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Research Collection
Doctoral Thesis
Mixing Phenomena Relevant to Thermal Fatigue in T-junctions
Author(s): Kickhofel, John
Publication Date: 2015
Permanent Link: https://doi.org/10.3929/ethz-a-010598898
Rights / License: In Copyright - Non-Commercial Use Permitted
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ETH Library
Diss. ETH No. 22904
MIXING PHENOMENA RELEVANT TO
THERMAL FATIGUE IN T-JUNCTIONS
A thesis submitted to attain the degree of
DOCTOR OF SCIENCES of ETH ZURICH
(Dr.sc. ETH Zurich)
presented by
JOHN LOUIS KICKHOFEL
M.Sc. Nuclear Engineering
ETH Zurich – EPF Lausanne
born on 20.10.1986
citizen of the United States of America
Examiners:
Prof. Dr. Horst-Michael Prasser (ETH Zurich), examiner
Prof. Dr. Eckart Laurien (University of Stuttgart), co-examiner
Prof. Dr. Yassin Hassan (Texas A&M University), co-examiner
dedicated to my parents, Carolyn and Louis
"When it came night, the white waves paced to and fro in the moonlight, and the wind brought the
sound of the great sea's voice to the men on shore, and they felt that they could then be interpreters."
- Stephen Crane (1871-1900), The Open Boat
I
Acknowledgements
This work and I owe a tremendous amount to the guidance and mentorship of my
Doktorvater Prof. Dr. Horst-Michael Prasser. I am forever grateful to have had the chance to
be educated and advised by such a knowledgeable, experienced and passionate
experimentalist over the course of such formative years.
While pursuing my doctoral degree I have had the opportunity to work alongside colleagues
who ensured an environment which was at once welcoming, humorous, supportive and
intellectually rewarding; one which I can only hope to experience again. Namely, those
colleagues are Robert Adams, Paolo D‘Aleo, Hassan Badreddine, Christian Bolesch, Ralph
Eismann, Nathan Lafferty and Abhishek Saxena, among others. I am especially thankful for
all of my colleagues at the Paul Scherrer Institute who have in countless discussions over the
years so adeptly fielded my questions.
I am, furthermore, very thankful for the intelligent and hardworking students who have
passed through our lab, without whom this work would not have been possible. Among them
are those who performed their Master‘s thesis work in the context of my dissertation topic:
Valentina Valori, Lukas Schmidt and Cosimo Trinca. I also had the great pleasure of
supervising Roman Ayer and Christophe Mortier while we navigated the challenges of
developing the new mesh sensor described herein.
I am indebted to the entire IKE/MPA team at the University of Stuttgart for their assistance in
ensuring our fruitful collaboration. Specifically, I would like to thank Prof. Dr. Eckhart
Laurien, Dr. Rudi Kulenovic and Karthick Selvam for their friendly, ready assistance,
patience and trust.
There are, naturally, many other individuals not mentioned here to whom I owe a great deal
with respect to this body of work. Funding has been generously provided by the Swiss
National Science Foundation project #200021_132659 and swissnuclear project #1320.
Finally, I would like recognize Sabina Näf for her steadfast love and companionship for
which I am so incredibly thankful, and also her entire family who have so seamlessly and
generously taken me in.
Zurich, 14th
September 2015
John Kickhofel
II
Abstract
The focus of this thesis is single-phase mixing in the vicinity of T-junctions in nuclear power
plants (NPP) in the context of the thermal fatigue phenomenon driven by large amplitude
water temperature fluctuations. Specific zones of safety-relevant piping in NPPs are known to
be at risk of developing surface and even through-wall crack networks, often in the vicinity of
T-junctions. At certain locations, turbulent mixing and/or thermal stratification are capable of
generating damage-inducing thermal fluctuations of appropriate frequency and amplitude.
Turbulent penetration in T-junctions with weak in-flow, as in the case of a leaking valve
scenario, while representing a mixing scenario from which commercial NPPs have in the past
suffered damage, has yet to be investigated in detail from a fluid-dynamic perspective. This
work has endeavored to provide a comprehensive, foundational exploration of this mixing
scenario experimentally with a high-density of data in space and time domains and in theory
through the utilization of time-resolved CFD simulations. To this end, an adiabatic T-junction
facility for the study of turbulent penetration was constructed and utilized. A large number of
experiments at the facility with custom built instrumentation in the form of wire-mesh
sensors have illuminated important phenomena related to thermal fatigue inducing scenarios,
such as the Farley-Tihange phenomena.
Another underdeveloped, yet highly practical domain related to thermal fatigue in NPP
piping is that of cross-flow mixing in T-junctions at high ΔT, approaching reactor operating
conditions. For the purpose of studying coolant mixing at these conditions, where thermal
stratification begins to dominate, a novel mesh sensor package has been developed and
patented. The new mesh sensor has been successfully trialed in high-temperature cross-flow
mixing experiments (at up to ΔT = 232ºC at 7 MPa) in collaboration with the University of
Stuttgart. The results elucidate not only the downstream temperature profile with
unprecedented resolution, but also countercurrent stratification developing upstream at high
Richardson numbers.
The new mesh sensor technology is potentially applicable to all NPP-relevant pipe flows in
both pressurized and boiling water reactors with a foreseeable temperature resistance of up to
350ºC at 22 MPa. It represents an evolutionary step from prior state-of-the-art in a robust,
scalable package design which could incorporate additional instrumentation in the form of
thermocouples or added mesh sensor layers for recovering velocity or interfacial area
concentration.
III
Zusammenfassung
Der Schwerpunkt dieser Arbeit liegt in der Mischung einphasiger Ströme in der Umgebung
von T-Verbindungen in Kernkraftwerken (KKW) vor dem Kontext der thermomechanischen
Ermüdung durch Temperaturfluktuationen mit hoher Amplitude. Dass bestimmte Zonen in
sicherheitsrelevanten Teilen des Rohrnetzes KKWs für Ermüdungsrisse anfällig sind,
insbesondere im Bereich von T-Verbindungen, ist bekannt. An bestimmten Stellen kann
turbulente Mischung und/oder thermische Schichtung zu thermischen Fluktuationen führen,
deren Höhe und Frequenz geeignet ist, Schäden zu verursachen.
Turbulentes Eindringen der Hauptströmung in schwach durchströmte Abzweigungen von T-
Verbindungen, wie es beispielsweise bei Ventillecks vorkommt, hat in der Vergangenheit in
KKWs zu Schäden geführt. Dieses Phänomen ist bisher nicht ausreichend untersucht worden.
Ziel dieser Arbeit war eine umfassende, grundlegende Untersuchung der turbulenten
Mischungsphänomene, sowohl experimentell als auch durch CFD-Simulationen. Mit diesem
Ziel wurde eine Versuchseinrichtung für die Untersuchung adiabatischer Mischungsvorgänge
aufgebaut. Eine grosse Zahl von Experimenten unter Verwendung von speziell für diesen
Zweck gebauten Gittersensoren hat einige wichtige Strömungsphänomene beleuchtet, die im
Hinblick auf thermo-mechanische Ermündung von grosser Bedeutung sind, beispielsweise
das Farley-Tihange Phänomen.
Ein anderes, wenig untersuchtes aber praktisch relevantes Gebiet ist die Mischung von
Kreuzströmen in T-Verbindungen bei grossen Temperaturdifferenzen, in denen die
Temperaturschichtung dominant ist. Zur Untersuchung der Kühlwassermischung unter diesen
Bedingungen wurde ein neuartiger Gittersensor entwickelt und patentiert. Der neue
Gittersensor wurde in Kooperation mit der Universität Stuttgart bei Temperaturdifferenzen
bis zu 232°C und Drücken von 7 MPa erfolgreich getestet. Die Resultate verdeutlichen nicht
nur das unterstromige Temperaturprofil mit bisher nicht erreichter Auflösung sondern zeigen
auch die Entwicklung einer Temperaturschichtung durch Gegenstrom im oberstromigen
Hauptast der T-Verbindung.
Die neue Gittersensortechnologie ist potenziell für alle relevanten Rohrströmungen in KKWs
mit Druck- und Siedewasserreaktoren einsetzbar, bis hin zu Temperaturen von 350°C und
Drücken von 22 MPa. Das robuste, skalierbaren Design erlaubt zudem die Integration von
Thermoelementen und zusätzlichen Gittersensorebenen. Letztere würden es ermöglichen, die
Verteilung der Strömungsgeschwindigkeit und der Grenzflächendichte über dem
Strömungsquerschnitt zu messen.
IV
Sommario
La ricerca descritta in questa tesi ha come obbiettivo lo studio dei fenomeni di miscelazione
termica che avvengono in prossimità delle giunzioni a T. La presenza di questi componenti
termoidraulici è molto comune nelle tubazioni delle centrali nucleari e spesso costituisce
teatro di fenomeni di fatica termica. Tale fenomeno mette a repentaglio l‘integrità meccanica
delle strutture e, pertanto, la sicurezza dello stesso impianto. L‘origine è attribuita alla
miscelazione turbolenta tra fluidi, spesso flussi d‘acqua, con una differenza di temperatura di
svariate decine di gradi. Lungo le tubazioni metalliche, infatti, le indotte stratificazioni
termiche e/o la miscelazione turbolenta sono in grado di generare fluttuazioni termiche di
rilevante ampiezza nonché frequenze che facilitano la propagazione di cricche nei materiali
costituenti le pareti dei condotti.
Il cosiddetto fenomeno di ―penetrazione turbolenta‖ nelle giunzioni a T in condizioni di
flusso debole, come nel caso di valvole che hanno ormai perso la loro tenuta, rappresenta uno
scenario tipico che, ancora oggi, è causa di preoccupazione per le centrali nucleari
commerciali. Ne consegue la necessità di uno studio maggiormente dettagliato dal punto di
visto fluidodinamico. Pertanto, in questo lavoro si è cercato di fornire una completa
esplorazione sperimentale dei fenomeni di miscelazione che ricalcano i casi succitati. Ciò è
stato reso possibile mediante dati con alta risoluzione spaziale e temporale mentre
teoricamente il contributo è stato apportato dall‘utilizzo di simulazioni in regime transitorio.
A tal fine è stata realizzata una sezione di test che ha permesso di emulare gli scenari di
miscelamento nelle giunzioni a T in condizioni adiabatiche. Inoltre, un vasto numero di
esperimenti è stato condotto tramite strumentazione costruita ad hoc, quale il wire-mesh
sensor, che ha permesso di giungere ad importanti osservazioni relative ai fenomeni di fatica
termica, come quelli avvenuti sia nella centrale di Farley che in quella di Tihange.
Il cross-mixing è un altro di quegli effetti ancora poco studiati nell‘ambito della fatica
termica. Esso risulta più evidente quando ci si avvicina alle condizioni operative reali delle
centrali nucleari, specialmente per alte differenze di temperatura. Allo scopo, poi, di
approfondire lo studio della fluidodinamica in presenza di tali condizioni si è reso necessario
lo sviluppo di un nuovo wire-mesh sensor capace di resistere ad alte pressioni e gradienti di
temperatura (7 MPa a ΔT = 232 °C). La nuova strumentazione è stata brevettata ed utilizzata
con successo in una campagna di misure in collaborazione con l‘Università di Stoccarda. I
risultati non solo hanno messo in luce i profili di temperatura a valle della giunzione a T, con
una risoluzione spaziale e temporale senza precedenti, ma hanno anche evidenziato una
stratificazione termica che si sviluppa a monte per alti valori del numero di Richardson.
Il nuovo equipaggiamento è potenzialmente applicabile a tutte quelle condizioni che si
trovano sia nei Pressurized che nei Boiling Water Reactors con un prevedibile limite in
temperatura che si spinge fino a 350 °C e pressioni fino a 22 MPa. Questo rappresenta un
ulteriore passo evolutivo allo stato dell‘arte, in quanto il progetto e la sua robustezza sono
facilmente scalabili. É anche prevista la possibilità di incorporare strumentazione aggiuntiva
V
come termocoppie, sensori capacitivi o altri wire-mesh sensor, in grado di misurare
grandezze fluidodinamiche rilevanti quali, ad esempio, i campi di velocità e la concentrazione
dell‘area di interfase.
VI
Résumé
Le thème central de cette thèse concerne le mélange à une phase à proximité de jonctions en
T dans les centrales nucléaires, dans le contexte du phénomène de fatigue thermique induit
par des fluctuations à large amplitude de la température de l‘eau. Des zones spécifiques de la
tuyauterie pertinentes pour la sureté des centrales nucléaires comportent un risque de
développer des réseaux de fissures en surface, et même, à travers la paroi à proximité des
jonctions en T. À certaines locations, un mélange turbulent et/ou une stratification thermique
sont capables de générer des fluctuations thermiques de fréquence et d‘amplitude appropriées
induisant des dommages.
Une pénétration turbulente dans les jonctions en T à faible débit entrant, comme dans le cas
d‘un scénario avec une valve fuyante, alors qu‘elle représente un scénario de mélange qui a
par le passé causé des dommages dans des centrales nucléaires commerciales, doit être à
présent investie en détail du point de vue de la dynamique des fluides. Ce travail s‘efforce à
fournir une exploration compréhensive et fondatrice du scénario de mélange par l‘expérience,
avec des données à haute densité spatiale et temporelle, ainsi que théoriquement, par la
simulation numérique CFD à résolution temporel. À cette fin, un banc expérimental,
constitué d‘une jonction en T adiabatique servant à l‘étude d‘une pénétration turbulente, a été
construit et mis en service. De nombreuses expériences conduites avec le banc expérimental
et une instrumentation sur mesure sous forme de grille sensorielle ont mis en lumière des
phénomènes importants en lien avec des scénarios induisant de la fatigue thermale tel que le
phénomène Farley-Tihange.
Un autre domaine encore sous-développé, néanmoins hautement pratique, lié à la fatigue
thermique dans la tuyauterie des centrales nucléaires, est celui du mélange à courant croisé
dans les jonctions de type T à haut différentiel de température approchant les conditions
d‘opération d‘un réacteur. La nouvelle grille sensorielle fut mise à épreuve avec succès lors
d‘expériences de mélange à courant croisé à haute température (jusqu‘à 232°C et 7MPa)
menées en collaboration avec l‘université de Stuttgart. Les résultats élucident non seulement
le profil de température en aval de l‘écoulement, avec une résolution sans précédents, mais
aussi la stratification à contre-courant qui se développe en amont pour les hauts nombres de
Richardson.
La grille sensorielle de technologie nouvelle peut être potentiellement appliquée sur chaque
écoulement dans les parties de la tuyauterie pertinentes d‘une centrale nucléaire à eau
pressurisée ou à eau bouillante avec une résistance à court terme à des températures
atteignant 350°C pour 22MPa. Elle représente une étape évolutive par rapport à la dernière
technologie de pointe, de par sa robustesse et son design évolutif pouvant incorporer une
instrumentation additionnel sous forme de thermocouples ou de couches de grilles
sensorielles supplémentaires afin de reconstituer la vitesse d‘une zone de concentration
interfaciale.
VII
Nomenclature
Latin Characters
f Frequency [Hz]
Fr Froude number [-]
I Raw signal [-]
K Number of ensemble averaged segments [-]
Mass flow rate [kg/s]
p Momentum [kg m/s]
Pr Prandlt number [-]
Q Volumetric flow rate typically [liters/min]
Re Reynolds number [-]
Ri Richardson number [-]
S Arc length [m]
St Strouhal number [-]
T Temperature [ºC]
(t,r) (Wire-) Mesh sensor crossing point
coordinates [-]
U Mean/bulk flow velocity [m/s]
u Local velocity [m/s]
UI Uniformity index [-]
#Db Non-dimensional branch line position [-]
#Dm Non-dimensional main/mixing pipe position [-]
Greek Symbols
α Womersley number [-]
ε Density difference [-] η Dynamic viscosity [kg/m s]
θ Mixing scalar [-]
κ Electrical conductivity [S]
ν Kinematic viscosity [m2/s]
ρ Momentum [kg m/s]
ρ Density [kg/m3]
σ Standard deviation
τ Time constant [s]
ω Angular frequency [Hz]
Vorticity thickness [m]
VIII
Subscripts
b Branch line
i x-component
j y-component
k z-component
m Main or mixing pipe
r Ratio of main pipe to branch line
RMS Root-mean squared
t,r All (Wire-) Mesh Sensor crossing points
Abbreviations
BWR Boiling Water Reactor
CFD Computer Fluid Dynamics
CVCS Chemical & Volume Control System
DAQ Data Acquisition system
EC Electrical Conductivity
EdF Électricité de France
EPRI Electric Power Research Institute
FEM Finite Element Modeling
FSI Fluid-Structure Interaction
HCF High Cycle Fatigue
HCTF High Cycle Thermal Fatigue
IKE Institute of Nuclear Technology and Energy Systems, University of Stuttgart
INSS Institute of Nuclear Safety System
KEPCO Korea Electric Power Corporation
LCF Low Cycle Fatigue
LES Large Eddy Simulation
LKE Laboratory of Nuclear Energy Systems, ETH Zürich
LMFBR Liquid Metal Fast Breeder Reactor
LWR Light Water Reactor
MPA Material Testing Institute, University of Stuttgart
NEA OECD Nuclear Energy Agency
NPP Nuclear power plant
PSD Power Spectral Density
PWR Pressurized Water Reactor
RANS Reynolds-Averaged Navier-Stokes
SGS Sub-grid Scale model
SNR Signal-to-Noise Ratio
TEC Thermal Expansion Coefficient
URANS Unsteady RANS
USNRC United States Nuclear Regulatory Commission
WALE Wall-adapting Local Eddy-viscosity model
WMS Wire Mesh Sensor
IX
Table of Contents Acknowledgements ........................................................................................................................ I
Abstract ......................................................................................................................................... II
Zusammenfassung....................................................................................................................... III
Sommario ..................................................................................................................................... IV
Résumé ......................................................................................................................................... VI
Nomenclature ............................................................................................................................ VII
1 Background ............................................................................................................................ 1
1.1 Five articles ...................................................................................................................... 1
1.2 Introduction ...................................................................................................................... 3
1.2.1 Fatigue....................................................................................................................... 3
1.2.2 Thermal fatigue ......................................................................................................... 3
1.2.3 Thermal stratification ................................................................................................ 6
1.2.4 In nuclear power plants ............................................................................................. 6
1.3 T-junctions ....................................................................................................................... 9
1.3.1 Cross-flow mixing .................................................................................................... 9
1.3.2 Cross-flow simulations ........................................................................................... 14
1.3.3 Turbulent penetration .............................................................................................. 16
1.3.4 Turbulent penetration CFD simulations.................................................................. 24
1.4 Parallels to other disciplines ........................................................................................... 26
1.4.1 Shear-driven cavity flow as an analogy to a dead leg ............................................. 26
1.4.2 Automotive flows analogous to cross-flow mixing ................................................ 26
1.4.3 Shear layer studies .................................................................................................. 27
1.5 Thesis structure and outline............................................................................................ 28
2 Outline of LKE T-junction facility..................................................................................... 30
2.1 Design............................................................................................................................. 30
2.1.1 Closed-loop configuration ...................................................................................... 31
2.1.2 Once-through configuration .................................................................................... 32
2.1.3 Measurement procedure .......................................................................................... 33
2.2 Instrumentation............................................................................................................... 35
2.2.1 Wire-mesh sensor.................................................................................................... 35
2.2.2 High-speed camera.................................................................................................. 41
2.3 Appendix ........................................................................................................................ 42
2.3.1 Error analysis .......................................................................................................... 42
2.3.2 Influence of the wire-mesh sensor .......................................................................... 44
X
2.3.3 Gain-magnitude frequency response ....................................................................... 44
3 Outline of experiments and simulation .............................................................................. 46
3.1 Phase 1 Experiments ...................................................................................................... 46
3.1.1 Geometry................................................................................................................. 46
3.1.2 Test matrices ........................................................................................................... 46
3.2 Phase 1 Large Eddy Simulation ..................................................................................... 50
3.2.1 Simulation test case................................................................................................. 50
3.2.2 Simulation methodology ......................................................................................... 50
3.2.3 Governing equations ............................................................................................... 50
3.2.4 Computational grid ................................................................................................. 53
3.2.5 Initialization ............................................................................................................ 54
3.3 Phase 2 Experiments ...................................................................................................... 56
3.3.1 Geometry................................................................................................................. 56
3.3.2 Test matrices ........................................................................................................... 57
3.4 Regarding the orientation of presented results ............................................................... 61
4 Turbulent penetration with in-flow ................................................................................... 62
4.1 Turbulent penetration and how it differs from cross-flow mixing ................................. 62
4.2 Flow characteristics at the entrance to the branch line................................................... 67
4.3 Onset of turbulent penetration (Ur < 100) ...................................................................... 71
4.4 Flow characteristics in the branch line (Ur = 100) ......................................................... 73
4.5 Flow characteristics in the branch line (100 < Ur < 3000) ............................................. 82
4.6 Global instabilities introduced by pump oscillations ..................................................... 85
4.6.1 Influence of pulsation amplitude ............................................................................ 85
4.6.2 Influence of pulsation frequency ............................................................................ 85
4.7 Influence of T-junction edge geometry .......................................................................... 88
4.8 Influence of density stratification ................................................................................... 90
4.9 Conclusion ...................................................................................................................... 95
5 Mesh sensor package ........................................................................................................... 97
5.1 Introduction .................................................................................................................... 97
5.2 The challenge in brief ..................................................................................................... 98
5.3 Prior state of the art ...................................................................................................... 100
5.4 Material testing ............................................................................................................. 102
5.5 Prototype design and in-house testing .......................................................................... 104
5.6 Capabilities in theory ................................................................................................... 109
5.7 Conclusion .................................................................................................................... 111
XI
5.8 Appendix ...................................................................................................................... 112
5.8.1 Alternate electrode materials ................................................................................ 112
6 Cross-flow mixing at high ΔT ........................................................................................... 114
6.1 Introduction .................................................................................................................. 114
6.2 Facility .......................................................................................................................... 115
6.3 Instrumentation............................................................................................................. 117
6.3.1 Mesh sensor module ............................................................................................. 117
6.4 Test Matrix ................................................................................................................... 119
6.5 Regarding the orientation of presented results ............................................................. 122
6.6 Downstream results ...................................................................................................... 123
6.7 Upstream results ........................................................................................................... 126
6.8 Combined analysis ....................................................................................................... 132
6.9 Conclusion .................................................................................................................... 136
6.10 Appendix ...................................................................................................................... 137
6.10.1 Mesh sensor calibration methodology .................................................................. 137
6.10.2 Noise filtering ....................................................................................................... 140
6.10.3 Gain-magnitude frequency response ..................................................................... 141
6.10.4 Calculation of instantaneous and maximum average thermal gradient ................ 141
6.10.5 Calculation of cold holdup area ............................................................................ 141
7 Outlook ............................................................................................................................... 143
8 Curriculum vitae................................................................................................................ 144
9 Publications ........................................................................................................................ 145
9.1 Patents .......................................................................................................................... 145
9.2 Peer-Reviewed Journal articles .................................................................................... 145
9.3 Peer-Reviewed Conference papers............................................................................... 145
10 Bibliography ....................................................................................................................... 147
1
1 Background
1.1 Five articles
The field of research encompassing the problem of thermal fatigue in the vicinity
T-junctions in nuclear power plant (NPP) piping has been active for a number of decades
now. Therefore, it enjoys a tremendous wealth of published experimental and theoretical
results, many of which are referenced in this thesis and consolidated in the remainder of this
introductory chapter. Prior to delving into a detailed introduction and review of the field, it is
my desire to convey to the reader five valuable publications (excluding large technical reports
and compilations, e.g. IAEA-TECDOC 1361, EPRI MRP-25, or those of the OECD Nuclear
Energy Agency), knowledge and understanding of which can provide a valuable overview of
the history and current state of affairs in the research community.
1. J. H. Kim, R. M. Roidt and A. F. Deardorff, "Thermal stratification and reactor piping
integrity", Nuclear Engineering and Design 139, 83-95 (1993).
M. Robert, J. H. Kim, R. M. Roidt and A. F. Deardorff, "Letter to the Editor and
Authors' Response", Nuclear Engineering and Design 144, 517-419 (1993).
This paper from Westinghouse and Electric Power Research Institute (EPRI), along
with the subsequent ―Letter to the Editor and Authors' Response,‖ must appear on this list for
their historical relevance alone, scientific value notwithstanding. Kim demonstrates some of
the very earliest turbulent penetration studies in the context of LWRs, exploring such
phenomena as in-flow leakage, swirl, and density stratification. Robert, at Électricité de
France (EdF), another pioneer of the subject, takes exception with some of the findings.
2. S. Chapuliot, C. Gourdin, T. Payen, J. P. Magnaud and A. Monavon, "Hydro-thermal-
mechanical analysis of thermal fatigue in a mixing tee", Nuclear Engineering and
Design 235 (5), 575-596 (2005).
The through-wall crack downstream of a T-junction at the Civaux 1 NPP in France in
1998 is without a doubt the most oft referenced accident related to high cycle thermal fatigue
due to turbulent mixing. Chapuliot at CEA Saclay, France tackled the broad problem of
―establish[ing] natural mechanisms (turbulence, pulsing and instability) which might be the
cause of any substantial thermo-mechanical loading in the piping,‖ and did so in the context
of the pipe failure at Civaux [1].
3. H. Kamide, M. Igarashi, S. Kawashima, N. Kimura and K. Hayashi, "Study on mixing
behavior in a tee piping and numerical analyses for evaluation of thermal striping",
Nuclear Engineering and Design 239 (1), 58-67 (2009).
This paper proved to be of a foundational nature in helping to systematize cross-flow
T-junction mixing nomenclature and provided valuable data regarding all three major mixing
2
types in cross-flow T-junctions where density effects do not play a major role. Select
experiments, performed in the important and scientifically prolific WALTON T-junction
facility, were simulated and mixing frequency characteristics investigated.
4. B. L. Smith, J. H. Mahaffy and K. Angele, "A CFD benchmarking exercise based on
flow mixing in a T-junction", Nuclear Engineering and Design 264, 80-88 (2013).
The ability of simulations to predict, with high accuracy, time-dependent velocity and
temperature distributions in T-junction mixing is recognized worldwide as an important
milestone. This publication is an overview of the OECD Nuclear Energy Agency (NEA) CFD
benchmark exercise based on cross-flow T-junction studies at Vattenfall Research and
Development in Sweden, written by the chairperson. It demonstrated that poor results may
befall the theoretician who does not take special care in meshing the T-junction as well as the
still questionable performance of time-resolved simulations in predicting peaks in velocity
and thermal mixing spectra.
5. J. Kickhofel, K. Selvam, R. Kulenovic, E. Laurien, and H.-M. Prasser, ―T-junction
cross-flow mixing with thermally driven density stratification,‖1 To be submitted.
In an effort to tie the scientific progress made in this thesis with the greater history of
the field, the final article in this list is a planned joint-publication reproduced in-part in
Chapter 6 of this thesis and in a highly condensed form in Kickhofel (2015) [2]. Described in
detail therein is the successful culmination of a multi-year collaboration between the
Laboratory of Nuclear Energy Systems (LKE)2 at the ETH Zurich and the Institute of Nuclear
Technology and Energy Systems (IKE)3 at the University of Stuttgart. A fruitful
measurement campaign was completed which saw valuable cross-flow T-junction mixing
data collected at reactor-like fluid conditions where density effects being to dominate and,
furthermore, the successful proof of concept testing of a novel mesh sensor package for high-
temperature high-pressure flows in pipelines, described in Chapter 5.
1 Working title.
2 Labor für Kernenergiesysteme
3 Institut für Kernenergetik und Energiesysteme
3
1.2 Introduction
1.2.1 Fatigue
Fatigue is the cyclic stressing of a material which after a number of loading-unloading
cycles may lead to crack initiation, growth and eventually operating component failure.
Failures due to fatigue are stochastic in nature and the damage is cumulative; there exists
approximate fatigue limits based on experimental data. The number of stress cycles (typically
tensile) N, until failure for a given material is referred to as low cycle fatigue (LCF) if N <
104 and high cycle fatigue (HCF) if N > 10
4. High cycle fatigue is an especially challenging
material behavior to predict since in some cases it may appear that the stress cycles are of a
magnitude below the material‘s elastic limit. This case is unlike LCF in which the elastic
limit is clearly exceeded during each cycle. Once a slip band has formed and a crack is
initiated, the tensile and compressive cycling acts to open and close the crack, resulting in
striations along the length of the crack as it grows due to local plastic deformation at the
crack front. For a variety of reasons it is possible that the crack may arrest, and hence the
uncertainty in fatigue life arises. Laboratory testing of fatigue life is an arduous process.
Typically, a stress cycle is applied to a sample at frequencies greater than 10 Hz until failure.
This process is repeated for many stress magnitudes such that an S-N plot (also known as a
Wöhler curve) may be generated. Note, however, that this result is only valid for a given
material under certain ambient conditions; ambient temperature, corrosion and irradiation
may have significant influences on fatigue life.
1.2.2 Thermal fatigue
Thermal fatigue is a special case of fatigue caused not by external mechanical
loadings but by thermal loadings resulting in stress-generating thermal expansion and
contraction within the material. It may be that the material, for example steel piping, is
mechanically constrained in some way in which case the fatigue is then classified as thermo-
mechanical in nature, this is often the case in engineering applications. A typical example of
thermal fatigue in the field of power generation is cyclic stresses in pipe walls driven by
locally fluctuating internal fluid temperatures. Given appropriate fluctuation amplitude and
frequency at the wall surface, such temperature fluctuations alone may generate crack
networks bringing about component failure. Thermal fatigue is often delineated in literature
between low cycle and high cycle thermal fatigue (HCTF). The high cycle variety is a more
common threat in engineering applications with water-steam cycles since the stresses induced
by fluid temperature alone are rarely sufficient to cause a failure after fewer than 104 cycles.
Significant research has been carried out on the subject of HCTF in the past decades in the
context of NPP reactor coolant systems (RCS) where temperature fluctuations of sufficient
amplitudes and appropriate frequencies have been found to exist.
The thermal inertia of a material, a function of thermal conductivity k, heat capacity c,
and material density ρ,
4
√ , (1-1)
is an important property which dictates, along with component geometry, which temperature
fluctuation frequencies will generate the largest stress amplitudes in a material sample. For
any given thermal inertia value there exists so called critical frequencies which describe the
frequency at which the maximum stresses can be expected under sinusoidal thermal loading,
for example hoop or axial stress in the case of a pipeline. On one hand, in the case of high
fluctuation frequencies, thermal inertia ensures that damaging stresses cannot yet form before
an alternate stress input, tensile or compressive, is encountered. While on the other hand,
fluctuations of sufficiently low frequency are unable to generate significant temperature
gradients in the material, as a result the elastic limit is never locally exceeded. A generalized
method for determining critical frequencies for hollow cylinders indicates that the most
damaging high cycle fluctuation frequencies for typical NPP stainless steels is between 0.1
and 10 Hz [3-5]. The theory behind the critical frequencies begins with a Henkel
transformation of the simplified sinusoidal thermal loading, from which temperature profile
in the thickness of the pipe wall may be determined, followed by the stress field [5-7].
The material science community has generated a large volume of valuable
information on material response to thermal fatigue, especially that of austenitic stainless
steels such as EN 1.4307 (X2CrNi18-9, ANSI 304L), and EN 1.4404 (X2CrNiMo17-12-2,
ANSI 316L). The broad, shallow crack networks that have been observed to form in such
steels due to thermal fatigue are referring to as ‗elephant skin.‘ The crack networks are the
result of thermal striping, also called crazing. It is believed that thermal striping is the result
of crack arrest due to high stress gradients within the material under the condition of HCTF
[8, 9]. As a result of arrested cracks, a component may remain intact as more and more cracks
are initiated. It is known that residual stresses, especially, in the vicinity of welds is often a
location in which crack networks may develop when exposed to thermal-fatigue inducing
temperature fluctuations. See photographs of thermal striping in Figure 1-1 and Figure 1-2.
Figure 1-1. (a) Thermal striping in the vicinity of a weld seam in the residual heat removal
system of a pressurized water reactor (PWR). (b) depth of crack network.[9, 10]
5
Figure 1-2. A 316L stainless steel sample, 14 mm thick (a) before and (b) after 55,600
quench cycles with ΔT = 275 K, showing a crack network formed due to thermal fatigue [11].
Lifetime predictions of stainless steel piping components is dependent on knowledge
of the loading spectrum delivered by turbulent mixing or stratified flows, complicated by
additional effects from conjugate heat transfer, for example. At the moment, significant
approximations and assumptions are made, while the degree to which these simplifications
are conservative is not well understood. Modern examples of assumptions in models for
thermal fatigue damage accumulation include assuming the temperature history as a sine
wave and then proceeding to calculate stress intensity factors, interpretable using Paris‘ law
[5]. Another method, common in industry, implements Miner‘s Rule via the rainflow
counting algorithm output given the real fluctuation history as input [12]. In contrast to the
sinusoidal or semi-variable loadings assumed in most laboratory material testing and
theoretical modelling of thermal fatigue, loading in industrial processes are characterized by
variable spectra.4 Such loadings, comprised of a wide range of fluctuation frequencies, may
include phenomena such as periodic overloading and so-called sequence effects. Sequence
effects, for example the degree to which high amplitude cycles followed by low amplitude
cycles is more or less damaging than the reverse case is still under investigation in austenitic
stainless steels. Such phenomena are also explored in the laboratory. Recently, Taheri (2013)
has published a non-conservative model for damage accumulation resulting from variable
amplitude loading with emphasis on the sequence effect [13].
The transition from knowledge of the temperature history from measurements at or
near a wall to understanding of how the material will respond to such loadings is crucial, in a
safety sense. Variable loading of piping material due to fluid temperature fluctuations
remains a great challenge to the material science community in both experimental and
theoretical domains. Due to a dearth of such fluid temperature data, there has recently been
an effort made to artificially generate representative surface thermal loads encountered during
turbulent mixing in pipes [14].
The crux of the problem of thermal fatigue due to turbulent mixing in the context of
industrial piping networks is that without knowledge of the location of potentially dangerous
thermal fatigue loadings within the network over-conservatism reigns. This conservatism can
may be manifest in two distinct ways; 1. as a simple limitation on allowable operating
conditions, e.g. allowable ΔT of the mixing fluids and/or 2. by choosing materials and
4 Sometimes referred to as complex loading.
6
designs which provide a too-large global safety margin for the whole network or sizeable
regions thereof. The following sections are intended to introduce some history and research
related to thermal fatigue in NPPs.
1.2.3 Thermal stratification
The thermally stratified single-phase liquid flows are known to be the culprit of
thermal fatigue by manifesting high amplitude thermal fluctuations by means of two distinct
mechanisms. The first, sometimes referred to as global stratification loading, is the result of a
typically low frequency time-dependent stratified layer height resulting in high amplitude
thermal fluctuations and a variable bending moment in the pipeline. The second mechanism
leading to potentially damaging stress reversals in a pipe are instabilities in the stratified layer
itself [15]. Modelling of these flows often takes account of the influence of the Richardson
[16].
1.2.4 In nuclear power plants
Cyclic fluid temperature fluctuations have been identified as a cause of cracking and
coolant leakage accidents in commercial nuclear power plants. High cycle thermal fatigue
due to coolant mixing has been responsible for thirteen through-wall cracks in the primary
circuit of commercial pressurized water reactor NPPs between 1982 and 1998, shown in
Figure 1-3 [17]. Historical data seems to suggest that thermal fatigue is not merely a lifetime
management issue, with many accidents occurring early in the 30, 40 or 60 years of
envisioned plant lifetime. Dahlberg (2007) in the final report of the European Commission
Network for Evaluating Structural Components thermal fatigue project concludes,
―In several instances thermal fatigue damage has developed within short times, even less than
a year. Hence the common classification of thermal fatigue as an ageing process (implying
that its probability increases progressively with time) is potentially misleading‖ [18].
Up to 2007, the OECD/NEA Piping Failure Data Exchange (OPDE) Project5 had
recorded 64 non-through-wall crack (wall thinning), 65 leak, and 3 structural failure incidents
for which thermal fatigue is believed to be the culprit [19]. Thermal striping and high cycle
thermal fatigue was the focus of the international community in the 1980‘s and 90‘s due to
cracks that had formed in NPP pressurizer surge lines due to thermal stratification. Prior to
that, in the context of liquid metal and molten salt reactors, the issue was recognized as a
potential threat as early as the mid 1970‘s due to the potentially high temperature gradients
and heat transfer coefficients of the moderators [20, 21]. Significant research on thermal
fatigue and thermal striping in fast reactor T-junctions as it related to mechanical codes has
been compiled in the IAEA TECDOC 1381, the result of a three year coordinated research
5 The project covers ―piping components of the main safety systems (e.g. ASME Code Class 1, 2 and 3)… [and
also] non-safety piping systems that, if leaking, could lead to common-cause initiating events such as internal
flooding of vital plant areas.‖
7
topic and computational benchmark exercise [22]. A motivating factor in that project was the
detection of a crack near a T-junction in the secondary loop of the French LMFBR Phenix, in
1991 [23].
After a thermal fatigue failure resulting in coolant leakage at Farley 26 in December of
1987, believed to be the result of large thermal gradients caused by coolant stratification, the
NRC released the now well-known Bulletin 88-08 to U.S. LWR operators entitled, ―Thermal
Stresses in Piping Connected to Reactor Coolant Systems‖ [17, 24]. The bulletin was focused
specifically on unisolable piping connected to the RCS. Two days after the release of 88-08,
its first supplement was published with the purpose to ―1) provide preliminary information to
addressees about an event at Tihange 1 that appears to be similar to the Farley 2 event and 2)
emphasize the need for sufficient examinations of unisolable piping connected to the reactor
coolant system (RCS) to assure that there are no rejectable crack or flaw indications‖ [25].
Tihange 1 was one of three Belgian NPPs at the time. Two subsequent supplements went on
to highlight the difficulty in detecting such cracks in stainless steel piping with ultrasonic
methods and shedding light on a third, representative through-wall crack accident in the RHR
of what was described only as ―foreign reactor plant‖7 [26, 27]. These bulletins precipitated
sizeable research projects funded by the utilities not only in the United States but also abroad.
The accident at the Farley 2 plant occurred in a branch line with a leaking check valve,
however, most of the initial research focused on thermal fatigue in more simplified scenarios,
namely without a leaking valve (in-flow) situation.
Figure 1-3. Through-wall crack incidents (red bars) and leak rates (black diamonds) vs. NPP
age between 1982 and 1998 as compiled by the IAEA in TECDOC 1361 [17].
Even before the Farley 2 accident, thermal shock and striping were studied in the
context of thermal stratification, especially in the pressurizer surge line and other
stratification-prone horizontal pipes was a source of concern and research. After 88-08
experiments as a part of the HDR (Heißdampfreaktor) Safety Program studying thermally
stratified flows in a horizontal pipe at large ΔT received ―renewed international attention‖
[15, 28-31]. Since the HDR tests, a number of general experimental investigations of
6 In the RCS loop B cold-leg safety injection line (ECCS) between a check valve and the RCS.
7 Later revealed to be Genkai Unit 1 in Japan.
8
thermally stratified flows related to nuclear engineering have been published including Jud
(1995) using brine and fresh water and Rezende (2009, 2012) with ΔT approaching 200ºC
[32-34]. Other researchers continue to focus on specific components such as the pressurizer
surge line in the experimental work of Qiao (2014) or CFD simulations of Boros (2008) [35,
36]. Also of interest since the late 80‘s has been countercurrent stratified flows in the cold leg
near its connection with the RPV downcomer, for example, Sibamoto (2000) with regards to
experiments at the ROSA/LSTF facility in Japan [37].
It was not until the 1998 accident at the newly constructed Civaux 1 NPP8 in France,
in which a 180 mm long through-wall crack in EN 1.4307 (ANSI 304L) stainless steel
downstream of a T-junction in the residual heat removal system resulted in a significant
coolant leakage rate of 500 l/min, that the issue of HCTF due to turbulent mixing downstream
of T-junctions started to be addressed by researchers en masse and detailed assessment
methods developed [1, 38-42]. In the case of the Civaux accident (a ‗new phenomena‘ at the
time) an incomplete understanding of locations in the pipe network where turbulent mixing
could manifest large amplitude temperature fluctuations at critical frequencies meant that the
piping network was not of a safe design for the particular operating conditions [43]. Radu
(2007) found semi-analytically that the critical frequencies for the Civaux 1 RHR piping
materials were 0.3 and 0.1 Hz for hoop and axial stresses, respectively [5]. The CEA,
Framatome and EdF intensively investigated the accident at the Civaux 1 plant with
publications related to research borne by the accident still appearing more than a decade later.
Part of their investigation was aimed at crack initiation under thermal fatigue, a major finding
was that, ―[t]hermal fatigue appears to be more damaging than uniaxial isothermal fatigue‖
[44, 45]. Impetus to better understand the phenomena, especially in the vicinity of
T-junctions has grown steadily and over the past decade and a half, especially in the field of
time-resolved CFD and finite element modeling (FEM). Despite this long history, the
prediction of thermal fatigue-prone zones remains a challenge.
8 PWR type N4, 1400 MWe
9
1.3 T-junctions9
High cycle thermal fatigue due to turbulent mixing in NPPs tends to occur in the
vicinity of T-junctions. It is a reality that in the coolant piping networks of commercial PWR
and BWR reactors there exists many 90 degree intersections between pipes of varying sizes.
T-junctions prone to large fluid temperature gradients tend to be located in the high pressure
injection (HPI), feed water makeup, residual heat removal (RHR), and emergency core
cooling systems (ECCS) of LWRs. Some may exist directly at the hot or cold leg of the RCS
in PWRs where small branch lines lead to auxiliary systems. T-junction mixing is of interest
in the context of thermal fatigue because it is a location at which a hot and cold flows are
regularly meeting, in a so-called ―joining‖ or ―confluence‖ T-junction flow where two
streams meet and exit together via a single conduit. It is for this reason that T-junctions have
been the epicenter of HCTF research in the field of nuclear engineering. The most common
manifestation of such mixing in LWRs is the case of a turbulent, typically hotter flow
approaching the T-junction in the main pipe met by a second, typically cooler flow
approaching from the branch line. Given these boundary conditions, a wide variety of mixing
scenarios are possible. For the sake of clarity, only the most common scenarios will be
discussed. Figure 1-4 is meant to systematize the nomenclature in this field of research and
indeed in this thesis. T-junction mixing in the context of thermal fatigue in NPPs can be
broken down into two major groups, cross-flow mixing and turbulent penetration. Section
1.3.1 and 1.3.2 will review experiments and simulations of cross-flow mixing, respectively.
In the same vein, Section 1.3.3 and 1.3.4 will explore past and current research related to
turbulent penetration.
Figure 1-4. Categorized T-junction mixing scenarios occurring in NPPs.
1.3.1 Cross-flow mixing
In cross-flow mixing (shown in an oft published schematic in Figure 1-5) velocity ratios are
such that turbulent mixing occurs almost entirely in the mixing pipe of the T-junction. This
9 The nomenclature is not limited to ―T-junction;‖ in open literature alternatives include ―Mixing Tee,‖ ―T-type
junction‖ and ―T-pipe,‖ among others.
10
type of mixing has been delineated further in published research based on the momentum
ratio of the incoming flows, see Table 1-1 [46]. The branch may be oriented horizontally or
vertically. An impinging jet results in branch line flow which impacts the far wall of the T-
junction (relative to the branch). The deflecting jet results in mixing more or less in the center
of the mixing pipe, while a wall jet does not contain enough inertia to escape far from the
wall of the mixing pipe. Figure 1-6 presents a sketch of each jet type. Each jet type may
produce characteristic frequencies downstream of the junction in both the velocity and
temperature fields as a result of large scale vortices formed due to vortex shedding of the
main flow obstructed by the branch flow, including a Karman vortex street or hairpin
vortices.
Jet type Momentum ratio
Wall jet pr > 1.35
Deflecting jet 0.35 < pr <1.35
Impinging jet pr < 0.35
Table 1-1. Traditional categorization of jet types in cross-flow T-junction mixing based on
Kamide (2009) [46].
Figure 1-5. Schematic of cross-flow mixing in a T-junction, figure adapted from Smith
(2013) [47].
(a) (b) (c)
Figure 1-6. Flow behavior in the case of an (a) impinging jet, (b) deflecting jet and (c) wall
jet, figure adapted from Sakowitz (2013) [48].
Cross-flow mixing has been intensively investigated in academia and industry,
typically at low temperatures. Naik (2010) references at least 16 previously published cross-
flow mixing studies in T-junctions since 1980, mostly in the field of nuclear engineering with
water used as the working fluid [49]. Widely cited experimental studies in T-junction cross-
flow mixing are introduced in Table 1-2.
11
12
Facility
Name/Location
Max
ΔT
[K]
Velocity
ratio
Ur
Main
pipe
diameter
[mm]
Branch
line
diameter
[mm]
Measurement
technique(s) Notes
Walker (2009)
[50]
- / Paul Scherrer
Institute,
Switzerland
0 0.4 –
1.67 51 51 WMS
Braillard (2007,
2009) [51, 52]
FATHER /
CEA, France 160 4 152 152
TC, fluxmeter
sensor, coefh
sensor
Civaux 1
accident
analysis
Braillard (2007,
2009) [51, 52]
FATHERINO /
CEA, France 75 3 54 54
TC, fluxmeter
sensor, coefh
sensor, IR
camera
Civaux 1
accident
analysis
Igaraishi (2002)
[53, 54]
Ogawa (2005)
[55]
Kamide (2009)
[46]
Kimura (2010)
[56]
WATLON/
Nuclear Cycle
Development
Institute, Japan
15 0.22 –
2.9 150 50 TC, PIV
Upstream
elbow, all
jet types
OECD/NEA
(2011)[57]
Smith (2011,
2013) [47, 58]
- / Vattenfall
Utveckling,
Sweden
38.6 1.0 –
2.35 190 123
TC, fluxmeter
sensor, coefh
sensor
OECD CFD
benchmark
Kuschewski
(2011, 2013)
[59, 60]
- / IKE/MPA
Universität
Stuttgart,
Germany
200 1.2 72 39 TC, PIV,
NWLED-IF
NWLED-IF
proof-of-
concept
Chen (2014)
[61, 62]
Zhang(2015)
[63]
EXTREME /
NTHU, Taiwan 90
0.037 –
0.16 208 21 TC
Present Work
[2]
- / IKE/MPA
Universität
Stuttgart,
Germany
240 1.2 72 39
TC, High
temperature
mesh sensor*
High
temperature
mesh sensor
proof-of-
concept
Table 1-2. Seminal experimental cross-flow mixing studies. *discussed in Chapter 5.
13
Large international consortiums continue to build and study cross-flow T-junction
mixing from both fluid dynamic and material science perspectives to this day, with increasing
emphasis on CFD code validation and the forming of practical thermal fatigue assessment
methods based on scientific research. The FATHER project was a direct result of the 1998
Civaux accident, it was a 1-1 mockup of the Civaux case built at CEA Cadarache in 2001 and
has since been followed up by the FATHERINO project and most recently the new
MOTHER project [51, 52, 64, 65]. Results and analysis from the FATHER facility continues
to be published [66-69]. The European Commission THERFAT project for thermal fatigue
evaluation in T-junctions which was active from December 2001 to November 2004 brought
together 16 organizations in seven countries to study T-junction mixing [70]. It was
recognized that,
―In general, the common thermal fatigue issues are understood and controlled by plant
instrumentation systems. However, incidents in some plants indicate that certain piping
system Tee-connections are susceptible to turbulent temperature mixing effects that cannot be
adequately monitored by common thermocouple instrumentation‖ [70].
After THERFAT, as a part of a roadmap to a European-wide methodology on thermal
fatigue, the Network for Evaluation of Structural Components (NESC) project was initiated
with ―special attention to turbulent mixing phenomena at mixing tees in light water reactor
systems,‖ bringing together 10 organizations from five European countries, concluding in a
2007 final report [18]. The NESC project generated two primary outputs. The first is a
database of cases of thermal fatigue including 45 ‗operational components‘ and 5 from
laboratory experiments. The second was a European Procedure for Assessment of Fatigue
Damage under Turbulent Mixing which, given certain screening criteria based on material
type and ΔT between incoming flows (for example ΔT = 80°C for austenitic stainless steels),
determines fatigue usage factors and the growth of ―postulated crack-like flaw[s]‖ [18].
The OECD NEA has supported CFD benchmarking activities related the T-junction at
the Vattenfall Research and Development Laboratory in Älvkarleby, Sweden which attracted
65 participants from around the world [71]. Experimental results from the Water Experiment
on Fluid Mixing in T-pipe with Long Cycle Fluctuation (WATLON) facility in Japan, which
also incorporated elbowed main pipes, were integral in forming the JSME ―Guideline for
Evaluation of High-Cycle Thermal Fatigue of a Pipe,‖ which is at once a guideline for
designing piping systems as well as a four step assessment procedure [72].
New T-junction test facilities continue to be built and modeled. The Experiments with
T-junction on Rapid and Emergent Mixing Effects (EXTREME) facility at the National Tsing
Hua University can reach a ΔT of 70K at flow rates suitable to encounter some upstream flow
of the cold branch fluid in the main pipe [61-63]. At the University of Stuttgart in Germany,
the Institute of Nuclear Technology and Energy Systems (IKE) and the Materials Testing
Institute (MPA)10
have since 2011 operated a T-junction facility, the Fluid–Structure
Interaction Setup Stuttgart T-junction, for the study of thermal fatigue and turbulent mixing
in the case of large fluid temperature differences [59-61]. The facility incorporates reactor-
10
Materialprüfanstalt
14
grade materials and can reach reactor-like conditions with ΔT approaching 240 [73]. The
EXTREME facility and the University of Stuttgart T-junction facilities have the benefit of
studying the mixing in a controlled laboratory environment with realistic working fluid
properties.
1.3.2 Cross-flow simulations
It has been recognized by the OECD NEA that thermal fatigue, the result of T-
junction mixing represents a ―nuclear reactor safety problem for which CFD analysis brings
real benefits‖ [71]. Computer fluid dynamics have historically played a significant role in
research and development related to NPPs, especially in the field of reactor safety [74-76].
With the steady decrease in cost of ever greater computing power it has recently become
practical and popular, within the last few years, to simulate single phase T-junction mixing
with time resolved large eddy simulations (LES). Studies on a wide range of parameters have
been simulated including investigations into the effect of T-junction geometry [77-79],
turbulence or subgrid-scale (SGS) model [39], structure of the mesh [80], time step [81], and
conjugate heat transfer [64, 82].
The fatigue failure at Civaux 1 was simulated using the CAST3M code developed by
the CEA [1, 83]. Two geometries were simulated, one which includes two additional
upstream bends in the branch line of the T-junction in question, see Figure 1-7. The thermal-
hydraulic and mechanical analysis indicated a concerning reality; it found that in the
simulation of the T-junction where only one upstream bend in the branch line was resolved
(Figure 1-7 left), ―no significant thermal or mechanical load was found,― at the position of the
experienced failure. When the upstream bends were included in the computation grid (Figure
1-7 right), however, the findings change dramatically: ―evidence was found of large-scale in-
stability of greater amplitude. This large-scale instability gave rise to pulses which were
characterised by the presence of significant thermal fluctuations‖ [1].
Figure 1-7. Mesh of T-junction from Civaux 1 NPP, figure adapted from Chapuliot
(2005) [1].
15
Recently, the T-junction research community has been focused primarily on CFD
validation of cross flow mixing cases. The OECD NEA CFD benchmarking activity based on
the cross flow T-junction mixing experiments at Vattenfall in Sweden has been completed
and analyzed [47, 58]. In Smith (2013), the organizers of the benchmark describe the exercise
and some of the main conclusions [47]. The results were limited to the fluid dynamic aspects
of the flow and did not include conjugate heat transfer with the wall. In terms of the top
scoring simulations in the benchmark exercise, LES claimed the top 9 of 29 positions and
reproduced the average and RMS of the flow variables with good accuracy some individual
submissions to the benchmark have been independently published [84-87]. It was observed
that the mesh plays an important role; even for highly refined meshes, just having the largest
number of cells does not guarantee strong results. Furthermore, the issue of peaks in the
power spectra of the thermocouple signal and PIV data was seen as an important test of the
codes‘ ability to reproduce the flow for the purpose of a thermal fatigue analysis, in this
regard the results were underwhelming.
Figure 1-8. Side-by-side comparison of cross-flow T-junction mixing at the Vattenfall
experiment and instantaneous temperatures in the mid-plane of the T-junction from LES
simulations, figure adapted from Odemark (2009) [86].
A major international consortium with 11 partners has been working on the Modelling
T-junction Heat transfer (MOTHER) project [65]. Once again cross-flow mixing is the topic
of concern. The project is managed by Vattenfall, Sweden, but carried out at the laboratories
of CEA in France. The primary goal of the project, which encompasses both experimental
and simulation activities, is the validation of CFD for fluctuating heat transfer. The
international community approaches a validated CFD suite for the cross-flow mixing issue.
Still to be shown, however, is whether such simulations are capable of accurately reproducing
turbulent mixing in more complex geometries (such as those including upstream or
downstream bends), at large ΔT, or the wide variety of mixing scenarios possible in T-
junctions based on velocity ratio (such as turbulent penetration). Advanced simulation work
is already being carried out on reactor condition flows and geometries. These include LES
simulations, some with conjugate heat transfer, at the IKE at the University of Stuttgart with
direct comparisons to experimental data from their T-junction facility [59, 60, 88, 89].
16
Figure 1-9. LES simulation results showing temperature fluctuation distribution for the case
of a wall jet in the WATLON facility geometry (left). Special attention is paid to the
formation of large hairpin vortices (right), figure adapted from Tanaka (2010) [90].
In Japan, CFD benchmarking efforts pursued in both private and public spheres utilize
experimental results from the WATLON facility (see Table 1-2). Results from that facility
were compared with in-house codes of the Japan Nuclear Cycle Development Institute,
DINUS-3 and AQUA, as well as the LES-based code MUGTHES of the JAEA [53, 55, 90-
93]. Although early simulations were not successful in reproducing accurately the
temperature fluctuations or their spectra, more recent efforts have proven to show good
agreement and have thereby advanced the understanding of the flow mechanisms. For
example results from the MUGTHES code have indicated that in the case of a wall jet,
‗mutual interaction‘ between the Karman vortex street and so-called hairpin-vortexes11
are
the dominant temperature-fluctuation-inducing phenomena; however, the results remain
sensitive to the Smagorinsky constant, with values below some threshold failing to reproduce
hairpin vortices [90, 94-96].
Qian and Kasahara, also in Japan, have for the past five years delved into the mixing
downstream of T-junctions as a means of predicting thermal loading. In a series of high
quality LES simulations of the WATLON cases, the most recent appearing in the first quarter
of 2015, the authors have investigated effects of SGS models, an important step prior to
coupling such codes with an FEM simulation. Their work includes detailed studies of the
influence of numerical schemes for convective term of the energy equation in the LES SGS
turbulence model [97-99]. Furthermore, at the Institute of Nuclear Safety System in Japan, a
number of simulation results have been published. These include DES and LES sensitivity
studies of results testing Smagorinsky constant and temperature diffusion schemes, as well as
FEM with boundary conditions based on CFD results, see Figure 1-912
[100-103]. Most
recently, simulations have been performed in search of long-period fluid temperature
fluctuations (St < 0.2) [104].
1.3.3 Turbulent penetration
11
Hibara (2004) and Sau (2008) show evidence of hairpin vortices in low Reynolds numbers experiments and
simulations, respectively. 12
Nakamura (2009) also mentions hairpin vortices as contributing to temperature fluctuations downstream of
the T-junction.
17
Turbulent penetration in T-junctions is a mixing scenario which has resulted in
component failure due to thermal fatigue in commercial NPPs [17]. The phenomena,
resulting from a T-junction branch line with zero velocity (a ‗dead leg‘) or weak in-flow or
out-flow (e.g. in a leaking valve scenario), is a multifaceted one once described in a
publication by a researcher at EdF as, ―a complex and somewhat amazing hydraulic
behavior‖ [105]. Turbulent flow from the main pipe interacts with a stagnant fluid or laminar
flow in the branch line resulting in a variety of mixing frequencies and large amplitude scalar
fluctuations localized at different axial and circumferential positions depending on a number
of factors. These factors include, but are not limited to, velocity ratio between the main pipe
and branch line, main flow Reynolds number, junction geometry, and fluid densities. Figure
1-10 shows a schematic of turbulent mixing at velocity ratios sufficient to result in shallow
turbulent penetration. From another perspective turbulent penetration may be the result of a
leaking value from a branch line in, for example, a T-junction with unequal branch diameters
as in Figure 1-11. Flow structures which play a major role in cross-flow mixing, such as
Karman vortex streets or hairpin vortices are not present in the case of turbulent penetration.
Figure 1-10. Schematic of the onset of turbulent penetration in a T-junction with equal branch
diameters.
A systematic exploration of the behavior of turbulent penetration under different flow
conditions and geometries is crucial in adding to the limited experimental data and essentially
nonexistent simulation results available with regards to mixing in T-junctions at high velocity
ratios.
18
Figure 1-11. Turbulent penetration in a T-junction with unequal branch diameters at high
velocity ratios, in the case of a leaking value. Adapted and colorized from IAEA TECDOC
1361 [17].
1.3.3.1 Dead leg
The most common turbulent penetration scenario in NPPs is that of mixing in a
branch line sealed at one end by a check valve. This mixing configuration is typically studied
with emphasis on thermally stratified layers in upward or downward oriented branches. Near
the T-junction the flow in the branch is characterized as being similar to cavity flow, while
deeper in the branch the flow becomes more chaotic and finally may exhibit coherent swirl.13
Thermal stratification may occur in the branch line between the deep branch region (far from
the T-junction), cooled by heat losses, and the near branch region (nearer to the T-junction)
which is cyclically supplied and re-supplied with hot fluid from the main pipe via turbulent
penetration. Cyclic of the stratified layer may result in significant thermal stresses within the
branch line. Earlier research in the context of thermal fatigue in dead legs, however, focused
on adiabatic turbulent penetration and mixing in horizontal branches. Here, the work of EdF
stands out [105-107]. Around the same time, in the U.S., Kim (1991) at EPRI also outlined
the so-called, ―Thermal stratification, cycling, and striping (TASCS)‖ issue in response to
USNRC NRC Bulletin 88-08 [108, 109].
A parameter of interest is turbulent penetration depth, specifically as a function of
main pipe flow velocity. Kim (1993) developed one of the first such correlations for turbulent
penetration depth as a function of main pipe velocity, shown in Figure 1-12 [110]. Tanimoto
(2002) observed that the penetration depth is dependent on the diameter of the branch line
rather than a ratio of the main pipe to branch line, and reconfirmed that higher velocities in
the main pipe result in deeper penetration depths [111]. The same group, a collaboration
between academic and industrial nuclear interests in Japan, went on to develop a heat balance
model and turbulent penetration depth prediction method for downward closed branches with
or without elbow for a limited range of main flow conditions [112-115]. At the time of
writing, the applicability of SST CFD simulations are being tested with regards to developing
models for the penetration depth and stratified layer location [116].
13
Nomenclature related to the cavity flow-like behavior of turbulent penetration includes ‗cellular‘ eddies and
vortices, while swirl in the branch line is sometimes referred to as a ‗spiral vortex‘ or ‗tornado eddy.‘
Confusingly, some authors refer to the entire turbulent penetration plume as cavity flow penetration.
19
Figure 1-12. Turbulent penetration depth vs. main pipe velocity in a dead leg with elbow,
experiments and theory plotted by Kim (1993) [110].
Fluid disturbances in the vicinity of the stratified layer, or simply the axial translation
of the stratified layer in time due to thermal dissipation, have been shown to be induced by
residual swirl at the furthest extent of the turbulently penetrating flow. The phenomena of a
swirl extending regularly into the branch line can be seen in the schematics of Nakamura
(2013) in Figure 1-13 [117]. Swirl in the branch line was investigated, and tangential velocity
experimental measured as early as 2000 by Shiraishi [118]. A relatively large volume of
information on the subject has been published, with early work focusing on the cavity flow
behavior in the branch line [119]. In the past it hast been noted that ―mixing in the branch
pipe is mainly due to a swirling mean flow,‖ however, the same researchers at EdF also
believed that main pipe flow with a Reynolds number of less than 2.5 million was incapable
of generating swirling turbulent penetration [120]. Twenty years later, these comments have
been disproven, however, the mechanisms which generate swirl and its intermittent nature
remains unclear. Nakamura (2013) admits, ―[r]easons for this spiral flow fluctuation were not
found‖ [117].
20
Figure 1-13. A schematic representation of turbulent penetration in a straight (top) or
elbowed (bottom) closed branch which results in a regularly penetrating swirl (‗spiral
vortex‘) interacting with a thermally stratified layer. Penetration depth is indicated by Ls and
Lb [117].
An invaluable body of research regarding turbulent penetration, in the case of a
downward oriented dead leg, has come from the Institute of Nuclear Safety System (INSS) in
in Japan.14
For the past decade experimental trials have, and continue to be performed at the
facilities of the INSS; their work often cites the thermal fatigue failure in 1999 of piping in
Kansai Electric Power Co. Inc. (KEPCO) Mihama Unit 2 as inspiration [121]. The inspection
of that particular accident revealed a 7 mm crack on the outer surface of the elbow in a
branch line of the letdown system in the CVCS. A series of publications and reports have
elucidated the phenomena turbulent penetration in a downward pointing branch line and
elbow leading to a horizontal closed end with a main pipe flow temperature of 65 ºC [117,
122-124]. Most recently, in late 2014, in a continuing effort to characterize the swirling
aspect of turbulent penetration, results of visual swirl observations in the branch were
reported [125]. These results indicate three velocity streamline patterns in the branch, shown
in Figure 1-14, where the first pattern tends to occur more frequently near the T-junction and
the third, farther from the junction, between the two regions small vortexes also appear
(Pattern 2). Furthermore, the group has investigated the effect of T-junction edge geometry
on penetration depth and behavior, finding, in part, that rounded edge T-junctions experience
less turbulent penetration than those with sharp edges [123].
14
The INSS was incorporated in March 1992 by KEPCO as a result of a steam generator tube rupture, also at
Mihama Unit 2, in February 1991. Some of their most recent work has yet to be published in English, references
to the Japanese publications are provided.
21
Figure 1-14. Figure adapted from Miyoshi (2014) showing three typical velocity streamline
profiles in a cross-section of the branch line [125].
Yet another consistent source of research on turbulent penetration in dead legs, in
both upwards, horizontal and downwards orientations, comes from EPRI. Kim (1991, 1993),
from Westinghouse, in collaboration with EPRI published dead leg experiments measuring
velocities in a horizontally oriented branch line with and without induced swirl in the main
pipe [108, 110]. In 1994 EPRI published their final TASCS program report which began in
1989 shortly after USNRC Bulletin 88-08. Unfortunately, the issues of stratification and
swirling remained enigmatic and the findings in the TASCS program could not predict the
accident at Farley 2. As leaks due to thermal fatigue continued to appear in NPP branch lines
towards the end of the last century, EPRI formed a task group to ―pro-actively‖ address the
problem [126]. Starting in the year 2000 EPRI began publicly sharing thermal fatigue
monitoring experience in auxiliary piping of the RCS [127-129]. Keller (2002, 2003), in
collaboration with EPRI, studied swirl in turbulent penetration using compressed air, in order
to achieve Reynolds numbers on the order of 107, in a T-junction with upwards oriented dead
leg branches [130-132]. The work of Keller and others culminated in 2004 in a ―Thermal
Cycling Screening and Evaluation Model‖ for non-isolable RCS branch lines, the details of
which, along with its 2008 addendum, remain proprietary [133-135]. As a part of the EPRI
Material Reliability Program (MPR-146), an ongoing program is designed to ―assist PWR
owners manage thermal fatigue concerns in normally stagnant, non-isolable reactor coolant
system branch lines‖ [126, 136-139].
1.3.3.2 In-flow
Turbulent penetration under the condition of in-flow into the branch line can be
shown schematically as a piping and instrumentation diagram, one example is shown in
Figure 1-15. This mixing scenario relies on two conditions: firstly that the pressure gradient
ensures flow from the high-pressure source to the RCS via the branch line and, secondly, that
the fluid is injected at mass flow rates well below that of the RCS (e.g. as would be the case if
a valve leaked). Such conditions may exist in NPPs, for example in the HPI system of some
Westinghouse plants where the discharge pressure of the injection pump is approximately
200 psi higher than the operating pressure in the RCS [140]. Furthermore, recall that the
accident at Farley 2 was a case of turbulent penetration with in-flow due to a leaking check
valve. The Farley 2 accident represents what is now understood to be one of the more
complex mixing scenarios possible in the vicinity of a T-junction in an NPP. It is for this
22
reason that this work focuses heavily on the issue of turbulent penetration in the case of a
weak in-flow.
Figure 1-15. Schematic of the thermal hydraulic case of turbulent penetration with in-flow in
an NPP. Inflow is ensured by the larger pressure behind the leaking valve and unisolable
piping present at the RCS [140].
Table 1-3 reviews the experimental works previously published in the field of
turbulent penetration mixing in T-junctions with in-flow. All prior works, aside from the
study of Zboray (2011) at the Paul Scherrer Institute, were performed outside academia at
Westinghouse, Mitsubishi, or EPRI [141]. Important to note, are studies of mixing in T-
junction mockups of a downcomer and intersecting cold leg in PWRs. In these studies a hot
flow travels down a vertically oriented main pipe before interacting with a horizontal branch
line carrying cold flow. Hassan (1982) presented experiments and simulations near the onset
of turbulent penetration in this small break LOCA case, providing a flow pattern map,
delineating zones of penetration and no penetration, as a function of cold and hot water
Froude number [142]. Later, Sibamoto (2000) published a 1D hydraulic model for the
stratification level in density-stratified countercurrent flow in the branch line based on data
from mixing with significant density difference at the ROSA/LSTF integral test facility and
an adiabatic experiment with brine simulating the heavier cold flow [37].
23
b
m
rU
UU
2
2
4
4
bbb
mmm
r
DU
DU
m
22
2
4bbb
bmmmr
DU
DDUp
ε Rem T-Junction
Geometry
Max
ΔT
[K]
Kim (1993)
[110]
340–
2.7E3 1.0E3–8.2E3 2.2E5–1.4E7 0.25 1.4E6 ? 0
Deutsch
(1997) [107]
100–400 676–2.7E3 3.3E4–5.3E5 0 9.0E5 Sharp 0
Nakamori*
(1998) [143]
2.5E3–
7.4E4 ? ? 0.33 ? ? 306
EPRI (2002)
[127]
2.4E3–
7.1E4 5.0E4–1.5E6 2.7E7–2.4E10 0.33 3.0E7 Rounded 303
Kim (2005)
[144]
33.3–
42 148–186 4.7E3–2.9E5 0.02 1.5E5 ? 50
Zboray
(2011) [141]
33.7–
77.8 33.7–76.9 0.7E3–1.45E3 0 6.2E4 Sharp 0
Present
Work Phase
1 [145, 146]
28.6–
400 28.6–400 1.0E3–2.0E5 0
4.2E4
–
7.6E4
Sharp 0
Present
Work Phase
2 [147]
1E3-3E3 750–822 3.0E6–3.3E6 0-0.08
6.5E4
1.1E5
Sharp &
Rounded 0
Table 1-3. Review of experimental turbulent penetration studies in T-junctions at high Ur.
*Unknown main pipe diameter, Dm. Mass flow rate ratio, , and momentum ratio, , are
defined as in Kamide (2009) [46].
EPRI and Westinghouse, in the publications of Kim (1991, 1993) mentioned earlier,
detailed their turbulent penetration experiments in a ―standard‖ 6‖ x 3‖ T-junction with
branch oriented perpendicular to gravity [108, 110]. Leakage flow simulations at the facility
were performed with a salt solution in the branch line, representing 100ºF (37.8ºC) leakage
into a 500ºF (260ºC) circuit, and visualized with a vegetable dye. Kim reports turbulent
‗bursts‘ disrupting the stratified layer in the branch, resetting its progress towards the T-
junction while delivering the mixed fluid back to the T-junction. Furthermore, at the velocity
ratios explored the cold tongue was found typically 3 to 4 branch diameters from the T-
junction, and only occasionally reached all the way to the T-junction.
Nakamori (1995, 1998) at Mitsubishi Heavy Industries in collaboration with the
Kyūshū Electric Power Company published monitoring experience at unisolable branch lines
in Japanese PWRs, in direct response to the accidents at Farley and Tihange [143, 148]. The
project, involving five Japanese PWR utilities and Mitsubishi, was tasked with investigating
―thermal stratification and its cycling due to the leak flow through the closed stop valve.‖
Visualization tests were carried out at a low temperature facility followed by small and large
leak high temperature testing at a PWR simulation loop. A test section representing portion of
the Farley 2 ECCS, where the thermal fatigue failure occurred, was exposed to similar fluid
flow conditions present at the time of the accident. Time dependent thermal stress analysis
was performed with the MARC code; conclusions include recognition of damaging thermal
cycling when the leak rate is large, e.g. equal to or larger than the what was encountered at
Farley 2 (159 kg/hr). It is recognized by Lund (1998), however, that the results of Nakamori
do not correspond with the location of the Farley through-wall crack (approximately 5.2
diameters from the T-junction), and therefore left unanswered the question ―what caused the
fatigue failure at Farley?‖ [24]. Kim (2005) reports additional in-flow and dead leg
24
experiments at reactor conditions in a mockup of Uljin Nuclear Power Plant Units 3 and 4
instrumented with thermocouples in the center of the piping. Stratification in both up-
horizontal and down-horizontal branches were explored, concluding in part that, ―[a]dditional
tests of turbulent penetration depth must be conducted systematically‖ [144].
In collaboration with EdF, EPRI instrumented a number of dead leg branch lines in
French NPPs with thermocouples to investigate temperature fluctuations due to turbulent
penetration for long durations, up to two operating cycles. More pertinent to this work,
however, were the tests performed at the Westinghouse-designed 900 MWe Blayais 1 NPP.
These experiments, also relying on thermocouple instrumentation attached to the outside of
the branch line, involved the injection of cold flow from the CVC to the RCS during
operation, essentially recreating the Farley-Tihange phenomenon [127].
The work of Zboray (2011) at the Paul Scherrer Institute, which could be considered
the precursor to the study of turbulent penetration in this thesis, performed experiments in a
T-junction with equal main pipe and branch diameters of 52 mm, at the facility of Walker
(2009) [50, 141]. The tests were performed in an adiabatic acrylic test section instrumented
with wire mesh sensors at velocity ratios up to 77, capturing the onset of turbulent penetration
at a depth of 1 diameter into the branch.
1.3.4 Turbulent penetration CFD simulations
The entirety of the aforementioned CFD simulations were performed in the context of
cross-flow mixing in T-junctions. Turbulent mixing in the case of turbulent penetration in the
branch line has not been nearly as thoroughly investigated in large part due to the
computational expense and complex meshing requirements. It is characterized by a large
recirculation zone, the result of main flow being slowed as it mixes with the incoming or
stagnant branch flow. That is to say, that a wide range of mixing frequencies and Reynolds
numbers are expected, including a transition between laminar and turbulent regimes in the
regions of interest. This is a very challenging case for single phase CFD, requiring long
simulation times.
A review of CFD results on the subject available in open literature is shown in Table
1-4. Hassan (1982) utilized the 3D steady-state code COMMIX-1A to simulate thermal
mixing and turbulent penetration at velocity ratios between 3 and 13.3 in the case of a vertical
main pipe simulating a downcomer and a branch line simulating the cold leg [142]. First
attempts at simulating turbulent penetration with a horizontal main and mixing pipe utilized
the standard k-ε turbulence model with a dead leg boundary condition. Early k-ε simulations
by Robert (1990) failed to reproduce the non-symmetric velocity field, due to swirling, in the
branch line [106]. Deutsch (1997) also showed k-ε to perform poorly in predicting
penetration depth at a velocity ratio of 400; promising results were shown rather with second
momentum turbulence closure models. Recently Ikeda (2007) performed k-ε simulations in a
downwards oriented branch pipe with buoyancy noting that the sheer force of the main flow
and friction losses at the wall in the branch pipe were important factors [149].
Ur Turbulence Flow scenario ε T-Junction ΔT Comparison
25
model
Geometry [K] with
experiment
Hassan
(1982)
[142]
3-13.3 COMMIX-1A
code In-flow 0.03 Sharp 73 Yes
Robert
(1990)
[105, 106]
- k-ε Dead leg 0 ? - Yes
Deutsch
(1997)
[107]
400 k-ε and SMC Dead leg 0 Sharp - Yes
INSS
(2014)
[117]
- none Dead leg 0.02 Sharp * Yes
Ikeda
(2007)
[149]
- k-ε Dead leg 0.02 Sharp 45 Yes
Kim (2013)
[144] 16950
URANS SST-
FEM
Dead leg
In-flow 0.25 ? 245 No
Lu (2013,
2015) [78,
79, 150]
- LES Dead leg
Out-flow - Sharp 50 No
Present
work [151] 100 LES In-flow 0 Sharp 0 Yes
Table 1-4. Review of published CFD simulations of turbulent penetration in T-junctions.
*10ºC and 20ºC branch-end wall temperatures.
The INSS is active not only in dead leg experiments but also has published a number
of CFD studies [124, 152, 153]. Their most recent publication describes DNS simulations of
straight and elbowed branch lines with heat loss and no leakage. Some simulation work on
the subject of in-leakage to a T-junction was performed by EdF in the 1990‘s and took
advantage of k-ε and second momentum closure turbulence models to simulate turbulent
penetration in a dead leg at a velocity ratios up to 400. Since then, publications related to the
issue have been largely absent. Recently, researchers at the Korea Institute of Nuclear Safety
performed coupled URANS-FEM simulations of turbulent penetration into a branch line with
elbows, concluding that, ―in-leakage has a high possibility of causing considerable structural
problems in RCS piping‖ [154]. The time step of 0.5 s in those simulations, however,
precluded an assessment of high frequency fluctuations seen in turbulent mixing near the
junction.
As for LES simulations, Lu (2013) has recently published results of out-leakage
simulations in a T-junction branch line, focusing, however, on stratification rather than
turbulent mixing [78, 79]. Utilities continue to focus on the issue of ―Thermal Fatigue in
Normally Stagnant Non-Isolable Reactor Coolant System Branch Lines,‖ as EPRI designates
it. They provide an entire ‗Product Set‘ on the topic including thermal fatigue evaluations and
thermal-cycling models [155]. There also exist models for predicting turbulent penetration in
dead legs based on heat transfer considerations.
26
1.4 Parallels to other disciplines
It is an easy mistake to limit the scope of one‘s research, knowledge, and overall
awareness to one‘s particular field, in this case, nuclear engineering.15
Therefore, as means of
combating this tendency, I wish to provide some information and references regarding
turbulent penetration mixing in other fields beyond nuclear engineering which typically go
entirely unnoticed (and uncited) within the research sphere directed at nuclear safety issues
related to HCTF in T-junctions. There are potentially significant amounts of knowledge
which may be garnered (and redundancy avoided) by looking beyond nuclear.
1.4.1 Shear-driven cavity flow as an analogy to a dead leg
Turbulent penetration mixing in T-junctions is highly similar to the long-active
research topic in fluid dynamics known as shear-driven cavity flow.16
The study of cavity
flows originates in the study of shear-driven compressible flows, specifically in the context of
flow acoustics. These flows occur typically over airframes with indentations which may take
on geometries such as shallow indentations or deep cavities resembling a T-junction branch
line. Non-compressible cavity flows have also been investigated. Typically, this field is based
in simulations, especially in 2D, as a means of model validation. The study of 3D deep cavity
flow (where the cavity is of depth greater than its characteristic length) begins to mimic very
closely the dead leg branch line situation in an NPP (when an incompressible fluid is
considered) albeit without significant thermal or buoyancy effects. These flows are typically
modelled, using a lattice Boltzmann method, as laminar or transition flows where the interest
lies in precisely simulating steady vortex structures in the branch. This field is potentially
valuable to nuclear engineers studying T-junction mixing in terms of both high quality CFD
and experimental results.
1.4.2 Automotive flows analogous to cross-flow mixing
One such non-nuclear field where turbulent mixing in T-junctions is of interest is in
the automotive industry, again in compressible flows. For example, recent research has
focused on cross-flow mixing in a T-junction with steady and pulsed inlet conditions as may
be found when applying exhaust gas recirculation in internal combustion engines. The work
of Sakowitz (2013, 2014) utilizes steady state RANS as well as time resolved LES
simulations. Flow patterns include all three major types of cross-flow mixing including wall
jet, deflecting jet and impinging jet in a T-junction with a branch diameter ratio of 0.5 [48,
156].
15
Fortunately, nuclear engineering is in itself a highly multidisciplinary endeavor. 16
Not to be confused with lid-driven cavity flows.
27
1.4.3 Shear layer studies
Finally, since the departure of the main flow into the branch must be recognized as an
important, initiating event in turbulent penetration mixing is it evident that fundamental
studies of shear flows are of value. In their seminal paper on the topic, Brown and Roshko
(1974) helped to elucidate the turbulent structures appearing in turbulent free shear layers
with high-speed footage [157]. More recently, work at the Paul Scherrer Institute has focused
on fundamental studies of shear layer mixing in flows with small and large differences in
density in stable and unstable configurations [158-160]. The facility hosting those
experiments, GEMIX, has also recently hosted measurements with a newly developed wall
heat flux sensor [161, 162].
28
1.5 Thesis structure and outline
The work covers two particular thermal-fatigue relevant mixing cases in T-junctions.
Chapters 2, 3, and 4 address the first of these scenarios: turbulent penetration mixing with in-
flow from the branch line. The second chapter introduces the LKE T-junction facility and
associated measurement instrumentation including details of the measurement procedure at
the facility, wire-mesh sensor construction and calibration methodology. Test matrices, along
with experimental and CFD simulation methodology are covered in Chapter 3. Chapter 4 is
an extensive analysis of the results as a whole, meant to generate a comprehensive
understanding of the turbulent penetration phenomena in the case of in-flow. Within these
chapters is described,
The design, construction, commissioning and utilization of an adiabatic single phase
T-junction facility for the study of turbulent penetration in the branch line in the
context of thermal fatigue.
An investigation of turbulent penetration in T-junctions with in-flow against the
penetrating main flow direction in the branch line by means of wire mesh sensors and
time-resolved CFD simulations.
Test matrices including T-junction geometry, density stratification, pulsatile flow and
velocity ratios up to 3000.
A detailed description of turbulent penetration behavior in the Farley-Tihange
phenomena, beyond what is available with regards to experiments or simulations in
open literature, including Kim (1993), Kim (2005), and Kim (2013) [110, 144, 154].
Chapters 5 and 6 are dedicated to the second mixing scenario which is cross-flow T-
junction mixing at high temperatures and pressure. Chapter 5 introduces the new, patented
high-temperature high-pressure mesh sensor package design, built for the purpose of cross-
flow mixing studies at the University of Stuttgart T-junction facility. This is followed by
results from mesh sensor prototype testing in cross-flow T-junction mixing experiments at
that facility, in Chapter 6. Major topics to be addressed include,
Design, construction, assembly, and proof of concept testing of a novel mesh sensor
package capable of withstanding high-temperature steam-water environments (up to
350ºC) at high pressures (up to 22 MPa).
Investigation of cross-flow mixing in T-junctions at reactor-like temperatures (256ºC)
and pressures (7 MPa) at the University of Stuttgart T-junction facility by means of
novel mesh sensor instrumentation.
29
Detailed description of flow patterns and mixing frequencies both downstream and
upstream of the T-junction at high Richardson numbers with strong thermally-driven
density stratification.
Finally, in Chapter 7 a brief outlook is provided.
30
2 Outline of LKE T-junction facility
2.1 Design
In the context of this work, a new T-junction facility (Figure 2-1) has been design and
constructed for the express purpose of studying turbulent penetration with a high density of
instrumentation, primarily in the form of wire mesh sensors (WMS). Prior to this work,
preliminary turbulent penetration experiments by Zboray (2011) were carried out at the T-
junction facility of Walker (2009) which was optimized for cross-flow mixing tests at
velocity ratios close to unity. The boundary conditions of these tests, in terms of turbulent
penetration, were therefore limited to the onset of turbulent penetration [50, 141]. The new
test facility described in this chapter was designed and instrumented for the case of weak
branch in-flow with a high degree of geometrical flexibility, allowing for various branch
diameters, sensor positioning, and T-junction geometry.
The facility operates under adiabatic conditions at atmospheric pressure. It is
comprised of an acrylic glass 90 degree T-junction and inlet run sections fed by flexible PVC
hose and PVC-U piping. Each branch contains a honeycomb section at the start of the acrylic
inlet sections for flow conditioning. Two high-density polyethylene feed tanks of 750 l
volume each separately supply the junction with tap water (approx. 150 µS/cm) in the main
pipe and deionized water (approx. 3 µS/cm) in the branch line such that electoconductive
measurement techniques, specifically WMSs (see Section 1.1), can distinguish mixing at the
T-junction. A waste tank of 1000 l volume acts as a sump for the working fluid.
31
Figure 2-1 Schematic of the T-junction facility including main and branch supply tanks,
waste tank, numbered solenoid valves, pumps, and flow meters.
The T-junction is supplied by two frequency-controlled centrifugal multistage pumps.
The main pipe pump (Grundfos CME) is capable of delivering in upwards of 200 liters per
minute (12 m3/h) while the branch pump (Grundfos CRE) is tasked with delivering less than
a single liter per minute (< 0.06 m3/h) against a relatively large hydraulic head. Manual
regulating valves downstream of the pump (PD1 and PD2) help to further reduce the branch
line flow rates, measured in Phase 1 experiments by a vortex flow meter and by an oval gear
positive displacement flow meter in Phase 2. An electromagnetic flow meter in the main
circuit delivers high accuracy flow velocity readings with a frequency of 8 Hz. A National
Instruments CompactRIO chassis interfaces with the LabView software on a PC. Solenoid
valve control is handled within a LabView Virtual Instrument and two tuned PID controllers
help to maintain the appropriate flow rates in the pumps. Information regarding tap water
conductivity is also fed into the program. During filling of the facility, air bubbles are flushed
(via Bubble0) while tap and deionized water are independently recycled through their
respective supply tanks.
2.1.1 Closed-loop configuration
The facility may operate in two configurations; the first, ―closed-loop‖ is used for
tests without density stratification The closed-loop configuration (Figure 2-2) allows for long
duration measurements to be performed which is beneficial from many points of view,
especially in reducing noise in mixing spectra while maintaining low frequency components
when ensemble averaging or in the search for long-period fluctuations. When mixing tap
water and deionized water at high velocity ratios the addition of small amounts of deionized
water, pre-mixed during the return trip from the T-junction to the tap water supply tank,
induces a change of 0.25% or less in the electrical conductivity over the course of a
measurement. To compensate for this already small disturbance the calibration procedure
takes advantage of the linear response of the WMS. The tap water calibration used during
data processing is the postulated sensor signal at the average tap water supply tank
conductivity during the measurement, calculated from a linear interpolation between two tap
water calibrations at known conductivities before and after the measurement series.
32
Figure 2-2. Closed-loop configuration at the T-junction facility. Mixed fluid exits the T-
junction and returns to the main pipe supply tank via the RV4 valve.
2.1.2 Once-through configuration
Once-through tests (Figure 2-3) are performed in the case of non-equal inlet flow
densities or if the velocity ratio is relatively low, such that considerable contamination would
occur by delivering the mixed fluid back into the main tank. Increased density in the branch
flow is achieved by adding sugar to the deionized water tank. The tank is mixed until
homogeneous and then a sample is taken and the density is measured with a hydrometer.
Measurement durations of 60 seconds were achieved when running the facility in the once-
through configuration; water in the mixing pipe is sent directly to a waste tank which is
drained after the measurement.
33
Figure 2-3. Once-through configuration at the T-junction facility. Mixed fluid exits the T-
junction into the waste tank via the Dump1 valve, to be drained.
2.1.3 Measurement procedure
Prior to the start of an experiment the facility is filled by the main pump which
recycles tap water from the Main Tank, via the T-junction. The branch pump recycles
deionized water from the Branch Tank. The Bubble0 valve is opened temporarily in order to
flush any air present in the circuit out with tap water via the branch line to the Waste Tank.
34
Figure 2-4. Flow in the T-junction during calibration recordings and initial condition prior to
a measurement. Gravity points into the page.
The experimental procedure is essentially consistent for all measurements at the
facility. The experiment starts when the SideFlow2 valve is opened (RecycleSide4 is then
closed), bringing deionized water into the branch line.17
The branch line flow rate is kept high
in order to completely flush tap water from the auxiliary piping and the branch itself. The
main flow is kept low during this flushing procedure. At this point the PID controller is
activated and seeks the set point flow rate in the branch. As the branch flow rate slows to the
set point, the main flow PID controller is also activated and the velocity in the main pipe
increases to its respective set point. As the flow rates approach the values for the given
experiment, turbulent penetration begins. The measurement begins at least 10 seconds after
both the branch and main flow velocity readings have stabilized. This procedure is shown
schematically at the T-junction in Figure 2-4.
17
It is at this point that in a once-through experiment the Dump1 valve would be opened and RV4 closed.
35
2.2 Instrumentation
2.2.1 Wire-mesh sensor
Single phase mixing in the vicinity of the T-junction was measured by an electrode-
mesh device known as a wire-mesh sensor (WMS) by recording the electrical conductivity of
the flow at many points in space between transmitter and receiver electrodes, in this case thin,
tensioned stainless steel wires. The WMS reads analog current detected in a multiplexed-
manner where each transmitter electrode is sequentially delivered a square-wave voltage
pulse (± 3V) during which all receiver electrodes are sampled in parallel. Cross-talk between
neighboring receivers or transmitters is suppressed by means of low-impedance drivers and
inputs for the transmitters and receivers, respectively. The measurement technology is
typically applied in, but not limited to, closed conduits such as flow channels or pipelines
where the conductivity is measured throughout the cross section of the duct with a typical
resolution, determined by the pitch of the electrodes, of 1 to 5 mm. The voltage pulses
through the transmitter electrodes are multiplexed at up to 10 kHz. In this manner the
conductivity of the fluid can be accurately measured by a WMS with high temporal and
spatial resolution. A schematic of the operating principle of the WMS can been see in Figure
2-5. More information can be found in Prasser (1998) [163]. The current signals are
converted to voltage and recorded by 12-bit analog to digital converters in the WMS data
acquisition (DAQ) electronics for the entire measurement duration prior to being transferred
via USB to a desktop computer.
The WMS accurately measures the conductivity of the flow only when calibrated.
Calibration of the WMS itself is not performed as a part of the experiments in this work. The
calibration of the WMS itself could be achieved with a solution of known resistivity in a
procedure analogous to the calibration of traditional conductivity cells. In practice, when we
are interested in conductivity only as a measure of a dimensionless mixing scalar used to
visualize single phase mixing, absolute conductivity values are not of interest. Wire-mesh
sensors have been effectively implemented in measuring single phase mixing of fluids with
different temperature by means of detecting the conductivity change of water with
temperature. Often, however, a salt tracer is introduced as a means of rendering the mixing
visible to the sensor. By recording uniform measurements of each working fluid, in this case
tap and deionized water, a baseline is set from which to measure scalar concentrations.
Signals are converted to a normalized scalar meant in this case to be analogous to fluid
temperature. This analogy is valid in the case of turbulent flows where turbulent diffusivity
dominates and is furthermore believed to introduce only small errors in the case of slower,
laminar flows sometimes discussed in this work since the thermal diffusivity of water and
mass diffusivity of NaCl solutions have similar magnitudes [164]. Salt tracer experiments
represent true adiabaticity since the walls are unable to absorb or dampen concentration
changes in the fluid. It has been shown to be the case, however, that the boundary layer acts
to dampen fluctuations in salt tracer concentration near the wall [160].
36
Figure 2-5. Schematic of the operating principle of the wire mesh sensor from Prasser (1998)
[163].
2.2.1.1 Construction
Sensors at the T-junction facility were designed in-house as a part of the thesis work
described herein. The components of a WMS include identical transmitting and receiving FR-
4 PCB boards on which 16 or 32 0.05 mm diameter EN 1.4404 (AISI 316L) stainless steel
wires are tensioned and soldered to solder pads on the boards parallel to one another with a
constant pitch of 1.68 mm or 1.56 mm, respectively. The boards are placed perpendicular to
one another forming a Cartesian wire-mesh separated by a thin 1.5 mm sealing plate made of
soft-PVC of hardness 77 Shore A which also acts to seal the conduit at this location. Acrylic
glass flanges with O-rings fix the WMS assembly in position in the branch line or mixing
pipe. Shielded cables with D-SUB 25 connectors connect the DAQ unit to the receiver and
transmitter PCB boards, respectively. Figure 2-6 shows the arrangement of the PCB boards
with a 26 mm diameter opening for the flow to the past through the wire-mesh as well as M6
bolt and centering pin (3 mm, h8) holes for connection and alignment with the flanged
piping. Embedded copper traces carry the signal from the solder pads to the D-SUB 25
connector. The PCB boards with 16-by-16 electrodes measures 160 mm x 80 mm x 3.2 mm
thick, those with 32 electrodes are slightly larger, 160 mm x 100 mm x 3.2 mm thick. In
Figure 2-7 a photo of a completed transmitter board with 32 electrodes is shown.
37
Figure 2-6. Schematic of transmitter and receiver PCB boards positioned perpendicular to
each other to form a 16-by-16 electrode (left) WMS and 32-by-32 electrode (right) WMS.
Flow passes through the center opening.
Figure 2-7. Photograph of a single PCB board with 32 electrodes, 64 soldering pads, two D-
SUB 25 connectors and sealing ring.
Of the crossing points, i.e. measurement points, 232 lie within the 26 mm diameter
flow area in the case of the 16-by-16 sensor, and 856 of the 32-by-32 electrode sensor lie
within the 50 mm diameter flow area. The orientation of the mesh and it‘s crossing-point
coordinate system (t,r) relative to gravity (pointing in the –z direction) is shown in Figure
2-8.
38
Figure 2-8. Convention for identifying individual crossing points (t,r). A 16-by-16 grid over a
26 mm flow area and a 32-by-32 grid is drawn over a 50 mm diameter flow area according to
the viewing orientation. Gravity is pointing downwards.
2.2.1.2 Installation
Installation of the sensors in the branch line or mixing pipe of the T-junction is
achieved in one of two ways depending on the sensor position. If the sensor is installed at the
T-junction itself, four screws are fed through the flanged end of the branch line or mixing
pipe along with two centering pins and fixed directly to the T-junction which is fitted with
Heli-Coil® inserts to avoid fracturing the component upon screw-tightening. For positioning
of the sensor within the branch line, flanged acrylic glass spacer pieces have been
manufactured to be connected directly to the junction. Sealing between the flanges and the
PCB boards is ensured by standard rubber O-rings. Figure 2-9 is a technical drawing of the
flange design. Furthermore, a photograph of a WMS installed in the branch line is shown in
Figure 2-10.
Figure 2-9. Flange design with four through-holes for tightening, two centering pin holes, and
O-ring housing. Values in mm.
39
Figure 2-10. A single 16-by-16 electrode WMS installed in the 26 mm diameter branch line
of the T-junction. Visible on the left is the 50 mm diameter main pipe, on the top right, the 50
mm diameter mixing pipe, and, on the bottom right, the 26 mm branch line.
2.2.1.3 Calibration methodology
The calibration procedure normalizes the signal I(t), the WMS can expect to measure
at every crossing point based on the working fluids. By means of calibration measurements of
each working fluid, the natural, albeit small, discrepancies in the cell constants between the
electrode wires at each crossing point in the sensor is accounted for. The calibration
procedure is carried out prior to ever measurement series, and every time the supply water is
exchanged.
The facility is circulated with tap water at which time a ―high‖ calibration (Ihigh)
signal is recorded for 2 seconds for all crossing points at the planned measurement frequency
(1600 Hz or 2500 Hz). The branch line valve (SideFlow2) is then opened allowing deionized
water to fill the branch line completely at which time a ―low‖ calibration (Ilow) is recorded,
also for 2 seconds. For once-through tests the low calibration measurement would take place
while the circuit was emptying into the waste tank via the T-junction. Also in the case of
once-through measurements, the calibrations are valid for the entire measurement duration
and therefore the mixing scalar is calculated at a given crossing point simply as,
(2-1)
where I(t) is the measured signal at a given crossing point and Ilow and Ihigh are the average of
the calibration values at that crossing point. Figure 2-11 shows the average signal strength at
each crossing point in a 16 transmitter, 16 receiver electrode sensor
In closed-loop operation some deionized water from the branch line is recycled into
the main tank over the course of a measurement, disturbing the conductivity of the main pipe
flow, and therefore also deviating it from the initial tap water calibration signal. A
conductivity meter showed that the change in conductivity between the initially calibrated
value and the tank conductivity at the end of a series of measurements was always less than
40
0.25%. For greater accuracy, two high calibration measurements were recorded for each
closed-loop measurement series at different conductivities, I‟high and I‟‟high for the purpose of
generating a linear interpolation between the crossing point signals during each calibration.
Knowing that the signal output of the WMS is linear with electrical conductivity, a tap water
calibration function, Ihigh = f(I‟high, I‟‟high, κmain), for each crossing point in the sensor was
computed for an arbitrary main tank conductivity, κmain. Then, given the average main tank
conductivity during the course of a closed-loop measurement, (based on a linear
interpolation of pre-and post-measurement readings), the normalized mixing scalar is,
(2-2)
Data acquisition software provided is by teletronic Rossendorf GmbH [165]. The
software controls the amplifier ‗pre‘ gain and ‗main‘ gain. It is necessary that these values are
set such that the measured signal is never saturated or very near saturation (i.e. always < 85%
of the maximum possible signal strength). Should the signal strength approach saturation not
only would there be a loss of information but there may also be unwanted artifacts introduced
in the form of cross-talk where receivers may detect current travelling from non-neighboring
transmitters.
Figure 2-11. Average normalized crossing point values from a two second tap water, Ihigh,
calibration (left) and a two second deionized water, Ilow, calibration (right) measurement.
The signal-to-noise ratio (SNR) is calculated as the reciprocal of the coefficient of
variation, that is the average of the raw signal (or mixing scalar) divided by the standard
deviation of that same signal,
⁄ (2-3)
In Figure 2-12 the signal strength has been calculated according to Eq. 2-3 for the
same calibration measurements shown in Figure 2-11. The SNR at high signal strengths is
more than two orders of magnitude larger than that at the lowest signal strengths. This owes
mostly to the reduction in average signal approaching the noise rather than a large change in
the noise itself. Note that the lower SNR of the low calibration has little effect on the
uncertainty of the measured dimensionless scalar due to the error propagation though Eq. 2-1
or, respectively, 2-2.
41
Figure 2-12. Signal to noise ratio for (left) a two second tap water, Ihigh, calibration and (right)
a two second deionized water, Ilow, calibration measurements.
2.2.2 High-speed camera
Some additional understanding has been gleaned from videos recorded by a high-
speed camera installed to observe turbulent penetration in the branch line. To visualize the
mixing two blue LED spotlights induced fluorescence in the fluorescein-doped main flow.
The camera, a HighSpeedStar 3, produced by LaVision, recorded the mixing at a frame rate
of 60 Hz at 1024 × 1024 pixels. The spotlights produce a light intensity of 600 μW/cm2 at a
wavelength of 470 nm, near the 480 nm peak in the excitation wavelength of fluorescein
sodium salt (emission wavelength 525 nm). Approximately 0.85 g of fluorescein was mixed
with 350 liters of tap water in the main tank. Additionally, a Nikon DSLR camera was
positioned above the branch line which recorded still images and video. Visual observations
without the assistance of a camera were also conducted.
42
2.3 Appendix
2.3.1 Error analysis
The instrumentation installed at the facility, specifically the flow meters and WMS,
introduce sources of error in the boundary conditions assumed at the T-junction. Table 2-1
shows the measurement errors cited by the manufacturers of each flow meter used at the
facility. In addition, an estimated measurement error of the WMS itself is provided. The error
shown in the table related to the WMS is not the error induced by the WMS due to its
disturbance of the flow which is more difficult to quantify (see Appendix Section 2.3.2).
Device Type Use Measurement
error
Measurement
frequency [Hz]
Krohne IFM 1010
K
Krohne IFC 010
Electromagnetic Main flow meter ±0.05% of full scale
±0.5% of reading 8
Gundfos VFM 1-12
QT Vortex
Branch flow meter
Phase 1
Section 3.1
±3% of full scale Response time < 3
seconds
KOBOLD
DOM-S10HR21Z3
Positive-
Displacement
Branch flow meter
Phase 2
Section 3.3
±1% of reading 1
Wire-Mesh Sensor Electrical
conductance
Mixing
measurement
instrumentation
±3.62% Up to 10000
Table 2-1. Measurement error associated with flow meters used at the facility during various
experiments, and the WMS.
A number of errors contribute to the WMS output. These include calibration error,
quantization error and error due to electronic noise. An estimation of each of these errors is
generated based on a representative calibration and measurement (Ur = 100, 180 s, 1600 Hz)
with a 16 transmitter, 16 receiver WMS installed in the branch line of the LKE T-junction
facility.
Fluctuations in the signal due to electronic noise during the tap water calibration near
the center of the mesh at crossing-point (8,8) and near the wall at (16,8) are shown in Figure
2-13 along with the time series of each signal from the 2 s (3200 sample) calibration
measurement. During the low-end calibration of the WMS with deionized water the
fluctuations induced by electronic noise are much larger relative to the mean signal. For
example, near the center of the mesh at crossing-point (8,8), μ = 33.7 and σ = 3.1.
In the case of the representative high and low calibration measurements the systematic
quantization error of the 12-bit WMS signal near the center of the mesh and near the wall is
defined as the change in mixing scalar induced by a change of 0.5 in the raw signal. For both
near-center and near-wall crossing-points (8,8) and (16,8) this error is very small, at 0.024%
based on a maximum signal, in this case, of less than 75% of saturation (in order to avoid
cross-talk, as discussed previously).
43
Figure 2-13. (top) Probability density function and normal-distribution fit at a central
crossing-point (8,8) and a near-wall crossing-point (16,8) extracted from a 2 s, 1600 Hz tap
water calibration measurement. (bottom) Time series of each signal.
Calibration error varies from trial to trial. The linearity of the WMS response has been
investigated by Rohde (2005) and Bulk (2012).[166, 167] The report of Rohde (2005)
describes linearity errors of up to ±3% within a similar range of conductivities as the working
fluids in the experiments presented herein.
Systematic error is incurred when running closed-loop experiments at the facility due
to the changing EC of the tap water in the main supply tank. At a velocity ratio of 100, for
example, measurements indicate a change in main tank conductivity of 1.4 μS/cm over a long
duration 660 s measurement. Given that the main flow conductivity chosen as the high-
reference for the calibration curve is the average conductivity during a measurements, the
maximum discrepancy in conductivity is ±0.7 μS/cm at the high end. In other words, the error
induced is largest when measuring water of EC equal to 100% tap water and is equal to
0.62%.18
For a large number of samples, statistical errors such as the quantization error and
error due to electronic noise are greatly reduced (as a function of √ ). Left over is the
calibration error due to the linearity of the signal and error incurred due to changing main
flow conductivity in closed-loop tests. These errors are dependent on the fluid EC. The
18
Since the deionized water in the branch line supply tank is unaffected by close-loop experiments, this error
vanishes at conductivities equal to the low calibration.
44
overall error is estimated as a sum of the maximum possible errors incurred by both
components for this representative measurement.
2.3.2 Influence of the wire-mesh sensor
The WMS is an intrusive measurement technique. The electrode grid enhances
turbulent mixing at sufficient flow velocities and represents a pressure drop. The pressure
drop coefficients of each sensor, based on the tabulated data of Idel'chick (1966) for plane
grids19
is approximately 0.06. Furthermore, the percentage of cross-sectional free area is
approximately 94% for both sensors [168] The recirculation of flow through the WMS in the
branch line is not the most typical flow scenario for the sensor. Traditionally WMSs have
been positioned in pipelines with a dominant unidirectional axial flow (such as the T-junction
mixing pipe), however, more and more frequently three layer and dual-WMS are being
installed in such flows. The influence of the WMS has been reported in cross-flow T-junction
measurements by Walker (2009) [50]. As cylindrical blunt bodies it is likely that the
electrodes induce vortex shedding at a variety of frequencies based on the local velocity.
Figure 2-14 shows the WMS reducing turbulent penetration depth when installed near the T-
junction (2Db) observed using fluorescein dye.
Figure 2-14. Visually observed turbulent penetration depth at velocity ratios up to 900 with a
WMS installed in the branch (WMS) and without (w/o WMS) along with logarithmic fits.
2.3.3 Gain-magnitude frequency response
Mesh sensor technology is not limited in frequency resolution by thermal inertia, but
rather by the spatial averaging of the measured quantity within the space between transmitter
and receiver electrodes, which leads to a low-pass filtering. The cut-off frequency is inverse
proportional to the average residence time of the fluid in this space; it is therefore dependent
on the flow velocity. We assume that the diffusion timescale is significantly small, such that
it can be neglected, and focus entirely on the advection of ions by the flow. The volume-
averaging performed by the sensor results in the failure to resolve the true conductivity
19
Specifically, Diagram 8-9.
45
fluctuation amplitude in the case of high frequency fluctuations transported through the mesh
grid.
A simple first-order low pass filter with transfer function,
, (2-4)
is sufficient to describe the frequency response of the sensor. The time constant, τ, of the
mesh sensor is defined as the quotient of the distance between electrode grids (1.5E-3 m) and
the fluid velocity. The real part of Eq. 2-4 is,
| |
√ . (2-5)
Assuming a fluid velocity of 0.05 m/s, τ = 3E-2 s. The gain-magnitude frequency response of
the mesh sensor, based on Eq. 2-5 is shown in Figure 2-15 (left) for multiple flow velocities,
while the PSD of the filter (based on τ = 3E-2) and of sinusoidal input is plotted in Figure
2-15 (right). Uncertainty in the frequency response of the mesh sensor is the result of
variability in local fluid velocity. For example, crossing points very near the wall will exhibit
a more damped power spectrum due to a combination of smaller eddies and local fluid
velocities.
Figure 2-15. Gain-magnitude frequency response of the WMS built for the LKE T-junction
facility for a number of fluid velocities.
46
3 Outline of experiments and simulation
3.1 Phase 1 Experiments
3.1.1 Geometry
In the first phase of experiments at the LKE T-junction facility the main pipe was a
flanged acrylic glass tube with Dm = 50 mm, meeting the branch line in a sharp edged T-
junction. The inlet run of the main pipe was 32Dm. The branch line is a half meter long
acrylic glass tube of diameter Db = 50 mm or 26 mm depending on the experiment. There is
an inlet run of at least 20Db for the 50 mm diameter branch, or at least 38Db in the case of the
smaller 26 mm diameter branch. The inlet run in the branch line changes depending on the
WMS position. Acrylic spacer pieces, comprised of a single thick flange, or a short pipe
capped by two flanges is installed between the T-junction and the WMS to position the
sensor at various non-dimensional locations x/Dm or y/Db within the turbulent penetration
plume, see Figure 3-1. The mixing pipe, defined as the pipe immediately downstream of the
T-junction, is also of diameter 50 mm and is 10Dm (500 mm) in length.
Figure 3-1. Sketch of acrylic glass flanged spacer pieces installed in the branch line for
positioning of the WMS.
3.1.2 Test matrices
As a first clarification of the turbulent penetration phenomena, the test matrix in Table
3-1 was completed using a WMS installed at various branch positions. Main pipe and branch
line Reynolds numbers are indicated in Table 3-1 for each tested velocity ratio. Main flow
rates were held steady at 100 l/min or 180 l/min while the branch line flow rate was varied,
always within the laminar regime. No density stratification was imposed.20
For each flow
combination a single WMS was positioned at y = 1, 1.5, 2 or 4Db (where y is measured from
the center of the T-junction), such that a 2D data set spanning the 3rd dimension, the branch
axis, could be constructed. Figure 3-2 shows a schematic of the WMS positions and the
20
Small density differences may result from a small ΔT of the two working fluids, as delivered from the
building network.
47
orientation of the coordinate axes. For some measurements a WMS was installed in the
mixing branch at x/Dm = 1, in addition to the branch line sensor, such that the two sensors
recorded the scalar mixing simultaneously.
Figure 3-2. Schematic of the T-junction with locations of the WMS measurement planes and
the orientation of the coordinate axes. Gravity runs through the page.
Ur Um
[m/s]
Ub
[m/s] Rem Reb
[l/min]
[l/min] y/Db
28.61 0.85 0.030 42441 1484 100 3.5 1, 1.5, 2, 4
33.31 0.85 0.025 42441 1274 100 3 1, 1.5, 2, 4
501 0.85 0.017 42441 849 100 2 1, 1.5, 2, 4
1002 1.53 0.0153 76394 764 180 1.8 2, 4
1502 1.53 0.0102 76394 509 180 1.2 2, 4
2002 1.53 7.64E-3 76394 382 180 0.9 2, 4
4002 1.53 3.82E-3 76394 191 180 0.45 4
Table 3-1. Test matrix for T-junction mixing tests with steady inlet conditions. 160 second
open loop measurements at 2500 Hz, 2170 second closed-loop measurements at 1600 Hz.
In addition to equal branch ratio experiments, tests with a 26 mm diameter branch line
were performed at velocity ratios from 50 to 100. Table 3-2 indicates the flow conditions for
which experimental data has been obtained in this geometry, i.e. a branch ratio of 0.52. The
Phase 1 T-junction configuration, with 26 mm branch line and velocity ratio 100, was
reproduced in the LES simulation, discussed in Section 1.1.
Ur Um
[m/s]
Ub
[m/s] Rem Reb
[l/min]
[l/min] y/Db
50 1.53 0.030 76394 792 180 0.97 2
75 1.53 0.020 76394 522 180 0.65 2
100* 1.53 0.015 76394 392 180 0.49 2
Table 3-2. 170 second measurements at 1600 Hz. *A 660 second duration measurement was
performed for this case for comparison with an LES simulation described in Section 1.1.
3.1.2.1 Pulsatile flow
Finally, artificial pulsations in the main pipe were induced as a means of studying
large scale (so-called global) instabilities. Such instabilities may be generated, for example,
by pump fluctuations. A thorough review of the physics of turbulent pulsating flow is outside
48
of the scope of this work. It should be noted, however, that a tremendous body of work
spanning decades does exist, mostly related to pipe flows.[169, 170]
In the case of a leaking valve scenario, such pulsatile instabilities could result in or
exacerbate the problem of thermal cycling in the branch line. Favored frequencies in the
mixing spectrum, which have been observed in prior experiments, as discussed in the
introduction, may be the result of global instabilities in the flow. A regularly extending and
receding turbulent penetration could manifest a strongly favored frequency at which the
scalar fluctuations are strongest. In order to investigate such a situation, forced oscillations
have been introduced by means of a sinusoidal voltage input to the frequency controller of
the main pipe supply pump, which induces sinusoidal flow rate oscillations with a high
degree of accuracy,
(3-1)
where Qm(t) is the time-varying main pipe volume flow rate, a is the amplitude of the
oscillations, f is the frequency and is the mean, baseline main pipe volume flow rate. A
series of measurements were recorded for different amplitudes and frequencies of the volume
flux oscillations. The transfer from sine wave input via the pump controller to a time-
dependent bulk velocity, which oscillates accordingly, is not entirely linear. Still, the
hydraulic pressure drop is nearly proportional to the square of the flow rate and the pump
head is nearly proportional to the square of the impeller rotation speed. The flow rate under
steady state conditions is thus proportional to the pump rotation speed, which is in turn
proportional to the control voltage supplied to the frequency transformer. The real transfer
function is slightly more complicated, especially due to the effect of flow acceleration and
deceleration, and some distortions from the sine wave profile may take place. It was
nonetheless decided to remain with a sine wave control of the pump and check the result via
the flow meter output. It was confirmed that the flow follows a traditional sine wave within
the time resolution (8 Hz) and accuracy (±0.05% of full scale and ±0.5% of the reading) of
the flow meter.
The velocity profile in pulsatile flows is dependent on the Womersley number21
,
defined as the ratio of transient inertial force to viscous force [171].
√
(3-2)
where ω is the angular frequency, the characteristic length is Dm, the main pipe diameter, and
ν is the kinematic viscosity. The definition also extends to the Reynolds and Strouhaul
numbers in the following manner,
√ (3-3)
21
Originally introduced in the context of arterial flows.
49
Where St is defined here, based on the main pipe as . Note that dynamic
similarity is guaranteed given the same Reynolds and Womserley numbers. These numbers
are reported for the pulsatile flow experiments in Table 3-3.
The 18-measurement test matrix chosen for the global instability measurements are of
exaggerated amplitude for the purpose of simplifying the understanding of trends under such
mixing conditions, see Table 3-3. Main pipe velocity oscillation amplitudes range from ±5%
to ±20% of the average velocity with a frequency of 0.1 Hz, while information regarding the
effect of the frequency of the main pipe oscillations is garnered from measurements with an
amplitude of ±10% at 0.1, 0.2, and 0.3 Hz. The WMS data was collected over 170 seconds at
1600 Hz. The T-junction geometry remains in the aforementioned configuration with all
acrylic pipes leading to the junction being 50 mm in inner diameter. The velocity ratio for all
measurements was 34.5.
Hz
Oscillation
amplitude, a
(% of )
Oscillation
amplitude
[m/s]
[-]
St
[-]
α
[-]
[m/s]
[m/s] y/Db
0.1
5
15
20
0.076
0.23
0.31
42441 0.006 39.6 0.85 0.025
1,
1.5,
2
0.1,
0.2,
0.3
10 0.15 42441
0.006
0.012
0.018
39.6
56.0
68.6
0.85 0.025
1,
1.5,
2
Table 3-3. Test matrix for T-junction mixing tests with pulsed flow in the main pipe.
50
3.2 Phase 1 Large Eddy Simulation
3.2.1 Simulation test case
A representative case of turbulent penetration was chosen from the Phase 1
experimental test matrices at the LKE T-junction facility to be reproduced by time-resolved
CFD simulation. While velocity ratios ranging from around 25 to 3000 have been
investigated experimentally in this thesis, a ratio of 100 was selected for comparison with a
large eddy simulation (LES). The velocity ratio, mass flow rate ratio, and momentum ratio
are, , , and , respectively. The momentum ratio is defined as in
the work of Kamide (2009) [46]. Note that the Reynolds number ratio is also 100 since the
fluid properties are assumed to be nearly identical. The main flow is firmly in the turbulent
regime with a Reynolds number of approximately 76,000 while the branch line in-flow is
laminar, Reb = 400. For comparison, momentum ratios above 1.35 represent a cross flow
mixing case known as a wall jet while Zboray (2011) has shown the onset of turbulent
penetration in earnest at a momentum ratio of approximately 700 [141].
This test case was investigated with a long duration WMS measurement at the LKE
T-junction facility. The measurement is 660 seconds in duration with a recording frequency
of 1600 Hz at a non-dimensional location y = 2Db in the branch line. The WMS data at this
position indicated a broad peak in the scalar mixing power spectrum near the downstream
wall of the branch centered around 6 Hz, indicating the presence of some kind of regular flow
instability.
3.2.2 Simulation methodology
The study of thermal fatigue due to turbulent mixing necessitates resolving time-
dependent temperature fields since the internal stresses induced in steel pipe walls are
dependent on the frequency of thermal fluctuations in the fluid. Far more computationally
expensive than unsteady RANS simulations and considerably cheaper than DNS, LES is the
tool of choice for simulating T-junction mixing in the nuclear engineering domain.
Simulating turbulent penetration in T-junctions requires simulating long flow times which put
the work at the periphery of what is today computationally reasonable. The 13 seconds of
simulation presented herein are the result of over 100,000 CPU-hours. The simulation was
performed with the commercial code Star-CCM+ version 8.04.007-R8 from CD-Adapco.
The simulation was setup as follows. An implicit LES with 2nd
order temporal
discretization and segregated solver with segregated species was utilized. A passive scalar, θ,
was included and solved for with the help of an additional transport equation using the
default value of Turbulent Schmidt number of 0.9, such that tap water was assigned a value
of θ = 1 and deionized water , θ = 0. Five inner iterations were performed for each time step
of 2.5E-3 seconds.
3.2.3 Governing equations
51
The LES methodology is based on separation of scales into resolved and subgrid
components. Fully resolved are large scale turbulences in time and space while modeling of
smaller, subgrid scale (SGS) eddies is achieved by incorporating an added viscosity. The
following discussion draws from the derivations and discussions found in the textbooks of
Pope (2000) and Sagaut (2007) and lecture notes by Celik (1999) [172-174].
Figure 3-3. A simplified schematic of scale separation in physical space and Fourier space
from Sagaut (2007) [173].
The LES governing equations and those of unsteady RANS follow an identical
formulation. However, rather than averaging the Navier-Stokes equations in time, LES
modifies these equations in the same way but in the spatial domain in an operation known as
filtering. The sub-gird-scale methodology is as follows, given a field u(x,t),
𝑢 𝒙 𝑢 𝒙 𝑢′ 𝒙 (3-4)
where 𝑢 𝒙 is resolved, in this case via a spatial filtering process described below and
𝑢 𝒙 is the unresolved SGS component, see Figure 3-3. In general, a variable 𝑢 𝒙 is
filtered in 3D space utilizing a convolution kernel G, in the following operation,
𝑢 𝒙 ∫ ∫ 𝑢 𝒙 ′
. (3-5)
The conservation equations for momentum and kinetic energy, as well as continuity
are filtered. A decomposition of the non-linear filtered product 𝑢 𝑢 is performed, the
decomposition being named after Leonard (1974) [175], which leads to the residual stress
tensor,
�� �� 𝑢 𝑢 . (3-6)
Noting the residual kinetic energy is,
, (3-7)
52
it follows that the deviatoric component22
of the residual stress tensor (from the anisotropic
part of the stress tensor) is,
. (3-8)
The hydrostatic, isotropic component is incorporated into to the filtered static pressure term.
It is , often referred to as the subgrid stress tensor, that must be modeled. Modeling of the
tensor is based on the hypothesis proposed by Boussinesq known as Boussinesq‘s turbulent
viscosity hypothesis which assumes a linear relationship between subgrid stress tensor
written above, and strain rate tensor [176]. Utilizing this hypothesis the previous equation
becomes,
, (3-9)
where is the eddy viscosity and is the resolved strain rate tensor,
(
). (3-10)
Essentially, the SGS turbulence is modeled via an eddy viscosity. Two major eddy
viscosity models are in use today for computing , they are the Smagorinsky model and the
Wall-Adapting Local Eddy-Viscosity (WALE) model. The WALE model is the default
model of its kind in the Star-CCM+ software, it has seen successful application for a number
of years. Ma (2008), for example, made an assessment of SGS models with experimental
backing, in simulations of turbulent flow in a water turbine; the WALE model performed the
best [177]. Furthermore, in the Vattenfall T-junction benchmark exercise LES simulations
utilizing the WALE model placed higher than those using the Smagorinsky model ranked by
comparison to thermocouple data [47]. Menter (2012) notes that the WALE model is the
simplest model able to automatically provide a zero eddy viscosity in laminar shear flows
which ―is especially important when computing flows with laminar turbulent transition‖
[178].
The simulation presented in this thesis was performed using the WALE model which
calculates the eddy viscosity as a function of velocity gradient,
(3-11)
where,
(3-12)
22
The other component being hydrostatic stresses.
53
is based on the square of the velocity gradient tensor,
(3-13)
(3-14)
The model accounts ―for the effects of both the strain and the rotation rate of the smallest
resolved turbulent fluctuations;‖ a model constant Cw, has been left unchanged with a value
of 0.544 [179]. This value of Cw has been shown to work well for a variety of turbulent
conditions, including channel flows [180].
3.2.4 Computational grid
A decision on the cell base size of the mesh was made based on the work of Addad
(2008) on optimal unstructured meshing for LES, later demonstrated in cross-flow mixing
simulations for the Vattenfall benchmark exercise published by Kuczaj (2010) [85, 181].
Essentially, the degree of grid refinement is chosen based on knowledge of turbulent length
scales. Since LES filtering addresses eddies on the order of the Kolmogorov scale by
implementing SGS models, the length scales of importance for meshing is rather the Taylor
microscale. This scale is defined as, √ 𝑢 , where the R subscript indicates the
values are obtained by a stead state RANS simulation while k and ε are the turbulent kinetic
energy and dissipation, respectively. A RANS simulation was performed for the Ur = 100 test
case using the Reynolds Stress Model. A field function was generated to compute the Taylor
microscale over the entire domain. The minimum Taylor microscale was approximately
0.275 mm. This data was converted into a mesh size table such that the polyhedral mesh base
size was made to vary with the local Taylor microscale. All regions with λR > 1 mm, such as
in the laminar portion of the branch line, were set to be meshed with a cell base size of 1 mm.
The result is a computational grid with half of the cells compared to one with a universal base
size determined by the smallest Taylor microscale. The mesh contains 6,451,848 polyhedral
cells.
The issue of wall treatment is critical. The decision on the choice of mesh
characteristics were taken with the findings of Jayaraju (2010) in mind in which LES
simulations were carried out using the Star-CCM+ and the WALE SGS model [182]. In his
work a strong case is made for the necessity of a fully resolved wall for simulating cross-flow
T-junction mixing. Specifically, an under-prediction of fluctuations in the temperature and
velocity fields in the vicinity of the walls and in the wall heat-flux was observed. Since wall
functions are derived from steady state conditions in pipe flow, they cannot necessarily be
trusted in more complex mixing geometries.
The extent of the computational domain is limited in the axis of the main pipe (x) and
extended beyond the region of expected deepest turbulent penetration, based on experimental
observations, along the branch axis (y). The domain resides in the region (-0.02 m < x < 0.03
m) and (-0.025 m < y < 0.13 m) where the origin lies in the center of the T-junction. In non-
54
dimensional terms, the branch boundary resides at y = 5Db. The decision to limit the extent of
the main pipe was primarily an issue of computational savings. Confidence in the domain
size was gained via experimental observations of this flow case with fluorescein dye which
did not appear to show mixing upstream of the branch in the main pipe. Figure 3-4 shows the
mesh as seen in the z = 0 mid-plane of the T-junction.
Figure 3-4. 6.45 million cell Polyhedral-prismatic mesh viewed in the z = 0 plane.
3.2.5 Initialization
Boundary conditions were not measured experimentally beyond bulk values recorded
by flow meters at the facility. Without detailed information about the velocity profiles at the
boundary of the LES domain, a fully developed profile is adopted and recognized as a
potential source of discrepancy when comparing the simulation and experimental results.
Fully developed profiles are generated for both the branch and main pipe in periodic k-ε
steady state RANS simulations. The periodic domains are of length 2πD as a means to
capture the effects of the largest potential eddies in the flow. The converged cross-sectional
velocity profiles from these precursory simulations are imported into the full T-junction
domain. Artificial turbulence is then induced in the main pipe (but not in the laminar branch
line) by the Synthetic Eddy Method which superimposes isotropic velocity field fluctuations
on the steady, developed velocity field from the periodic domain simulation [180]. This
method requires as input the turbulent intensity I, and turbulent length scale l, both of which
have been calculated based on correlations for pipe flow as follows,
, where
the Reynolds number is defined as a function of the hydraulic diameter, ⁄ ,
and l = 0.038Dm, respectively. The main pipe turbulent intensity at the inlet boundary is
3.92% and the turbulent length scale is 1.9E-3 m.
Initialization proceeded as follows. In order to reduce the time necessary for the LES
simulation to start producing meaningful results, a steady state RANS simulation was
performed using the Reynolds Stress Model. Once converged, the switch was made to LES
and approximately 3 seconds of flow time were simulation in a 12.3 million cell mesh with
uniform polyhedral base size of 0.275 mm, equivalent to the smallest Taylor microscale
encountered within the domain. After confirming the convergence of the simulation, and
55
observing qualitatively realistic mixing in the branch line as expected from experimental
results, the mesh was transitioned to the 6.45 million cell grid with polyhedral size based on
the local Taylor microscale, with an upper cell base size limit of 1 mm, for the remainder of
the simulation.
56
3.3 Phase 2 Experiments
3.3.1 Geometry
In Phase 2, the LKE T-junction geometry was modified such that the main pipe was
reshaped into a rectangular duct.23
The modified main pipe geometry, demonstrated by
Robert (1992), Deutsch (1997) and, among others, researchers at the INSS in Japan, was
implemented at the LKE T-junction by shrinking the main pipe cross-section in order to
achieve higher flow velocities (sometimes referred to as ‗blocking‘) [105-107, 124]. The new
main pipe conduit was manufactured from two acrylic halves bonded to form a rectangular
flow area 10 mm in width and 50 mm in height, with hydraulic diameter 16.67 mm
(henceforth, Dm). The hot or cold leg in a PWR has an inner diameter of, for example,
0.74 m, therefore the curvature seen at the junction by a standard 2‖ (50 mm) or 4‖ (102 mm)
diameter branch line is small. For this reason we find acceptable the use of a rectangular
cross section of the main pipe for the purpose of turbulent penetration experiments.
Furthermore, Tanimoto (2002) concluded in-part that, ―[t]he penetration length is
dependent not on the diameter ratio of the branch pipe to the main loop but on the
diameter of the branch pipe‖ [111]. Intersecting the main pipe on its tall side is the same
Db = 26 mm branch line from Phase 1. The inlet run in the main pipe is now 34.1Dm. A
sketch of the Phase 2 geometry is shown in Figure 3-5.
Figure 3-5. Sketch of Phase 2 LKE T-junction geometry with 10 mm rounded edge, 10 mm
wide (by 50 mm tall) main and mixing pipe and 26 mm diameter branch line. Shown are the x
and y-axes located at the origin from which dimensionless branch position is defined. Gravity
is directed opposite the z-axis. Red arrows indicate main flow, blue arrows indicate branch
flow. View (a, top) shows the x,y plane, while (b, bottom) shows the x,z plane.
23
For the sake of continuity, the nomenclature will remain unchanged; ‗main pipe‘ still refers to the conduit in
which turbulent main flow is traveling prior to its arrival at the T-junction.
57
The second design phase also saw the introduction of modifications to the junction
geometry. Recognizing the potentially large importance of the edge geometry at the
intersection of the main pipe and branch line, an additional T-junction with a curved edge
with constant radius of curvature at the intersection with the branch line was manufactured
(also visible in Figure 3-5). The branch line is connected to the junction, as usual, with
acrylic spacer pipes for the adjustment of the WMS position. Only a single WMS is installed
in the branch at a given time and no WMS is present downstream in the mixing pipe.
3.3.2 Test matrices
The introduction of a reduced area main pipe in Phase 2 of the LKE T-junction
facility design enabled higher main flow velocities and higher velocity ratios, up to 3000, to
be explored. High speed camera footage was recorded for velocity ratios ranging from 50 to
900 while WMS measurements were performed between Ur = 400 and 3000. Experiments at
these higher velocity ratios look to describe the turbulent mixing behavior deeper into the
branch line. Additionally, a two-axis test matrix explores, with WMSs, T-junction geometry
and density effects by introducing a deionized water-sucrose solution as the branch line
working fluid.
The following text matrix is intended to explore higher velocity ratios, up to 3000. In
addition, the effect of main flow Reynolds number is investigated at a fixed velocity ratio of
2000. All tests were carried out at two branch positions, y = 3.73Db and 5.73Db, where y is
the distance from the precipice of the branch line (the new origin of the coordinate system).
The large amount of turbulent penetration at these velocity ratios means that measurements at
positions close to the junction (e.g. 1, 1.5, and 2Db etc.) are trivial; in the branch line at these
positions the scalar is essentially 100% tap water. The full test matrix was carried out in both
sharp edged and rounded edge T-junctions for a total of 20 measurements, see Table 3-4.
Each measurement was recorded at 1600 Hz for a duration of 180 s.
Ur Qm Um Rem Qb Ub Reb
1000 173.49 5.78 96000 0.184 0.0058 149.76
2000 117.47 3.92 65000 0.062 0.0019 50.7
2000 144.58 4.82 80000 0.077 0.0024 62.4
2000 173.49 5.78 96000 0.092 0.0028 74.88
3000 173.49 5.78 96000 0.061 0.0019 49.92
Table 3-4. Test matrix with 26 mm diameter branch line.
Most academic research in the field of T-junction mixing utilizes sharp edged T-
junctions, while forged stainless steel components in NPPs tend have a large radius of
curvature at the junction. Two T-junctions have been tested, one with sharp edges and one
with a curved edge (r = 10 mm). The two junctions share the same hydraulic diameter, 16.67
mm, in the main and mixing pipe. Henceforth, ‗T-junction geometry‘ will refer to the degree
to which the edges of the intersecting channels are rounded or curved, sometimes called the
welding chamfer although it is equivalent to a fillet.
58
3.3.2.1 Density and edge geometry
Another important parameter in T-junction mixing, as it relates to the reality in NPPs
is the density of the coolant and its temperature dependence. In the case of a leaking valve
scenario, the water entering the branch line is of a much lower temperature than the main
flow, especially in the case when the hot flow is directly from the hot or cold leg of the RCS.
In the normally stagnant fluid behind valves in branch lines heat loses have a strong negative
impact on fluid temperatures above ambient. Density difference generated by addition of
sucrose to the deionized water supply of the branch line at the LKE T-junction has allowed
for a number of tests at the facility with density differences , of 0.024 to
0.088 (density ratios ρr, of 0.98 to 0.91).
Adiabatic single phase mixing experiments have been carried out in the past with
artificial density difference in a variety of conduit geometries including T-junctions [110,
158]. While the mixing scenario of interest calls for a colder branch flow to meet a hotter
main flow at the T-junction, in adiabatic tests it is therefore proposed to increase the density
of the branch flow artificially using a solute, typically sucrose or calcium chloride. In the
presented experiments, sucrose is chosen to increase the density of the branch flow. Large
density differences between two incoming flows were achieved which would otherwise
require a pressurized high-temperature test facility. Figure 3-6 shows the increase in the
relative density of water with increased sucrose mass concentration; at 20ºC at around 30%
concentration by mass the solution becomes saturated.
ε
[-]
Edge radius, r
[mm] Measurement duration (s)
Iso-dense 0 0 & 10 170 (closed-loop)
Sucrose 1 0.024 0 & 10 60 (once-through)
Sucrose 2 0.051 0 & 10 60 (once-through)
Sucrose 3 0.070 0 & 10 60 (once-through)
Sucrose 4 0.088 0 & 10 60 (once-through)
Table 3-5. Test matrix including density stratification and T-junction geometry.
Table 3-5 shows some details of the density-enhanced experiments performed in
Phase 2. All tests were carried out at a velocity ratio of 2000 where Um = 3.92 m/s,
Rem = 6.5E4 and Ub = 2.0E-3 m/s. Wire-mesh sensor measurements were performed, as
above, at two branch positions, y = 3.73Db and 5.73Db for every flow case. Data was
recorded at a frequency of 1600 Hz.
59
Figure 3-6. Relative density of deionized water vs. weight concentration of sucrose. Beyond
30% sucrose by weight, precipitation of sucrose in the solution occurs.
The use of sucrose rather than calcium chloride (which would enable greater densities
to be reached) was required due to the signal saturation experienced by the WMS in the
presence of highly conductive fluids. While realistic density differences may be approached,
viscosities found at high temperatures in LWR piping cannot be appropriately matched. Fluid
properties for all tests are shown in Table 3-6 along with two representative reactor cases
from a PWR which have not been investigated at the LKE T-junction facility. Viscosity
values are gathered from literature based on the density of the solution. The densities and
viscosities are averages between the values during the individual WMS experiments at
3.73Db and 5.73Db.
Reb
[-]
Rer
[-]
ρm
[kg/m3]
ρb
[kg/m3]
ρr
[-]
ε¹
[-]
ηb
[cP]
ηr
[-]
Frb
[-]
Ri
[-]
ΔT
[K]
Iso-dense 51 1.3E3 997 997-998 1 0 1.00 1 - 0
Sucrose 1 43 1.5E3 997 1021 0.98 0.024 1.17 0.85 3.3 0.092 0
Sucrose 2 34 1.9E3 997 1050.5 0.95 0.051 1.48 0.67 1.5 0.44 0
Sucrose 3 28 2.3E3 997 1072.5 0.93 0.070 1.78 0.55 1.1 0.83 0
Sucrose 4 23 2.8E3 997 1093.5 0.91 0.088 2.21 0.45 0.9 1.2 0
Reactor
1* 34 1.2E6 950 1005* 0.945 0.055 0.99 0.25 - - 100
Reactor
2* - - 851 1005* 0.847 0.15 0.99 0.15 - - 200
Table 3-6. Fluid properties related to the test matrix shown in Table 3-5. *Examples based on
a branch line fluid temperature of 20°C at 15 MPa pressure. Estimated Reynolds numbers.
Density difference ε, is an important parameter which has a significant impact on
turbulent mixing in T-junctions. Furthermore, the Froude number is commonly used to
characterize flows with large density differences between species. The dimensionless number
is a function of velocity, reduced gravity, and a characteristic dimension. We use the
following definition of the Froude number based on branch line values,
60
√ , (3-15)
where ′ is the reduced gravity defined as gravity multiplied by the density difference,
where the density difference is defined as,
, (3-16)
See Table 3-6 for Fr numbers. Also referenced is the Richardson number, defined here as
. (3-17)
This definition of the Richardson number is identical to that found in Chapuliot (2005) for
cross-flow mixing. The values found here, however, are three orders of magnitude higher
owing to the slow branch line velocity [1].
61
3.4 Regarding the orientation of presented results
The orientation of the WMS data contour plots, as well as cross-sectional simulation
results from the branch line, shown in the following chapter are always oriented as sketched
in Figure 3-7, unless explicitly stated. Regarding the definition of the coordinate axes
orientation, the orientation is defined as the center of junction (i.e. intersection of the center
of the main pipe and center of the branch line) in Phase 1, and in the middle of the branch
line at the precipice between the main pipe and branch line in Phase 2.24
The x-axis runs from
the origin down the mixing branch, the y-axis from the origin into the branch line, and the z-
axis is oriented, as usual, with +z pointing in the direction opposite to gravity. Figure 3-7
shows two viewing perspectives, one describing the viewing orientation of WMS data for the
case of installation in the mixing pipe, and the other for results in the branch line.
Figure 3-7. Representative position of the WMS and data viewing orientation for installation
in the mixing pipe (left) looking away from the T-junction and branch line (right) looking
towards the T-junction.
When WMS results are plotted, they are plotted on a normalized scale based on the
tap water (θ = 1) and deionized water (θ = 0) signal values at every crossing point. The color
bar in contour plots is scaled such that tap water is red and deionized water is blue.
Furthermore, when specific crossing points are described, for example when showing a time
sequence of the signal at a particular location, or a power spectra, they are referenced as a
Cartesian coordinate (Transmitter t, receiver r), recall Figure 2-8. Often, positions in the
branch line are referred to as being near the ―upstream wall‖ or ―downstream wall‖ based on
the orientation seen in Figure 3-7.
The RMS of the scalar is always calculated as,
√
∑
, (3-18)
where is the average in time of the scalar during the measurement period. The scalar RMS
is the square root of the scalar variance which is equivalent to the integral over the PSD of the
scalar signal.
24
Regarding the definition of the origin, in the case of an artificially reduced main flow area as in the case of the
rectangular cross section of the main pipe in Phase 2, the definition chosen here is common practice.
62
4 Turbulent penetration with in-flow
The following chapter draws on findings from three sources described in detail in the
previous chapter: 1. wire-mesh sensor measurements performed at the LKE T-junction, 2.
Star-CCM+ LES simulation performed at a velocity ratio of 100 with a 50 mm main pipe and
26 mm branch line, 3. high-speed camera footage. Note that all discussion is related to iso-
dense mixing, until Section 4.8 where experiments with a heavier branch flow are analyzed.
4.1 Turbulent penetration and how it differs from cross-flow mixing
Turbulent penetration in T-junctions is a flow configuration categorically different
than cross-flow mixing. Although, in the case of turbulent penetration, mixing between
branch and main flows continues in the mixing pipe downstream of the T-junction, its
character is unlike mixing at the same location at velocity ratios near unity (i.e. cross-flow
mixing). To varying degrees on a spectrum between the dead-leg case ( ) and that of
velocity ratios near the onset of turbulent penetration ( ), turbulent penetration in the
branch line renders flow at and downstream of the T-junction ‗pre-mixed.‘ The consequence
being that in the mixing pipe large amplitude scalar fluctuations are unlikely, if not
impossible, and thereby the mixing pipe is no longer a region of interest with regards to
thermal fatigue.
Simultaneous measurements by WMSs in the branch line and mixing pipe at the same
non-dimensional positions were analyzed. Figure 4-1 (left) shows comparison between the
scalar fluctuation profile in the mixing pipe and branch line, both one diameter from the T-
junction at a velocity ratio of 33.3 where the main tap water flow is normalized to 1 and the
deionized branch flow to 0 (sharp-edged T-junction, Dm = 50 mm Db = 50 mm). Maximum
scalar fluctuations present in the mixing pipe at this position are approximately half of that
found at an equal distance into the branch line. Further mitigating the relevance of these
fluctuations are their high frequency nature. A normalized PSD from two near-wall positions
in both the branch line and mixing pipe are plotted in Figure 4-1 (right). Scalar fluctuations in
the mixing pipe at x =1.0Dm are characterized by high frequencies and low amplitudes; while
in the branch line, damped high frequencies result in low frequencies (< 10 Hz) contributing
far more to the scalar RMS, relative to the same location in the mixing branch.
63
Figure 4-1. (left) RMS of the scalar in the mixing pipe at x = 1.0Dm (top) and the branch line
at y = 1.0Db (bottom). (right) PSD of scalar fluctuations near the wall (mm values represent
distance from the wall) indicated by red dots in contours on left, Ur = 33.3.
Turbulent penetration results in the flow exiting the T-junction through the mixing
pipe in what could be described, in the nomenclature of cross-flow T-junction mixing, as a
weak wall jet. Upon exiting the branch line the fluid is accelerated down the mixing pipe in a
concentrated, crescent shaped near-wall region, seen in Figure 4-1 (left, top), likely dictated
by the turbulent velocity profile in the main flow. A time series near the downstream wall25
in
the branch line and mixing pipe are show in Figure 4-2 for a velocity ratio of 50. In the
mixing pipe at x = 1.0Dm fluctuations are notable for their high frequency and low amplitude
nature visible already before a more detailed spectral analysis. Meanwhile, in the branch,
pulsations of main flow (i.e. turbulent penetration), some with amplitudes of 50% of the
scalar, are visible on a much larger characteristic time scale.
25
According to the measurement orientation, see Figure 3-7.
64
Figure 4-2. Signal from crossing points near the wall (16,31) in the mixing pipe and in the
branch line.
The profile of the mixing spectra downstream of the T-junction during turbulent
penetration is found to be highly similar, in slope and shape, to the spectra at similar locations
in cross-flow mixing cases. Figure 4-3 shows a comparison of the PSD at a crossing point
near the wall in the mixing branch for the case of cross-flow mixing at Ur = 1 in the facility
of Walker (2009) versus in the branch line of the LKE T-junction facility for the case
turbulent penetration at Ur = 50 26
[50]. Both flow configurations result in a nearly flat
spectrum across low frequencies in the mixing pipe followed by a steepening around 10 Hz.
The only major difference between the spectra is that the amplitude across all frequencies is
significantly higher in the cross-flow mixing scenario, indicating a higher scalar RMS, as
anticipated. The PSD near the downstream wall in the branch line at Ur = 50 is also plotted
and, as suspected, shows weighting heavily on the low frequency side with a rapidly damped
high frequency contribution akin to a low-pass filtering. This is expected in the sense that the
average Reynolds number in the branch line, even in the case of violent turbulent penetration
at high Ur, is far less than in the mixing pipe. A reduction in the turbulent kinetic energy of
the flow and the presence of a recirculation region (i.e. where thermal cycling occurs) leads
naturally to less high frequency high amplitude fluctuations and more power in the low
frequencies of the spectrum.
Figure 4-3 A comparison of PSD at locations of high RMS in the branch line (y/Db) and
mixing pipe (x/Dm) at Ur = 50 (Dm = Db = 50 mm) compared with the results of Zboray
(2011) at Ur = 1 (Um = 0.5 m/s, Dm = 52 mm) in the mixing pipe [141].
Time resolved CFD simulations (Dm = 50 mm, Db = 26 mm) corroborate these
experimental measurements (Dm = 50 mm, Db = 50 mm) with regards to mixing downstream
of the T-junction for a non-unity branch ratio geometry. Having outlined the flow behavior in
the mixing pipe in the case of turbulent penetration and its apparent lack of threatening
characteristics (in a HCTF-sense), the remainder of this chapter will focus on the turbulent
mixing occurring in the branch line itself.
26
The Walker (2009) facility having main, branch, and mixing pipe inner diameters of 52 mm, marginally larger
than the 50 mm pipes of the LKE T-junction pipes, as configured in this measurement.
65
As discussed initially in Section 1.3.3.1, turbulent penetration depth is a value of
interest in T-junction mixing studies. Visual observations in a 26 mm branch line without
accompanying WMS, by employing a fluorescein-doped main flow, indicate a logarithmic
dependence of turbulent penetration depth on the velocity ratio, see Figure 4-4. A fit function
has been generated for velocity ratios up to 900 and main flow Reynolds numbers up to
1.3E5,
, (4-1)
with an R2 of 0.9319. An increase in main flow Reynolds number at a fixed velocity ratio is
also shown to enhance the depth of main flow ingress into the branch line.
Figure 4-4. Turbulent penetration depth in an empty (no WMS) 26 mm branch line as a
function of velocity ratio with logarithmic fit.
There are some typical distributions of the time-averaged scalar and fluctuating scalar
(RMS) profiles in the branch line at ‗shallow‘ depths during the onset of turbulent
penetration, however, prior to a description of the flow behavior in a mostly time-averaged
sense, it is valuable to understand the highly transient nature of turbulent penetration. Figure
4-5 and Figure 4-6 show two pairs of such scalar distributions, which, while dissimilar, were
both manifest within a short period of time. Nonetheless, the flow is not totally chaotic and
on a large enough time scale an average profile with a distinct, interpretable scalar
distribution is measured. It is evident from the measurements that the main flow appears in
the branch (at any significant depth) initially along the downstream wall of the branch. This
has been shown to be a valid description for all velocity ratios, branch ratios, and branch
geometries explored. Since the WMS was never installed closer than 1.0Db in the branch line,
the LES is relied on for a more complete understanding of the flow behavior at the mouth of
the branch line.
66
Figure 4-5. Two frames from a measurement in a 26 mm branch at 5.73Db exhibiting vastly
different scalar distributions for a given boundary condition, in this case Ur = 2000.
Figure 4-6. Two photographs separated in time by 100 ms showing a sudden change in
turbulent penetration depth in a 26 mm branch line. Main flow is visible in green.
67
4.2 Flow characteristics at the entrance to the branch line
The flow at the T-junction is reminiscent of turbulent cavity flows. A great deal of
research has focused on compressible cavity flows in the context of aeronautical engineering
acoustics. Analogously, these flows exhibit wavy instabilities developing after the main flow
separates at the upstream wall of the cavity, which then are sheared by the downstream wall
of the cavity. At some velocity ratios, such as the simulated case of Ur = 100, the shear layer
also contains large instabilities in the scalar field, rather than the velocity field alone. Figure
4-7 shows a snapshot of the uj velocity field (contour rings) and scalar field (filled contour) in
the z = 0 mid-plane of the T-junction at the branch mouth where the instabilities are clearly
seen.
Figure 4-7. Free shear layer instabilities in velocity (contour lines) and scalar field (filled
contour) forming after main flow boundary layer separation (flow right to left). Instantaneous
snapshot with three large waves each with positive and negative uj velocity areas.
The limited distance (≤ 26 mm) and time (approximately ≤ 20 ms) in which the
instabilities have to form when crossing the branch mouth results in waves which, while
breaking, never fully roll over to form the large billows often associated with such shear
layers. They are reminiscent of the famous turbulent mixing shadowgraphs downstream of a
splitter plate by Brown (1974), or of certain atmospheric flows, see Figure 4-8 [157]. The
area of low pressure behind each wave entrains branch fluid into the turbulent main flow, a
phenomena described variously as ‗gulping,‘ ‗enfolding,‘ or ‗entanglement;‘ some of this
fluid exits the T-junction through the mixing pipe. While on the other hand, main flow wave
crests, upon being sheared by the downstream wall of the branch may catapult into the branch
line. The result of this countercurrent flow in the branch line is a second shear layer growing
into the center of the branch in the broad recirculation zone. While the region of shear itself is
unbounded and therefore could be described as a free shear layer, the proximity of the wall
boundary layer plays an important role. This second shear layer defines the central axis of the
recirculation zone.
68
Figure 4-8. Instabilities forming at the branch mouth in the mid-plane of the T-junction (left),
similar, slower instabilities may exist in air masses (right, photo credit: Brooks Martner,
NOAA/ETL).
Figure 4-9. Top view of the T-junction from LES. Well-defined free shear layer growing
with progression across the mouth of the branch shown in a contour plot of average ui (left)
and, similarly, a second shear layer within the branch visible in the average uj field (right).
Both shear layers are visible in average velocity contour plots in Figure 4-9, recall
that by definition a shear layer is a region of significant velocity gradient. The shear layers
can also be isolated by plotting the magnitude of the strain rate tensor S, calculated from the
velocity field. Where the tensor is defined as,
(
), (4-2)
with magnitude based on the inner product,
‖ ‖ √ (4-3)
The strain rate magnitude of the shear layer due to turbulent penetration in the branch is
significantly less than the fast moving free shear layer over the mouth of the branch. It is for
this reason that in Figure 4-10 two different color bar scales are used to discern both zones of
elevated strain rate magnitude.
69
Figure 4-10. Top view of the T-junction from LES. Magnitude of the strain rate tensor is
plotted on different scales such that both shear layers are visible (circled in red).
Time-averaged analysis of the two shear layers occurring in turbulent penetration
mixing is performed with simulations results from the z = 0 plane. The two shear layers are
visible in the average ui and uj velocity fields, respectively. As the main flow boundary layer
separates from the wall a free shear layer is born which precipitates the formation of coherent
large scale instabilities. The strong velocity shear between the fast main flow and branch line
flow, which at the precipice of the branch exhibits near-zero mean ui velocity, causes the
shear layer to grow. The velocity difference is ΔU = Umi - Ubi. The main flow free stream
velocity is defined at the center of the velocity profile in the main branch where, Umi = 1.83
m/s. The mean velocity is equal to ⁄ m/s and the constant
⁄ . The branch line free stream velocity is more difficult to calculate because
of the recirculation zone therein, for this reason some, in the study of cavity flow, have opted
against the calculation of the momentum thickness, favoring rather vorticity thickness as a
means of quantifying the shear layer growth [183]. The vorticity thickness is defined in this
case as | 𝑢 ⁄ | ⁄ [157].
The instabilities are disturbed by the oncoming wall, some of the main flow is
catapulted into the branch line with sufficient –uj velocity as to generate a shear layer in the
branch line, perpendicular to the layer previously discussed. Without traditional boundary
conditions, this shear layer is very difficult to characterize. Nonetheless, a pseudo vorticity
thickness may be calculated. The Ubj is the free stream velocity of the in-flow to the branch
line while the main flow ingression is given a variable free stream velocity based on the
maximum –uj velocity in each line profile through the shear layer, | | such that
| | | 𝑢 ⁄ |
⁄ .
The free shear layer vorticity thickness growth across the mouth of the branch can be
seen in Figure 4-11. The vorticity thickness grows linearly, as is typical of such flows, with a
slope of 0.3. Upon reaching a maximum value of approximately 6.5 mm the thickness
collapses rapidly just prior to the downstream edge of the branch at its intersection with the
main pipe. The second shear layer growing in the branch is much broader than the first, and
although ΔU is smaller than in the first layer, the vorticity thickness, also shown in Figure
70
4-11, is an order of magnitude smaller, being always less than 0.8 mm,. Furthermore, the
increase in vorticity thickness increases into the branch with a mostly linear trend, the slope
being 0.02.
Figure 4-11. Development of the vorticity thickness of the free shear layer at the mouth of the
branch (left) and within the branch (right) with moving average fits.
At a higher velocity ratios (e.g. Ur > 2000), or in the case of a dead leg, it has been shown the
penetration depth of the main flow extends much farther into the branch resulting in the
absence of scalar mixing in the vicinity of the branch mouth. At the simulated velocity ratio
of 100, however, the shear layer is stable both in the velocity field and scalar field such that
periodic scalar fluctuations are present and may be followed far into the branch. The spectra
of scalar mixing along with the uj velocity field is plotted in Figure 4-12, at least two
dominant frequencies are present in the mixing layer in both fields.
Figure 4-12. Power spectral densities at the center of the mouth of the branch line (see black
dot in insert) showing peaks centered around 51 and 86 Hz (vertical black dotted lines) in
both the scalar and uj velocity fields, computed from an LES simulation.
71
4.3 Onset of turbulent penetration (Ur < 100)
The onset of turbulent penetration in the branch line is characterized by a single,
coherent zone of mixing in an area surrounding the downstream wall of the branch. In scalar
average and fluctuation profiles from WMS measurements. For the estimation of the
penetration depth, only few axial measuring positions are available with the WMS
instrumentation. At Ur = 28, the penetration depth starts exceeding one pipe diameter, at Ur =
33, two diameters, and at Ur = 100, the tap water flow penetrates beyond four branch line
diameters.
The mixing region in the branch line grows with increasing velocity ratio, 28 to 50,
while the highest main flow concentrations of up to 50% remains fixed to the wall. Near the
depth of farthest penetration, however, this region appears to separate slightly from the
downstream wall (see Figure 4-13, 2Db at Ur = 50). Scalar fluctuations measured in these
experiments, which are of the utmost interest when discussing thermal fatigue, are seen to
vary tremendously in terms of location (e.g. proximity to the conduit walls) and magnitude
throughout the turbulent penetration region, see Figure 4-13. Initially, at the lowest velocity
ratios for which turbulent penetration extends to the neighborhood of 1Db (i.e. to the first
available measuring position of the WMS), the region of highest scalar average and RMS
overlap near the right wall. As the velocity ratio increases the penetration along the right wall
becomes steadier, as seen in the higher average scalar, therefore causing the region of highest
scalar RMS to transition to the area in which the average scalar gradient is highest. A
crescent shaped region of high RMS is formed, extending from the top wall to the bottom
wall. Far from the junction, near the extent of the turbulent penetration at the end of the
thermal cycling region, which is extended by increasing velocity ratio, the maximum of the
scalar average and fluctuation profiles are again overlapping and concentrated at the right
side wall. It is in this region, at the deepest WMS measurement cross section, that the RMS
has its highest global values (per velocity ratio).
The behavior, in general, is the result (as verified by LES) of a free shear layer in the
main flow as the flow passes the leading (upstream) edge of the branch line, followed by the
impact of these turbulent eddies, now deviated slightly into the branch line, into the trailing
(downstream) edge of the branch line. A fraction of the main flow is then sheared off and
propelled by its own momentum into the branch line along the wall until all momentum is
lost against the encroaching branch line flow.
72
Figure 4-13. Contour plots of the normalized average scalar (left) and scalar RMS (right) in
the branch line for three velocity ratio cases up to 50.
73
4.4 Flow characteristics in the branch line (Ur = 100)
The present section is primarily dedicated to reviewing a time-resolved CFD
simulation27
of turbulent penetration mixing at a velocity ratio of 100 (Rem = 76,394) in the
LKE T-junction, for which there is experimental data from WMSs. The average velocity
field, shown in Figure 4-14 (right) demonstrates the coherence of the recirculation zone
within the branch line, appearing as an oval shape in the branch extending to 3Db. At the
downstream wall of the branch the average fluid velocity is its fastest anywhere in the branch
at up to approximately 0.45 m/s or nearly 30% of the mean main flow velocity. The velocity
field vectors aim directly into the branch and slightly towards the center of the channel,
reducing in magnitude until the 180 degree turn back towards the junction is made at very
low speed. In the upstream half (x < 0) of the branch in the mid-plane the average velocity
vectors are directed in the –y direction with little deviation until near the branch where a
growing +i component exists, completing the oval-shaped recirculation zone. The mean
velocity field and instantaneous velocity field at an arbitrary time is seen in Figure 4-14 (left).
In a snapshot of the velocity field in time it is evident that fluid behavior at the downstream
wall of the junction, in which the mean velocity magnitude is large and its direction is
dominated by the +j component, is not steady. Rather, clear evidence of pulsations in the
form of local high or low +j velocity vectors is present along the wall.
Figure 4-14. Snapshot of an instantaneous velocity field (left) and the mean velocity field
(right) with a cutoff of 0.6 m/s in the z = 0 mid-plane of the T-junction. The highest velocities
are found in the shear layer at the branch entrance. The snapshot indicates pulsations along
the downstream wall of the branch slowing and forming a coherent recirculation zone in the
average map.
Past research by EdF in a larger geometry with an order of magnitude higher main
flow Reynolds number saw significant swirling in the branch [105-107]. By analyzing the
velocity data, for example mean of uz velocity in the mid-plane (Figure 4-14 left), it is
27
LES setup and methodology described in Section 1.12.
74
possible to see the first signs of weak swirling in the branch line at Ur = 100. Additionally,
the mean velocity along the axis of the branch line, uj, also shown in Figure 4-15, indicates
that the main flow moves from the downstream wall of the branch to the upstream wall not
through the mid-plane of the branch (i.e. swirling transports it from one wall to the other).
Figure 4-15. Mean uk velocity (left), mean uj velocity toward the T-junction (uj < 0, middle)
and away from the T-junction (uj > 0, right) in the branch line indicating weak swirling in the
turbulent penetration.
The average scalar as viewed in the mid-plane (z = 0) of the T-junction indicates a
broad region of mixing with the highest average scalar in the branch located against the
downstream wall. The scalar maintains a value above 0.6 along the wall a number of
diameters into the branch. Mixing reduces the average scalar deeper the branch and
eventually the main flow reaches its farthest average depth in the branch on the upstream
wall, see Figure 4-16 (middle). A snapshot of the scalar indicates coherent instabilities
forming after the separation of the main flow at the upstream edge of the branch. These
instabilities are sheared by the downstream wall of the branch and appear to enter the branch
very close to the wall. At a greater depth the partially mixed main flow appears in the branch
as plumes of varying scalar concentration. For example, in Figure 4-16 (left) a large plume of
scalar approximately 0.7 is seen, and at a location farther into the branch another plume is
seen with a scalar value closer to 0.2. Finally, the scalar RMS in the mid-plane, shown in
Figure 4-16 (right), indicates a concentrated region of high RMS near the downstream wall of
the branch centered at 3Db. Another area of elevated RMS is observed in the shear layer
between the main flow and mouth of the branch.
75
Figure 4-16. The instantaneous scalar (left), time-averaged scalar (middle) and the RMS of
the scalar (right) in the mid-plane of the T-junction.
A cross-sectional view, as viewed looking towards the junction, of the mixing in the
branch is presented in Figure 4-17 for a series of non-dimensional positions from 1Db to 4Db
steps of 1Db, in. At 1Db the center of the branch cross section contains an elevated average
scalar and RMS, also visible in Figure 4-16 (a) as the growing shear layer. A high scalar
average and low RMS is present in a thin layer along nearly the entire circumference of the
downstream side of the branch. At 2Db the scalar remains elevated near the wall, decreasing
steadily from downstream wall across the pipe to the upstream wall. By 3Db the average
scalar is almost uniform through the cross section while the scalar RMS indicates a region of
high RMS on the downstream half of the pipe in the region of thermal cycling. Finally, the
average scalar is nearing zero throughout most of the cross-section at 4Db and some diluted
main flow resides in the upper corner of the upstream wall. Although the scalar has a
relatively low average value the RMS is still elevated at this depth, near the farthest extent of
the penetration.
76
Figure 4-17. Average scalar (top row) and scalar RMS (bottom rom) for various non-
dimensional positions in the branch, from LES.
Thermal cycling in the branch line of a T-junction is the result of a non-steady
turbulent penetration depth along the branch axis. Thermal cycling occurs near the extent of
the average turbulent penetration where the highest scalar RMS values are observed. The
thermal cycling region is isolated as 90% of the maximum scalar RMS in the branch line, in
Figure 4-18. The region of thermal cycling is a contiguous saddle shape which is nearly
symmetric across the z = 0 mid-plane and located against the downstream wall of the branch.
The proximity of the region of highest scalar RMS to the wall of the conduit is important to
recognize as a point of concern for the conduit integrity.
Figure 4-18. Region of > 0.9 max
RMS in the branch line in the z = 0 plane (left) and looking
towards the T-junction (right). The region found to be contiguous and lies along the
downstream wall of the branch in the neighborhood of y = 3Db.
The uniformity index (UI) is typically accredited to Weltens (1993), and is calculated
as follows,
77
∑ | |
| | ∑ , (4-4)
where θ is the scalar quantity, in this case the scalar average or RMS, θf is the cell face value,
and Af is the area of the face [184]. A uniform scalar distribution would have a UI of unity.
The index helps to characterize the recirculation zone in terms of degree of average mixing
within the pipe cross section. In this way zones in which the turbulent mixing is poorly
distributed or incomplete are identified. The UI was computed based on cross sectional data
in steps Δy = 1 mm though the entire branch.
Scalar fluctuations at the outer skin of the mesh can be interpreted as the boundary
condition for the pipe inner wall since only the fluid in the pipe has been simulated. While it
is important not to lose sight of the physical reality: the strong damping effect of conjugate
heat transfer, between a steel conduit and the fluid, on the fluctuations compared to the
adiabatic simulation herein. Note, however, that the location of peak RMS at the inner wall in
cross-flow mixing studies have been shown to be the same in both cases (in the presence or
absence of conjugate heat transfer) [82]. Therefore, in an effort to better evaluate the
locations at which the greatest non-uniform near-wall mixing occurs a weighted UI was
calculated for sections of the wall. The branch line wall has been divided into circumferential
bands 1 mm in axial length. The UI of the scalar RMS is calculated over each band
individually. As a means of giving greater weight to those bands with high UI and high RMS
a weighting factor w, which is equal to the maximum of the scalar RMS in the region of
interest is multiplied by the UI such that, , see Figure 4-19.
Figure 4-19. Uniformity Index (UI) of the scalar average in cross-sectional slices and the
weighted UI (UIw) of the scalar RMS over 1 mm thick circumferential sections of the branch.
The PSD is invaluable in interpreting turbulent mixing in the context of the thermal
fatigue problem. It is possible that the scalar fluctuations could be threatening at first glance,
i.e. of large amplitude, but have a frequency for which NPP piping steels are impervious.
The PSD has been calculated as follows,
*∫
+
(4-5)
78
where θ(t) is the signal from each crossing point and tend is the duration of the signal. The
duration and frequency of the WMS measurements allow for more confidence in PSD
calculations due to the ability to ensemble average the signal while maintaining the most
important frequencies (roughly 0.1 Hz and higher). Zero padding of the PSD is avoided by
cutting additional signal collected beyond the nearest 2n data points. For example in the case
of 170 second measurements at 1600 Hz, less than 7 seconds are cut from the end of the
measurements for the purpose of computing the PSD with exactly 218
data points such that
there is no interpolation in the frequency domain.
The normalized PSD in the branch line at crossing points with high RMS at Ur = 50,
for example, at various depths in the branch line, all show a similar tendency towards high
amplitude at low frequencies, see Figure 4-20. Notable is the damped amplitude of high
frequency fluctuations at the deepest WMS position at this velocity ratio, 2Db. The same
phenomena is present in the higher velocity ratio case, Ur = 200; there it can be seen that near
the extent of the turbulent penetration, at 4Db in the branch line, high frequency fluctuations
are an order of magnitude weaker in the PSD.
Figure 4-20. PSD at WMS crossing points (t,r) of high RMS for various branch line locations
at a velocity ratio of 50.
Calculations discussed and shown previously in Section 1.1 and in Figure 4-12,
instabilities forming in the shear layer at the precipice of the branch line that are known to
contain dominant frequencies in the velocity and scalar spectra. As a means of tracing the
lineage of these characteristic frequencies as the shear layer grows and the instabilities are
redirected into the branch line, the PSD of the scalar field has been calculated (based on the
LES simulation at Ur = 100) along an L-shaped path, see Figure 4-21.28
The frequency domain is non-dimensionalized by introducing the Strouhal number,
calculated based on the branch line diameter and main flow velocity , where
Um = 1.53 m/s. Ensemble averaging of the signal spectra helps in discerning peaks and other
28
Details of the L-shaped path are as follows: with a step size of Δx = 1 mm, the PSD is computed in the z = 0
plane from (x,y) coordinate (0.012, 0.026) (1 mm past the upstream wall of the branch line and 1 mm into the
branch) to (-0.012, 0.026) (1 mm away from the downstream wall of the branch line and 1 mm into the branch).
At this point the stepping is made into the branch such that Δy = 1 mm starting from (-0.0128, 0.026) ending at
(-0.0128, 0.091), or y = 3.5Db.
79
regions of interest; for this purpose Bartlett's method has been executed in generating the
following PSD [185]. The full length signal is cut in to K-segments of duration tk, with 0%
overlap and without windowing,
∑ . (4-6)
The PSD is then computed for each segment of duration tk and all K spectra are then averaged
to create the final, ensemble averaged spectrum,
*∫
+
, (4-7)
⟨ ⟩
∑
. (4-8)
It is furthermore observed that there is a somewhat dominant frequency of scalar mixing at
the extent of turbulent penetration in the branch line, in the region of highest scalar RMS.
The normalized scalar PSD along the path of turbulent penetration into the branch,
shown in Figure 4-21, indicates a drastic weakening of the initially dominant peaks, centered
around St = 0.95 and 1.38 (55.9 Hz and 81.2 Hz), in the region of instabilities across the
branch mouth. Retardation of the main flow and mixing within the branch brings the scalar
fluctuation frequencies into the range relevant to thermal fatigue, St = 0.0017 – 0.17 (0.1 to
10 Hz), by the time the upstream progress of main flow in the branch fully stalls. Unluckily,
this is also the location of highest scalar RMS; the thermal cycling region.
Figure 4-21. The normalized, ensemble averaged (K = 4) scalar PSD vs. St number calculated
from LES results plotted a series of locations along a path (shown in sub-figure) from the
separation point of the main flow, across the mouth of the branch line and into the branch
along the downstream wall to a depth of 3.5Db. The darkest plotted line color indicates the
first path location while the lightest indicates the last in the branch.
80
There is a sweeping transition from high frequency scalar mixing in the turbulent
main pipe to low frequency fluctuations in the turbulent penetration plume in the branch. The
fractional contribution to the total RMS of three St bins is shown in Figure 4-22. As the shear
layer induces scalar mixing upon interaction with the branch fluid, between 70 and 80% of
the scalar RMS is the result of high frequency (St > 0.8) scalar fluctuations. The mid
frequency, 0.2 < St < 0.8 (11.7 to 47 Hz) component of the PSD grows steadily in influence
at the expense of the high frequency fluctuations, such that half of the scalar RMS is due to
fluctuations in this frequency rage near the junction edge at the downstream wall of the
branch. The trend upon moving from the start of the branch to the end of the path at a depth
of 3.5Db indicates a steady transition of power from the high and mid frequencies into the low
frequencies. Nearly 100% of the total scalar variance near the downstream wall of the branch
at 3.5Db is the result of low frequency scalar fluctuations. Furthermore, the scalar RMS,
normalized to the maximum along the path reaches its maximum when fluctuations are
completely within the low St bin. As the last of the scalar spectrum power exits the high and
middle frequency range in the branch line, the RMS increases rapidly to its largest value
before decreasing; the scalar RMS remains the result of low frequency mixing.
Figure 4-22. Fractional contribution to the scalar variance of fluctuations from three Strouhal
bins, high (St > 0.8), medium (0.2 < St < 0.8), and low (St < 0.2) and normalized scalar RMS
at each position along the L-shaped path, calculated from LES results.
For the purpose of comparison the LES results were interpolated onto a 16-by-16 grid
in the branch cross-section identical to that of the experimental data from the WMS. The LES
results are found to systematically under predict the average scalar across the branch at 2Db,
as is shown in Figure 4-23. Both experiment and LES show a weak gradient in the average
scalar from the left side of the branch to the right. The LES result accurately predicts the
maximum RMS value in the cross section, however, the location and trend across the branch
are both under predicted and over predicted depending on the location.
81
Figure 4-23. Plots of the average scalar (left) and RMS of the scalar (right) across the middle
of the branch pipe at 2Db at each WMS crossing point location from experiment and LES
simulation.
The PSD near the downstream wall of the branch line at 2Db measured by the WMS
compares well with the findings of the LES simulation. While the magnitude of the RMS is
not identical, when the spectra are plotted on top of each other, as in Figure 4-24, both
experiment and simulation anticipate a broad peak or plateau in the spectra around 6-7 Hz at
the location of crossing point (8,15). The LES simulation shows less power in the high
frequencies due to the filtering performed by the governing equations, whereas the WMS
may measure additional fluctuations at high frequencies due to electronic noise. A similar
agreement was also found in other locations.
Figure 4-24. Ensemble averaged PSD at a position near the wall (shown on the right) in the
branch line at a depth of 2Db from WMS measurements (K = 128) and LES simulation
(K = 16).
82
4.5 Flow characteristics in the branch line (100 < Ur < 3000)
Turbulent penetration at higher velocity ratios, Ur = 100 to 400, appears to be similar
in behavior to that at lower velocity ratios with the exception of the final, deepest
measurement cross section, see Figure 4-25. At 2Db a continuation of the trend seen at lower
velocity ratios, in which the main flow average concentration is highest at the downstream
wall, is present. In this case, however, the concentrations of tap water are significantly higher
at the same axial position, between 60 and 80% across the entire cross section for the Ur =
200 case, for example. The scalar RMS at 2Db shows the typical crescent shape around the
region of highest average.
By 4Db a breakdown of the scalar average symmetry about the pipe mid-plane has
occurred and the main flow appears in highest average concentration along the bottom of the
pipe rather than remaining vertically centered near the right side wall as for lower velocity
ratios. This shift results also in a disturbance of regularity in the RMS profiles. What can be
noted, however, is the elevated levels of the RMS, to nearly 0.35 across a sizeable portion of
the top wall of the branch line for a velocity ratio of 400. The sudden break in symmetry here
is believed to be attributable to two factors. The first is swirling of the flow and the second is
related to a weak buoyancy due to the different working fluids. Petrov (2015) has shown
evidence of buoyancy effects in mixing between deionized and tap water [186]. Here the
buoyancy may also be the result of small temperature differences between the main and
branch flows.
Figure 4-25. Normalized average scalar (left) and RMS (right) in a 50 mm diameter branch
(Dr = 1) for three velocity ratio cases up to 400, and two WMS sensor positions.
83
Figure 4-26. Scalar average and RMS profiles measured by a WMS at three branch positions
during mixing at Ur = 2000 in a 26 mm branch and rounded edge T-junction.
Figure 4-26 shows results from WMS measurements at a velocity ratio of 2000 at
three branch depths. Interpretable is strong evidence of swirling. Rather than the highest
concentration appearing at the downstream wall of the branch line, the scalar is concentrated
in a very similar way at the upstream wall, at 3.73Db. Deep in the branch at 7.73Db the
average scalar is very low at the bottom of the branch but RMS values remain high,
indicating transient turbulent penetration at this depth. The swirl direction may be due to
small density difference between the tap water and deionized water (as discussed above),
caused by slight inclinations in the section, or a real effect independent of the idiosyncrasies
of the experimental setup and based solely on the geometry and Reynolds number29
[105].
Additional experiments been carried out showing the manner in which increased
turbulent penetration is with increasing Reynolds number for a fixed velocity ratio (Figure
4-27) and vice versa for a fixed Reynolds number with increasing velocity ratio (Figure
4-28). In these WMS measurements, shown at 5.73Db the average scalar profile appears to be
influenced, in part, by the laminar velocity profile of the incoming deionized water flow
reducing the average scalar in the center of the conduit.
29
Robert (1992) notes the example of non-symmetrical flow separation in certain symmetric geometries as a
potential cause of turbulent penetration in the branch line.
84
Figure 4-27. Scalar profiles measured by a WMS at 5.73Db indicates increased turbulent
penetration with main flow Reynolds number for a fixed velocity ratio.
Figure 4-28. Scalar profiles measured by a WMS at 5.73Db indicates increased turbulent
penetration with increasing velocity ratio for a fixed main flow Reynolds number.
85
4.6 Global instabilities introduced by pump oscillations30
4.6.1 Influence of pulsation amplitude
When comparing the behavior of turbulent penetration for a main volume flow rate
oscillation amplitude, a, ranging from ±0% to ±20% at 1.5Db (see Figure 4-29), a few
observations are apparent. The average of the scalar, while maintaining the tendency of
penetration at the right wall of the branch line, tends to increase in magnitude with increasing
amplitude of the velocity oscillations. The RMS of the scalar transitions from a profile
indicative of a steady turbulent penetration (Qm ± 0 to 5%) to a much higher RMS at the wall
indicating that the region of thermal cycling encompassed a region which includes 1.5Db (Qm
± 10 to 20%). In general, in the branch line the average scalar tends to decrease while the
RMS increases with increasing a.
The penetration depth, which has been shown in this work, among others, to be an
increasing function of the velocity ratio, cycles between larger and larger ranges of depth in
the branch line with increasing main flow velocity oscillation amplitudes which results in the
higher scalar RMS values [141].
Figure 4-29. Contour plots at 1Db of the normalized time-averaged scalar and scalar RMS
measured by a WMS for the steady case of Ur = 34.5 and for Qm oscillations ranging in
amplitude from ±5% to ±20% at 0.1 Hz frequency.
4.6.2 Influence of pulsation frequency
Wire-mesh sensor data recorded for main flow oscillation frequency from 0.1 Hz to
0.3 Hz (see Figure 4-30) predicts trends in the scalar and RMS as function of f. The
corresponding Strouhaul (St) and Womersley (α) numbers are reported in the test matrix in
30
Recall the experimental procedure for these tests, described in Section 3.1.2. All tests are carried out in a
sharp edged T-junction with equal branch ratio, Dm = Db = 50 mm.
86
Table 3-3. Within this range of Womersley numbers there is no indication of a change in
regime in terms of a mixing pattern. The measurements indicate that the average scalar
converges on the steady (f = 0) Qm profile from below with increasing Womersley number
(corresponding to increasing pulsation frequency). The scalar maintains the same profile in
the branch line but with a decreasing amplitude for decreasing Qm pulsation frequencies. The
opposite trend appears in the scalar RMS profiles in which it is evident that the RMS is
elevated for any Qm oscillations and tends to decrease towards the steady-Qm case from above
(i.e. from higher RMS values shrinking down to the stead- Qm profile) as the oscillation
frequency grows.
Figure 4-30. Contour plots at 1.5Db of the normalized time-averaged scalar and scalar RMS
for the steady case of Ur = 34.5 and for Qm oscillations ranging in frequency from 0.1 to 0.3
Hz with ±10% amplitude.
Measurements show that given the inlet condition of a pulsatile main flow, a sizeable
fraction of the total variance present in the scalar mixing PSD is concentrated at the same
frequency f, as the main flow velocity oscillations, especially in regions of high scalar RMS.
A peak in the mixing spectrum is present for all test cases, while for some it is more
prominent than others. For example, the peak magnitude in the PSD grows considerably
between the cases Qm ± 5% to 20%, regardless of the frequency. It is interesting to visualize
the change in peak magnitude for regions of high RMS and low RMS. Figure 4-31 shows a
ensemble averaged (K = 4), normalized PSD of a crossing point signal near the downstream
wall in the branch line, in the region of high RMS, and near the upstream wall, in a region of
low RMS, for the case of a steady main flow and oscillating main flow at f = 0.1, 0.2 and 0.3
Hz. The PSD shows peaks at the respective main flow pulsation frequencies. Hence a
transition between the velocity domain in the main flow (input) and scalar domain in
turbulent penetration mixing (output) takes place in the branch line. A weak dampening of
the peak amplitude in the PSD from the 0.1 Hz to 0.3 Hz case is apparent. When comparing
the spectrum from the region of high RMS (Figure 4-31 right) and low RMS (Figure 4-31
left) for the same flow conditions, a significant dampening of the peaks is seen. That is, in
87
regions of high scalar RMS, a major portion of the scalar RMS magnitude is the result of
scalar fluctuations at the Qm oscillation frequency while in regions of low scalar RMS a
smaller fraction of the RMS is derived from fluctuations at f Hz.
Figure 4-31. Normalized PSD at a crossing point near the upstream wall (left) near the
downstream wall (right) of the branch line from the WMS measurements in which the main
flow inlet oscillation frequency was varied. Flow condition, Ur = 34.5 Qm ± 10% at 1.5Db.
A plot of the peak amplitude in from an ensemble averaged (K = 16), normalized PSD
(Ur = 34.5, Qm ± 10%, f = 0.3 Hz, at 1.5Db) at every crossing point horizontally across the
branch line from left to right helps to show the steady increase of the peak magnitude with
increasing RMS, see Figure 4-32. This indicates the power delivered to the main flow
oscillation frequency is amplified in regions of higher RMS in the turbulent penetration
region, akin to a resonance, since the normalization of the PSD renders the spectrum
independent of the RMS magnitude. Also notable is the presence of a second harmonic peak,
at 0.6 Hz, appearing about half way across the pipe as the peak at 0.3 Hz, and the scalar RMS
both grow larger.
Figure 4-32. Magnitude of the ensemble averaged (K = 16) PSD (from the WMS
measurement plane at 1.5Db) at 0.3 Hz, 0.6 Hz and 0.9 Hz (left axis), along with the scalar
RMS (right axis), for each crossing point across the middle of the branch line, from (16,1) to
(16,32). Flow condition Ur = 34.5, Qm ± 10%, f = 0.3 Hz.
88
4.7 Influence of T-junction edge geometry
For the case of a rounded edge at the intersection of the conduits at the T-junction the
main flow boundary layer separation point upon reaching the branch line is no longer
necessarily located at a fixed point in space31
as in the sharp edge geometry (i.e. at the edge).
When a sharp edged junction is in place at high velocity ratios the shear layer forming after
the separation point at the upstream wall of the branch has been shown in time resolved CFD
simulations to result in large scale instabilities of with characteristic frequencies which are
then sheared and injected into the branch line along the downstream wall (see Section 1.1)
[151]. The flow behavior at a T-junction with curved edge is less straightforward.
Four WMS measurements are presented from two different branch positions in a
sharp edged T-junction and at the same two locations in a T-junction with a curved edge of
radius 10 mm, see Figure 4-33. At 3.73Db the average scalar is high (θ > 0.85) and the RMS
low (θRMS < 0.1) in the entire cross-section. Little if any difference is detected between the
mixing in the sharp edged and curved edge T-junction at this position. Upon closer
inspection, however, there is a slightly higher scalar concentration in a crescent shape along
the left side of the branch. At the following WMS position, at 5.73Db the symmetry across
the midline has been broken and a higher concentration of tap water is found more often in
the bottom of the branch.
Figure 4-33. The scalar average (left) and RMS (right) across the branch cross-section at two
positions in each T-junction geometry, measured by a WMS. Flow condition, Ur = 2000, Um
= 3.92 m/s, Rem = 6.5E4.
At 5.73Db the highest RMS values appear between the wall and the center of the pipe
with values of 0.2 to 0.25+. When the T-junction is rounded the same behavior is exhibited at
both measurement positions. In the case of a rounded edge, however, significantly less
turbulent penetration is detected, along with larger scalar fluctuations. The PSD has been
calculated at crossing points of high RMS in both T-junction geometries and WMS branch
positions; see Figure 4-34. Closer to the T-junction high frequencies dominate the spectra and
little effect is seen from curved junction edge. Most of the scalar fluctuations at 5.73Db are
31
The separation point on the curved wall is due to an adverse pressure gradient (strong flow deceleration) in
the boundary layer.
89
occurring at low frequencies for both T-junction geometries. At the same position, two peaks
in the spectrum are visible at this crossing point only in the case of the fileted edge, at
approximately 17 and 23 Hz.
Figure 4-34. Normalized PSD
32 at crossing points of high RMS at 3.73Db (10,10) and 5.73Db
(5,14) in a sharp edge and curved edge (r = 10 mm) T-junction, Ur = 2000.
32
In this case estimated by Welch‘s method using no overlapping and a Hann window.
90
4.8 Influence of density stratification
Unlike turbulent penetration with iso-dense fluids in the branch line and main pipe,
where large time-averaged scalar gradients are seen only deep in the branch line, density
differences (between main and branch fluids) results in the branch flow being present,
unmixed or weakly mixed in high concentrations much closer to the T-junction. Furthermore,
instead of reaching a maximum near the penetration depth, scalar fluctuations may exhibit
high values across a wide range of axial distances, the result of flow stratification. Note that
the Froude number based on the branch line velocity is always subcritical in the following
experiments.
Figure 4-35. Schematic of the Farley-Tihange phenomenon as observed at the LKE T-
junction facility.
Time histories of these experiments provide evidence of the Farley-Tihange
phenomena (see Figure 4-35), phenomena responsible for through-wall cracks in US and
European NPPs, previously described in Section 1.2.4. The heavy branch flow may be forced
to recede by the turbulent penetration at regular intervals such that at the bottom of the
conduit cyclic thermal shock, large amplitude variations in the scalar, occurs. Figure 4-36
demonstrates a scalar time series measured at the bottom of the branch line in which regular,
large scale pulsations are present. These pulsations are due to the heavy branch flow
occasionally reaching forward to the WMS position (3.73Db). Furthermore, the PSD in the
cross-section of the pipe, Figure 4-37 indicates that the pulsations at the bottom of the conduit
have a dominant frequency of 0.1 Hz. This mixing behavior represents a thermal fatigue
threat as demonstrated in the Farley and Tihange coolant leak accidents.
Figure 4-36. Signal time series from a crossing point near the bottom of the branch line in the
case of turbulent penetration with weak, dense in-flow (right). Present are large amplitude
fluctuations (highlighted in red). Data from a WMS measurement in a sharp edged junction at
3.73Db, ε = 0.059.
91
Figure 4-37. Normalized PSD at every crossing point from the bottom (blue) to the top of the
branch (orange). Calculated from a WMS measurement in a sharp edged junction at 3.73Db,
ε = 0.059.
Figure 4-38 shows the average scalar as measured by the WMS for density
differences ranging from 0.024 to 0.088 at positions 3.73Db and 5.73Db. Firstly, at the nearer
position to the junction increasing density stratification introduces a significantly lower
average scalar concentration at the bottom of the branch as compared to iso-dense mixing.
For weak stratification, the case of mixing with ε = 0.024, the average scalar may reach
values approaching 0.5 at the bottom of the pipe. As the branch fluid density is increased, a
larger zone of low average scalar forms in the bottom of the branch and eventually, at ε =
0.088, a zone of average scalar between 0.05 and 0.15 is found in the bottom third of the
branch. The density stratification has introduced areas of large average scalar gradients, as
high as 0.09 θ/mm at the interface between the fluids. In iso-dense mixing cases the average
scalar is almost uniform across the entire branch line cross section. At 5.73Db we see sharply
stratified flow in the cross-section leading to very strong average scalar gradients of nearly
0.12 θ/mm. The exception is for the small density difference of 0.024 where there is still
noticeable blurring of the average scalar across the interface between the fluids.
Figure 4-38. The scalar average is plotted across the branch cross-section at two positions for
each density difference.
92
Figure 4-39. The RMS of the scalar is plotted across the branch cross-section at two positions
for each density difference.
The RMS of the scalar indicates negligible scalar fluctuations at 3.73Db when no
density difference between the fluids is present. As the branch line fluid density is increased
the scalar RMS is found to be as high as 0.3 at the bottom of the pipe at the turbulent
interface between the two fluids as seen in Figure 4-39. Already for the case of ε = 0.051 the
interface exists independent of the bottom wall of the branch; deionized water is running
more or less steadily underneath the penetrating tap water. The trend is as follows: the scalar
RMS is reduced slightly at the bottom of the branch, where the average scalar is near 0 and
the maximum of the RMS is found rather just above the bottom, again at the interface
between the two fluids, and finally at the edges of the interface near the left and right walls at
ε = 0.088.
Deeper in the branch line (5.73Db) where in iso-dense mixing experiments elevated
RMS values were present throughout the cross-section, the introduction of even small density
differences again has a drastic effect. For small Δρ between the working fluids, ε = 0.024, the
mixing is strongly damped and reduced in spatial extent and although the maximum of the
RMS is still sizeable at 0.25 it exists at such elevated values only at a few crossing points on
one side of the interface between the fluids. In the remainder of the cross-section RMS values
are near zero. With increasing density difference the scalar RMS at 5.73Db is elevated in only
a single row of crossing points across the branch, i.e. ≤ 1.63 mm in vertical expanse. In this
row RMS values may reach above 0.15. Although scalar fluctuations are negligible above
and below the mixing layer, it should be noted that an order of magnitude difference is seen
between the RMS in the penetrating main flow on top of the interface and the heavy branch
flow below. For example, above the interface RMS values are typically in the range 0.02 to
0.05 while below the interface they are below 0.005.
Figure 4-40 shows the development of the stratified scalar interface with increasing
branch fluid density. The curves are the result of averaging the middle two crossing point
columns of the WMS. It is evident that even weak density stratification strongly affects the
behavior of turbulent penetration in the horizontal T-junction when compared to flows with
ρr = 1, especially deeper in the branch. At that position we see already at a density difference
of 0.051 the average scalar interface is smaller than the spatial resolution of the WMS, hence
the overlapping profiles. At 3.73Db an S-curved scalar profile is only present for the largest
density difference, 0.088.
93
Figure 4-40. Vertical scalar average profiles (through the center of the WMS measurement
plane, two column-average) indicating flow stratification for each experiment at 3.73Db (left)
and 5.73Db (right).
An increasing density difference causes an increase in the maximum average scalar
gradient vertically through the center of the cross-section at 5.73Db, see Figure 4-41. The
gradient, ⁄ approaches 0.08 θ/mm at the highest density differences (Ri ≈ 5800)
while the largest change in ⁄ is observed between Ri ≈ 1550 and 3350 after which
increasing Ri has a lesser effect on the scalar gradient. Near the branch at 3.73Db, the trend as
a function of Richardson number is inconclusive based on the four density difference cases.
What is clear is a reduction in thermal gradient with increase main flow Reynolds number,
owing to an increase in turbulent penetration and therefore turbulent kinetic energy which
acts to disrupt the formation of stratification between main and branch flows, thereby
reducing the scalar gradient in the time-averaged sense.
Figure 4-41. Maximum average scalar gradient ⁄ across the center of the pipe
cross-section (along the z-axis) vs. Richardson number with respect to branch line position
and main flow Reynolds number.
A density difference between the fluids gives rise to a power spectrum with
significantly more amplitude in the low frequencies near the T-junction where RMS values
are also significantly higher. At 5.73Db where mixing is relegated primarily to the narrow,
94
wavy interface between the fluids, some preferred mixing frequencies arise, described below.
Figure 4-42 shows the PSD at the crossing point of highest RMS for each experiment; when a
density difference is present, this point always lies somewhere in the interface between the
fluids.
Figure 4-42. Ensemble averaged PSD at crossing points of highest scalar RMS, wherever
they may be in the cross-section, for each experiment at 3.73Db and 5.73Db.
Two areas of interest deserve mention regarding the spectrum at 5.73Db. Firstly, there
is a large plateau around 6-9 Hz, which does not exist in the absence of density difference.
This plateau precipitates a steepening of the slope of the spectra for all four artificial density
cases. At higher frequencies, there is a peak in the PSD for all experiments in the vicinity of
28 Hz which is more pronounced with higher density difference. In the absence of density
difference the spectrum shows no major changes in slope at this position.
95
4.9 Conclusion
Experiments have been carried out in a new adiabatic T-junction facility at velocity
ratios up to 3000 to better understand the behavior of turbulent penetration in T-junctions
with in-flow in a nuclear-safety context as it relates to HCTF. The main findings and
takeaways include,
Database of adiabatic experimental results with high spatial and temporal resolution
downstream of the T-junction and in the branch line for a wide range of high velocity
ratio, turbulent-penetration-inducing boundary conditions.
Comprehensive description of turbulent penetration with in-flow including elucidation
of the Farley-Tihange phenomena, the effect of density stratification, velocity ratio,
pulsatile flow and T-junction geometry on turbulent mixing by means of adiabatic
experiments and a large eddy simulation.
Region of largest scalar fluctuations is concentrated in a wall-attached zone in the
case of iso-dense turbulent penetration in T-junctions at velocity ratios around 100.
Shear layer formed across the mouth of the branch line due to separation of the main
flow plays an important role in turbulent penetration mixing, especially with regards
to critical mixing frequencies.
Recognition of characteristic mixing frequencies related to the Farley-Tihange
phenomena in T-junction branch lines with in-flow.
Portions of the experimental and theoretical work discussed in this chapter has been
or is expected to be published in peer-reviewed journal publications, peer-reviewed
conference proceedings, or in the theses of Master‘s students supervised by myself at the
ETH Zurich LKE. Specifically,
1. Master‘s thesis of Valori (2012): ―T-junction mixing with low side flows‖ [187]
2. Master‘s thesis of Schmidt (2013): ―Experimental and Numerical Investigation of
Turbulent Penetration Mixing in a Low Side Branch Flow Rate‖ [188]
3. Master‘s thesis of Trinca (2014): ―Thermal Loads Determination For Fatigue
Assessment In Low Side Flow T-junctions‖ [189]
4. Kickhofel, J., Valori, V., and Prasser, H.-M., ―Turbulent Penetration as a Thermal
Fatigue Problem in low Side Flow T-Junctions,‖ Nuclear Thermal Hydraulics and
Safety 8 (NTHAS8), Beppu, Japan, December 9-12, 2012.
5. Kickhofel, J. and Prasser, H.-M., ‖Large Eddy Simulation of Turbulent Penetration in
a T-junction,‖ International Congress on Advances in Nuclear Power Plants (ICAPP
2014), Charlotte, U.S.A., April 6-9, 2014.
6. Kickhofel, J., Trinca, C., and Prasser, H.-M., ‖The Influence of Density Stratification
and T-junction Geometry on Turbulent Penetration,‖ International Topical Meeting on
96
Nuclear Thermal Hydraulics, Operation and Safety (NUTHOS-10), Okinawa, Japan,
December 14-18, 2014.
7. Kickhofel, J. and Prasser, H.-M, ‖Turbulent Penetration in T-junction Branch Lines
with Leakage Flow,‖ Nuclear Engineering and Design 276, 43–53, 2014; doi.org/t4g.
8. Kickhofel, J. and Prasser, H.-M., ―Large Eddy Simulation of Turbulent Penetration in
a Horizontal Adiabatic T-junction with Leakage Flow,‖ Nuclear Engineering and
Design, in review, 2015.
97
5 Mesh sensor package
5.1 Introduction
Experimental measurements of single and two-phase flows at high temperatures and
pressures are invaluable sources of information for theoreticians, researchers and
professionals in the field of nuclear engineering. A great deal of research in the nuclear
thermal hydraulic domain is carried out at low temperature or in adiabatic test facilities at
atmospheric pressure, such as the turbulent penetration studies described in Chapter 4. The
transition from data gathered from such tests to a clearer understanding of thermal hydraulic
or fluid dynamic behavior at the working conditions of an NPP, known as scaling, is
nontrivial. The challenges of scaling could be avoided by the capturing of more experimental
data, of a higher density in space and time than is traditionally possible, from existing test
facilities (e.g. integral-type33
) which are constructed to operate nearer to or at the full
temperature and pressure conditions found in NPPs [190-192]. This is achievable only with
innovative instrumentation.
To this end, it is the intention of this chapter to introduce a new high-temperature
high-pressure resistant mesh sensor34
―package‖ design which is relatively uncomplicated
compared to the current state-of-the-art and whose sealing methodology and materials allow
for potential expansion or modification of the internal sensor structure [193]. The sensor
design potentially greatly expands on the breadth of operating temperatures and pressures
previously possible with mesh sensor technology to encompass not only the thermal-
hydraulic domain of BWRs but also that of PWRs.
The first full-scale prototype of the new mesh sensor has been designed and built for
the measurement of T-junction cross-flow mixing at high temperatures (up to 280°C) and
pressures (8 MPa) at the University of Stuttgart T-junction facility, described along with
results from the new mesh sensor in Chapter 6. The sensor utilizes the same electronic
principle and data acquisition system as traditional WMS technology developed by Prasser
(1998), and implemented at the LKE T-junction facility (Section 2.2.1) [163]. The sensor
design incorporates some classic and other, more innovative engineering materials. The
testing of these materials is described in Section 1.1 followed by the detailed description of
the prototype sensor (Section 1.1) and a discussion of its maximum potential operating
conditions (Section 1.1). The appendix of this chapter explores alternate sensor designs and
suitable alternate materials which were investigated to various degrees during the sensor
research and development process.
33
Examples of which include PWR PACTEL in Finland, PKL in Germany, and ROSA/LSTF in Japan. 34
Since the sensor does not utilize wires, the term is dropped when referring to this sensor.
98
5.2 The challenge in brief
The engineering effort exhausted in designing a high-temperature-capable mesh
sensor is in large part dedicated to materials considerations. Recall the words of engineering
material guru Michael F. Ashby,
“There has never been an era in which the evolution of materials was faster and the sweep of
their properties more varied. The menu of materials has expanded so rapidly that designers
can be forgiven for not knowing that half of them exist. Yet not-to-know is, for the designer, to
risk failure: innovative design, is enabled by the imaginative exploitation of new or improved
materials” [194].
Indeed a great deal of time has been spent searching for appropriate materials (including the
utilization of Ashby plots) during the development of the mesh sensor package with the goal
of leaving no stone unturned, so as not to miss a potentially game-changing ceramic, alloy or
adhesive, etc. The material attributes of primary importance include some combination of
thermal expansion, electrical resistivity, Young‘s modulus and yield strength, depending on
the particular component. And while Ashby estimates (circa 2009) that, ―[t]here are maybe
more than 50,000 materials available to the engineer,‖ whole classes of those materials are
unavailable at temperatures near or above 300°C [195]. Essentially, only metals, ceramics
and a handful of exotic materials are suitable. That already dwindling list of options is shrunk
considerably when considering the corrosive operating environment: deionized water, vapor
and even boiling. Above 300ºC the use of electrically insulating materials such as PTFE,
PEEK or epoxies is impossible at worst or ill-advised at best. Above 327ºC, flexible,
electrically resistive perfluoroelastomers such as DuPont™ Kalrez® also reach their stated
limits.
Thermal expansion of materials must be accounted for where assemblies comprising a
variety of materials each with different thermal expansion coefficients (TEC) are expected to
encounter elevated temperatures and large thermal gradients. As a first step towards a high-
temperature mesh sensor which may be capable of measuring at temperatures and pressures
approximately equivalent to those found in BWRs, the aim has been to construct a prototype
mesh sensor package for up to 280ºC and 8 MPa. At these ambient conditions, some
thermoplastics, elastomers and epoxies remain usable.
Two primary challenges are faced when designing a mesh sensor for high-temperature
high-pressure flows. First among them, dictating a great deal of the overall design, is the
choice of a suitable electrode material. Due to thermal expansion the stainless steel wires
typically used in mesh sensors would go slack and droop at high temperatures, even if pre-
tensioned to near their yield strain. Such wires do not exhibit the necessary elasticity to
compensate their axial thermal expansion at high temperatures. Truth be told, none of the
dozens of wire materials investigated, be them elemental or alloy, have the necessary
combination of corrosion resistance and elasticity. The option then becomes one of using a
stiff electrode material or stainless steel wires with individual springs for maintaining tension.
The second challenge is sealing the sensor, maintaining the internal pressure of the conduit in
99
which it is installed while allowing for the passage of signal carriers between the sensor and
the DAQ box. Previously published technology relied on epoxies which sometimes required
active cooling.[196]
100
5.3 Prior state of the art
Prior state of the art is detailed primarily in publications by Prasser (2008), Dudlik
(2008), Pietruske (2007) as well as in patents and reports originating from the
Forschungszentrum Rossendorf (FZR, now HZDR) in Germany [196-201]. These
publications demonstrate two distinct high-temperature mesh sensor designs, of which both
have relied on high-temperature epoxies, rated to 180ºC, to ensure an effective pressure
barrier. A review of mesh sensor technology for high-temperature high-pressure flows is
shown in Table 5-1.
Table 5-1. Prior state of the art and the new mesh sensor package.
The rod-electrode type design utilized large electrodes, by WMS standards, of 5 mm
in height and 1.5 mm width (with a leaf-shape cross section to reduce pressure drop) which
were fixed on one end and allowed to thermally expand freely, along their axis, on the other.
This design, first implemented in the MTLoop facility at the Forschungs Zentrum
Rossendorf (FZR, now HZDR), went on to be manifest in successful measurement campaigns
at the PPP facility (in DN50 and DN100) of UMSICHT in Germany and the PMK-2 test
facility (in DN80) at the KFKI-AEKI in Hungary as a part of the OECD/NEA Primary
Coolant Loop Test Facility (PKL-2) Project35
[203]. These sensor ranged in size from a
DN100 version with 16 transmitter and 16 receiver electrodes rated for 250ºC at 7 MPa, to a
DN50 8 x 8 electrodes version rated for 180ºC also at 7 MPa. The extension in sensor
temperature resistance from 180ºC to 250ºC was achieved with the help of an integrated
water cooling circuit, outside of the pressure barrier but within the sensor flanges, to ensure
the integrity of the epoxy sealing.
A spring-based mesh sensor design, described by Pietruske (2007), benefits from thin
0.25 or 0.12 mm diameter stainless steel wire electrodes while the overall construction is
admittedly, ―extremely complicated‖ [198]. Thermal expansion and contraction is managed
by a system of compression or tensile springs in concert with ceramic insulation pearls,
requiring extensive machining of the sensor flanges. Two sensor constructions were
manufactured, assembled, and tested in steam-water and air-water multiphase flows at the
TOPFLOW facility at FZR, both with 3 mm wire pitch and 2 mm between the two layers.
35
In the framework of the EURATOM project WAHALoads.
Electrode
material/type
Design
Temperature
[°C]
Tested
Temperature
[°C]
Tested
Pressure
[MPa]
Conduit
size
[DN]
Electrodes
Manera (2001)
[202]
Stainless steel
wires 120 116 .12 40 16-by-16
Pietruske
(2007) [198]
Stainless steel
wires 286 280 6.5
200
50
64-by-64
16-by-16
WAHALoads
Project [196,
197, 199]
Stainless steel
lentil-rods
180
180
250
180
180
250
1
1
4
50
100
80
8-by-8
16-by-16
12-by-12
Present Work
[2]
Stainless steel
capillaries 350 265 7-8 80 16-by-16
101
The smaller sensor was of 16-by-16 electrodes for a DN50 conduit, the larger, comprised of
64 x 64 electrodes was installed in a DN200 pipeline. The maximum temperature and
pressure ratings for both sensors were declared to be 7 MPa and the corresponding saturation
temperature of 286ºC. Unlike the lentil-rod sensors, these sensors measured flows at their
temperature and pressure limits. The larger of the two sensors prohibited the installation of all
12 bolts in the DN200 flanges, only 8 could be utilized, which meant a special licensing
procedure had to be carried out with the authority responsible for pressurized equipment.
102
5.4 Material testing
Extensive material testing has been performed in the context of the new mesh sensor
development. A new autoclave (Büchi AG versoclave Typ 3E) has been integrated into the
LKE laboratories for the purpose of material and prototype testing in water/steam
environments at high temperatures and pressures. The autoclave is capable of heating a 3 liter
volume to a maximum temperature of 300ºC at up to 10 MPa, see Figure 5-1.
Figure 5-1. Schematic and photograph of Büchi AG autoclave used for material testing
related to the mesh sensor package development.
For testing, 750 ml of deionized water was placed in the volume along with the
material or assembly to be trialed. Heating then proceeded, typically as in Figure 5-2, such
that as the temperature rises beyond 100ºC nucleate boiling occurs in the water. The
autoclave was then vented briefly to expel air, resulting in a saturated liquid-vapor mixture
which tended towards superheated vapor rather than to water due to the chosen specific
volume. Conditions seen by the tested materials was extreme (i.e. conservative) in that they
were tested in water, steam, and in the presence of boiling. Material tests were performed at
temperatures up to 285ºC at saturation pressure where the maximum temperature was held for
minutes or many hours depending on the test. All materials which went into the prototype
design for which some uncertainty existed regarding suitability for use in high-temperature
water or steam (e.g. ceramics or insulation materials) were tested for at least 1 hour at around
280ºC and saturation pressure (approx. 6.9 MPa).
103
Figure 5-2. A typical temperature profile measured by a PT100 thermocouple in the autoclave
during a material test.
104
5.5 Prototype design and in-house testing
The mesh sensor package is notable for a separation of the pressure barrier
construction from the mesh sensor itself. The result is a package design which allows for a
variety of potential sensor designs to be incorporated. Two steel housing flanges comprise the
bulk of the sensor package, they act to provide a cavity within the pressure barrier of the
facility which is large enough that a mesh sensor and associated wiring may be mounted. The
two flanges, the ‗primary‘ and ‗lid‘ flange, surround and secure the mesh sensor sandwich, as
in a sketch of the mesh sensor package in Figure 5-3.
Figure 5-3. CAD drawing of the mesh sensor package installed in DN80 PN100 flanged
pipeline of inner diameter 71.8 mm.
The housing flanges allow for transport of the mesh sensor as a pre-assembled unit
which needs only to be installed on-site between standard flanges in the pipeline. The design
maintains the ability to execute the usual sealing strategy for the flanged pipeline in which
the sensor is installed, in this case that for DN80 PN100 flanges (eight M24 bolts). The
primary housing flange accepts the mesh sensor, centering pins and compression springs. The
lid flange acts as an adapter to seal the sensor inside of the primary housing flange while also
providing the appropriate facing, e.g. tongue and groove, to the pipeline flange. Two 10.7
mm diameter conduits are machined into the primary flange perpendicular to the axis of the
flow conduit and to one another. It is through these conduits that the 16 transmitter and 16
receiver signal carriers (‗transmission wires‘) are passed, separately, from the mesh sensor to
the multi-element feedthrough glands, there passing through the pressure barrier. The wires
are then connected to a D-SUB 25 terminal which is linked to the analog-to-digital DAQ box.
Between the primary flange and the feedthrough glands, stainless steel hoses 20 cm in length
are installed. The purpose of the pressure hoses is to provide greater physical separation
between the sealing glands, which have a temperature rating of 260ºC, and the heat source, be
it the fluid itself or external heating mats. The glands are rated for pressures up to 8.3 MPa.
A consequence of the additional space in the conduit provided by the housing flanges
is that the gasket which ensures sealing between the two flanges is of larger diameter than
105
those found in the standard pipeline connections. The gasket located between the housing
flanges is of inner/outer diameter (ID/OD) Ø116/140 mm such that the sealing area is similar
to that of the standard Ø90/120 mm gaskets found in a tongue and groove DN80 PN100
flange. This means non-negligible stress in the form of torsion acts on both housing flanges.
CATIA V5 FEM has been performed based on a 300°C ambient with 100 MPa internal
pressure and conservative forces on the gasket surfaces were estimated based on 200 N·m
bolt torque. Results show maximum von Mises stresses of 290 MPa in the primary housing
flange and 350 MPa in the lid flange. These values are well above the Rp0.2 offset yield
strength of standard stainless steels at 300°C. Therefore, the stainless martensitic chromium-
nickel-molybdenum steel 1.4418 was chosen for the sensor package housing flanges,
although alternatives do exists, see Table 5-2. With a yield strength of 580 MPa at 300ºC,
high Cr content, and the addition of Molybdenum, 1.4418 is an ideal candidate for the
requirements of the sensor package in high-temperature steam-water environments. Another
potential material is 17/4 PH, a commercially common martensitic chromium-copper
precipitation hardened steel with high strength and good corrosion resistance [204].
Steel Rp 0.2% at
300°C (MPa)
Heat
Treatment Classification
1.4571 (316Ti)
X6 CrNiMoN 22-5-3 145 Annealed Austenitic
1.4550
X6 CrNiNb 18-10 136 Annealed Austenitic
1.4542 (17/4 PH)
X5 CrNiCuNb 17-4 650 P960 Martensitic
1.4418
X4 CrNiMo 16-5-1 580 QT900 Martensitic
Table 5-2. Comparison of steel yield strengths at elevated temperature. Options for HTWMS
housing flanges include 1.4418 and 1.4542. Yield strength data from Key to Steel (Verlag
Stahlschlüssel) [204].
Figure 5-4. Calculated von Mises stresses on the lid flange from a CATIA V5 FEM
simulation.
The sensor itself is comprised of three ceramic plates which are held in place by two
1.5 mm diameter centering pins and compressed together by four small springs housed in the
primary flange. The ceramic plates are made of Photoveel II, a proprietary-blend machinable
nitride ceramic manufactured by Ferrotec Europe GmbH, which has a rated thermal shock
106
resistance of 600 K, making it suitable for environments where large temperature gradients
are expected such as in stratified flows or thermal shock scenarios [205]. More information
on Photoveel II as well as SHAPAL Hi-M SOFT, a suitable alternative ceramic, are shown in
Table 5-3. Two 3 mm thick ceramic plates act to hold and position the receiver and
transmitter electrodes, respectively, by employing sixteen 0.6 mm wide 0.6 mm deep grooves
per plate. The result is a minimum separation of approximately 2.4 mm between the electrode
layers. A third, 1.5 mm thick ceramic plate, completes the stack, ensuring electrical isolation
of the uppermost layer of electrodes from the lid flange.
Table 5-3. Ceramic materials suitable for a high-temperature mesh sensor operating in
steam-water environments with large thermal gradients.
The 16 receiver and 16 transmitter electrodes are positioned with a pitch of 4.49 mm
such that 208 crossing points lie within the 71.8 mm diameter pipe. A schematic and photo of
the substrate and a photograph of the sandwich construction in-situ with electrodes is shown
in Figure 5-5. The electrodes are EN 1.4404 (ANSI 316L) stainless steel capillaries of mean
ID/OD 0.31/0.57 mm. Splicing between the electrodes and transmission wires is made with
EN 1.4404 (ANSI 316L) stainless steel crimps of ID/OD 0.67/0.90 mm. The transmission
wires are PTFE insulated stranded wire with nineteen 0.10 mm OD silver coated copper
conductors.
Name Ceramic blend
TEC
[E-6 mm
/mm°C]
Thermal shock
resistance ΔT [K]
Bending Strength @
25°C [MPa]
Ferrotec Photoveel II Proprietary nitride
ceramic 1.4 600 440
SHAPAL™ Hi-M SOFT¹
Proprietary
aluminum nitride
ceramic
4.8 400 300
107
Figure 5-5. Sketch of a single ceramic substrate for positioning 16 electrodes (top).
Photograph of the Photoveel II ceramic rings and electrodes installed in the housing flanges
(bottom).
Testing of the sensor at the LKE was performed in a purpose-built test-section
facility, shown in Figure 5-6. It is comprised of a 0.5 m long EN 1.4404 (ANSI 316L) pipe
welded on one end to a hemispherical cap, and on the other to a DN80 PN100 flange. A
second DN80 PN100 flange is welded directly to an end cap. Swagelok® connectors were
welded to the top and bottom end caps (3x and 1x, respectively). The prototype sensor is
flanged between the two components. The elongated nature of the setup is intended to allow
for efficient heating when wrapped with a heating tape.
108
Figure 5-6. Photograph of test section (left) and drawing with values in mm (right) for
pressure and temperature testing of the mesh sensor package prototype.
The section has a 3.1 liter internal volume, similar to that of the autoclave. Cold
pressure tests were performed with a hand pump while the section was full of water. Nitrogen
may also be used to pressurize the facility. For hot tests, the setup includes resistance heating
tapes with PID control and glass fiber insulation. Pressure is read manually from a
manometer.
109
5.6 Capabilities in theory
By selecting different materials within the same design concept, a second generation
sensor would be capable, in theory, of measuring steam-water flows in conduits at up to
22 MPa and 350ºC. Sealing the package at higher pressures, above those found in
commercial PWR power plants, requires only an upgraded feedthrough gland. Commercially
available multi-element feedthrough glands are built to withstand up to 22 MPa pressure. The
graphite gaskets typically used in flanged pipelines, already present in the prototype design,
are already able to withstand very high pressures (25 MPa). The greater challenge in high-
temperature mesh sensor design tends to be achieving temperature resistance. It remains
necessary to insulate the electrical conductors in the sensor from one another in the absence
of the traditional high-temperature insulator, PTFE which cannot withstand long term
operation above 300ºC. The solution is polyimide insulation, often classified as a type of
enamel insulator for metal conductors. Polyimide insulated wiring is commercially available
in a wide range of sizes and conductor types (at far higher prices than PTFE) and, according
to discussions with manufacturers, can withstand operating temperatures of at least 350ºC in
steam-water environments. Figure 5-7 shows, schematically, past high-temperature mesh
sensor designs relative to the current state of the art developed as a part of this thesis work
within a temperature-pressure-space assumed to be present in a water ambient.
Figure 5-7. Diagram (not to scale) showing the temperature and pressure capabilities of prior
state-of-the-art (left) and the current theoretical capabilities of the new mesh sensor package
(right, in red).
Aside from a discussion of design modifications for the increased pressure and
temperature resistance of the sensor, it is also worth describing ways in which the sensor
design could be expanded to incorporate additional instrumentation. The ability to easily
house two mesh sensors or a three layer mesh sensor opens the door to the measurement of
important flow properties, in addition to EC, at high temperatures and pressures. Prasser
(2013), inspired by Cox (1977), has described a generalized cross-correlation technique for
the reconstruction of fluctuating velocities well suited for data from a pair of mesh sensors
installed in a turbulent flow [206, 207] Furthermore, the a method for reconstruction of
interfacial area concentration, a valuable parameter in 1D nuclear safety thermal hydraulic
codes, has also been develop and improved for data from mesh sensor pairs [208-210].
110
Furthermore, Shaban (2014) has developed a novel flow rate measurement method based on
void fraction signals from a WMS, this method benefits significantly from the use of dual
WMS units versus one alone [211]. Note that mesh sensor technology has also seen
successful implementation as a capacitance sensor for two-phase gas-oil flow distributions
[212, 213].
Figure 5-8. Sketches of a mesh sensor package incorporating a pair of 32-by-32 mesh sensors
along with eight multi-element feedthroughs in a DN80 PN100 housing. Adapted from
Kickhofel (2014) [193].
The additional space necessary for more sensor layers is at hand. A shortening of the
lid flange tongue is required, see Figure 5-8 (right). The strength of a flange of this geometry
has not been analyzed by way of FEM, however, it is foreseeable that it could be made
bulkier in order to increase its torsion resistance. The additional signal carriers can be
provided for by more boreholes in the primary housing flange along with additional multi-
element feedthroughs, if necessary, see Figure 5-8 (left). A single multi-element feedthrough
can pass up to 60 wires through the pressure barrier.
111
5.7 Conclusion
A new mesh sensor construction has been designed for operation in high temperature
(potentially up to 350°C) and pressure (upper limit of 22 MPa) pipelines by implementing
novel materials, assemblies and a new sealing methodology. The mesh sensor package design
is scalable so as to be compatible with standard flanged pipelines of size estimated to be <
DN100 and > DN10. The invention solves the problems discussed related to prior state of the
art while at the same time allowing the sensor to operate at higher temperatures and to be
manufactured and assembled more easily and more cheaply. The pressure barrier is no longer
guaranteed by an epoxy, as in past designs by other researchers, but rather by a standard
graphite gasket between the housing flanges, the same type that would normally be sealing a
bolted flange joint, and commercially available threaded sealing glands. While still
maintaining space for the standard number of bolts for a given flange size, such sealing
glands could conceivably allow for a very high number of electrode signals to be extracted.
The ability to carry a large number of conductors through the pressure barrier, in addition to
the housing flange design, enables the installation of multiple mesh sensors, three layer
sensors, or other instrumentation such as thermocouples, enabling the reconstruction of
additional flow properties from measured data.
A 16-transmitter, 16-receiver prototype sensor has been constructed for a DN80
pipeline; its individual components and some assemblies thereof have been tested in an
autoclave at temperatures up to 285ºC in a liquid water-vapor environment with boiling at
saturation pressure. The prototype has also undergone pressure tests at a facility built at the
LKE for commissioning the sensor prior to proof-of-concept testing at the University of
Stuttgart.
Portions of the work discussed in this chapter have been patented or are included in
project reports of Master‘s students supervised by myself at the ETH Zurich LKE.
Specifically,
1. Kickhofel, J. and Prasser, H.-M., ‖Grid Sensor Package,‖ European Patent
Application EP14198142, ETH-Invention-No. 2014-053, Priority date December 16,
2014.
2. Semester project report of Ayer (2014): ―Design, Construction, and Implementation
of High Temperature, High Pressure Wire Mesh Sensors‖
3. Semester project report of Andermatt (2015): ―Capillary Based Wire Mesh Sensor for
High Temperature and High Pressure Applications‖
112
5.8 Appendix
5.8.1 Alternate electrode materials
The stainless steel capillaries currently incorporated in the mesh sensor design would
likely deflect unacceptable amounts, such that the quality of the measurement is disturbed,
should they face high velocity flows. Added stiffness could be achieved with a material with
higher Young‘s modulus, such as Chromium. Within the housing flange design, an early
prototype of the mesh sensor sandwich incorporated stiff electrodes fixed on both ends to the
ceramic substrate by a high-temperature non-EC epoxy which performed well in autoclave
tests (EPO-TEK® OE188). The electrodes were made of twisted, 1K tow carbon fiber yarn
with a 120 µm layer of nickel deposited by electroless nickel plating, for improved stability
and EC. The electrodes were fixed without fear of damage because carbon fiber exhibits a
very small (assumed to be negligible) negative, transitioning to slightly positive, axial
thermal expansion between 20°C and 300°C. Induction brazing spliced the electrodes and
transmission wires using silver as a filler metal. The sensor design based on nickel plated
carbon fiber electrodes was tested in-house and at the University of Stuttgart T-junction
facility, where it failed due to epoxy liftoff which resulted in the displacement of the
electrodes.36
The liftoff was deemed to be the result of a combination of a TEC mismatch
between the epoxy (with TEC 68E-6 mm/mm above the glass transition temperature) and the
Photoveel II ceramic (TEC 1.4E-6 mm/mm) and vibrations in the facility reaching the bond
line.
To reach the small electrode diameters of 0.12 to 0.25 mm found in spring-based
sensor designs it is unlikely that there is any suitable material in rod or capillary form which
would not deflect unacceptably in a turbulent flow across the pipe diameters of interest. The
extension of the sensor to multiphase flows would benefit from a modified sensor sandwich
design integrating thinner electrodes. The transition to a spring based design can be
conceptualized within the current housing design. Ideally, such a design would rely on
custom-stamped springs significantly smaller in size than traditional compression or tension
coil springs. Short of a spring-based design, some testing has been performed with the
widespread shape-memory-alloy NiTi (also known as nitinol) which is manufactured in wire
form in many diameters [214].
An intriguing property of SMAs, for the mesh sensor designer, is their
pseudoelasticity (the result of a stress-induced crystal phase transformation) which allows for
the reversible deformation of large strains (>5%); strains which would otherwise result in the
plastic deformation of typical mesh sensor electrode materials. The yield strain of SMAs is
more than sufficient to compensate for electrode thermal expansion in high-temperature mesh
sensors [215]. Unfortunately, the pseudoelasticity of NiTi is lost long before reaching the
temperatures of interest (i.e. 250°C to 350°C). New SMAs based on NiTi with ternary
element addition, typically Palladium, extend the transition temperature, and therefore the
operating temperature limit of the material, to approximately 220°C [216, 217]. Such
materials may already be acquired commercially, albeit at high cost, from DYNALLOY Inc.
36
In this version the ceramic substrates were smooth rings without electrode-housing grooves.
113
As the maturity of these ternary SMAs advances, they may represent an ideal material for a
fixed-wire high-temperature mesh sensor.
114
6 Cross-flow mixing at high ΔT
6.1 Introduction
Collaboration between the ETH Zurich LKE and the University of Stuttgart IKE
undertaken as a part of this thesis has seen the Stuttgart T-junction facility taken to its highest
operating temperature, resulting in a bulk ΔT of 232 K between main and branch flows at
7 MPa pressure, during the proof-of-concept testing of the high-temperature high-pressure
mesh sensor package described in Chapter 5. This chapter explores the results of those
measurements in detail. Section 1.1 describes the T-junction facility at the University of
Stuttgart followed, in Section 1.1, by a detailed description of the mesh sensor module
installed for the purpose of mixing measurements. The test matrix, four different flow inlet
temperature boundary conditions, and experimental procedure at the facility during and
between measurements is found in Section 1.1. Results and analysis are divided into
measurements downstream and upstream of the T-junction in Sections 1.1 and 1.1,
respectively.
115
6.2 Facility
At the epicenter of the T-junction facility at the University of Stuttgart, known as the
Fluid-Structure Interaction (FSI) test facility, is a sharp edged forged EN 1.4550 (ANSI 347,
X6 CrNiNb 18-10) austenitic stainless steel T-junction with reduced carbon content in
accordance with the German KTA 3201.1 [73]. The facility is shown schematically in Figure
6-1 along with the properties of the working fluid (deionized water with EC between 5 and 10
μS/cm at 20°C) and flow conditions. A main pipe with inner diameter Dm = 71.8 mm carrying
hot water at a constant mass flow rate of 0.4 kg/s (turbulent flow) encounters a perpendicular,
horizontal branch pipe of inner diameter Db = 38.9 mm with room temperature water flowing
at a rate of 0.1 kg/s (transition flow). Downstream of the T-junction the flow is then split
according to the mass flow rate ratio and recycled back to the T-junction; the flow headed for
the branch line first passes through a heat exchanger. The mass flow rate ratio at the T-
junction is such that at low ΔT = Tm – Tb a wall-jet type flow pattern is manifest downstream
of the T-junction at these flow rates. At higher ΔT, the cold branch line flow quickly sinks to
the bottom of the mixing pipe downstream of the T-junction and only weakly mixes with the
hotter, lighter main flow. More information about the flow behavior at the facility beyond the
findings articulated in this cahpter is described in the work of Kuschewski (2011, 2013,
NWLED-IF experiments), Klören (2012, 2013, LES simulations), and, most recently, Selvam
(2014, 2015, LES simulations) [59, 60, 88, 89, 218, 219]. The hot flow is measured once per
minute 1015 mm upstream of the T-junction in the center of the main pipe by a thermocouple
(XTM3) while the temperature in the branch flow is measured with the same frequency by a
thermocouple in the center of the branch line flow 2940 mm upstream of the T-junction
(XTM4).
Figure 6-1. Piping and instrumentation diagram of the FSI test facility at the University of
Stuttgart adapted from Kuschewski (2013) [60]. Temperature and velocity in the main pipe
represent maximum, bulk values.
116
The facility is operated at temperatures up to 256°C (measured by XTM3) and
pressures up to 8 MPa. Resistance heating pads along the length of the main pipe inlet run are
regulated by a PID controller with reference thermocouples located between the mats and the
outer walls of the conduit. Heating of the circulated working fluid proceeds in the main pipe
at a typical rate of 40 K/hour. Meanwhile, the room temperature flow from the branch line
never ceases, such that mixing is always occurring at the T-junction. The flange system used
in the main pipe and mixing pipe are standard, specifically DN80 PN100, with the exception
of the inner diameter (71.8 mm) which is custom. With the exception of the T-junction, the
piping is comprised of austenitic stainless steel EN 1.4571 (ANSI 316Ti, X6CrNiMoTi17-12-
2). Flanged modules 340 mm in length neighbor the T-junction. Two modules in the main
pipe upstream of the T-junction and three in the mixing pipe downstream allow for the
installation of measurement instrumentation at a variety of locations.
At high main flow temperatures, stratification in the flow results in large thermal
stresses in the facility which induce a bending moment in the pipeline, which is not
anchored.[220] This behavior has been investigated in FEM simulations by the MPA
Stuttgart based on temperature profiles from LES with conjugate heat transfer [221]. Two
simulations were performed based on main flow temperatures of Tm = 120 and 280ºC. At
120ºC, before the onset of cold upstream flow, modules downstream of the T-junction rises to
a level slightly higher than the T-junction module. Significant upstream flow at 280ºC results
in the T-junction module along with the first two upstream modules rising significantly such
that downstream modules are no longer horizontal to gravity but slightly sloped. It cannot be
excluded that this phenomenon may have an effect on mixing behavior at the T-junction.
117
6.3 Instrumentation
6.3.1 Mesh sensor module
The mesh sensor package prototype, described in Chapter 5, was fixed to a flanged
‗spacer‘ module of reduced length manufactured for adapting the sensor to the Stuttgart T-
junction facility. Four thermocouples were installed at four circumferential positions on the
outer wall of this shortened module. A photograph of the mesh sensor module installed
upstream of the T-junction is shown in Figure 6-2. The orientation of the mesh when installed
is shown in Figure 6-3 where the viewing orientation is looking away from the T-junction.
The free cross-section across both electrode layers is approximately 77% and the pressure
drop coefficient, again estimated from Idel'chick (1966), is 0.26 [168].
Figure 6-2. Mesh sensor package (red box) installed upstream of the T-junction at -3.5Dm,
thermocouples on the outer wall of the mesh sensor module spacer (green box), and
additional thermocouples (blue boxes), are shown installed at the FSI test facility.
Figure 6-3. Sensor sandwich comprising three ceramic plates and stainless steel capillary
electrodes. The orientation of the sensor is shown as if viewed from the T-junction, the
Cartesian mesh is tilted 22.5º relative to gravity.
118
The calibration of the mesh sensor relies on a nearby thermocouple to compute a
relationship between the raw mesh sensor signal (which is proportional to the EC of the fluid)
at a given crossing point and temperature. Since mixing downstream of the T-junction cannot
be excluded (nor can mixing upstream at higher temperatures), calibration of some crossing
points near the bottom of the pipe is a challenge. Full details of the calibration methodology
is presented in Appendix Section 6.10.1. The resolution of the sensor in terms of EC is high
and is limited primarily by electronic noise. Signal post-processing as a means to filter noise
is described in Appendix Section 6.10.2. A linear function is used to describe mesh sensor
signal as a function of temperature across the range of interest (roughly 60 to 200ºC). The
gain-magnitude frequency response of the mesh sensor and thermocouples are discussed in
Appendix Section 6.10.3.
At four positions (0º, 90º, 180º and 270º) on the mesh sensor module spacer 1 mm K-
type thermocouples were installed. These thermocouples had a measurement frequency of 0.5
Hz. Additional thermocouples at the facility at various in-wall and in-flow depths
(measurement frequency 100 Hz) as well as those related to the heating mats may be utilized
to track the flow behavior. All thermocouples, as well as the associated acquisition device,
were provided and managed by researchers at the University of Stuttgart.
119
6.4 Test Matrix
Two measurement campaigns were performed at the Stuttgart T-junction facility; both
saw the temperature in the main pipe rise from room temperature to 256°C in the center of
the main flow, as measured by the XTM3 thermocouple, over the course of roughly 8 hours
at 7 MPa pressure. During the first campaign the mesh sensor measurement plane was located
at y = 3.5Dm. The second campaign saw the mesh sensor installed upstream of the T-junction
at -3.5Dm with additional thermocouples placed on the mesh sensor module spacer at -5.5Dm.
Both configurations are shown in
Figure 6-4. Configuration of the Stuttgart T-junction facility during the first (top) and second
(bottom) measurement campaigns. Main flow travels right to left, gravity is directed into the
page.
120
Figure 6-5. Temperature history recorded once per minute in the center of the main pipe
(XTM3) and branch line (XTM4) upstream of the T-junction, dotted lines represent analyzed
fluid temperature test cases.
The heating was occasionally stabilized for some minutes, such that longer
measurements with better statistics could be acquired. Four test cases have been isolated for
deeper analysis; they are main flow temperatures of 165±1ºC, 181±1ºC, 201±1ºC and
256±1ºC with a branch flow temperature of 22±1ºC. The main pipe and branch line
temperature histories are shown in Figure 6-5 for both measurement campaigns. Due to
instability in the main flow temperature in the second measurement campaign, the Tm =
201±1 ºC case is left unanalyzed. The main and branch mass flow rates were equal for all
three test cases: = 0.4 kg/s and = 0.1 kg/s. The fluid conditions in all four test cases
are enumerated in Table 6-1. The Froude number is defined, along the lines of Eq. 3-15, as,
√ , (6-1)
where ′ is the reduced gravity and the mixture velocity Umix is defined as the sum of
superficial velocities,
, (6-2)
where A is the main pipe flow area. The Prandlt number is defined as,
⁄ , (6-3)
where cp is the specific heat, μ is the dynamic viscosity, and k is the thermal conductivity. It
represents the ratio of viscous diffusion rate to thermal diffusion rate. In the branch fluid, Pr
is between 6.4 and 6.9 for all test cases while in the far less viscous main flow, in the highest
temperature case, Pr is around its minimum in water, 0.83.
Herein the Richardson number is calculated as,
, (6-4)
121
where ⁄ is the density difference. This definition of the Richardson
number is similar to that found in Chapuliot (2005) with the difference being the use of the
mixture velocity rather than the branch line velocity [1]. Finally, the momentum ratio is
defined as in Kamide (2009) as [46],
. (6-5)
Test case Tm
[ºC]
ΔT*
[K]
ρm
[kg/m3]
ρr*
[-] ε
*
Ur*
[-]
pr
[-]
Rem
[E4]
Rer
[-]
Fr
[-]
Ri
[-]
#1 165 143 906.3 0.91 0.094 1.30 3.58 4.27 12.12 1.62 3.7
#2 181 159 889.9 0.89 0.11 1.32 3.64 4.71 13.37 1.52 4.2
#3 201 179 867.6 0.87 0.13 1.35 3.74 5.26 14.94 1.41 4.9
#4 256 232 793.0 0.79 0.21 1.48 4.10 6.81 19.35 1.22 6.6
Table 6-1. Fluid conditions for each experimental case including Reynolds, Froude and
Richardson numbers. Subscript r represents the ratio between main and branch flow water.
*Based on Tb = 22-24ºC, ρb = 1000.6 kg/m3, Ub = 0.084 m/s.
122
6.5 Regarding the orientation of presented results
Both downstream (Campaign #1) and upstream (Campaign #2) mesh sensor data is
presented from the perspective of the T-junction in Sections 1.1, 1.1 and 1.1. A schematic of
the data viewing orientation with coordinate axes is shown in Figure 6-6.
Figure 6-6. Representative position of the mesh sensor and data viewing orientation (always
looking away from the T-junction) for mesh sensor installation at 3.5Dm downstream of the
T-junction in the mixing pipe (Campaign #1, left) or -3.5Dm upstream in the main pipe
(Campaign #2, right).
By interpolating the mesh sensor data onto a polar coordinate space, results are analyzed
along a perimeter half of the mesh sensor pitch (2.24 mm) inside the inner pipe wall, i.e. at a
radius of 33.66 mm. Via this interpolation, the position of the stratified layer on the left-side
and right-side pipe wall may be reported as angular position along the arc with length S, see
Figure 6-7. Furthermore, the maximum gradient of the temperature along the arc
⁄ , is also calculated both as time-averaged values as well as time-resolved values.
See Appendix Section 6.10.4 for details.
Figure 6-7. Sketch of variables related to stratified flow in the T-junction. Angular positions
α1 and α2 represent the location of maximum thermal gradient ⁄ along the circular
perimeter (in red) with r = 33.66 mm
123
6.6 Downstream results
The mesh sensor module positioned at 3.5Dm elucidates the and TRMS profiles within
the cross-section of the pipeline. It is a considerable advantage of the mesh sensor compared
to traditional thermocouples that local gradients are resolved far better due to the dense
matrix of measuring location. Figure 6-8 shows plots of both mean and fluctuating
temperature fields as measured by the mesh sensor for all test cases. Density differences
between the hot main flow and cold branch flow are seen to play a strong role in the mixing
behavior downstream of the T-junction. As the main flow temperature increases (and thereby
the water density decreases) the mixing zone downstream of the T-junction, as measured by
the extent of elevated temperature fluctuations in the cross-section, tends to sharpen. As the
mixing zone shrinks the amplitude of temperature fluctuations increases to around TRMS = 10
K. All tests show similar profiles in which a mixing layer between hot main flow and cold
branch flow spans the inner diameter of the pipe. The mixing layer in the profile is oriented
perpendicular to gravity except in the first test case where the layer appears to be oriented
approximately 20º relative to the horizontal. Below the mixing layer, cold fluid temperatures
(< 75ºC) are measured even in mixing at the highest ΔT (Tm = 256ºC). The measured flow
profiles cannot be categorized within the traditional low-ΔT cross-flow mixing nomenclature
of Kamide (2009) [46].
The temperature profiles measured in the third and fourth test cases are unreliable in
the hot fluid region at the top of the pipeline due to the ambiguous dependency of the EC of
water versus temperature (see Appendix Section 6.10.1). In the important lower portions of
the pipe cross-section, where temperatures are below 200ºC, the temperature profile can be
reported with confidence knowing that temperatures in the bottom of the pipe have risen to
these levels. The zone of average cold fluid at the bottom of the pipe is greatly reduced in
area, especially at Tm = 256ºC while the minimum average temperatures, of 70 to 80ºC, are
only marginally elevated compared to lower ΔT cases. Of all test cases, temperature
fluctuation amplitudes are highest in the mixing zone found in the fourth test and,
furthermore, the fluctuations in this case are the most localized.
124
Figure 6-8. Time-averaged (top row) and RMS (bottom row) of temperature in the cross-
section of the pipeline measured by the mesh sensor 3.5Dm downstream of the T-junction.1
Viewing orientation is looking away from the T-junction.
Figure 6-9. Ensemble averaged (K = 8) PSD at crossing-points (right) of highest TRMS for
each test case.
The PSD, computed at the crossing point measuring the highest TRMS for each test
case (see Figure 6-9) does not indicate a preferred frequency of mixing except in the fourth
test, in which frequencies between 1.6 Hz and 2.4 Hz show a plateau of high amplitude. The
spectrum from Test #1 is weighted slightly more towards the high frequencies relative to the
1 Technical difficulties with the 6
th transmitter electrode resulted in an intermittent signal which also affected its
neighboring transmitters. Therefore, the average and RMS plots in those three rows of crossing points are
compiled not from the whole 180 s measurement but from the portion in which the 6th
transmitter was
functioning properly. Nonetheless, it is evident a signal of questionable validity remains in the 5th
, 6th
, and 7th
transmitter electrodes and therefore quantitative discussion related to those positions is avoided.
125
other tests. Apart from this, the four spectra are similar in shape. Power spectra at some
positions measured by the mesh sensor show similarities with spectra from downstream in-
flow (2 mm from inner wall) thermocouples at different positions. For example, in Figure
6-10 the thermal mixing spectrum from near the wall in the mesh sensor at a circumferential
position of 219° (based on a conventional polar coordinate system in the cross-section) is
shown to be similar to the spectrum 1.5Dm further downstream at 324.5° yet is dissimilar to
the spectrum downstream at nearly the same circumferential position, 234.5°. This
asymmetry may be the result of the swinging motion of the heavy cold flow as it progresses
down the main pipe, described by both Klören (2011) and Selvam (2015) in mixing cases
with lower ΔT [82, 218]. This swinging motion may also explain the tilted layer of high
temperature gradient see in the profile in Figure 6-8.
Figure 6-10. PSD measured near the wall by the mesh sensor in Test #4 along with that from
a downstream thermocouple measurement.
126
6.7 Upstream results
Upstream flow in the T-junction, the result of a slow turbulent main flow and large
density differences between the main and branch flows generating a stratified countercurrent
flow, is a significant feature of the flow behavior at high ΔT at the facility. The formation and
progression of upstream flow with increasing ΔT, starting at the T-junction, may be tracked
by a combination of thermocouples in the walls of the main pipe, on the outside of the main
pipe, and by the mesh sensor.1 Specifically, measurement points are present at -0.96 (1.5 mm
from inner wall), -1.58 (1.8 mm from inner wall), -3.5 (mesh sensor module), -5.9 (outer
wall), -10.1 (outer wall) and –40.7Dm (outer wall). The onset of upstream flow has been
found to be more akin to a thermal shock than a slow, ramped cooling of the bottom of the
conduit. Therefore, thermocouples, even those on the outside wall of the main pipe, measure
a sudden plummet in the temperature which can help to localize in time the moment upstream
flow reached the measurement location. The thermal inertia of the wall naturally results in a
slightly delayed indicator. This delay is neglected, for simplicity, since the time-scales of the
upstream flow progression are large relative to that of heat transfer within the steel pipe wall.
The penetration depth of the upstream flow into the main pipe extends more than
2.92 m based on thermocouple readings. The upstream penetration of the cold branch flow as
a function of ΔT is shown in Figure 6-11. The position of the mesh sensor (-3.5Dm) appears to
represent the approximate vicinity of a sharp reduction in the rate of upstream cold flow
penetration with increasing ΔT. The reproducibility of these measurements in another facility
may be hindered by the heating of the upstream flow by the heating pads which are installed
around the main pipe starting at approximately -13.6Dm. This heating could conceivably slow
the upstream flow progression by introducing an additional heat source.
Figure 6-11. Data points represent the ΔT (= Tm - Tb) at which upstream flow was detected (as
a drop in temperature) at thermocouples measurement locations or the mesh sensor during
both the first and second measurement campaigns. Vertical dotted line represents the location
at which heating pads surrounding the pipe end.
1 Recall that all thermocouple instrumentation was the property of the University of Stuttgart.
127
The upstream flow onset, as measured by the mesh sensor, includes a number of
important features. First and foremost is the rate with which the temperature is seen to
decrease at the bottom of the main pipe at -3.5Dm. A number of crossing points at the bottom
of the pipe detect a sudden drop in temperature for which the cold branch line water is
responsible. Part of the initial decrease in temperature2 includes a portion in which the fluid
temperature drops from 140 to 100ºC at a rate of approximately -130 K/s [30]. Near the wall,
the temperature fluctuations recorded at two crossing points near the pipe-bottom are
TRMS(16,11) = 6.3 K and TRMS(15,11) = 8.4 K in the first 10 seconds after the onset of
upstream flow. The fluctuations are greatly reduced in magnitude some 10‘s of seconds later,
between 30 and 40 s after the onset of upstream flow to TRMS(16,11) = 3.1 K and TRMS(15,11)
= 5.2 K.
Figure 6-12. Temperature history at three mesh sensor crossing points (see locations relative
to mesh sensor sandwich, right) at the bottom of the main pipe (location indicated Figure 6-3)
as cold upstream flow is detected at -3.5Dm.
Figure 6-13. Temperature history at thermocouples placed on the outside wall of the mesh
sensor spacer section (see locations relative to pipe-wall cross-section, right) at -5.5Dm as
cold upstream flow is detected at the bottom of the pipe.
2 The temperature history is reminiscent of thermal shock experienced in thermal stratification tests in a mockup
of horizontal feedwater piping at the HDR-facility in the 1980‘s, discussed in Section 1.2.4. Specifically, Figure
7 of Wolf (1989).
128
Detection of the onset of upstream flow outside of the pipeline is shown in Figure
6-13. Outside of the 8.55 mm thick steel wall at the bottom of the conduit (T7), due to the
sudden presence of cold upstream flow from the branch line, a sudden decrease in
temperature at a maximum rate more than two orders of magnitude lower than in the flow is
recorded. The thermal inertia of the pipeline limits the maximum rate of temperature decrease
is approximately -1.14 K/s at -5.5Dm in this thermal shock situation. The temperature
stabilizes approximately 15 minutes after the onset of upstream flow after decreasing from
154 to 94ºC. Note that the stabilization of the temperatures on the side (T11) and top (T13) of
the conduit are not the result of upstream flow but due to the PID heating program regulating
the main flow heating, preparing for test case #1.
Figure 6-14. Time-averaged (top row) and RMS (bottom row) of temperature in the cross-
section of the pipeline measured by the mesh -3.5Dm sensor upstream of the T-junction.
Viewing orientation is looking away from the T-junction.3
Mean and fluctuation temperature and fluctuation profiles are shown in Figure 6-14
for Test #1, #2 and #4 upstream of the T-junction. In Test #1 the mesh sensor measures a
small amount of upstream flow at the very bottom of the pipe with temperature of
approximately 100ºC. Neighboring crossing points see a mean temperature increase of over
30ºC. The highest temperature fluctuations are found in the thin layer between the cold
upstream flow and the hot main flow. The remainder of the cross-section shows negligible
temperature fluctuations. With higher ΔT in Test #2, the amount of upstream flow in the pipe
3 Technical difficulties with the 6
th transmitter electrode resulted in an intermittent signal which also affected its
neighboring transmitters. Therefore, the average and RMS plots in those three rows of crossing points are
compiled not from the whole 180 s measurement but from the portion in which the 6th
transmitter was
functioning, in the case of Test #1. Nonetheless, it is evident a signal of questionable validity remains in the 5th
,
6th
, and 7th transmitter electrodes and therefore quantitative discussion related to those positions is avoided.
Insufficient up-time was found in the 6th
transmitter electrode in Test #2 and #4, it has therefore been left blank.
129
cross section is increased and the temperature gradient between the zone of upstream flow
and the hot flow is considerably larger. The RMS of the temperature, however, is decreased
compared to the lower ΔT case. Finally, by including interpretation of the and TRMS profiles
from the fourth test case it can be concluded that the fraction of cold fluid in the cross section
is increasing with increasing ΔT, this trend is quantified later in this chapter.
The maximum time-averaged thermal gradient near the pipe wall ⁄ ,
increases drastically after the onset of upstream flow, which occurs at the sensor position (-
3.5Dm) between Ri = 3.53 and 3.65, to values of around 4 K/mm at both the left and right
walls, see Figure 6-15. The average thermal gradient at the edges of the stratified layer
increases sharply as a function of Richardson number, thereafter. Around Ri = 5 the
magnitude of ⁄ plateaus at between 9 and 11 K/mm at the right and left walls,
respectively.
Figure 6-15. Maximum average thermal gradient ⁄ near the wall -3.5Dm upstream
of the T-junction vs. Richardson number. The onset of upstream flow is apparent in the step
change (indicated by dotted red arrow) in thermal gradient around Ri = 0.48.
For a perspective of the time-dependent behavior of the cold flow upstream of the
T-junction, the angular position of the stratified layer at the right (α1) and left walls (α2) of the
pipe is plotted as a function of time during test cases #1, #2 and #4 in Figure 6-16. The
angular position of the stratified layer upstream of the T-junction, a zone of countercurrent
stratified flow, fluctuates in a range sometimes larger than 20º within one second at the right
and left wall, respectively, during the first test case (Ri = 3.7). Already at Ri = 4.2 in Test #2
the interface is far more stable, showing few disturbances during 10 s. Similarly, at the
highest ΔT, in the final test case with a Richardson number of 6.6, while having risen in the
pipe the interface shows fluctuations of only 5 to 6º at each wall.
130
Figure 6-16. Position of maximum thermal gradient ⁄ over the course of 10
seconds along the right (α1) and left walls (α2) pipe upstream of the T-junction at -3.5Dm.
Although the location of largest thermal gradient with respect to the near-wall
arc in the flow does not exude a dynamic nature, the magnitude of that thermal gradient is not
steady in time, even in Test #4. Figure 6-17 shows the time history of the thermal gradient
⁄ at locations α1 and α2 for the same 10 s measurement as in the previous figure.
Note that the instantaneous thermal gradient near the wall is significantly higher than the
average gradients shown in Figure 6-15, the result of movement of the interface blurring the
average gradient.
Figure 6-17. Maximum thermal gradient ⁄ over the course of 10 seconds along
the left (bottom) and right (top) walls in the pipe
Figure 6-18 shows the PSD for two test cases at three crossing points near the bottom of the
main pipe (recall Figure 6-3 right). At Tm = 165ºC (Test #1) the highest RMS is measured at
(15,11), the PSD at this position shows a plateau at frequencies below 0.7 Hz without
evidence of a preferred mixing frequency. A larger portion of the RMS of the temperature
arises from low frequencies in the mixing layer (15,11) than above (14,11) or below it (16,11)
. In the case of a larger temperature difference, in Test #2, the crossing point (14,11) lies
131
within the mixing zone between the cold upstream flow and the hot main flow. The mixing
spectrum at this crossing point also exhibits a plateau at lower frequencies with a peak at 0.1
Hz. Considering the materials and geometries of interest, 0.1 to 1 Hz is typically cited as the
range of interest related to thermal fatigue [222]. Timperi (2010) has conducted an LES
simulation of an HDR thermal stratification experiment in which a horizontal DN400 mockup
of a feedwater line is exposed to stratified flow between hot water at 210 and cold water at
60; the most dominant frequency found in the mixing layer is reported to be ―a little less than
1 Hz‖ [31].
Figure 6-18. Ensemble averaged PSD (K=4) at three crossing points near the bottom of the
main pipe in Test #1 (left) and #2 (right).
A regularly extending and receding upstream flow could result in thermal fatigue in
the main pipe analogous to the case of turbulent penetration in the branch line, e.g. the
Farley-Tihange phenomena. As discussed in Section 4.8, that mixing scenario sees a cold
tongue of water impinging into a branch line filled from the main pipe with much hotter
water [223]. In the case of the measurement campaigns at the Stuttgart T-junction facility,
since the heating program calls for a continuous rise in Tm, the penetration depth of the
upstream flow only extends and does not appear to extend and recede in a transient manner,
within the resolution of the available instrumentation at the facility.
132
6.8 Combined analysis
A compilation of mesh sensor data from measurements at the T-junction facility
indicate that the cold branch flow is being split between the mixing pipe and main pipe in
larger and larger fractions with increasing density difference, explaining the decreasing cold
flow area with increasing ΔT in the mixing pipe along with the concurrent increase in the
main pipe. The trend towards symmetric stratified profiles upstream and downstream may be
exacerbated by the fluid-structure interaction occurring at the facility, in the sense that the T-
junction becomes the highest point in the facility at high temperature. The mixing scenarios
are categorized according to ΔT in Figure 6-19. The experiments provide the opportunity to
investigate temperature distributions in thermally stratified flows with presumably different
velocity gradients, upstream versus downstream of the T-junction, within the same mixing
scenario.
Figure 6-19. Schematic description of flow behavior at the Stuttgart T-junction facility at
low, mid, and high ΔT.
Made possible by the mesh sensor is the analysis of the thermal gradient, both in the
center of the pipe and near the walls, as well as the area of cold flow within the pipe cross-
section. Downstream of the T-junction the time-averaged temperature in the cross-section, as
viewed from the side of the pipe in Figure 6-20 (left), shows the somewhat linear behavior of
the temperature profile at the bottom of the pipe with steepening slope as ΔT increases
between Test #1 to #4. Meanwhile, upstream of the T-junction in Figure 6-20 (right), where
the interfacial friction between cold and hot fluids is presumably stronger due to the
countercurrent flow pattern, the thermal profile takes on a distinct S-shape with steeper
profile than found downstream.
133
Figure 6-20. Thermal gradient profile viewed in the plane of the mesh sensor. Each semi-
transparent bar represents time-averaged temperature measured by a crossing point of the
sensor. Dotted boxes approximately isolate the mixing zone.
The maximum thermal gradient in the center of the cross-section (see Appendix
Section 6.10.4) downstream of the T-junction is found to be a linearly increasing function of
Richardson number over a large range from Ri = 1.78 to 6.57 (ΔT = 78 to 232ºC), see Figure
6-21. In absolute terms, the maximum thermal gradient more than doubles from around 4
K/mm to 9.5 K/mm at 3.5Dm. Each data point represents the gradient of temperature from a
5-second time-averaged mesh sensor signal extracted from each consecutive full 180 s
measurement during the heating of the facility. Upstream of the T-junction the thermal
gradient prior to upstream flow onset is low, around 1 K/mm and increases slowly with Ri
number. The onset of upstream flow results in a jump in the maximum thermal gradient
found in the centerline (shown with dotted red arrow Figure 6-21) to around 8 K/mm. The
stratified layer sharpens further resulting in a maximum thermal gradient of around 14.5±1
K/mm between Ri = 4.5 and 6.6, significantly higher than found downstream of the T-
junction.
134
Figure 6-21. Maximum average thermal gradient ⁄ across the stratified layer in
the center of the pipe cross-section vs. Richardson number. The onset of upstream flow is
apparent in the step change (indicated by dotted red arrow) in thermal gradient around
Ri = 3.6.
As deduced previously in a qualitative sense from profiles measured by the mesh
sensor (recall Figure 6-8), the cold holdup area appears to decrease 3.5Dm downstream of the
T-junction with increasing ΔT. Figure 6-22 shows quantitatively the trend in cold holdup as
% of the total flow area (see Appendix Section 6.10.5) versus Ri number. Indeed it happens
that the cold flow area below the stratified layer shrinks with increasing Ri number while,
concurrently, the same holdup area -3.5Dm upstream of the T-junction increases with Ri
number. As the Richardson number increases beyond 6 the holdup area upstream of the T-
junction becomes larger than downstream at the same non-dimensional positions (±3.5Dm).
As Ri increases, it has steadily less influence on the proportional area of heavier cold flow in
the cross-section both upstream and downstream of the T-junction.
Figure 6-22. Cold holdup % in the pipe cross section vs. Richardson number 3.5Dm
downstream -3.5Dm and upstream of the T-junction.
The results indicate a steady transition to an increasingly stratified flow as the main
pipe flow temperature increases. The time-averaged location of the stratified layer may be
discerned both downstream and upstream of the T-junction by localizing the largest time-
135
averaged near-wall thermal gradient. Since the stratified layer spans the conduit, it is possible
to discern two peaks in ⁄ around the inner perimeter of the pipe; one peak corresponds
to one side of the thermal discontinuity at the border between hot and cold fluids, the other
peak corresponding to the other side of this layer spanning the cross-section, recall Figure
6-7. The position of these maxima gives some indication of pipe wall locations prone to
cyclic loading due to instabilities in the stratified layer. Figure 6-23 shows the angular wall
positions α1 and α2, of maximum average thermal gradient ⁄ , downstream (left,
subscript ‗d‘) and upstream (right, subscript ‗u‘) of the T-junction. The stratified layer moves
downwards with Richardson number downstream of the T-junction, and moves upwards
upstream of the T-junction. The shift is small, however, with α2d moving from 214º to 225.4º
and α1d to as little as 310.4º. Upstream, the position of the interface between cold branch flow
moving underneath and counter to the hot main flow rises slightly between Ri = 3.65 and 6.57
to positions 327.4º and 216.9º.
Figure 6-23. Location of maximum average thermal gradient near the wall ⁄ ,
3.5Dm downstream (left) and -3.5Dm upstream (right) of the T-junction vs. Richardson
number.1
1 Missing data for α1d is the result of a malfunctioning 6
th transmitter electrode initially discussed with regards to
Figure 6-8.
136
6.9 Conclusion
The measurements described in this chapter are party to a series of proof-of-concept
tests performed at the University of Stuttgart T-junction facility of a new mesh sensor
package for high-temperature and high-pressure flows, especially those related to nuclear
safety, described in Chapter 5. T-junction mixing with reactor-like temperature differences
between main pipe and branch line flows has been investigated at bulk temperatures of up to
256ºC. Instrumentation included thermocouples installed on the pipe outer wall, in-wall and
in-flow as well as a novel mesh sensor capable of measuring high-temperature and high-
pressure flows at high frequency (in this case 10 kHz) with high spatial resolution (in this
case 208 measurements points in the flow with a pitch of 4.49 mm). The mesh sensor
package, measuring EC, is used here to measure single phase mixing in the T-junction
without a salt tracer by means of a calibration routine based on the temperature dependence
of the EC of water. The mesh sensor was installed both downstream and upstream of the T-
junction where it elucidated the flow average and fluctuating temperature profiles. Four
boundary conditions, in particular, were investigated for extended durations of up to 10
minutes. These included mixing at main pipe flow temperatures ranging from 165ºC to
256ºC. The mixing behavior downstream of the T-junction cannot be described within the
usual categorizations of cross-flow mixing in T-junctions while upstream mixing appears
typical of countercurrent stratified flows found in other contexts.
The mesh sensor indicates a thermally stratified layer between cold fluid in the
bottom portion of the pipeline and hot fluid on top. As the Richardson number increases, the
interface between the main flow and branch flow in the mixing pipe becomes sharper and
contains larger amplitude temperature fluctuations. Downstream, the area of cold fluid in the
cross-section is seen to decrease with increasing Tm such that the highest temperature
fluctuations near the wall at the mesh sensor position move downwards along the walls from
the middle portion of the pipeline.
The upstream flow phenomena, cold flow penetrating more than 3 meters into the
main pipe underneath the incoming hot main flow has been documented in detail thanks to
the mesh sensor. The result of a stratified flow with high Richardson number, the cold flow
rests in a stable way on the very bottom of the pipe with temperature fluctuations residing in
a thin layer not thicker than the pitch of the mesh sensor. The thermal shock which occurs
when the cold upstream flow arrives at a particular location at the pipe bottom, in this case
measured at -3.5Dm upstream (in the flow, by the mesh sensor) and at -5.5Dm (outer wall, by
a thermocouple) of the T-junction was quantified. Furthermore, the cold holdup area of the
upstream flow was found to increase with Richardson number.
Portions of the work discussed in this chapter are to be published in peer-reviewed
conference proceedings as,
1. Kickhofel, J., Selvam, K., Huber, H., Laurien, E., and Prasser, H.-M.. ―Mesh Sensor
for High Temperature and High Pressure Applications,― 16th International Topical
Meeting on Nuclear Reactor Thermalhydraulics (NURETH-16), Chicago, USA,
August 30 - September 4, 2015.
137
6.10 Appendix
6.10.1 Mesh sensor calibration methodology
The mesh sensor measures the EC of a small volume of fluid at each crossing point
between a transmitter and a receiver wire of the mesh. Typically, single phase mixing
experiments, such as studies of turbulent mixing at T-junctions, would utilize a salt tracer to
differentiate the main flow from the branch flow and therefore capture the mixing process as
in mixing studies at the LKE T-junction discussed in Chapter 4. The addition of a tracer was
not permitted at the Stuttgart T-junction facility and therefore the measurements rely on the
varying EC of water with temperature. The ion product Kw = [H+][OH-] (also referred to as
the dissociation constant), of pure water has been measured by Marshall (1981) over a wide
range of temperatures and pressures and subsequently accepted by the International
Association for the Properties of Water and Steam (IAPWS) [224]. Figure 6-24 (left) shows
the EC of pure water versus temperature at 7 MPa based on the correlation and coefficients of
Marshall (1981) [224].
Figure 6-24. EC vs. temperature (left) according to the correlation of Marshall (1981) for
pure water, and EC vs. temperature (right) from experiments with NaCl solutions at high
pressure from Quist (1967) [224, 225].
Truly pure water, however, does not exist in an engineering context. Measurements
by a handheld meter at the T-junction facility found the circulated water to have EC of 7-9
μS/cm1, which results in a different shape of the ion product versus temperature curve. It has
been shown, for electrolyte solutions such as NaCl, for example, that EC is essentially linear
to 200ºC over a wide range of pressures, see Figure 6-24 (right) [225]. The mobility of ions in
the water are the dominating contribution, compared to the self-dissociation of H2O, to the
EC as a function of temperature especially at elevated temperatures in the range of interest.2
The peak in EC is the result of ionic association counterbalancing the ionic mobility as the
1 A slight increase in working fluid room temperature EC of approximately 2 μS/cm was noted in campaign
before and after measurements, presumably due to corrosion products. 2 The sharp decrease in viscosity of water vs temperature as it is heated above room temperature is the reason
for increased ionic mobility.
138
density of water continues to decrease with temperature. The nonlinearity of EC as a function
of temperature, seen especially below 100ºC, is lost with an increase in impurities. Therefore,
a linear behavior of the EC of the water over a range between approximately 60 and 200ºC
has been assumed.
The calibration of the mesh sensor at the Stuttgart T-junction is performed using the
raw data collected from the full day of heating and cooling the facility, with the sensor
installed upstream of the T-junction. For the calibration of each crossing point, a single
reference thermocouple was chosen. The reference thermocouple, XTM3, described earlier in
Section 1.1, lies in the center of the flow 765 mm upstream of the mesh sensor. It would be
incorrect to assume that the temperature at XTM3 is equal to the temperature across the
whole of the mesh sensor plane. A number of factors are at play; firstly, there is no heating of
the flow between XTM3 and the mesh sensor plane; some heat losses and mixing can be
expected. Secondly, and more importantly, at a Reynolds number of 54,000 (at 200ºC) in the
main pipe the flow is not sufficiently turbulent such that a flat temperature profile is achieved
in the pipe cross section. A top-to-bottom temperature gradient in the main pipe is expected
to exceed 10-15 K at high water temperatures based on thermocouple measurements at the
facility. Indeed it was observed that the signals from the crossing points close to the top of the
pipe cross-section change from increasing to decreasing tendency earlier during the heat-up
process than those close to the bottom. Therefore, a least squares regression was performed to
best estimate the reference temperature at each mesh sensor crossing point Tt,r, as a function
of reference thermocouple temperature Tr, at time tmax of highest crossing-point signal. This
approach takes benefit from the assumption that the maximum EC is always found at a
temperature of 240°C. The reference temperature Tr measured by XTM3 is different from
240°C in the same instant. By knowing the relationship between the reference temperature
Tr(tmax,t,r) and Tt,r(tmax,t,r) at the time of maximum signal at each crossing point (when
Tt,r(tmax,t,r) = 240°C) that relationship then helps to convert Tr(t) measured at any other time to
an estimated crossing point temperature Tt,r(t). The available data was analyzed to create a
table containing the reference temperature Tr(tmax) at the moment the turning point is reached
for each crossing point (t,r) of electrodes at its known spatial coordinates (z,x).
A least squares regression seeks the planar fitting to these 3D points of the form (z, x,
Tr(tmax)). The plane Tr + A + Bz + Cx describes the distribution of temperature in the pipe
cross section at the location of the mesh sensor which is known to exhibit a gradient from top
to bottom at high temperatures. The x-component is included to account for the possibility of
upstream swirl influencing the temperature profile along this axis, although a flow
straightening device is installed. The minimum of the function,
∑ ∑
, (6-6)
is sought via,
, (6-7)
139
where Tt,r(tmax,t,r) is defined for all (t,r) crossing points as 240ºC: the temperature
corresponding to the maximum signal, and therefore maximum EC, at each crossing point.
The reference thermocouple reading, Tr at the time of maximum signal at crossing point (t,r),
tmax,t,r varies. In this way a function for the estimated temperature at each crossing point at
any given time, Tt,r = Tr(t) + A + Bzt,r + Cxt,r, may be generated assuming a tilted-planar
temperature profile in the cross section at 240ºC. The regression finds the following values, A
= 1.8139 [K], B = 701.8 [K/m] and C = 17.8 [K/m] indicating a top-to-bottom gradient in the
pipe of up to approximately 49 K and very little temperature change from left-to-right . The
coefficients B and C are only representative for the conditions of a hot facility at about
240°C. It is plausible to assume that the temperature gradients are proportional to the
difference between the reference and the ambient temperature. Therefore, a further step is
taken to scale the coefficients B and C with main flow temperature:
′ (
) (
), (6-8)
and similarly for C‟(t). With this correlation, the estimated temperature at the mesh sensor
was corrected for all available data points recorded during the heat-up phase.
An example of the relationship between the corrected reference temperature, Tt,r, and
the mesh sensor signal, θ, is shown in Figure 6-25. Visible is the peak in the EC of the water
at 240ºC. The region in which the crossing points are calibrated is where the signal shows
linear dependence to the temperature. A linear fit is made in this region for each crossing
point which becomes function which converts the raw measured signals to temperatures.
Figure 6-25. Plot of raw mesh sensor signal vs. estimated temperature at a crossing point near
the top of the pipe. The function which describes the linear fit, shown in red, is that which
converts signal values to temperature at this crossing point for any given measurement
dataset.
The presence of cold upstream flow at the sensor, present sometimes even during the
heat-up process, precludes the generation of complete calibration data for the crossing points
of the sensor at the bottom of the pipe, as in the case of the downstream calibration. We
therefore rely on the linear behavior of the EC of the fluid as a function of temperature in
140
calibrating these crossing points for temperatures that we could otherwise not verify being
experienced at those locations at the bottom of the pipe where mixing interferes.
6.10.2 Noise filtering
Care has been taken to filter noise from the mesh sensor signal while maintaining
integrity of the signal as it relates to real fluid temperature fluctuations. Wire-mesh sensors
are known to be somewhat susceptible to electrical perturbations, which leads to a
superposition of the signals both with noise and glitches. Measurements recorded at 10 kHz
enable a variety of filtering measures to be implemented while maintaining more than
adequate sampling rates. Grounding of the pipeline to the DAQ system and shielded cables
was performed to reduce the noise as much as reasonably possible at the Stuttgart T-junction
facility. In order to further reduce electronic noise visible in the sensor signal, a median filter
approach has been implemented.
The 1-D median filter replaces each value with the median of a windowed range
around that value. We have chosen a window size of 14 values (a ‘14-order‘ median filter) in
order to eliminate large amplitude high frequency electronic noise and glitches observed in
some chosen reference signals. More information, such as boundary effects when
implementing the filter can be found in textbooks [226]. Figure 6-26 shows a sample signal
with and without filtering. Only the very high frequency portions of the spectrum are affected
by the filtering.
Figure 6-26. A comparison between one seconds of raw signal recorded by the mesh sensor,
and the corresponding PSD, in the mixing layer downstream of the T-junction with and
without median filtering.
By integrating the PSD we find that θRMS post-filtering is reduced by 3.7%. The
power spectrum remains largely unchanged at lower frequencies with 99.3% of the scalar
variance retained for a frequency domain of up to 500 Hz. Given the Reynolds number of the
flow and eddy turnover times we do not expect fluctuations in the fluid temperature at
frequencies above 500 Hz to be meaningful. No noise filtering has been performed on
thermocouple signals.
141
6.10.3 Gain-magnitude frequency response
The frequency response of K-type thermocouples at the Stuttgart T-junction facility
has been investigated in the past by researchers at the IKE. The well-known low-pass
filtering effect present in the thermocouples is the product of their thermal inertia. The gain-
magnitude frequency response of the mesh sensor, based on the earlier discussion related to
the LKE T-junction WMSs in Appendix Section 2.3.3, is shown along with the thermocouple
response in Figure 6-27.
Figure 6-27. Gain-magnitude frequency response of thermocouples at the facility and of the
mesh sensor for a number of fluid velocities.
6.10.4 Calculation of instantaneous and maximum average thermal gradient
For higher resolution in the cross-section, mesh sensor data was passed through a 2D
cubic interpolation function in MATLAB onto a 64 x 64 Cartesian grid such that the new data
is C2 continuous. Two columns, corresponding to a width of 2.24 mm, were then averaged
row-wise such that a top to bottom temperature profile in the center of the conduit was
generated from the calibrated, median filtered mesh sensor data. Within the lower half of this
profile a maximum of the temperature derivative , was found and is reported as the
maximum thermal gradient. The mesh sensor data used in computing average values over a
wide range of Richardson numbers were calculated from 10 kHz signals, 5 seconds in
duration extracted from each full 180 s measurement.
The calculation of thermal gradient along an arc near the wall , has been
calculated based on mesh sensor data interpolated (again with a cubic spline interpolation)
onto a polar space with 128 angular positions at a radius half of the sensor electrode pitch less
than the pipe radius, i.e. 33.66 mm. Once again, average values are based on 5-second long
signals, one from each measurement file.
6.10.5 Calculation of cold holdup area
142
Cold (branch) flow holdup was calculated as follows. Crossing points measuring
below a threshold temperature,
(6-9)
where Tm is the most recent main flow temperature recorded by reference thermocouple
(XTM3) and is the minimum average temperature calculated from the five second
mesh sensor signal were labeled as cold flow and given a value of 1 in the 16-by-16 2D
holdup matrix. Values above the threshold were set to 0. The 2D holdup matrix is multiplied
element-wise by a weight matrix, W, which takes into account the reduced measurement area
of crossing points near the wall of the conduit.
(∑ ∑
) (6-10)
where A is the pitch of the sensor squared, 20.14 mm2. An example of a 2D holdup matrix is
shown for an arbitrary time step in Figure 6-28. Note that the plot is not oriented with gravity
pointing downwards.
Figure 6-28. Instantaneous weighted cold holdup at Ri = 0.98 3.5Dm downstream of the
T-junction.
143
7 Outlook
The experiments related to turbulent penetration herein represent a stepping stone
from which future studies can build. They provide a large amount of data to investigate and
interpret in the context of future, related endeavors. More experiments are necessary to better
understand the effects of additional parameters, such as fluid viscosity, on the mixing
behavior in the branch line. Simulations are an ideal tool to more comprehensively
understand the phenomena at work. This mixing scenario remains on the periphery of (and
beyond) that which time-resolved CFD simulations can today feasibly capture. The CFD
simulation of such mixing scenarios where long simulations times are necessitated remains a
challenge which will only become easier with enhanced computational means. Especially
valuable is to strive for improve simulation techniques and grid-generation practices for this
complex case of turbulent-laminar flow interaction based on the simulation and findings
presented herein.
The value of the mesh sensor as a tool for investigating high-temperature high-
pressure flows should not be understated. The sensor is not limited in applicability to cases
relevant to thermal fatigue in T-junctions but could be implemented in a wide range of safety-
relevant flows, including two-phase flows and those outside of the field of nuclear
engineering. An enhanced design including multiple mesh sensors, thermocouples or other
complementary instrumentation would result in a powerful measurement suite within one
device capable of exploring a wide-breadth of NPP safety-relevant flows. The proof-of-
concept measurements and sensor design herein represent a significant milestone towards a
more straightforward, affordable and accessible means of capturing cross-sectional data at
high resolution at reactor operating conditions. The observed mixing phenomena in the
presence of strong density stratification should bring about a reconsideration of cross-flow
mixing classifications and awareness of new zones, specifically upstream of the T-junction,
where thermal fatigue may pay a role.
144
8 Curriculum vitae
John Kickhofel
Date of Birth: October 20, 1986
Place of Birth: San Mateo, CA, U.S.A.
Nationality: American
Email: [email protected]
Education
02/2011 – 09/2015
08/2013 - 12/2013
08/2008 - 05/2010
07/2004 - 04/2008
Work Experience
06/2009 - 12/2009
05/2008 - 09/2008
Doctor of Science candidate
Laboratory of Nuclear Energy Systems, Institute of Energy Technology
Department of Mechanical and Process Engineering
ETH Zurich, Switzerland
Supervised by Prof. Dr. Horst-Michael Prasser
Diplôme d‘université in International Nuclear Law
Université Montpellier 1, France
Master of Science in Nuclear Engineering
Joint degree ETH Zurich - EPF Lausanne, Switzerland
Bachelor of Science in Physics
Georgia Institute of Technology, U.S.A.
Research, Engineering, Manufacturing and Sustaining (REMS) Intern
Schlumberger Oilfield Services, Sugar Land, TX, U.S.A.
Supervised by Dr. Dean Homan
145
9 Publications
9.1 Patents
1. Kickhofel, J. and Prasser, H.-M. (2014), ‖Grid Sensor Package,‖ European Patent
Application EP14198142, ETH-Invention-No. 2014-053, Priority date December 16,
2014.
9.2 Peer-Reviewed Journal articles
1. Kickhofel, J. and Prasser, H.-M., ―Large Eddy Simulation of Turbulent Penetration in
a Horizontal Adiabatic T-junction with Leakage Flow,‖ Nuclear Engineering and
Design, in review, 2015.
2. Kickhofel, J. and Prasser, H.-M, ‖Turbulent Penetration in T-junction Branch Lines
with Leakage Flow,‖ Nuclear Engineering and Design 276, 43–53, 2014; doi.org/t4g.
3. Zboray, R., Kickhofel J., Damsohn, M., and Prasser, H.-M., "Cold-neutron
tomography of annular flow and functional spacer performance in a model of a
boiling water reactor fuel rod bundle," Nuclear Engineering and Design 241, 3201 –
3215, 2011; doi:10.1016/j.nucengdes.2011.06.029
4. Kickhofel, J., Zboray, R., Damsohn, M., Kaestner, A., Lehmann, E.-H., Prasser, H.-
M., ―Cold Neutron Tomography of Annular Coolant Flow in a Double Subchannel
Model of a Boiling Water Reactor,‖ Nuclear Instruments and Methods in Physics
Research Section A 651, 297-304, 2011; doi:10.1016/j.nima.2011.01.062
5. Kickhofel, J., Mohamide, A., Jalfin, J., Gibson, J., Thomas, P., Minerbo, G., Wang,
H., and Homan, D., ―Inductive Conductivity Tensor Measurements for Flowline or
Material Samples,‖ Review of Scientific Instruments 81, 075102, 2010;
doi:10.1063/1.3449320
9.3 Peer-Reviewed Conference papers
1. Kickhofel, J., Selvam, K., Huber, H., Laurien, E., and Prasser, H.-M., ―Mesh Sensor
for High Temperature and High Pressure Applications,― 16th International Topical
Meeting on Nuclear Reactor Thermalhydraulics (NURETH-16), Chicago, USA,
August 30 - September 4, 2015.
2. Kickhofel, J., Trinca, C., and Prasser, H.-M., ‖The Influence of Density Stratification
and T-junction Geometry on Turbulent Penetration,‖ International Topical Meeting on
146
Nuclear Thermal Hydraulics, Operation and Safety (NUTHOS-10), Okinawa, Japan,
December 14-18, 2014.
3. Kickhofel, J. and Prasser, H.-M., ‖Large Eddy Simulation of Turbulent Penetration in
a T-junction,‖ International Congress on Advances in Nuclear Power Plants (ICAPP
2014), Charlotte, U.S.A., April 6-9, 2014.
4. Kickhofel, J., Valori, V., and Prasser, H.-M., ―Turbulent Penetration as a Thermal
Fatigue Problem in low Side Flow T-Junctions,‖ Nuclear Thermal Hydraulics and
Safety 8 (NTHAS8), Beppu, Japan, December 9-12, 2012.
5. Kickhofel, J., Fokken, J., Kappula, R., and Prasser, H.-M., ‖Steady State RANS
Simulations of Temperature Fluctuation in a Single Phase Turbulent Mixing,‖
International Congress on Advances in Nuclear Power Plants (ICAPP 2012), Chicago,
U.S.A., June 24-28, 2012.
147
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