.
Kudinov, “The TALL-3D facility design and commissioning tests for validation
of coupled STH and CFD codes,” Published in Nuclear Engineering and Design,
vol. 290, 2015. — Contribution: Analytical support to the experiment design
process, STH simulations, participation in conducting the experiments.
III. K. Kööp, D. Grishchenko, P. Kudinov “Automated calibration and validation
of RELAP5 input model against TALL-3D facility experimental data”,
Submitted to Nuclear Engineering and Design 2018.
IV. K. Kööp, M. Jeltsov, D. Grishchenko, P. Kudinov “Pre-test analysis for
identification of natural circulation instabilities in TALL-3D facility”, Published
in Nuclear Engineering and Design, Volume 314C, 2017.
V. M. Jeltsov, K. Kööp, D. Grishchenko, P. Kudinov “Pre-test analysis of an LBE
solidification experiment in TALL-3D”, Submitted to Nuclear Engineering and
Design 2018. — Contribution: Analytical support with STH simulations for
selection of geometry and location of the solidification test section.
Journal publications not included in the thesis
Yu. B. Vorobyev, P. Kudinov, M. Jeltsov, K. Kööp, and T.V.K. Nhat, “Application of
information technologies (genetic algorithms, neural networks, parallel
calculations) in safety analysis of Nuclear Power Plants,” Proceedings of the Institute
for System Programming of RAS, volume 26, 2014. Issue 2, pp.137-158. —
Contribution: RELAP5 simulation results of TALL-3D facility have been used as
comparative material.
G. Bandini, M. Polidori, A. Gerschenfeld, D. Pialla, S. Li, W. Ma, P. Kudinov, M.
Jeltsov, K. Kööp, K. Huber, X. Cheng, G. Bruzzese, A. G. Class, D. P. Prill, A.
Papukchiev, C. Geffray, R.-J. Macian, and L. Maas, "Assessment of Systems Codes
and Their Coupling with CFD Codes in Thermal-Hydraulic Applications to
Innovative Reactors," Nuclear Engineering and Design, Submitted, 2014. —
VI
Contribution: A review paper where the work of myself and our European partners
is described and discussed.
A. Papukchiev, M. Jeltsov, K. Kööp, P. Kudinov and G. Lerchl, "Comparison of
different coupling CFD–STH approaches for pre-test analysis of a TALL-3D
experiment". Nuclear Engineering and Design 2015. — Contribution: In this paper
different code coupling approaches are compared, ours included.
V.-A. Phung, S. Galushin, S. Raub, A. Goronovski, W. Villanueva, K. Kööp, D.
Grishchenko, P. Kudinov “Characteristics of debris in the lower head of a BWR in
different severe accident scenarios”, Nuclear Engineering and Design, Volume 305,
15 August 2016. — Contribution: I contributed to the paper by running genetic
algorithm calculations connected to MELCOR severe accident simulation code.
Conference publications not included in the thesis
M. Jeltsov, F. Cadinu, W. Villanueva, A. Karbojian, K. Kööp and P. Kudinov, "An
approach to validation of coupled CFD and system thermal-hydraulic codes," 14th
International Topical Meeting on Nuclear Reactor Thermalhydraulics (NURETH-
14), Toronto, Ontario, Canada, September 25-29, 2011
M. Jeltsov, K. Kööp, P. Kudinov, W. Villanueva, "Development of domain
overlapping STH/CFD coupling approach for analysis of heavy liquid metal thermal
hydraulics in TALL-3D experiment," CFD4NRS-4, OECD/NEA and IAEA
Workshop, Daejeon, Korea, September 10-12, 2012
M. Jeltsov, K. Kööp, P. Kudinov, W. Villanueva, "Development of multi-scale
simulation methodology for analysis of heavy liquid metal thermal hydraulics with
coupled STH and CFD codes," NUTHOS-9 conference, Kaohsiung, Taiwan,
September 9-13, 2012
M. Jeltsov, K. Kööp, D. Grishchenko, A. Karbojian, W. Villanueva, P. Kudinov,
"Development of TALL-3D Facility Design for Validation of Coupled STH and CFD
Codes," NUTHOS-9 conference, Kaohsiung, Taiwan, September 9-13, 2012
G. Bandini, E. Bubelis, M. Schikorr, M.H. Stempnievicz, A. Lázaro, K. Tucek, P.
Kudinov, K. Kööp, M. Jeltsov, L. Mansani, "Safety Analysis Results of
Representative DEC Accidental Transients for the ALFRED Reactor," International
Conference on Fast Reactors and Related Fuel Cycles: Safe Technologies and
Sustainable Scenarios (FR13), Paris, France, March 4-7, 2013
M. Jeltsov, K. Kööp, P. Kudinov and W. Villanueva, "Development of a domain
overlapping coupling methodology for STH/CFD analysis of heavy liquid metal
thermal-hydraulics," The 15th International Topical Meeting on Nuclear Reactor
Thermalhydraulics (NURETH-15), NURETH15-466, Pisa, Italy, May 12-15, 2013
VII
A. Papukchiev, M. Jeltsov, C. Geffray, K. Kööp, P. Kudinov, R.-J. Macian, and G.
Lerchl, "Prediction of Complex Thermal-Hydraulic Phenomena Supplemented by
Uncertainty Analysis with Advanced Multiscale Approaches for the TALL-3D T01
Experiment", Proceedings of the 12th International Probabilistic Safety Assessment
and Management Conference (PSAM 12), Honolulu, Hawaii, June 22-27, 2014
I. Mickus, K. Kööp, M. Jeltsov, Y.B. Vorobyev, W. Villanueva, and P. Kudinov, "An
Approach to Physics Based Surrogate Model Development for Application with
IDPSA, " Proceedings of the 12th International Probabilistic Safety Assessment and
Management Conference (PSAM 12), Honolulu, Hawaii, June 22-27, 2014
A. Papukchiev, G. Lerchl, C. Geffray, R.-J. Macián, M. Jeltsov, K. Kööp, and P.
Kudinov, "Coupled 1D-3D Thermal-Hydraulic Simulations of a Liquid Metal
Experiment Supplemented by Uncertainty and Sensitivity Analysis, " Application of
CFD/MCFD Codes to Nuclear Reactor Safety and Design and their Experimental
Validation (CFD4NRS-5), OECD/NEA and IAEA Workshop, Zurich, Switzerland,
September 9-11, 2014
Jeltsov, M., Kööp, K., Villanueva, W., Grishchenko, D., Kudinov, P., 2014.
"Validation of a CFD Code Star-CCM+ for Liquid Lead-Bismuth Eutectic Thermal-
Hydraulics Using TALL-3D Experiment," The 10th International Topical Meeting on
Nuclear Thermal-Hydraulics, Operation and Safety (NUTHOS-10) NUTHOS10-
1269 Okinawa, Japan, December 14-18, 2014. Atomic Energy Society of Japan
Phung, V., Galushin, S., Raub, S., Goronovski, A., Villanueva, W., Kööp, K.,
Grishchenko, D., Kudinov, P., 2015. Prediction of Corium Debris Characteristics in
Lower Plenum of a Nordic BWR in Different Accident Scenarios Using MELCOR
Code, 2015 International Congress on Advances in Nuclear Power Plants (ICAPP),
May 03-06, 2015
A. Papukchiev, C. Geffray, M. Jeltsov, K. Kööp, P. Kudinov, D. Grishchenko,
"Multiscale analysis of forced and natural convection including heat transfer
phenomena in the TALL-3D experimental facility,” The 16th International Topical
Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-16), At Chicago, IL,
USA, August 30-September 4, 2015
I. Mickus, K. Kööp, M. Jeltsov, D. Grishchenko, P. Kudinov, J. Lappalainen,
"Development of TALL-3D test matrix for APROS code validation", The 16th
International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-
16), At Chicago, IL, USA, August 30-September 4, 2015
D. Grishchenko, K. Kööp, M. Jeltsov, I. Mickus, and P. Kudinov “TALL-3D test
series for calibration and validation of coupled thermal-hydraulics codes”, The 17th
VIII
International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-
17) Qujiang Int’l Conference Center, Xi’an, China, September 3 - 8, 2017
M. Jeltsov, K. Kööp and P. Kudinov “Coupled CFD-STH Analysis of Liquid Metal
Flows”, STAR Global Conference 2017, Berlin, Germany, March 6 - 8, 2017
IX
ACKNOWLEDGEMENTS
I would like to thank my supervisor Pavel Kudinov for making this thesis work
possible.
I would also like to thank my co-supervisors, all my colleagues in Nuclear Power
Safety and Nuclear Engineering divisions, my family and friends who have
supported me through it all.
Thank you!
This work has received funding from the 7th Framework Programme European
Commission Project THINS No. FP7-249337 and the Euratom research and training
programme 2014-2018 under the grant agreement No 654935 (SESAME).
X
XI
TABLE OF CONTENTS
Abstract ....................................................................................................................... I
Sammanfattning........................................................................................................ III
List of publications ..................................................................................................... V
Acknowledgements ................................................................................................... IX
1. Background .......................................................................................................... 1
1.1. Lead-cooled fast reactors .................................................................................. 2
1.2. LFR modelling and simulation ......................................................................... 3
1.3. Validation methodology .................................................................................... 4
1.4. Goals, tasks and thesis structure ...................................................................... 6
1.5. Main achievements ........................................................................................... 6
2. Numerical analysis tools ...................................................................................... 9
2.1. RELAP5 ............................................................................................................. 9
2.2. GA-IDPSA ......................................................................................................... 9
3. Application of GA to RELAP5 input parameter calibration ............................... 11
3.1. CIRCUS-IV facility ........................................................................................... 11
3.2. RELAP5 input calibration ............................................................................... 12
4. TALL-3D experimental facility .......................................................................... 19
4.1. Description of TALL-3D ................................................................................. 20
4.2. Example experimental results ........................................................................ 24
5. RELAP5 TALL-3D model validation against TALL-3D data............................. 29
5.1. Input model development and solution verification ...................................... 29
5.2. model calibration and validation .................................................................... 33
6. Natural circulation Instabilities in TALL-3D facility ........................................ 41
6.1. Searching for instabilities ............................................................................... 41
6.2. Experimental results ....................................................................................... 46
7. Code coupling ..................................................................................................... 49
8. TALL-3D Solidification test section ................................................................... 55
9. Summary ............................................................................................................ 63
Bibliography .............................................................................................................. 65
XII
BACKGROUND | 1
1. BACKGROUND
A large number of nuclear reactors in operation today are classified as Generation II
reactors. These power plants, some as old as 50 years, are associated with aging
technology and production of highly radioactive nuclear waste. Generation III
(developed through the 90’s) and Generation III+ reactors provided evolutionary
improvement to the design of conventional water-cooled nuclear power plants,
reduced the reliance on active core cooling and increased grace time during loss of
coolant accidents by adding passive safety systems [1]. However, issues with nuclear
waste production and storage, proliferation resistance and overall sustainability of
the nuclear fuel remain.
Eight specific goals were defined for Generation IV nuclear energy systems to
rethink the technological approaches instead of incremental, marginal
improvements [2]:
1. Provide sustainable energy generation that meets clear air objectives and
delivers long-term availability of systems and effective fuel utilisation.
2. Minimise and manage nuclear waste and notably reduce the long-term waste
storage burden.
3. Have a clear life-cycle cost advantage over other energy sources.
4. Have a level of financial risk comparable to other energy projects.
5. Operations should excel in safety and reliability.
6. Have a very low likelihood and degree of reactor core damage.
7. Eliminate the need for offsite emergency response.
8. Be the least desirable route for theft of weapons-usable materials and provide
increased physical protection against acts of terrorism.
Based on these goals, Generation IV International Forum1 selected six new nuclear
energy system designs for further research and development [2]:
• LFR (Lead-cooled fast reactor)
• SFR (Sodium-cooled fast reactor)
• MSR (molten salt reactor)
• SCWR (Supercritical-water-cooled reactor)
• GFR (Gas-cooled fast reactor)
• VHTR (Very-high-temperature reactor)
1 The Generation IV International Forum (GIF) is an international endeavour set up to carry out the research and development needed for the next generation nuclear energy systems.
2 | BACKGROUND
Out of these six technologies, LFR systems will be focused on in this thesis work.
1.1. LEAD-COOLED FAST REACTORS
Lead-cooled fast reactors feature a fast neutron spectrum, they operate at high
temperature and low pressure, use either liquid lead or lead-bismuth eutectic (LBE)
alloy as a primary coolant. LFRs are considered as one of the most promising among
the proposed six Generation IV designs (Figure 1).
Lead and lead bismuth alloys have low neutron moderation resulting in a fast
neutron spectrum, which in turn allows for effective burning of minor actinides.
They are also chemically inert and do not release energy in accident condition (as
compared to sodium-water interaction). Since LFRs can be operated at atmospheric
pressures, the loss of coolant accident can be all but eliminated by installing a guard
vessel.
Figure 1: Generic LFR schematics.
High density of the coolants enhances natural circulation development compared to
conventional water-cooled reactors. Paired with simple primary flow path and a low
core pressure drop allow heat removal from the core via natural circulation during
loss of offsite power or loss of flow accidents.
Several LFR designs are under development in the world today [3]. Most notable are
SVBR (Russia) [4], BREST (Russia) [5], SSTAR (USA) [6] and ALFRED (EU) [7].
However, there are technical challenges to overcome in order to make LFR designs
viable commercially. Technology roadmap for Generation IV nuclear energy systems
foresees main research and development activities regarding corrosion and lead
BACKGROUND | 3
chemistry management system, development of instrumentation for the core and
fuel with corresponding handling technology [8].
In addition to these efforts, advanced modelling and simulation is listed as an
important next challenge as design and safety analyses of Generation IV metal
cooled reactors must rely on simulations due to lack of operational experience, ever
evolving design and stringent safety requirements.
1.2. LFR MODELLING AND SIMULATION
Challenges for modelling and simulation of pool-type LFR systems stem from the
original intended use of the codes that are being applied in design and licensing of
these reactors [9]. 1D system thermal-hydraulics (STH) codes like RELAP5 [10] and
TRACE [11] were originally designed to be applied to water-cooled reactor systems
with high (forced) coolant mass flow rates. These codes were extensively
benchmarked against plant data [12] and other code results [13] as well as used in
reactor design and licensing [14].
Parts of the systems (e.g. core, some designs of the heat exchangers, secondary
coolant system, etc.) can be simplified into 1D elements resolved by STH codes.
However, 1D STH codes are unable to capture complex 3D phenomena in pool-type
reactors. Transient thermal stratification and mixing in the pool and in the lower
plenum (e.g. in case of asymmetric circulation) render STH codes unable to provide
adequate modelling of physical phenomena. In addition, during loss of flow or
overcooling transients, solidification of the coolant can occur in the primary system,
which 1D STH codes are unable to simulate.
Computational fluid dynamics (CFD) codes are capable of resolving the 3D effects,
however applying these methods with high resolution for the whole primary system
result in prohibiting computational cost. In addition, the number of calculations
needed to cover a wide range of design and beyond-design-basis accidents further
complicates the issue.
One of the proposed solutions is to divide the primary system into 1D and 3D
regions, apply STH and CFD codes separately on the respective domains and
exchange data between the codes [15]–[19]. Coupling STH and CFD codes allows the
user to achieve necessary accuracy with reduced computational cost, however it also
introduces additional source of uncertainty due to the coupling method (e.g.
selection of which data, when in time and where in space is exchanged between the
codes is a non-trivial problem). To be able to apply advanced computational
methods in design and safety analysis these methods need to be validated.
4 | BACKGROUND
1.3. VALIDATION METHODOLOGY
Successful validation is a prerequisite for application of standalone and coupled STH
and CFD codes in design and safety analysis. Significant progress has been
previously made in the field of code validation methodology development [20]–[22].
The ultimate goal of the validation process is to develop sufficient evidences for a
robust decision on selected specific application (intended use). A successful
validation process is:
a) Connected with the intended use, e.g. through the code acceptance criteria;
b) Systematic and complete, i.e. all uncertainty sources addressed;
c) Iterative, e.g. new data from dedicated validation experiments or from code
application to risk analysis can require changes in the validation process; and
d) Converging.
General validation process (Figure 2 [23], [24]) has three main stages aiming to
reduce (i) numerical uncertainty (outlined in red); (ii) experimental and respective
model input uncertainty (outlined in green); in order to characterize (iii) the model
form uncertainty (outlined in blue).
Figure 2: Iterative approach to the validation process [23], [24].
BACKGROUND | 5
The process of validation starts with defining the criteria for decision on code
adequacy for intended use. This criteria can be expressed for example in terms of
predictive capability maturity model (PCMM) [20]–[22]. The outcome of the
validation process is characterization and (if necessary for improvement of
robustness of supported decisions) reduction of the code (model) uncertainty.
Design of the experiment is an important part of the validation process. For
successful validation, experimental design and supporting analytical activities
should be tightly coupled in order to ensure that:
i. code (model) uncertainty is the dominant contributor to the overall code
prediction uncertainty;
ii. relevant regimes and phenomena can be addressed in the tests;
iii. experimental response is sufficiently sensitive to the possible variations of
initial/boundary conditions;
Convergence criteria for the numerical model should be fulfilled for the relevant
experimental conditions. Code input model development usually requires
calibration of uncertain input parameters using a dedicated set of tests. Lack of
numerical convergence and ad-hock calibration of the uncertain model input
parameters based only on the engineering judgement are among the most
ubiquitous “user effects” in the validation process. Code input models can be often
“tuned” by a user to perform well for a specific transient, while lacking general
predictive capabilities for other transients.
In order to reduce the user effects, systematic sensitivity studies are necessary in
order to objectively identify major contributors to the uncertainty (Figure 2).
Experimental evidences are then used in order to reduce the input and experimental
uncertainties. This process is applied iteratively, to make sure that the initial guesses
of the user on the possible ranges of the uncertain input parameters has no effect on
the calibrated model input. In principle the process of sensitivity analysis and data
collection should be user agnostic and converge to the same conclusion with respect
to the code validity.
At the final stage of the process all sources of uncertainties are propagated through
the physics model to obtain the simulation SRQs with uncertainties. Calculated SRQ
values are then compared to the experimental SRQs (validation dataset). The
disagreement between the simulation and the experiment is quantified by applying
a validation metric operator.
Based on the results, the code performance can be concluded to be adequate or not
adequate for the intended use, or a decision to perform an additional iteration of the
validation process can be made. Each new iteration commonly also involves
improvement of the experiment.
6 | BACKGROUND
1.4. GOALS, TASKS AND THESIS STRUCTURE
The ultimate goal of this work is to provide contribution towards development of
methods, data and tools for qualifying multiscale codes in application to design and
licensing of Generation IV nuclear reactor systems. In this thesis we focus on the
following tasks:
• Development and application of methods for automated input calibration and
code validation in case of multiple uncertain input parameters and system
response quantities (SRQs) to minimise the “user effects” [25]. – Addressed
in Chapter 3 (Paper I). Similar methods were also widely used in this work
for other applications (Chapter 5 and 6).
• Development of an experimental facility TALL-3D, suitable for validation of
standalone and coupled STH and CFD codes in application to metal cooled
systems. Defining test procedures and operational conditions in order to
provide data on physical phenomena of importance for safety and code
validation [26], [27]. – Addressed in Chapters 4 and 8 (Papers II and V).
• Development of standalone system thermal-hydraulics code input model for
simulation of the experimental facility and quantification of uncertainties in
the code predictions using experimental data. – Addressed in Chapter 5
(Paper III).
• Identification of experimental conditions with natural circulation flow
instabilities in TALL 3D facility for STH code benchmarking [28] and
validation. – Addressed in Chapter 6 (Paper IV).
• Development of coupling algorithms for STH and CFD codes based on the
domain overlapping approach and validation of the coupled codes [19]. –
Addressed in Chapter 7.
1.5. MAIN ACHIEVEMENTS
1. An approach to data post-processing was developed and implemented in
order to enable selection of any combination of SRQs in the STH code output
as a fitness function used in the genetic algorithm (GA) of global optimum
search. This feature is necessary for automated calibration of the input and
code validation in case multiple input and output parameters.
2. Contribution to TALL-3D facility development including
a. STH analysis to support facility design that should feature thermal-
hydraulic feedbacks between 1D and 3D components;
b. Identification of operational parameters for dedicated tests on
calibration of measurement equipment, STH codes input calibration
and model validation;
BACKGROUND | 7
c. Carrying out experiments to produce validation grade data for
standalone and coupled code validation.
3. Application of the validation methodology with TALL-3D data using
advanced computational methods for automatic calibration and validation of
STH code RELAP5.
4. Application of different automated approaches to identification of domain of
natural circulation instability and limit cycle oscillations in TALL-3D facility.
Experimental conditions for confirmation of the existence of the instability
region were proposed and experiments carried out.
5. Contribution to development, implementation and validation of the coupling
approach for STH and CFD codes.
6. Analysis in support of design parameters of the new solidification test section
in TALL-3D experimental facility. The aim of the analysis was to enhance
TALL-3D capabilities in studying natural circulation instabilities.
8 | BACKGROUND
NUMERICAL ANALYSIS TOOLS | 9
2. NUMERICAL ANALYSIS TOOLS
2.1. RELAP5
STH code RELAP5 [10] has been extensively utilized as the modelling and
simulation tool in this thesis work. RELAP5 was developed by the Idaho National
Engineering Laboratory (INEL) for the United States Nuclear Regulatory
Commission (NRC) with the goal to provide best estimate analysis of pressurized
water reactors.
RELAP5 features coupled kinetics, one-dimensional heat transfer and two
component hydrodynamics based on six-equation two-fluid model.
In the work related to LFR system analysis, a custom RELAP5/Mod3.3 version with
lead or LBE as working fluids [29] and a heat transfer correlation by
Seban/Shimazaki (Eq. 1) has been used:
𝑁𝑢 = 5 + 0.025 ∙ 𝑃𝑒0.8 (1)
where the Péclet number (𝑃𝑒 = 𝐿𝑢/𝛼) is the ratio of transport rates by convection to
thermal diffusion; 𝐿 is characteristic length, 𝑢 is local flow velocity and 𝛼 is thermal
diffusivity (𝛼 = 𝜆/𝜌𝑐𝑝) where 𝜆 is thermal conductivity, 𝜌 is density and 𝑐𝑝 is specific
heat.
LBE properties used with the RELAP5 executable are shown in Table 1.
Table 1: LBE correlations used in the RELAP5 calculations [30].
Property SI unit Correlation Density kg m-3 𝜌 = 11065 − 1.293 ∙ 𝑇
Sound velocity m s-1 𝑢𝑠 = 1855 − 0.212 ∙ 𝑇
Bulk modulus Pa 𝐵𝑠 = (35.18 − 1.541 ∙ 10−3 ∙ 𝑇 − 9.191 ∙ 10−3 ∙ 𝑇2) ∙ 109
Isobaric specific heat J kg-1 K-1 𝑐𝑝 = 164.8 − 3.94 ∙ 10−2 ∙ 𝑇 + 1.25 ∙ 10−5 ∙ 𝑇2 − 4.56 ∙ 105 ∙ 𝑇−2
Dynamic viscosity Pa s 𝜂 = 4.94 ∙ 10−4 ∙ exp (754.1/T)
Thermal conductivity W m-1 K-1 𝜆 = 3.284 + 1.617 ∙ 10−2 ∙ 𝑇 − 2.305 ∙ 10−6 ∙ 𝑇2
2.2. GA-IDPSA
GA-IDPSA is an Integrated Deterministic Probabilistic Safety Analysis (IDPSA) tool
employing genetic algorithms (GA) to identify global optimums in multidimensional
parameter space [31], [32]. GA-IDPSA is extensively utilized in STH code input
model calibration (Paper I [25] and III) as well as in limit cycle oscillation regime
search (Paper IV [28]) for this thesis work.
10 | NUMERICAL ANALYSIS TOOLS
GA is often used to optimise solutions to engineering [33], economic [34], computer
science [35] and supply chain problems [36]. This wide use of genetic algorithms can
be attributed to their inherent ability to work with discreet as well as continuous
parameters, capability of handling large parameter space and potential for parallel
computing for shortening the analysis time.
GA mimics the natural selection process using a fitness function (FF) to evaluate
genes in a population. Crossover operation on genes with high fitness will produce
new candidates for the next generation in the population. Mutation of a gene will
ensure stochastic randomness in the next generation to avoid getting “trapped” in a
local maximum and cover the parameter space with sufficient samples. Users of GA
need to predetermine the ratio between crossover and mutation, describe the FF and
the parameter space by listing parameters included in the analysis as well as value
ranges.
A schematic of GA-IDPSA workflow used in the thesis work is shown in Figure 3.
Figure 3: Workflow for coupled GA-IDPSA and RELAP5.
APPLICATION OF GA TO RELAP5 INPUT PARAMETER CALIBRATION | 11
3. APPLICATION OF GA TO RELAP5 INPUT PARAMETER
CALIBRATION
Validation of system thermal-hydraulics codes is an important step in application of
these codes to reactor design and safety analysis. This is achieved by comparing
predicted and experimental system response quantities (SRQs) while considering
experimental and modelling uncertainties.
Parameters which are required for the code input but are not measured directly in
the experiment can become an important source of uncertainty in the code
validation process. These parameters can be component dimensions (due to 1D
simplification of the space), local pressure losses, heat transfer coefficients etc.
Quantification of such parameters is often called input calibration. Calibration and
uncertainty quantification become challenging when the number of uncertain input
parameters and SRQs is large and dependencies between them are non-trivial.
The goal of this part of the thesis work is to develop an automated approach to
RELAP5 input calibration and validation. The work is performed using experimental
data on two-phase natural circulation flow instability. The main purpose is to
increase robustness and to reduce the effect of engineering judgment on the outcome
of code validation process.
3.1. CIRCUS-IV FACILITY
CIRCUS-IV is a natural circulation facility designed for investigation of two-phase
flow instabilities in boiling water reactors at low pressure [37]. The facility consists
of a test section (four parallel heated channels with individual bypasses), a heat
exchanger at the top of the facility, a downcomer and a preheater in a buffer vessel
below the downcomer (Figure 4). For the purposes of code calibration and validation
effort, experiments were performed with only one active and three inactive channels.
Three CIRCUS-IV experiments were used in this work, all performed at atmospheric
pressure and 2.5 kW heater power (Table 2). Experimental setup and uncertainties
are discussed in detail in Paper I [25].
Table 2: Test conditions and corresponding regimes.
Test Inlet temperature (°C) Test regime
S-1 89.0 ±1 Single-phase steady state
I-1 92.8 ±1 Two-phase instability
I-2 99.8 ±1 Two-phase instability
12 | APPLICATION OF GA TO RELAP5 INPUT PARAMETER CALIBRATION
Figure 4: CIRCUS-IV facility schematics with indicated pressure (P), temperature
(T) and flow (F) measurement locations.
Characteristic inlet mass flow rates for tests S-1, I-1 and I-2 are shown in Figure 5
where periodic flashing for I-1 and I-2 can be observed.
Figure 5: Inlet mass flow rates in CIRCUS-IV single channel experiments.
3.2. RELAP5 INPUT CALIBRATION
In case of both manual and automatic calibration, system response quantities
(SRQs) need to be defined to evaluate the code performance against experimental
measurements. Given the complex physical phenomena present in CIRCUS-IV
experiments, a combination of a number of different SRQs is considered.
APPLICATION OF GA TO RELAP5 INPUT PARAMETER CALIBRATION | 13
A fitness function that represents the overall quantitative difference between the
experiment and the simulation guides the search for global optimum in case of
automatic code input model calibration (Eq. 2).
𝐹 =
1
𝑁∑
𝑤𝑖
𝐴𝑖
𝑁
𝑖=1
|𝑥𝑖 𝑠𝑖𝑚 − 𝑥𝑖 𝑒𝑥𝑝
𝑥𝑖 𝑒𝑥𝑝| (2)
where 𝐹 is the fitness; 𝑁 is the number of SRQs in the function; 𝑤𝑖 is a weighting
factor for each SRQ; 𝐴𝑖 is normalization factor for each SRQ; 𝑥𝑖 𝑠𝑖𝑚 is the simulated
value or the SRQ; 𝑥𝑖 𝑒𝑥𝑝 is the measured value for the SRQ.
Based on the test setup and the phenomena present in the experiment, several SRQs
were identified as of interest and are listed in Table 3.
Table 3: Parameters in the input calibration FF.
# SRQ Normalization
factor % (Ai)
Weighting factor (Wi) matrix
W1 W2 W3 W4 W5 W6
1 Inlet Channel Flow Rate 2 1 1 1 1 10 10
2 Oscillation Period 2 1 1 1 1 1 10
3 Inlet All Channels Temperature 0.5 1 10 10 10 10 10
4 Inlet Heated Channel Temperature 0.5 1 10 10 10 10 10
5 Inlet Riser Temperature 0.5 1 1 1 3 3 3
6 Middle Riser Temperature 0.5 1 1 1 3 3 3
7 Outlet Riser Temperature 0.5 1 1 1 3 3 3
8 Inlet Downcomer Temperature 0.5 1 1 3 3 3 3
9 Inlet Pressure 0.1 1 1 1 1 1 1
Normalization factors in Table 3 are based on acceptable error ranges for
nodalization qualification [9]. Normalization is needed to objectively compare the
importance of SRQs based on their physical properties.
Weighting factors in the fitness function allow the user to further specify SRQ
importance. To evaluate the sensitivity of the fitness function towards the weights of
individual SRQs, six combinations of weighting factors were tested (W1-W6 in Table
3).
It is important to note that in an ideal case where simulated SRQ value equals the
experimentally measured value (Fitness is zero), the choice of the weight becomes
of negligible importance. Therefore, if the combination of SRQs is possible to achieve
numerically by the code and the number of calculations is great enough to capture
these scenarios, the choice of weights has little effect on the end goal of finding the
optimal solution. In case of numerically unachievable optimal scenario or low
number of calculations, the weights influence the final solution.
14 | APPLICATION OF GA TO RELAP5 INPUT PARAMETER CALIBRATION
Table 4: Uncertain input parameters and ranges for calibration.
# Uncertain input parameter Minimum value
S-1/I-1/I-2
Maximum value
S-1/I-1/I-2
1 Heated channel power [W] 2375 2625
2 Inlet channel heat loss [W] 0 600
3 Heated channel heat loss [W] 0 200
4 Riser heat loss [W] 0 400
5 Upper plenum pipe heat loss [W] 0 400
6 Lower buffer vessel temperature BC* [°C] 85/90/97 95/100/105
7 Upper buffer vessel temperature BC* [°C] 85/90/92 95/100/102
8 Heat exchanger temperature BC* [°C] 65 80
9 Steam dome void fraction [-] 0.5 1.0
10 Inlet forward flow loss coefficient [-] 24 32
* BC stands for boundary condition.
A number of uncertain input parameters were identified in the RELAP5 CIRCUS-IV
model. Some were not measured in the experiment (e.g. heat losses, steam dome
void fraction, flow loss coefficient) and some were measured but with a large
uncertainty (e.g. temperature at the buffer vessels, heater channel power). Uncertain
input parameters and the ranges for global optimum search are shown in Table 4.
Table 5: Normalized differences between experimental and simulated SRQs for test
S-1.
# SRQ
Manual
calibration
[%]
GA W1
40 x 40 [%]
GA W1
80 x 80 [%]
Acceptable
error [%]
1 Inlet Channel Flow Rate -2.184 -2.913 -0.485 ±2.0
2 Inlet All Channels Temperature 0.259 -0.044 0.268 ±0.5
3 Inlet Heated Channel Temperature -0.652 0.116 -0.001 ±0.5
4 Inlet Riser Temperature -0.356 0.032 0.109 ±0.5
5 Middle Riser Temperature -0.320 -0.250 -0.098 ±0.5
6 Outlet Riser Temperature -0.107 -0.302 -0.091 ±0.5
7 Inlet Downcomer Temperature -0.540 -0.244 -0.176 ±0.5
8 Inlet Pressure 0.267 0.296 0.273 ±0.1
Fitness function value (W1) 102.9 79.9 55.7
In case of single-phase steady state test S-1, two genetic algorithm (GA) calculations
were performed with uniform weighting factors (W1 Table 3). Population size and
number of generations were set to 40 and 80 respectively. In both cases the mutation
to crossover ratio was 0.5. The difference between simulation and experiment SRQs
is shown in Table 5 where in addition to GA calculations, a manually calibrated input
[38] is compared to evaluate the performance of automated calibration process.
Calibrated uncertain input parameter values are presented and further discussed in
Paper I [25].
APPLICATION OF GA TO RELAP5 INPUT PARAMETER CALIBRATION | 15
The errors in temperature prediction were found within the acceptable range for
both GA calculations whereas the error in prediction of the inlet flow rate was
acceptable for GA with 80 population × 80 generation and slightly higher than
acceptable for 40 population × 40 generation. The error in prediction of the inlet
pressure was higher than acceptable level but lower than measurement error. Both
calibrated inputs provide smaller values of the fitness function compared to manual
calibration (Table 5).
A single GA calculation with 80 members of population and 80 generations can take
equivalent of ~80 days of serial computations, while GA run with 40 population
members and 40 generations takes 4 times less time. Therefore, results obtained
with GA 40 members × 40 generations are considered as optimal in terms of
computational cost versus reduction of the fitness function value.
Six GA-IDPSA calculations were set up and carried out using the provided uncertain
input parameters with ranges and weighted fitness functions with SRQs for both I-1
and I-2 tests. Population size and number of generations was set to 40 with mutation
to crossover ratio 0.5. The resulting most optimal scenarios for each six cases were
compared to manual calibration of the input (see Figure 6 and Figure 7). Note that
in Figure 6 the fitness for each optimal scenario was re-evaluated using W1
conditions for ease of comparison.
Figure 6: Fitness comparison of calibrated inputs (W – weight, M – manual).
Values for optimal scenarios were re-calculated using W1 weights for comparison.
For test I-1, all inputs calibrated with GA performed quantitatively better than the
manually calibrated input. Out of the six weighting factor combinations all but W5
managed to capture the oscillation period (Figure 7).
For test I-2, calibrated inputs with W1 and W6 resulted in fitness values comparable
to the manual calibration. Qualitatively incorrect oscillation patterns were predicted
with the inputs using W2, W3, W4 and W5 (Figure 7).
16 | APPLICATION OF GA TO RELAP5 INPUT PARAMETER CALIBRATION
Analysis done with manually calibrated input and using GA calibration with W5
(where inlet flow rate weight was increased) provided more accurate results for the
maximum flow rate but overestimated the period.
Figure 7: Comparison of experimental (E), manual (M) and GA calibrated inputs.
Predicted SRQ values were in general agreement with each other and with
experimental data. The differences were generally within the ranges of the
measurement errors and experimental uncertainties. The best input calibrated by
GA provided slightly better or equivalent results to those obtained with manual
calibration for majority of the SRQs.
Ranges for uncertain input parameter calibration, calibrated values and ranges for
code validation are further discussed in Paper I [25].
Individual SRQs are most commonly used for comparison between code prediction
and experiment in validation. However, it is important to note that good agreement
in individual SRQs does not necessarily mean the code is capable of successfully
predicting different SRQs simultaneously. Results shown in Figure 8 indicate that
the maximum inlet flow rate and the oscillation period are not predicted by the code
simultaneously.
While in case of calibration the GA fitness function was set to minimize the
difference between the simulation and experiment, in case of uncertainty
propagation the goal of the optimization is to identify the boundaries of the SRQ
response given the uncertain input parameter ranges identified in the calibration
process. To evaluate the efficiency of GA, results obtained with random sampling of
the same uncertain input parameter space are also presented in Figure 8.
It is evident that GA is able to identify the edges of uncertainty domain more
efficiently compared to random sampling. However, random sampling provides data
which can be directly used for assessment of probabilistic characteristics.
APPLICATION OF GA TO RELAP5 INPUT PARAMETER CALIBRATION | 17
Figure 8: Maximum inlet flow rate and period for tests I-1 and I-2. Blue and green
symbols correspond to the maximum (positive) and minimum (negative)
difference between experimental and predicted values of the maximum flow rate
respectively. Purple symbols denote random sampling and yellow symbols
calibrated (W6) input results.
It is recommended to carry out multiple input calibration calculations with varying
initial ranges and weighting factors to show that the results of calibration and
validation do not depend on initial selection of uncertainty ranges.
CONTRIBUTION TO PAPER I [25]: Development and implementation of the
methodology. GA-IDPSA calculations were prepared and executed. A complex
system of RELAP5 results post-processing in MATLAB for evaluating the fitness
function and importing calculated values back into GA-IDPSA was developed, tested
and executed by the author.
18 | APPLICATION OF GA TO RELAP5 INPUT PARAMETER CALIBRATION
TALL-3D EXPERIMENTAL FACILITY | 19
4. TALL-3D EXPERIMENTAL FACILITY
The main design goal for the TALL-3D facility is to provide experimental data on
thermal-hydraulics phenomena for validation of stand-alone and coupled System
Thermal-Hydraulics (STH) and Computational Fluid Dynamics (CFD) codes [39].
To achieve this goal, the facility has to provide [21], [40]:
• mutual feedbacks between 1D phenomena resolved by STH and 3D
phenomena resolved by CFD;
• a possibility to isolate subsections of the facility with well-defined boundary
conditions to provide separate effect validation of standalone codes;
• multiple measurement points and operation regimes to provide sufficient
number of constraints for uncertain input parameter calibration.
For validation of standalone STH codes, the following phenomena should be
appropriately simulated, and the experiment instrumented accordingly:
• Drag;
• Steady state heat transfer;
• Transient heat transfer;
• Stability of natural circulation;
• Thermal inertia of the loop sections;
• Heat losses as a function of temperature.
For validation of standalone CFD codes, the list of phenomena of interest:
• Free jet flow;
• Jet impingement on a surface;
• Jet induced recirculation flow in a pool;
• Thermal stratification;
• Mixing;
• Thermal inertia of the structures;
• Turbulence.
In support of the experimental facility design numerous STH code calculations were
performed to identify most promising combination of system dimensions and
operational conditions. This work was done iteratively with constant input from
other members of the TALL-3D development team and with the help of CFD
calculations.
20 | TALL-3D EXPERIMENTAL FACILITY
4.1. DESCRIPTION OF TALL-3D
TALL-3D thermal hydraulic loop facility is shown in Figure 9 [39].
Figure 9: Schematics of the TALL-3D experimental facility with main components.
TALL-3D EXPERIMENTAL FACILITY | 21
The primary side working fluid of TALL-3D is liquid lead-bismuth eutectic (LBE)
[41], whereas secondary side is operated using Dowtherm RP coolant [39]. Heat is
transferred between the primary and secondary side via a counter-current heat
exchanger located in the top of the right-most leg of the loop (generally referred to
as the heat exchanger leg or simply HX-leg). Secondary heat exchanger consisting of
a radiator and a fan is used to remove the heat from the secondary loop.
The pin-type main heater of the TALL-3D facility is located in the bottom of the left-
most primary leg, which is also referred to as the main heater leg (MH-leg). In
addition to the main heater, the primary side can be heated using the pool-type test
section heater in the lower part of the middle leg, also known as the 3D test section
leg (or 3D-leg). Flow in the primary circuit can be forced using an Electric Permanent
Magnet (EPM) pump located in the heat exchanger leg. In natural circulation, LBE
flow is driven by the difference in coolant density in the primary legs, which can be
created by the heaters and heat exchanger. Main parameters of the facility are shown
in Table 6.
The facility has been instrumented extensively with more than 500 measurement
and control data channels. The loop can be effectively divided into several
subsections for separate effect input calibration and section by section code
validation. In-flow thermocouples and pressure transducers provide measurements
of inlet and outlet LBE temperatures and pressures, so that transient boundary
conditions can be provided for each subsection. LBE flow is measured in the HX-leg
and 3D-leg with Coriolis flow meters, whereas flow in MH-leg is estimated from the
mass balance.
Table 6: TALL-3D facility parameters.
Parameter Value
Total facility height 6967 mm
Primary side height 5830 mm
Primary side width 1480 mm
Loop pipe inner diameter 27.8 mm
Main heater power 27 kW
3D test section heater power 15 kW
Test section inner height 200 mm Test section inner diameter 300 mm Test section inlet pipe inner diameter 17 mm
The primary side of the TALL-3D facility can be modelled using one-dimensional
flow model used in an STH code. The outlet temperature of the pool-type test
section, however, can be affected by three-dimensional transient flow phenomena
such as mixing of thermally stratified pool [39]. In steady state conditions, the test
22 | TALL-3D EXPERIMENTAL FACILITY
section outlet temperature can be determined using heat balance. Thus, STH codes
are expected to predict the flow in the primary loop in steady state operation, as long
as the overall heat balance and pressure drop over the test section can be properly
modelled.
The 3D test section is a cylindrical pool with an inner height of 200 mm and inner
diameter of 300 mm (Figure 10). The pool can be fully mixed (uniform temperature
distribution) or thermally stratified. The upper two–thirds of the test section are
equipped with two rope heaters with adjustable power (7.5 kW each) coiled around
the circumference. Activation of the heaters can drive the development of thermal
stratification in the pool. A circular inner plate is installed in front of the outlet of
the test section to divert the inlet jet laterally, thereby facilitating mixing of the pool.
In case of low flow rate, the inlet jet might have insufficient momentum to penetrate
into and mix the stratified layer. Thus, temperature distribution in the pool depends
on the heater power and flow conditions.
In total 154 thermocouples are installed in the test section to measure temperature
on the walls and in the bulk of the pool. Instantaneous temperature at the outlet of
the test section affects development of the transient natural circulation in the loop.
Figure 10: 3D test section schematics and photo showing the test section without
insulation (pre-assembly).
The experimental uncertainty of temperature measurement is ±1 K for TCs in the
test section and ±2 K for TCs in the rest of the loop. Several TC offset tests with high
flow rate were performed to reduce the experimental uncertainty in the temperature
readings. The methodology and results are described in a conference paper [42]. The
TALL-3D EXPERIMENTAL FACILITY | 23
accuracy of the Coriolis flow meter at nominal flow is 0.1% and can be as high as 3%
at 0.005 kg/s. The uncertainty of the differential pressure transducers is ±40 Pa for
DP1-4 groups and ±162 Pa for the DP5 group over the EPM pump section [39].
Figure 11: Images from the TALL-3D facility construction process.
Pre-test simulations of TALL-3D transients demonstrated an important effect of
heat losses and thermal inertia on the flow and temperature characteristics,
especially in natural circulation regimes. Special attention in the design was devoted
to the estimation of the effects of the heat losses through insulation and thermal
inertia of the metal structures of the loop. The ambient air temperature necessary
for modelling of the heat losses is measured at 3 different elevations.
24 | TALL-3D EXPERIMENTAL FACILITY
4.2. EXAMPLE EXPERIMENTAL RESULTS
First series of commissioning tests were carried out in order to verify the existence
of the feedbacks between the 3D phenomena in the test section and system loop
behaviour predicted in the pre-design and pre-test analyses.
A representative forced to natural circulation transient results are shown in Figure
12 and Figure 13. The transient was initiated from a forced circulation steady state.
At time zero the EPM pump was tripped while power in the main heater and in the
3D test section heater were kept constant. After a transition period of approximately
25 minutes, natural circulation steady state was established in the loop.
Figure 12: Transient T01.03 LBE mass flow rates.
The initial and final steady state conditions are summarized in Table 7. Transient
initiating pump trip is followed by the abrupt decrease of the flow rates in all legs
with faster flow redevelopment in the main heater leg. Flow reversal is observed in
the test section leg for about 240 s (Figure 12). During this period LBE temperature
in the main heater leg decreases (see Figure 13) and reduced flow rates in the test
section leg allow heat up and development of thermal stratification in the 3D pool
(Figure 14).
TALL-3D EXPERIMENTAL FACILITY | 25
Figure 13: Transient T01.03 LBE in-flow temperatures.
Table 7: T01.03 transient initial and final steady state conditions.
Parameter Forced circulation steady state
Natural circulation steady state
MH electric power [W] 4972 4972
Test section electric power [W] 5078 5078
HX LBE mass flow rate [kg/s] 4.793 0.674
Test section LBE mass flow rate [kg/s] 1.827 0.337
Test section inlet LBE temperature [°C] 262 227
Test section outlet LBE temperature [°C] 279 341
MH section inlet LBE temperature [°C] 262 227 MH section outlet LBE temperature [°C] 274 328 HX section inlet LBE temperature [°C] 277 323 HX section outlet LBE temperature [°C] 262 237
At about 280 seconds after transient initiation, buoyancy force in the 3D leg becomes
larger than that in the main heater leg. The flow in the 3D leg accelerates in the
vertical direction filling the leg with hot LBE (exceeding 380◦C) accumulated in the
test section. The flow acceleration leads to partial mixing of the pool and reduction
of the test section outlet temperature, while the flow rate is reduced (to almost
stagnation), and temperature increases in the main heater leg. This leads to main
heater outlet temperatures rising up to 460°C and test section outlet temperatures
dropping down to 340°C. Such periodic flow oscillations continue for another 20
26 | TALL-3D EXPERIMENTAL FACILITY
min with gradually decaying amplitudes and eventually a steady state natural
circulation is established in the loop.
LBE temperatures measured in the 3D test section pool are shown in Figure 14.
During the transient the flow in the test section pool was fairly symmetric as the
maximum temperature difference between symmetrically located TCs did not
exceed four degrees.
Figure 14: LBE temperatures measured at different locations in the 3D test section
pool.
From these initial experimental tests, it can be concluded that the facility features
strong mutual feedbacks between 1D and 3D phenomena and therefore provides
necessary data for validation of the coupled codes. Extensive instrumentation
present in the facility provides a possibility to isolate sections of the primary loop to
provide separate effect and integral validation of standalone STH and CFD codes
with well-defined boundary conditions for each section.
The TALL-3D facility was built and first operated under EU project THINS. The list
of transient experiments performed for the THINS project is shown in Table 8. In
continuation to THINS project, several more transients were conducted under EU
project SESAME (see Table 9).
TALL-3D EXPERIMENTAL FACILITY | 27
Table 8: THINS project TALL-3D transient experiments.
Name
Initial steady state Final steady state
Oil
in
let
tem
per
atu
re
HX
ma
ss f
low
ra
te
MH
po
wer
TS
po
wer
HX
ma
ss f
low
ra
te
MH
po
wer
TS
po
wer
kg/s kW kW kg/s kW kW °C T01.08 4.1 2.6 4.8 0.6 2.6 4.8 65 T01.09 4.3 2.6 4.8 0.6 2.6 4.8 61 T01.10 3.3 3.2 4.0 0.6 3.2 4.0 85 T02.03 4.3 6.3 - 0.5 2.8 4.0 95 T02.04 4.2 2.1 - 0.6 2.1 5.2 145 T02.06 4.2 1.7 - 0.5 1.7 5.2 145 T03.01 0.5 2.3 - 0.5 2.3 4.8 140 T06.01 0.6 2.6 4.8 4.3 2.6 4.8 61 T09.01 0.6 3.2 4.0 0.4 - 4.0 85 T11.02 0.5 2.8 4.0 0.5 1.8 4.9 95
Table 9: SESAME project TALL-3D transient experiments.
Name
Initial steady state Final steady state
Oil
in
let
tem
per
atu
re
HX
ma
ss f
low
ra
te
MH
po
wer
TS
po
wer
HX
ma
ss f
low
ra
te
MH
po
wer
TS
po
wer
kg/s kW kW kg/s kW kW °C TG03.S301.01 4.6 3.2 5.5 0.5 3.2 5.5 62 TG03.S301.02 4.6 2.5 4.9 0.5 2.5 4.9 63 TG03.S301.03 4.7 0.7 10.3 * 0.7 10.3 126 TG03.S301.04 3.3 3.2 4.0 0.5 3.2 4.0 86 TG03.S301.05 3.3 3.2 4.2 0.5 3.2 4.2 86 TG03.S301.06 4.8 1.1 10.6 0.6 1.1 10.6 116 TG03.S301.07 4.8 0.5 5.6 0.4 0.5 5.6 133 TG03.S302.01 4.3 2.3 - 0.5 2.3 4.9 141 TG03.S306.01 0.5 2.5 4.8 4.6 2.5 4.8 63 TG03.S307.01 0.5 3.2 5.5 4.6 8.6 - 62 TG03.S310.01 4.6 8.6 - 0.5 8.6 - 62 TG03.S311.01 0.5 3.2 4.0 0.5 0.6 6.7 86
28 | TALL-3D EXPERIMENTAL FACILITY
CONTRIBUTION TO PAPER II [39]: Conducted all pre-test RELAP5 STH
simulations needed for selection of facility dimensions, operational regimes and
requirements to positioning of instrumentation. Participation in operating the
facility during the experiments. Contributed to the development of operational
safety procedures.
RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D DATA | 29
5. RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D
DATA
To be able to apply coupled STH-CFD codes to analysis of TALL-3D experimental
facility both standalone and coupled codes need to be validated. The goal of RELAP5
TALL-3D model validation is therefore to evaluate the capability of the model for
use in coupled STH-CFD simulations.
5.1. INPUT MODEL DEVELOPMENT AND SOLUTION
VERIFICATION
Figure 15: Illustration of TALL-3D RELAP5 model nodalization with main heater
heat structure (1), 3D test section heater heat structure (2), expansion tank time
dependent volume (3), secondary side inlet time dependent volume (4), secondary
side outlet time dependent volume (5), EPM pump heat structure (6).
A RELAP5 input model for TALL-3D described in the paper [28] is used in this work.
The model is mainly composed of pipe structures with node size of ~10 cm. Heat
structures represent pipe walls and insulation layer. Additional heat structures are
used for the main and 3D test section heaters, main valves and flanges in the primary
side. Time-dependent volumes are used to represent the expansion tank at the top
of the facility as well as the inlet and outlet of the secondary side. Constant inlet
30 | RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D DATA
temperature and flow rate are assumed for the coolant in the secondary side of the
primary heat exchanger.
Space-time convergence of the STH model was evaluated using an analytic inlet
temperature peak propagated through the main heater leg at a constant mass flow
rate of 0.4 kg/s. The peak amplitude and period were selected in a conservative way
to cover representative experimental values seen during THINS project
experimental campaign [39]. The inlet temperature peak and the response of the
model is shown in Figure 16.
Figure 16: Temperature peak propagation through main heater leg model with
various node sizes.
20 cm long nodes in the main heater leg pipe structures result in approximately
3.5 % reduction in temperature peak absolute value when compared to relatively
small, 2 cm long nodes. However, it must be noted that heat transfer in RELAP5 is
modelled only in radial direction and no axial conduction is simulated. This means
that cases with low flow rates, when conductive heat transfer dominates over
convective in the experiment, the simulation will not be able to predict axial heat
diffusion in the loop, unless numerical diffusion can partially compensate for the
lack of the physical model. Thus an “optimal” grid resolution should be used in
simulations. It is a common misunderstanding that continuous reduction of node
size would improve the accuracy of the prediction in STH codes and is in detail
described in [9].
Similar study was conducted for time convergence where the time step was varied
between 10-2 seconds and 1 second. RELAP5 automatically reduces the time step
when Courant limit is reached and no difference in the result was observed. Based
RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D DATA | 31
on the results of the space and time convergence studies it is decided to use time step
of 0.1 sec (to account for larger mass flow rates) and node size of 0.1 m for the
following analysis.
Any STH code input model can contain uncertain input parameters (UIPs). These
can be flow loss coefficients, simplified representation of 3D structures in the 1D
model, temperature dependent material properties or other parameters that are not
directly measured in the experiment. The importance of a specific uncertain
parameter and its influence on system response quantities (SRQs) can be identified
with a sensitivity study. A large number of SRQs were used in this work due to
inherent complexity of the feedbacks between the primary loop and test section
phenomena.
In this work an extended Morris method [43] implemented in DAKOTA code [44] is
used for sensitivity study. In total 22 SRQs with 18 UIPs were analysed including
forced and natural circulation steady state mass flow rates for all three primary legs
as well as initial and final steady state temperatures for the inlet and outlet of the
two heated and one cooled section. In addition, more complex system response
quantities were used such as duration of negative mass flow rate in the 3D-leg during
forced to natural circulation transition, minimum mass flow rate in the 3D-leg and
maximum temperatures at the outlets of the heated sections. Uncertain input
parameters and the respective ranges used in the analysis are show in Table 10.
Table 10: Uncertain input parameters and ranges used in the sensitivity study.
UIP Range Main heater power ± 5% TS heater power ± 5% Initial mass flow rate ± 3% Secondary mass flow rate ± 10% Secondary inlet temp ± 2 ºC Gap size ± 5 mm Pump heating power ± 100 W Flange HS length ± 10 mm Valve HS length ± 35 mm Pump bare metal HSL ± 10% Pool Top/Bottom HSL ± 10% Gap conductivity coeff. ± 10% HX wall conductivity coeff. ± 10% T-junction k-loss straight ± 20% T-junction k-loss bend ± 20% EPM pump k-loss ± 20% Pump bare metal capacity coeff. ± 10% Pool Top/Bottom capacity coeff. ± 10%
32 | RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D DATA
The geometry of the pool-type section in the facility is such that heat losses occur not
only in the radial direction, but also in the axial direction from the pool top and
bottom sides. This cannot be modelled explicitly in RELAP5 since the code only
resolves radial heat transfer in heat structures but can be compensated in the input
model by increasing a “virtual” heat structure area connected to pipe nodes at the
top and bottom of the pool. A sensitivity study using test section leg natural
circulation mass flow rate as a system response quantity shows the importance of
Pool Top/Bottom HSL parameter in such modelling technique (Figure 17). In Figure
17 and Figure 18, parameters in the legend are sorted in descending order of Morris
modified mean (µ) value which is the mean elementary effect. The standard
deviation of the elementary effects is displayed on the y-axis and is indicative of non-
linearity in the response.
Figure 17: Sensitivity study results for test section leg natural circulation mass flow
rate SRQ.
The 3D test section pool virtual heat structure size is the fourth most influential
model uncertain parameter for natural circulation mass flow rate prediction after
heater powers and local flow loss in the pump channel (Figure 7).
An example of the results for test section maximum outlet temperature SRQ is
shown in Figure 18. It is apparent that the heat exchanger modelling has a large
effect on the temperatures in the primary side. RELAP5-Mod3.3 used in this work
does not have Dowtherm RP fluid properties implemented and as such only LBE or
water can be used as a working fluid. Using LBE in modelling of the secondary side
is unfeasible, as temperatures would need to drop below solidification point of
RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D DATA | 33
126 ºC. Using water however has its own complications related to heat transfer
efficiency of the heat exchanger. In the current model, a combination of water as
working fluid and heat exchanger wall conductivity to simulate the efficiency was
used. Calibration of the heat exchanger and other sections is discussed in more detail
in the next chapter.
Figure 18: Sensitivity study results for test section maximum outlet temperature
SRQ.
It is important to note that the results of the sensitivity study are dependent on the
selection of ranges for the uncertain input parameters (UIP). Lack of knowledge
increases ranges for UIPs, sensitivity study in turn tells if this lack of knowledge
dominates the model output or not. Ranges of the parameters that dominate the
model output uncertainty must be deduced from the experiment in the model input
calibration process. The calibration can be used to assess both UIP range and its
mean. If calibration changes the ranges, SA results can also change. Therefore,
calibration and SA are a part of an iterative process that should be repeated until
further changes in the outcome become marginal for the task at hand (e.g. screening,
reduction of uncertainty, model design) Figure 2.
5.2. MODEL CALIBRATION AND VALIDATION
An automated calibration approach, aiming to minimize user effect using divide and
conquer method [25], was selected in this work. The full facility code input model
was divided into 10 sections (see Figure 19), each individual section having inlet and
34 | RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D DATA
outlet temperature, pressure drop over the section as well as mass flow rate in the
corresponding leg measured in the experiment.
Calibration of the model was done using experimental data from four experiments
performed in SESAME project. The experiments were selected based on the quality
of the steady state natural circulation data (e.g. minimal drift in facility
temperatures) and are described in Table 11 and representative system response
curves are shown in Figure 20.
Figure 19: RELAP5 input model schematic showing: (1) main heater riser, (2) right
bottom bend, (3) top left corner, (4) HX flow meter, (5) bottom T-junction, (6)
EPM pump, (7) top T-junction, (8) main heater, (9) heat exchanger and (10) 3D
test section.
Sections shown in Figure 19 are numbered and their inputs calibrated in order of
complexity starting with the main heater riser section. It is a straight pipe with no
valves, flanges or other complex structures. The dimensions as well as material
properties of the stainless-steel pipe and the surrounding insulation are well known
and constant over the section. The only uncertainty lies in the geometry of the rope-
type pre-heaters coiled around the pipe, creating a gap between the stainless-steel
pipe and the insulation. In the input model heat structures, the gap between the
insulation and steel pipe is represented by a material with properties between air
and insulation. The thickness of this material is predefined at maximum thickness
RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D DATA | 35
of the pre-heater, but the temperature dependent conductivity is calibrated to match
the temperature drop over the section.
Table 11: Calibration experiments.
# Name
Initial steady state Final steady state
Oil
in
let
tem
pe
ratu
re
HX
ma
ss
flo
w r
ate
MH
po
wer
TS
po
we
r
HX
ma
ss
flo
wra
te
MH
po
wer
TS
po
we
r
kg/s kW kW kg/s kW kW °C
1 TG03.S301.02 4.5 2.6 4.9 0.5 2.6 4.9 62
2 TG03.S301.04 3.3 3.2 4.0 0.5 3.2 4.0 86
3 TG03.S302.01 4.4 2.4 0 0.5 2.4 4.4 141
4 TG03.S306.01 0.5 2.6 4.9 4.6 2.6 4.9 63
Figure 20: Representative parameters of the four experiments used in model
calibration.
In addition to gap conductivity, flange and valve heat structure lengths, 3D test
section pool wall heat structure length, heat exchanger wall conductivity coefficient
36 | RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D DATA
and heat loss magnitude through EPM pump un-insulated steel pipe wall are used
as uncertain parameters in the input model.
Lumping all uncertainties from thermal losses into a single parameter for each
section in the facility allows the user to run an automated global optimum search to
identify calibrated parameter values for each given experimental condition. This
method results in a range for any given uncertain parameter based on optimum
values for all experimental conditions used in the calibration. With a large numbers
of available calibration experiments probability distributions can be assigned to the
uncertain parameter value ranges. In this work, uniform distribution is assumed for
all ranges as the number of used experiments was small.
To evaluate the performance of the calibrated RELAP5 TALL-3D input model, a
validation experiment was selected, and model system response quantities
compared to the experimental values. A forced to natural circulation transient
TG03.S301.01 from the SESAME project experimental campaign was selected as the
validation experiment (see Table 12). The selected transient is used as a benchmark
for coupled code qualification and it is therefore necessary to first evaluate single
STH code capability to capture system behaviour.
Table 12: Validation experiment.
# Name
Initial steady state Final steady state O
il i
nle
t
tem
pe
ratu
re
HX
ma
ss
flo
w r
ate
MH
po
wer
TS
po
we
r
HX
ma
ss
flo
wra
te
MH
po
wer
TS
po
we
r
kg/s kW kW kg/s kW kW °C
1 TG03.S301.01 4.7 3.2 5.6 0.6 3.2 5.6 62
Using uncertain parameter ranges from model calibration phase as an input and
Wilks formula [45] for sample size determination, 93 RELAP5 TALL-3D input
models were created providing 95/95 confidence. To form the bounding upper and
lower time-series, all maximum and minimum values for all 93 results of each SRQ
were considered.
The resulting upper and lower values for system response quantities are shown with
comparison to the experimental values in Figure 21. It is important to emphasize
that the upper and lower bounds shown in Figure 21 do not represent any specific
transient but are an overall maximum or minimum value for all 93 transients.
Therefore, the shape of the bound is not indicative of the model behaviour.
RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D DATA | 37
Figure 21: Comparison of experimental system response quantities and results of
the uncertainty study with variable heat exchanger wall conductivity coefficient.
Figure 21 suggests that the SRQs are sensitive to the suggested ranges resulting in
up to 40 ºC difference between the upper and lower bounds. This sensitivity can be
attributed to section 9 (heat exchanger) modelling as described in section 5.1. To
check the hypothesis, an additional uncertainty propagation calculation was
performed keeping the heat exchanger wall conductivity coefficient constant to
38 | RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D DATA
optimal value found for this specific validation transient. The resulting system
response upper and lower bounds can be seen in Figure 22.
Figure 22: Comparison of experimental system response quantities and results of
the uncertainty study with fixed heat exchanger wall conductivity coefficient.
After removing the uncertainty due to the heat exchanger modelling from the
analysis, the resulting difference in system response is in a more reasonable 10 ºC
range. Apparent deficiencies in 1D modelling of a 3D component are also more
RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D DATA | 39
visible now compared to previous analysis results. STH code underestimation of 3D
test section inlet temperature and overestimation of the corresponding outlet
temperature during the first 10 minutes is due to inherent inability to simulate three-
dimensional mixing in the pool. Furthermore, absolute peak values in main heater
outlet temperature are also underestimated during oscillatory period between 10
and 25 minutes of the transient. This can be attributed to nodalization effect as
described in solution verification section.
Even though the number of calibration experiments used was small, propagating the
uncertainty through the code resulted in a large uncertainty bound in the output
SRQs. This is partially due to the cumulative nature of the effect of UIPs (e.g. several
UIPs contributing to the total uncertainty in heat losses in a given primary side leg).
These UIPs could in principle be combined into a single UIP for each leg reducing
the overall uncertainty range. However, in conditions where position of heat losses
or their distribution over the leg is important (e.g. during natural circulation
conditions) this simplification can lead to unphysical results.
A large number of calibration experiments would allow probability distribution
functions to be quantified for each UIP range allowing in turn for quantification of
the confidence in given ranges. This would be easier to implement in smaller scale
experimental facilities.
Deficiencies in STH codes (e.g. absence of Dowtherm RP fluid) can require custom
modelling approaches that contribute to the overall uncertainty in the input model.
The results of the uncertainty propagation confirm the hypothesis that 1D system
codes can capture LBE loop-type systems in steady states but have difficulties in
describing transients with significant influence of 3D phenomena (e.g. transition
from thermal mixing to stratification). Given the intended use of the RELAP5 input
model as a part of coupled STH-CFD code, where 3D test section is simulated with
CFD and corresponding section thermal-hydraulics in RELAP5 are corrected, the
model performance is considered adequate.
40 | RELAP5 TALL-3D MODEL VALIDATION AGAINST TALL-3D DATA
NATURAL CIRCULATION INSTABILITIES IN TALL-3D FACILITY | 41
6. NATURAL CIRCULATION INSTABILITIES IN TALL-3D
FACILITY
Pre-test analysis is vital for proper choice of experimental conditions at which the
experimental data is most useful for code validation and benchmarking. The goal of
this work is to identify optimal conditions in TALL-3D facility that can be used for
validation of standalone STH and coupled STH-CFD codes.
Previous tests in TALL-3D facility indicate oscillatory flow behaviour that can
develop between the two competing hot legs [39]. However, it was not immediately
clear if periodic flow and temperature oscillations in TALL-3D facility can last for a
long time without change in their amplitude and frequency.
Phenomena of periodic flow oscillations under steady boundary conditions are of
interest due to the importance of natural circulation instability for safety of
Generation IV reactors [46]. Furthermore, the presence of periodic phenomena
(especially limit cycle oscillations) provides challenging data for code validation
because of relatively long transient times and sensitivity of the transient
characteristics (such as flow recovery from stagnation, the period of the oscillations,
etc.) to the modelling of thermal and local flow losses.
Timing on the flow redistribution between different flow paths in the facility during
natural circulation instabilities can be highly sensitive to the modelling of thermal
and flow losses making it a challenging test for STH code benchmarking.
Experimental exploration and identification of long term natural circulation
instabilities is a very difficult task, given the number of tests which would be needed
as well as practical limitations in operation of the facility.
The objective of this work is to investigate the possibility of existence of long term
natural circulation instabilities in TALL-3D facility and to identify optimal test
conditions suitable for standalone STH validation, considering operational limits of
the facility.
6.1. SEARCHING FOR INSTABILITIES
TALL-3D RELAP5 model described in chapter 5.1 is used for searching for the
conditions at which transition from forced to natural circulation can result in a
periodic flow instability and limit cycle oscillations.
In all of the simulations, the power of the main heater and 3D test section heater are
constant throughout the transient. The transient is initiated by tripping the EPM
pump. Secondary side heat removal is adjusted for every simulation based on the
42 | NATURAL CIRCULATION INSTABILITIES IN TALL-3D FACILITY
combined electrical power of the two heaters. All transient calculations are
performed for 15 000 seconds to capture system behaviours with long period.
The mass flow rates through the two heated legs in natural steady state are
dependent on the balance of heat input and heat losses to the ambient air. We are
looking for the combinations of the 3D test section and main heater powers that will
result in natural circulation flow instability and limit cycle oscillations. A heat
balance over the 3D test section can be predicted by RELAP5 for steady state
conditions, thus it is expected that the prediction will be more reliable when the mass
flow rate changes in 3D test section leg are negligible.
In a general case, when the number of free parameters is large, and the range of the
parameter values significant, such search might take significant amount of
computational time. To reduce the number of simulations on one hand and to find
more details about the optimal heater powers for development of natural circulation
instabilities on the other hand, a two-step procedure is applied.
First, a search for the test conditions where oscillatory flow behaviour can be
expected within wider ranges of the input parameters is conducted. A global
optimum search tool GA-NPO based on the genetic algorithm [31] (more details in
section 2.2) is applied to identify the regions in the input parameter space where
oscillations can occur. Then, a grid study is performed to calculate system response
near the identified instable domain.
Two objectives were defined for the GA search process:
i. finding scenarios with limit cycle oscillation that might be challenging for
prediction by STH codes and,
ii. minimizing 3D effects to enable separate effect STH validation.
Respectively, the FF was defined as the amplitude of flow oscillations in the MH leg
divided by the minimum mass flow rate in the MH leg. This means the fitness value
is larger in case of oscillatory behaviour at low MH leg mass flow rates and smaller
if oscillatory behaviour occurs at high MH leg mass flow rates. The latter indicating
possible flow regime change in the 3D test section, an operating regime not
accurately resolved by STH codes.
The mass flow rate amplitude was calculated by evaluating the difference between
the maximum and minimum flow rates during a 5000 seconds period. To eliminate
the influence of oscillations occurring at the start of the transient and to focus on
identification of quasi periodic, long term oscillatory flow behaviour, the FF was
evaluated after 10000 seconds from the initiation of the transient. As for the
parameter space, both heater powers were varied between 500 and 7500 W.
NATURAL CIRCULATION INSTABILITIES IN TALL-3D FACILITY | 43
Obtained fitness function values are shown in Figure 23, where calculations marked
with black dots represent cases that did not successfully finish due to flow stagnation
and consequently critically high temperatures in the heated sections. As can be seen
in the figure, the cases that have largest values of FF (corresponding to the larger
amplitudes of periodic flow instabilities) where found at the lower boundary of the
main heater power (500 W) and at relatively high 3D test section heater power (6220
W). This also explains the sampling density being much higher in the region with
lower main heater power. The parameter space is reasonably covered also in the
regions where oscillations do not occur as a result of stochastic element in the GA
search process.
Figure 23: GA-NPO results for an oscillatory behaviour search in the MH leg. Black
filled circles represent failed calculations (due to reaching temperatures outside of
the ranges for calculation of material properties), coloured circles represent
successful calculations where colour denotes the value of the scenario FF.
A grid study was conducted in order to further investigate the parameter space in
the vicinity of flow instabilities region. Oscillatory behaviour of the mass flow rate in
the main heater leg was found to occur only at relatively low main heater powers,
therefore the main heater power is sampled from 200 to 1500 watts with a step of
25 watts and the 3D test section heater power is sampled from 3250 to 15000 watts
with a step of 250 watts, increasing the maximum value compared to GA search.
In total 2544 calculations were performed to study the oscillatory behaviour region
in addition to 448 calculations that were needed by the genetic algorithm analysis to
identify the region of interest in the first place.
44 | NATURAL CIRCULATION INSTABILITIES IN TALL-3D FACILITY
Figure 24: Applying the fitness function used in the GA-NPO search to the
scenarios simulated for the grid study for a better comparison. Black circles
represent failed calculations, coloured circles represent successful calculations
where colour denotes the value of the scenario FF.
Figure 25: MH leg mass flow rates [kg/s] for selection of cases in the grid study.
Red cross indicates a failed calculation.
NATURAL CIRCULATION INSTABILITIES IN TALL-3D FACILITY | 45
To visualize the results, the same fitness function is used for the grid study as was
used in the global optimum search calculations. The results are shown in Figure 24.
Cases marked with black dots resulted in LBE temperature going out of the range of
the material property tables in the code (stagnation of the flow in the MH leg).
Several oscillatory flow regimes are present in this parameter space as can be seen
in Figure 25. Scenarios with very low MH power result in constant negative flow in
the MH leg (left blue area in Figure 24). Increasing the MH power first leads to
stagnation of flow (black area in Figure 24) which leads to the numerical failures.
Further increase of the MH power will result in development of oscillatory behaviour
(light blue to red area in Figure 24). Transition to fast decaying oscillations is
observed at even higher MH power (right blue area in Figure 24).
Decay ratio (DR) of the mass flow rate oscillations was used to identify occurrence
of limit cycle oscillations (LCO). For each simulation, mass flow rate in the MH leg
was evaluated and last two oscillation peaks automatically identified. DR was
defined as a ratio:
𝐷𝑅 =
�̇�𝑝𝑒𝑎𝑘(𝑁) − �̇�𝑎𝑣𝑔
�̇�𝑝𝑒𝑎𝑘(𝑁 − 1) − �̇�𝑎𝑣𝑔 (3)
where �̇�𝑝𝑒𝑎𝑘(𝑁) and �̇�𝑝𝑒𝑎𝑘(𝑁 − 1) are values of the flow rate at the last and the
previous peak of the flow rate respectively; �̇�𝑎𝑣𝑔 is an average mass flow rate and
was estimated using a linear fit to capture long term increasing or decreasing flow
rate trends. DR values larger / smaller than 1 indicate growing / decaying amplitude
of the oscillations respectively. The LCO condition is reached when the DR is equal
to unity.
An example of the simulation with DR closest to unity (with 800 W in the main
heater and 12000 W in the 3D test section heater) is shown in Figure 26. At the end
of the transient, the evaluated DR is equal to 1.001. It can be seen from the figure
that after the initial period, the system is close to a limit cycle. This is further
visualized in lower right graph in Figure 26 where the mass flow rates of the two
competing hot legs are plotted against each other.
The parameters that drive the oscillatory behaviour of the mass flow rate are the
balance between the power-to-heated volume ratios in the hot legs, the residence
time of the LBE in a given heated volume and the time it takes for the heated LBE to
pass through the riser of each leg. After initial pump trip at time zero, the mass flow
rate in the MH leg drops and becomes negative. Loop behaviour at this time is driven
by the 3D test section heater. After ~15 minutes, the flow in the MH leg recovers and
an oscillatory behaviour develops in the loop.
46 | NATURAL CIRCULATION INSTABILITIES IN TALL-3D FACILITY
Figure 26: A scenario with DR closest to unity.
Relatively high power in the 3D test section results in the LBE flow circulating
mainly between the 3D leg and the HX leg. As the flow in the MH leg nearly
stagnates, the average LBE temperature in the MH leg rises increasing the buoyancy
force. Once the hydrostatic pressure at the inlet of MH leg falls below the pressure
at the inlet to 3D leg, the mass flow in the MH leg accelerates moving the hot LBE
from the main heater leg to the heat exchanger leg. At the same time, MH leg is filled
with cold LBE at the inlet. This results in temporary decrease in the buoyancy force
acting on the LBE in the MH leg. This result in the next cycle of near stagnation of
the flow in the main heater leg.
As seen in Figure 26, the main heater section outlet temperature oscillates with an
amplitude of 100°C while 3D test section and heat exchanger outlet temperatures
remain relatively constant (oscillation amplitude of 5°C).
6.2. EXPERIMENTAL RESULTS
Experimental validation of possible long term natural circulation instabilities in
TALL-3D was done with an experiment using MH heater at 755 W and 3D test
section heater at 10400 W. Secondary side mass flow rate was set to 1 kg/s (54%
pump power) and oil temperature at the inlet of the HX at 126°C. Initial steady state
was achieved with 4.76 kg/s LBE mass flow rate in the heat exchanger leg. At time
zero the EPM pump was stopped and natural circulation developed.
NATURAL CIRCULATION INSTABILITIES IN TALL-3D FACILITY | 47
Experimental results for mass flow rates and temperatures of LBE in the primary
system are shown in Figure 27 and Figure 28. It is clear from the results that natural
circulation instabilities can be achieved experimentally in TALL-3D facility.
Figure 27: Mass flow rates in the three legs during verification experiment.
Figure 28: LBE temperatures at key locations during verification experiment.
This work related to natural instability region identification in the TALL-3D
experimental facility resulted in an international benchmark in EU project SESAME.
48 | NATURAL CIRCULATION INSTABILITIES IN TALL-3D FACILITY
CODE COUPLING | 49
7. CODE COUPLING
As discussed in the background, the main motivation behind coupling 1D STH and
3D CFD codes is to achieve the required accuracy with affordable computational
effort. Recent works on code coupling in the field of nuclear safety include [16], [47]–
[52].
In general, coupling methodologies can be divided into two main approaches [53]:
• Domain overlapping – STH resolves the whole facility, CFD resolves the
3D domain and STH solution is corrected according to CFD solution.
• Domain decomposition – STH resolves only 1D domain of the facility,
CFD resolves the 3D domain and boundary conditions are exchanged
between the codes.
The illustration of the two approaches with TALL-3D facility example can be seen in
Figure 29.
Figure 29: Domain overlapping and decomposition coupling approaches.
In this work, the two codes used for coupling were Star-CCM+ (CFD) and RELAP5
(STH). The lack of access to source code for both codes was a restriction in
developing an efficient coupling algorithm as information exchange between
RELAP5 and Star-CCM+ had to be executed out of random access memory (using
text files).
50 | CODE COUPLING
To choose a coupling approach several aspects of the specific coupling application
need to be considered. The amount and type of variables that are to be exchanged
need to be identified, the locations of 1D-3D boundaries need to be defined and the
frequency of the data exchange must be evaluated.
TALL-3D facility was designed to provide clear locations for the information to be
exchanged between the codes. The boundaries of the 1D and 3D domains (3D test
section inlet and outlet) are instrumented with the in-flow thermocouples and
pressure transducers. The information to be exchanged is temperature and mass
flow rate of LBE as well as pressure drop over the section.
A representative TALL-3D experiment features forced to natural flow transient with
a period of time during which mass flow rates in the legs fluctuate driven by
buoyancy. A relatively long time (~10000 seconds) is usually necessary to reach a
steady state natural circulation. To avoid code stability issues at low flow rates and
discontinuity in the STH solution, the domain overlapping approach was selected
for application to TALL-3D facility.
Star-CCM+ and RELAP5 were coupled using a built-in java macro capability of Star-
CCM+. This enables easy access to Star-CCM+ variables and execution of external
scripts.
The algorithm composes of the following steps (see also Figure 30):
1. A common steady state is achieved in both STH and CFD codes.
2. Coupling time step starts with STH calculation providing boundary
conditions (flow rate and inlet temperature) to CFD.
3. CFD calculates the same coupling time step.
4. Difference in STH and CFD solutions is evaluated against a convergence
criterion (e.g. a difference between outlet temperatures in STH and CFD).
5. Based on the difference, correction terms are calculated for STH in order to
achieve the same solution for the outlet parameters as provided by CFD.
6. If needed, STH calculates a new solution for the same coupling time step until
convergence criterion or maximum iteration limit is reached. If convergence
is not reached, coupling time step should be decreased. If number of
iterations to achieve the convergence is small, the coupling time step can be
increased to increase overall computational efficiency.
7. Return to step 2.
STH model is composed of the whole facility including valves, heaters as well as EPM
pump. Therefore, change in mass flow rate in the system (e.g. pump trip) or changes
in the 3D test section inlet temperature (defined by the loop behaviour) will be
resolved by the STH model. In order to reflect these changes in the CFD boundary
conditions during the same coupling time step, it is important to initiate coupling
CODE COUPLING | 51
time step with a single STH calculation. When coupling was initiated with a CFD
calculation, the boundary conditions had to be extrapolated from previous time
steps. This method failed to capture a rapid mass flow rate change during the
coupling time step.
Figure 30: STH-CFD coupling flowchart.
Internal STH and CFD time steps can be equal or smaller than the coupling time step
(see Figure 31). The selection of the coupling time step is governed by the timescales
of the phenomena in the simulation. STH solution not converging to the CFD
solution is one indication that the coupling time step should be reduced.
Figure 31: Time steps in coupled codes.
52 | CODE COUPLING
The temperature correction is done with a set of “virtual heaters” connected to each
STH node (shown as red elements in Figure 32) of the 3D test section model. The
virtual heaters are constructed of a material with negligible heat capacity and high
conductivity to minimize the time it takes for the heaters to change the LBE
temperature in the nodes.
Figure 32: Exchange of data between STH and CFD.
Coupling algorithm calculates the temperature difference for each node in STH and
corresponding volume in CFD. It then evaluates how much additional energy should
be provided to (or removed from) each node to match the temperature distribution
in the CFD solution.
Correcting the temperature distribution in the test section has an effect on the
hydrostatic component of the pressure drop over the 3D test section. In case
additional pressure drop correction is needed (e.g. large local flow losses due to jet
interactions with the flow deflection plate at high flow rates), k-loss coefficient in the
test section pool outlet junction is evaluated from CFD simulation and corrected in
STH.
The algorithm can resolve both forward and reverse flows automatically. When the
algorithm identifies flow reversal in the STH solution, the inlet and outlet
boundaries are changed in CFD and STH.
To evaluate the performance of the developed coupled RELAP5 - Star-CCM+ code,
a forced to natural circulation transient was simulated with standalone RELAP5 and
with coupled RELAP5 – Star-CCM+. The results were compared to the experiment
and are shown in Figure 33 and Figure 34.
CODE COUPLING | 53
Figure 33: Comparison of standalone STH, coupled STH-CFD and experimental
mass flow rate in the 3D leg.
Figure 34: Comparison of standalone STH, coupled STH-CFD and experimental
LBE temperatures at the inlet and outlet of the test section.
These initial results indicate significant improvement of the RELAP5 solution when
coupled with Star-CCM+.
CONTRIBUTION TO CODE COUPLING: Developed RELAP5 inputs, carried
out all RELAP5 calculations and contributed significantly to the overall development
of the coupling methodology.
54 | CODE COUPLING
TALL-3D SOLIDIFICATION TEST SECTION | 55
8. TALL-3D SOLIDIFICATION TEST SECTION
Coolant solidification is a phenomenon of potential safety importance for liquid
metal cooled fast reactors. Solidification can affect local heat transfer and lead to
partial or complete blockage of coolant flow path. This in turn might lead to failure
of decay heat removal systems.
Figure 35: Possible solidification location in an LFR heat exchanger during loss of
flow and overcooling accident.
Prediction of possible outcomes for scenarios with complex interactions between
local physical phenomena of solidification and system scale natural circulation
behaviour is subject to modelling uncertainty. Development and validation of
adequate models requires validation grade experimental data [54].
A modification to the TALL-3D experimental facility is envisioned under EU project
SESAME, adding a solidification test section (STS) to the system where active
cooling of the test section walls would allow for local solidification of LBE. When
changing an existing experimental configuration, the influence of the change upon
the whole system behaviour has to be investigated. Prior to the implementation of
solidification test section, TALL-3D was mainly used for providing validation data
for standalone STH and CFD codes. An important property of the facility has been
the “competition” between the two hot legs resulting in flow instabilities at natural
circulation conditions. During TALL-3D initial designing phase it was foreseen that
the short-term flow instabilities in the facility could be amplified by increasing the
volume of the main heater leg. In the pre-STS configuration, LBE volume in the 3D-
leg is approximately four times that of the main heater leg. Assuming equal (or less
56 | TALL-3D SOLIDIFICATION TEST SECTION
asymmetric) configuration of the two hot legs a more pronounced parallel channel
instabilities can be present [55].
TALL-3D system analysis with solidification test section was performed using the
RELAP5 model of the facility. RELAP5, being a 1D STH code, does not provide
options to simulate solidification and all calculations were performed with no
cooling of the STS focusing on the natural circulation instabilities of the system. The
goal of the analysis is to verify that increasing the main heater leg volume by adding
an additional test section will result in an increased instability in the facility at
natural circulation conditions.
The effect of nodalization in the model input was analysed using simulations with 1,
3 and 6 nodes for STS with dimensions H=300 mm, D=92.1 mm. The dimensions
correspond to 11 times increase of the flow area and respective added volume of ~1.8
litres. Increasing the number of nodes increases the amplitude of the flow
oscillations as shown in Figure 36 (reduced numerical diffusion). There is only a
relatively small quantitative difference between the results obtained with 3 and 6
nodes (10 and 5 cm node height, respectively). The onset of instability is predicted
in both cases, only the amplitude is slightly under-predicted with 3 nodes. However,
mesh with 6 nodes will be used in the following analysis.
Figure 36: Results of the RELAP5 TALL-3D STS nodalization study.
Several cases of forced to natural circulation transient with constant power of 2.5
kW in both heaters were simulated (see Table 13). In each case the location of the
STS was in the main heater leg just above the heater.
TALL-3D SOLIDIFICATION TEST SECTION | 57
Table 13: RELAP5 simulations with varying STS diameter.
Simulation STS Diameter
[mm]
Added Volume
[l]
5x flow area 62.3 0.5
15x flow area 107.9 1.8
25x flow area 139.3 3.0
99x flow area 277.2 12.3
Figure 37: Mass flow rate in the main heater leg for different STS configurations
with varying diameter.
Figure 38: Main heater outlet temperature for different STS configurations with
varying diameter.
Figure 37 and Figure 38 show that a STS volume of about 1.8 – 3.0 litres would be
sufficient to create a possibility for instable natural flow circulation when main
58 | TALL-3D SOLIDIFICATION TEST SECTION
heater and 3D test section heater powers are equal. The results in the figures are
compared to the original design (indicated ORIGINAL) without the added volume
(using only standard TALL-3D piping with volume of 0.125 litres).
First series of pre-test simulations were performed with STS positioned above the
main heater in the main heater leg. Further analysis was conducted with STS
positioned at the top of the main heater leg, just below the expansion tank Figure 39.
Results (Figure 40) show that higher position for the STS pool would result in more
stable flow conditions than lower position.
Figure 39: Possible future STS locations in TALL-3D facility.
Figure 40: Mass flow rates in all three primary legs with STS positioned at high and
low elevations.
TALL-3D SOLIDIFICATION TEST SECTION | 59
Based on the results of RELAP5 and Star-CCM+ pre-test analysis (CFD analysis is
described in detail in Paper V), requirements for instrumentation, safety and
manufacturing, the final configuration of the TALL-3D facility with STS is defined
(Figure 41).
Figure 41: TALL-3D facility with proposed solidification test section.
60 | TALL-3D SOLIDIFICATION TEST SECTION
TALL-3D solidification test section (Figure 42) is a rectangular vessel made of
stainless steel with inlet at the bottom and outlet at the top (nominal flow direction).
The left side of the STS has a rectangular flange to which different instrumentation
can be connected. The top and right side are equipped with active water cooling. The
pool inner dimensions are 200x200x52 mm. The inlet and outlet pipes adjacent to
the test section have rectangular profile with inner dimensions of 27x52 mm. For the
connection to the TALL-3D piping those are further reduced to circular cross-section
with inner diameter of 27.8 mm. The wall thickness around the solidification section
is 7 mm. The front and back walls are additionally equipped with stiffeners to
minimize bulging.
Figure 42: STS design with FBG probes.
Three sets of instrumentation have been chosen for the measurement of the
solidification front and characterization of the flow in the STS pool:
• Thermocouples for temperature measurement outside and inside the pool,
• Fiber Bragg gratings (FBGs) for temperature measurement inside the pool,
• Ultrasound Doppler Velocimetry (UDVs) for measurement of the LBE
velocity and location of the solidus front.
TALL-3D SOLIDIFICATION TEST SECTION | 61
CONTRIBUTION TO PAPER V: TALL-3D facility with various STS designs was
analysed. The dimensions of the test section, positioning of the section in the loop
and possible feedbacks during natural circulation were investigated; most promising
parameters for facility modification proposed.
62 | TALL-3D SOLIDIFICATION TEST SECTION
SUMMARY | 63
9. SUMMARY
The ultimate goal of this thesis work is to provide contributions towards
development of methods, data and tools for qualifying multiscale codes and facilitate
their application to design and safety analysis of Generation IV metal cooled
reactors.
An approach to data post-processing was developed and implemented in order to
enable selection of a large number of SRQs in the STH code output as a fitness
function in the global optimum search. This feature was instrumental for automated
calibration of the input model and code validation reducing the “user effect” on the
resulting uncertainty estimation. Complex system of data processing and exchange
between STH code RELAP5, post-processing scripts in MATLAB and global
optimum search tool GA-IDPSA was developed and applied to all code calibration
and validation activities presented in the thesis.
The developed search methodology was instrumental in identification of natural
instability region in TALL-3D facility operational parameter space. Experimental
verification of said instability region resulted in an international benchmark test in
EU project SESAME for support of code qualification activities.
Contributions to TALL-3D facility development include RELAP5 analysis to support
facility design featuring thermal-hydraulic feedbacks between 1D and 3D
components, identification of operational parameters for dedicated tests on
calibration of measurement equipment as well as carrying out experiments to
produce validation grade data for standalone and coupled code validation. Data
produced at the TALL-3D facility has been used by a number of European
institutions for code qualification purposes. In addition, TALL-3D facility RELAP5
model was calibrated and validated for application with coupled STH-CFD code.
Contributions to coupled code development include RELAP5 TALL-3D input model
development for data exchange and an implementation of the algorithm, for STH
solution corrections according to CFD simulation. Coupled code methodology
development resulted in RELAP5-Star-CCM+ coupled code which improved
considerably standalone RELAP5 solution during forced to natural circulation
transient.
In support of TALL-3D facility modifications to include solidification test section,
RELAP5 model was used to evaluate the natural circulation instabilities at equal
powers of the main and 3D test section heaters. STS dimensions and location
selection were based on STH code analysis allowing more symmetric instabilities in
natural circulation regime in the TALL-3D facility in the future. Flow reversals,
64 | SUMMARY
induced by the symmetric instabilities, in both hot legs will increase the difficulty of
accurate code prediction and therefore increase the value of experimental data.
BIBLIOGRAPHY | 65
BIBLIOGRAPHY
[1] D. Bodansky, Nuclear energy: principles, practices, and prospects. Springer Science
& Business Media, 2007.
[2] U.S. DOE Nuclear Energy Research Advisory Committee and The Generation IV
International Forum, “A Technology Roadmap for Generation IV Nuclear Energy
Systems,” GIF-002-00, Dec. 2002.
[3] A. Alemberti, V. Smirnov, C. F. Smith, and M. Takahashi, “Overview of lead-cooled
fast reactor activities,” Prog. Nucl. Energy, vol. 77, pp. 300–307, 2014.
[4] A. V. Zrodnikov, G. I. Toshinsky, O. G. Komlev, V. S. Stepanov, and N. N. Klimov,
“SVBR-100 module-type fast reactor of the IV generation for regional power
industry,” J. Nucl. Mater., vol. 415, no. 3, pp. 237–244, 2011.
[5] Y. G. Dragunov, V. V. Lemekhov, V. S. Smirnov, and N. G. Chernetsov, “Technical
solutions and development stages for the BREST-OD-300 reactor unit,” At. Energy,
vol. 113, no. 1, pp. 70–77, 2012.
[6] C. F. Smith, W. G. Halsey, N. W. Brown, J. J. Sienicki, A. Moisseytsev, and D. C.
Wade, “SSTAR: The US lead-cooled fast reactor (LFR),” J. Nucl. Mater., vol. 376,
no. 3, pp. 255–259, 2008.
[7] G. Grasso et al., “The core design of ALFRED, a demonstrator for the European lead-
cooled reactors,” Nucl. Eng. Des., vol. 278, pp. 287–301, 2014.
[8] OECD Nuclear Energy Agency, “Technology Roadmap Update for Generation IV
Nuclear Energy Systems,” 2014.
[9] A. Petruzzi and F. D’Auria, “Thermal-hydraulic system codes in nulcear reactor safety
and qualification procedures,” Sci. Technol. Nucl. Install., vol. 2008, no. vi, pp. 1–16,
2008.
[10] N. R. C. Job and W. Code, “RELAP5 / MOD3 Code Manual,” 1995.
[11] U. S. NRC, “TRACE V5. 0 Theory Manual-Field Equations, Solution Methods, and
Physical Models,” United States Nucl. Regul. Comm., 2010.
[12] T. Hamidouche, A. Bousbia-Salah, M. Adorni, and F. D’Auria, “Dynamic
calculations of the IAEA safety MTR research reactor Benchmark problem using
RELAP5/3.2 code,” Ann. Nucl. Energy, vol. 31, no. 12, pp. 1385–1402, Aug. 2004.
[13] W. L. Woodruff, N. A. Hanan, R. S. Smith, and J. E. Matos, “A comparison of the
PARET/ANL and RELAP5/MOD3 codes for the analysis of IAEA benchmark
transients,” in Abstracts and papers of the 1996 International RERTR Meeting, 1996,
p. 233.
[14] C. M. Allison and J. K. Hohorst, “Role of RELAP/SCDAPSIM in nuclear safety,” Sci.
Technol. Nucl. Install., vol. 2010, 2010.
66 | BIBLIOGRAPHY
[15] M. J. Thurgood, J. M. Kelly, T. E. Guidotti, R. J. Kohrt, and K. R. Crowell,
“COBRA/TRAC-A thermal hydraulics code for transient analysis of nuclear reactor
vessels and primary coolant systems. NUREG/CR-3046,” NUREG/CR-3046, vol. 1.
US Nuclear Regulatory Commission, 1983.
[16] D. L. Aumiller, E. T. Tomlinson, and R. C. Bauer, “A Coupled RELAP5-3D/CFD
methodology with a proof-of-principle calculation,” Nucl. Eng. Des., vol. 205, no. 1–
2, pp. 83–90, Mar. 2001.
[17] F. Cadinu and P. Kudinov, “Development of a ‘ Coupling-by-Closure ’ Approach
between CFD and System Thermal-Hydraulics Codes .,” Fluid Dyn., pp. 1–12, 2009.
[18] M. Jeltsov, K. Kööp, W. Villanueva, and P. Kudinov, “Development of multi-scale
simulation methodology for analysis of heavy liquid metal thermal hydraulics with
coupled STH and CFD codes,” in Nuthos-9, 2012, pp. 1–18.
[19] M. Jeltsov, K. Kööp, P. Kudinov, and W. Villanueva, “Development of a domain
overlapping coupling methodology for STH/CFD analysis of heavy liquid metal
thermal-hydraulics,” in NURETH-15, The International Topical Meeting on Nuclear
Reactor Thermal-Hydraulics, Pisa, Italy, MAY 12-17, 2013, 2013, pp. 1–18.
[20] W. L. Oberkampf and C. J. Roy, Verification and Validation in Scientific Computing.
Cambridge University Press, 2010.
[21] W. L. Oberkampf and T. G. Trucano, “Verification and Validation in Computational
Fluid Dynamics,” Albuquerque, New Mexico, Apr. 2002.
[22] C. J. Roy and W. L. Oberkampf, “A comprehensive framework for verification,
validation, and uncertainty quantification in scientific computing,” Comput. Methods
Appl. Mech. Eng., vol. 200, no. 25–28, pp. 2131–2144, Jun. 2011.
[23] I. Mickus, “Quantitative Approach to APROS Code Validation against TALL-3D
Experimental Data,” KTH Royal Institute of Technology, 2015.
[24] P. Kudinov, D. Grishchenko, I. Mickus, K. Kööp, and M. Jeltsov, “TALL-3D setup
for first series,” SESAME Project Report D4.5, 2016.
[25] V. A. Phung, K. Kööp, D. Grishchenko, Y. Vorobyev, and P. Kudinov, “Automation
of RELAP5 input calibration and code validation using genetic algorithm,” Nucl. Eng.
Des., vol. 300, pp. 210–221, 2016.
[26] F. Cadinu, M. Jeltsov, W. Villanueva, K. Kööp, A. Karbojian, and P. Kudinov,
“Program of work for experimental tasks, software development and validation tasks
on TALL (KTH contribution),” THINS deliverable D5.2.01/M5.2.01, Stockholm,
Sweden, 2011.
[27] M. Jeltsov, F. Cadinu, W. Villanueva, and a Karbojian, “An Approach to Validation
of Coupled CFD and System Thermal-Hydraulics Codes.,” in Nureth-14, 2011.
[28] K. Kööp, M. Jeltsov, D. Grishchenko, and P. Kudinov, “Pre-test analysis for
identification of natural circulation instabilties in TALL-3D facility,” Nucl. Eng. Des.,
vol. 314, pp. 110–120, 2017.
BIBLIOGRAPHY | 67
[29] G. Barone, N. Forgione, D. Martelli, and W. Ambrosini, “System codes and a CFD
codes applied to loop- and pool-type facilities,” Tech. Rep. CERSE-UNIPI RL
1530/2013, 2013.
[30] V. Sobolev, “Database of thermophysical properties of liquid metal coolants for GEN-
IV,” SCK•CEN-BLG-1069, 2010.
[31] Y. Vorobyov and T.-N. Dinh, “A Genetic Algorithm-Based Approach to Dynamic
PRA Simulation,” in ANS PSA 2008 Topical Meeting - Challenges to PSA during the
nuclear renaissance, 2008.
[32] I. Mickus, K. Kööp, M. Jeltsov, Y. Vorobyev, W. Villanueva, and P. Kudinov, “An
approach to physics based surrogate model development for application with IDPSA,”
in PSAM 2014 - Probabilistic Safety Assessment and Management, 2014.
[33] R. P. M. Silva, A. C. B. Delbem, and D. V. Coury, “Genetic algorithms applied to
phasor estimation and frequency tracking in PMU development,” Int. J. Electr. Power
Energy Syst., vol. 44, no. 1, pp. 921–929, Jan. 2013.
[34] R. Aguilar-Rivera, M. Valenzuela-Rendón, and J. J. Rodríguez-Ortiz, “Genetic
algorithms and Darwinian approaches in financial applications: A survey,” Expert
Syst. Appl., vol. 42, no. 21, pp. 7684–7697, Nov. 2015.
[35] C. H. Lin, “A rough penalty genetic algorithm for constrained optimization,” Inf. Sci.
(Ny)., vol. 241, pp. 119–137, Aug. 2013.
[36] B. W. Cheng and C. L. Chang, “A study on flowshop scheduling problem combining
Taguchi experimental design and genetic algorithm,” Expert Syst. Appl., vol. 32, no.
2, pp. 415–421, Feb. 2007.
[37] C. P. Marcel, M. Rohde, and T. der Hagen, “Out-of-phase flashing induced
instabilities in the CIRCUS facility,” in Proceedings of the 11th International Topical
Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11), 2005, pp. 1–7.
[38] V.-A. Phung, P. Kudinov, D. Grishchenko, and M. Rohde, “Input calibration and
validation of RELAP5 against CIRCUS-IV single channel tests on natural circulation
two-phase flow instability,” Sci. Technol. Nucl. Install., vol. 2015, 2015.
[39] D. Grishchenko, M. Jeltsov, K. Kööp, A. Karbojian, W. Villanueva, and P. Kudinov,
“The TALL-3D facility design and commissioning tests for validation of coupled STH
and CFD codes,” in Nuclear Engineering and Design, 2015, vol. 290, pp. 144–153.
[40] M. Jeltsov, K. Kööp, W. Villanueva, D. Grishchenko, and P. Kudinov, “Validation of
a CFD Code Star-CCM + for Liquid Lead-Bismuth Eutectic Thermal-Hydraulics
Using TALL-3D Experiment,” in The 10th International Topical Meeting on Nuclear
Thermal-Hydraulics, Operation and Safety (NUTHOS-10), 2014, pp. 1–14.
[41] C. Fazio et al., “Handbook on Lead-bismuth Eutectic Alloy and Lead Properties,
Materials Compatibility, Thermal-hydraulics and Technologies-2015 Edition,” 2015.
[42] D. Grishchenko, K. Kööp, M. Jeltsov, I. Mickus, and P. Kudinov, “TALL-3D test
series for calibration and validation of coupled thermal- hydraulics codes,” Nureth-
68 | BIBLIOGRAPHY
17, 2017.
[43] M. D. Morris, “Factorial sampling plans for preliminary computational experiments,”
Technometrics, vol. 33, no. 2, pp. 161–174, 1991.
[44] B. M. Adams et al., “A Multilevel Parallel Object-Oriented Framework for Design
Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity
Analysis,” Sandia Tech. Rep. SAND2014-4633, no. 2010–2183, 2011.
[45] S. S. Wilks, “Determination of Sample Sizes for Setting Tolerance Limits,” Ann.
Math. Stat., vol. 12, no. 1, pp. 91–96, 1941.
[46] F. Roelofs et al., “European Outlook for Lmfr Thermal Hydraulics,” in NURETH-16,
Chicago, IL, August 30-September 4, 2015, 2015, pp. 7414–7425.
[47] H. Gibeling and J. H. Mahaffy, “Benchmarking Simulations with CFD to 1-D
Coupling,” in Joint IAEA/NEA Technical Meeting on the use of Computational Fluid
Dynamics (CFD) Codes for Safety Analysis of Reactor Systems, Pisa, Italy, 2002.
[48] W. L. Weaver, E. T. Tomlinson, and D. L. Aumiller, “A generic semi-implicit
coupling methodology for use in RELAP5-3D,” Nucl. Eng. Des., vol. 211, no. 1, pp.
13–26, Jan. 2002.
[49] D. Bertolotto, A. Manera, S. Frey, and H.-M. Prasser, “Single-phase mixing studies
by means of a directly coupled CFD/system-code tool,” Ann. Nucl. Energy, vol. 36,
no. 3, pp. 310–316, Apr. 2009.
[50] A. Papukchiev, G. Lerchl, J. Weis, M. Scheuerer, and H. Austregesilo, “Development
of a coupled 1D-3D thermal-hydraulic code for nuclear power plant simulation and its
application to a pressurized thermal shock scenario in PWR,” 2011.
[51] R. Bavière, N. Tauveron, F. Perdu, E. Garré, and S. Li, “A first system/CFD coupled
simulation of a complete nuclear reactor transient using CATHARE2 and TRIO_U.
Preliminary validation on the Phénix Reactor Natural Circulation Test,” Nucl. Eng.
Des., vol. 277, pp. 124–137, 2014.
[52] T. Watanabe, Y. Anoda, and M. Takano, “System–CFD coupled simulations of flow
instability in steam generator U tubes,” Ann. Nucl. Energy, vol. 70, pp. 141–146, Aug.
2014.
[53] A. Papukchiev, M. Jeltsov, K. Kööp, P. Kudinov, and G. Lerchl, “Comparison of
different coupling CFD-STH approaches for pre-test analysis of a TALL-3D
experiment,” Nucl. Eng. Des., vol. 290, pp. 135–143, Aug. 2015.
[54] W. L. Oberkampf and B. Smith, “Assessment Criteria for Computational Fluid
Dynamics Validation Benchmark Experiments,” in 52nd Aerospace Sciences
Meeting, 2014.
[55] J. C. Chato, “Natural convection flows in parallel-channel systems,” J. Heat Transfer,
vol. 85, no. 4, pp. 339–345, 1963.