thermal management of solid oxide cell systems with

Thermal Management of Solid Oxide Cell

Systems with Integrated Planar Heat Pipes

Wärmemanagement von Hochtemperaturfestoxidzellen

(SOFCs / SOECs) mit integrierten planaren Heatpipes

Der Technischen Fakultät der Universität Erlangen-Nürnberg

zur Erlangung des Grades

DOKTOR-INGENIEUR

vorgelegt von

Marius Dillig

aus Bamberg

Als Dissertation genehmigt von der Technischen Fakultät der

Friedrich-Alexander-Universität Erlangen-Nürnberg

Tag der mündlichen Prüfung: 18.11.2016

Vorsitzender des Promotionsorgans: Prof. Dr.-Ing. Reinhard Lerch

Gutachter: Prof. Dr.-Ing. Jürgen Karl

Prof. Dr. Peter Wasserscheid

I

Vorwort/Acknowledgement

Die vorliegende Arbeit entstand im Rahmen meiner Tätigkeit als wissenschaftlicher

Mitarbeiter am Lehrstuhl für Energieverfahrenstechnik der Friedrich-Alexander-Universität

Erlangen-Nürnberg.

An erster Stelle möchte ich mich bei Herrn Prof. Dr.-Ing. Jürgen Karl herzlichst für seine

Betreuung, die Diskussionen und sein großes Vertrauen bedanken. Seine stets positive

Herangehensweise an kleine und größere Hindernisse und das offene, wie

abwechslungsreiche Arbeitsumfeld haben wesentlich zum Entstehen dieser Arbeit

beigetragen. Mein besonderer Dank gilt ebenso Herrn Prof. Dr. Peter Wasserscheid für sein

Interesse an meiner Arbeit und die Übernahme des Zweitgutachtens.

Meinen Kollegen am Lehrstuhl, die mich während meiner Promotionszeit begleitet haben,

bin ich natürlich dankbar für den ständigen Erfahrungsaustausch, die unzählbare (und

unbezahlbare) Unterstützung und den privaten Spaß, der das Arbeitsklima am EVT zu einem

ganz besonders angenehmen machten. Besonderer Dank geht an die langjährigen Begleiter

Jonas Leimert, Katharina Großmann, Daniel Höftberger, Rainer Reschmeier, Thomas

Plankenbühler, Dominik Müller, Michael Neubert, Peter Treiber, Yin Pang, Bernhard

Gatternig und Christoph Baumhakl. Ebenso möchte ich mich bei allen Studenten bedanken,

die mich mit ihren Abschlussarbeiten sehr unterstützt haben.

An meine Kollegen in Werkstatt, Labor und Sekretariat geht ein wichtiger Dank,

insbesondere an Birgit von Jezierski, Rudolf Klüger, Veniamin Stefan, Matthias Görz, Günther

Preininger und Hildegard Stork, deren Hilfe und Engagement ich jederzeit sehr zu schätzen

wusste.

Meinen Eltern und meiner Familie möchte ich hier ebenfalls besonders danken für deren

immerwährende Unterstützung, Rat und Motivation - nicht nur in den vergangenen Jahren.

Les plus grands remerciements j’aimerais exprimer à l’amour de ma vie, Anahí. Sans ton

amour, ton inspiration, ton encouragement constant et ta façon de faire disparaître mes

pensées négatives, rien n’aurait été possible.

Nürnberg, im Juni 2016 Marius Dillig

III

Abstract

This thesis contributes to the development of an advanced thermal control of solid oxide cell

(SOC) stacks and systems. Core of the approach is the integration of planar liquid metal heat

pipes into the interconnector structure targeting a reduction of stack internal temperature

gradients and an improved heat extraction / supply from the stack. This promotes load

flexibility of the thermal stress intolerant ceramic cells as well as thermal system integration

for both fuel cell and electrolysis operation of SOCs. Higher degrees of endothermal internal

steam reforming in natural gas fired fuel cells become possible.

In a first step, a comprehensive design study evaluates the capillary and vapor space

structures for these heat pipe interconnectors. Experimental evaluation in a planar heat pipe

test rig proved that planar thin heat pipes for the temperature range between 650°C – 870°C

with overall thicknesses down to 4 mm based on elementary sodium are possible. In

horizontal operation, the prototypes designed for 100 x 100 mm² SOCs demonstrated heat

transfer rates up to 1000 W, corresponding to equivalent thermal conductivities up to 17 kW

m-1 K-1. The lab-scale study evaluates long-term behavior of the heat pipe up to 2000 h and

assesses countermeasures to the main degradation mechanism, i.e. the hydrogen

deactivation.

A test rig for planar solid oxide cells capable of fuel cell as well as electrolysis operation

provides an experimental environment for a short stack design adapted to heat pipe

integration. Based on 100 x 100 mm² ESC cells (NiO/GDC | 10Sc1CeSZ | LSCF) an evaluation

of the developed planar heat pipe interconnectors is carried out, with detailed analysis of

stack internal temperature distribution. The results clearly prove the thermal incorporation

and the temperature gradient flattening effect of planar heat pipes, especially for fuel cell

operation and internal reforming conditions. In SOFC operation under full internal reforming

conditions the heat pipe reduces stack internal temperature from 43 K to 15 K. Combined

with additional heat transfer studies trough the stack set-up, these experimental findings are

used to calibrate a numerical stack model.

In a final step, this allows a thermal layout of full-size SOC stacks with integrated planar heat

pipes. Analysis results show how the integration frequency of heat pipe layers improves

temperature gradients and that strong reductions of stack air ratio down to

electrochemically necessary air ratios (e.g. 1.5) are possible. In particular for small-scale,

decentralised CHP-systems this leads to an impressive increase in system efficiency, by

improving mainly thermal efficiency but also internal power consumption of the ancillary air

blower.

V

Kurzfassung

Diese Arbeit trägt zur Entwicklung eines verbesserten Wärmemanagements von Stacks und

Systemen aus Festoxidbrennstoffzellen (Solid Oxide Fuel Cells) bei. Kern des Ansatzes ist die

Integration von planaren Alkalimetall-Heatpipes in die Interkonnektorstruktur der Stacks,

mit dem Ziel, interne Temperaturgradienten zu reduzieren und optimierte Wärmeabfuhr / -

zufuhr zu ermöglichen. Dies erlaubt eine Verbesserung der Lastflexibilität der

spannungsempfindlichen keramischen Zellen und der thermischen Integration sowohl des

Brennstoffzellen, als auch des Elektrolysebetriebs. Ein höherer Grad an stackinterner

Reformierung von erdgasgefeuerten Stacks wird so ebenfalls ermöglicht.

In einem ersten Schritt wurden Kapillarstrukturen und Dampfraumgeometrie für den Einsatz

in Heatpipe-Interkonnektoren entwickelt und optimiert. Experimentelle Untersuchungen in

einem Leistungsprüfstand, der für planare Heatpipes entwickelt wurde, zeigten, dass dünne

planare Heatpipes mit Dicken bis zu 4 mm auf Basis von elementarem Natrium für den

Temperaturbereich 650 – 870°C möglich sind. Im horizontalen Betrieb konnten diese

Prototypen, die etwa für 100 x 100 mm² große SOCs ausgelegt wurden, Wärmeüber-

tragungsleistungen bis zu 1000 W demonstrieren, was effektiven thermischen Leitfähig-

keiten von bis zu 17 kW m-1 K-1 unter nahezu isothermen Bedingungen entspricht. Die Labor-

untersuchungen erprobten das Start-up sowie Langzeitverhalten der Heatpipes bis zu 2000 h

und Gegenmaßnahmen zum Hauptdegradationsmechanismus, der Wasserstoffdeaktiverung.

Ein Stackprüfstand für Festoxidzellen, der sowohl für Brennstoffzellen- als auch für

Elektrolysebetrieb geeignet ist, stellt eine experimentelle Umgebung dar, um Shortstacks,

angepasst auf die Heatpipeintegration, dort zu vermessen. Auf der Basis von 100 x 100 mm²

elektrolytgestützten Zellen (NiO/GDC | 10Sc1CeSZ | LSCF) und dem ferritischen Stahl

CROFER 22 H als Interkonnektormaterial wird eine Bewertung der entwickelten Heatpipe-

Interkonnektoren durchgeführt. Die Resultate zeigen, dass die thermische Integration der

Heatpipes zu einer deutlichen Reduktion der Temperaturgradienten führt, insbesondere im

Brennstoffzellbetrieb und bei direkter interner Dampfreformierung von Methan. Im SOFC-

Betrieb mit vollständiger interner Methanreformierung führt die planaren Heatpipe

beispielsweise zu einer Reduktion der max. internen Temperaturdifferenzen von 43 auf 15 K.

In Kombination mit einer zusätzlich durchgeführten Analyse der thermischen Widerstände

innerhalb der SOC-Stacks wurden diese Ergebnisse dazu verwendet, ein numerisches

Stackmodell mit planaren Heatpipes zu erstellen.

Dieses Modell ermöglicht schlussendlich die Auslegung vollständiger SOC-Stacks mit

integrierten planaren Heatpipes. Es zeigt, wie die Frequenz der Heatpipeebenen und die

Stackausgestaltung (Zellgröße, Interkonnektormaterial) die Temperaturprofile beeinflussen

und dass eine deutliche Reduktion des benötigten Luftüberschusses des Stacks bis auf die

elektrochemisch notwendig Menge (z.B. λ = 1.5) möglich ist. Insbesondere für dezentrale

KWK-System bringt diese Reduktion des Luftüberschusses deutliche Effizienzgewinne,

VI

hauptsächlich durch eine Verbesserung des thermischen Systemwirkungsgrades, aber auch

durch Reduktion des Eigenverbrauchs des Luft-/abgasgebläses.

VII

Content

Vorwort/Acknowledgement .............................................................................................. I

Abstract ........................................................................................................................... III

Kurzfassung ...................................................................................................................... V

Nomenclature .................................................................................................................. XI

1. Introduction ............................................................................................................... 1

1.1 Motivation ................................................................................................................... 1

1.2 Objectives of this work ................................................................................................ 3

1.3 Approaches .................................................................................................................. 4

2. Fundamentals of Fuel Cell Thermodynamics ............................................................... 7

2.1 The ideal electrochemical cell ..................................................................................... 7

2.2 SOFCs and SOEC stacks – set-ups and materials ......................................................... 9

2.2.1 Solid oxide cells .................................................................................................... 9

2.2.2 Stack set-up ........................................................................................................ 12

2.2.3 Interconnector materials ................................................................................... 13

2.2.4 Sealing materials ................................................................................................ 14

2.3 Irreversible effects of real cells and stacks ................................................................ 14

2.3.1 Operation voltage losses .................................................................................... 14

2.3.2 Fuel and air utilisation ........................................................................................ 15

2.4 Reversibility of fuel cell operation – electrolysis ....................................................... 17

2.4.1 Steam electrolysis .............................................................................................. 17

2.4.2 Co-electrolysis of CO2/H20 mixtures .................................................................. 19

2.5 Internal reforming of fuels ........................................................................................ 19

3. State-of-the-art of thermal control of SOCs .............................................................. 23

3.1 Cell degradation due to internal temperature gradients .......................................... 23

3.1.1 Chemical cell degradation .................................................................................. 23

3.1.2 Mechanical stack degradation due to temperature gradients .......................... 24

3.2 Thermal control of SOFC stacks ................................................................................. 27

3.2.1 Control by gas flows ........................................................................................... 27

Content

VIII

3.2.2 Advanced cooling concepts ................................................................................ 30

3.2.3 SOFC thermal system integration ...................................................................... 31

3.3 Heat pipe cooling applied in other types of fuel cells ............................................... 33

3.4 Fundamentals on planar heat pipe operation ........................................................... 35

3.4.1 State-of-the-art on planar heat pipes for low temperature applications .......... 37

3.4.2 Liquid metal micro heat pipes ............................................................................ 39

4. Numerical modeling of thermal stack behavior......................................................... 41

4.1 Modeling approaches ................................................................................................ 41

4.1.1 Geometry and materials .................................................................................... 41

4.1.2 Assumptions and simplifications ........................................................................ 41

4.1.3 Calculation domains ........................................................................................... 43

4.1.4 Discretization and mesh generation .................................................................. 44

4.2 Numerical model of the solid oxide cell stack ........................................................... 45

4.2.1 Governing equations .......................................................................................... 45

4.2.2 Electrochemical .................................................................................................. 46

4.2.3 Species transfer .................................................................................................. 51

4.2.4 Methane steam reforming ................................................................................. 52

4.2.5 Heat production ................................................................................................. 53

4.2.6 Heat transfer ...................................................................................................... 54

4.2.7 Thermal contact resistance ................................................................................ 57

4.3 Conclusions ................................................................................................................ 58

5. Development of planar heat pipe interconnectors .................................................... 59

5.1 Design and layout of planar liquid metal heat pipes ................................................. 59

5.1.1 Selection of working fluid ................................................................................... 59

5.1.2 Capillary structure design ................................................................................... 61

5.2 Manufacturing and filling procedure of planar heat pipes ....................................... 66

5.2.1 Heat pipe fabrication and cleaning .................................................................... 66

5.2.2 Filling procedure ................................................................................................. 67

5.3 Performance testing of planar heat pipes ................................................................. 70

5.3.1 Experimental set-up ........................................................................................... 70

5.3.2 Experimental procedure ..................................................................................... 72

Content

IX

5.3.3 Performance measurement results ................................................................... 77

5.3.4 Dynamic testing of planar heat pipes – Start-up behavior ................................ 82

5.3.5 Long-term operation of planar heat pipes ......................................................... 84

5.4 Analysis of hydrogen resistance ................................................................................ 89

5.4.1 Hydrogen permeation and deactivation of planar heat pipes ........................... 89

5.4.2 Approaches avoiding hydrogen deactivation .................................................... 91

5.4.3 Experimental study............................................................................................. 93

5.4.4 Hydrogen permeability of CROFER22H .............................................................. 99

5.4.5 Alkali hydride formation ................................................................................... 100

5.5 Conclusions .............................................................................................................. 103

6. Experimental evaluation of solid oxide cell short stacks with planar heat pipes ....... 105

6.1 SOFC-Test Rig ........................................................................................................... 105

6.2 Experimental set-up for heat pipe stack integration .............................................. 108

6.2.1 Basic stack design ............................................................................................. 108

6.2.2 Sealing concept ................................................................................................ 110

6.2.3 Heat pipe integration ....................................................................................... 111

6.2.4 Temperature measurement instrumentation.................................................. 112

6.3 Experimental results ................................................................................................ 114

6.3.1 Short stack preparation and evaluation ........................................................... 114

6.3.2 Temperature profile analysis ........................................................................... 119

6.4 Stack internal thermal contact resistances ............................................................. 124

6.4.1 Experimental method ....................................................................................... 124

6.4.2 Evaluation procedure ....................................................................................... 127

6.4.3 Measurement uncertainties ............................................................................. 129

6.4.4 Results and Discussion ..................................................................................... 130

6.5 Comparison with numerical results and error estimations..................................... 134

6.6 Conclusions .............................................................................................................. 138

7. Design guidelines for stacks and systems ................................................................. 139

7.1 Layout of SOC stacks with planar heat pipes .......................................................... 139

7.1.1 SOFC hydrogen operation ................................................................................ 140

7.1.2 SOEC operation ................................................................................................ 146

7.1.3 Natural gas operated stacks ............................................................................. 147

Content

X

7.2 Advanced SOFC system concepts with integrated planar heat pipes ..................... 150

7.2.1 System evaluation of HP integrated CHP SOFC systems .................................. 150

7.2.2 Integration with advanced system concepts ................................................... 156

8. Summary and conclusion ........................................................................................ 159

References ..................................................................................................................... 163

List of figures ................................................................................................................. 175

List of tables .................................................................................................................. 183

Permissions ................................................................................................................... 185

XI

Nomenclature

Abbreviations

AISI American Iron and Steel Institute

AU Air utilization

ASC Anode supported cell

ASR Area specific resistance

CFD Computational fluid dynamics

CHP Combined heat and power

CLA Center line average

EDX Energy - dispersive X-ray analysis

EMF Electromotoric force

ESC Electrolyte supported cell

EVT Institute for Energy Process Engineering, University Erlangen-Nürnberg

FID Flame ionization detector

FU Fuel utilization

F5 Forming gas: 5% H2 in N2

GA Gas analyzer

GC Gas chromatograph

GDC Gadolinium doped ceria

HGR Hot gas recycle

HHV Higher heating value

HP Heat pipe

HPR Heatpipe-Reformer

HT-PEM High temperature proton exchange membrane fuel cell

ID Induced draft

IGCC Integrated gasification combined cycle

LHV Lower heating value

LSCF Lanthanum strontium cobalt ferrite

LSF Lanthanum strontium ferrite

LSM Lanthanum strontium manganite

MFC Mass flow controller

MIC Metallic interconnector

MRT Mean radiant temperature

MSC Metal supported cell

Nomenclature

XII

OCV Open circuit voltage

PID Proportional integral differential (controller)

RANS Reynolds averaged Navier-Stokes-(equations)

S/C Steam to carbon ratio

ScSZ Scandium stabilized zirconia

SEM Scanning electron microscope

SL Standard liter

SOC Solid oxide cell

SOEC Solid oxide electrolysis cell

SOFC Solid oxide fuel cell

SU Steam utilization

TCR Thermal contact resistance

TEC Thermal expansion coefficient

TPB Triple phase boundary

TSO Transmission system operator

UDF User defined function

WGS Water-gas-shift (reaction)

YSZ Yttrium stabilized zirconia

Latin symbols

𝐴𝑖 Area of i [m²]

C Molar concentration [mol L-1]

𝐷 Diffusivity [m² s-1]

d Diameter of wire in screen mesh [m]

Ea Activation Energy [J mol-1]

𝐹 Farady constant [96485.3365 A s mol-1]

g Gravity of earth [9.81 m s-2]

Δ𝑅𝐺 Gibbs enthalpy of reaction [kJ mol-1]

ℎ Height [m]

Δ𝑅𝐻 Enthalpy of reaction [kJ mol-1]

𝛥ℎ𝑣𝑎𝑝 Enthalpy of vaporisation [kJ mol-1]

ℎ𝑖 Specific heat transfer coefficient of situation I [W m-2 K-1]

ℎ𝑗 Specific enthalpy of species j [kJ mol-1]

𝑖 Current density [A m-2]

Nomenclature

XIII

𝑗 Gas flux [mol s-1 m-2]

𝐾𝑊𝐺𝑆 Equilibrium constant of water gas shift reaction [-]

𝑘 Pre-exponential factor

𝑘𝑖 Thermal conductivity of material i [W m-1 K-1]

𝑘𝑆𝑅 Kinetic constant of reaction SR

l length [m]

LHV Lower heating value [kJ kg-1] or [kJ mol-1]

𝑀 Mesh number of screen wire mesh [-]

𝑀𝑖 Molar mass of i [kg mol-1]

Me Merit number [W m-2]

mNa Sodium mass [g]

𝑖 Mass flow [kg s-1]

𝑛 Exponential coefficient [-]

𝑛𝑒𝑙 Number of electrons [-]

𝑛𝑖 Mole content [-]

𝑖 Molar flow rate [mol s-1]

p Pressure [Pa]

pi Partial pressure [Pa]

𝑃𝑒𝑙 Electric power [W]

P Permeability [mol m-1 s-1 Pa-0.5]

𝑄 Thermal energy, heat [J]

Transferred thermal power [W]

Area specific thermal power flux [W/m²]

𝑅 Ideal gas constant [8.3144 J K-1 mol-1]

𝑅𝑗 Reaction mass source [kg s-1]

𝑅𝑜ℎ𝑚 Ohmic resistance [V A-1]

𝑅𝑡ℎ Heat transfer resistance [K W-1]

𝑟 Reaction rate [mol s-1]

𝑟 Radius [m]

s Length of conduction pathway [m]

Specific area [m-1]

S Crimping factor of screen mesh [-]

𝑆𝑚 Mass source [kg s-1]

𝑆ℎ Heat source [J s-1]

T Temperature [K]

Nomenclature

XIV

t Time [s]

t Thickness [m]

u Velocity [m s-1]

ui Uncertainty of parameter i

V Voltage [V]

𝑉𝛥𝐻 Heating value equivalent voltage [V]

𝑉𝑁 Nernst-Voltage [V]

𝑉𝑜𝑐𝑣 Open circuit voltage [V]

𝑉𝑖 Volume of i [m³]

xH2O,min Minimal required mass of water [kgH2O/kgFuel]

X Conversion [-]

𝑧𝑒𝑙 Number of electrons transferred per reaction [-]

Greek symbols

𝛼 Power law exponent [-]

𝛽 Charge transfer coefficient [-]

𝛾 Surface tension [N m-1]

𝛾𝑖 Stoichiometric coefficient of reactant i [-]

𝛿 Thickness [m]

휀 Volumetric porosity [-]

𝜖𝑖 emissivity of surface i [-]

𝜙 Tilt angle of heat pipe [°]

𝜅 Heat capacity ratio [-]

𝜆 Air/fuel ratio [-]

𝜂 Dynamic viscosity [kg s-1 m-1]

𝜂𝑖 Overpotential i [V]

𝜌 Density [kg m-3]

Σ Excess steam ratio [-]

𝜎 Stefan-Boltzmann constant [5.670373 × 10−8 W m−2 K−4]

𝜎𝑖 Electric conductivity of material I [A V-1]

Θ𝑐 Contact angle [°]

𝜏 Viscous stress [N m-2]

1

Chapter 1

1. Introduction

1.1 Motivation

Electric power generation systems will undergo fundamental changes in the coming

decades. Striking indicators of this necessity are the negative price trends in Germany’s

electricity markets in conjunction with the strong increase of grid intervention costs.

Average day ahead spot market fell from approx. 70 €/MWh in the last quarter of 2008 to

only 28 €/MWh in 4th quarter of 2015 [EPEX SPOT2015] while redispatch activities by

German transmission system operators (TSOs) tripled to 139 Mio. € in 2014. Renewable

feed-in management actions even increased by more than tenfold to 1.5 TWh (or 1.4 % of

EEG production) in 2014 [BNetzA2015]. These numbers demonstrate impressively how

conventional electricity supply has to adapt to current needs. Centralized, steady Rankine-

based thermal power plants will have to be replaced by flexible, decentralized systems that

operate as back-up partner to highly volatile solar and wind driven power generation.

Solid oxide cells are compelling products for these upcoming business fields. Due to their

modularity, fuel flexibility and reversibility they address markets both for distributed power

and heat generation as well as surplus electricity storage. Operated as fuel cells (SOFC) they

offer excellent part load behaviour, highest electric efficiencies up to 60% even for very

decentralised power generation and suitability for carbon monoxide, methane and yet

higher hydrocarbons.

As reversed process water electrolysis is one of the common entry steps to most of chemical

energy storage systems, hydrogen solid oxide electrolysers (SOEC) target the production of a

large variety of synthetic fuels. Compared to low temperature electrolysis systems this high

temperature technology benefits from very favorable thermodynamic conditions increased

temperature levels (Gibbs enthalpy of electrolysis decreases from 286 kJ/mol at ambient

temperature to 183 kJ/mol at 900°C). Thus, SOEC system may increase electrolysis efficiency

significantly below 4.5 kWh/(Nm³ H2) , i.e. above 67 % LHV-based efficiency, what state-of-

the-art alkaline and PEM – electrolyzers reach today [Smolinka2011] and come close to

hydrogen’s lower heating value (LHV) of 3.0 kWh/(Nm³ H2).

However, high competitiveness in the described markets requires simple, integrated and

load flexible systems. Therefore, large scientific and technical advances have been made

within the last years in particular regarding solid oxide cell materials and structure of the

Chapter 1: Introduction

2

electrolyte and both electrodes. Despite this, for SOC systems the above named key features

are inevitably interwoven with the question of thermal management and thermal

integration of the stacks. In fuel cell operation the thermodynamic enthalpy balance and

electrochemical loss produce a significant amount of waste heat, typically in the range of 20

– 50% of fuel’s LHV. The high power density of the planar stack structure and the limit to

stack internal temperature gradients outreach heat transfer by conduction within the stacks.

In steady operation, the thermal control is mostly realized by means of excess air cooling,

reducing thermal efficiencies considerably. A coupling of solid oxide cell system (SOFC and

SOEC) to volatile electricity sources additionally implies strong load gradients, thus strong

changes in internal heat consumption / production rates and consequently changing

temperature profiles within the stacks. Resulting mechanical stress within the sensible

ceramic cell can induce micro cracking and lead to a strong reduction of cell lifetime. Thus,

the theoretically fast electric load adaptation of SOCs is intensely restricted by inertial

thermal adaption of cell and stack and the need to prevent fracture of cell components.

Consequently, advanced stack temperature control strategies of high temperature solid

oxide systems are required. This thesis therefore evaluates the approach to integrate liquid

metal heat pipe technology into the planar stack structure, an idea that was developed

within the EU-project BioCellus [Karl2009] and is equally under consideration for low

temperature fuel cell technology. Figure 1.1 shows the basic idea and concept of planar heat

pipes integrated to the interconnector structure of a SOFC stack. Due to an evaporation –

condensation cycle of the liquid metal working fluid inside the heat pipe, the interconnector

becomes an almost isothermal body. The high heat transfer rates of the heat pipe allow heat

distribution within the stack and an extraction of high temperature (HT) heat from the stack.

Stack internal temperature gradients, with all their negative consequence for solid oxide cell

operation and long-term stack stability, are lowered and the need for cooling air shrinks. The

technology promises the opportunity of very high thermal system integration with

secondary processes such as fuel pre-reforming, solid fuel gasification and heat storages.

Objectives of this work

3

1.2 Objectives of this work

The main objective of this thesis is to gain an understanding of the mechanisms and

processes for the development of an advanced thermal control of solid oxide cell stacks with

planar liquid metal heat pipes. Since this evaluation is influenced by a large variety of

boundary conditions and system aspects the overall objective is subdivided into two main

tasks:

Development and evaluation of planar liquid metal heat pipes

The objective is to provide an analysis of possible layouts for heat pipes integrated into the

structure of planar solid oxide cell stacks. Target of the development shall be a small

additional volume occupation, a direct thermal integration and an adequate performance. A

major part of this work is dedicated to the capacity of heat pipes are able to provide

required heat transfer rates depending on structural design and stack orientation, analyze

long-term degradation, and provide an understanding of the effects caused by stack internal

gas environments.

Thermal analysis and layout of solid oxide cell stacks with integrated heat pipes

A second important task of this thesis is analyzing the thermal effects of planar heat pipes

within the SOC stack structure. An experimental evaluation of SOC short stacks shall

demonstrate the effects on temperature gradients and the possibility to extract or supply

heat from/to the stack. The analysis is used to develop and calibrate a numerical stack model

with integrated planar heat pipes. This model finally shall serve as a basis for the layout of

full scale stacks and advanced SOC systems.

Figure 1.1: Concept of SOC stacks with integrated planar heat pipe interconnector layers, designated to themperature gradient flattening and heat extraction from the stack.

SOFC

SOFC

SOFC

metal interconnector

Cell temperature

Fuel supply

heat

High air supply

Standard SOFC stack operation: high cooling air

SOFC

SOFC

SOFC

metal interconnector

wickcondensation

evaporation

planarheat pipemetal interconnector

Cell temperature

Fuel supply

HT heat

Low air supply

SOFC stack operation with planar Heat pipes:low cooling air

Heatpipe temperature

Chapter 1: Introduction

4

These tasks require a broad experimental test program to gain knowledge on the proposed

system. As major milestones, planar heat pipes prototypes including manufacturing and

testing set-up need to be built, an SOFC / SOEC test-rig and an adapted planar stack design

are required.

1.3 Approaches

This thesis tackles the defined objectives based on multiple steps for thermodynamic system

evaluations. Figure 1.2 shows an overview of its basic structure. After a short introduction to

fuel cell thermodynamics (chapter 2) the problems caused by heat generation in solid oxide

fuel cell stacks are illustrated and existing approaches to thermal control available in

literature are evaluated (chapter 3). An overview of state-of the art development of planar

heat pipe technology defines the starting point for developments of planar heat pipe

(chapter 5). Here in particular heat pipe capillary layout, manufacturing and an experimental

performance evaluation are at focus. Heat transfer power depending on capillary structure,

start-up and long-term effects is compared to theory and allows an improved understanding

of heat pipe limitations. A discussion of SOC stack related gas environments, i.e. the effects

of hydrogen atmosphere, concludes this part.

The evaluation of thermal stack behavior due to planar heat pipes is subdivided into two

steps. A 3-D numerical model of the stack is set up, which is able to account for all relevant

heat generation effects within an SOC stack (chapter 4). Electrochemistry, as well as gas

phase reactions, such as methane reforming, are included into the modelling set-up. In order

to account for the complex heat transfer mechanisms within the stack, the model defines

the necessity of an experimental study of thermal contact resistance. This preliminary stack

evaluation is carried out in a first step in chapter 6 assuring a precise representation of stack

internal temperature gradients and the influence of planar heat pipes thereon. In a second

step, an experimental evaluation of complete SOC short stacks is carried out. Cross-flow

stacks with up to 3 cells and integrated planar heat pipes are designed and set-up in an high

temperature fuel cell / electrolysis test rig. Evaluations of stack internal temperature profiles

demonstrate the effects of planar heat pipes in stack structures in various operation

conditions. The experimental studies are used for calibration and verification of the

numerical stack model.

In a final step, the three main part of this work, i.e. heat pipe evaluations, numerical and

experimental stack testing are joint together in order to provide guidelines for SOC stack and

system layout (chapter 7). This chapter seeks giving parametric help to stack designer that

consider using planar heat pipes in full-scale stacks. In particular, effects of cell sizing and

required heat pipe frequencies are discussed with respect to the temperature gradients. The

subsequent review of possible advanced SOC system concepts and efficiency improvements

due to thermally integrated solid oxide cell system with planar heat pipes concludes this

thesis.

Approaches

5

Figure 1.2: Scope of this work

Numericalworks

Experimental evaluations

Theory &Literature

Stack & System layout

Fuel CellThermodynamics

II

State of the art of thermal stack control

III

Numeric model of thermal stack behavior

with heat pipes

IV

Development andevaluation of planar

heat pipes

VExperimental

evaluation of short stacks

VI

Design guidelines forstacks & systems

VII

7

Chapter 2

2. Fundamentals of Fuel Cell Thermodynamics

Fuel cells are electrochemical systems allowing the direct conversion of chemical energy into

electricity. No detour via combustion and thermodynamic cycle engines is required that

leads to limitation by Carnot’s law. Despite offering highest conversion efficiencies for

chemical fuels, SOFCs were not able to compete with internal combustion engines and

turbines in the past. This economic shortfall is about to disappear since distributed

generation efficiency, thermal system integration and process reversibility for electricity

storage purposes have become main design objectives.

2.1 The ideal electrochemical cell

A solid oxide electrochemical cell consists of two electrodes, where locally separated an

oxidation and a reduction reaction takes place. Oxygen ions and electrons operate as charge

carriers.

𝑂2 + 4𝑒− ↔ 2𝑂2− 𝐴𝑖𝑟 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 (2.1)

2 ℱ + 2 𝑂2− ↔ 2 ℱ𝑂 + 4𝑒− 𝐹𝑢𝑒𝑙 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 (2.2)

2 ℱ + 𝑂2 ↔ 2 ℱ𝑂 𝑂𝑣𝑒𝑟𝑎𝑙𝑙 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 𝑤𝑖𝑡ℎ 𝛥𝐻𝑅 (2.3)

Here, ℱ stands for fuel molecule and may in principle be any oxidizable fuel, in particular

hydrogen, carbon monoxide or higher hydrocarbons (with slight adaptations of

stoichiometry). Thermodynamically, the fuel cell represents an open system with exchanges

of mass m of species i, heat Q and work Wt (in this case electrical work) with its

environment (Figure 2.1). The reactions are invertible and both electricity production as well

as electricity consuming electrolysis reaction is possible.

Chapter 2: Fundamentals of Fuel Cell Thermodynamics

8

Conservation of energy describing the energy balance of a basic electrochemical cell as well

as the second law of thermodynamics for a reversible process apply

It results that, as for other thermodynamic processes, only a part of the chemical energy can

be converted into technical work Wt. This part is the Gibbs enthalpy of reactions.

Consequently, even under reversible conditions heat 𝑄𝑟𝑒𝑣 is released or consumed

amounting to

The electrochemical cell produces work W𝑡 in form of electric current. For an infinitesimal

reaction rate 𝑑𝑛 and thus flow of electric charges 𝑑𝑞 the cell voltage 𝑉 is derived from

where 𝑧𝑒𝑙 gives the number of exchanged electrons (charge e) per reaction. Including the

conversion of charges and units expressed by Faraday F constant (= 𝑁𝐴 ∙ 𝑒), one obtains the

Nernst voltage 𝑉𝑁 or electromotoric force (EMF)

Figure 2.1: The energy balance of a fuel cell

𝑊𝑡 + 𝑄𝑟𝑒𝑣 = Δ𝑅𝐻 (2.4)

Δ𝑅𝑆 − 𝑄𝑟𝑒𝑣𝑇= 0 (2.5)

W𝑡 = Δ𝑅𝐻 − 𝑇 Δ𝑅𝑆 = Δ𝑅𝐺 (2.6)

𝑄𝑟𝑒𝑣 = Δ𝑅𝐻 − Δ𝑅𝐺 (2.7)

δW𝑡 = Δ𝑅𝐺 ∙ 𝑑𝑛 = 𝑉 ∙ 𝑑𝑞 = 𝑉 ∙ (𝑧𝑒𝑙 ∙ 𝑒 ∙ 𝑑𝑛) (2.8)

𝑉𝑁 = −Δ𝑅𝐺

𝑧𝑒𝑙 ∙ 𝐹 (2.9)

Electrochemicalcell

SOFCs and SOEC stacks – set-ups and materials

9

In equivalence, a theoretic voltage according to reaction enthalpy to gaseous products or

lower heating value (LHV) of the fuel can be defined [Karl2006]

representing the theoretic maximum of the Nernst voltage of an electrochemical cell under

any condition (𝑇 → 0).

In consequence, maximum thermodynamic efficiency 𝜂𝑡ℎ of the ideal fuel cell, or a real cell

close to open circuit configuration results as

2.2 SOFCs and SOEC stacks – set-ups and materials

2.2.1 Solid oxide cells

Solid oxide cells are high temperature electrochemical cells and represent in their basic

structure in a gas tight membrane separating fuel and oxygen gas spaces. This membrane

consists itself in several functional layers (Figure 2.2): A fuel electrode (anode in SOFC

operation), an electrolyte, a cathode structure and eventually some diffusion barriers

between these main elements. In fuel cell operation – as described in the following – the

fuel is oxidized at triple phase boundaries of anodes porous structure. Electrons are released

and conducted to the electrical interconnection sites. From there, they flow via an external

circuit to the cathode and are able to provide electrical work. A crucial factor for electricity

generation is thus the electric insulation properties of the electrolyte.

At the cathode, oxygen in air or an equivalent oxidant is reduced with the help of supplied

electrons. The resulting oxygen ions are conducted through the electrolyte to the fuel

electrode where they oxidize the fuel. This O2- - ion conductance of the ceramic electrolyte is

the reason why an SOFC may use all chemical fuels in theory, thus is able to directly convert

hydrogen as well as carbon monoxide, methane or even higher hydrocarbons and carbon.

Consequently, reaction products form at fuel electrode, at air electrode only oxygen

concentration changes.

Cell designs provide two main types of cells: Planer cells, as commonly used today and

studied in this work or tubular cells, a concept intensively persecuted by Siemens-

Westinghouse and others in the past.

𝑉𝐻 = −Δ𝑅𝐻

𝑧𝑒𝑙 ∙ 𝐹= −

𝐿𝐻𝑉

𝑧𝑒𝑙 ∙ 𝐹 (2.10)

𝜂𝑡ℎ = Δ𝑅𝐺

Δ𝑅𝐻=𝑉𝑁𝑉𝐻

(2.11)


10

Mechanical stability of the membrane-electrode-assembly is provided by one of the three

main layers. In electrolyte supported cells (ESC), the electrolyte has the required thickness

(e.g. 150 µm) to guarantee this stability, resulting in increased cell resistances.

Electrode supported cells by contrast, allow very thin electrolyte layers (e.g. 5 µm). Mainly

the anode supported cell (ASC) concept is used where a 0.5-0.7 mm thick porous anode

structure carries the active cell structure. The choice of the support layer in consequence,

has an important influence on operation temperatures of the SOFC. Electrolyte supported

cells require higher operating temperatures (>800°C) to reduce ohmic resistance of the

electrolyte, ASCs allow operation below 800°C.

For all support concepts a relatively close matching of thermal expansion (TECs) coefficients

between the functional layers is required in order to prevent cracking during cooling down

to ambient temperature after cell sintering.

Electrolyte

The electrolyte is the central part of the solid oxide fuel cells, as it is responsible for the

oxygen ion conduction. Nernst himself already identified zirconium oxide ZrO2 providing high

ion conductivity [Singhal2003]. Other requirements are good gas tightness, low electron

conductivity and low degradation rates in oxidizing and reducing environments.

Ion conductivity of the ZrO2 can be significantly improved when a M2O3 type oxide serves as

dopant (M being a triad cation). Due to the resulting defect in crystal structure the O2- ions

can move more easily through the electrolyte structure, comparable to electrons in doped

semi-conductors. Most common ZrO2 doping material is Y2O3 and the resulting composition

is commonly named YZS (for yttria stabilized zirconia) with a maximum conductivity for a

concentration of 8 mol%.

Figure 2.2: Structure and functional principle of a solid oxide cell (here SOFC operation)

triple phase boundary:fuel, Ni, electrolyte

CH4 + H2O

fuel

SyngasH2 + CO

O2-

H2O

CO2

e

air

electrolyte

cathode

anode

e

H

HH

HHH

H

HO

H

H

HH

HHH

H

OO

HO

H

HH

HH

HH

HO

H

HOH

O2

+

-

O2

O2-O2-

O2

O2

excess air

anodeoff gases

HH

diffusion barrier

electric loadcell

volt

age

V

current I

H2


11

Further materials in use are ScSZ (scandium stabilized zirconia) that applies scandium oxide

as dopant and provides high ion conductivity for lower temperatures. The SOCs investigated

in this work consist of ScSZ as electrolyte material. Doping CeO2 with Gadolinium oxide

(GDC: gadolinium doped ceria) creates an electrolyte material with equally low resistance

that is often used for the cermet (ceramic - metal) structure of the fuel electrode.

Fuel electrode

The fuel electrode has to combine electrical and ion conductivity with catalytic activity in

order to increase kinetics of oxidation reaction between fuel and oxygen ions. These three

requirements translate into the necessity of so-called triple phase boundaries where gas

phase, electrolyte and metal meet and the reaction can take place. Nickel applied in a

porous ceramic – metal structure (cermet) resulted to be the most successful candidate

combining catalytic activity, electric conductivity and long-term stability. Additional to the

ion conducting electrolyte a minimum content of approx. 30% nickel is necessary to

guarantee fully established metallic interconnections. Depending on the cell supporting

concept, diffusion effects of fuel and product gas in the porous cermet structure can be a

current limiting factor at high power densities.

The broad catalytic activity is both, an important advantage as well as a drawback of Ni-

electrodes. On the one hand, Ni accelerates methane steam reforming as well as shift

reaction and is thus the main reason that SOFC can directly operate on unreformed natural

gas. Equally however, Ni facilitates Boudouard reaction as well as methane cracking leading

to the danger of anode carbon deposition when using carbon containing fuels.

An important consequence of the use of Ni as catalyst is anodes’ high sensibility to sulphur

contamination. Gases supplied to the SOFC thus have to contain mainly H2S concentrations

below 1 ppm [Baumhakl2014]. Ni-oxidation and subsequent structural damage due to fuel

starvation is a further anode property that has important consequences on SOFC operation.

Oxygen electrode

Cathodes for SOFCs (anodes in SOEC operation) have to possess similar properties as fuel

electrodes: high catalytic activity for oxygen reduction, high electrical conductivity despite its

porosity and compatibility mainly to the electrolyte. Early cathodes applied platinum as

catalyst, but soon less expensive perovskites revealed their suitability [Nomura1978].

Lanthanum-manganite (LaMnO3)-based materials became consequently the most common

air electrode. For intermediate temperature SOFCs (below 800°C) a strontium doping is

applied to lanthanum manganite (LSM) in order to increase electrical conductivity. For the

use with ceria based electrolytes, as later in the experimental section of this work, a

lanthanum strontium cobalt ferrite oxide (LSCF) is commonly used. In order to reduce

compatibility issues between YSZ-electrolyte and LSM, typically a two layer cathode is

chosen. The layer close to electrolyte is a mixture between cathode and electrolyte material

with a TEC in between two pure structures and providing an ionic conductivity. To prevent

detrimental reactions between LSCF cathodes and YSZ electrolytes, ceria based diffusion

barriers are used [Chandra2006].


12

An unfortunately important property of perovskite cathodes is the poisoning effect of

chromium (Cr). Chromium leads to a blocking of active sites at the triple phase boundaries at

the electrolyte cathode interface [Sun2009]. As almost all metallic interconnectors contain

chromium to form chromium-oxide as protective layer, Cr evaporates from the surface at

high temperatures and causes severe degradation of the catalytic activity of the cathode. In

consequence, interconnector design has to prevent Cr-evaporation.

2.2.2 Stack set-up

Since power densities of solid oxide cells typically are in the range of max. 1 W cm-2 and

voltage levels are low, it is necessary to increase the number of cells to reach relevant

powers. Planar cells are stacked in series in order to provide technically usable voltage

levels. The interconnector or bipolar plate realizes the electric connection and gas

separation of anode and cathode of neighbouring cells. Contacting materials, such as Ni-

contact grids, as well as sealings are additionally applied between interconnectors and the

SOCs. The entire set-up with typically 50 – 150 repeating units results in one fuel cell stack.

Besides interconnection and gas flow separation, an important task of the stack is fuel and

(in many cases) air manifolding. The stack leads the input gases from one single supply line

to every repeating unit of the stack and collects off-gases for further treatment (post

combustion, anode gas recycling). Comparable to heat exchanger set-ups, there exist three

major concepts how fuel and air stream are manifolded within the stack: co-flow, counter-

flow, and cross-flow. All three concepts have particular effects on temperature fields within

the stack. The cross-flow set-up however is the simplest one regarding sealing concept, since

no additional cell framing is necessary.

Figure 2.3: SOC stack set-ups and gas manifolding concepts, sealings and frames are not displayed. Left: cross-flow. Right: counter-flow (co-flow similar)

Interconnector

SOC - stack

Fuel supply

Air supply

solid oxide cell

Interconnector

Fuel supplyAir supply


13

2.2.3 Interconnector materials

Requirements for interconnector materials are high electric conductance, gas tightness as

well as thermal and chemical stability in oxidizing as well as reducing environments. Its

thermal expansion coefficient has to be in accordance with other SOC stack materials to

avoid thermal stress on ceramic cells.

Ceramic interconnectors are possible, however this option comes with high material costs.

Therefore, current developments focused on metallic interconnectors that are suitable for

SOC application.

The major problems of metallic interconnector are the formation of low conductance oxide

layers and chromium evaporation that leads to cathode poisoning by formation of

chromium-manganite-spinells [Frank2009].

Material engineering provides two main classes that are suitable for SOFC use due to

adapted TECs (see Table 2.1): Chromium based alloys with high chromium content and

ferritic steels. Austenitic steels, that are typical high temperature materials, are not

considered since their TEC in the range 20 – 800°C is approx. 20 ∙10-6 K-1 and thus too far off

from other SOFC materials.

Plansee CFY [Plansee2015] is a representative of chromium based alloys with approx. 95 %

chromium, 5% iron and some yttrium. Its TEC is well adapted to those of typical electrolytes

and hence it is commonly used for electrolyte supported cell stacks.

CROFER 22H is a ferritic steel with 20 - 24 % of chromium and some minor components

showing a TEC closer to that of a Ni/YSZ-cermet. Therefore, it is mainly applied in ASC cell

stacks. Its composition is furthermore optimized to form dense spinel layers that provide low

ohmic resistance and prevent Cr-evaporation.

Table 2.1: Thermal expansion coefficients of typical cell and stack materials averaged in the stated temperature range

Material TEC 10-6/K Temperature range Source

3YSZ 10.9 25 - 1000°C [Fleischhauer2014]

8YSZ 10.5 30 - 800°C [Tietz1999]

6ScSZ 10.7 25 - 1000°C [Fleischhauer2014]

10ScSZ 10.5 30 – 800°C [Tietz1999]

LSM 10.8 to 13.1 30 - 800°C [Kuebler2010]

LSCF 18.5 30 -1000°C [Petric2000]

NiO 14 [Kuebler2010]

40% Ni + 60% 8YSZ 12.5 30 – 800°C [Tietz1999]

CROFER 22H 11.8 20 – 800°C [ThyssenKrupp2010]

Plansee CFY 10.6 25 – 800°C [Plansee2015]

Glass sealing 10.6 to 11.0 30 – 660°C [Stark2012], [Kerafol2009]


14

Nevertheless, all the interconnectors are normally coated with lanthanum manganite spinels

(or similar) [Trebbels2009] on air electrode side before use in stacks. On fuel electrode a

galvanic nickel coating can equally be applied to provide long-lasting contacts to the Nickel

contact mesh.

2.2.4 Sealing materials

Sealing materials in SOFC stacks have to provide a gas tight barrier in the gap between cell

and interconnector to prevent gas mixing between fuel, air flows and the environment.

Therefore, they have to fulfil following requirements [Schillig2012]:

- Adapted thermal expansion coefficient: the TEC of the sealing has to be adapted to

ceramic cell and metallic interconnector material to prevent cracking between heat

up and cool down phase of the stack. The TEC difference should ideally be below

0.5 ∙ 10−6 K−1

- Low electric conductivity: low internal parasitic currents are required for high stack

efficiency, area specific resistance should be above 1 kΩm.

- Gas tightness: Gas leaks lead to uncontrolled burning of fuel and a reduction of

Nernst voltage. At room temperature leakage rates should lie within the range of

1 − 5 ∙ 10−4 mbar l s−1cm−2

- Chemical and thermal stability: Since SOFC stacks need to reach over 40.000

operation hours for commercial applications the sealing has to be stable at operation

temperature, both in oxidizing, humid and reducing environment. Due to malign

effects of some sealing components, evaporating rate needs to be low.

Typically, for stack application glass or glass ceramic sealings with main components SiO2,

Na2O, CaO, Al2O3, Li2O, and other alkali or earth alkali oxides are applied. Heating the entire

stack above flow point of the glass (typically above stacks operation temperature) leads to a

firm soldering of the stack components.

Elastic sealing concepts base on metallic sealings, such as silver and gold wires or mica

sealings and require high and constant compression forces [Wiener2006]. This translates

into the needs of a steady stack tensioning. There also exist hybrid stack sealings based on

glass coated mica gasket that provide a flexible and compressible sealing concept, that

additionally does not require the high temperature soldering step [Rautanen2014].

2.3 Irreversible effects of real cells and stacks

2.3.1 Operation voltage losses

Real solid oxide cells are subject to several irreversibilities that reduce electrical efficiency

compared to chapter 2.1. In operation with current densities 𝑖 ≠ 0 additional overvoltages

Irreversible effects of real cells and stacks

15

Δ𝑉𝑖 due to activation energy at reactive sites, ohmic losses mostly in the electrolyte and gas

diffusion effects in electrodes occur. Detailed descriptions of these losses, leading to the

formation of the typical i-V curve of the electrochemical cell (Figure 2.4) can be found in

chapter 4.2. In fuel cell operation, these losses lead to a reduction of actual cell voltage 𝑉

below Nernst voltage and provoke irreversible heat production 𝑄𝑖𝑟𝑟:

This heat production equivalently to reversible heat balance is liberated directly at the site of

reaction within the cell structure.

One can define a voltage efficiency to bring Nernst voltage and operation voltage 𝑉 in

relation

2.3.2 Fuel and air utilisation

A further loss compared to the theoretic optimum happens in real operation since typically

fuel conversion is not complete, i.e. 10 - 30% of the fuel remains unused in anode off-gas.

This is mandatory for fuel electrode’s catalyst protection (Ni-oxidation at too high local

oxygen partial pressures) and to keep current density high, also in fuel off-gas regions of the

cell. Thus, a current efficiency 𝜂𝑖, often referred as Faradaic efficiency, describes that not the

entire fuel is converted into an electron flow.

FU is the fuel utilization at the anode side. The unused fuel is mainly oxidized in direct

combustion afterburners outside the stack, creating an additional heat flow 𝐹𝑈 of:

Since the afterburner is normally placed outside the stack structure, this heat does not

directly contribute to stacks energy balance. In advanced system concepts, a partial anode

fuel recycle is applied in order to increase overall fuel utilization.

The complete fuel to electricity efficiency 𝜂𝑒𝑙 of the real fuel cell may thus be calculated by

multiplying the three beforehand defined efficiencies.

𝑄𝑖𝑟𝑟 = (𝑉N − 𝑉) ∙ 𝑧𝑒𝑙 ∙ 𝐹 (2.12)

𝜂𝑉 =𝑉

𝑉𝑁 (2.13)

𝜂𝑖 =𝑖

𝑖𝑚𝑎𝑥 = 𝐹𝑈 (2.14)

𝐹𝑈 = (1 − 𝐹𝑈) ∙ Δ𝑅𝐻 ∙ 𝑓𝑢𝑒𝑙 (2.15)

𝜂𝑒𝑙 = 𝜂𝑡ℎ ∙ 𝜂𝑉 ∙ 𝜂𝑖 = −𝑉 ∙ 𝑖

fuel ∙ Δ𝑅𝐻 (2.16)


16

For typical state-of-the-art SOFC systems operating at 0.75 to 0.8 V per cell, net electrical

efficiency (LHV based) between 0.35 (1 kW, Hexis AG1) and maximum 0.6 (2.5 kW,

SolidPower2; 250kW Bloom Energy3) is reached, mainly depending on fuel reforming

approach.

Thermal efficiency of a SOFC system in CHP configuration is correspondingly defined as

based on the usable amount of heat 𝑄𝑡ℎ𝑒𝑟𝑚 that depends on system configuration and

temperature levels.

The air ratio λ, as it is used in this work, is defined following the definition in SOFC use, as

inlet oxygen amount over oxygen balance of cell/stack including post-combustion.

𝜆 =𝑂2,𝑖𝑛

𝑂2,𝑝𝑟𝑜𝑑/𝑢𝑠𝑒𝑑 (2.18)

In consequence for SOFC operation an air ratio of 1 describes a stoichiometric rate of air

compared to the inlet fuel.

1 Datasheet Hexis Galileo 1000N, operation on CPOX reformed natural gas

2 Datasheet SolidPower BlueGen, partially internal steam reformed natural gas

3 Datasheet Bloom Energy ES-5710, partially internal steam reformed natural gas

𝜂𝑡ℎ𝑒𝑟𝑚𝑎𝑙 =𝑡ℎ𝑒𝑟𝑚

fuel ∙ Δ𝑅𝐻 (2.17)

Figure 2.4: Local energy balance of a SOC in both operation modes at two operation voltage levels V1 and V2 of a SOC, i-V-curve calculated for typical ASC parameters [Dillig2012] at 800°C, fuel composition 80% H2, 20% H2O

Fuel Cell OperationElectrolysis

thermoneutral point

exothermal endothermal exothermal

i / A cm-²

V/

V

0.4 0.8-0.8 -0.4

0.40

0.80

1.20

1.60

Reversibility of fuel cell operation – electrolysis

17

2.4 Reversibility of fuel cell operation – electrolysis

2.4.1 Steam electrolysis

Fuel cell operation as described above is a reversible process. Inverting electrical polarization

of solid oxide cells leads to high temperature electrolysis operation of the electrochemical

cell, often referred as SOEC (for solid oxide electrolysis cell). This process was already

described in the 1980s by Dönitz within the HotElly project led by Dornier GmbH

[Dönitz1984; Dönitz1985; Dönitz1980] but lost scientific interest during the 90s. In the last

decade the process again returned into focus of several SOFC research institutes, such as

CEA (France), EIFER (Germany), Risoe (Denmark) and others [Laguna-Bercero2012], mainly

due to the increased interest in electrolysis for electricity storage and synthetic fuel

purposes. Being the reversed fuel cell operation the overall reaction of steam electrolysis is

equivalent to

𝐻2𝑂(𝑔) → 1 2⁄ 𝑂2 + 𝐻2 𝛥𝐻𝑅 = + 241.8 kJ/mol (2.19)

with electrode reactions

𝐻2𝑂(𝑔) + 2𝑒− → 𝐻2 + 𝑂

2− cathode (2.20)

𝑂2− → 2𝑒− + 1 2⁄ 𝑂2 anode (2.21)

According to equation (2.6) work and reversible heat flow change their signs, both electrical

energy and heat have to be supplied to the ideal process. The advantage of performing high

temperature electrolysis becomes clear, when considering Figure 2.5. Δ𝑅𝐺 representing the

electric work necessary for water split declines from 228.6 kJ mol-1 at ambient conditions to

188.5 kJ mol-1 at 800°C, thus a reduction by 18 %. However, reversible heat demand 𝑇 Δ𝑅𝑆

for the reaction increases, but this heat demand can be partly or completely be covered by

internal irreversible heat production during cell operation (Figure 2.4). The heat balance of

the cell operating on water vapour results in

Thus, the so called thermoneutral voltage, i.e. 𝑄 = 0 in electrolysis operation is attained

when operation voltage is equivalent to 𝑉𝐻. In this case the entire electrical energy is

converted into chemically stored energy and no losses occur in this idealized step. For higher

current densities and thus higher irreversible losses the process becomes exothermal, while

operation below thermoneutral voltage, at lower current densities, is endothermal and

requires additional heat supplies.

𝑄 = 𝑄𝑟𝑒𝑣 + 𝑄𝑖𝑟𝑟 = (Δ𝑅𝐻 − Δ𝑅𝐺) + (Δ𝑅𝐺 −

𝑉

𝑧𝑒𝑙 ∙ 𝐹) = Δ𝑅𝐻 −

𝑉

𝑧𝑒𝑙 ∙ 𝐹 (2.22)


18

Thermodynamic and voltage efficiency of electrolysis are defined accordingly

Faradaic efficiency being always 1 since the entire current is used for the separation of the

water molecule.

According to this definition, electric efficiency thus may be above 1 for operation voltages

below thermoneutral operation, always considering that an additional reversible heat supply

is required in that case.

Besides direct internal reutilisation, a second advantage arises from high temperature

electrolysis. While low temperature processes have to provide evaporation enthalpy 𝑄𝑒𝑣𝑎𝑝

Figure 2.5: Energy balance under reversible fuel cell operation, thermodynamic data according to [Chase1998]

𝜂𝑡ℎ = 𝑉𝐻𝑉𝑁

(2.23)

𝜂𝑉 = 𝑉𝑁𝑉

(2.24)

𝜂𝑖 = 1 (2.25)

𝜂𝑒𝑙 = 𝜂𝑡ℎ ∙ 𝜂𝑉 =fuel ∙ Δ

𝑅𝐻0

𝑉 ∙ 𝑖 (2.26)

0

50

100

150

200

250

300

350

273 473 673 873 1073 1273 1473

Ener

gy d

eman

d [

kJ/m

ol]

Temperature [K]

H2O

(l)

H2O (g)

∆RH(H2O,g)

PEM / alkaline electrolysis SOEC

∆RH(H2O,l)

total energy

Internal reforming of fuels

19

internally at cell level, i.e. by electric work, high temperature electrolysis is fed with steam

and evaporation can be done by low temperature heat. This evaporation enthalpy of 40.6 kJ

mol-1 of the water at 1 bar, representing approx. 17% of the LHV of hydrogen is potentially

supplied by waste heat from secondary processes (e.g. Sabatier-Process).

In total, potential electrical efficiency gains (i.e. internal reuse of cell irreversible losses and

external evaporation) sum up to approx. 35% compared to the low temperature processes.

Combined with the potential reversible operation of fuel cell and electrolysis operation, this

leads to promising storage concepts.

2.4.2 Co-electrolysis of CO2/H20 mixtures

Solid oxide cells are also capable of electrochemically separating carbon dioxide into carbon

monoxide and oxygen [Ebbesen2009; Nguyen2013; Stoots2008] according to the complete

reaction:

𝐶𝑂2 → 12⁄ 𝑂2 + 𝐶𝑂 𝛥𝐻𝑅 = +283.0 kJ/mol (2.27)

Even steam and CO2 electrolysis can be operated in parallel with desired mixing ratios.

This co-electrolysis is in particular interesting for the production of syngas and subsequently

synthetic fuels, namely methane, methanol or Fischer-Tropsch liquid fuels for the use in

transportation [Schimanke2012]. It is more complex than pure steam electrolysis since

several internal reactions may occur at the fuel electrode, such as reversible shift reaction,

methanation reaction, or reversed direct internal steam reforming.

2.5 Internal reforming of fuels

Solid oxide fuel cells are an appealing technology also due to their internal reforming and

shift activity of the anode catalysts. Methane steam reforming incorporated into the stack

structure reduces systems complexity, i.e. an additional externally heated reformer, when

operated on natural gas, the most abundant gaseous fuel so far. The endothermal reactions

and the possibility of direct heat reutilisation promise thermodynamic efficiency gains

compared to low temperature fuel cell applications.

Mainly the flowing homogeneous reforming reactions (enthalpies according to [Chase1998])

are to occur at the Ni-anode.


20

𝐶𝐻4 + 𝐻2𝑂 ↔ 𝐶𝑂 + 3 𝐻2 𝛥𝐻𝑅 = + 206.2 kJ/mol (2.28)

𝐶𝑂 + 𝐻2𝑂 ↔ 𝐶𝑂2 + 𝐻2 𝛥𝐻𝑅 = − 41.2 kJ/mol (2.29)

𝐶𝐻4 ↔ 𝐶 + 2 𝐻2 𝛥𝐻𝑅 = + 74.9 kJ/mol (2.30)

2 CO ↔ 𝐶 + 𝐶𝑂2 𝛥𝐻𝑅 = − 172.5 kJ/mol (2.31)

The minimum mass of water xH2O,min required for complete reformation can be calculated

according to equation (2.32).

Typically, the reforming is performed at higher amounts of water, as required by the

stoichiometry, to prevent carbon deposition according to equations (2.30) and (2.31), since

especially Ni-YSZ anodes are vulnerable [Iida2007]. The excess steam ratio Σ (equation

(2.33)) follows analogously the definition of excess air ratio λ of fuel cell operation and for

oxygen-free fuel (methane, ethane) it is equivalent to the ratio of steam to carbon S/C.

No carbon deposition was observed for S/C ratios of 1.5 – 1.6 for methane

[Sangtongkitcharoen2005] but higher hydrocarbons require additional excess steam.

Typical S/C ratios for direct internal reforming on Ni-anodes of SOFCs operated on natural

gas lie in the range of 1.8 to 2.5 [Mogensen2011]. These ratios are considerably lower

compared to industrial steam reforming, due to the negative effect of high steam

concentrations on reversible cell voltage and overall system efficiency.

The kinetics of the endothermic steam reforming reaction at Ni-anodes are significantly

faster than the electrochemical cell reaction, resulting in some major issues for complete

internal reforming of the methane. This is mainly caused by a high Nickel content of the

anode that is required to provide adequate electric conductivity. Due to the fast

endothermal reforming the reaction causes an immediate sub-cooling of the fuel inlet zone

of the cell while electrochemistry generates a continuous heating towards the outlet,

leading to significant thermal stress situations.

A power law expression with exponents 𝛼, derived from data fitting can describe the

reactions rate as a function of kinetic constant k and the partial pressures of the relevant

species i (CH4, H2O, H2, CO, CO2).

𝑥𝐻2𝑂,𝑚𝑖𝑛 =𝑀𝐻2𝑂

𝑀𝐶𝐻𝑥𝑂𝑦∙ (1 − 𝑦) =

18

12 + 𝑥 + 16 ∙ 𝑦∙ (1 − 𝑦) [

𝑘𝑔𝐻2𝑂

𝑘𝑔𝐹𝑢𝑒𝑙] (2.32)

Σ = 𝑥𝐻2𝑂

𝑥𝐻2𝑂,𝑚𝑖𝑛= 𝑆/𝐶 (2.33)

Internal reforming of fuels

21

According to the overview in [Mogensen2011] the constant k follows an Arrhenius approach

with activation energy 𝐸𝐴 of approx. 100 kJ mol-1 and exponents 𝛼𝐶𝐻4 between 0.85 and 1.3

and 𝛼𝐻2𝑂 between -0.35 and -1.25 depending on anodes parameters. 𝑘0 is assumed by

[Ahmed2000] to be 8542 mol s-1 m² bar-0.5.

In SOFC modelling, it is assumed that water gas shift reaction is fast compared to steam

reforming and that it is at equilibrium at all time [Mogensen2011].

Reforming kinetics and electrochemical modelling of a single cell (in detail described in

[Dillig2012]) can be combined in a 1-D model, to give a first look at energy balances of a

methane-fueled SOFC. Figure 2.6 shows how species and energy balance evolve in an

exemplary SOFC operated on unreformed methane and steam (S/C =2) at 0.75 V and an

average current density of 0.4 A cm-2. Due to the high kinetics of the reforming reaction, the

cells heat balance 𝑄𝑡𝑜𝑡

is subdivided into an endothermal and exothermal region. At fuel inlet, steam reforming

rapidly converts the methane to syngas and overall heat balance is strongly endothermal. In

downstream regions, remaining reforming activity is very low and the exothermal

electrochemical behavior overweights. For typical operation conditions (i.e. fuel uses),

integrated heat balance of the SOFC with full internal reforming stays exothermal.

−𝑟𝐶𝐻4 = 𝑘 ∙∏𝑝 𝑖𝛼𝑖

𝑖

(2.34)

𝑘 = 𝑘0 ∙ 𝑒𝑥𝑝(𝐸𝐴𝑅𝑇) (2.35)

𝑄𝑡𝑜𝑡 = 𝑄𝑆𝑅 +𝑄𝑊𝐺𝑆 + 𝑄𝑟𝑒𝑣 + 𝑄𝑖𝑟𝑟 (2.36)


22

It can be concluded how important stack internal heat transfer and thermal management

consequently is to SOCs. In particular, in the case of internal reforming high heat transfer

rates from endothermal to exothermal regions are required in order to leverage full

benefits. But also in fuel cell and electrolysis operation on reformed fuel or elementary

hydrogen, thermal control plays an important role for all operation modes.

Figure 2.6: Gas species evolution and energy balance in an isothermal co-flow SOFC cell (i = 0.4 A cm2, V = 0.75 V, 800°C) under full internal methane steam reforming conditions (S/C = 2 𝐸𝐴 = 95 kJ mol-1, 𝑘0 = 8542 mol s-1 bar-1 m², 𝛼𝐶𝐻4 = 0.85, 𝛼𝐻2𝑂 =-0.35, WGS in equilibrium)

H2

H2O

O2 (cathode)

endo- exothermal cell operation

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 0.2 0.4 0.6 0.8 1

con

cen

trat

ion

/ -

dimensionless flow parallel position / -

CO2CO

CH4

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0 0.2 0.4 0.6 0.8 1

ener

gyb

alan

ce/

W c

m- ²

dimensionless flow parallel position / -

electric energy

reaction heat of reforming reaction

total heat balance

electrochemical heat balanceirreversible and reversible

endo- exothermal cell operation

23

Chapter 3

3. State-of-the-art of thermal control of SOCs

3.1 Cell degradation due to internal temperature gradients

3.1.1 Chemical cell degradation

Fuel cell lifetime specific energy costs are depending, in addition to investment cost, on

three main factors: efficiency, power density and degradation. These factors are opposing

targets, as for instance lower operation voltages normally increase power density, but

decrease efficiency. Higher operation temperature however increases efficiency and even

power density, but has a negative influence on degradation rates, cell lifetime [Stehlík2009]

and system costs due to more expensive materials [Ivers-Tiffée2001]. But not all degradation

effects amplify with increased temperature.

The main temperature induced degradation mechanisms are summarized in Table 3.1. It can

be concluded that mainly anode concerning degradation mechanisms, as well as electrolyte

aging above 900°C, increase with higher temperatures, especially on hot spots within the

stack. Chromium evaporation from metallic interconnectors additionally increases with

rising temperature. By contrast, a significant cooling below the design point operation

temperature has adverse effects regarding carbon depositions and cathode poisoning

[Hagen2006].

Thus, resulting temperature gradients over one solid oxide cell always cause an acceleration

of degradation compared to design point layout. Only for isothermal cell behavior, chemical

degradation rates can be optimized to one design operation temperature. Addtionally, these

temperature gradients may be interpreted as a further indirect efficiency or power density

loss for the electrochemical cell. Assuming that temperature hotspots have to be avoided

and a maximum local operation temperature is defined for the cell, a high temperature

gradient results in a large sub-cooling of certain cell regions. Due to strong temperature

dependency of ohmic cell losses, cell performance is significantly decreased in these cooler

areas and cell resource are not used optimally. In isothermal operation this performance loss

is avoided and the cell can be operated in much more uniform current density at a higher

average level.

Chapter 3: State-of-the-art of thermal control of SOCs

24

Table 3.1: Degradation mechanism depending on cell temperature according to [Stehlík2009; Yokokawa2008]

Location Mechanism Effect Temperature influence

Air electrode (cathode)

cathode decomposition

reduction of catalytic activity and electric conductivity, reduction of TPBs

↑

Electrolyte electrolyte aging (e.g. YSZ)

reduction of ionic conductivity ↑ > 900 °C

Fuel electrode (anode)

Ni-oxidation Reduction of catalytic activity, interruption of conduction pathways, reduction of TPBs, cracking

↓

Ni-discharge Reduction of catalytic activity, interruption of conduction pathways, reduction of TPBs

↑

Ni-sintering Reduction of TPBs, reduction of catalytic activity,

↑

Carbon-deposition

Reduction of gas diffusivity, reduction of catalytic activity/destruction of catalyst, blocking of gas flow cross section

↓

Contact interconnector - electrode

Contact corrosion Increase of contact resistance ↑

Metallic interconnector

Chromium evaporation

Deactivation of active centers of TPBs on air electrode

↑

3.1.2 Mechanical stack degradation due to temperature gradients

A coupling of solid oxide cell system (SOFC and SOEC) to volatile electricity sources implies

strong load gradients. Thus, strong changes in internal heat consumption/production rates

appear and in consequence the stack and its cells are subject to dynamically changing

temperature profiles. Resulting thermo-mechanical stress within the ceramic cell can induce

(micro) cracking of the electrolyte and structural instability [Lowrie2000]. The electrolyte

loses one of its main functions, the physical separation of fuel and gas flow. This leads to a

strong reduction of cell performance and may in extreme cases cause instantaneous death

of the entire stack. There has been some experimental work on crack development and

mechanical behavior of cells (see Figure 3.1), with however very few results

[Fleischhauer2014] on experimental evaluation of fracture in real stacks.

Cell degradation due to internal temperature gradients

25

Comparing thermal stress due to temperature gradients to fracture stress of typical

electrolyte materials (see Table 3.2) in many cases show that electrolyte should withstand

those loads with cracks, while experimental post-mortem analysis of cell provides opposite

results and shows fractured cells. According to literature, this is explainable if some minor

cracks created during manufacturing are included into explaining the mechanisms.

Subcritical crack growth

Cracks, e.g. produced during tape casting of the electrolyte, having a sub-critical size, tend to

grow under certain condition, which is called sub-critical crack growth. Once critical size is

reached, the components fail immediately since crack size expands spontaneously. Time to

reach this critical crack size and consequently cell failure 𝑡𝑓 depends mainly on applied stress

to the electrolyte:

where 𝑡𝑓 is the failure lifetime at a reference stress 𝜎0; n is a constant, and 𝜎 is the applied

stress. Thermal stress thus can increase subcritical crack growth and lead to fracturing

events in stacks design lifetime. Fleischhauer [Fleischhauer2014] demonstrated on post-

mortem analysis of electrolyte supported cells from Hexis Galileo system that local cracks of

mm-size, formed during start-up or cool-down due to surface imperfections, can serve as

crack origin under thermal stress conditions during operation. Consequently, even per-se

subcritical thermal stress situations with stress in the range of max. 50 MPa, thus far lower

than electrolyte strength, promote this crack expansion and cell failure.

Figure 3.1: Left: Anode side of ruptured cell after operation (source: [Fleischhauer2014], reprinted with permission from Elsevier), right: electrolyte damage in cross section (source: [Malzbender2007], reprinted with permission from Elsevier)

𝑡𝑓

𝑡0= (𝜎0𝜎)𝑛

(3.1)


26

Table 3.2: Cell material strength

Type, Composition

Producer Data Temperature Source

Electrolyte, (8YSZ)

Kerafol Fracture stress 𝜎𝑓 =

156 MPa 1000°C [Lowrie2000]

Electrolyte, (3YSZ)

Nippon Shokubai

Characteristic strength 𝜎𝑓 = 250 MPa

Weibull modulus m=19

950°C [Fleischhauer2014]

Electrolyte, (6ScSZ)

Nippon Shokubai

Characteristic strength 𝜎𝑓 = 250 MPa

Weibull modulus m=19

950°C [Fleischhauer2014]

Further stack related problems, in particular fuel leakage and contact loss between

electrodes may occur [Adams2012]. Thus, the theoretically fast electric load modulation of

SOCs is intensely restricted by inertial thermal adaption of cell and stack and the need to

prevent fracture of cell components [Liso2011]. Thermal gradients within the stack structure

are to be minimized, notably for cyclic load changing operation conditions.

Delamination of cell layers

Another degradation mechanism of cells due to thermal gradients is the delamination of

functional layers of the SOFC. Both, anode electrode as well as cathode may lose contact to

the oxygen ion conducting electrolyte. Thermal stress reduces the adhesion forces to the

electrolyte surface and partly delamination appears [Ivers-Tiffée2001]. The reduced contact

area inhibits the O2--ions from migrating from the cathode to the reactive TPBs on the anode

side. Figure 3.3 shows SEM images of cell cross sections. One can clearly observe the

delaminated electrodes resulting from thermal cycling and thermal stress on the functional

cell layers.

Figure 3.2: Crack formation process according to [Fleischhauer2014]

Channel cracks in anode after

sintering due toTEC differeces

Pre-crack stress formation at

imperfections ofinterconnector

surfaces,

Stable microcrack formation

in electrolyteduring heat up orcool down phase

Crack growth andcell rupture at high thermal stress areas

during operation

electrolyte

anode

cathode

MIC

Thermal control of SOFC stacks

27

Sealing degradation

Proper and enduring operation of SOC stacks depends additionally to cell behaviour, on the

mechanical integrity of stack sealing. In particular rigid sealing concepts, such as glass solder

based sealings or ceramic sealing pastes as applied by most of the stack manufacturers,

provide very good initial leakage rates, but degrade rapidly during cycling operation. The

brittle materials, after soldering, tend to subcritical crack growth due to their very low

elasticity [Wiener2006]. Thermal stress is considered more severe than solely mechanical

stress for crack initiation and growth [Mahapatra2010]. A fatigue fracture to cycling

temperature stress is the consequence. Experimental analysis of silicate glass between

Crofer 22 APU and YSZ electrolyte showed that up to 300 thermal cycles are possible, if

heating rates are kept very low (3 K/min), but decreases significantly with higher heating

rates.

This behaviour may be avoided applying compressible sealings such as mica sealings or

metallic sealings [Rautanen2009]. These however demand further complexity increase of the

stack design, in order to provide the required compression and an additional electrical

insulation. Hybrid sealing concepts such as mica sealings with thin external glass coatings

[Rautanen2014] provide compressible sealing behaviour even at lower compressions of

around 0.1 MPa.

3.2 Thermal control of SOFC stacks

3.2.1 Control by gas flows

The mass flow of gases that is stoichiometrically necessary to maintain fuel cell

electrochemical reaction, i.e. air ratio 𝜆 close to one and fuel uses as high as possible, is

normally not large enough to provide sufficient heat capacity to control stack temperatures

Figure 3.3: Right: SEM image of Ni/YSZ anode delamination from electrolyte; a gap (black area) results (source: [Hsiao1997], reprinted with permission from Elsevier), Left: delaminated LSM-cathode (source: [Ivers-Tiffée2001], reprinted with permission from Elsevier)


28

at reasonable temperature differences. For this reason, the possibly low air ratios of SOFC

stacks are significantly increased in practical applications to provide an additional cooling

effect. State-of the art SOFC system are almost all based on this cooling approach. Table 3.3

gives an overview of typical air ratios of systems with different reforming approaches.

Depending on the size of the system air ratios between 3.5 and 7.5 are required for natural

gas fired SOFC stacks.

For hydrogen operated SOFC stacks this value is even increased to 𝜆 = 4 − 10 [Apfel2006],

due to the lack of cooling by endothermal reforming or fuel dilution (as in CPOX reforming).

Table 3.3: Typical stack air ratios during operation

Type, Composition

Producer Size, Reforming method Air ratio

Source

ESC, planar Hexis 1 kW, CPOX 3.5 – 4.2

own measurement

(system simulation)

FZ Jülich 50 kW, SR (external) 7.5 [Blum2011]

(system simulation)

FZ Jülich 50 kW, SR (internal, fuel recycle)

3.8 [Blum2011]

ASC, planar FZ Jülich 20 kW , SR (50 %, external) 5.5 [Peters2014]

ESC, planar Fraunhofer IKTS 1 kWel, CPOX 4.5 - 5 [Pfeifer2014]

HT-PEM System simulation (for comparison only)

1 kW, pure H2 9.6 [Harikishan Reddy2012]

Figure 3.4 shows the gas temperature increase between stack inlet and outlet computed for

an adiabatic stack operation for different fuels and operation modes. The adiabatic

approximation estimates maximum gas temperature rises and is increasingly close to reality

for large stacks and cell sizes. Calculations are performed for typical stack operation

conditions, i.e. cell voltage of 0.75, fuel use of 0.8 at 800°C. Methane operation is displayed

for CPOX pre-reforming (with air, 𝜆 = 0.27) and both partial pre-reforming (approx. 50 %,

555°C equilibrium temperature) and full stack internal steam reforming with steam to

carbon ratios (S/C) of 2. A restriction of gas flow temperature increase to e.g. 140 K

throughout the stack already leads to significant air ratios of 3.5 (CPOX) to 7 (pure H2). Only

full internal reforming could theoretically be operated on lower air ratios, but the additional

temperature effects of fast reforming reaction have to be considered.

The drawbacks of a stack cooling by increased air ratio are however a concern to system

developers. High volume flows through stack manifold, flow channels and heat exchangers

lead to high pressure drops and thus large blower power needs and high system parasitics.

Typical values for a 21.3 kWDC stack operated on natural gas (50 % steam pre-reforming)

[Peters2014] and 𝜆 = 5.5 are a blower power of approx. 2.4 kW. This represents over 10 %


29

of the electric stack output, reducing net electric efficiency considerably. Oversizing blowers

and heat exchangers due to excess air ratios is furthermore to be paid by increasing system

investment cost for the SOFC system.

Figure 3.4: Exhaust gas temperature increase for adiabatic SOFC stack operation (heat transport only by gas flows); Stack operation at 800°C, U = 0.75 V per cell, fuel use FU = 0.8; Fuel: pure hydrogen operation, catalytic partial oxidation (CPOX) of methane with air ratio 0.27 and steam reforming (SR) with S/C=2 of methane. Both partial pre-reforming (approx. 50%) and full stack internal reforming are displayed.

A third drawback of this cooling method is a decreasing thermal efficiency for the SOFC

system operated in combined heat and power operation. Sensible heat losses increase

proportionally to air flow rate and the shift of the dew point of exhaust gases reduces latent

heat recovery significantly. An increase of the cathode air ratio from 1.5 to 5 for a SOFC

operation with CH4 - fuel (steam reformed S/C = 2) decreases exhaust gas dew point from

approx. 65°C to 40°C. For pure hydrogen operation, dew point similarly shifts from approx.

68°C to 42°C. If heat recovery temperatures are able to access this temperature level, the

difference of this shift is equivalent to a condensation enthalpy of approx. 19 % of the LHV

(for the steam reformed CH4) or 17 % (for pure hydrogen operation), thus resulting in a

thermal efficiency loss of the same magnitude in that case.

For SOEC - operation the thermal energy balance is much lower and the cooling needs are

much less pronounced. For thermoneutral operation, it is evident that no cooling is required.

Figure 3.5 shows gas temperature increase between inlet and outlet computed for an

adiabatic stack operation for different operation voltages and reactants (H2O and CO2). In

the case operation voltage deviates from thermoneutral point, adiabatic temperature

differences reach high values, if very low or no air is applied for cooling. A steam electrolysis

operation at e.g. 1.35 V generates an adiabatic temperature difference of approx. 200 K if no

0

100

200

300

400

500

600

700

800

0 2 4 6 8 10

Ad

iab

atic

te

mp

ratu

rein

crea

se /

K

Air ratio / -

pure H2 operation

CH4, CPOX (λ=0.27)

CH4, SR partly external (555°C; S/C =2)

CH$, SR stack internal (S/C=2)

typical operation range

CH4

SOFC


30

dilution of the produced oxygen is desired and may therefore require an additional cooling

concept.

Figure 3.5: Exhaust gas temperature change for adiabatic SOEC stack operation (heat transport only by gas flows); Stack operation at 800°C, steam use uf = 0.8. Both water and CO2 electrolysis are displayed.

3.2.2 Advanced cooling concepts

[Peters2014] proposed a thermally integrated SOFC module, where SOFC stack, off-gas

burner, air pre-heater and pre-reformer are integrated into one stack set-up (see Figure

3.6.). The concept, still using gas flows as sensible heat carriers to stack cooling, targets high

system compactness and low exhaust gas temperatures in order to benefit from

condensation enthalpy of the off gases.

Within the EU-project Biocellus [Karl2009] the approach of inserting liquid metal heat pipes

was under evaluation in order to thermally integrate SOFC cell stack with endothermal

biomass gasification reactors. During the project stack concepts based on planar and tubular

cells were examined, applying cylindrical liquid metal heat pipes (see Figure 3.4) [Brost2005;

Hesse2006].

In the case of a planar stack design with ASC cells from FZ-Jülich interconnectors partly from

Plansee ITM, partly made by 1.4742 were applied. Stack design was based on an internal

manifolding, crossflow concept. Cylindrical heat pipes made from Inconel 600 (2.4816) were

placed into drilled cavity in a thick HP-Interconnector layer, however without detailing

effects of differing thermal expansion coefficients nor heat transfer resistance of the contact

interface, that certainly restrict the concepts potential. During test of prototype stacks no

negative effects of hydrogen deactivation were reported, concluding that the interconnector

thickness as well as the contact interface led to a sufficient reduction of hydrogen

permeation (see chapter 5.4).

-500

-400

-300

-200

-100

0

100

200

300

400

500

0 0.5 1 1.5 2 2.5 3

adia

bat

ic t

emp

ratu

rein

crea

se /

K

air ratio / -

SOEC

H2O H2 + 0.5 O2

CO2 CO + 0.5 O2


31

Figure 3.6: Integrated SOFC stack module (source: [Peters2014], reprinted with permission from Wiley)

The stack concept for electrolyte supported tubular SOFC based on an insertion of in-series

connected tubular fuel cells (4 cells or 16 battery cells) in a complex tubular heat pipe body.

This however created large problems to gas tightness and electrical series interconnection of

the cells. Additionally, heat transfer from cells to heat pipe is restrained and due to the

complex geometry, heat pipe manufacturing is laborious for relatively low thermal powers.

In conclusion, the planar stack concept was considered more promising, despite the existing

problems of the cylindrical heat pipe concept.

3.2.3 SOFC thermal system integration

Fryda et. al. [Fryda2008] proposed a system integration of solid oxide fuel cells and

allothermal biomass gasification that was investigated within the EU-project Biocellus. The

concept proposes the external heating of a biomass gasifier, called heat pipe reformer (HPR)

[Karl2014] with SOFC excess heat via integrated sodium heat pipes. They performed a

system analysis of a 170 kWel system with 34% electrical efficiencies. Their 0-D thermal stack

evaluation led to the conclusion that large efficiency gains are possible due to a strong

reduction in fuel cell air stoichiometry. Advances regarding process design, i.e. gas cleaning

and tar resistance of an SOFC were on focus within the project and as mentioned above first

test stacks have been built to evaluate HP integration to SOFC stack. The proposed concept

furthermore poses challenges regarding thermo-mechanical stability, electrical insulation

and congruent sizing of gasifier and SOFC system in a real set-up.


32

Figure 3.7: Prototypes of cylindrical heat pipe integration to planar SOFC stacks (left) or tubular SOFCs (right) (Source: [Hesse2006])

However, the study demonstrated the large potential of efficiency gains and system

simplification due to thermal integrations based on heat pipe technology. [Santhanam2016]

lately analysed a similar approach with coupling of SOFC, biomass gasification, and

additional a gas turbine based on heat pipes.

Heat pipe cooling applied in other types of fuel cells

33

Figure 3.8: Flowchart of the combined SOFC/allothermal biomass gasification system (source: [Fryda2008], reprinted with permission from Elsevier)

3.3 Heat pipe cooling applied in other types of fuel cells

Literature provides several proposals of integrating heat pipe technology to PEM-fuel cells.

Many works however are mainly theoretic concepts, based on numerical models

([Firat2012], [Shahsavari2012]) or only consider separated fuel cell / heat pipe development

([Vasiliev2009],[Burke2009],[Zhang2012]).

[Supra2014; Supra2013] carried out an extensive study of different stack integrated cooling

concepts for high temperature PEM fuel cells. These operate in temperature range between

120 – 180°C and therefore liquid water cooling (as for normal PEMs) is not suitable if the

stack pressure is not increased significantly. HT-PEMs in consequence pose similar thermal

control questions as SOFC systems. Supra proposed several internal concepts based on

cooling fluids such as air, water and synthetic heat transfer fluids (Fragoltherm S-15-A). The

coolant flow passes through dedicated interconnectors with cooling channels. As an

alternative approach an externally Fragoltherm S-15-A cooled concept with state-of-the-art

cylindrical copper/water heat pipes (d=3mm) was under evaluation. The pre-fabricated heat

pipes were integrated into one interconnector structure and transferred the thermal heat to


34

the external cooling cycle (Figure 1.1). For the 200 cm² stack operated at 500 mA cm-2 Supra

proposed a heat pipe cooled interconnector every 3 cell layers. Overall, he estimated a large

potential for heat pipe cooling for high power stacks, in particular for large cell sizes.

Figure 3.9: Advanced cooling concepts for HT-PEMs and the effect on temperature profiles. Thermal oil, air cooled interconnector plates and tubular heat pipes integrated to heat pipe interconnector (source: [Supra2014])

[Niemasz2007] described the direct integration of heat pipe functionality into the

interconnector structure. By producing the heat pipe and the bipolar plate from the same

material (a silicon-pyrex bond) they are able to avoid manufacturing issues. Water serves as

working fluid due its high merit number (equation (3.2)) in the low temperature operation

range of HT-PEM.

[Rullière2007] proposes the use of planar heat pipes applied for the cooling of power

electronics for low temperature fuel cell applications and carries out experimental

performance evaluation of the so-called two phase heat spreaders (TPHS).

Recently, [Oro2015] reported a heat pipe performance study for PEM fuel cells stacks. He

studied a concept close to Supra’s work, with tubular heat pipes inserted into the

interconnector structure of a stack.

Faghri investigated several concepts to improve heat removal from DMFC-Stacks

[Faghri2005],[Faghri2008]. Figure 3.10 shows two proposed heat pipe integrations. The

upper concept describes cylindrical micro heat pipes directly incorporated within the contact

rib structure of the carbon bipolar plate, promising perfect thermal integration. The complex

inte

rco

nn

ecto

r h

alf

shel

ls

ther

mo

cou

ple

po

siti

on

ing

exte

rnal

co

olin

g cy

cle

hea

t p

ipes

external cooling cycle

heat pipes

interconnector half shells

thermocouplepositioning

operation point: 500 mA cm-2

position in stack / mm

heat transfer fluid (internal, every cell) -

heat transfer fluid (internal, every third cell) -

heat transfer fluid (external, heat pipe) -

air(internal, every cell) -

tem

per

atu

re/

°C

Fundamentals on planar heat pipe operation

35

manufacturing task however could limit its potential. Concept b) describes a flat planar heat

pipe consisting in porous wick structure and gas flow channels integrated to the

interconnector. Faghri estimated that in case of technological implementation, large benefits

for thermal stack management by reducing temperature profiles are realizable.

Figure 3.10: Concepts for micro heat pipe integrated into DMFC stack structure (source: [Faghri2008], reprinted with permission from Taylor&Francis)

3.4 Fundamentals on planar heat pipe operation

Heat pipes are sealed cavities filled with small amounts of heat transfer liquids (in the case

of high temperature applications above 650°C mainly Sodium Na or Potassium K). They

provide large heat transfer rates due to evaporation-transport-condensation cycles of the

heat carrier within the heat pipe as sketched in Figure 3.11. They are passive devices that are

driven by external heat sources or sinks, even without or against gravity, as a result of

capillary forces created in the internal wick structure. In spite of the high heat transfer rates,

only small temperature differences between evaporation and condensation zones are

formed being mainly caused by heat conduction through the casing and capillary structure.

Thus, the heat pipe can be assumed as an almost isothermal heat transport device within its

working limits [Reay2006].

Anode/cathodeflow channels

Micro heat pipe(transverse cross section)

Carbon bipolar plate

Micro heat pipe (axial cross section)


Anode/cathode flow channels


Vapor space

Porouswick

Lining


36

Figure 3.11: Set-up and functioning of a (planar) heat pipe

Heat transfer capabilities of different working fluids depend on several fluid properties.

Many authors [Chi1976; Peterson1994; Reay2006] combine main influence parameters

surface tension 𝛾′, enthalpy of vaporization 𝛥ℎ𝑣, liquid density 𝜌′ and dynamic viscosity 𝜂′

into a characteristic value, named merit number Me.

𝑀𝑒 describes the geometry-independent heat transfer performance of a working fluid at a

certain operation temperature. The alkali metals suitable for SOC temperature range (above

650°C) show high merit numbers. Sodium provides the highest overall potential with 𝑀𝑒

about 10 times above best low temperature working fluids (water).

Though, final heat transfer capabilities of heat pipes do not only depend on working fluid

properties. Since geometry, orientation and capillary structure have important influence on

heat pipe performance, literature describes several heat transfer limitations 𝑄𝑖 of heat pipes

(see Table 3.4). They mainly depend on the flow regime in the gas phase (sonic limitation,

viscous limit), on the pressure balance in the capillary structure (capillary and burnout limit)

and on interactions of gas and liquid flow (entrainment limit). In consequence, the maximum

theoretic heat transfer 𝑚𝑎𝑥 of a heat pipe results as temperature depending order of these

limits.

For graphical representations of these heat transfer limits, see chapter 5.3. Exact

determination of maximum heat pipe transfer performance however, requires experimental

analysis. In numerical calculations, heat pipes that operate below performance limit can be

approximated as materials with very low heat transfer resistance (compare [VDI2006]).

liquid – flow

condensationevaporation

planarheat pipe vapour – flow

vapour space

Qin Qout

wick

EVAPORATOR ADIABAT ZONE CONDENSER

casing

ADIABATIC ZONEEVAPORATOR CONDENSER

𝑀𝑒 = γ′ 𝛥ℎ𝑣 𝜌′

𝜂′ (3.2)

𝑚𝑎𝑥(𝑇) = min𝑖(𝑄𝑖

𝑙(𝑇)) (3.3)


37

Table 3.4: Heat pipe heat transfer limits as defined by [Chi1976; Peterson1994; Reay2006]. x’ describes property x of liquid phase, x’’ of vapor phase at saturation point

Limit Physical description Formula of heat transfer limit 𝑸𝒊𝒍 [W]

Sonic Reaching sonic speed in vapor phase. Equivalent to effects in laval nozzle 𝐴′′ 𝜌′′ 𝛥ℎ𝑣√[

𝜅′′ 𝑅 𝑇′′

2 (𝜅′′ + 1)]

Viscous

Viscous forces in vapor flow restrict heat transfer. Is reached when pressure drop in vapor flow is equivalent to absolute pressure after evaporator.

(𝑑ℎ′′)2 ∆ℎ𝑣𝜌′′𝑒𝑣𝑎𝑝𝑝′′𝑒𝑣𝑎𝑝𝐴𝑔

64 𝜂′′ 𝑙𝑒𝑓𝑓

Entrainment Vapor flow drag applies shear force to liquid flow in open capillary structure.

𝐴′′ ∆ℎ𝑣√ 𝛾′ 𝜌′′

2 𝑟ℎ,𝑘

Capillary

Pressure loss due to liquid and vapor flow balances capillary pressure provided by capillary structure reduced by gravity induced pressure loss / gain

depending on flow regime:

𝑄𝑐𝑎𝑝𝑙 | ∆𝑝′(𝑄𝑐𝑎𝑝

𝑙 ) + ∆𝑝′′(𝑄𝑐𝑎𝑝𝑙 ) =

2𝛾′ cos(Θ𝑐)

𝑟𝑒𝑓𝑓− 𝜌′𝑔𝑙𝑔𝑒𝑠sin (𝜙)

Burnout

Formation of vapor bubbles and films within capillary structure that inhibits liquid flow Dry-out of evaporator

2 𝛾′ 𝑇′′

𝛥ℎ𝑣𝜌′′ 𝑅𝑒𝑣𝑎𝑝,𝑘

2 𝜆′ 𝐴𝑒𝑣𝑎𝑝

3.4.1 State-of-the-art on planar heat pipes for low temperature applications

There is a major interest for thermal management of electronic equipment, since thermal

power densities, of e.g. CPU, surpass those of nuclear reactors by orders of magnitude.

Consequently, there has been a lot of recent work on developing flat miniature heat pipes

for low temperature applications (up to 70°C). A basic overview over recent development

results, experimental and theoretical analysis can be found in literature [Groll1998;

Zaghdoudi2011]. Table 3.5 shows an excerpt of different planar heat pipe designs reported

in literature. A large quantity of research work has been done especially on grooved flat heat

pipes, with rectangular or triangle grooves [Khrustalev1996; Lefèvre2012; Lefèvre2008;

Rullière2007], allowing mostly directed heat transport. They described a relatively easy

manufacturing of casing structure that can be extruded if casing material is Aluminum or

Copper. [Peterson1993] also describes the fabrication of micro heat pipes by etching in

silicon wafers. Planar heat pipes applying porous materials [El-Genk2007; Kalahasti2002;

Wang2000] or screen mesh layers [Lefèvre2012], that provide true 2-D heat spreading

capabilities, have also been studied for those low temperature applications. Flat heat pipes

with screen meshes that show overall thicknesses down to 0.9 mm have been demonstrated

[Khandekar2003].


38

There exists furthermore a large variety of literature on theoretical analysis of these devices

such as in [Aghvami2011], [Do2008], [Sonan2008], [Lefèvre2006], [Carbajal2007]. Most of

the recent literature focuses on describing flow regimes in grooved capillary structures and

concluding heat pipe performance limitations.

Figure 3.12: Left: Axial grooves as capillary structure for planar heat pipes (source: [Chen2015], reprinted with permission from Elsevier). Right: Designs for micro heat pipes with less than 1mm width of edge (Source: [Reay2006]).

Table 3.5: Exemplary prototypes of planar heat pipes

Temperature range

Working fluid

Casing material

Capillary structure

Size [mm]

Source

10 – 60°C n-Pentane

Copper Axial grooves 400 x 400 µm

90 x 80 x 9 [Lips2011]

20 - 40°C Methanol Copper

screen mesh (325) layers /covered grooves

267 x115x 5.5 [Lefèvre2012]

20 – 100°C Water Copper Mesh 100 copper screen

300 x 150 x 19 [Adami1990]

40 -60°C Water Aluminum open-cell nickel foam wick

600 x 600 x 64 [Queheillalt2008]

40°C Acetone Aluminum Grooves 200µm x 400 µm

300 x 50 x 2.5 [Chen2015]

650°C Sodium / pottasium

Hastelloy-X Honeycomb sandwich panels,

150 x 102 x 25 [Basiulis1982]

1. 7 mm 0.2 mm0.2 mm

0.2 mm

3.0 mm

excerpt of section AA

Vapor Space

Casing

Liquid


39

Figure 3.13 shows a typical set-up and performance evaluation procedure for planar low

temperature heat pipes. The heat pipe is exposed to a two-dimensional heat source and an

uniform cooler region. Heat pipe surface temperatures are recorded and e.g. rise of

condenser temperature is used as indicator for performance limitation. In case of low

temperature heat pipes optical evaluation of flow/boiling regimes is possible if the HP casing

is transparent [Kalahasti2002].

Figure 3.13: Left: typical set-up for performance evaluation of low temperature heat pipes. Right: wall temperature profile along a low temperature two-phase heat spreader (TPHS) in horizontal orientation at different cooling loads (source: [Rullière2007], reprinted with permission from Elsevier)

3.4.2 Liquid metal micro heat pipes

Targeting high temperature applications, main scientific work focuses on tubular heat pipes,

mainly using Na, K or NaK alloys as heat transfer fluid [Anderson1993].

Little interest has been shown on planarization or miniaturization of liquid metal heat pipes.

[Basiulis1982] proposed a flat honeycomb sandwich structure for scramjet cooling (see

Figure 3.14). Capillary structure consisted in metal screen, moreover vapor space was kept

open by perforated honeycomb elements. Potassium or Sodium served as working fluid.

[Brost2005] proposed a manufacturing of planar heat pipes by diffusion bonding in order to

prevent bulging at higher temperatures. Some preliminary test concerning material

preparation and surface treatment with Inconel 601 sheets were carried out. The research

group concluded that diffusion bonding for joining heat pipe parts is applicable. A large

advantage of diffusion bonding is that vacuum annealing of the casing material is directly

integrated into this manufacturing step.

Furthermore, low deformation rates of up to 3% of the casing due to bonding are reported.

Compared to standard welding techniques this seems to be a considerable improvement, in


40

particular for large planar structures. However, no process parameters for typical SOFC

materials are available. No final manufacturing of planar heat pipes is reported.

However, due to comparable fluid properties and thus Merit numbers of water and sodium

or potassium in the targeted temperature range of 650°C to 850°C (0,29 ∙ 109 kW/m² for

water at 50°C, 2,1 ∙ 109 kW/m² for Na at 800°C and 0,73 ∙ 109 kW/m² for K at 800°C)

[Reay2006] results from low temperature heat pipe research can be used as a starting point

for the development of flat high temperature heat pipes.

Figure 3.14: Left: Low temperature heat pipe open cell structure (source: [Queheillalt2008], reprinted with permission from Elsevier) Right: High temperature liquid metal honeycomb heat pipe (source: [Basiulis1982])

top facesheet

wickable honeycombnotched to allow liquid flow, perforated toallow vapor flow

metal screen sintered tointernal faces to allow in plane flow of liquid alongfaces

41

Chapter 4

4. Numerical modeling of thermal stack behavior

4.1 Modeling approaches

4.1.1 Geometry and materials

The objective of modeling a SOFC / SOEC cell stack is to evaluate the influence of integrating

heat pipes for temperature control and temperature gradient reduction into the stack

structure. Therefore, based on several examples in literature [Al-Masri2014; Laurencin2008;

Laurencin2011; Peksen2013; Udagawa2007] a steady-state, finite volume model of a planar

electrolyte supported SOC stack has been established. The model represents the

characteristic excerpt of such a stack, i.e. a section with heat pipe interconnector and

corresponding number of cell repeating units. Repeatability throughout the stack originates

by setting adapted symmetric/adiabatic boundary conditions.

Stack geometry is modeled close to the experimental stack set-up in chapter 6. A cross flow

regime for fuel and air flow is chosen. Hybrid mica sealings (Thermiculite 866 LS) realize

stack internal sealing between cell and interconnector structure. Cell and interconnector size

is variable in order to account for increased cell sizes. The heat pipe interconnector is

modeled with a variable number of neighboring repeating units without heat pipe (2-10) in

order to account for its stacking frequency. Heat pipe geometry is set according to results of

chapter 5, however no internal structures (capillary structure, gas vapor space) are included

into the model.

4.1.2 Assumptions and simplifications

In order to set-up a 3D-SOC stack model that is capable of evaluating thermal effects of heat

pipe iteration to the stack structure, certain general assumptions and simplifications are

necessary. For the calculations in ANSYS Fluent a pressure based solver with second-order

upwind interpolation method was applied.

Electrochemical

- The cell domain incorporating the SOFC with its electrode / electrolyte structure is a

solid bulk volume where the entire electrochemical reaction heat is generated.

Chapter 4: Numerical modeling of thermal stack behavior

42

Table 4.1. Geometry and materials

Model parameters Source

Solid oxide cell type Electrolyte supported cell 10Sc1CeSZ, thickness

150 µm, screen printed electrodes (20 µm)

[Kerafol2010]

Cell size 100x100; 200x200; 300x300 mm²

Interconnector CROFER 22H, Plansee CFY

Thickness: 2000 µm,

Flow channels:

width=2mm, spacing=4mm

depth: air 700 µm, fuel: 500 µm

[ThyssenKrupp2010]

[Plansee2015]

Sealing Hybrid mica sealings (Thermiculite 866 LS);

thickness: 700 µm

[Flexitallic2013]

Ni-contact grid Not modeled, thermal transfer behavior

included in contact resistance

Cathode contacting

paste

Not modeled, thermal transfer behavior

included into contact resistances

Heat pipe

interconnector

Thickness 4.5 mm,

active area: according to cell size

Fluids

- The stack is operated at ambient pressure

- Laminar flows in the cathode and the anode channel (ideally mixed at entrance).

Typical Reynolds numbers in flow channels range between 𝑅𝑒 = 1 on fuel side up to

approx. 𝑅𝑒 = 1000 (for high air ratios) on oxygen electrode. These values lying

below the critical Reynolds number 𝑅𝑒𝑐𝑟𝑖𝑡 of approx. 2300 justify this assumption.

- Potentially turbulent manifold regions are treated as laminar equivalently since flow

regimes in this area are not of main importance for desired thermal results.

Therefore, no turbulence model, such as k-epsilon for RANS (Reynolds-averaged

Navier-Stokes) equations, is required.

- Diffusion of species in laminar flow is modeled according to Fick’s law

- For carbon containing fuels only steam reforming (SR) and water gas shift (WGS) are

considered. Heterogeneous reactions, such as Boudouard reaction or methane

pyrolysis are neglected

Solid structures

- All the transport coefficients (mainly heat conductance of solids) are constant and

independent of temperature.

Modeling approaches

43

- The stack operates in the temperature range of 700 – 1000°C and all material

properties that are constants are chosen for this temperature range.

Heat transfer:

- The radiative heat transfer inside the stack is incorporated to thermal contact

resistance (see discussion below).

- Perfect sealing behavior of internal sealings, no leackage effects

- Heat losses to hotbox environment based on radiation only, no heat loss by

convection or conduction in gas supply piping

Electric

- Joule heating due to electrical current is small. This heat source is neglected in the

model.

- No in-plane voltage difference within interconnector. Each calculation cell of one

SOFC is polarized uniformly.

4.1.3 Calculation domains

Real processes in SOCs are a combination of fluid transport, heat transfer, electron transfer

and electrochemistry. In order to bring the coupled problem in a numerically computable

form, a subdivision of calculation tasks according to Figure 4.1 is chosen. The

electrochemical complex of porous anode structure with its TPB sites, electrolyte’s oxygen

ion flux and cathode are simplified into the computational domain Cell, where the overall

electrochemical process is modeled.

Figure 4.1: Schematic diagram of calculation scheme for SOEC /SOFC simulations

UDFheat

source

UDFchem

source

H2 H2O

Air

yH2

yH2O

computitionalmesh cell

Tcell

UDFchem

sourceyO2

,

O

O2

Laminar flow

Diffusion

Electro-chemistry- activation- ohmic

Solid interconnector(el. current)

Reality Fluent Modell

Diffusion

Ni-mesh

AnodeElectrolyte

Cathode

Fuel

Inter-connector

Air

Fuel

Inter-connector i

Cell i

Air

Inter-connectori+1

volumetric reactions

Thread

Inter-connector


44

Diffusion processes, as in the contacting grid and porous electrodes are incorporated into

this calculation domain based on diffusion overpotentials. The FLUENT model realizes

electrochemical calculations within the Cell domain based on a user defined function

(UDF_heatsource). This function was developed within this thesis based on the approach

described in chapter 4.2.2. Cell temperature Tcell in the calculation domain as well as gas

concentrations yi in neighboring fluid domains serve as input variables, while the user

controlled cell operation voltage as exogenous parameter. UDF_heatsource calculates the

corresponding Nernst voltage 𝑉𝑛, current density 𝑖 and heat production density of the

corresponding finite volume.

In order to account for species conversion (e.g. H2 to H2O) due to electrochemical reaction,

the FLUENT model applies further user defined functions in the Fuel and Air domains. These

functions (UDF_chemsource) access current density in the neighboring volume in the Cell

domain and use the information to calculate mass source / sinks of the corresponding

species participating in the electrochemical reaction.

In consequence, it is necessary for the developed UDF_functions to access variables of

calculation volumes in neighboring threads (e.g. a volume from Cell must access variable

from neighboring volume in Fuel). As displayed in Figure 4.2, an iterative forwarding process

based on wall-shadow/wall relations within the calculation mesh realizes this data access

(see [ANSYS2012] for details). Some Cell volumes are not in direct vicinity to gas domains,

but to interconnector ribs in order to represent correctly the thermal contacting situation

within the model (Figure 4.2 right). A two-step redirecting process allows the participation of

those volumes to the electrochemical calculation, as (not modeled) electrode diffusion in

reality transports gases there.

Figure 4.2: Schematic of accessing variables in neighboring calculation threads

4.1.4 Discretization and mesh generation

Discretization is based on a finite volume method. Mesh generation for all geometries under

research applies dedicated software, i.e. ANSYS meshing.

Due to the user defined functions that realize electrochemical calculations it is necessary to

provide a well-structured mesh in order to allow assessment of heat production and mass

sources correctly. Therefore, geometry close to the experimentally used geometry has been

cell i cell k

cell z

thread cell

threadfuel

wall

shadowwall

cell i cell k

cell z

thread cell

threadinter-connector

wall shadowwall

cell w

wall

threadfuel

Numerical model of the solid oxide cell stack

45

modeled, that is however based on regular distance that allow a perfectly quad structured

mesh. Figure 4.3 shows an example of such a mesh for an excerpt of a 2-cell short stack. The

stack is divided into relevant cell zones that correspond to physical domains such as air, fuel,

interconnector and cell.

Cell sizing was chosen in order to keep calculation time for short stacks moderate in order to

allow parameter analysis to a certain degree. Typically for short-stack simulations, mesh

sizes between 200 000 and 600 000 elements are applied. The uniformly used quad shape of

the elements leads to very high mesh quality regarding orthogonal quality, skewness,

Jacobian ratio and warping. However, due to thin structures resented in the model (e.g. SOC

thickness of 0.15 mm, as according to the cells used in experiments) aspect ratio of the cells

ranges up to 10. In order to keep calculation effort reasonable, this was considered

acceptable. Grid independency tests were executed prior to calculation and showed only

small deviations when improving aspect ratios.

Figure 4.3: Small excerpt of SOC stack meshing of a 2-cell shortstack. Different colors / arrows indicate cell threads that are separated by split walls and may be attributed thermal contact resistances

4.2 Numerical model of the solid oxide cell stack

4.2.1 Governing equations

The modeling of gas flows in fluid zones applies the conservation laws of mass, momentum

and energy of incompressible laminar flows. For a finite volume dV the following

fundamental equations apply under stationary conditions 𝜕 𝜕𝑡 =⁄ 0 :

Continuity

Mass of all chemical species is conserved in fluid domains, with respect to changes in

composition due to electrochemical reactions and fuel internal reaction.

SOC cell

sealing

air

fuelHP- interconnectorcasing

HP interior

contactribs

air in

airout

fuelout fuel

in


46

∇(𝜌𝑗 𝒖) = 𝑆𝑚,𝑗+𝑅𝑗 (4.1)

𝑆𝑚,𝑗 is a mass gain of a chemical species j. In order to model electrochemical reaction mass

gains 𝑆𝑚,𝑗 are placed into the fuel or air domain and account for creation of reactions’

products and consumption of reactions’ educts corresponding to current density i.

Equivalently, fuel internal reactions are treated via the net rate of species production 𝑅𝑗 .

Momentum

(𝜌 𝒖 ∙ ∇)𝒖 + ∇𝑝 − ∇ ∙ 𝜏 = 0 (4.2)

Momentum conservation applies to fluid domains. No gravimetrical or external forces to

fluids are considered. The overall pressure drop of fluids through the stack is an important

result of viscous forces ∇ ∙ 𝜏. Density 𝜌 results from mole fractions 𝑦𝑗 in the gas by

𝜌 = ∑ 𝑦𝑗𝑗 𝜌𝑗.

Energy

For fluid domains energy conservation states as

∇ ∙ [𝒖(𝜌 ℎ + 𝑝)] − ∇ ∙ (𝑘∇𝑇) = 𝑆ℎ,𝑖 (4.3)

𝑆ℎ,𝑖 is a volumetric heat source due to a chemical reaction i, such as methane steam

reforming (SR) or water gas shift (WGS). Kinetic energies of gas streams as well as energy

transfer due to viscous dissipation and species diffusion are neglected. ℎ describes the

enthalpy of the gas as a mass weighted (mass fraction 𝑤𝑗) sum of its species composition

ℎ = ∑ 𝑤𝑗𝑗 ℎ𝑗 .

For solid domains this simplifies to

−∇ ∙ (𝑘∇𝑇) = 𝑆ℎ,𝑒𝑐 (4.4)

as only conduction appears as heat transport vector. 𝑆ℎ,𝑒𝑐 is a volumetric heat source to

account for heat of reaction of the electrochemical reaction within the SOC cell.

4.2.2 Electrochemical

The electrochemical model relates cell voltage to current density, cell temperature, and

cathode and anode species concentration. Therefrom, electrical energy consumption and

heat balance of the cell can be derived.


47

In order to model electrochemical reactions, i.e. oxygen ion transport between fuel and air

electrode through the ion conduction electrolyte, solely hydrogen oxidation and steam

electrolysis as the reverse process are taken into account.

𝐻2 + 1 2⁄ 𝑂2 ↔ 𝐻2𝑂(𝑔) 𝛥𝐻𝑅 = − 241.8 kJ/mol (4.5)

In case of carbon containing fuel such as methane or carbon monoxide containing syngas

from methane reforming, no direct electrochemical conversion of the species CO, CO2 or CH4

are considered. Direct electrochemical conversion of larger hydrocarbons however is low

compared to hydrogen conversion ([Park2000], [Mogensen2003]) and therefore methane’s

overall direct contribution is neglectable. Only at fuel inlet regions, where hydrogen fraction

is low, electrochemical activity may be underestimated, however with little consequence

due to low temperature levels.

Furthermore, due to the homogenous gas reactions in the fuel domain (SR and WGS) as

described in chapter 4.2.4, water gas shift reaction is particularly fast and can thus be

supposed close to equilibrium.

[Hauth2011] showed that Nernst potential in a gas mixture in equilibrium composition is

equivalent for every oxidation reaction under consideration, since only the gradient of

oxygen partial pressure between electrodes is of importance.

𝑉𝑁 = −𝛥𝑅𝐺(𝑇, 𝑝0, 𝑝𝑖)

𝑛𝑒𝑙𝐹= 𝑅𝑇

4𝐹∙ ln (

𝑝𝑂2𝑎𝑛𝑜𝑑𝑒

𝑝𝑂2𝑐𝑎𝑡ℎ𝑜𝑑𝑒) (4.6)

In consequence, hydrogen oxidation reaction provides the same Nernst voltage 𝑉𝑁 as carbon

monoxide oxidation in a gas mixture in equilibrium.

𝑉𝑁 = −𝛥𝑅𝐺0

𝐻2(𝑇)

𝑧𝐻2𝑒𝑙 𝐹

−𝑅𝑇

𝑧𝐻2𝑒𝑙 𝐹

ln (𝑝𝐻20 ∙ 𝑝0

0.5

𝑝𝐻2 ∙ 𝑝𝑂20.5)

𝑉𝑁 = −𝛥𝑅𝐺0

𝐶𝑂(𝑇)

𝑧𝐶𝑂𝑒𝑙 𝐹

−𝑅𝑇

𝑧𝐶𝑂𝑒𝑙 𝐹

ln (𝑝𝐶𝑂2 ∙ 𝑝0

0.5

𝑝𝐶𝑂 ∙ 𝑝𝑂20.5)

(4.7)

The cell potential 𝑉𝑐𝑒𝑙𝑙 is assumed constant throughout one solid oxide cell, due to very low

electric resistances in metallic interconnectors. It can be expressed as the local Nernst

voltage of cell 𝑉𝑁′ , depending on local species concentrations, decreased (SOFC) or increased

(SOEC) by irreversible losses due to the electric current during operation such as ohmic

losses in the electrolyte as well as activation (𝜂𝑎𝑐𝑡) and concentration overpotentials 𝜂𝑐𝑜𝑛𝑐 in

the electrodes:

𝑉𝑐𝑒𝑙𝑙 = 𝑉𝑁′ − (𝑅𝑜ℎ𝑚𝑖 + 𝜂𝑎𝑐𝑡

𝑎𝑛 + 𝜂𝑎𝑐𝑡𝑐𝑎𝑡 + 𝜂𝑐𝑜𝑛𝑐

𝑐𝑎𝑡 + 𝜂𝑐𝑜𝑛𝑐𝑎𝑛 ) (4.8)

As described above solely Nernst voltage of hydrogen oxidation is considered for

determining cell potential. Based on thermochemical databases [Chase1998] this work uses


48

temperature depending Gibbs reaction enthalpy 𝛥𝑅𝐺0(𝑇) of hydrogen oxidation

approximated to:

𝛥𝑅𝐺0(𝑇) = 245996𝐽

𝑚𝑜𝑙− 53.853

𝐽

𝑚𝑜𝑙 𝐾 ∙ 𝑇 (4.9)

Estimation of cell electrical resistance

Total cell losses 𝜂𝑡𝑜𝑡 are approximated from detailed individual cell losses in order to receive

temperature depending area specific resistance 𝐴𝑆𝑅(𝑇) as a linear approximation. This

seem justified since measured iV-curves of used ESC cells [Kerafol2010] are linear showing a

small influence of activation losses due to high temperatures as well as concentration losses

only at very high current densities (electrolyte supported cells with thin anode structure).

𝜂𝑡𝑜𝑡 = 𝑅𝑜ℎ𝑚(𝑇) 𝑖 + 𝜂𝑎𝑐𝑡𝑎𝑛 (𝑇, 𝑖) + 𝜂𝑎𝑐𝑡

𝑐𝑎𝑡(𝑇, 𝑖) + 𝜂𝑐𝑜𝑛𝑐𝑐𝑎𝑡 (𝑇, 𝑖) + 𝜂𝑐𝑜𝑛𝑐

𝑎𝑛 (𝑇, 𝑖) (4.10)

⇔𝜂𝑡𝑜𝑡 ≈ 𝐴𝑆𝑅(𝑇) ∙ 𝑖 (4.11)

It was shown that syngas, e.g. from pre-steam-reformed methane fuel, SOFC performance is

similar to humidified H2 operation [Hanna2014]. Therefore, area specific resistance (ASR)

values describing for cell performance are considered equivalent for hydrogen and syngas

both obtained from pre-reforming or cell internal steam reforming.

For the individual components the total ohmic resistance of the solid structure of the cell is

taken as a serial combination of resistance of electrodes and electrolyte. Resistance of

interconnects are assumed to be negligible

𝑅𝑜ℎ𝑚(𝑇) = 𝛿𝑎𝑛

𝜎𝑎𝑛+

𝛿𝑒

𝜎𝑒(𝑇) +

𝛿𝑐𝑎𝑡

𝜎𝑐𝑎𝑡+ 𝑅𝑐𝑜𝑛𝑡𝑎𝑐𝑡 (4.12)

As a main contribution herein, temperature depending conductivity values 𝜎𝑒(𝑇) for the

described 10ScSZ electrolyte for the ESC cells from Kerafol with thickness 𝛿𝑒 have been

obtained from [Haering2005; Singhal2003] and estimated by the approach

𝜎𝑒(𝑇) = 223𝑆

𝑐𝑚∙ exp (

8.371 𝐾⁄

𝑇) (4.13)

Ohmic resistances of electrodes are neglected due to their small layer thickness in ESC cells.

Electrical contact resistances in stack depend largely on detailed stack design and contacting

regime. According to [Guan2011] it may vary between 1.43 and 0.19 Ohm cm-2 depending

on the contacting regime. Therefore, it has to be experimentally adapted according to real

stack behavior.


49

The activation overpotential describes the voltage losses of a SOC due to kinetic limitations

of the electrode reactions. These losses can be described by applying the Butler-Volmer

equation, which relates activation overpotentials to current densities with the help of the

factors of exchange current density for anode and cathode respectively.

𝑖 = 𝑖0,𝑎𝑛 [exp (𝛽𝑧𝑒𝑙𝐹 𝜂𝑎𝑐𝑡

𝑎𝑛

𝑅𝑇)−exp((𝛽 − 1)

𝑧𝑒𝑙𝐹 𝜂𝑎𝑐𝑡𝑎𝑛

𝑅𝑇)] (4.14)

where 𝑖0,𝑎𝑛 is the exchange current density and 𝛽 a charge transfer coefficient commonly

approximated to 0.5 [Chan2001].

The Butler-Volmer equation can be converted by the use of a widely accepted simplifying

approach [Zhao2011]:

𝜂𝑎𝑐𝑡𝑎𝑛 =

2𝑅𝑇

𝑧𝑒𝑙𝐹sinh-1 (

𝑖

2𝑖0𝑎𝑛) (4.15)

which leads to the simplified Tafel approximation that is however only valid for high current

densities:

𝜂𝑎𝑐𝑡𝑎𝑛 =

2𝑅𝑇

𝑧𝑒𝑙𝐹𝑙𝑛 (

𝑖

𝑖0𝑎𝑛) (4.16)

For the anode and cathode electrodes, exchange current densities 𝑖0 depend on

temperatures and activation energies according to the Arrhenius law with a pre-exponential

factor.

𝑖0𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒 =

𝑅𝑇

2𝐹𝑘𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒 exp(

−𝐸𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒

𝑅𝑇) (4.17)

Table 4.2. Input Parameters to electrochemical model

model input parameters value source

Pre-exponential factor 𝑘𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒 𝑘𝑎𝑛 = 6.54 ∙ 1011 A V−1 m−2

𝑘𝑐𝑎𝑡 = 2.35 ∙ 1011 A V−1 m−2

[Udagawa2007]

Activation energy 𝐸𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒 𝐸𝑎𝑛 = 1.4 ∙ 105 J mol−1

𝐸𝑐𝑎𝑡 = 1.37 ∙ 105 J mol−1

[Udagawa2007]

Conductivity electrolyte 𝜎𝑒(𝑇) = 223 S cm−2 ∙ exp (

8.37

𝑇/𝐾)

[Haering2005;

Singhal2003]

Effective diffusivity 𝐷𝑒𝑓𝑓𝑎𝑛 = 1.0 ∙ 10−5 m s−2 [Laurencin2011;

Udagawa2007]


50

Further potential losses occur during cell operation due to the restriction of mass transport

by diffusion within the electrodes. The actual potentials to be used in Nernst equation to

determine the cell potential are those at the three phase boundary (TPB) within the

electrode 𝑝𝑇𝑃𝐵. Since Nernst potential computes using the gas concentrations within the

flow channel 𝑝𝑖∞, a correction has to be executed by introducing the anode concentration

overpotential (cathode accordingly):

𝑝𝐻2𝑇𝑃𝐵 = 𝑝𝐻2

∞ −𝑅𝑇𝛿𝑎𝑛

𝑧𝑒𝑙𝐹 𝐷𝑒𝑓𝑓𝑎𝑛 ∙ 𝑖

𝑝𝐻2𝑂𝑇𝑃𝐵 = 𝑝𝐻2𝑂

∞ +𝑅𝑇𝛿𝑎𝑛

𝑧𝑒𝑙𝐹 𝐷𝑒𝑓𝑓𝑎𝑛 ∙ 𝑖

(4.18)

𝜂𝑐𝑜𝑛𝑐𝑎𝑛 =

𝑅𝑇

𝐹ln (𝑝𝐻2𝑇𝑃𝐵 ∙ 𝑝𝐻2𝑂

∞

𝑝𝐻2∞ ∙ 𝑝𝐻2𝑂

𝑇𝑃𝐵 ) (4.19)

Concentration levels at three phase boundary can be obtained via effective diffusion

coefficients of the electrode 𝐷𝑎𝑛𝑒𝑓𝑓

[Laurencin2011]. Cathode overpotential 𝜂𝑐𝑜𝑛𝑐𝑐𝑎𝑡 is neglected

assuming O2 pressure within TPB near free flow concentration [Udagawa2007].

In a final step the area specific resistance (ASR, equation (4.11)) is estimated applying a last

square fit to an exponential function in order to improve calculation speed for 3D-stack

models. For the given parameter set cell polarization results to:

𝐴𝑆𝑅 (𝑇) = 124.765 Ωm² ∙ exp(−0.00696 1 𝐾⁄ ∙ 𝑇) (4.20)

Figure 4.3 show exemplary polarization curves of SOC cells according to above described

model and the linear approximation via ASR calculation. Since activation losses are more

important at reduced temperatures, linear approximation is less precise and results in non-

negligible impreciseness. For temperatures above 800°C however, linear approximation

seems to be justified for electrolyte-supported cells, as considered in this model.

For real stack applications this ASR of mere cell has to be increased by an additional

electrical contact resistance, due to non-ideal contacting between electrodes and

interconnector.


51

Figure 4.4: Calculated polarization curves for ESC cells, and linear approximation based on ASR

4.2.3 Species transfer

The model, which the user defined function is based on, assumes solely hydrogen / steam

taking part within the electrochemical reaction with stoichiometric coefficients 𝛾𝑖 and the

surface area specific reaction rate 𝑟𝐻2.

𝛾𝐻2𝐻2 + 𝛾𝑂2𝑂2 𝑟𝐻2 → 𝛾𝐻2𝑂𝐻2𝑂 (4.21)

Reaction rate of electrochemical hydrogen conversion 𝑟𝐻2 is proportional to local current

density.

𝑟𝐻2 =𝑖

2𝐹 (4.22)

Contributions of carbon containing fuel (e.g. mainly CO/CH4) are neglected for

electrochemical considerations. This is justified by rather low direct electrochemical

conversion speeds of CH4 and a fast WGS reaction at operation temperature bringing CO/H2

and CO2/H2O almost instantly into equilibrium. Electrochemical conversion 𝐶𝑂,𝑒𝑙 is thus

indirectly modeled by an additional electrochemical conversion of hydrogen and a

subsequent shift reaction rate 𝐶𝑂,𝑊𝐺𝑆 .

𝑟𝐻2 = 𝐻2,𝑒𝑙 + 𝐶𝑂,𝑒𝑙 (4.23)

𝐶𝑂,𝑒𝑙 = 𝐶𝑂,𝑊𝐺𝑆

with

0.4

0.6

0.8

1

1.2

1.4

-1 -0.5 0 0.5 1

Vce

ll/

V

current density i / A cm-2

y = 124.76505e-0.00696x

R² = 0.99606

0

0.2

0.4

0.6

0.8

1

1.2

600 800 1000 1200

ASR

/ V

A-1

cm²

T / °C

full model

linear approx.

SOFC

SOEC


52

𝐶𝑂 +1

2𝑂2

𝐶𝑂,𝑒𝑙 → 𝐶𝑂2 (4.24)

𝐶𝑂 + 𝐻2𝑂 𝐶𝑂,𝑊𝐺𝑆 → 𝐻2 + 𝐶𝑂2 (4.25)

The finite volume model computes volumetric species mass sources of the electrochemical

reaction for each volume 𝛿𝑉 of a cell with contact area 𝛿𝐴 to the SOC in a specific fluid

domain.

𝑆𝑚,𝑗 = 𝑟𝐻2 𝛾𝑗 𝑀𝑗𝛿𝑉

𝛿𝐴 , 𝑗 ∈ [𝐻2, 𝑂2, 𝐻2𝑂] (4.26)

4.2.4 Methane steam reforming

Since methane steam reforming reaction is a major cause of stack internal temperature

gradients, the model includes the corresponding homogenous gas reactions (SR and WGS).

Steam reforming reaction (SR) is implemented as a forward only volumetric gas reaction

with reaction rate 𝑟𝐶𝐻4. A power law expression, derived from data fitting can describe the

reactions rate as a function of kinetic constant 𝑘𝑆𝑅 and the partial pressures of the relevant

species i (CH4, H2O, H2, CO)

𝑟𝑆𝑅 = 𝑘𝑆𝑅 ∙∏𝑝 𝑖𝛼𝑖

𝑖

(4.27)

The reaction rate constant is computed using the Arrhenius expression

𝑘𝑆𝑅 = 𝑘𝑆𝑅0 exp (−𝐸𝑆𝑅

𝑎 𝑅𝑇)⁄ (4.28)

where 𝑘0 is pre-exponential factor and 𝐸𝑎 the activation energy of the reaction.

Water gas shift reaction however is implemented as reversible reaction with forward and

backward reaction rates to tend towards equilibrium concentration. Forward reaction rate

𝑘𝑊𝐺𝑆𝑓

computes similar to equation (4.28), while backward reaction 𝑘𝑊𝐺𝑆𝑏 is obtained from

𝑘𝑊𝐺𝑆𝑏 =

𝑘𝑊𝐺𝑆𝑓

𝐾𝑊𝐺𝑆 (4.29)

where 𝐾𝑊𝑆𝐺 is the equilibrium constant of water gas shift reaction. In consequence, in

equilibrium, i.e. 𝐾𝑊𝑆𝐺 = 1, forward and backward reaction counterbalance themselfes.

Table 4.3 shows parameters used in this work to implement steam reforming kinetics. Water

gas shift reaction constant is set considerably faster than SR, in order to bring WGS close to

equilibrium, as described in literature.


53

Table 4.3. Input parameters to homogenous gas reactions in anode flow channels for methane steam reforming and water gas shift reaction on SOFC anodes, adapted from [Mogensen2011], [Ahmed2000]

reaction parameter value

SR Arrhenius rate

- Pre-exponential factor 𝑘𝑆𝑅0

- Activation energy 𝐸𝑆𝑅𝑎

85 420 kmol s-1 m-³

95 kJ mol-1

Rate exponent

- CH4

- H2O

- CO

- CH4

0.85

-0.35

0

0

WGS Arrhenius rate

- Pre-exponential factor 𝑘𝑤𝑠𝑔0

- Activation energy 𝐸𝑤𝑠𝑔𝑎

1 ∙ 107 kmol s-1 m-³

95 kJ mol-1

Rate exponent of all reactants 1

4.2.5 Heat production

The steady-state thermal balance of the solid oxide cell considers internal heat sources /

sinks due to electrochemical and homogenous gas reactions as well as heat transfer

between solid structures and gas streams.

The heat sources 𝑆ℎ,𝑒𝑐 are assumed within the solid cell structure and they depend on local

thermodynamic and electrochemical boundary conditions:

𝑆ℎ,𝑒𝑐 =𝑖

2𝐹∆𝑅𝐻 − 𝑖𝑉𝑐𝑒𝑙𝑙 (4.30)

For fuel cell operation, 𝑆ℎ,𝑒𝑐 is always exothermal, in SOEC 𝑆ℎ,𝑒𝑐 positive (below

thermoneutral cell voltage), 0 or negative (above thermoneutral cell voltage). Heat of

electrochemical reaction 𝛥𝑅𝐻(𝑇) is obtained by

𝛥𝑅𝐻(𝑇) = −(240425J

mol− 7.0476

J

mol K ∙ 𝑇) (4.31)

Heat release by methane steam reforming 𝑆ℎ,𝑆𝑅 occurs directly in fuel gas flows and is

𝑆ℎ,𝑆𝑅 = 𝑟𝑆𝑅 ∆𝑅𝐻𝑆𝑅 (4.32)

where Δ𝑅𝐻𝑆𝑅 is specific reaction enthalpy of the steam reforming reaction.

The subsequent water gas shift reaction is treated accordingly.


54

𝑆ℎ,𝑊𝐺𝑆 = (𝑟𝑊𝐺𝑆𝑓

− 𝑟𝑊𝐺𝑆𝑏 )∆𝑅𝐻𝑊𝐺𝑆 (4.33)

4.2.6 Heat transfer

Heat pipe modeling

The heat pipe interconnector is modeled based on a subdivision into two parts (compare

Figure 4.3). Heat pipe casing is represented by a standard interconnector material (Crofer

22H or CFY). The second part is the HP interior, that models with very high heat conductivity

(𝑘𝐻𝑃 = 15000 𝑊𝑚−1𝐾−1) , thus very small internal temperature gradients. This

assumption bases on experimental results in chapter 5.3. Additionally, assuming that the

heat pipe operates within its working limits and no performance reduction is prevailing. Heat

pipe internal pressure drops and thus saturation temperature differences are considered

neglectable.

Heat transfer from the isothermal inner part to the heat pipe casing is model based on a

heat transfer approach displayed in Figure 4.5 [VDI2006]. For the heat transfer within casing

the thermal resistance of capillary structure is considered.

Figure 4.5: Thermal resistance representation of heat transfer in planar heat pipe (left: detailed, right: as modeled in this work)

Effective heat conductivities of liquid saturated capillary structures calculate according to

[Zohuri2011] to

Wire screen: 𝑐𝑎𝑝 = 𝑘′ [(𝑘′+ 𝑘𝑤𝑖𝑟𝑒)− (1− )(𝑘′− 𝑘𝑤𝑖𝑟𝑒)]

𝑘′+ 𝑘𝑤𝑖𝑟𝑒+ (1− )(𝑘′− 𝑘𝑤𝑖𝑟𝑒) (4.34)

Grooves: 𝑐𝑎𝑝 = (𝑘′ 𝑘𝑐𝑎𝑠𝑒𝑠𝐴𝑅ℎ𝐴𝑅)+ 𝑏𝐴𝑅𝑘

′ (0,185 𝑠𝐴𝑅𝑘𝑐𝑎𝑠𝑒+ ℎ𝐴𝑅𝑘′)

(𝑠𝐴𝑅+ 𝑏𝐴𝑅)(0,185 𝑠𝐴𝑅𝑘𝑐𝑎𝑠𝑒+ ℎ 𝑘′) (4.35)

Heatsource

Heat sink

𝑅𝑐𝑎𝑝𝑒𝑣𝑎𝑝

𝑅𝑐𝑎𝑝𝑒𝑣𝑎𝑝

𝑅𝑐𝑎𝑠𝑒𝑒𝑣𝑎𝑝 𝑅𝑐𝑎𝑠𝑒

𝑎𝑑 𝑅𝑐𝑎𝑠𝑒𝑒𝑣𝑎𝑝

𝑅𝑐𝑎𝑝𝑎𝑑 𝑅𝑐𝑎𝑝

𝑒𝑣𝑎𝑝𝑅𝑐𝑎𝑝𝑒𝑣𝑎𝑝

𝑅𝑝𝑐𝑒𝑣𝑎𝑝

𝑅𝑣𝑎𝑝𝑎𝑑 𝑅𝑝𝑐

𝑒𝑣𝑎𝑝

𝑅c se 𝑅c se

𝑅c 𝑅c

𝑇𝑒𝑣𝑎𝑝 𝑇𝑐𝑜𝑛𝑑

𝑇𝑎𝑑vapourspace

capillary

casing


55

Porous Structures: 𝑐𝑎𝑝 = 𝑘′ [(2𝑘′ + 𝑘𝑏𝑢𝑙𝑘)+ 2 (1− )(𝑘′− 𝑘𝑏𝑢𝑙𝑘)]

(2 𝑘′+ 𝑘𝑏𝑢𝑙𝑘)+ (1− )(𝑘′− 𝑘𝑏𝑢𝑙𝑘) (4.36)

𝑘′ represents the conductivity of the liquid working fluid while 𝑘𝑏𝑢𝑙𝑘 describes the solid

capillary structure with volumetric porosity 휀.

Heat transfer through the cell planes

Heat transfer to the stack environment is, apart from sensible gas flows, restricted to

radiation heat exchange to predefined environment with a mean radiant temperature 𝑇∞

and global emissivity 1. Average emissivity of the stack’s external surface is approximated to

0.9 [VDI2006].

Stack internal heat transfer bases on heat transfer by conduction in bulk materials,

convection in gas flows and radiation in gas channels.

Heat transfer perpendicular to fuel cell planes happens as a serial / parallel connection of

individual resistances of each heat transfer pathway. The heat transfer resistance of an

entire repeating unit of the stack 𝑅𝑟𝑢 can thereby be obtained by adding up the individual

contributions of serial and parallel thermal resistances 𝑅𝑖𝑠 and 𝑅𝑖,𝑗

𝑝 :

This combination of resistances may be considered to be made of three basic types:

conduction in solid material as well as contact conduction, convection in the gas channels

and thermal radiation, as depicted in Figure 4.6.

Figure 4.6: Left: schematic representation of heat transfer mechanisms perpendicular to cell plane in SOFC stacks; right: Representation with thermal resistances, colored according to relative contribution for a typical stack situation at 800°C (see Table 6.5)

cell

interconnectorcathode

radiativeheattransfer

conduction in contact ribs

thermal contactresistance

convect. heat

transfer

Ni-mesh

interconnectoranode

relative resistance

Rc2

Rc4

Rc4

Rc1

Rc3

𝑅𝑟𝑢 =∑[𝑅𝑖𝑠 + (∑

1

𝑅𝑖,𝑗𝑝

𝑗

)

−1

]

𝑖

=Δ𝑇

𝑡𝑟𝑎𝑛𝑠 (4.37)


56

Conduction in solids can be described applying Fourier’s law and in consequence thermal

resistance of conduction can be expressed as:

with s, the length of conduction pathway, 𝐴𝑐𝑜𝑛𝑑, the cross section, and k, the thermal

conductivity of the corresponding material. Typical thermal conductivity values for materials

used for stack construction can be found in Table 4.4.

Table 4.4: Thermal conductivity of typical stack materials

Material Thermal conductivity /

(W m-1 K-1)

Source

Stainless steel 1.4541 AISI 321 14.79 + 0.0145 ∙ 𝑇[𝐾] [Touloukian1972]

Crofer 22H 16.90 + 0.0091 ∙ 𝑇[𝐾] [ThyssenKrupp2010]

Plansee CFY (through plane) 34.84 + 0.0045 ∙ 𝑇[𝐾] [Plansee2015]

YSZ (8 mol%) 1.71 + 2.2 ∙ 10−4 ∙ 𝑇[𝐾] [Limarga2012;

Schlichting2001]

Ni-YSZ 3.74 + 9.3 ∙ 10−4 ∙ 𝑇[𝐾] [Uhlenbruck]

LSM 3 [Ki2010]

Mica Thermiculite 866 / 866LS 0.19 [Hoyes2013]

Glass sealing (Keraglas ST K02) 0.85 + 5.1 ∙ 10−4 ∙ 𝑇[𝐾] [Samal2015]

Nickel (< 600 K) 121 − 9.6 ∙ 10−2 ∙ 𝑇[𝐾] [Touloukian1972]

(> 600 K) 53.4 + 2.0 ∙ 10−2 ∙ 𝑇[𝐾] [Touloukian1972]

Thermal conductivity of wire screen mesh in z-direction (perpendicular to screen plane) is a

more complex material property and the objective of many previous experimental and

theoretical investigations [Alexander1972; Chang1990; Hsu1996; Koh1973; Li2006;

Madhusudana1996]. Mainly mesh properties and wire contact areas have to be considered.

For this study, an empirical approach for the effective thermal conductivity based on

[Alexander1972; Li2006] has been used:

Volumetric porosity 휀 of the screen mesh can be obtained from [Marcus1972]:

M represents the mesh number, d mesh diameter and S a crimping factor that can be

assumed to 1.05 [Li2006].

Convective heat transfer resistance is described by

𝑅𝑐𝑜𝑛𝑑 =𝑠

𝑘 ∙ 𝐴𝑐𝑜𝑛𝑑 (4.38)

𝑘𝑒𝑓𝑓 = 𝑘𝑓𝑙𝑢𝑖𝑑(𝑘𝑠𝑜𝑙𝑖𝑑 𝑘𝑓𝑙𝑢𝑖𝑑⁄ )(1− )0.59

(4.39)

휀 = 1 − 𝜋𝑆𝑀𝑑/4 (4.40)


57

with the heat transfer coefficient ℎ𝑐𝑜𝑛𝑣 and the relevant surface area 𝐴𝑐𝑜𝑛𝑣.

Radiative transfer resistance is generally described as

where 𝑟𝑎𝑑 denotes heat transfer by radiation over a temperature difference Δ𝑇.

Approximating emissivity of oxidized stainless steel surface to 1 and assuming small

temperature differences Δ𝑇, linearization can be applied to radiation heat transfer:

where 𝜖𝑆𝑂𝐹𝐶 denotes the emissivity of the corresponding electrode of the SOFC and 𝐴𝑟𝑎𝑑 the

relevant radiative surface. Complex radiation geometries requiring view factor calculation

are simplified to standard heat exchange situation between infinite surfaces with view

factors of 1.

Therefore, a highly temperature depending approximation for radiation heat transfer

resistance 𝑅𝑟𝑎𝑑 can be obtained by

4.2.7 Thermal contact resistance

To describe thermal conduction, contact joints such as the contact interface between

interconnector and Ni-mesh (𝑅𝑐1), Ni-mesh and anode electrode of the SOFC (𝑅𝑐2) as well as

cathode and the interconnector (𝑅𝑐3) play a major role. This is confirmed by a relative

evaluation of individual contributions for a typical SOFC set-up at 800°C, according to Figure

4.6 (already including the results of this work). Contact resistances restrict heat conduction

through the stack, being the main contributor ahead to heat convection and radiation.

Contact resistances vary in a very large range depending on materials, surface treatments,

applied compression forces and temperature range. Because of roughness and unevenness,

the contact between the surfaces of two solids exists only in few points

[Madhusudana1996]. Even in a relatively good contact with some compression force, the

actual contact area is only 1 to 2%. Thus, analytical approaches to compute the contact

resistance are complex and require detailed knowledge of the contact interface. According

𝑅𝑐𝑜𝑛𝑣 =1

ℎ𝑐𝑜𝑛𝑣 ∙ 𝐴𝑐𝑜𝑛𝑣 (4.41)

𝑅𝑟𝑎𝑑 =Δ𝑇

𝑟𝑎𝑑 (4.42)

𝑟𝑎𝑑 = 𝜎 ∙ 𝜖𝑆𝑂𝐹𝐶 ∙ 𝐴𝑟𝑎𝑑[(𝑇 + Δ𝑇)4 − 𝑇4] ≈ 4 𝜎 ∙ 𝜖𝑆𝑂𝐹𝐶 ∙ 𝐴𝑟𝑎𝑑 𝑇

3 ∙ Δ𝑇 (4.43)

𝑅𝑟𝑎𝑑(𝑇) =1

4 𝜎 ∙ 𝜖𝑆𝑂𝐹𝐶 ∙ 𝐴𝑟𝑎𝑑 𝑇3 (4.44)


58

to [Madhusudana1996] for an aluminum – stainless steel contact in vacuum e.g. the heat

transfer resistance may vary from 626 W m-2 K-1 up to 690 kW m-2 K-1 by varying center line

average (CLA) roughness from 1 µm to 0.1 µm and contact pressure from 0.1 to 100 MPa at

ambient temperature. Surface roughness, pressure [Sadowski2010; Singhal2005] and

temperature [Wahid2004] have thus an important influence that can hardly be determined

analytically. Therefore, an experimental evaluation is required in particular to determine the

contact resistance between the various materials and geometries that appear within an

SOFC stack situation. Various authors [Liu2015; Madhusudana1996; Wang2012] present an

approach on how to access contact information based on a heat transfer measurement set-

up.

In consequence, combined with the analytic calculation of other heat transfer phenomena

this work performs an experimental study (results in chapter 6) to determine the heat

transfer and values for the contact resistance between individual stack components, such as

the interfaces between interconnector and Ni-mesh, Ni-mesh and anode, cathode and

interconnector as well as between interconnector and sealing.

4.3 Conclusions

This chapter described the set-up of a full stack SOFC / SOEC model for CFD simulation in

order to examine effects of planar heat pipe integration to stack structure. In order to

account for relevant influences the model is capable of accounting for coupled flow,

electrochemical and thermal transfer effects within the stack structure. As heat pipe

integration is particularly promising for situations with direct internal methane steam

reforming, the corresponding volumetric chemical gas reactions and relevant kinetics are

included into the set-up. Heat pipes are modeled following the basic approach of

representation by a high conductance solid. However, for this assumption to be justified the

heat pipes have to operate within their performance limits.

The experimental section in the upcoming chapters provides necessary data to determine

heat pipe working limits, to tune boundary conditions and to determine thermal contact

resistances for heat conduction through the stack. Based on these results, the calibrated

model is capable of performing the desired stack layout for planar heat pipe integration.

59

Chapter 5

5. Development of planar heat pipe interconnectors

5.1 Design and layout of planar liquid metal heat pipes

In order to approach the objective of producing planar high temperature heat pipes for the

incorporation into SOC interconnectors a screening of realized concepts for planar low

temperature applications and standard high temperature has been performed (chapter

3.4.1). Based on the results of the state-of-the-art research and the project targets, main

design criteria for planar high temperature heat pipes for the use in SOFC applications are

defined as:

- operation at typical SOC temperatures (650°C – 900°C) and in stack gas environment

(contact to anode/ cathode gases)

- adaptability of wick and casing concept to interconnector structure (interconnector

material, conductivity, sealing concept)

- horizontal operation at relevant heat transfer rates: bidirectional and two

dimensional heat transfer possible

- low casing material use thus low heat pipe thickness

- easy manufacturing / low manufacturing costs

Parts of the results described in this chapter can also be found in [Dillig2014].

5.1.1 Selection of working fluid

The typical SOFC operation temperature ranges from 650°C to 900°C depending on the

electrolyte material and thickness i.e. support design (from metal supported or anode

supported cells to electrolyte supported cells). In this temperature range mainly alkali metals

are of interest as heat pipe working fluids. They are nontoxic, unlike mercury or cadmium,

and suitable for contact with stainless steel casings at operation temperature, contrarily to

zinc (Zn), magnesium (Mg) or Lithium (Li). As displayed in Figure 5.1 mainly sodium (Na),

potassium (K) and NaK, an alloy of both mentioned metals, lie in the temperature and

pressure limits of planar interconnectors for SOC. Rubidium (Rb) and caesium (Cs) are also of

potential interest but are rather rare, high pricey metals. Handling these materials demands

high caution due to their strong reaction with ambient air.

Chapter 5: Development of planar heat pipe interconnectors

60

Alkali metal properties are obtained from [Ohse1985] and vapor pressures of sodium used in

this work are approximated by

𝑝𝑠𝑎𝑡(𝑇[°𝐶]) = (2.84 ∙ 106 𝑇4 − 4.73 ∙ 103 𝑇3 + 2.68 𝑇2 − 511.09 𝑇) 𝑃𝑎 (5.1)

Upper working pressure of the planar heat pipe is limited to maximum ambient pressure in

order to avoid bulging of the structure. However, if the design of the planar heat pipe

assures resistance to bulging, e.g. due to internal casing interconnections, absolute working

pressures above 1 bar are permissible up to total strength of the structure. There is no

definitive lower operating pressure limit but with decreasing internal pressures two

performance limiting effects increase. Firstly, lower pressure results in lower vapor density,

thus increasing vapor speeds, and finally the reach of sonic limitation of the heat pipe

transfer power. Secondly, inert non-condensable gases being always present inside the heat

pipe in a certain amount occupy large parts of the inner volume at very low pressures. This

leads to increasing inactive zones and to a strong deactivation at low pressures.

Experimental results in chapter 5.3 hereunder show, that for thin planar interconnectors

approximately 0.1 bar as lower pressure limit seems to be reasonable. Therefore, the

operation range of sodium can be approximated to 670°C to 875°C equivalent, thus, to

almost the entire operation range of typical solid oxide cells.

As mentioned above the heat transfer performance of a working fluid can be roughly

evaluated with the merit number Me

Figure 5.1: Vapor pressure of different alkali metals suitable as heat pipe working fluid (data according to [Reay2006], [Ohse1985] and [Anderson1993]) and typical SOFC operation ranges for metal supported cells (MSC), anode supported cells (ASC) and electrolyte supported cells (ESC) as to [Tucker2010]

0

0.5

1

1.5

2

500 600 700 800 900 1000

Vap

or

pre

ssu

re /

bar

Temperature / °C

NaNaKeutK

Hg

Li

pmax

pmin

ESC

ASC

MSC

Cs

possible workingfluid states in planar heat pipes

Design and layout of planar liquid metal heat pipes

61

𝑀𝑒 =𝛾′ Δℎ𝑒𝑣𝑎𝑝 𝜌

′

𝜂′

(5.2)

that sets capillary forces (surface tension 𝛾′, evaporation enthalpy Δℎ𝑒𝑣𝑎𝑝 and density 𝜌′)

and liquid flow friction (dynamic viscosity 𝜌′) of the liquid in relation. The merit number of

sodium in the temperature range of 700 - 800°C is approximately constant at 2.1∙

1012 W/m², for potassium 3 times lower at 8 ∙ 1011 W/m² and eutectic NaK, an alloy of 67.5

mol% potassium and 32.5 mol% sodium approx. 9 ∙ 1011 W/m². Therefore, sodium is the

preferred working fluid for standard SOC operation temperature of planar heat pipes.

Only for intermediate temperature operation, e.g. below 700°C, or when increased

operation pressure is required to minimize non-condensable gas buffers, the use of

potassium or NaK comes into focus. Additionally, when looking at start-up behaviour a

particular interest has to be contributed to eutectic NaK (molar composition: 0.675 K, 0.325

Na) due to its very low melting point at -13°C [O'Donnel1989], hence being liquid at ambient

temperature. A detailed evaluation and discussion of start-up behavior can be found in

chapter 5.3.4. A strong drawback of NaK as working fluid however is the intrinsically non-

isothermal operation of the heat pipe due to the changing composition between evaporator

and condenser zone. Assuming rectification-like behaviour in the small vapor space of a

planar heat pipe leads to a separation of Na and K with Na in the evaporator and K

concentrated in the condenser part. In the extreme case of complete separation the

maximum temperature difference Δ𝑇𝐻𝑃,𝑚𝑎𝑥 can be obtained by the differences of the

saturation pressures

𝛥𝑇𝐻𝑃,𝑚𝑎𝑥 = 𝑇𝑠𝑎𝑡(𝑝𝐻𝑃, 𝑁𝑎) − 𝑇𝑠𝑎𝑡(𝑝𝐻𝑃, 𝐾)

(5.3)

For an evaporator operation at 850°C this maximum temperature difference results to be

approx. 120 K, i.e. relatively high if isothermal operation is the primary objective.

5.1.2 Capillary structure design

Based on the literature study and the state-of-the-art approaches for low temperature heat

pipes in chapter 3.4 several design concepts for planar heat spreaders have been developed

(see Figure 5.3). The main difference is based on the lay-out of the capillary structure that

provides the driving force to liquid phase flow and thus closing the heat pipe working cycle

by condensate return. Pure gravity driven condensate flow, so called thermal syphon, is not

considered due to a desired bi-directional operation and an optimal spreading of the

working fluid.

Capillary pressure is directly correlated to the characteristic size of the structure, the

capillary radius 𝑟𝑒𝑓𝑓,𝑚𝑖𝑛, liquid surface tension of the working fluid γ and contact angle Θ𝑐.


62

It can be expressed by an equivalent height ℎ𝑐𝑎𝑝 that a liquid rises against gravity.

𝑝𝑐𝑎𝑝 = 2γ′𝑐𝑜𝑠 Θ𝑐𝑟𝑒𝑓𝑓,𝑚𝑖𝑛

= 𝜌′𝑔ℎ𝑐𝑎𝑝 (5.4)

Table 5.1: Effective curvature radius of capillary structure according to [Chi1976]

structure 𝐫𝐞𝐟𝐟,𝐦𝐢𝐧 description

Wire screen mesh 1 2⁄ (𝑑𝑤 + 𝑤𝑚𝑒𝑠ℎ) 𝑑𝑤: wire diameter

𝑤𝑚𝑒𝑠ℎ: mesh width

Rectangular grooves 𝑤 w: channel width

Flat housing gap 𝑠𝑔𝑎𝑝 𝑠𝑔𝑎𝑝: housing gap width

Sintered structure 0.41 𝑟𝑐 𝑟𝑐: corn radius

The calculation of the effective capillary radius for the different designs under evaluation is

summarized in Table 5.1. The resulting capillary height for the experimentally studied

structures according to Table 5.3 differ considerably from approx. 1 m of the sintered metal

plates R35, to only approx. 1-2 cm of a coarse screen mesh with mesh size 8 (i.e. 8 meshes

per inch, with 𝑑𝑤 = 0.6 𝑚𝑚 and 𝑤𝑚𝑒𝑠ℎ = 2.5 𝑚𝑚), calculated for sodium at 800°C (Figure

5.2). These capillary heights give a first approximation of the maximum length that a heat

pipe could operate against gravity. Furthermore, one can conclude that the strong capillary

forces that apply for liquid metals, e.g. for sodium are over 3 times higher than those of

water. Therefore, even relatively coarse structures, as the Mesh 8 used as spacer for the

vapor channel, provoke capillary heights that are in the range of ten times of the structure

size. Consequently, a blocking of vapor channels is of particular danger for sodium as

working fluid and heat pipe design has to counteract. Fine capillary structures have to be in

contact with the coarse region to extract working fluid therefrom. Precise control of the fluid

inventory has to assure the filling of the fluid transport structure without surplus that may

block vapor flows.

For alkali metal, in particular sodium, the wetting angle on metal surfaces is assumed

constant and close to zero, as in consequence cos Θc can be assumed to 1 for all cases

(compare Table 5.1).

Table 5.2: Typical wetting angles of alkali metals

Contact Temperature range Wetting angle Reference

Na – Ni 99.2 520 – 720°C 4.9° – 5.4° [Bader1977]

Na – 304 L 520 – 720°C 1.7° – 2.4° [Bader1977]

Na – W 99.95 520 – 720°C 1.5° – 2.5° [Bader1977]


63

Figure 5.2: Capillary heights in porous structures under evaluation for planar heat pipes, calculated for typical working fluids (Na, K, NaK) at 800°C and low temperature fluids (H2O, NH3) at 20°C for comparison

Based on the design criteria originating from working fluid choice several concepts for thin

planar heat spreaders have been developed for experimental evaluation. Figure 5.3

summarizes these concepts that characterize as follows:

- Design A applies several layers of woven wire screen mesh as capillary structure and

metal spacer to keep the vapor volume open. The structures are spot welded into the

casing before closing

- Design B: thin rectangular grooves are machined into the casing to provide the

capillary forces. The grooves can be unidirectional or bi-directional, in order to allow

real 2-dimensional heat transfer with in the planar heat pipe. The vapor channel is

supported against ambient pressure by machined spacing elements.

- Design C uses several layers of fine screen mesh with high mesh numbers as wick for

liquid transport sandwiched with coarse wire screen mesh as spacers. In this case

mesh size of the coarse mesh has to be sufficiently large to be low capillary active

and thus to avoid a blocking of the vapor flow by condensate droplets in this region.

All layers are spot welded onto the casing structure.

1.00

10.00

100.00

1000.00

0.00 0.10 0.20 0.30 0.40 0.50

cap

illar

y h

eigh

t /

mm

0.50 1.00 1.50 2.00

capillary radius / mm

Sinter-metal R35


64

- Design D: Capillary is provided due to thin gaps between casing structures. Fluid

transfer is only possible in predefined directions. Spacer structure and vapor

channels are directly machined into the casing.

- Design E: Sintered metal powders or metal foams of different pore size serve as

capillary structure. Vapor channels may be machined into casing or into sintered

structure directly. Improved manufacturing processes may provide the sintering

directly onto the casing.

Figure 5.3: Design concepts (A-E) for planar high temperature heat spreaders

Applying the above presented design concepts a variety of planar heat pipe prototypes has

been manufactured for evaluation purposes. These prototypes sized in dimensions with 200

x 120 mm² or 270 x 200 mm² and thickness depending on the internal capillary structure

between 2 and 6 mm. Due to their pure conceptual evaluation purpose, the heat pipes

possess no gas flow channels or gas manifoldings, as necessary for final SOFC applications.

The evaluation applied mainly casings fabricated from standard high temperature steel,

1.4841 [Deutsche Edelstahlwerke2008], as for its basic similarity to SOFC steels.

Compatibility to CROFER 22 H [ThyssenKrupp2010] as the target interconnector material was

demonstrated thereafter. Table 5.3 provides an excerpt of the fabricated planar heat pipe

prototypes with details on the applied capillary structure. For woven screen meshes the

number of individual layers and the corresponding mesh number (mesh per inch) is

specified. Figure 5.4 displays an SEM image of the capillary structure of prototype 270-12,

design C with a screen mesh with mesh number 187 based on Ni-wire (described in Table

5.5.)

heat pipe housing

wick mesh

spacer

heat pipe housing

grooves

heat pipe housing

wick mesh

coarse mesh

A) Screen mesh as wickstructure separated byspacing elements

B) Rectangular grooves withvapor space seperators

C) Sandwich design withfine screen mesh layersas and coarse mesh asvapor space separator

D) Small flat housing gap asplanar capillary structure

E) Porous medium as wickstructure

heat pipe housing

porous structureheat pipe housing

spacer

Capillary for Na-transport


65

Table 5.3: Excerpt of the fabricated planar heat pipe prototypes for design concept evaluation (further prototypes listed in Table 5.5)

HP

ID Type Size [mm] Capillary structure

Wick

/casing

material

Na inventory

design / real

[g]

3 A 200 x 120 x 6 |3 Mesh 70 (Köper)| 1.4841

/1.4841 9.0 / 10

4 A 200 x 120 x 6 |3 Mesh 78| 1.4841

/1.4841 9.7 / 10

6 A 200 x 120 x 6 |3 Mesh 98| 1.4841

/1.4841 8.4 / 10

9 A 200 x 120 x 4 |1 Mesh 98| 1.4841

/1.4841 2.8 / 3.3

10 A 200 x 120 x 4 |2 Mesh 98| 1.4841

/1.4841 5.6 / 6.5

7 B 200 x 120 x 6 Grooves, w =500 µm, t=500 µm, - / 1.4841 9.0 / 10

8 C 200 x 120 x 4 |2 Mesh 98|Mesh 8|2 Mesh 98| 1.4841

/1.4841 8.1 / 10

12 D 200 x 120 x 5 Gap distance 0.15mm, width = 4 mm - / 1.4841 1.4 / 3.2 13 D 200 x 120 x 5 Gap distance 0.15mm, width = 4 mm - / 1.4841 2 / 3.2

11 E 200 x 120 x 6 Sintered meshing (GKN SIKA FIL 5)

105x185x2, 휀 = 0,6975 1.4841 25 / 15

14 E 200 x 120 x 6 Porous sinter structure (Plansee A30Ni), grain size up to 50 µm,

105x185x1.5 mm, 휀 = approx. 0.5

Tungsten / 1.4841

9.9 / 10

15 E 200 x 120 x 6 Porous sinter plate 105 x 185 x 3 mm

R35 pore size: 35 µm, 휀 = 42.4 %

1.4541 / 1.4841

15.1 / 18.7

16 E 200 x 120 x 4 Nickel foam 105 x 185 x 2 mm,

Pore size: 450 µm Ni /

1.4841 17.6 / 21.4

Figure 5.4: SEM-image of Design C, prototype 270 – 12. Left: view on capillary structure, right: cross section of casing with spot-welded screen mesh.

100 µm 100 µm


66

Figure 5.5: Prototypes for design concepts (A-E) of planar high temperature heat spreaders

5.2 Manufacturing and filling procedure of planar heat pipes

5.2.1 Heat pipe fabrication and cleaning

High temperature stainless steel, in this study 1.4841 and 1.4541, serves as casing and wick

material for first tests, while for the desired SOC applications tailor made SOFC - materials, in

particular CROFER 22 H or Plansee CFY, are on focus and are tested separately.

The casing of the described planar heat pipes with screen meshes or other capillary structure

consists of two single steel sheets in an original thickness of 1-3 mm. Depending on design

concepts, milled profiles provide the vapor transport during operation or serve as pocket for

the insertion of the capillary structure to guarantee the transport of liquid. Prior to milling

procedure the steel sheets are annealed for at least 2 hours at 650°C in a high temperature

furnace, with heating / cooling rates below 10 K/min, in order to reduce stress that results

from sheet fabrication. Thereafter, pocket milling can be performed on a standard machine

set-up without the risk of heavy warping.

After milling, the casing receives the capillary structure according to design A – E, which is

spot-welded to the casing in order to assure good contact. Tungsten Inert-Gas welding joins

two plates together and adds two capillary stainless steel pipes (d = 3 – 4 mm) that are

necessary for filling procedure. Welding has to apply low current densities and work with

caution in order to keep warping low and assure planarity of the metal sheets.

heat pipe housing

wick mesh

spacer

a) Screen mesh layers as wick

structure separated by

spacing elements

heat pipe housing

b) Rectangular axial grooves

with vapour space separators

heat pipe housing

wick mesh

coarse mesh

c) Sandwich design with fine

screen mesh layers as wick

and coarse mesh as vapour

space separator

heat pipe housing

spacer


d) Small flat housing gap as

planar capillary structure

heat pipe housing

porous structure

e) Porous medium as wick

structure

f) Prototype sandwich design

A) Screen mesh as wickstructure separated byspacing elements

B) Rectangular grooves withvapor space seperators

C) Sandwich design withfine screen mesh layersas and coarse mesh asvapor space separator

D) Small flat housing gap asplanar capillary structure

E) Porous medium as wickstructure

Manufacturing and filling procedure of planar heat pipes

67

Improved welding concepts, such as laser-welding have been experimentally tried but did

not show improved results regarding stability and gas tightness, without detailed design and

process optimization. For mass manufacturing however, this and diffusion welding

[Gerken1965; Welcon2005] are very promising technologies, that could substantially

improve welding quality and/or costs. Furthermore, a direct fabrication by rapid-

prototyping procedures, such as direct metal laser sintering [Pham1998], could combine

casing, gas flow field manufacturing and capillary structure preparation to only one

fabrication step, providing a large potential for manufacturing optimization.

Prior to filling the heat pipe with sodium, the manufactured prototype has to be cleaned to

ensure wetting of the walls and the mesh with liquid as well as for guaranteeing that no

impurities lower the performance of the heat pipe. The cleaning routine proposed by Dunn

[Reay2006] is slightly modified to adapt it to the existing materials and methods and has

proven its utility in several tests. First, the heat pipe is washed internally with deionized

water. After that the heat pipe is filled with 15 wt% hydrochloric acid and put for 30 minutes

in an ultrasonic bath at 50°C to support the cleaning process. After the heat pipe is rinsed

again with deionized water and the operation with HCl is repeated in the ultrasonic bath for

30 minutes. This process is carried out as well with acetone. After the last rinse cycle the

heat pipe is dried for 10 hours in an oven to remove all water and acetone residues and

make the heat pipe ready for the filling process.

Table 5.4: Planar heat pipe cleaning procedure

Step Duration

Rinse with demineralized water -

Ultrasonic bath (HP filled with HCl 15%) 30 min


Ultrasonic bath (HP filled with HCl 15%) 30 min


Ultrasonic bath (HP filled with Aceton) 30 min


Dry in drying oven at 120°C 10 h

5.2.2 Filling procedure

The required amount of working fluid inventory is calculated from free volume in the

capillary structures (e.g. from porosity 휀) and an additional filling factor, by default chosen

to 1 for planar heat pipe that offer very low vapor space.

The filling process is operated in a glove box that is first filled with pure inert gas (Ar or N2) to

form an oxygen free atmosphere in order to prevent oxidation of the bare sodium. Electric


68

heating blocks enclose the heat pipe as well as the filling cone in order to provide a sufficient

heat supply for a liquid filling procedure. The heat pipe interior is swept with inert gas.

Vacuum packed sodium (Dr. Bilger Umweltconsulting, purity 99.9%) is opened in the glove

box, cut into required amounts and filled piecewise into the filling cone, placed on one of the

filling capillaries of the planar heat pipe. After heating the pure sodium over its melting point

(e.g. > 97.8°C for sodium at atmospheric conditions) the metal begins to melt and can be

carefully pressed into the heat pipe with pressured inert gas (Figure 5.7, left) by opening the

needle valve with caution. The filling pipe is crimped to be gas tight in the glove box and

sealed afterwards by a TIG weld point, whereas the venting pipe stays open for the following

evaporation process and is sealed only by closing the venting pipe’s built-in valve. Due to the

small filling pipe diameter and small amount of solid Na2O-slag remaining from the oxidized

Na-pellets, the sodium content could not always be ideally controlled during filling.

Weighting of the filled heat pipes determined filling deviations as displayed in Table 5.3.

Figure 5.6: Left: Heat pipe filling set-up, mounted in glovebox. Right: Heat pipe evacuation set-up for heat pipe degassing and activation

Before activating and subsequent closing of the heat pipe, outgassing is a mandatory step,

since wick and casing material heated under vacuum during heat pipe operation release

dissolved gases (mainly H2 and N2). If not being removed before closing the heat pipe, these

gases form a non-condensable gas buffer, deactivating parts of the condensing zone of the

heat pipe. This negative effect is of particular concern for planar high temperature heat

pipes, since casing-to-volume-ratio is high and operation pressures are rather low (i.e. below

atmospheric pressure).

N2

TIR

Exhaust

Trace heating > 150°C

TI

Na (l)

Planar Heat Pipe

Mounted in glove box for

inert environment

N2

Exhaust

Planar Heat Pipe

Mounted high temperature insulation

Filling pipe closed by weld point

PIR

TIR

ceramic heaters

vaccum pump

vaccum control

crimp anvil

TIR

7 TCs on HP-surface

Manufacturing and filling procedure of planar heat pipes

69

The outgassing and activation takes place in an insulated environment where the heat pipe

placed in thermosyphon position can be heated up to operation temperature by the heating

elements on its bottom (Figure 5.7, right). Thermocouples (14 x type K) placed on the HP

casing indicate temperature distribution and thus activation status of the planar heat pipe. A

vacuum pump (Oerlikon Leybold S 1.5) providing a hand valve controllable vacuum pressure

is connected to the venting pipe of the heat pipe. Steadily ramping power (approx. 10 K/min)

heats the heat pipe gradually (1) until typical heat pipe operation temperature is reached

(typically 800°C for sodium) as displayed in Figure 5.7. The inside pressure is kept above

saturation pressure for occurring temperature at approx. 0.7 bar by constantly evacuating in

order to prevent gases from entering the heat pipe. After reaching target temperature, this

status stays constant for 60 min to allow degassing of inert gases dissolved in working fluid,

wick and casing material (2). Results of [Moraw1986] and [Ishikawa2003] indicate that at

elevated temperatures outgassing follows an exponential behavior and rather short

outgassing is necessary. Longer outgassing seems recommendable, especially for long-term

heat pipe operation at low operation pressure levels.

After this outgassing hold, the operating pressure is carefully further decreased by closing

successively the air valve in the connection line to the vacuum pump until the pressure

reaches the boiling curve of the working fluid (3). The reach of saturation line can be

observed by slightly dropping temperatures in the evaporator zone due to flash-boiling and a

growth of isothermal temperature profile towards the top of the heat pipe. Once saturation

line is reached at desired pressure level and temperature, the heating power is increased

stepwise, resulting in a gradual enlargement of the isothermal zone (4). This procedure

continues until all temperature-measuring points show isothermal condition, i.e. all inert

gases left the set-up and a pure sodium vapor liquid equilibrium is reached within the heat

pipe. The venting pipe now is to be closed, first by vacuum tight crimping and after complete

cooling (5) by a TIG weld point.

Figure 5.7: Planar heat pipe degassing and activation procedure in the sodium phase diagram

temperature ramp10 K/min

0

0.2

0.4

0.6

0.8

1

1.2

500 600 700 800 900 1000

Vap

ou

rp

ress

ure

/ b

ar

Heat pipe temperature / °C

Naliq

(1)

pamb

outgassing hold

heating power increase untilcompleteactivation

(2)

(4)

(3)

(5)

temperaturedecreaseafter closingthe heat pipe

pressurereductionuntil flash

Navap


70

5.3 Performance testing of planar heat pipes

5.3.1 Experimental set-up

For heat transfer rate measurements and performance tests of a flat heat pipe the

experimental set-up shown in Figure 5.8 has been designed. The heat pipe is bedded in

microporous high temperature insulation, type WDS High from Porextherm (thermal

conductivity below 0.06 W m-1 K-1 at 800°C) of 100 mm thickness. Planar ceramic heating

elements (glow igniters from Bach RC GmbH (8 x 230 W) or Taiwan KLC Cooperation (5 x

600W)) provide high temperature heat from a planar, relatively isothermal surface within

the heating zone of 50 - 70 mm length at one end of the heat pipe. The width of the heating

zone can be controlled by manually connecting different numbers of heating elements

enabling 2-D heat transfer experiments. Power input to the heater is controlled via pulse-

duration modulated solid state relays. Due to relatively high frequent switching the heating

power can be assumed continuous. Divided by an adiabatic zone in the central part of the

heat pipes an air cooler is placed on the opposite side to remove the transmitted heat.

Internal structure and air guidance of the cooler is optimized to provide an isothermal heat

sink over the width of the heat pipe. A mass flow controller (MFC) controls the inlet air flow

and thus the cooling power (accuracy: +/- 0.008 𝑎𝑖𝑟).

Figure 5.8: Experimental set-up of planar heat pipe performance measurements (side view).

Two K-type thermocouples (+/- 1.5 K) measure air temperatures at the inlet and outlet and

thus a cooling power measurement is established. 2D-temperature distribution of the heat

pipe is recorded via 14 K-type thermocouples (+/- 0.0075 |𝑡|) located on top of the heat pipe

housing (for distribution of thermocouples see Figure 5.9). The entire arrangement is slightly

pressed between the upper and lower insulation layers in order to provide good contact of

thermocouples and to bring heat pipe and cooling / heating surfaces in touch. This structure

can be rotated to adapt heat pipe tilt angle 𝜙 between -90° (against gravity operation), 0°

(horizontal operation) and 90° (gravity assisted operation). The tilt angle is measured with an

electronic spirit level with an accuracy of 1°. The experimental set-up is fully automated by a

programmable logic controller (PLC) that allows continuous data logging.

contactscooler

insulation

planar heatpipe

ceramic heatersair cooler

positions of thermocouples

90°

0°

- 90°

φ

Performance testing of planar heat pipes

71

Figure 5.9: Distribution of heat pipe zones (evaporator, adiabatic, condenser) and thermocouples in planar heat pipe test rig for HP270 measurements (top view).

For the performance evaluation experiments, heat pipe isothermal temperature THP was

kept constant controlled by a PID controller acting on the ceramic heater elements. The

actual temperature of the planar heat pipe is detected by averaging thermocouples TC 6,

TC 7, TC 8, TC 12, TC 13 and TC 14, which lie in the isothermal zone of the heat pipe and are

not subject to evaporator overheating or condenser cool out in the described experiments.

To protect the heat pipe from bulging or casing failure, i.e. internal overpressure over

ambient pressure, a temperature increase of any thermocouple above the temperature limit

of 870°C stops heater operation.

Figure 5.10: Distribution of heat pipe zones (evaporator, adiabatic, condenser) and thermocouples in planar heat pipe test rig for HP270 measurements.


72

5.3.2 Experimental procedure

The experimental investigation focuses on heat transfer power measurements and the

evaluation of corresponding temperature profiles. Since heating elements have to be cooled

in order to prevent overheating of metal contacts and due to other parasitic heat losses

through insulation, power supply to the heater cannot be taken as evaluation parameter.

Hence, cooler power is taken as heat pipe power measurement after being corrected by the

experimentally determined parasitic heat flow into the cooler 𝑝𝑎𝑟 via the insulation and the

heat losses to the environment 𝑙𝑜𝑠𝑠. Cooler power is obtained by air mass flow and

enthalpy difference between inlet and outlet conditions.

𝐻𝑃 = 𝑐𝑜𝑜𝑙 − 𝑝𝑎𝑟 + 𝑙𝑜𝑠𝑠 = 𝑎𝑖𝑟[ℎ(𝑇1) − ℎ(𝑇2)] − 𝑝𝑎𝑟 + 𝑙𝑜𝑠𝑠 (5.5)

The parasitic and loss heat flux is estimated to

𝑝𝑎𝑟 = 0.03 𝑊 𝐾−1 ∙ (𝑇ℎ𝑒𝑎𝑡𝑒𝑟 − 𝑇𝑐𝑜𝑜𝑙𝑒𝑟) (5.6)

𝑙𝑜𝑠𝑠 = 0.01 𝑊 𝐾−1 ∙ (𝑇𝐻𝑃 − 𝑇𝑎𝑚𝑏) (5.7

Based on the given accuracies errors for heat transfer rates are estimated to approx. +/- 2 %,

for heat pipe temperatures to +/- 6 K (thermocouples type K, class 2) and for thermocouple

positioning to +/- 5 mm. Error bars have been exemplarily calculated for Figure 5.11.

Temperatures are measured on the upper side of the heat pipe where only heat extraction

due to heat losses occurs and temperature drop within capillary structure and heat pipe

casing can be estimated to 0 K. Thus, the recorded temperature profiles are assumed to

represent adiabatic temperatures 𝑇𝑎𝑑. According to the applied modelling approaches in

Figure 4.5 (compare [VDI2006]) these temperature have to be corrected by wall and capillary

resistances 𝑅𝑐𝑎𝑠𝑒 and 𝑅𝑐𝑎𝑝 in order to obtain heat pipe temperature drop 𝑇𝑒𝑣𝑎𝑝 − 𝑇𝑐𝑜𝑛𝑑.

Therefrom, heat pipe resistance 𝑅𝐻𝑃 and equivalent heat conductivity 𝐻𝑃 may result.

𝑅𝐻𝑃 =𝑇𝑒𝑣𝑎𝑝 − 𝑇𝑐𝑜𝑛𝑑

𝐻𝑃=

𝑙

𝐻𝑃 𝐴 (5.8)

𝑇𝑒𝑣𝑎𝑝 = 𝑇𝑎𝑑 + 𝐻𝑃 𝑠𝑐𝑎𝑠𝑒𝑘𝑐𝑎𝑠𝑒 𝐴𝑒𝑣𝑎𝑝

+𝐻𝑃 𝑠𝑐𝑎𝑝

𝑐𝑎𝑝 𝐴𝑒𝑣𝑎𝑝 (5.9)

𝑇𝑐𝑜𝑛𝑑 = 𝑇𝑎𝑑 − 𝐻𝑃 𝑠𝑐𝑎𝑠𝑒𝑘𝑐𝑎𝑠𝑒 𝐴𝑐𝑜𝑛𝑑

−𝐻𝑃 𝑠𝑐𝑎𝑝

𝑐𝑎𝑝 𝐴𝑐𝑜𝑛𝑑 (5.10)

Experimental data of heat pipe performance measurements has been obtained with a

systematic procedure. The heat pipe was placed in starting position (according to Figure 5.9)


73

and was heated until isothermal operation under zero cooling load conditions. Subsequently,

cooling load (via air flow), heating power (via pulse duration) or operation angle - depending

on control regime - was stepwise increased awaiting each time the reach of a steady state

operation, i.e. constant heat transfer rates and temperatures. Heat pipes duty was

iteratively increased until heat transfer limitation of the heat pipe was reached.

Dry-out as indicator for heat pipe performance

In this work, and in accordance to literature [Lefèvre2012; Reay2006; Wang2011], the

prototype heat pipes are considered to reach power limitation when an evaporator dry out

or burn out is detected.

Figure 5.11: Temperature recordings (above image) and temperature profiles (down) of HP270-9 in horizontal operation under stepwise increasing cooling load until dry-out of evaporator

power

Co

olin

gp

ow

er /

W

T 5

dry-out

partial dry-out20 K

0

50

100

150

200

250

830

835

840

845

850

855

860

865

870

875

880

2400 3400 4400 5400

Tem

per

atu

re /

°C

Time / s

T6 [°C] T7 [°C]T8 [°C] T9 [°C]T10 [°C] T18 [°C]

800

810

820

830

840

850

860

870

880

0 50 100 150 200 250

Tem

per

atu

re /

C

Position / mm

2360 s 3000 s 4300 s

5000 s 5500 s 5820 s

heater adiabatic cooler

dry out


74

According to chapter 3.4 this effect occurs due to the inability of the capillary structure to

transport sufficient heat transfer liquid back to the evaporator. Due to the lack of

evaporative cooling a rapid rise of evaporator temperatures in comparison to isothermal

heat pipe temperature indicates this dry-out. Figure 5.11 shows the exemplary behavior of

HP270 – 9 at 850°C heat pipe temperature under increasing cooling loads. The planar heat

pipe remains very isothermal - temperatures differing only by a few Kelvin - for cooling loads

up to 209 W. For 209 W a light overheating of the evaporator occurs, that however stays

below 10 K. This is caused by a local or partial dry out of a small area of the evaporator and is

not considered a power limitation yet. When further increasing cooling load, a very rapid

increase of evaporator temperature (T5) can be observed while other temperatures stay

constant. It is assumed, that any increase over 20 K above isothermal heat pipe temperature

THP is thus an indication for a complete dry-out and the reaching of a power limitation. The

maximum heat transfer without reaching evaporator dry-out is considered maximum heat

pipe duty, causing some inaccuracy due to step sizing.

A second approach to evaluate heat pipe performance and to determine capillary limitation

bases on variation of the heat pipe tilt angle. Here, due to rotation of the entire set-up the

relative orientation of evaporator / condenser and gravity varies under constant cooling

loads. While orientation in gravity field has no influence on other heat pipe operation

parameters, there is a strong influence on internal pressure balance of the heat pipe, where

∆𝑝𝑐𝑎𝑝,𝑚𝑎𝑥 ≥ ∆𝑝𝑙 + ∆𝑝𝑣 + ∆𝑝𝑔𝑟𝑎𝑣 (𝜙) (5.11)

is the condition for isothermal operation.

Figure 5.12: Temperature profiles of HP270-8 at varying tilt angles and constant cooling flows (2 sm³h-1 ( = 370 W) at 0° slightly decreasing with tilt angle to 310 W at -90°)

500

550

600

650

700

750

800

850

900

0 50 100 150 200 250

Tem

per

atu

re /

C

Position / mm

90 ° 50 ° 0 °

-50 ° -80 ° -90 °

dry out

cool out



75

Gravity pressure loss ∆𝑝𝑔𝑟𝑎𝑣 (𝜙) increases with higher heat pipe tilts whereas ∆𝑝𝑙 and ∆𝑝𝑣

pressures losses due to liquid and vapor flow, and ∆𝑝𝑐𝑎𝑝,𝑚𝑎𝑥 representing the driving

capillary pressure stay constant. In consequence, an overheating of the evaporator can be

directly assigned to reaching capillary limitation of the heat pipe.

Figure 5.12 shows HP270-8 for changing tilt angles under constant cooling air flow of

2 sm³h-1 (equivalent to 370 W at 0°, slightly decreasing with increased tilt). At -80° to -90° tilt

against gravity a dry out of evaporator can be observed by a sudden rise of T5 temperature

and loss of isothermal condition.

Cool-out due to excess working fluid in condenser

Figure 5.12 equally shows a temperature decrease in the condenser section of the heat pipe.

A drop of temperatures happens at the condenser when further increasing the tilt angle.

This so-called cool out has been described by [Marshburn1973] and is explained by

increasing amounts of working fluid accumulating in the condenser end, that inhibits

condensation of the vapor in this area followed by a lack of condensation heat or blocks heat

transport through heat pipe walls (compare Figure 5.13). According to [Reay2006] this effect

is of particular importance in heat pipes of low diameters and thus also in flat heat pipes

where only a very small vapor space volume exists and a certain amount of excess working

fluid is chosen. It may be avoided by reducing the amount of working fluid in the heat pipes,

as well as by decreasing wick pore radius in order to provide higher capillary force to keep

the entire wick saturated. The occurrence of the cool-out with increased tilt angles without

observing evaporator overheating is not considered a heat pipe performance limitation,

whereas it clearly increases temperature drop over the heat pipe and therefore may be a

limiting factor for certain heat pipe applications. For performance measurement it has to be

considered though, since condenser temperatures decrease and thus air cooler power

lowers for increased tilt angles.

Figure 5.13: Cool-out of planar heat pipes (adapted from [Hoogeboom2014])

evaporatorend

working fluid

g


76

‘Cold finger’ due to non-condensable gases

A similar temperature profile effect as the cool-out described above is caused by the

presence of non-condensable gases after heat pipe activation and closure. Due to the

constant working fluid vapor flow towards condenser section of the heat pipe all non-

condensable gases are transported towards the condenser end. The accumulation of these

gases creates a gas buffer that prevents working fluid from entering and condensing in this

area. In consequence, no condensation heat is released and temperatures decrease. This

effect is often referenced as ‘cold finger’, due to the subcooled part at the condenser end.

Assuming ideal gas behavior, being justified by the high temperature and moderate pressure

levels, the size of this inactive zone can be calculated depending on non-condensable gas

amounts 𝑛𝑛𝑐 𝑔𝑎𝑠 and open vapor cross section 𝐴𝑜𝑐𝑠 to

𝑙𝑖𝑛𝑎𝑐𝑡 =𝑅 𝑇𝐻𝑃 𝑛𝑛𝑐 𝑔𝑎𝑠

𝑝𝑠𝑎𝑡(𝑇𝐻𝑃) 𝐴𝑜𝑐𝑠 (5.12)

Figure 5.14 shows the typical behavior of this non-condensable gas buffer with variation of

the heat pipe temperature. With increasing operation temperatures and thus increasing

internal pressures, the gas buffer is compressed and occupies less vapor space. Saturation

pressure of sodium increases from 0.04 bar at 600°C to 0.47 bar at 800°C explaining the

observed decrease of inert gas zone by a factor of approximately 6 in this temperature

range.

Figure 5.14: HP 4 in horizontal position (𝜙 = 0°) with increased heating power and constant air coolant flow, showing a reduction of the non-condensable gas zone at the end of the cooler section for increased internal pressure levels.

heater adiabat cooler

200

300

400

500

600

700

800

0 50 100 150 200

Tem

per

atu

re /

C

Position / mm

159 W 233 W

298 W 368 W

439 W 502 W

569 W 628 W

675 W

measuredactive length

theory


77

Using temperature profiles of Figure 5.14 and heat pipe geometry, a non-condensable gas

amount of approx. 6.0 ∙ 10−6 mol can be assumed for HP4. In comparison to the sodium

inventory of 9.6 g, i.e. 0.42 mol, this gas amount is very low, but still shows an important

influence on heat pipe operation. Deviations from theory (i.e. equation (5.12)), observed for

low temperatures, can be explained by the extension of the gas buffer into the adiabatic

zone, where effects on temperature profiles are less developed.

A low temperature operation of the planar heat pipes (< 650°C) therefore seems to be

acceptable only if adequate excess space for non-condensable gases is provided, while for

operation points close to atmospheric pressure the problem can be handled with slight over

dimensioning of heat pipe area. Improving the filling procedure, i.e. better steel and sodium

degassing of dissolved gases and advanced heat pipe closing techniques might additionally

reduce the amount of non-condensable gases in order to even avoid excess space in the

condenser zone. A more detailed discussion of the non-condensable gas buffers arising from

hydrogen permeation is presented in chapter 5.4.

5.3.3 Performance measurement results

Evaluation of wick structures

A variety of heat pipe prototypes according to Table 5.3 was tested in the described

experimental procedure in order to evaluate capillary structure performance and to

determine suitable HP designs. Figure 5.15 shows exemplary heat transfer rates and

temperature profiles for several heat pipes and a dummy HP (manufactured of solid stainless

steel sheets without internal structure, 1.4841) for horizontal operation (heat pipe tilt angle

= 0° ).

Figure 5.15: Heat transfer rates and temperature profiles for exemplary prototypes in horizontal position (𝜙 = 0°) at maximum heat transfer before dry-out.


0

100

200

300

400

500

600

700

800

900

0 50 100 150 200

Tem

per

atu

re /

C

Position / mm

HP 4: 665 W

HP 8: 701 W

HP 16: 291 W

HP 12: 259 W

HP 7: 142 W

HP 15: 105 W

Dummy: 85 W

heat pipe housing

wick mesh

spacer

heat pipe housing

wick mesh

coarse mesh

Design C

heat pipe housing

porous structure

heat pipe housing

spacer


heat pipe housing

grooves

Design A

Design B

solidmaterial

Design E

Design D


78

It can be observed that HP prototypes with screen mesh wicks (design A, cross section 4 x

120 mm²) show isothermal operation even for high heat transfer rates up to 740 W,

representing axial heat transfer densities of over 100 W cm-² cross section. Compared to

typical stack operation conditions, with heat production rates in the order of 0.2 to

0.5 W cm-² cell area, the measured axial heat transfers are in the range of the required rate

to cool SOFC stacks with 1000 to 3000 cm² of cell area per heat pipe, i.e. in the range of 10

to 30 cells (100 cm²) per heat pipe. Hence, several cell layers can be cooled by a single heat

pipe interconnector, if heat transfer rates between stack layers are sufficiently high. Design

C (HP 8) as a sandwich of screen meshes with varying pore size that provide both capillary

and vapor structure showed equivalent behavior to design A prototypes. However, for too

small pore sizes of the vapor space screen mesh (HP 270 - 20, wick pore size 0.5 mm, not

displayed) no operating heat pipe could be manufactured, presumably due to a blocking of

the vapor flow.

Heat pipes with machined axial grooves or other casing integrated capillary structure show

poorer (HP 12) or almost no (HP 7) heat pipe effect in horizontal position. However, for

thermosiphon position (𝜙 > 0°) a better performance is observed. In addition, due to the

rather laborious manufacturing procedure of grooved structures, it is concluded that

applicability of design B and D for the planar heat pipe interconnectors in this work is

limited. Design D, after optimization, may result as a very promising design for mass

production of interconnectors by deep-drawing [Stelter2007].

Behavior of the exemplary porous structures applied in planar design E heat pipes is also

displayed in Figure 5.16.

Figure 5.16: Temperature profiles for exemplary design E prototypes HP 15 and HP 16 with differing tilt angle at approx. 100 W transferred power.

approx . 100 W

HP 15 HP 16


500

550

600

650

700

750

800

850

900

0 50 100 150 200

Tem

per

atu

re /

C

Position / mm

0 °

30 °

60 °

-30 °

0 50 100 150 200

Position / mm

0°

30°

60°

-30 °


approx . 100 W500 µm500 µm


79

Depending on porosity and pore sizes the capillary structures are able to create capillary

pressures, apart from Plansee A30Ni in HP14 where no heat pipe effect could be detected in

horizontal operating conditions (presumably due to an incomplete formation of open pores

in the sinter structure). HP15 and thus R35 sinter plates creates almost constant behavior

under varying tilt angles due to small pore radius and thus high capillary forces. It shows

almost ideal isothermal operation with temperature differences of only few K between

heater and cooler section. Maximum heat transfer is however limited to approx. 100 W, but

with almost constant operation even against gravity. The relatively large pore Nickel foam

(HP16) with pore sizes of approx. 450 µm shows low capillary pressure. Heat transfer under

horizontal conditions is hardly maintained and high thermosiphon tilts lead to rapid

formation of cool-out of the condenser zone. Operation against gravity (𝜙 < 0°) is hardly

possible.

Figure 5.17 gives an overview of the performance results of the evaluated design prototypes.

Design A and C prototypes, based on screen mesh as capillary structure clearly resulted to be

of highest performance with lowest temperature drops from evaporator to condenser.

Adding (calculated) temperature drops over the HP casing, one can conclude an effective

heat conductivity that reaches up to 18 000 W K-1m-1 for the best performing heat pipes.

Figure 5.17: Summary of wick structure analysis. Maximum measured heat transfer rates 𝐻𝑃,𝑚𝑎𝑥,

temperature drops Δ𝑇 and calculated temperature differences in HP casing. Lower

diagram indicates the resulting effective conductivities 𝐻𝑃 of the HP

Design A E

max

. hea

ttr

ansf

er/

W

-60

0

60

120

180

240

300

360

420

480

540

-100

0

100

200

300

400

500

600

700

800

900

tem

per

atu

red

rop

/ K

B C D

measured heattransfer limit

measured

at

in casing

HP

3

HP

4

HP

6

HP

9

HP

10

HP

12

HP

7

HP

8

HP

11

HP

13

HP

14

HP

15

HP

16

/ W

m-1

K-1

0

5000

10000

15000

20000effective conductivityof heat pipe


80

Heat transfer behavior was equally studied under asymmetrical heating conditions in the

heating zone (one side heated, other side unheated). It was concluded that isothermal

operation of the heat pipe can even be provided when 2-D heat transfer is necessary,

providing a remarkable advantage for planar heat pipes in SOFC stack applications.

Evaluation and optimisation of sandwich design (design C)

Design C prototypes showed the best performance behavior and simple capillary structure

manufacturing. Therefore, further investigations focused on this design approach. Several

prototypes with varying mesh size have been tested in order to evaluate and optimize

capillary and vapor space structures. Table 5.5 gives an excerpt of further studied design C

prototypes.

Table 5.5: Excerpt of the fabricated planar heat pipe prototypes for performance evaluation and optimization of design C

HP-ID Type Size [mm] Capillary structure

Wick

/casing

material

Na inventory

design / real

[g]

270-7 C 270 x 120 x 6 |2 Mesh 98|Mesh 8|2 Mesh 98| 1.4841

/1.4841 14.4 / 10


/1.4841 7.2 / 8.5

270-9 C 270 x 120 x 4 |3 Mesh 98|Mesh 8|3 Mesh 98| 1.4841 /1.4841

21.6 /10


/1.4841 9 / 10

270-12 C 270 x 120 x 4 |4 Mesh 187|Mesh 8|4 Mesh 187| Ni

/1.4841 12.1 / 10

270-13 C 270 x 120 x 4 |2 Mesh 187|Mesh 8|2 Mesh 187| Ni

/1.4841 6.1 / 8

270-20 C 270 x 120 x 2 |2 Mesh 187|Mesh40|2 Mesh187| Ni

/1.4841 12.1 / 10

The experimental performance evaluation is combined with a theoretical analysis of heat

pipe operation limits computed according to Table 3.4. Figure 5.18 displays simulated heat

transfer limitations for HP270-11, 12 and 13 due to gas viscosity (viscous limit), gas velocity

(sonic limit), gas-liquid-flow interactions (entrainment limit), wick properties (capillary limit)

and evaporation (boiling or burnout limit). [Bertele2013] describes the details of this

calculation. Circles indicate experimentally obtained operation points of the studied heat

pipes. The study demonstrates that calculated performance limits characterize well the real

heat pipe behavior in horizontal operation at varying temperatures. Mainly capillary

restrictions limit heat transfer capacities over a large range of temperatures. In

consequence, optimizing the capillary structure is still the first approach to improve


81

performance. Only at low temperatures below 650°C viscous limitation predominates, thus

being mainly important for start-up behavior.

Figure 5.18: Performance measurement of Design C prototypes with different capillary structures and computed heat transfer limits.

Remaining deviations of experimentally obtained heat transfer limits and theoretical values

are caused by simplifying assumption for liquid and vapor flow pressure drops as well as

uncertainties in determination of exact wick properties (e.g. permeability).

Figure 5.19 displays heat pipe behavior of the design C prototypes at varying tilt angles,

plotted versus the expected capillary limit. As predicted, thin structured HP270-12 and 13

mesh (mesh 187) creates stronger capillary height and thus allows improved performance

for against gravity operation. Coarse mesh structure (HP270-11), however raises less flow

resistance and allows better heat pipe performance in thermosiphon operation.

500 700 900

bournout limit

entrainment limit

sonic limitcapillary limit

measured heattransfer limit

viscous limit

500 700 900 500 700 900

Temperature / °C Temperature / °C Temperature / °C

Hea

tp

ipe

limit

atio

ns

/ W

HP 270 - 11 HP 270 - 12 HP 270 - 13

Calculated heat transfer limits at horizontal operation (0°)


82

Figure 5.19: Performance evaluation of design C prototypes under different tilt angles.

5.3.4 Dynamic testing of planar heat pipes – Start-up behavior

An important criterion of heat pipes in SOC applications is its dynamic performance

behavior, such as for system start-up / shut down and during load / temperature changes.

An analysis of heat pipe theoretic performance limits shows that in particular viscous limit

decreases strongly for intermediate temperature below approx. 600°C. This is caused by an

increased fluid viscosity and by a large gas flow velocities due to low saturation pressures

within the heat pipe.

When starting a heat pipe from cold state at ambient temperature one observes a strongly

non-isothermal start-up behavior similar to the schematic description in Figure 5.20.

According to [Tolubinskii1978] in a first phase when the working fluid is in partly solid, heat

transfer to condenser solely happens by heat conduction, and a large temperature

difference to evaporator occurs (until t2). In a second phase, a continuum flow slowly

establishes throughout the vapor space of the heat pipe and replaces the low heat

transmitting free molecular flow. This leads to a rapidly increasing condenser temperature

and causes high temperature gradients (t2 to t4). From a transition temperature T* with

fully established vapor flow regime onwards, the heat pipe can, with respect to the viscous

performance limit, be heated up isothermally (t4 onwards). Based on the works of

[Jang1995] a transition temperature of T*=790 K is estimated for the typical heat pipes of

design C as used in this work.

-90 -60 -30 0 30 60 90

tilt angle / °

0

200

400

600

800

1000

1200

-90 -60 -30 0 30 60 90

tra

nsf

er l

imit

/ W

tilt angle / °

-90 -60 -30 0 30 60 90

tilt angle / °

capillarylimit theory

HP 270 - 12 HP 270 - 13HP 270 - 11

measuredmaximumheat transfer


83

Figure 5.20: Left: Schematic start-up of liquid metal heat pipe from room temperature at constant heating rate (adapted from [Jang1995]). Tm = melting temperature, T* = transition temperature, Ts = stationary temperature, Right: own experimental measurements, T* calculated for design C prototype HP270-13

This behavior has important consequences for the use of liquid metal heat pipes in SOC

stacks. A detailed experimental analysis of planar liquid metal start-up behavior was carried

out by [Wintergerst2015]. He analyzed design C heat pipe prototypes similar to HP270-13.

For detailed information on experimental procedure, it is referred to this work.

The temperature gradients (temporal and local) until reaching transition temperature T* are

very high compared to typical heating rates permitted for SOFC stacks (1 K min-1). Even at

slow overall heating rates of the heat pipe, the gradient reached much higher local values (>

10 K min-1) in phase t3-t4. Thus, a heating of SOFC stacks from room temperature via high

temperature heat pipes is estimated very demanding in terms of mechanical stability of the

stack structure. Therefore, experiences recommend heating up SOC stacks from room

temperature to transition temperature by convective heating, instead of heating by heat

pipes.

Figure 5.21 shows local temperature gradients at the condenser end between TC 16 / 10 and

TC 17 / 18 of the test set-up during start-up from temperatures above transition

temperature. Initial heat pipe temperature and heat-up gradient were varied. Based on heat

capacity of the set-up the heat-up gradient corresponds to a heating power. The diagram

shows how heat-up from starting temperatures above transition temperature T* can be

realized under isothermal conditions. It demonstrates that for temperatures above 600°C

high heat-up rates can be realized under isothermal heat pipe operation. This could open the

possibility of a rapid start-up of SOFC stacks from a stand-by hold at around 600°C at low

thermal stress conditions.

Time

Tem

pe

ratu

re T*

Tm

fluid phase

vapor phase

Solid Solid and liquid Liquid

Free molecular flow Transition Continuum Flow

Ts

t1 t3 t4t20

100

200

300

400

500

600

700

800

900

0 25 50 75

Tem

per

atu

re /

°C

Time / min

heat-up rate 10K min-1

T*

Tm

Ts

evaporatortowardscondenser


84

Figure 5.21: Maximum temperature gradient in condenser during start-up from different initial temperatures and with varying heat-up rates for HP similar to HP270-13.

5.3.5 Long-term operation of planar heat pipes

For the integration into SOC stacks with targeted lifetime of above 50’000 h, the heat pipe

design has to provide corresponding long-term operation capabilities. Firstly, choosing

correct material combinations for working fluid, casing and wick material avoids material

compatibility issues. According to [Reay2006] the alkali metals Na and K, show good

compatibility with stainless steels as well as nickel and nickel-based-alloys like Hastelloy X at

temperatures between 510 and 850°C. [Rosenfeld2004] reports experimental evaluation of

sodium heat pipes with stainless steel (AISI 316 L) casing and nickel capillary structure of up

to 115’000 h at temperature levels between 650 and 700°C. Life times over 10’000 h of

liquid alkali metal heat pipes with stainless steel casing were also reported by

[Matsumoto1997]. Casing failures in liquid metal heat pipes are mainly caused by impurities

that drive corrosion mechanisms [Bricard1990] and can only be avoided by proper cleaning

mechanisms of the working fluid.

A second cause of degradation arises from non-condensable gases dissolved in casing, wick

and working fluid. The active length of the planar heat pipe decreases due to an outgassing

rate over several hundreds of hours after closing [Ishikawa2003]. In consequence, relative

active length 𝑙𝑎𝑐𝑡(𝑡) of a heat pipe with an area specific degassing rate 𝑑𝑒𝑔𝑎𝑠 of casing /

capillary structure material, 𝐴𝑜𝑐𝑠 the open cross section of the vapor space, the specific

surface area of the used internal structures and 휀 the porosity of the vapor channel (1 in

case of open volume) results as

𝑙𝑎𝑐𝑡(𝑡) = 1 −𝑉𝑑𝑒𝑔𝑎𝑠 (𝑡)

𝐴𝑜𝑐𝑠 ∙ 𝑙𝐻𝑃≈ 1 −

𝑅 𝑇𝐻𝑃𝑝𝑠𝑎𝑡(𝑇𝐻𝑃)

(

휀)∫ 𝑑𝑒𝑔𝑎𝑠 𝑑𝜏

𝑡

0

(5.13)

0

0.5

1

1.5

2

2.5

520 540 560 580 600 620 640

max

tem

per

atu

re g

rad

ien

t /

K m

m-1

starting temperature / °C


85

Degassing of the working liquid is assumed complete after the filling procedure as described

in 5.2.2., due to the iterative boiling of the working fluid. It is clearly visible that the

factor (/휀), denoting the specific surface area in relation to the free vapor volume is of

particular importance for planar heat pipe interconnectors, where a low thickness is a major

target. In particular, for design C, the sandwich design with different layers of screen mesh,

the casing/wick surface to vapor volume ratio is very high and operation pressures are rather

low (< 1 bar). Table 5.6 shows the comparison of HP270-12 and a capillary-structure

equivalent cylindrical heat pipe. The difference in surface to volume ratio by factor 17.5

shows the strongly increased risk of deactivation by material outgassing of the planar heat

pipes.

Table 5.6: Specific surface to free volumes of planar and cylindrical heat pipes of equivalent capillary structures

HP6 HP270 -

12

Cylindric HP dint = 33 mm,

same capillary as HP270 -12

Specific internal surface [mm² / mm] 109 1465 656

Free vapor volume [mm³ / mm] 98 105 832

Surface to volume ratio 휀⁄ [mm² / mm³] 10.2 13.8 0.79

Experimental evaluation of the fabricated heat pipe prototypes over medium-term (HP 6,

230 h) and long-term operation (HP270-12, 2200 h) searched confirmation of a continuous

functioning and the identification of deactivation speed due to material outgassing.

The medium-term measurements in air atmosphere over a period of 230 h showed constant

heat transfer rates of the heat pipe, however a slight increase in temperature differences

between evaporator and condenser from 5 K to 15 K. The long-term test over 2200 h

operated the heat pipe horizontally at 800°C adiabatic temperature and constant cooling air

flows (550 W initial transfer power). Due to power / pressurized air cut-offs, the heating /

cooling interrupted three times during the test run. Figure 5.22 shows temperature

recordings throughout the experiment.

Temperature profiles in Figure 5.23 demonstrate the increased deactivation developing from

condenser side of the heat pipe and are used to estimate deactivation speeds. Relative

active length 𝑙𝑎𝑐𝑡(𝑡) was estimated by linear extrapolation of the first non-isothermal

thermo-couple 𝑇𝑖 at position 𝑙𝑖 by the conduction only temperature gradient (=maximum

detected gradient in all measurement points) (𝜕𝑇

𝜕𝑥)𝑚𝑎𝑥

𝑙𝑎𝑐𝑡(𝑡) =𝑙𝑖 − (𝑇𝑖 − 𝑇𝐻𝑃)

𝑙𝐻𝑃 (𝜕𝑇𝜕𝑥)𝑚𝑎𝑥

(5.14)


86

Figure 5.22: Long-term operation (over 2100 h) behavior of HP 270-12 in horizontal operation at 550 W heat transfer and 800 °C adiabatic temperature.

Figure 5.23 right shows the evolution of relative active length and heat transfer during the

2200 h test of HP270 – 12. The experiment demonstrated the continuous operation of the

planar heat pipe design, and revealed only a small power reduction of < 10% over the

complete test run, i.e. from 550 W to approx. 500 W. Evolution of active length over time

shows a strong deactivation behavior at the beginning and an asymptotic trend after first

1000 hours.

Figure 5.23: Temperature profiles during long-term test operation of a planar heat pipe HP 270-12

600

650

700

750

800

850

0 500 1000 1500 2000

tem

per

atu

re /

°C

time / h

test rig down, full thermal cycle

coolingair off cooling

air off

data recording offtest rig normal operation

T17/18T16/10

other TCs

600

650

700

750

800

850

0 50 100 150 200 250

tem

per

atu

re /

°C

position / mm

25 h

250 h

500 h

800 h

1400 h

2100 h


lact(1400 h)

linact(800 h)

linact(25 h)

linact(1400 h)

lact(800 h)

active length lact(25 h)

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000

rel.

acti

ve le

ngh

t /

-re

l. p

ow

er /

-

time / h

active lengthright side

active lengthleft side

rel. power transferred to air cooler

logarithmic trend

len

gth


87

Figure 5.25 summarizes the measured degradation rates of the mid- and long-term

experiment. For HP270-12 an active length decrease of approx. 10 % kh-1 over 2000 h was

obtained. HP 6 shows a lower inactive length growth over 220 h compared to HP270-12. This

corresponds with its lower surface to volume ratio of 10200 m-1 vs. 13800 m-1 for HP270-12

(Table 5.6). Reduced condenser temperatures lead to lower heat transfer to the air cooler

and thus cause a power reduction being therefore an indirect degradation effect of non-

condensable gases.

After terminating test runs the heat pipes have been opened, carefully deactivated in a

Propanol – water mixture (5 vol% H20 in C3H8O) and finally rinsed with demineralized water.

The heat pipes showed clean, shiny casing surfaces and no evidence for corrosion. Post-

mortem SEM analysis of HP270-12 displayed in Figure 5.24 show no microstructural changes

of wick material or casing. Neither material reduction of mesh nor casing (Figure 5.26) were

detected and it was concluded that no material compatibility problems impede long-term

operation of the planar heat pipe.

In consequence, the developed planar heat pipes are suitable for long-term operation, as

long as active length decrease is handled. An improved outgassing and baking-out procedure

before filling should help to reduce this problem, by reducing the amount of dissolved gases

in the casing and capillary materials. Additionally, some inactivation may be permitted by

initial over dimensioning of the condenser area.

Figure 5.24: Post-mortem SEM analysis of HP270-12 capillary structure (from evaporator).

5 µm 5 µm

55.7 µm55.4 µm


88

Figure 5.25: Comparison of degradation rates of planar heat pipes HP 6 and HP 270-12 per 1000 h

Figure 5.26: Cross section SEM analysis of HP270-12 (evaporator) after 2100 h. EDX mapping of Fe (red dots) and Ni (yellow dots)

-0.3

-0.2

-0.1

0

0.1

0.2

heat transfer power active length

8.59 % 13.10 %

-3.58 %

-15.54 % -19.33 %

-9.70 %

par

amet

erch

ange

/ 1

00

0 h

-1

HP 6, 220 h

HP 270-12220 h, 2100 h

25 µm 10 µm

Analysis of hydrogen resistance

89

5.4 Analysis of hydrogen resistance

The hydrogen atmosphere which is in contact with the interconnector plates on the fuel side

of solid oxide cells is another important fact to be considered for long-term stability (see

[Leimert2016]). Hydrogen permeation through metallic membranes cannot be neglected –

unlike as for other gases, e.g. nitrogen or air - but has to be taken into account.

5.4.1 Hydrogen permeation and deactivation of planar heat pipes

The molar gas flux j through a metallic material depends on diffusion (Fick’s law) and

solubility of the gas (according to Sievert’s law) and can be stated according to following

correlation (Richardson law) [Jung1996]:

𝑗 = −𝑃(𝑇)

𝑠∙ [(𝑝𝐻2,1)

𝑛− (𝑝𝐻2,2)

𝑛] (5.15)

where 𝑝𝐻2,1 and 𝑝𝐻2,2 are the partial pressure levels at both sides of a membrane with

thickness s and P being the permeability of the concerned metal, which is of particular

importance since hydrogen permeability through metallic membranes is exponentially

temperature depending. The exponential coefficient 𝑛 depends on the gas and solid material

and determines whether transport is limited either by diffusion (𝑛 → 1) or solution (𝑛 → 0.5

for diatomic gases). Hydrogen permeation through metallic membranes shows the second

behavior and n thus is mostly assumed to be 0.5 [Eschbach1963].

The temperature dependency of the permeability is reflected using an Arrhenius type

approach

𝑃(𝑇) = 𝑃0 ∙ exp (−𝐸𝑝

𝑅𝑇) (5.16)

where 𝑃0 is permeability constant and 𝐸𝑝 activation energy of permeability.

Permeability data for some typical austenitic and ferritic steels is broadly available in

literature [Forcey1988; Jung1996; Maroni1979; Van Deventer1980]. It has to be considered

however, that these data mostly apply for bare metallic surfaces and are not entirely

applicable for steels in all gas atmospheres. Oxide layer formation and quality are important

influence factors that may vary permeability significantly [Metz2005].

A problem from hydrogen permeability arises due to a self-enrichment of the heat pipe

atmosphere with non-condensable hydrogen as displayed in Figure 5.27: In-diffusing

hydrogen from SOFC’s anode side is transported by the constant Na-vapor flow to the

condenser end of a heat pipe where it leads to an increase of inactive length of the heat pipe

[Karl2014].


90

Figure 5.27: Scheme of the inactivation of heat pipes due to hydrogen permeation with temperature and partial pressure profiles within heat pipe (compare [Leimert2016])

The induced temperature drop in this region (especially if the heat pipe is used to extract

heat from a SOFC stack) causes an exponential reduction of hydrogen permeability in this

zone and low hydrogen permeation rates out of the heat pipe. Hydrogen from the H2

atmosphere however can continue to diffuse into the heat pipe in its active zone, since

internal partial pressure of hydrogen is low and temperature keeps being high there. This

mechanism continues until flows reach an equilibrium state for the hydrogen content 𝑛𝐻2.

𝑑𝑛𝐻2𝑑𝑡

= ∫ 𝑗(𝑥)𝑤𝐻𝑃𝑑𝑥 = 0 (5.17)

Introducing external hydrogen partial pressure 𝑝𝐻2, working pressure of the heat pipe

𝑝𝑠𝑎𝑡,𝑁𝑎(𝑇𝐻𝑃,𝑎𝑐𝑡) and assuming discrete temperatures 𝑇𝐻𝑃,𝑎𝑐𝑡 , 𝑇𝐻𝑃,𝑖𝑛𝑎𝑐𝑡 as a sharp limit of the

hydrogen buffer according to Figure 5.27 leads to

𝑗𝑖𝑛 ∙ (𝑙𝐻2𝑤𝐻𝑃) − 𝑗𝑜𝑢𝑡 ∙ (𝑙𝑖𝑛𝑎𝑐𝑡𝑖𝑣𝑒𝑤𝐻𝑃) = 0 (5.18)

Therefrom, inactive length of the heat pipe results as:

𝑙𝑖𝑛𝑎𝑐𝑡 =𝑃(𝑇𝐻𝑃,𝑎𝑐𝑡 )

𝑃(𝑇𝐻𝑃,𝑖𝑛𝑎𝑐𝑡 )

𝑠𝑖𝑛𝑎𝑐𝑡𝑠𝑎𝑐𝑡

[𝑝𝐻2

𝑝𝑠𝑎𝑡,𝑁𝑎(𝑇𝐻𝑃,𝑎𝑐𝑡) − 𝑝𝑠𝑎𝑡,𝑁𝑎(𝑇𝐻𝑃,𝑖𝑛𝑎𝑐𝑡)]

0.5

∙ 𝑙𝐻2 (5.19)

For materials with permeability according to equation (5.16) a temperature reduction in the

inactive zone, thus, plays a crucial role. Decreasing 𝑇𝐻𝑃,𝑖𝑛𝑎𝑐𝑡 to 600°C compared to 𝑇𝐻𝑃,𝑎𝑐𝑡 at

800°C results in an increase of 𝑙𝑖𝑛𝑎𝑐𝑡 by a factor of almost 5, for instance. In consequence,

even low partial pressure atmospheres of hydrogen at the evaporator end can lead to strong

anode H2 atmosphere pH2 > 0

H2 buffer Active zoneNa(g)

condensation zone

planar Heat Pipe

H2 H2 H2

wick

p

psat, Na (THP,act)psat, Na (THP,inact)

pH2,HP pNa,HP

T

THP,actTHP,inact

model

real

air atmosphere pH2 = 0linact

lH2


91

deactivation problems of the heat pipe, especially of planar heat pipes, as inner pressure is

limited to atmospheric pressure. Analytical deactivation dynamics predict a very fast

deactivation of planar heat pipes within minutes due to low vapor volumes compared to

casing surface.

5.4.2 Approaches avoiding hydrogen deactivation

Hydrogen deactivation is a fundamental issue when operating high temperature heat pipes

in hydrogen containing atmospheres. On basis of equation (5.19) it is possible to identify

approaches that reduce or avoid hydrogen deactivation of the planar heat pipe

interconnector (for details see [Weyerer2014]):

- Decreasing the permeability ratio 𝑃(𝑇𝐻𝑃,𝑎𝑐𝑡 ) 𝑃(𝑇𝐻𝑃,𝑖𝑛𝑎𝑐𝑡 )⁄ between active and

inactive heat pipe area. This may be realized by either choosing a material with a low

activation energy 𝐸𝑝 (equation (5.16)) or by applying coatings with increased /

decreased permeabilities.

- Avoiding cooling out of inactive HP area, i.e. decreasing temperature drop

𝑇𝐻𝑃,𝑎𝑐𝑡 𝑇𝐻𝑃,𝑖𝑛𝑎𝑐𝑡⁄ .

- Geometric adaptation to decreasing casing thickness ratio 𝑠𝑖𝑛𝑎𝑐𝑡 𝑠𝑎𝑐𝑡⁄ or hydrogen

contact length

- Increasing hydrogen pressure ratios by increasing working pressure of the heat pipe

(e.g. due to a switch of the working fluid [Karl2014]) being limited by ambient

pressure or decreasing hydrogen pressure in contact to heat pipe casing.

Based on 1-D discretized solving of equation (5.17), taking into account a continuous

temperature profile, the above listed approaches are numerically evaluated. Simulation

results (see Figure 5.28 hereunder) provide a first theoretic evaluation of the potential of the

different approaches. Material properties, especially permeabilities used in this calculation

are obtained from

- AISI 316 L (representing HP casing): 𝑃0 = 2.36 ∙ 10−7 mol m-1s-1Pa0.5, 𝐸𝑝 =

63.5 kJ mol−1 [Van Deventer1980]

- Ag: 𝑃0 = 8.51 ∙ 10−8 mol m-1s-1Pa0.5, 𝐸𝑝 = 100.0 kJ mol

−1 [REB Research &

Consulting1996]

- W: 𝑃0 = 7.60 ∙ 10−7 mol m-1s-1Pa0.5, 𝐸𝑝 = 132.2 kJ mol

−1 [Steward1983]

- Na, K, Cs vapor pressures from [Ohse1985]

- NaK, eutectic composition 67.5 % K, 32.5 % Na; vapor pressure according to

[Anderson1993]


92

Figure 5.28: Numerical parameter study of hydrogen deactivation and its mitigation in planar high temperature heat pipes. Boundary conditions of base case (blue): working fluid: Na, casing: AISI 316 SS, scase = 1mm uncoated, lHP=270 mm, lH2 = 0.5 lHP, 𝑇𝐻𝑃,𝑖𝑛𝑎𝑐𝑡 = 650°𝐶,

transition zone temperature gradient: 𝜕𝑇𝐻𝑃,𝑖𝑛𝑎𝑐𝑡/𝜕𝑥 = 5 K/mm, 𝑝𝐻2 = 0.5 bar

0

0.2

0.4

0.6

0.8

1

700 750 800 850 900

acti

ve le

ngt

h /

-

heat pipe temperature Tact / °C

0

0.2

0.4

0.6

0.8

1

700 750 800 850 900

acti

ve le

ngt

h /

-


0

0.2

0.4

0.6

0.8

1

700 750 800 850 900

acti

ve le

ngt

h /

-


0

0.2

0.4

0.6

0.8

1

700 750 800 850 900

acti

ve le

ngt

h /

-


1.0

0

0.2

0.4

0.6

0.8

1

700 750 800 850 900

acti

ve le

ngt

h /

-


0

0.2

0.4

0.6

0.8

1

700 750 800 850 900

acti

ve le

ngt

h /

-


variation of thickness coating of casing face tohydrogen atmosphere

variation of inactivetemperature

variation of working fluid

variation of length

variation of hydrogen

atmosphere

800 °C

750 °C

700 °C

600 °C

650 °C

Na

NaKK

Cs

0.50 bar

0.25 bar

0.10 bar

1.00 bar

0.5

0.25

0.1

1/1

1/21/3

1/4

uncoated

Ag, 50 µm

Ag, 100 µm

W, 5 µm


93

Generally, maximizing pressure levels inside the heat pipe – with the constraint of

atmospheric pressure for planar heat spreaders – helps to keep the inactive zone small.

Thus, for operation temperatures below 750°C it is recommended to switch working fluid to

potassium or NaK due to its higher saturation pressure.

It can furthermore be concluded that temperature difference between active zone and

inactive zone has to be kept small, reducing heat extraction capacities at lower temperature

levels. An active temperature control of condenser zone may be mandatory if the inactive

zone is cooled over 100K below hydrogen contact area. Applying countermeasures by design

can improve active length considerably. A variable casing thickness that impedes hydrogen

in-diffusion and facilitates hydrogen exit can increase active length to over 90% of the heat

pipe in SOFC applications if the inactive zone’s temperature is kept high and neglecting the

effects of possible oxide layers.

A partly coating of the heat pipe exterior with low permeability materials is a further

approach to avoid the hydrogen problem. The anode interconnector side is coated with a

Nickel coating to provide long-term stability [Nielsen2006], thus, just a second coating is to

be applied. In particular low permeability metals, i.e. tungsten with a permeability 3 orders

of magnitude below ferritic steel, promise very small deactivation lengths. Studies of

physical vapor deposited (PVD) tungsten showed however that thin coatings of 2 µm do not

significantly influence the permeability of a sample due to remaining open pores, while

vacuum plasma sprayed (VPS) 200 µm films reduced hydrogen permeation remarkably

[Golubeva2011]. Another possible option to counter the hydrogen problem is increasing

permeability in cooling region, in order to promote diffusion to the ambient [Karellas2008].

A control of chromium oxide layer growth and structure showed large impact on hydrogen

permeability [Metz2005].

5.4.3 Experimental study

The hydrogen deactivation process is studied in an adapted experimental set-up according

to Figure 5.29 where a hydrogen atmosphere partly encloses an active heat pipe,

comparable to a situation in an SOFC stack. Therefore, design C prototypes (prototypes

according to Table 5.7) equipped with a H2-chamber are installed in the set-up with

thermocouple placing as described above. Figure 5.30 shows the typical behavior of a

standard design C prototype heat pipe under evaluation (situation comparable to base case

in Figure 5.28). Once the active heat pipe running steadily for over 130 h is contacted to a

hydrogen atmosphere (with pH2 = 0.5 bar) an almost immediate drop in transferred power

and a break-down of isothermal operation occurs within approx. 2 h. Figure 5.28 left displays

the evolution of the heat pipe temperature profile during this deactivation process. An

active length of approximately 41% can be concluded according to equation (5.14). After

sweeping the heat pipe environment with nitrogen, hydrogen permeates out of the heat

pipe and its functioning is entirely restored to the level before deactivation process

(temperature profiles at 131 h and 171 h).


94

Table 5.7: Excerpt of the fabricated planar heat pipe prototypes for hydrogen deactivation tests (based on design type C)

HP-ID Size [mm] Capillary structure Wick /casing

material Mitigation principle

270-10 270 x 120 x 6

|2 Mesh 98|

Mesh 8

|2 Mesh 98|

1.4841

/1.4841

Intermediate air layer (100

µm), hydrogen membrane

500 µm

270-14 270 x 120 x 5

|2 Mesh 187|

Mesh 8

|2 Mesh 187|

Ni /1.4841 Anode / Air casing thickness

variation 2/1

270-15 270 x 120 x 6

|2 Mesh 187|

Mesh 8

|2 Mesh 187|

Ni /1.4841 Anode / Air casing thickness

variation 3/1

270-16

270 x 120 x 4

Silver coated

100 µm

|2 Mesh 187|

Mesh 8

|2 Mesh 187|

Ni /1.4841 Silver coating (galvanic silver

deposition, 100 µm)

270-16

/2

270 x 120 x 4

|2 Mesh 98|

Mesh 8

|2 Mesh 98|

Ni /CROFER

22H Casing material change

This deactivation can entirely be explained by hydrogen permeation effects. The formation

of large inactive zones due to non-condensable hydrogen zones is completely, but slowly,

reversible when the heat pipe is placed into pure nitrogen / air environment. The

experimental evaluation was used to calibrate the numerical model (i.e. transition zone

temperature gradient 𝜕𝑇𝐻𝑃,𝑖𝑛𝑎𝑐𝑡/𝜕𝑥 ) that generated the results displayed in Figure 5.28.

According to the results in the numeric study, several approaches have been tested to

improve heat pipes active length in a typical SOC stack configuration.

Figure 5.29: Flow diagram for hydrogen degradation measurements of planar heat pipes

N2

H2 FIC

TID

TID

FIC

FIC

pressurized air

heatercooler

vent

vent

H2 -chamber

MFC air:max. 10 sm³h-1

MFC N2:max. 1000 smlm

MFC H2:max. 1000 smlm

planar HP


95

Figure 5.30: Deactivation and reactivation of HP 270-6 due to hydrogen permeation after 131 h constant horizontal operation.

Variation of casing thickness:

Two prototypes (HP270-14, HP270-15, according to table Table 5.7) with varying casing

thickness of 𝑠𝑖𝑛𝑎𝑐𝑡 𝑠𝑎𝑐𝑡⁄ = 1/2 and 1/3 have been evaluated in order to validate the

numerically predicted improvements according to Figure 5.28. The experimental

measurements however did not provide any significantly improved hydrogen resistance. It is

assumed that surface effects such as oxide layers that are formed on the steel surfaces have

a non-neglectable effect on hydrogen permeability [Metz2005]. According to [Heimes1986]

and [Möllenhoff1984; Möllenhoff1986] so-called permeation inhibition factors of 10-1000

occur depending on the quality of the oxide layer of the corresponding steel.

Coating of heat pipe casing:

A prototype (HP270-16) with a protective Silver-coating (100 µm, galvanic deposition) on the

heat pipe casing that is in contact with the hydrogen atmosphere has been manufactured.

The coating however did not show any beneficial effect on hydrogen resistance. Due to an

almost complete delamination / destruction of the silver coating in contact with the

hydrogen atmosphere no clear and final evaluation of the coating was possible and the

concept was no longer under consideration.

400

500

600

700

800

900

0 100 200

Tem

per

atu

re /

C

Position / mm

131 h

135 h

136 h

144 h

171 h

p_H

2 /

bar

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0

50

100

150

200

250

300

350

400

450

125 135 145 155 165 175

Hea

t tr

ansf

er /

W

Operation time / h

14

4 h

13

6 h

17

1 h

13

5 h

13

1 h

Heat transfer

p_H2



96

Figure 5.31: HP270-16 with 100 µm Ag coating. Before(left) and after (right) operation in hydrogen atmosphere

Intermediate air layer

The schematic in Figure 5.32 (right) shows the basic idea of an intermediate air layer to

mitigate hydrogen deactivation: an additional layer is brought between heat pipe casing and

hydrogen containing atmosphere (i.e. anode contact of the SOFC). This layer consists in a

diffusion-open porous structure that allows ambient air to diffuse freely and to provide

pO2 > 0 in this intermediate layer. Hydrogen permeating from the anode gas flow through

the hydrogen membrane reacts with the available oxygen in this porous layer and hydrogen

partial pressure is reduced to very low levels close to 0 that are no danger to heat pipe

activity. Figure 5.32 displays the experimental evaluation of HP270-10 showing constant

operation over more than 35 h at 220 W without any sign of hydrogen deactivation despite

the hydrogen atmosphere of pH2 = 1 bar. This approach thus presents itself as very useful to

avoid hydrogen inactivation, but comes with certain drawbacks regarding SOFC stack

integration. The additional intermediate air layer leads to an increase in thermal transfer

resistance into the heat pipe and leads to additional needs for proper stack sealing. Applying

thermal contact resistances as obtained in chapter 6.4, an intermediate air layer with mesh

198 results in an additional heat transfer resistance of approx. 10 ∙ 10−4 m2K W−1, roughly

one third of a stack repeating unit. For a typical SOFC heat flux density of 0.5 W cm−2 (e.g.

for 5 cells) into the heat pipe, this results in additional temperature gradient of 5 K, a value

that seems to be completely acceptable. Furthermore, a durable, low resistance electric

contact between hydrogen membrane and porous structure has to be assured by spot-

welding or equivalent.

towardshydrogen

atmosphere: coated with100 µm Ag

towardsambient:uncoated

before after


97

Figure 5.32: Deactivation free operation of HP270-10 in hydrogen atmosphere (pH2=1 bar) due to intermediate layer.

CROFER 22H as casing material

A special focus has to be set on using special pre-designed SOFC steels such as CROFER 22 H

(1.4750), CROFER 22 APU (1.4760) [ThyssenKrupp2010] or Plansee ITM that are chromium

rich ferritic steels in order to adapt thermal expansion coefficients (TECs) to electrolyte

ceramics. Further typical SOFC alloys, in particular the chromium based super-alloy Plansee

CFY [Plansee2015] with approximately 95% chromium and 5% iron, are also relevant for SOC

stack production, but are not considered in this work. Plansee CFY is applied through powder

sintering and no well-established welding or brazing procedures are available, however are

mandatory for proper heat pipe manufacturing. This work uses CROFER 22 H,

state-of-the-art ferritic SOFC steel, as interconnector material for SOC stack prototypes and

thus for heat pipe interconnectors. While for heat pipe performance evaluations its behavior

is close to other high temperature steels, the analysis of hydrogen deactivation behavior of

planar CROFER heat pipes requires an experimental study, since no hydrogen permeation

data exists in literature.

Heat pipe 270-16-2 performance evaluation in hydrogen atmosphere under increasing

hydrogen partial pressures showed almost no reduction of active length of the heat pipe at

800°C (compare Figure 5.33) but showed stronger deactivation for lower temperatures. At

700°C active length reduced slowly to approx. 60 %. This behavior can hardly be explained by

applying typical steel permeabilities of comparable ferritic chromium steels (e.g. 𝑃0 = 2.44 ∙

10−7mol (m ∙ s ∙ Pa0,5)−1, E𝑝 = −53900 J(mol∙K)-1 [Jung1996]), that would predict

deactivation similar to 1.4841 as casing material.

4

vapour spaceMesh 8

capillary structureMesh 98

HP-casing 1mm

Air gap, Mesh 198

Hydrogen membrane

H2pH2 >> 0

Ambientair

700

750

800

850

900

0 100 200

Tem

per

atu

re /

K

Position / mm

before H2 atmosphere

2 h in H2 atmosphere

35 h in H2 atmosphere


symmetryplaneplanar HP

pH2 > 0


98

Figure 5.33: Deactivation free operation of HP270-16-2, casing of CROFER 22H, in hydrogen atmosphere (up to pH2=1 bar rest N2) at 800°C and 700°C .

It is therefore assumed that oxide layer formation is the important factor that is responsible

for this heat pipe behavior. CROFER 22H is designed to reduce chromium evaporation that

leads to degradation effects on SOFC cathodes. Therefore, CROFER 22H contains small

percentages of Mn, La, Al, Si, Ti, Nb and V, which influence oxide layer growth [Tanabe1984].

Furthermore, above the chromium oxide (Cr2O3) a (Mn,Cr)3O4 – spinel layer forms that is

able to substantially reduce chromium evaporation from the interconnector (by up 75 %

according to [Stanislowski2006]) due to its tightness. Figure 5.34 shows an SEM/BSE image

of ferritic steel (similar to CROFER) with enhanced spinel formation properties. There exists

some evidence that this layer formation is not only mitigating chroming evaporation but in

the same way could effectively reduce hydrogen permeation [Korinko2005]. In consequence,

the behavior displayed in Figure 5.33 may be interpreted as a consequence of the spinel

layer formation. At 800°C the hydrogen permeation was reduced by the slowly established

and therefore dense (Mn,Cr)3O4 layer in the H2 chamber. The fast layer growth in contact

with ambient air resulted probably in higher permeability as described by [Metz2005]. The

deactivation at 700°C may therefore be caused by both the reduced heat pipe internal

pressure as well as due to a changing spinel layer. The fast temperature change from 800°C

to 700°C could have led to micro cracks in the dense layer structure and increased hydrogen

permeability causing the observed deactivation.

0

0.2

0.4

0.6

0.8

1

1.2

100

150

200

250

300

350

400

55 65 75 85 95 105 115 125 135

Hea

t tr

ansf

er /

W

Operation time / h

p_H

2 /

bar

Heat transfer

p_H2

heater adiabatic cooler94

h

88

h

69

h

THP=800 °C THP=700 °C

500

550

600

650

700

750

800

850

0 100 200

Tem

per

atu

re /

C

Position / mm

69 h88 h94 h98 h132 h

13

2 h

98

h


99

Figure 5.34: Chromium oxide and spinel layer formation on CROFER at 900°C in air (source: [Froitzheim2008], with permission from Elsevier)

5.4.4 Hydrogen permeability of CROFER22H

In order to provide data for heat pipe interconnector layout, a first experimental evaluation

of hydrogen permeability of CROFER 22 H was carried out at EVT, with details available in

[Waldhör2015]. Thin, 200 µm membranes were placed in a permeation test set-up according

to Figure 5.35 and permeation rates were measured based on GC-concentration

measurement in permeate sweep gases. Results displayed in Figure 5.36 clearly show lower

hydrogen permeabilities for CROFER 22 H than for 1.4841 and 1.4341. In consequence,

hydrogen deactivation of planar heat pipe interconnectors may benefit from this property

under certain conditions. Equally, it is however possible that deactivation intensifies in SOC-

stack environments due to varying oxide layer qualities in different gas environments. A

more profound analysis of CROFER permeabilities in different gas environments should

therefore be carried out prior to using HP-interconnectors without further permeation

barrier.

Figure 5.35: Measurement set-up (left) and measurement cell (right) for hydrogen permeation measurements.

TIRC

TIRC

FIC

FIC

FIC

GC

H2

humidfier

permeate

retentatefeed

sweep

furnace

N2

N2

TC 1 TC 2

flangeDN 60 gaskets

metalmembraned = 65 mm

feed H2 retentate H2

sweep N2 permeate N2 + H2


100

Figure 5.36: Measured hydrogen permeabilities of CROFER 22H (1.4755), 1.4841 and 1.4301 in humidified hydrogen (standard deviations of measurement shown)

5.4.5 Alkali hydride formation

Sodium hydride (NaH) is a ionic product of the reaction of molecular hydrogen with (liquid)

sodium. It is only stable in its solid phase, up to an upper temperature limit depending on

hydrogen pressure (e.g. 425°C at ambient pressure for Na).

𝑁𝑎 (𝑙) + 1 2⁄ 𝐻2(𝑔) Δ𝐻𝑅= −56.4 𝑘𝐽/𝑚𝑜𝑙→ 𝑁𝑎𝐻(𝑠) (5.20)

Formation of other alkali metal hydrides is similar. Enthalpies of hydride formation of

relevant alkali metals Li, Na and K are Δ𝐻𝑓,𝐿𝑖(𝑠) = −77.71 kJ mol−1,

, Δ𝐻𝑓,𝑁𝑎 = −56.4 kJ mol−1 and Δ𝐻𝑓,𝐾 = −57.82 kJ mol

−1 respectively [Chase1998]. For

lithium also a liquid LiH phase exists due to the more elevated temperatures. Detailed phase

diagrams for binary alkali metal - hydrogen systems have been computed with the software

Factsage based on data from [Stull1985] and are displayed in Figure 5.37.

Alkali metal hydride formation allows an interpretation by the subsequent mechanism

displayed in Figure 5.38. Heat pipe internal pressure is determined by the temperature of

the active heat pipe zone and can be assumed almost uniformly throughout the entire heat

pipe. Consequently, formation temperature of alkali hydrides is solely depending on heat

pipe active zone temperature and can be computed according to Figure 5.37.

1E-13

1E-12

1E-11

1E-10

0.0008 0.0009 0.001 0.0011

H2

per

mea

bili

ty /

mo

l m-1

s-1Pa

-0.5

Temperature-1 / K-1

800 750 700 650850900950

Temperature / °C

1.4301

1.4841

1.4755


101

Figure 5.37: Phase diagrams of binary alkali metal - hydrogen system in heat pipes – calculated with Factsage on basis of [Stull1985]. Exemplary determination of NaH formation limit (= approx. 400 °C) in coldfinger for HP operated at 800C in active zone.

In case the temperature in the inactive zone of the heat pipe drops below the formation

temperature of the alkali hydride, the conversion of the liquid alkali metal begins and

hydrogen of the established hydrogen buffer is consumed. This initiates an opposing trend

to heat pipe deactivation and thus may lead to a quasi-equilibrium situation between

hydrogen permeation and its reaction in alkali hydride formation as long as elementary alkali

metal is still available.

Figure 5.39 shows the dynamics of hydrogen deactivation with a fast initial deactivation due

to the increasing hydrogen buffer and the start of an equilibrium phase as soon as NaH

formation temperature at approx. 400°C for 800°C heat pipe operation temperature is

reached. The constant hydrogen formation / reactivation cycle may provoke the

instationary operation at that point. Ongoing consumption of the alkali metal leads

obviously to a slow blocking of the wick and to a complete deactivation of the heat pipe, due

to a further increase of the hydrogen buffer.

Figure 5.38: Basic mechanism of metal hydride induced deactivation of high temperature heat pipes

0

200

400

600

800

1000

0 0.5 1

p / bar0 0.5 1

p / bar

500

700

900

1100

1300

1500

0 0.5 1

p / bar

NaH (s)

Na (g) + H2 (g)

KH (s)

K (l) + H2 (g)

K (g) + H2 (g)Li (g) + H2 (g)

Li (l) + H2 (g)

LiH (l)

LiH (s)

0 0.5 1 0 0.5 1 0 0.5 1

Na (l) + H2 (g)

T Li/

°C

T Na

+ K

/ °C

Ambient H2 atmosphere

H2 buffer

T

Tf,NaH

NaH Active zone

THP

Na(g)

Na(l) in wick structure

Heat Pipe


102

Figure 5.39: Dynamics of hydrogen deactivation with NaH formation after hydrogen environment at t=0. Left diagram: Solid black line shows cold end temperature of heat pipe, data points indicated inactive length of heat pipe in relation to entire heat pipe length. Right: Temperature profiles during initial heat pipe deactivation and starting of NaH formation.

A decomposition of the hydrides, i.e. a complete reactivation of the alkali metal heat pipe, is

feasible by heating the heat pipe over the formation limits. When hydrogen pressure

surpasses external hydrogen pressure, hydrogen permeates out of the heat pipe and the

heat pipe is gradually reactivating. In particular, for planar heat pipe structures, this

reactivation process has to be carried out with caution. A fast heating of the entire heat pipe

far over hydride formation temperature (e.g. > 500°C for sodium), would lead to a complete

release of hydrogen, thus to a massive increase of heat pipe internal pressure. At 500°C

decomposition pressure of NaH is 6.59 bar, while at 600°C decomposition pressure rises

already up to 50.3 bar. Hence, a casing failure, in particular for planar heat pipe structures,

would be the certain consequence if temperature increase happens faster than permeation

can carry away the hydrogen.

For continuous operation of heat pipes in hydrogen atmospheres this hydride formation

limit has to be considered. System design has to assure the avoiding of cooling below the

limit, even if some degree of hydrogen deactivation of the heat pipe is permitted.

Consequently in experimental studies, hydride formation leads to misinterpretation of the

inactivation time and length. It is important to assure that the critical temperature is

avoided, e.g. by restricting cooling power to a maximum amount. Accordingly, for SOFC stack

set-ups this temperature limitation is also relevant to avoid complete failure of planar heat

pipe interconnectors.

200

300

400

500

600

700

800

900

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50

Hea

t p

ipe

cold

en

d [

°C]

Rel

ativ

e in

acti

ve h

eat

pip

e vo

lum

e [-

]

t / h

cold end temperature

Relative inactive length

Instationary behaviordue to NaH formation

Hea

tp

ipe

cold

end

tem

per

atu

re/

°C

rela

tive

inac

tive

hea

tp

ipe

len

gth

/ -

0

100

200

300

400

500

600

700

800

900

0 50 100 150 200 250

Tem

per

atu

re/ C

Position / mm

Start initial deactivation t=0

Initial deactivation t=4500 s

Initial deactivation t=7500 s

End initial deactivation t=11500 s

Final deactivation t= 56 hours

Active lengthafter initial deactivation

NaH formationtemperature


Conclusions

103

5.5 Conclusions

The chapter reports the design, development and manufacturing approaches for planar high

temperature heat pipes as heat spreading interconnectors in SOC stacks. Experimental

studies proved that planar thin heat pipes for the temperature range between 650°C – 870°C

with overall thicknesses down to 4 mm based on elementary sodium are possible. Best heat

transfer rates are obtained for screen meshed heat pipes in a sandwich design where mesh

198 provides the capillary structure while a mesh 8 screen assures the upkeep of heat pipe

shape and thus of the vapor space. In horizontal operation, the prototypes demonstrated

heat transfer rates up to 1000 W, corresponding to equivalent thermal conductivities up to

17000 W m-1 K-1, a value far above stainless steel (30 W m-1 K-1, [Touloukian1972]) or even

copper (350 W m-1 K-1, [Touloukian1972]) at 800°C. Comparing experimental findings to

theoretical heat transfer limits of tubular heat pipes, in particular the relevant capillary limit,

showed very good agreement for the meshed planar heat pipes in horizontal operation. The

resulting correlations are operational for predicting heat pipe performance limits and assist

numerical stack layout.

Besides long-term operation tests, a main focus was set on the hydrogen deactivation

problem of the heat pipes. This mechanism was identified particularly challenging for SOC

application of planar heat pipe. Below atmospheric working pressure, thin wall thicknesses

and high external hydrogen pressure cause rapid heat pipe deactivation, typically in less than

1 hour. Based on this fast deactivation mechanism, countermeasures are discussed in an

analytical study. Experimentally however, only the introduction of a thin intermediate air

barrier layer succeeded in a secure mitigation of the problem, at cost of decreased heat

transfer to the heat pipe (additional temperature difference < 5K). The promising hydrogen

dense properties of CROFER 22H have been discovered and a first experimental

quantification of permeability was carried out. However, a more detailed experimental

evaluation needs to establish a process guidance in order to fully benefit from these

findings.

105

Chapter 6

6. Experimental evaluation of solid oxide cell short stacks

with planar heat pipes

6.1 SOFC-Test Rig

The experimental SOC short stack evaluation was carried out in a test rig conceived for fuel

cell and electrolysis operation (also published in [Dillig2015b]). Figure 6.2 shows flow

diagram of the automated fuel cell test rig and auxiliary equipment. The test rig itself is

equipped with mass flow controllers (MFC) (Bronkhorst) for H2 (up to 10 slm), N2 (up to 20

slm) and a rotameter for purge gas (5 % H2 in N2, Arcal F5 from Air Liquide) supply on the

anode side (always referenced to fuel cell operation). A direct steam generator fed by de-

ionized water via a liquid MFC (Bronkhorst) for steam flows up to 300 g h-1 provides

humidification or steam for electrolysis operation. An additional gas mixing panel provides

further 16 MFCs (Brooks) for additional gas, e.g. CO, CO2 and CH4 with maximum flows of

1000 smlm which can be used to dose pure methane and clean or artificially contaminated

syngas to the stack. On cathode side, an air mass flow controller doses activated carbon

cleaned, dehumidified and filtered air from the compressed air supply or bottled nitrogen.

Figure 6.1: View of SOC short stack test rig at EVT

Flare

GA

gas mixingpanel

Stack set up

Furnace

push rod

Chapter 6: Experimental evaluation of solid oxide cell short stacks with planar heat pipes

106

Off-gases are condensed by cooling water driven gas coolers and are either vented (cathode

off-gas) or combusted in a flare (anode off-gas). A gas analysis unit, driven by an ejector

pump (with flows below 0.5 SL/min) samples off-gases to a gas analyser (ABB Caldos,

Magnos, Uras) for the measurement of H2, CH4, CO, CO2 and O2 concentrations. Gas

manifolding is realized from the downside of the stack through the bottom of the furnace

and load support.

The short stacks are mounted in an electrically heated hood-type furnace (9 kW, 1-zone, PID

controlled), that can be lifted for stack installation. The lower base interconnector plate and

the upper interconnector plate have an electrical connection to the power supply (TDK

lambda, GEN16-150) / electric load (arranged by EBZ Dresden GmbH) to close the external

load / supply circuit. Figure 6.3 shows the wiring scheme of the load circuit of the test rig.

High current switches provide the possibility to switch between operation modes during

solid oxide cell operation and invert stack polarization. The diode based load can control

stack voltage in combination with the power supply during fuel cell mode and is bypassed

for electrolysis power supply. Stack current may vary from 0 up to 150 A and stack voltage

from 0 to 16 V. The test rig is designed for short stacks up to 8 cells. Pt wires can be

contacted to each interconnector level of the short stack in order to measure operation

voltages of each cell and the overall stack operation voltage. Stack current is measured via a

shunt resistance of 1 mOhm.

A pneumatic tensioning system allows loading the stack up to 3000 N. The force is applied

with a stainless steel push rod from above pressing the stack against the support below. The

stack tensioning is maintained even during power cut-offs.

SOFC-Test Rig

107

Figure 6.2: Flow sheet of SOFC / SOEC shortstack test rig

Water

Demineral-ization

FIC

MFC H2O: max. 300 g/h

N2

FIC

MFC N2: 20 slm

H2

FIC

MFC H2: 10 slm

Air

FIC

MFC N2: max. 20 slm

Dehumid(Silica Gel)

Activated carbon Particle

Filter

Air

PM

FI

Purge Gas (5% H2 in N2)

Injection steam generator

Humidifier

TIR

TIR

TIC

TIR

TIR

TIR

20 stack temperature

thermo couples el. furnace heating3 x 2 kW

Gas analyser

FI

Air

N2

trace heated line (200°C)

cooling waterfeed

Natural gasFlare

gas sampler

electronic load / power

supply

Off-gas

Condensate

FIC MFC N2: max. 1000 smlm

CH4

FIC MFC N2: max. 1000 smlmCO

gas mixing panel

up to 16 gases possible

MFC N2: max. 1000 smlm

5%H2 in N2FIC

PM

pneumatic stack

compression

cooling waterreturn

gas analysis

Dehumid(Silica Gel)

PIR

PIR

PIR

PIR


108

Figure 6.3: Wiring scheme of SOC test rig designed by EBZ Dresden, providing fuel cell and electrolysis mode operation

6.2 Experimental set-up for heat pipe stack integration

6.2.1 Basic stack design

The short stack set-up for the heat pipe integration is based on planar solid oxide cells

placed in a cross – flow design. For all measurements electrolyte supported cells from

Kerafol GmbH sized 100 x 100 mm² with active areas of 88 x 88 mm² based on 150 µm thick

electrolyte of scandium/cerium doped zirconia (10Sc1CeSZ) are used [Kerafol2010]. The fuel

electrode consists in nickel oxide / gadolinium-doped ceria (NiO/GDC) with an intermediate

layer of screen printed gadolinium-doped ceria. A lanthanum strontium cobaltite ferrite

(LSCF) oxygen electrode with a diffusion barrier of screen printed gadolinium-doped ceria

between electrolyte and oxygen electrode is manufactured and optimized by Kerafol GmbH

for electrolysis operation. Ceramic housing operation of these cells in electrolysis mode

under relatively high current densities of 0.9 A/cm² is reported over several thousand hours

with degradation rates below 10 mV / 1000 h [Brisse2014].

In order to provide the possibility of manufacturing planar heat pipes by welding, CROFER

22H (1.4755) serves as interconnector material instead of more adapted chromium based

materials (e.g. Plansee CFY). The slight mismatch of thermal expansion coefficients (TEC)

between 10ScSZ of approx. 10.5 ∙ 10-6 K-1 [Tietz1999] and CROFER 22H [ThyssenKrupp2010]

of approx. 11.8 ∙ 10-6 K-1 in the range 25 – 800°C was accepted due to a not entirely rigid

sealing approach (see 6.2.2).

Electric power supply

16 V, 150 A

load

high current relais

high current relais

shunt resistance

0.001 Ω SOFC cell 1

+

-

cell 1 voltage

SOFC cell 2

SOFC cell n

Pt-wire

fuel cell operation

electrolysis operation

0

1

0

1

0

1

1

0

+-

+-

+-

Experimental set-up for heat pipe stack integration

109

Figure 6.4: Stack design for 4-cell stack with planar heat pipe interconnector

The interconnectors are manufactured of metal sheets with internal fuel and air manifolding

and milled flow fields for fuel and air supply to the respective electrode. Figure 6.4 shows

this manifolding and flow field concept that allows a planar heat pipe stacking, where

extraction of heat from the stack is possible.

Contacting on anode side is improved with nickel current collecting screen meshes (99.6 %

Ni) of variable thickness and mesh number (mesh sizes 80-180). Total mesh thickness is

adapted to balance anode sealing thickness in order to get a planar cell placement. The

contact mesh is spot welded onto the anode interconnector flow field before setting up the

stack. Applying the spot welding apparatus (WELMA 2000, Robbe) with current peaks up to

2500 A, a dense welding spot pattern is executed on the mesh. Lanthanum strontium

cobaltite ferrite (LSCF) contact paste (from NexTech Materials) is applied green on the

cathode flow field contact ribs during stack assembly in order to improve contact on cathode

side. Neither nickel coating on anode nor protective coating against chromium evaporation

is used to improve long-term stability of the stack set-up. The experiments are conceived for

a first evaluation of the heat pipe concept and therefore no improved degradation

resistance is necessary. For long-term testing however, an improved interconnector

preparation will be mandatory.

fuel in

air out fuel outtensioning

interconnector

Ni contact mesh

cell (ESC)

sealing anode

Planar

Heat Pipe

Stack top plate

stack

repeating

unit

sealing cathode

gas supply

gas manifold

air in


110

Figure 6.5: Installed 3-cell short stack with heat pipe interconnector in SOC test rig

6.2.2 Sealing concept

Commercial stack designs mostly apply glass sealing tape in order to seal interconnectors

and cells within the stack. For the first tests of heat pipe integration this sealing concept

however brings two major drawbacks: Firstly, it is a very rigid sealing that does not allow

minor movements due to slight material mismatches and heat pipe particularities. Secondly,

firing schedules of these glass seals demand heating up to e.g. 930°C [Kerafol2009], i.e.

above saturation temperature of sodium under ambient pressure. 930°C is equivalent to an

internal pressure of 1.5 bar leading to a bulging of the planar heat pipe structure and

damages to the stack during joining process.

Therefore, compressible gaskets from Flexitallic (Thermiculite 866 or Thermiculite 866LS

[Hoyes2013]) realize the stack internal sealing in this work. These mica based sealings are

designed for low compression SOFC applications. They are hybridized with a thin layer of

glass coating on each side that adapts to surface irregularities and closes microstructural

gaps. This leads to a significant reduction of leakage rates by a factor of ten at low gasket

stresses, e.g. 0.1 MPa compared to uncoated mica sealing [Flexitallic2013].

No auxiliary cell frame is used in the applied sealing concept. 0.7 mm thick Thermiculite

866LS provides shape cut gaskets for anode and cathode side (compare Figure 6.6), that

provide direct sealing due to their thermal activity and compressibility. Cathode sealing is

closely placed into machined channels, while Nickel mesh spot welded to the anode

interconnector side balances sealing thickness on the anode side. The stack is loaded with

0.5 – 1 kN resulting in average stresses of approx. 0.2 - 0.4 MPa on the gasket.

HP interconnector

current connectors

voltage probes

stack tensioning

Gas pre-heaters

thermocouples

furnace base

plate


111

Figure 6.6: Sealing concept of short stack based on compressible gaskets

6.2.3 Heat pipe integration

The heat pipe interconnector design (displayed in Figure 6.7) bases on the planar heat pipe

design developed at the institute of energy process engineering (EVT) and described in

chapter 5. The casing was milled into CROFER 22H sheets, pre-treated at 650°C during 90

min for stress relieving, with the cathode flow fields machined on the external side. Screen

meshes woven from high temperature steel wire (X15CrNiSi25-21, 1.4841) provided the

internal capillary structure, required to distribute the liquid working fluid (details see Table

6.1). Coarse meshes ensured the upkeep of heat pipe vapor space during below atmospheric

pressure operation (according to design C). This 2-D open arrangement allows a thermal

transport in all directions within the interconnector plane and therefore an ideal heat

spreading. The heat pipe interconnector is closed with a top plate carefully welded together

by tungsten arc welding (GTAW, low current density). After filling procedure and heat pipe

activation according to chapter 5, hydrogen protection was set up by an intermediate air

layer. Therefore, a Mesh 198 stainless steel wire screen was spot welded on the heat pipe

casing. A hydrogen membrane with a milled anode flow field was equivalently spot welded

onto this set-up, sealed with Thermiculite gaskets around the gas flow channels.

Table 6.1: Heat pipe interconnector design parameters

Heat pipe parameter Value Material

Outer dimensions 270 x 130 x 4.5 mm CROFER 22 H (1.4755)

Capillary structure Screen Mesh (Mesh 98)

d = 130 µm, w=200 µm

Screen Mesh (Mesh 187)

d=56 µm, w=80 µm

Stainless steel

X15CrNiSi25-21

(1.4841)

Vapor space Screen Mesh (Mesh 8)

d = 600 µm, w=2500 µm

Stainless steel

X15CrNiSi25-21 (1.4841)

Sodium content 10.0 g +/- 1 g Na 99.9 %

Degasing time 3 h at 800°C, 0.047 MPa

anode sealing

(semi-transparent) solid oxide cell

(anode up)

cathode sealing


112

The manufactured heat pipe interconnectors weere tested before application within the

short stacks and showed maximum heat transfer above 400 W for horizontal and almost

perfectly isothermal operation at operation temperature 800°C.

Figure 6.7: Explosion view of the heat pipe interconnector

Figure 6.8: Images of the heat pipe interconnector: a) open with capillary and mesh structure; b) cathode flow field; c) with SOFC placed

6.2.4 Temperature measurement instrumentation

The short stacks are set up in order to evaluate the effect of the planar heat pipe

interconnector on temperature distribution within the stack. Temperature profile recording

within the short stack was realized with a total of 20 thermocouples (type K/N, d=0.75 - 1.0

mm) placed within the short stack. The thermocouples were inserted into small holes or

channels drilled respectively milled parallel to gas flows into the interconnectors. Figure 6.9

shows the distribution of thermocouple groups within the short stacks. 5 thermocouples are

2 x Mesh 98

2 x Mesh 98

1 x Mesh 8

Mesh 198

Gaskets0.7 mm

Anode hydrogen membranewith anode flow field

Heat pipeinterconnector bodywith cathode flowfield

filling pipes

heat pipe top plate

a) b) c)


113

placed in each boundary layer interconnector of the stack, i.e. within the upper anode

interconnector (TC A) and the lower cathode interconnector (TC C). 9 thermocouples

measure intermediate interconnector temperatures (TC M). Thermocouples TC C and TC A

are placed equidistantly distributed in air flow direction, where the main temperature

gradient is expected, while thermocouples TC M record temperature profiles in both flow

directions (compare Figure 6.10). The 1.1 mm holes with depth up to 115 mm were spark

eroded into the interconnector after its manufacturing and provide access for the

thermocouples. In the case of heat pipe integration the thermocouples TC M are placed in

channels within the intermediate air layer between heat pipe casing and hydrogen

membrane (compare Figure 6.7). A further group of thermocouples (TC HP) is in contact to

the heat pipe casing outside the stack (but still inside the furnace). These thermocouples are

shielded and isolated against the furnace environment with insulation glass tape.

Thus, the thermocouple insertion did not affect flow field design and had only neglectable

effect on thermal behavior of the stack. A comparison of grouped thermocouples (TC C, TC

M, TC A) in an isothermal copper calibrator showed very small deviations of the

thermocouples themselves of +/- 0.2 K at 800°C but relevant deviations of +/- 1.5 K due to

the impreciseness of compensation temperature measurement within the transducer

(Bernecker und Rainer, AT6402).

Figure 6.9: Distribution of thermocouple groups in the different layers of a two cell stack

SOFC

SOFC

metal interconnectorplanarheat pipeinterconnector

Fuel

interconnectorTC A

TC C

TC HP

TC HP

SOFC

SOFC

metal interconnectorinterconnector

Fuel

interconnectorTC A

TC C

TC HP

withoutHeatpipe

withHeatpipe

TC M

TC M


114

Figure 6.10: Distribution of thermocouples in the intermediate interconnectors

6.3 Experimental results

6.3.1 Short stack preparation and evaluation

Stack conditioning

After setting up the stack, but prior to electrochemical operation, the short stacks pass a

conditioning cycle, developed according to cell manufactures (Kerafol GmbH) indications

(see Table 6.2). Stacks are heated from room temperature with a moderate temperature

gradient of 4 K/min to 300°C. Inert gas and air flows sweep fuel and air electrode during

further heat up to 850°C at 2 K/min. Once temperature ramp finishes, the reduction phase of

the nickel-cermet on fuel cells anode starts. Highly diluted hydrogen (F5 in ambient

temperature humidified nitrogen) is used to guarantee a slow reduction of the NiO to

elementary Ni without damaging the anode structure. After an initial reduction phase of 60

min, nitrogen flow is stepwise reduced. For final conditioning, forming gas is step by step

replaced by hydrogen, until a 50 % H2 / 50 % N2 mixture is reached. After finishing this

procedure the stack is considered fully operational.

TC M 1

TC M 2

TC M 3-7

TC M 8

TC M 9

20

40

40

20

Air

Fuel

Topview anode

Experimental results

115

Table 6.2: Stack heat up and reduction program on basis of a 1-cell short stack

Step Temperature

gradient set

point (duration)

F5

[SL min-1]

N2

[SL min-1]

H2O H2

[SL min-1]

Air Flow

[SL min-1]

Heat Up 1 4 K / min 300°C 0 0 0 0 0

Heat Up 2 2 K / min 850°C 0 0.5 0 0 1.0

Reduction 1 850°C

(60 min)

0.5 2.0 Bubbler

(25°C)

0 1.0

Reduction 2 850°C

(90 min)

0.5 2.00.5 Bubbler

(25°C)

0 1.0

Conditioning 850°C

(30 min)

0.50 0.5 Bubbler

(25°C)

0 0.5 1.0

iV-curve evaluation and electrical resistances (ASR values)

The stack evaluation experiments were performed at oven temperatures fixed at levels

between 775 and 830°C, while the stack temperature was obtained as by averaging internal

thermocouples that provide a different temperature. The stack iV-polarization curves are

recorded for SOFC as well as SOEC operation mode with standard gas environments. For iV-

curve acquisition in both SOFC and SOEC current steps of 1 A, i.e. 13 mA cm-², were hold for

approx. 90 s while voltage of each cell is recorded and subsequently averaged over steady

state of each step.

Figure 6.11 shows a typical polarization curve recorded for a 1-cell short stack design. It is

recorded at approximately 850°C stack temperature and in 50 % H2 / 50 % H2O fuel gas

environment in order to provide comparability to manufactures data for the corresponding

cell type. It is clearly visible that the performance of the cell tested in the above presented

stack set-up is not able to reach the performance of the manufacturers measurements. SOFC

as well as SOEC operation indicated an area specific resistance (ASR) of approx. 0.64 V A-1

cm2 compared to 0.23 V A-1 cm2 given by Kerafol. The drop in performance shows the

increase of electrode contact resistance in the stack compared to ceramic housing

operation. Ideal planarity, perfect cathode contacting with Pt-meshes, platinum paste and

leak free ceramic sealing are the reasons that lead to that performance deviation.

Figure 6.12 displays the evaluation of iV-polarization curves for changing stack temperature

levels in order to evaluate internal leakage behavior and cell contacting in the stack.

Analysing open circuit voltage behavior (OCV) and comparison with theory shows slight

deviations Δ𝑉 from expected Nernst voltages 𝑉𝑁 that can be assigned to sealing

imperfections within the stack.


116

Figure 6.11: Comparision of iV-curves in SOFC and SOEC operation mode between manufacture’s data in ceramic housing and own measurements in 1-cell stack.

The leakage rate 𝑙𝑒𝑎𝑘,𝑂2 and the voltage deviations can be brought into the following

relation for the assumption of a leak from cathode to anode side

Based on the results an internal leakage rate of approximately 3 - 16 % could be estimated

depending on the different stack set-ups.

It is in particular increased with internal heat pipe interconnectors due to a certain non-

planarity of the manufactured prototypes. This value lies in the upper range of typical values

for stacks based on glass sealings that are in the range of 1 % - 2 % [Jensen2016] and

therefore a temperature compensation was necessary for evaluation due to the heating

effect of the leakage.

Based on the slope of the polarization curves, the ASR values can be obtained that show the

expected increase at lower temperatures due to increasing polarization losses. Comparing

these to data from Kerafol, partly extrapolated to lower temperatures shows that mainly cell

internal resistances are responsible for this behavior and that electric contacting resistance

stays approximately constant at different operation temperatures. The experiments show

that for correct electrical stack description an electrical contact resistance has to be added

to the pure ASR of the cells as obtained in ideal housing set-ups. The size of this additional

resistance strongly depends on the quality of the cell contacting.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

volt

age

/ V

current density / A cm-²

SOFCSOEC

data by Kerafolceramic housing, fuel: Ni-contact meshair: Pt-contact meshTop = approx. 860°Canode: 30 l h-1 H2O, 30 l h-1 H2cathode: 60 l h-1 air

measured data1 cell short stackTop = approx. 850°Canode: 36 l h-1 H2O, 36 l h-1 H2cathode: 72 l h-1 air

Δ𝑉 = 𝑉𝑁 − 𝑉𝑂𝐶𝑉 =𝑅𝑇

2𝐹𝑙𝑛 (

1 + 2𝑙𝑒𝑎𝑘,𝑂2/𝐻2𝑂

1 − 2𝑙𝑒𝑎𝑘,𝑂2/𝐻2) (6.1)


117

Figure 6.12: Evaluation of stack gas tightness / leakage behavior and electric contact under varying temperatures in SOFC operation on H2/H2O mixture

Load cyclic operation of the stack

The SOC short stack can operate both in fuel cell as well as electrolysis mode. Therefore,

evaluation effects on temperature distribution are carried out in reversible operation. Figure

6.13 shows iV-curves and temperature behavior of a 1-cell stack under varying current

densities. Due to a switch in fuel composition for SOEC operation, a step both in voltage as

well as in temperature (due to minor fuel leakage) is observed. This step and the non-

isothermal stack even at OCV-conditions can be corrected, if only temperature difference is

measured. Thereby, absolute thermocouple deviations are also corrected. SOFC curves

demonstrate the clearly increased heat balance in this operation mode resulting in stronger

temperature influence. The diagram however only displays small temperature effects of the

reaction heat of max. 15 K for SOFC operation at 0.42 A cm-2 due to the single cell set-up. In

consequence, thermal effects of electrolysis are very low. Comparing results to theoretic

heat production , shows that experimental results represent well the expected curves.

Thermoneutral electrolysis operation can be detected at approx. 1.29 V cell operation

voltage.

0

0.05

0.1

0.15

0.2

0.25

0.3

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6

volt

age

/ V

current density / A cm-²

850 °C

825 °C

800 °C

775 °C

0.6 slm H20.6 slm H2O1.2 slm Air

po

wer

/ W

cm

- ²

V /mV Experim.OCV

Calcul.VN

850 °C 910 923 13

825 °C 915 931 16

800 °C 924 938 14

775 °C 931 946 15

ASR / Ω cm-2

Experimental ASR

ROhm

[Kerafol]Ract + Rdiff

[Kerafol]estimatedel. contactresistance

850 °C 0.78 0.20 0.08 0.50

825 °C 0.87 0.25* 0.11* 0.51

800 °C 1.01 0.31* 0.15* 0.55

775 °C 1.18 0.38* 0.20* 0.60

*extrapolated from cell manufactures data


118

Figure 6.13: Individual TC temperatures compared to polarization curve (right) and averaged stack temperature difference to OCV operation compared with calculated cell heat production (left) of a 1-cell stack. Operation conditions: Tfurnace=850°C, mechanical load=0.5 kN, SOFC operation: VH2 = 0.5 SL / min, VN2 = 0.5 SL / min, SOEC operation: VH2 = 0.6 SL / min, mH2O = 30 g/h; Vair = 1 SL / min

Due to the invertible power supply an alternating fuel cell-electrolysis operation, as targeted

in an SOC based storage system, is possible. Figure 6.14 demonstrates a 1-cell stack

operated over 100 full SOFC / SOEC cycles. SOFC load was set to 15 A, while SOEC operated

with 20 A, due to a higher voltage reserve. Cycles lasted 15 min for each operation mode,

with a short break in order to bring stack current to 0 A and to perform a current load free

switching. The experiment proves that alternating operation is possible and has relevant

effects on stack temperatures. Due to the rather low current densities (SOFC: 0.2 A cm-2) and

the only 1-cell arrangement, these effects only show amplitudes around 5 K in this case. At

full stack sizes with state-of the art current densities (0.5 to 1.0 A cm-2) these variations are

supposed to provoke stack damaging thermal stress cycles.

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

-2

0

2

4

6

8

10

12

-0.8 -0.4 0 0.4

tem

per

atu

re d

iffe

ren

ce /

K

current density / A cm-2

Datenreihen2

Datenreihen3

cell

volt

age

/ V

calc

ula

ted

hea

tp

rod

uct

ion

/ W

cm

- ²

SOFCSOEC SOFCSOEC

thermo-neutralpoint

1.29 V

voltage

TC C 1-5

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

856

859

862

865

868

871

874

877

880

-0.8 -0.4 0 0.4

stac

k te

mp

erat

ure

s /

°C

current density / A cm-2


119

Figure 6.14: Reversible SOC operation of a 1-cell stack over 120 SOFC / SOEC cycles. Operation conditions: Tfurnace=850°C, mechanical load=0.5 kN, VH2 = 0.6 SL min-1, mH2O = 30 g h-1; Vair = 1 SL min-1; cycle time: 30 min

6.3.2 Temperature profile analysis

The short stacks were fed with different fuels, e.g. H2-H2O mixtures, N2 diluted H2, and

unreformed methane with steam addition for internal steam reforming. Steam-to-carbon

ratio was maintained to avoid carbon formation on Ni-electrodes (S/C≥2). Detailed flow

rates are indicated in Table 6.3.

Table 6.3: Experimental conditions applied during temperature profile evaluation for 2-cell short stacks

Test run Fuel flow H2

[SL min-1]

N2

[SL min-1]

H2O

[g/h]

CH4

[SL min-1]

Air Flow

[SL min-1]

SOFC hydrogen without HP 1.5 1.5 0 0 3.0

SOFC hydrogen with HP 1.5 1.5 0 0 3.0

SOFC CH4 without HP 0 0 96.4 1.0 2.0

SOFC CH4 with HP 0 0 96.4 1.0 2.0

SOEC without HP 1.8 0 90.0 0 3.0

SOEC with HP 1.8 0 90.0 0 3.0

0

0.7

1.4

0

20

40

0 10 20 30 40 50 60

curr

ent

/ A

volt

age

/ V

400

0

5

10

15

20

25

0

0.5

1

1.5

volt

age

/ V

0

0.2

0.4

0.6

0.8

864

866

868

870

872

33 33.2 33.4 33.6 33.8 34

tem

per

atu

re /

°C

curr

ent

/ A

flo

wH

2/

H2O

/ l

min

-1

time / h

time / h

SOEC

SOFC


120

Several 1- and 2-cell short stack set-ups, with and without integrated planar heat pipe

interconnectors (HP) have been evaluated. Due to the higher significance of the findings,

mainly results of the 2-cell arrangement are shown hereunder.

Open circuit voltages were in the range of what is theoretically expected, but 10 – 50 mV

lower, due to non-ideal sealing of the cells. Figure 6.15 shows polarization curves of a 2-cell

short stack arrangement with and without integrated heat pipe. One can conclude the non-

ideal contacting and sealing of the cells particularly in the case with heat pipe integration

into the short stack. This is mainly due to manufacturing and welding procedures during heat

pipe fabrication, resulting in non-ideally planar surfaces in the range of some 100 µm over

the cell.

Figure 6.15: Voltage polarization curves for the two cell stacks with and without integrated heat pipe interconnectors (HP). Furnace temperature: 830°C, SOFC operation: 1.5 SL min-1 H2, 1.5 SL min-1 N2, 3.0 SL min-1 air, SOEC operation: 1.5 SL min-1 H2, 90 g h-1 H2O, 3.0 SL min-1 air, power densities averaged over both cells for each stack arrangement.

For temperature distribution measurements relatively high current densities with very low

(for SOFC) or high (for SOEC) voltages have been used in order to provoke high reaction

enthalpies and thus a big thermal influence. In general, the higher the current density, the

more evident are thermal effects. This is especially important in our arrangement of a 2-cell

short stack, where temperature profiles are much less pronounced than in a complete stack

since boundary effects and ambient influence are very relevant.

For better comparison of the effects of heat pipe integration and in order to eliminate the

influence of thermocouple (TC) inaccuracy and possible leakage effects the temperature

difference Δ𝑇𝑗 of each thermocouple j versus open circuit operation 𝑇𝑗,𝑂𝐶𝑉 is calculated

based on:

power with HP

power without HP

SOEC SOFC

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

po

wer

den

sity

/ W

cm-2

volt

age

/ V

current density / Acm-2

V cell 1 with HPV cell 2 with HPV cell 1 without HPV cell 2 without HP


121

Δ𝑇𝑗 = 𝑇𝑗 − 𝑇𝑗,𝑂𝐶𝑉 (6.2)

where 𝑇𝑗 is the temperature of a specific thermocouple under a certain load condition.

Figure 6.16 demonstrates the effects of heat pipe integration on layer-averaged stack

temperatures for hydrogen operation. Depending on current densities stack temperature

and external heat pipe temperatures increases. The influence of current density and thus

electrochemical heat production on the external heat pipe temperature clearly indicates the

thermal integration of the heat pipe into the stack. Heat is transported out of the stack and

released to furnace environment proved by an increase in the external temperature of the

heat pipe. Consequently, stack temperature increase (7.6 K at 0.45 A cm-² on anode side,

11.4 K on cathode) is clearly below the temperature ΔTwithoutHP without heat pipe integration

(13.0 K at 0.45 A cm-² on anode, 17.5 K on cathode). Applying controlled cooling of the

external parts of the heat pipe, e.g. for gas preheating, the temperature increase of the heat

pipe could be balanced and thus, stack temperature further decreased. One can conclude

from the measurements that a control of heat pipe temperature could limit the stack

temperature rise ΔTc.HP to 1.0 K on anode and 5.8 K on cathode, thus to a quarter of the

increase that was measured without heat pipe integration. This first effect however, could

also be reached by an increase in excess air flow for cooling purposes.

Figure 6.16: Influence of current density on average in plane temperature for two cell stacks with and without integrated heat pipe interconnectors (HP). Furnace temperature: 830°C, SOFC operation: 1.5 SL min-1 H2, 1.5 SL min-1 N2, 3.0 SL min-1 Air, SOEC operation: 1.5 SL min-1 H2, 90 g h-1 H2O, 3.0 SL min-1 air, external temperatures of heat pipe averaged over the isothermal part of heat pipe outside the stack. 𝛥𝑇𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝐻𝑃 indicates

temperature increase without HP, while 𝛥𝑇𝑐.𝐻𝑃 shows residual temperature increase for a temperature controlled HP.

SOFCSOEC-4

0

4

8

12

16

20

24

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

tem

per

atu

re d

iffe

ren

ce t

o 0

A o

pe

rati

on

/K

current density / Acm-2

average T anode with HPaverage T cathode with HPaverage T anode without HPaverage T cathode without HPexternal temperature heat pipe


122

Therefore, Figure 6.17 shows the effects of heat pipe integration to in cell plane

temperature gradients within the stack during SOFC operation. The diagram displays fuel

flow and air flow parallel temperature measurements, thus a quasi-2-D profile of the cell

plane. In the case without heat pipe integration central temperatures increase most

significantly with increasing currents while temperatures towards the outside of the stacks

are kept lower due to the strong boundary effects of the 2-cell stack. Cell-plane internal

temperature differences of up to 15 K are detected. In the comparable case for the stack

with the integrated planar heat pipe, 2-D temperature profiles are significantly reduced. In

both, anode and cathode flow direction, one can observe a very flat temperature profile

with differences of up to a few K only. Temperature profiles are only slightly influenced by

current increases and kept at a very stable, almost isothermal level for the corresponding

cell plane.

Figure 6.17: In cell plane temperature distributions for 2-cell stacks operated in SOFC operation under different current loads. Blue lines indicate air flow parallel temperature profiles, red lines fuel flow parallel temperature profiles. Left: Without heat pipe integration to the stack structure. Right: Heat pipe interconnector designed according to table 2 integrated into the stack structure between the two cells.

850

860

870

880

890

900

0 0.2 0.4 0.6 0.8 1normalised position air flow / -

SPfurnance: 830°CVH2/VN2: 1.5/1.5 Nl/min

Vair: 3 Nl/minI= 0 .. 40 A

850

860

870

880

890

900

0 0.2 0.4 0.6 0.8 1normalised position air flow / -



0

0.2

0.4

0.6

0.8

1

850 860 870 880 890 900



0

0.2

0.4

0.6

0.8

1

850 860 870 880 890 900



temperature / °C

tem

per

atu

re/

°C

no

rmal

ised

po

siti

on

fuel

flo

w/

-

no

rmal

ised

po

siti

on

fuel

flo

w/

-

temperature / °C

tem

per

atu

re/

°C

cathode, without HP cathode, with HP

anode, without HP anode, with HP


123

Due to the rather small stack and cell sizes and limited current densities the overall effect on

pure hydrogen operation are relatively low. In order to provoke more significant

temperature profiles an internal steam reforming situation has been used, supplying

unreformed methane and steam (S/C = 2) to the stack. Flow rates assure that endothermal

fuel reforming reaction enthalpies outweigh electrochemical heat generation for all current

regimes due to a low fuel utilization of max. 0.1 for the highest current densities. For an

assumed complete reforming reaction this corresponds to a heat production of 0.89 W cm-2

compared to a maximum electrochemical heat production of 0.21 W cm-2. Consequently, the

total additional heat demand is between 0.68 and 0.89 W cm-2 depending on current load of

the stacks.

Measurements resulting in Figure 6.18 summarize the thermal effects of the above stated

heat duty on the 2-cell stacks, with and without integrated planar heat pipes. Close to the

inlet of the fuel one can observe an almost immediate drop in stack temperature compared

to open circuit hydrogen operation due to the highly kinetic reforming reactions taking

place. This leads to high temperature differences up to 43 K and in full stack situations to

very strong gradients with harmful effects on mechanical cell structure and rigid (glass)

sealings. Furthermore, due to strongly increased ionic resistances in the electrolyte these

subcooled areas are much less electrochemically active and thus decrease cell power and

efficiency. An integrated planar heat pipe in the experiments is able to reduce these strong

thermal effects to maximum temperature differences of 15 K and to flatten thermal gradient

pattern. Measurement data indicate that the integrated heat pipe structure balances

endothermal and exothermal stack regions as observable in Figure 2.6 and allows internal

heat shifting. Full stack internal natural gas reforming could be possible due to this heat

balancing mechanism, without high excess air flows, intense preheating and heat exchange

subsystems.

Figure 6.18: Temperature profiles of fuel flow parallel measurements in 2-cell stacks operated on unreformed methane steam mixtures (S/C=2). Temperatures indicate difference to open circuit hydrogen operation with and without integrated heat pipe interconnectors (HP). Furnace temperature: 830°C, SOFC operation: 1 SL min-1 CH4, 3 SL min-1 air

-60

-50

-40

-30

-20

-10

0

0 0.2 0.4 0.6 0.8 1

tem

pe

ratu

re d

iffe

ren

ce t

o 0

A

op

era

tio

n w

ith

H2/N

2/

K

normalised position fuel flow / -

0 A, without Heatpipe

20 A, without Heatpipe

0 A, with Heatpipe

20 A, with Heatpipe

Change in Heatpipe temperature(controllable)

K

K


124

6.4 Stack internal thermal contact resistances

6.4.1 Experimental method

Measurement set-up

For a calibration of the numerical model, the stack internal thermal contact resistances are

key parameters that can hardly be determined by complete stack measurements. For this

reason, an experimental evaluation (also described in [Dillig2015a]) was carried out in a test

rig conceived for high temperature contact resistance measurements similar to set-ups

proposed in literature [Liu2015; Madhusudana1996].

Figure 6.19 displays the basic set-up of the steady-state heat transfer measurement. A

thermal contact zone is established between two stainless steel cylinders (diameter d = 30

mm, upper cylinder height h+ = 80 mm, lower cylinder height h- = 70 mm, material: 1.4541,

AISI 321) with well-known thermal conductivity behavior for temperatures up to 1500 K

(used approximation kSS[W/mK] = 14.79 + 0.0145 T[K], [Touloukian1972]). The upper

cylinder partly incorporates a ceramic heating element from Bach RC GmbH (Pmax=300 W,

Tmax=1000°C), that provides the thermal power sources by electric heating. The lower

stainless steel cylinder contains an internal air cooler on its lower end that can be operated

with cooling air supplied by the supporting pipes of the set-up, controllable with a mass flow

controller (MFC, Brooks). Thereby, a steady-state heat flux from the heating element

through the contact set-up can be established. Compression weights placed on the upper

part of the set-up apply a constant compression force to the thermal joint. Contact pressure

can be adjusted from 9.8 kPa upwards, in steps of 11.5 kPa referring to total cross section of

the set-up.

High temperature insulation from Promat (Microtherm MPS, 25 mm, k = 0.034 W m-1 K-1 at

800°C) shielded with aluminum foil to the outside encloses the measurement cell and

assures very low radial heat losses for the measurement set-up. Temperatures are recorded

using 6 type K thermocouples (d = 1 mm, accuracy +/-0.004 T) placed in the center of the

cylinders with defined intervals of 10 mm (see Figure 6.21). A programmable logic controller

(PLC) operates the entire set-up, records measurement data and provides a PID-controller in

order to set interface temperature 𝑇𝑖𝑛𝑡 to predefined steps. Due to high frequent pulse

width modulation (PWM) heating is assumed continuous.

Stack internal thermal contact resistances

125

Figure 6.19: Set-up of measurement cell for high temperature contact resistance measurements.

Table 6.4: Measurement set-up parameters

Measurement set-up parameters Value

Cylinder diameter 30 mm

Cylinder material Stainless steel, 1.4541

Stack flow set-up Crossflow

Contact ribs height Anode: 0.5 mm

Cathode: 0.7 mm

Rib width / Flow channel width 2 mm / 4 mm

Fluid environment Air

Thermal contact set-up

In order to evaluate thermal contact conductance of typical heat transfer situations in SOFC

stacks, several measurement set-ups have been chosen (see Figure 6.20). The principal test

set-up (set-up 1) was a typical stack repeating unit used for SOFC / SOEC experiments at our

facilities for heat pipe integration tests (see chapter 6.2). Figure 6.19 shows the geometry of

this repeating unit. It mainly consists of the interconnector contact ribs machined into the

test cylinders of 1.4541 (in stack applications interconnector material is CROFER 22H, with

comparable heat conductivities). As for the real SOFC stack set-up, a cross flow situation is

chosen. On the anode side (upper cylinder) a Nickel contact consisting of 3 layers of Ni 99.6,

mesh 80, is spot welded onto the contact ribs with several weld points.

cooling air

stainlesssteel

cylinder

cooler section

thermocouplesT1-T6

ceramic heatingelement

high temperatureinsulation

contactinterface

compressionweights

stack repeatingunit

top view lowersteel cylinder


126

Figure 6.20: Thermal contact set-ups (explosion view)

The volumetric mesh porosity is approximately 0.7 resulting in an effective heat conductivity

of approximately 2 W m-1 K-1. The cells used for this evaluation are electrolyte-supported

cells (ESC) from Kerafol, with 150 µm thick 10Sc1CeSZ electrolyte. The cells cut into disc

shape with diameter 30 mm were used for these measurements. Cathode contacting was

enhanced with LSCF contact paste from NexTech Materials applied green between cathode

electrode and interconnector contact ribs. In order to access singular contact resistances,

further set-ups have been chosen. With set-up 2, only mesh contact resistances were

evaluated by placing the above described Ni-mesh between the two test cylinders with

interconnectors. Here, it is assumed that both thermal contacts between mesh and

interconnectors are equivalent. For measurement set-up 3 a single SOFC cell was placed

between the two cylinders contacted on both sides with LSCF contact paste to the

interconnector contact ribs. Assuming similar behavior of anode and cathode electrodes

(mainly due to their very low layer thickness), only contact resistance 𝑅𝑐3 on both sides and

cell conductive resistance are assumed to contribute to total resistance in this case.

SOFC stacks resemble not only stack cells and contacting materials, but also contain gas

manifoldings i.e. regions where interconnector layers are separated by gas sealings, in order

to distribute fuel and oxidant gases. To account for the contact situation, a test set-up 4 has

been studied where the thermal resistance of different sealing materials was evaluated.

Typical sealants like glass sealings (here Keraglas ST K02, 0.3 mm from Kerafol) and mica

sealings (here Thermiculite 866, 0.7 mm from Flexitallic) or hybrid sealings (here

Thermiculite 866LS, 0.7 mm from Flexitallic) have been applied between two test cylinders.

These were similar to the before described cylinders, planar however, without containing

the contact ribs structure. The mica sealing and hybrid mica with thin glass layer for

sealing

· Thermiculite 866, 0.7 mm

· Thermiculite 866LS, 0.7 mm

· Keraglas ST K02, 0.3 mm

ESC-cell

Ni – mesh3 layers mesh 80spot welded

contact ribs anode

LSCF paste

contact ribs cathode

interconnector(1.4541)

interconnector(1.4541)

Set-up 1Stack repeating

unit

Set-up 2only contact

mesh

Set-up 3only SOFC - cell

Set-up 4sealing, no ribs


127

improved sealing behavior were used without joining procedure. Keraglas ST K02 sealing was

joined according to firing schedule at 930°C.

6.4.2 Evaluation procedure

A measurement procedure similar to literature [Liu2015; Wang2012] was applied. The

contact situation was set up between the cylinders and the contact temperature was

stepwise (100 K) increased from 150°C to 800°C. Each temperature step was hold until

stationary heat transfer conditions were obtained and no further drift in temperature or

heating power could be observed. Experimental evaluation follows a stepwise procedure.

Thermal contact resistance (TCR) is defined by:

where 𝑅𝑡ℎ denotes the resistance of the entire contact situation at the corresponding

interface temperature 𝑇𝑖𝑛𝑡, 𝑡𝑟𝑎𝑛𝑠 the heat flux perpendicular to the interface, ΔT the

temperature difference at the contact interface. 𝑇𝑖𝑛𝑡+ and 𝑇𝑖𝑛𝑡

− describe temperatures on the

upper respectively lower interface of the contact.

In this work the obtained results are used to calculate unit conductances or specific heat

transfer coefficient ℎ𝑐𝑜𝑛𝑡𝑎𝑐𝑡 of the contact joints

Due to the well isolated measurement set-up, heat flux in the stainless steel cylinder is

assumed to be 1 – dimension in vertical (z-) direction and radial heat flux can be neglected. A

numerical analysis of the test set-up (see Figure 6.22) confirmed this isothermal assumption

for the cross section of the set-up. The heat flux resulted to be very uniform through the

contact interface.

Consequently, heat transfer 𝑡𝑟𝑎𝑛𝑠 through the contact interface can be obtained from

where 𝑡𝑟𝑎𝑛𝑠+ and 𝑡𝑟𝑎𝑛𝑠

− are given by

𝑅𝑡ℎ(𝑇𝑖𝑛𝑡) =Δ𝑇𝑖𝑛𝑡

𝑡𝑟𝑎𝑛𝑠=𝑇𝑖𝑛𝑡+ − 𝑇𝑖𝑛𝑡

−

𝑡𝑟𝑎𝑛𝑠 (6.3)

ℎ𝑐𝑜𝑛𝑡𝑎𝑐𝑡 = (𝑅𝑡ℎ ∙ 𝐴𝑐𝑜𝑛𝑡𝑎𝑐𝑡)−1 (6.4)

𝑡𝑟𝑎𝑛𝑠 =1

2(𝑡𝑟𝑎𝑛𝑠

+ + 𝑡𝑟𝑎𝑛𝑠− ) (6.5)


128

Here 𝑇𝑖 (𝑖 = 1, . . ,6) denotes the temperature of the thermocouple at measurement position

i, with a relative height 𝑧𝑖 (see Figure 6.21). For reasons of simplicity thermal conductivity in

the stainless steel cylinder 𝑘𝑠𝑠 is evaluated for average cylinder temperature 𝑇𝑎𝑣𝑔.

Interface temperatures 𝑇𝑖𝑛𝑡, 𝑇𝑖𝑛𝑡+ and 𝑇𝑖𝑛𝑡

− can be obtained by a linear extrapolation of the

temperature profiles along the cylinders due to Fourier’s law of thermal heat conduction:

Single contact resistance, e.g. of the interface anode electrode – Ni-mesh are not accessible

separately, since each set-up includes several contact situations. Therefore, a variety of

measurement set-ups has been chosen where total heat transfer and contact resistance are

recorded (for set-ups see Figure 6.20).

Contact resistance values for singular interfaces can be obtained by combining analytic heat

transfer calculations 𝑡𝑟𝑎𝑛𝑠 and measurement data 𝑡𝑟𝑎𝑛𝑠 in order to set-up a system of

heat transfer equations k

that can be solved by determining the unknown contact resistance values 𝑅𝑐1, 𝑅𝑐2, 𝑅𝑐3 by

minimizing analytical deviation from measurement results:

𝑡𝑟𝑎𝑛𝑠+ =

1

2(𝑘𝑠𝑠(𝑇𝑎𝑣𝑔)

𝑇1 − 𝑇3𝑧1 − 𝑧3

)

𝑡𝑟𝑎𝑛𝑠− =

1

2(𝑘𝑠𝑠(𝑇𝑎𝑣𝑔)

𝑇4 − 𝑇6𝑧4 − 𝑧6

)

(6.6)

𝑇𝑖𝑛𝑡 =1

2 (𝑇𝑖𝑛𝑡

+ + 𝑇𝑖𝑛𝑡− )

𝑇𝑖𝑛𝑡+ = 𝑇3 −

𝑡𝑟𝑎𝑛𝑠+

𝑘𝑠𝑠(𝑇𝑎𝑣𝑔) (𝑧3 − 𝑧𝑖𝑛𝑡

+ )

𝑇𝑖𝑛𝑡− = 𝑇2 +

𝑡𝑟𝑎𝑛𝑠−

𝑘𝑠𝑠(𝑇𝑎𝑣𝑔) (𝑧𝑖𝑛𝑡

− − 𝑧4)

(6.7)

Δ𝑇𝑖𝑛𝑡,𝑘

𝑡𝑟𝑎𝑛𝑠,𝑘=∑[𝑅𝑖,𝑘

𝑠 + (∑1

𝑅𝑖,𝑗,𝑘𝑝

𝑗

)

−1

]

𝑖

(6.8)

min𝑅𝑐1,𝑅𝑐2,𝑅𝑐3

∑|𝑡𝑟𝑎𝑛𝑠,𝑘 − 𝑡𝑟𝑎𝑛𝑠,𝑘|

𝑘

(6.9)


129

Figure 6.21: Left: Calculation of interface temperatures and temperature differences for the contact resistance measurement of set-up 1 at 800°C contact temperature, Gaussian error bars of temperature measurements and inaccuracies of positioning are smaller than displayed markers; right: Geometry of test specimens for thermal contact measurements.

6.4.3 Measurement uncertainties

Uncertainties in the experiment for thermal resistance measurements under consideration

arise from thermocouple errors due to wrong calibration, comparison temperature and heat

loss via TC casing, errors from thermal conductivity of the stainless steel 𝑘𝑠𝑠 and

uncertainties of cross sectional area. Temperature inaccuracy 𝑢𝑇 is assumed to be ± 0.004 T.

Uncertainties of thermal conductivity 𝑢𝑘 are estimated with +/- 5 % precision, of vertical

positioning of the thermocouples 𝑢𝑧 +/- 0.5 mm and of the cross sectional area of the

contact interface 𝑢𝐴 is estimated to be +/- 5 %.

Uncertainties of final heat transfer h are computed using Gaussian error propagation

according to:

T1

T2

T5

T6

thermal contactinterface

0

10

20

30

40

50

60

70

600 700 800 900 1000

Ver

tica

l po

siti

on

z /

mm

Cylinder temperature / °C

T1

T2

T3

T4

T5

T6

z

30

720 770 820 870

0

1000

2000

3000

rib cathode

Ni- mesh

rib andoe

SOFC

solid steel

solid steel

Rc2

Rc3

Rc1

Tint

Temperature / °C

35.0

36.0

37.0

34.0

Posi

tio

n /

mm

35.0

37.0

34.0

36.0

rib anode

T3

T4


130

The partial derivatives of the heat transfer coefficients have been analytically determined

from the equation set (6.3) to (6.7).

The corresponding error bars are given with the measurement results. Uncertainty

estimation of the calculated contact resistances 𝑅𝑐𝑖 applied a comparable approach based

on the obtained heat transfer uncertainties and are displayed in the figures. Further

uncertainties regarding the heat transfer calculation approach e.g. for the mesh conduction

are not considered here.

Figure 6.22: Left: Uniformal heat transfer in contact interface according to numerical evaluations, Right: comparison with experimental validation via radial movement of the thermocouples with casing thickness t = 0.2 mm, small deviations from central temperature measurements can be almost completely explained by heat conduction in the thermocouple casing.

6.4.4 Results and Discussion

Figure 6.23 left displays the results of the heat transfer measurement of set-up 1, where

different compression forces are applied. The first measurement campaign with 32.8 kPa

load was carried out with not-preoxidized steel, while the following measurements were

executed with the same set-up (thus already oxidized) but different loads. It can be observed

that contact compression in the relevant range between 21 – 44 kPa does not have a major

influence on the heat transfer through the set-up. However, results show that oxidation and

plastic deformation at high temperatures during the first run improve thermal contact at low

temperatures for the following measurements. Therefore, only measurements after initial

oxidation and deforming due to a first heat up to 800°C have been used for further

evaluation.

Heat flux throughcontact W/m² K

4.21 e+04

4.09 e+04

4.15 e+04

0

100

200

300

400

500

600

700

800

900

0 0.01 0.02 0.03 0.04 0.05

T /

°C

radial distance from centre / m

780

785

790

795

800

805

810

0 0.01 0.02

T [°

C]

t=0.1 mm

t=0.2 mm

steel insulationgap

assumedtemperature profile

measured data

𝑢ℎ = √∑(𝜕ℎ

𝜕𝑇𝑖)2

𝑖

𝑢𝑇2 +∑(

𝜕ℎ

𝜕𝑧𝑗)

2

𝑗

𝑢𝑧2 + (𝜕ℎ

𝜕𝑘)2

𝑢𝑘2 + (

𝜕ℎ

𝜕𝐴)2

𝑢𝐴2 (6.10)


131

Figure 6.23: Left: Heat transfer measurement (normalized to cylinder cross section) through full stack set-up, (set-up 1) for different load situations, blank steel or pre-oxidized steel, error bars are only shown for 32.8 kPa and 21.3 kPa measurement.Right: Resulting heat transfer rates (based on cylinder cross section) for different stack-relevant set-ups, pre-oxidized steel surfaces, 44.3 kPa contact pressure.

Figure 6.23 right shows the resulting specific heat transfer rates through the set-ups

according to Figure 6.20 with error estimations following equation (6.10). Heat transfer rates

are significantly increasing with temperature for all three set-ups, due to strong temperature

dependency of thermal radiation. Heat transfer for set-up 3 is clearly higher than in other

cases (especially for low temperatures) as a result of the increased contact conductance due

to cathode contacting paste applied according to Figure 6.20. These values are used to

compute resistances at the contact points within one SOFC repeating unit following the

procedure described in equation (6.8) and (6.9). Figure 6.24 shows the outcomes of this

approach, heat transfer resistances normalized to actual contact area that may be used for

heat transfer simulation e.g. in computational fluid dynamics (CFD) models. Display errors

show measurement uncertainties that however do not account for deviations between

theory and experiment for the calculated heat transfer resistances (e.g. mesh thermal

conductivity). The results show that thermal contact between cathode and interconnector

ribs is best, presumably due to LSCF contact paste, but showing low temperature influence.

In contrast, interface contacts between mesh and interconnector ribs as well as anode are

worse due to the low number of contacting points. One can clearly observe the high

temperature dependency of the contact resistance itself, especially for contact Rc2, where

radiation between porous anode and Ni-mesh is one of the main contributors to heat

transfer (see Figure 4.6).

0

100

200

300

400

500

600

0 200 400 600 800 1000

Hea

t tr

ansf

er /

(W

/ m

- ² K

-1)

Contact temperature / °C

set-up 1, full repeating unit

set-up 3, cell only

set-up 2, mesh only0

100

200

300

400

0 200 400 600 800 1000

Hea

t tr

ansf

er /

(W

m- ²

K-1

)


32.8 kPa, not pre-oxidized

21.3 kPa, oxidized

44.3 kPa, oxidisedoxidized


132

Figure 6.24: Heat transfer resistance of the different contact points within a repeating unit of the stack (Rc1: interconnector ribs – Ni-mesh; Rc2: Ni-mesh – anode; Rc3: cathode – interconnector ribs).

The measured contact resistances are in the range of 3 cm² K W-1 (Rc3) to 8.5 cm² K W-1

(Rc2) at 800°C for the set-up in ambient atmosphere, which is in good accordance with the

wide spreading typical values obtained for solid contacts [Madhusudana1996]. It has to be

mentioned that a change in anode atmosphere, besides its influence on gas channel

convective heat transfer has also an effect on contact resistances.

Table 6.5: Resulting heat transfer resistances for stack repeating unit at different temperature levels (for graphic representation see Figure 4.6)

relevant cross-section 350°C 650°C 800°C

10-4 m² 10-4 K m² W-1 10-4 K m² W-1 10-4 K m² W-1

𝑅𝑐𝑜𝑛𝑑,𝑖𝑛𝑡𝑐𝑎 7.07 0.22 0.20 0.19

𝑅𝑐𝑜𝑛𝑑,𝑟𝑖𝑏𝑐𝑎 2.36 0.31 0.28 0.27

Rc3 2.36 4.65 3.85 3.38

𝑅𝑐𝑜𝑛𝑣𝑐𝑎 4.71 97.69 72.96 65.27

𝑅𝑟𝑎𝑑𝑐𝑎 4.71 224.00 68.88 43.84

RSOFC 7.07 1.03 0.99 1.09

Rc2 7.07 14.34 9.54 8.18

Rmesh 7.07 4.06 3.50 3.26

𝑅𝑟𝑎𝑑𝑎𝑛 4.71 201.60 61.99 39.46

𝑅𝑐𝑜𝑛𝑣𝑎𝑛 * 4.71 8.37 6.11 5.40

Rc1 2.36 8.68 6.06 4.29

𝑅𝑐𝑜𝑛𝑑,𝑟𝑖𝑏𝑎𝑛 2.36 0.22 0.20 0.19

𝑅𝑐𝑜𝑛𝑑,𝑖𝑛𝑡𝑎𝑛 7.07 0.22 0.20 0.19

Rru 7.07 41.17 30.24 26.13

* R_conv_an corrected to fuel atmosphere at anode (H2/H2O = 1:1)

0

5

10

15

20

25

0 200 400 600 800 1000

Co

nta

ct r

esis

tan

ce /

(cm

² K

W-1

)


Rc1

Rc2

Rc3

Comparison with numerical results and error estimations

133

Figure 6.25: Heat transfer measurement through SOFC sealing materials (set-up 4) at constant contact compression of 83 kPa.

According to [Madhusudana1996], gas gap conductance plays an important role when

considering low compression thermal contacts. For fluids with high thermal conductivity

(e.g. H2) the value of gas contact conductance can vary considerable compared to air (by a

factor of approx. 6). Therefore, it is expectable that contact resistance in anode atmosphere

(Rc1 and Rc2) is lowered compared to the measurements in ambient air.

To complete thermal contact resistances required for numerical or CFD simulation of stacks,

heat transfer rates through typical SOFC sealing materials have been experimentally

determined. Set-up 4 according to Figure 6.20 placed either mica sealing or glass sealing

between two plain steel cylinders, machined and sanded without any gas channel structure.

Before experimental evaluation, the glass sealing set-up was joined at 930°C according to

joining procedure given by the manufacturer. Results of heat transfer rates and thermal

contacts resistances (Rc4) are displayed in Figure 6.25. As a result thermal contact resistance

with mica sealing is approximately two orders of magnitude higher than with glass sealing,

partly due to lower thermal conductivity of the bulk material but mainly due to the

differences in interface resistance. The joining procedure brings the glass sealing in very

close thermal contact to the steel cylinders and a very low thermal contact resistance, close

to 0 can be assumed.

0

100

200

300

0 200 400 600 800

Hea

t tr

ansf

er h

/ (

W m

- ² K

-1)

Contact temperature T / °C

h 866

h 866 LS

h glass x 10e-2

0

5

10

15

20

0 200 400 600 800

Co

nta

ctre

sist

ance

Rc4

/ (c

m²

W K

-1)

Contact temperature T / °C

Rc 866 LS

Rc 866

Rc glass


134

6.5 Comparison with numerical results and error estimations

Experimentally obtained temperature profiles and thermal contact resistances serve as basis

for validation and calibration of the numerical stack model presented in chapter 4. Results

based on fuel cell operation with hydrogen fuel as well as methane were used for these

evaluations. Contrarily, results in electrolysis operation are not considered since they only

provided very low temperature gradients (of only a few K) in the experiments. These are

overrun by inaccuracies of the measurements and effects due to stack internal leakage. In

order to compare temperature distributions, in additional to thermal resistances, the

electrical resistance behavior (ASR) of the stack has to be calibrated to experimentally

obtained results of the set-up as e.g. shown in Figure 6.26:

𝐴𝑆𝑅 (𝑇𝑐𝑒𝑙𝑙) = 0.0324 𝑉

𝐴𝑚² ∙ 𝑒𝑥𝑝(−0.00696 ∙

(𝑇𝑐𝑒𝑙𝑙 − 273.15)

1 𝐾) (6.11)

ASR values were similarly applied for pure hydrogen operation as well as for stack operation

on methane with direct internal reforming on anodes. Figure 6.26 proves that the ASR fit for

H2 well represents the iV-curve for CH4 operation.

Methane steam reforming kinetics were set in accordance with chapter 2.5. Pre-exponential

factor k of steam reforming (SR) was set to 85420 kmol m-3 s-1, activation energy to 95 kJ

mol-1, rate exponent of CH4 to 0.85 and of H2O to -0.35. Kinetics of water-gas-shift reaction

(WGS) are set to k = 85.4 ∙ 10³ kmol m-3 s-1, activation energy to 95 kJ mol-1, assuring that

WGS is considerably faster than SR and thus constantly close to equilibrium. Backward

reaction for WGS is enabled.

Figure 6.26: Comparison of measured and experimentally calculated SOFC polarization curves (ASR used in FLUENT model was fit to accord to experimentally determined cell performance according to equation (6.11)). Furnace temperature: 830°C, SOFC H2 operation: 1.5 SL min-1 H2, 1.5 SL min-1 N2, 3.0 SL min-1 Air, CH4 operation: 1 SL min-1 CH4, 96 g h-1 H2O, 3.0 SL min-1 air

0

5

10

15

20

25

0

0.2

0.4

0.6

0.8

1

1.2

0 2000 4000 6000

volt

age

per

cel

l / V

i / A m-²

po

wer

per

cel

l/ W

FLUENT simulation

experimental data

Pel

Vop


135

Since experiments were based on short stack set-ups with maximum 2 cells, thermal

influence of surroundings is very important and furnace boundary conditions play a very

important role. However, these boundary conditions could only be determined to a certain

degree since furnace wall temperatures / stacks support temperatures and several heat

transfer coefficients could only be estimated. Therefore, an operational situation with strong

temperature gradients, i.e. the steam reforming case without heat pipe interconnector, was

used to set thermal boundary conditions to stack surroundings. This calibrating situation is

displayed in Figure 6.27 left. Heat transfer to furnace environment was therefore described

by surface emissivities of 1 and furnace mean radiation temperature (MRT) to 1133 K. Heat

transfer coefficient from stack to upper and lower baseplate for stack compression was set

to 250 W m-2 K-1. These boundary conditions were kept constant when evaluating the model

in the different operation set-ups with and without heat pipe interconnector.

Figure 6.27 shows temperature distributions obtained from experiments and CFD modeling

during full internal reforming operation of a two-cell stack with and without heat pipe

interconnector at a moderate stack current of 20 A. The left distribution indicates the clear

drop in temperature due to endothermal reaction by approx. 30 K that is equivalently

predicted by numerical results. The right distribution shows how the introduction of the heat

pipe interconnector is able to reduce the large temperature drop. The numerical model is

able to reproduce quantitatively the observed effect up to a certain accuracy and predicts a

clear reduction of the cell internal temperature difference to approx. 10 K.

Figure 6.27: Comparison between numerical and experimental results of in plane temperature profiles 2 cell stacks operated on unreformed methane steam mixtures (S/C=2). Temperatures with (right) and without (left) integrated heat pipe interconnectors (HP) are shown. Furnace temperature: 830°C, SOFC operation: 1.0 SL min-1 CH4, 96 g h-1 H2O, 3.0 SL min-1 air, stack current: 20 A

1107 K

1104 K1099 K1111 K1125 K1129 K

1098 K1104 K1109 K1118 K

1103 K

1108 K

1102 K

1108 K

1105 K

1102 K

1112 K

1122 K

Air

Fuel

m0 0.03 0.06 0.09 0.12 0.15

0.03

0.06

0.09

0.12

m

1117 K

1118 K1114 K1119 K1127 K1124 K

1114 K1117 K1119 K1123 K

1117 K

1119 K

1117 K

1119 K

1113 K

1114 K

1113 K

1113 K

Air

Fuel

m0 0.03 0.06 0.09 0.12 0.15

0.03

0.06

0.09

0.12

m

activecell area

activecell area

T in K

1098 11321109 1121

measuredtemperatures

simulationresults


136

Reforming activity of the SOC anode structure is further evaluated by analyzing anode off

gas concentrations. Figure 6.28 shows results of gas analyzer measurements of dried exhaust

gas of a 2-cell stack operated on unreformed methane at a S/C-ratio of 2 at 830°C furnace

temperature. At OCV conditions the GA measures a H2 : CO ratio of approx. 4.3 that is close

to thermodynamic equilibrium ratio of 4 at stack operation temperature and a CO : CO2 ratio

of approx. 2. Methane off-gas concentration however is 2.8 mol% compared to a complete

reforming according to thermodynamics equilibrium model. FLUENT simulation also

previews a small methane concentration of approx. 1.2 mol% in anode off-gas due to the

kinetic restrictions. Additionally, in experimental stack evaluation, a certain amount of gas

may pass the anode gas channels without reaching the catalytic surface of anode, thus

without being reformed. These differences in methane reforming can partly explain

deviations between simulation and experimental evaluation of the dry off-gases. A second

effect however is certainly stack leakage or loss of pre-dominantly hydrogen. The trends of

concentration changes at increasing current densities are in good accordance with the

FLUENT modelling set-up.

Figure 6.28: Dry off-gas concentrations (after condensation) of the exhaust gas of 2-cell stacks operated on unreformed methane steam mixtures (S/C=2) at different stack currents. Filled column show values measured at the experimental set-up with gas analyzer, hatched column results of FLUENT model. Furnace temperature: 830°C, SOFC operation: 0.5 SL min-1 CH4, 48 g h-1 H2O, 1.5 SL min-1 N2, 3.0 SL min-1 air

Figure 6.29 shows the experiment – model comparison of fuel parallel temperature profile

for a larger number of operational cases based on constant thermal boundary conditions to

the furnace. The model is able to represent the effects of an introduction to the SOC stack

up to a level that is required for stack layout purposes. Especially, it displays the effect of the

heat pipe to the flatten temperature profiles and is able to provide heat for internal steam

0%

10%

20%

30%

40%

50%

60%

70%

0 10 20 35

dry

off

-gas

sp

ecie

s co

nce

trat

ion

s/

-

stack current / A

H2

CO2

CO

CH4

GA measurement FLUENTsimulation

rest: N2


137

reforming reactions, which are quantitatively represented. The remaining deviations are

mainly caused by stack internal fuel leakage that leads to increased temperatures where the

fuel reacts with oxygen from the cathode side. It is observable that the fuel leakage caused

temperature increases of around 10 K at singular TCs in some measurements, what had to

be considered for the evaluation in the above described matter. In particular, these leakage

effects are responsible that no meaningful comparison of the numerical model and

experimental data is feasible for the SOEC operation, where very small temperature effects

appeared experimentally.

Figure 6.29: Temperature profiles of fuel flow parallel measurements in 2 - cell stacks operated on hydrogen (up) / unreformed methane steam mixtures at S/C=2 (down). Temperatures indicate difference to open circuit hydrogen operation with and without integrated heat pipe interconnectors (HP). Furnace temperature: 830°C, H2 operation: 1.5 SL min-1 H2, 1.5 SL min-1 N2, 3.0 SL min-1 Air, CH4 operation: 1.0 SL min-1 H2, 2.0 SL min-1 Air

1130

1135

1140

1145

1150

1155

1160

1165

1170

1175

1180

0 0.25 0.5 0.75 1 1.25 1.5

tem

per

atu

re [

K]

rel. fuel parallel position [-]

0 A

15 A

25 A

40 A

SOFC position

FLUENT simulation

measureddata

1130

1135

1140

1145

1150

1155

1160

1165

1170

1175

1180

0 0.25 0.5 0.75 1 1.25 1.5

tem

per

atu

re [

K]


SOFC position

0 A

15 A

25 A

35 A

FLUENT simulation measured

data

1080

1090

1100

1110

1120

1130

1140

0 0.25 0.5 0.75 1 1.25 1.5

tem

per

aure

[K

]


0 A

20 A

SOFC position

FLUENT simulation

measureddata

1080

1090

1100

1110

1120

1130

1140

0 0.25 0.5 0.75 1 1.25 1.5

tem

per

atu

re [

K]


SOFC position

0 A

20 A

FLUENT simulation

measureddata


138

6.6 Conclusions

In this chapter a stack set up as well as an experimental evaluation of solid oxide cells stacks

operated with integrated planar heat pipes were presented. The results show how a stack

with the improved thermal control based on liquid metal heat pipes can be basically

designed and temperature measurements inside the short stacks demonstrate the

functionality. The measurements prove the thermal integration and the capability of the

new interconnector structure to extract heat of reaction from the stack to supply it to

secondary processes, or enable an enhanced temperature control mechanism beyond excess

air cooling. 2-D temperature profile measurements demonstrate the clear temperature

gradient reduction within the cell layers by a factor of 3 – 4, thus the provision of isothermal

conditions and stress reduction to cells and sealings. In particular for stacks operated on

natural gas with high degrees of internal steam reforming, the approach of integrated planar

heat pipes leverages strong thermal benefits and reduce temperature drops at fuel inlet

significantly.

A supplementary experimental evaluation provided data for the thermal contact resistances

inside the SOC stack structure. This is a main parameter in order to evaluate heat transport

through the stack und thus calculate the effects of planar heat pipes on full scale stacks.

The obtained data and stack internal temperature profiles are used to calibrate the

numerical stack models developed in chapter 4. Therewith, the model is operational for the

final generation of layout guidelines for full-scale stacks.

139

Chapter 7

7. Design guidelines for stacks and systems

7.1 Layout of SOC stacks with planar heat pipes

Based on the experimental results obtained from heat pipe interconnector development

(chapter 5) and the evaluation of the stack behavior (chapter 6) that were applied to the

numerical stack model (chapter 4), some final guidelines for SOC stack design and layout

with planar heat pipe interconnectors are summarized in this chapter.

The objective is to provide information on the influence of planar heat pipes on stack

internal temperature gradients and its implications for current density distributions inside

the SOC stacks, depending on stack size, heat pipe interconnector frequency and heat

transfer duties.

In order to keep results comparable all SOC applications in this chapter are based on the

model described in chapter 4 and on a single definition of a temperature depending area

specific resistance (ASR) of the cell in the stack. This definition differs from the mere

resistance of a single cell in a perfect contacting environment as according to equation

(4.20).

𝐴𝑆𝑅 (𝑇𝑐𝑒𝑙𝑙) = 0.0240 𝑉

𝐴𝑚² ∙ 𝑒𝑥𝑝(−0.00739 ∙

(𝑇𝑐𝑒𝑙𝑙 − 273.15 𝐾)

1 𝐾) (7.1)

This ASR is a typical value used for ESC cells in the stack environment in corresponding

operation temperature ranges between 800 and 950°C. These cells and this temperature

range are used independently from variating interconnector materials, since mainly effects

on temperature gradients are on focus. Operation temperature limitations of interconnector

materials and differences between thermal expansion coefficient of ESC cells and chromium

based alloys as well as ASC cells and ferritic steels are neglected.

For the stack layout considerations of this chapter no final decision for a mitigation concept

against hydrogen deactivation has been taken and the mere heat pipe interconnector is

modeled. If, for instance, the intermediate air layer concept was chosen, an additional heat

transfer resistance into the heat pipe would have to be included. As demonstrated by the

measurements in the previous chapter 6.4 this additional resistance sums up to approx.

10 ∙ 10−4 m² K W-1 roughly one third of a stack repeating unit. For a heat flux density of

Chapter 7: Design guidelines for stacks and systems

140

0.5 W cm-2 into the heat pipe, this results in an additional temperature gradient of 5 K that

has to be considered.

7.1.1 SOFC hydrogen operation

Figure 7.1 shows the numerical CFD results of an SOFC stack operated on hydrogen. For all

simulated cases, average operation voltage of the cells and average current density is kept

constant at 0.75 V per cell and 0.4 A cm-2 respectively. Fuel use was fixed to the typical value

0.75 and stack’s air ratio is set to 5, a value resulting rather low for large stack sizes as high

temperature differences result.

Figure 7.1: In plane cell temperature profiles of SOFC stack (200mm cells/ CFY interconnector) on hydrogen operation. Min and max cell temperatures are tagged. Operation conditions: average stack operation voltage per cell: 0.75 V, current density: 0.4 A cm-1, fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5)

thermalrepeatingunit

cells

1060T

in [

K]

1260

Air

Fuel

1277 K

1055 K

cell 1

cell 5

……

…

HPthermalrepeatingunit

1060

Tin

[K

]

1260

Air

Fuel

1173 K

1110 K

1060

Tin

[K

]

1260

Air

Fuel

1244 K

1115 K

Layout of SOC stacks with planar heat pipes

141

Gas inlet temperatures for fuel and air as well as heat pipe temperatures were used as

control parameters in order to keep above mentioned constraints constant. The images

demonstrate how a hotspot at fuel upstream/air downstream corner forms. For the

simulated conditions a large temperature difference up to over 200 K is formed. The

equivalent situation is displayed for a stack with heat pipe interconnectors at a frequency of

10 cells per thermal repeating unit. The figure presents temperature profiles cell 1, closest to

the heat pipe and cell 5 with maximum distance. An overall reduction of temperature

gradients can be observed. However, due to the heat transfer towards the heat pipe, cell 5

shows largest temperature differences of 129 K compared to only 63 K at cell 1. The largest

in-cell temperature gradient in cell 5 (the cell with maximum distance to the HP layer) is

taken as evaluation criteria for the effectiveness of heat pipe integration.

The graph in Figure 7.2 displays how the introduction of heat pipe interconnectors reduces

temperature gradients (here maximum temperature differences in cell layers) depending on

interconnector material and number of cell layers between 2 neighboring heat pipe

interconnectors. The results show, that small stacks based on 100 x 100 mm² cells are still

reasonably controllable at the chosen air ratio with temperature differences of up to 125 K

(75 K) in one cell layer for CROFER 22H (CFY) as interconnector material. A reduction of this

gradient to 50 % at the cell providing highest temperature gradients requires a relatively

high frequency of heat pipe interconnectors of 4 to 6 cells. Increasing cell size, as a pathway

to larger fuel cell systems, leads to dramatically increasing temperature differences.

Figure 7.2: Maximum temperature differences at cell level for SOFC operation on hydrogen depending on number of cells per heat pipe interconnector for different solid oxide cell sizes and interconnector materials. Operation conditions: average stack operation voltage per cell: 0.75 V, current density: 0.4 A cm-1, fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5)

0

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150

200

250

300

350

max

cel

l tem

per

atu

re d

iffe

ren

ce [

K]

chromium basedalloy, e.g. CFY

CROFER 22 H

Interconnectormaterial:


142

At the pre-selected air ratio of 5 and without further measures, the resulting differences for

cells of 200 x 200 mm² or even 300 x 300 mm² reach levels that cannot be tolerated. In

standard design SOFC stacks a significant increase of air ratio would be required. Here, the

introduction of heat pipe interconnectors reduces the cell layer internal gradients drastically

and even lower frequencies of 8 cells per heat pipe lead to decrease of the 50 % at the cell

farest from the HP interconnector. One can furthermore deduce that temperature gradients

are less shaped when chromium based interconnector materials as CFY (approx. 60 W m-1 K-1

at 800°C) are applied compared to ferritic steel interconnectors (thermal conductibility of

Crofer: 26 W m-1 K-1 at 800°C). An increased thickness of the interconnector material has an

effect proportional to this variation in thermal conductivity.

Based on these possible gradient reductions due to the heat pipe interconnector an

increased average operation temperature is possible if maximum cell temperature is kept

constant. This seems reasonable since system optimization tends to increase temperatures

that are limited by maximum operation temperature of stack materials. Following this

argumentation the use of heat pipe interconnectors directly translates into an increase in

stack power density (Figure 7.3).

Figure 7.3: Left: Possible average stack temperature increase at constant maximum cell temperature, Right: Resulting current density increase. Operation conditions: average stack operation voltage per cell: 0.75 V, initial current density: 0.4 A cm-1, fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5)

The simultaneous creation of interlayer temperature differences in z-direction through the

stack is a major drawback of the introduction of heat pipes at lower frequencies (more cells

between two interconnectors) to SOC stacks in order to reduce in plane temperature

gradient. Figure 7.4 shows the temperature profile of a thermal stack repeating unit with 10

cells between two heat pipe interconnectors. In order to provoke heat flow from the cells in

0

25

50

75

100

125

150

incr

ease

of

aver

age

cell

tem

epra

ture

[K

]

0.00

0.10

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0.30

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rel.

incr

ease

ave

rage

ccu

rren

t d

ensi

ty /

-

Interconnectormaterial: CROFER only

Interconnectormaterial: CROFER only


143

the center towards the heat pipe, a temperature increase is necessary to overcome the

thermal (contact) resistances that were obtained in chapter 6.4. It is visible that these

temperature differences lead to important local temperature differences between the cell

layers. In the presented case for a stack operated on hydrogen with relatively low air ratios,

the maximum temperature of cell 1 closest to HP interconnector reaches 1150 K while the

maximum temperature of cell 5 at the center position between two interconnectors reaches

1266 K thus over 110 K higher temperatures at the hot spot of fuel entry and air exhaust.

Minimum temperatures at these cells only differ by 10 K.

Figure 7.4: Representation of temperature profiles within a SOFC stack repeating unit operated on hydrogen and 10 cells per heat pipe interconnector layer. Stack size: 200 x 200 mm² cells, average 0.75 V per cell, 0.4 A cm-², fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5), CROFER 22H interconnector material

This intercellular temperature gradient brings two major drawbacks of heat pipe

introduction. Firstly, the different average cell temperatures lead to different strains of the

cells and interconnectors in vertical direction through the stack. Figure 7.5 presents the

maximum difference in mean cell temperature of two neighboring cells in the examined

stack set-ups. Depending mainly on cell size and HP frequency, cell-to-cell temperature

differences up to 30 K appear provoking strain deviations in the range of approx. 0.0003

(mm/mm). Sealing materials have to cope with these strain gradients and need to withstand

the resulting stress.

Heatpipe Interconnector

cell1

cell5

Repeating unit stack

Air inlet

Fuel inlet1087

Tin

[K

]

1256


144

Figure 7.5: Maximum average temperature difference between two neighboring cells in stack Operation conditions: Stack operation voltage per cell: 0.75V, current density: 0.4 A cm-2, fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5)

A second drawback of the resulting temperature differences is a strong variation of cells’

ASR value mainly caused by decreasing ohmic resistance at higher temperature. This effect is

partly counterbalanced by a locational decrease in Nernst voltage and a slightly decreasing

cell operation voltage, but the lower electrical resistance leads to an important increase in

local current densities, especially at fuel entries. In consequence, the high fuel consumption

there may lead to local fuel starvation in downstream of gas flow channels in cells close to

the center between two heat pipe interconnectors.

Figure 7.6: Current density profiles under SOFC operation in a stack with 1 HP with 10 cell layers. Left: cell 1 (neighboring the HP interconnector), Right: cell 5 (maximum distance of HP) stack 200 x 200 mm² cells, 0.75 V, 0.4 A cm², fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5), CROFER 22H interconnector material

0

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/ K

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O

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0 x

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0 m

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m

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R

O

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0

i in

[A

cm

- ²]

1.6

Air

Fuel

equilibrated fuel use: y(H2)_min = 0.22

0

i in

[A

cm

- ²]

1.6

Air

Fuel

zone of high risk of fuel starvation at high fuel uses: y(H2)_min = 0.13


145

Figure 7.6 displays current density profiles and the resulting density profiles at the anode’s

exist of the cells closest and furthest to the heat pipe interconnector in the SOFC stack. Due

to constant total stack current trough each cell the cell voltage levels from cell 1 to cell 5

differ from 721 mV to 761 mV. In spite of this adaption, the hotspot in cell 5 leads to a

significant increase in current densities and decreased local hydrogen content of only 0.13

compared to 0.25 in average. This effect however is mainly relevant for cross-flow stack

concepts.

Figure 7.7 shows the combined design considerations for heat pipe interconnectors in

CROFER based stacks. Heat transferred to the heat pipe interconnector is plotted against

heat transfer limits of the planar heat pipe for varying cell sizes and HP-frequencies. The

aspect ratio of the heat pipe describes the length to width ratio, i.e. a heat pipe with aspect

ratio 5 for cells of 200 mm has 200 mm width and 1000 mm length. As a result, even for

large cells and low HP-interconnector frequencies, the performance of the heat pipes allows

heat transfer over several cell lengths. A thermal coupling of SOFC stacks and secondary

processes, such as pre-heaters, endothermal reactors or heat storage devices is therefore

possible within the displayed limits.

Figure 7.7: Layout of heat pipe interconnectors for stacks based on CROFER 22 H depending on HP-aspect ratio = length / width. HP interconnectors designs as in Table 6.1 in horizontal operation. Operation conditions: Stack operation voltage per cell: 0.75V, current density: 0.4 A cm-2, fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5),

0

100

200

300

400

500

600

0 100 200 300 400

hea

t tr

ansf

er /

W

cell size / mm

HP total transfer limit Cumulated heat transfer to heat

pipe in stack repeating unit


146

7.1.2 SOEC operation

Already discussed in the experimental section, heat of reaction in case of electrolysis

operation of SOC stacks is far lower than in typical SOFC operation cases. This leads to

intrinsically lower heat duties and temperature gradient formation throughout the stack. For

operation close to thermoneutral voltage at approx. 1.29 V per cell, almost no heat transport

is required and thermal management is of less concern than for fuel cell operation.

However, in endothermal operation, electrolysis can work at particularly high electrical

efficiencies, i.e. at 1.15 V/cell operation voltage, electrical cell efficiency is above 1. In this

case however, external heat supply is required and system heat losses have a strongly

negative effect on system’s efficiency. In consequence, unnecessary heat losses are to be

reduced as far as possible and cooling air free operation (𝜆𝑆𝑂𝐸𝐶 = 0) is desirable. As further

benefit, the produced oxygen is not diluted with nitrogen and can be a side product of

electrolysis operation.

Figure 7.8 shows the influence of heat pipe interconnectors in endothermal SOEC operation

under low or no cooling air loads. Temperature gradients are low, even under endothermal

operation and require fewer countermeasures.

Figure 7.8: Influence of heat pipe interconnectors on SOEC stacks. Left: Temperature profiles at endothermal operation with varying air ratios. Left: Average cell current densities in SOEC operation with different HP-interconnector frequencies. SOFC stack: 200 x 200 mm² cells, 1.15 V, 0.4 A cm², cathode: 0.05 H2, 0.95 H2O, SU= 0.75 (Σ = 1.33), anode: air, CROFER 22H interconnector material

1040

1050

1060

1070

1080

1090

1100

1110

1120

1130

-0.1 -0.05 0 0.05 0.1

cell

tem

per

atu

re /

K

steam flow parallel position / m

Temperature of furnace / HP and gas inlet

cell 5

cell 1

2000

2500

3000

3500

4000

4500

aver

age

cell

curr

ent

den

sity

/ m

A c

m-2

stack power increase


147

Though, the operation temperature level of the stack falls significantly below surrounding

temperature and gas inlet temperature (up to 75K at 𝜆𝑆𝑂𝐸𝐶 = 0). This causes an important

drop in stack power density when the stack is operated at constant cell voltage. Right part of

the figure demonstrates how heat pipes in the interconnector structure of the stack assist

heat supply and keep stack temperature level high. Even at low frequencies with 1 HP per 10

cell layers, the stack power can be improved by approx. 40 % at 𝜆𝑆𝑂𝐸𝐶 = 0.

Furthermore, when modulating SOEC stack power between thermal states, e.g. peak power

in exothermal mode at cell voltages above 1.29 V and low power, high efficient endothermal

operation, the temperature gradients within the stack are kept low. Resulting dynamic

thermal stress is thus reduced and cell and sealing failure due to crack growth can be

avoided.

7.1.3 Natural gas operated stacks

One major application of SOFC technology is its use in small scale natural gas based CHP-

systems. Based on the internal steam reforming capabilities, SOFCs offer particularly high

efficiencies in this configuration. Due to the relatively high reforming kinetics of SOC anode

structures, a certain degree of pre-reforming of the fuel is commonly applied, before leading

the fuel into the stack. Supply of entirely unreformed methane to the stack leads to strong

sub-cooling of the upstream regions of the cells, causing strong thermal gradients at this

point. Furthermore, the strong decrease in temperature in these areas restricts O2--ion

conductivity and thus electrochemical activity. Consequently, fuel inlet regions contribute

little to stack electrical power and reduce average current density.

Figure 7.9 shows temperature profiles of a SOFC stack operated on unreformed methane (33

mol%) and steam (66 mol%) as fuel. In the displayed set-up a heat pipe interconnector is

introduced into the stack every ten cell layers.

Figure 7.9: Representation of temperature profiles within a SOFC stack repeating unit operated on unreformed methane / steam mixtures as fuel (S/C = 2) and 10 cells per heat pipe interconnector layer. Stack size: 200 x 200 mm² cells, average 0.75 V per cell, 0.4 A cm-², fuel: 0.34 CH4, 0.64 H2O, H2=0.02, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5), CROFER 22H interconnector material

Heatpipe Interconnector

cell1

cell5

Repeating unit stack

Air inlet

Fuel inlet1034

Tin

[K

]

1223


148

It is visible that the entering fuel getting in contact with Ni-containing porous fuel anodes

leads to a strong temperature drop at the fuel inlet. Due to the electrochemical activity, the

cell temperatures rise towards the fuel and air outlet of the cells, resulting in hot spot

formation at the downstream corner. Maximum cell layer temperature differences arise

between subcooled inlet region and electrochemical hotspot. In the displayed case for 200 x

200 mm² sized cells, with one heat pipe per 10 cells, a maximum cell temperature difference

in the most distant cell (cell 5) of 189 K is the consequence.

The planar heat pipe interconnector in this case does not only extract heat from the stack

but transports heat from pre-dominantly exothermal regions to endothermal, steam

reforming dominated ones. Due to the restricted heat transfer through the stack in vertical

direction only part of the required heat for gas phase reactions can be supplied by the planar

heat pipe structure and still a strong sub-cooling of cells that are not in vicinity to HP is

generated. Figure 7.10 shows a simplified heat balance of one stack repeating unit (1 HP and

10 cells) for a stack operation with an air ratio of at 𝜆 = 5. A significant part of the

exothermal heat from the electrochemical reaction and ohmic losses (156 W) is transferred

to the HP-interconnector, where it is internally cycled back to endothermal stack regions.

This recycled heat 𝐻𝑃,𝑟𝑒𝑓 is able to supply 66 W to the gas phase steam reforming reaction

per repeating unit, representing approx. 24 % of the required heat 𝑟𝑒𝑓 (summing heat of

reaction of steam reforming 𝑆𝑅 and water gas shift 𝑊𝑆𝐺).

𝑟𝑒𝑓 = 𝑆𝑅 + 𝑊𝑆𝐺 (7.2)

For the displayed configuration, a larger part of the required power is directly transferred by

conduction and convection within the normal stack structure (Qdir,ref).

𝑟𝑒𝑓 = 𝐻𝑃,𝑟𝑒𝑓 + 𝑑𝑖𝑟,𝑟𝑒𝑓 (7.3)

Furthermore, the heat pipe still requires some external cooling (i.e. 96 W), since

electrochemical reaction heat exceeds endothermal reforming needs. Only small part (26 W)

of the heat is removed directly with gas streams or stack losses.

The right graph in Figure 7.10 shows how the ratio of heat pipe recycled heat to total

reforming heat 𝐻𝑃,𝑟𝑒𝑓 𝑟𝑒𝑓⁄ varies with heat pipe frequency, air ratio and degree of

reforming. The diagram shows that in case of SOFC stacks with high HP frequencies up to 80

% of the endothermal heat demand can be supplied by heat recycling via the HP. Due to

stronger sub-cooling in case of complete internal reforming, larger parts of the required heat

can be supplied by heat pipe structure.


149

Figure 7.10: Left: Simplified heat balance of a stack repeating unit operated on full internal steam reforming of methane, indicating the recycle flow within the heat pipe structure. Right: heat ratio of heat pipe recycled heat to total reforming heat depending on HP frequency, degree of reforming and air ratio. Stack size: 200 x 200 mm² cells, average 0.75 V per cell, 0.4 A cm-², fuel: 0.34 CH4, 0.64 H2O, H2=0.02, FU= 0.75, cathode: air, CROFER 22H interconnector material

In consequence of this heat recycling within the heat pipe interconnector, stack internal

temperature differences are reduced. In state-of-the-art stacks partial pre-reforming and an

increased air ratio assure a limiting of these temperature differences. Typically, air ratios are

chosen lower than for pure hydrogen operation (due to the cooling effect of the

endothermal reaction) and are set within the range 4 – 6.

Figure 7.11 shows maximum cell temperature differences within one cell structure for SOFC

stacks with varying HP frequencies and air ratios. The graph demonstrates how decreased air

ratios are possible due to the use of planar HP interconnectors. Even for low frequencies of

10 cells / HP, for the displayed case of 200 mm cell size, a reduction of the air ratio from 5 to

below 2 is possible without increasing stack internal temperature differences. When

maintaining the air ratio constant in this case, a gradient neutral switch to full internal

reforming is possible. The beneficial consequences regarding thermal efficiency of SOFC

based CHP systems are discussed in the next chapter. A switch to complete internal

reforming reduces systems complexity and the need of external heat exchanger

considerably. The abandonment of an external steam-reforming unit may counterbalance

the additional costs of the HP structures within the stacks. For higher HP frequencies, both a

strong reduction of air ratios and a switch to complete internal reforming are possible. Air

ratio reduction in these cases is mainly restricted by electrochemical considerations due to a

possible air starvation at the cathode.

0.00

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0.60

0.70

0.80

0.90

1.00

, ref

/

ref

[-]

CH4, S/C=2, 50 % pre-reformed

CH4, S/C=2, full internal reforming

HP

15

6 W

91 W

66

WSR + WSG:

271 W

205 W(76 %)

26 WSOFC: - 387 W

Cells

Stack

internal energy flows forHP_10_cells, full reforming,

(24

%)

CH4,

CH4,

.

.


150

Figure 7.11: Maximum cell temperature differences, depending on HP frequency, degree of reforming and air ratio. For the stack without HP a higher maximum air ratio is considered. Stack size: 200 x 200 mm² cells, average 0.75 V per cell, 0.4 A cm-², fuel: 0.34 CH4, 0.64 H2O, H2=0.02, FU= 0.75, cathode: air, AU= 0.2, CROFER 22H interconnector material

7.2 Advanced SOFC system concepts with integrated planar heat

pipes

7.2.1 System evaluation of HP integrated CHP SOFC systems

A short final discussion based on Aspen Plus simulations shall analyse system benefits due to

an advanced cooling concept based on planar heat pipes. Figure 7.12 shows the (simplified)

typical process layout of a SOFC stack operated on steam-reformed natural gas in a CHP

configuration, e.g. the layout of a micro-CHP for residential purposes in the range of 2 – 5

kWel. The exhaust gases are used in order to preheat fuel and air flows, to provide heat of

evaporation for steam production and reaction enthalpy to (partial-) steam pre-reforming.

CH4, S/C=2, 50 % pre-reformed


0

50

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300

350

max

cel

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atu

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state of the art stackand operation

reducedtemperaturegradient due toHP integration

CH4,

CH4,

Advanced SOFC system concepts with integrated planar heat pipes

151

Figure 7.12: Standard natural gas fired SOFC-system in CHP configuration with exemplary temperatures and powers for parameter set according to Table 7.1

After the pre-heaters for gas streams and the water evaporator the off-gases at temperature

Texhaust supply the remaining heat to a heating grid with a certain temperature level (e.g. 30 –

60°C for residential heating and 80 - 130°C for large scale or industrial heating grids). This

final heat exchanger cools off-gases to TCHP and thereafter, an ID fan provides the pressure

difference in cold off-gases to suck gas stream through the entire system.

Table 7.1: Parameter set for standard system simulation

Parameter Value

Fuel CH4, S/C =2

Air ratio, Fuel use 𝜆 = 5, 𝐹𝑈 = 0.8

Cell voltage 0.75 V

Pre-reforming 50 % steam reforming (i.e. approx. 560°C)

Total pressure drop 150 hPa [Peters2014]

Blower efficiency 50 %

Inverter efficiency 97 %

System control 1% [Peters2014]

Figure 7.12 provides typical temperature and powers for a parameter set-up according to

Table 7.1.

Even when assuming low temperature level of heat use at 50°C, a large contribution to the

rather low total system efficiency of approx. 76 % is caused by an inefficient heat use caused

by the required air ratio of 5. Due to the dilution of anode off-gases with cooling air the dew

point of the exhaust gases decreases down to approx. 41°C. Therefore, none of the latent

A

C

natural gas (CH4)

Air

H2O (l)

post combustor

DC

AC

Pel, ac

Qtherm

Texhaust

blower

exhaust

SR + preheat

pump

DESULV

EVAP + preheat

preheat

SOC stack

TCHP

25°C, AR = 5

25°C

25°C

560 °C

50°C

Pel, dc

189 °C

938 °C5 kWLHV

2.9 kWel

2.5 kWel

0.3 kWel

1.3 kWth

700 °C


152

heat within the exhaust gas (22% of fuel’s LHV at S/C =2) can be accessed. The strong sub-

cooling of certain stack regions due to internal reforming (compare with chapter 7.1.3)

causes additionally the necessity of decreasing cell voltage to 0.75 V in order to keep power

density high. This set-up without anode off-gas recycling can be represented with a Sankey

plot as displayed in Figure 7.13.

Figure 7.13: Sankey plot of a standard SOFC Process with (Pre-) Steam Reforming simulated with Aspen Plus - conditions: 50% Pre-reforming (at 560°C), 50% internal reforming in cell, air ratio =5, stack fuel use =0.8, avg. cell temperature 810°C, air blower efficiency= 0.5

Demonstrated by numerical investigations in the previous chapters, heat pipes incorporated

into the SOFC stack structure allow a significant reduction of excess air flow for cooling and

thermal stack management (e.g. by heat transfer from exothermal stack regions to

endothermal ones as demonstrated in Figure 7.10). In all SOC applications, the reduced air

flow decreases blower power and thus system’s internal consumption considerably. Table

7.2 shows how the blower consumption varies with the air ratio in typical system layout (as

displayed in Figure 7.12).

Table 7.2: Simulated pressure loss and blower needs at reduced air flows (at constant stack geometry, design point air ratio = 5, isentropic efficiency of blower =0.5)

Air ratio

[-]

Stack pressure loss

[mbar]

Pblower / LHVfuel

[-]

5 (design point) 150 0.057

3 54 0.013

1.5 14 < 0.01

113 %100 %

CH4in

Stack

(FU = 0,80)

(AR = 5)

Anode

Off-Gas

Cell

(750 mV)DC AC - net

+

-

Steam

(Pre-)Reformer

25%

Exhaust heat

101 % 58 %

43 %

~50 %

QSR

13 %8 %

LHV based

26 %

(111 % HHV)

Available for heating

(condensation at 50 °C)

16 % (+ 11%)

Air blower +

Parasitics13 %

Qref,int


153

The net electric efficiency may thus be increase by up to 4 % when reducing excess air ratio

from 5 to 1.5 due to an advanced cooling based on heat pipes. This however is true if

geometry stays comparable and advanced cooling concept does not lead to increasing stack

and heat exchanger compactness.

Even more important when applying SOFC systems in a CHP configuration, the reduced air

flow particularly improves thermal efficiency and thus the total energy efficiency. In the low

temperature CHP regime (35 - 60°C), with condensing technology as applied in residential

heating, an increased dew point of exhaust gas permits high latent heat gains. For high

temperature CHP applications (80 – 130°C), typically in commercial or industrial

environment, the reduced air flow increases substantially the usability of the sensible heat in

exhaust gas flow. Figure 7.14 shows thermal efficiencies for different air ratios plotted

against the off-gas temperature. For a natural gas based SOFC system with an exhaust

temperature of 50°C, thermal efficiency may be increased significantly by up to 18 % of

fuel’s LHV, when air cooling needs are reduced from air ratio 5 to 1.5. This reduction is in

particular possible when applying heat pipe cooling to the stack. For high temperature CHP

efficiency gains are lower and limited to reducing sensible heat losses by decreasing air

flows. A reduction of the air ratio from 5 to 1.5 leverages thermal efficiencies gains of

approx. 5 - 10% of fuel’s LHV for a heat use at 100°C.

Figure 7.14: Thermal efficiencies of SOFC-CHP systems depending on fuel type, air ratio and level of heat use (exhaust temperature). Standard SOFC process with (Pre-) Steam Reforming - conditions: 50% Pre-reforming (at 560°C) of methane, S/C = 2, 50% internal reforming in cell, stack fuel use =0.8, cell voltage 0.75 V, It is assumed perfect heat recuperation for pre-heating gases, no parasitic heat losses of stack and system.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

20 40 60 80 100 120

ther

mal

eff

cien

cy /

-

exhaust gas temperature / °C

Hydrogen

dew point shift

Low temperatureCHP range

Residential heatingonly

High temperatureCHP range

Industrial scale andheating grids

increasedsensibleheat use

CH4 (SR)

temperature of CHP heat use / °C


154

For hydrogen operated stacks a similar conclusion can be deduced while latent gains are

slightly smaller (latent heat only 18 % of fuel’s LHV in off-gases) but possible sensible heat

recovery is more pronounced due to higher air ratio in standard air cooling set-ups.

These thermal efficiency gains leveraged by heat pipes may play an important role

concerning the legal framework of CHP-systems and resulting subsidies. 2004/8/EG

[EU2004] claims primary energy gains (PEG) of CHP compared to reference efficiencies of

separated heat and power generation. According to 2011/877/EG the reference efficiency of

gas based heat 𝜂𝑡 𝑟𝑒𝑓 and power generation 𝜂𝑡 𝑟𝑒𝑓 are 0.9 and 0.525 respectively. Primary

energy gains (PEG) of the SOFC system based on steam reforming displayed in Figure 7.13

calculate by

𝑃𝐸𝐺 = 1 −1

𝜂𝑡 𝐶𝐻𝑃𝜂𝑡 𝑟𝑒𝑓

+𝜂𝑒𝑙 𝐶𝐻𝑃𝜂𝑒𝑙 𝑟𝑒𝑓

(7.4)

and are positive. However, in CPOX based micro CHP systems with low electrical efficiency,

thermal efficiency has to be high in order to satisfy legal CHP standards and air ratio is a key

to assure primary energy gains.

Based on planar heat pipe interconnectors new system concepts are possible that reduce

the necessity of auxiliary components (Figure 7.15). The left sketch proposes a stack external

but thermally integrated reformer concept. SOFC stack and the steam reformer are placed

within one hotbox and are thermally connected with planar heat spreaders integrated to

stack structure. Advantages of this arrangement could be, additional to lower air ratios, a

higher average current density in the stack as the endothermal cooling at fuel entrance is

reduced. Moreover, the external reformer may use on-purpose designed catalysts and be

less sensitive to side reactions such as carbon deposition at reduced steam ratios or sulfur

poisoning.

The right design, by contrast, proposes a full internal reforming approach where air and fuel

preheating is provided in a one-step heat pipe pre-heater. Bearing higher temperature

gradients, this pre-heater allows direct heating of low temperature gases, in particular in

pure hydrogen operation where large amount of waste heat are available. Temperature

gradients due to full internal reforming are kept acceptable due to integrated HPs. System

complexity is significantly reduced in this set-up, since smaller sized heat exchanging and no

reforming components are required.


155

Figure 7.15: Improved system integration based on planar heat pipe technology for natural gas fired SOFC-system in CHP configuration. Left: full external reformer coupled by heat pipes. Right: One-step heat pipe preheater and fully internal reforming.

In both set-ups, the reduced high temperature heat re-use from off-gas streams lowers the

requirements of temperature increase in the post combustor. In consequence, a higher

effective fuel use and thus a (better) anode off-gas recycling becomes possible. Thereby,

steam as a reforming agent is internally provided and in ideal design no further water supply

and evaporation is required.

To conclude this qualitative evaluation of possible SOFC-CHP layouts, Figure 7.16 gives a

Sankey-graph of an Aspen Plus analysis of the proposed systems with external pre-reformer

based on the heat pipe technology. Main electrical efficiency gains arise due to reduced

temperature gradients in cells, thus slightly increased cell voltage to 0.78 V per cell

compared to 0.75 V in Figure 7.13, reduced blower power and pre-dominantly due to anode-

off-gas recycling. Thermal efficiency is significantly improved due to the low exhaust gas

losses at an air ratio of only 1.5. In this example, overall system efficiency could be improved

by up to 20% points compared to the reference layout. Part of these gains can also be

accessed by other system concepts, however the results clearly prove the large potential of

the planar heat pipe technology.

A

C

Air

DC

AC

post combustor

exhaust

blower Qtherm

SOC stackHP

HP-coupledreformer

preheat

Pel, ac

Pel, dc

DESULV

anode recycle

natural gas (CH4)

TCHPTexhaust

5 kWLHV

< 0.1 kWel

< 0.1 kWel

1.7 kWth 50°C

3.2 kWel

3.4 kWel

25°C

25°C, AR=1.5

951°C

575°C

700 °C

A

C

Heat pipe coupled pre-

heater

DC

AC

DESULV

NG (CH4)

anode recycle

SOC stackHP

Pel, ac

post combustor

Pel, dc

25°C

575°C

Air

exhaust

blower Qtherm

TCHP

Texhaust

25°C, AR=1.5

58

5°C

50°C

810°C

951°C

1.7 kWth

< 0.1 kWel

3.2 kWel

< 0.1 kWel

5 kWLHV


156

Figure 7.16: SOFC with heat pipe process integration simulated with Aspen Plus - conditions: 50% anode off-gas recycling, 100% pre-reforming (at 800°C), no internal reforming in cell, air ratio 𝜆 = 1.5 (no high excess air required due to HP, stack fuel use =0.8, avg. cell temperature 840°C, air blower efficiency= 0.5, 4% parasitic losses

7.2.2 Integration with advanced system concepts

Additional to CHP application for heating purposes in residential or industrial heating grids

up to 130°C, SOFC systems are discussed as heat source for high temperature processes. This

includes concepts that base on a coupling with thermal gasification of solid fuels, heat

storage or dehydrogenation reactions and typically require heat reuse above 300°C.

Figure 7.17 left shows exhaust gas temperatures Texhaust of a SOFC system according to the

system displayed in Figure 7.12 after ideal pre-heating of air and fuel to stack operation

temperature. Fuel composition, i.e. hydrogen or natural gas with steam reforming, as well as

fuel use are relevant influences on off-gas temperatures. The system’s air ratio however

results to be the main influence parameter on exhaust gas temperatures. An SOFC for

example working on pure hydrogen (CPOX reformed natural gas almost equivalent), at an air

ratio of 5, a fuel use of 0.8 and gross electrical efficiency of approx. 45 % (an equivalent cell

voltage of 0.75 V per cell) may produce off- gases at maximum at 365°C when neglecting

system heat losses.

The consequences of the resulting temperature level for high temperature heat applications

can be observed in the right part of Figure 7.17 where a q-T diagram of the exhaust gases is

shown. High air ratios restrict the usable amount of high temperature heat from SOFC

systems to low percentages. E.g. for the given example of a hydrogen-fueled SOFC with an

air ratio of 5, only approx. 8 % of fuels LHV are available for heat use at 300°C (including a

temperature difference of 20 K within the heat exchanger).

140 %100 %

CH4_in

Stack

(FU = 0,80)

(AR = 1.5)

Anode Off-Gas

(50% Recycle)QSR

Cell

(780 mV) DC AC - net

+

-

28 %

112 % 67 %

45 %

~

Air blower +

Parasitics

63 %

26 %14 % 4 %

Transfered

by Heat pipe

Steam

(Pre-)Reformer

Exhaust heat

33 %

Available for heating

(condensation at 50°C)

(11%)

LHV based

(111 % HHV)


157

Figure 7.17: Thermal efficiencies depending on air ratio, exhaust temperature and fuel type. Standard SOFC process with pure hydrogen or (pre-) steam reforming – conditions (CH4): 50% pre-reforming (at 560°C) of methane, S/C = 2, 50% internal reforming in cell, stack fuel use = 0.8, cell voltage 0.75 V. It is assumed perfect heat recuperation for pre-heating gases, heat losses of stack and system to environment Qloss are set to 0 in the displayed lines. Heat capacities of off-gases assumed constant.

This result handicaps concepts that use the SOFC system as heat source for secondary high

temperature processes. For advanced hydrogen storage systems, e.g. as proposed by

[Teichmann2012] and [Brückner2014] based on organic hydrogen carrier liquids (LOHCs)

such as Marlotherm, almost one third of the fuels LHV is needed for dehydrogenation of the

carrier medium. The heat is required at a temperature level above 300°C. With standard

thermal stack management concepts, that require air ratios of 5 – 10 for pure hydrogen

operation, only a small or no part of this heat can be supplied to the endothermal reaction.

In consequence, the solid oxide fuel cell as an electricity converter does not improve storage

system efficiencies and is comparable to PEM as long as the air ratio stays high for cooling

needs.

Here, the introduction of the proposed heat pipe interconnectors and the resulting

possibility of largely decreased air ratios, improves the thermal heat use from exhaust gas

flows significantly. At an air ratio of 1.5 in the above-described example, approx. 38 % of

fuel’s LHV are available for use above 300°C and a profitable heat re-use for complete

dehydrogenation of the hydrogen storage molecule is possible.

An even further increased heat use at very high temperature levels close to SOFC operation

temperature can be reached, if the heat pipe directly connects the stack and the

endothermal secondary process e.g. within one hotbox. In this configuration, heat transfers

0 0.2 0.4 0.6

0

100

200

300

400

500

600

700

800

0 2 4 6 8 10

SOFC

exh

aust

tem

per

atu

re /

°C

air ratio / - sensible heat / LHVfuel

0

100

200

300

400

500

600

700

800

0 0.2 0.4 0.6

SOFC

exh

aust

tem

per

atu

re /

°C

sensible heat / LHV_fuel


158

almost isothermally to the secondary process. Thereby, thermally integrated external steam

reforming of larger fuel molecules (gasoline, diesel) or even solid fuels such as coal and

biomass becomes imaginable [Fryda2008].

As an additional application, stack integrated heat pipes enable a direct coupling of SOFCs to

high temperature storage systems based on CaO-CaCO3 loops [Aihara2001; Höftberger2016]

or alkali metal salts (such as NaCl).

The passive and reversible heat transfer from and to the storage could thereby lead to a

SOFC standby at operation temperature and enable real cyclic interruptible operation of the

stacks. The use of such an SOFCs as an auxiliary power unit could largely broaden the range

of applicability of SOC technologies.

159

Chapter 8

8. Summary and conclusion

This thesis contributes to the efforts being made to improve thermal management of solid

oxide cell stacks. In particular for decentralized cogeneration systems or reversible and load

flexible SOCs the thermal control is a key question regarding stack durability and thermal

efficiency.

In this work the new approach of integrating planar high temperature heat pipes to the

interconnector structure has been proposed. A comprehensive design study evaluated

capillary and vapor space structures for these heat pipe interconnectors.

Experimental evaluation in a heat pipe test rig proved that thin planar heat pipes for the

temperature range between 650°C – 870°C with overall thicknesses down to 4 mm based on

elementary sodium are possible. Best heat transfer rates are obtained for screen meshed

heat pipes in a sandwich design where a mesh 200 screen provides capillary structure while

a mesh 8 screen assures the upkeep of the vapor space. In horizontal operation, the

prototypes designed for 100 x 100 mm² SOCs demonstrated almost isothermal heat transfer

rates up to 1000 W, corresponding to equivalent thermal conductivities up to 17 kW m-1 K-1.

This heat pipe performance is suitable for stacks with high power densities (> 0.5 W cm-2)

and several cell layers per heat pipe (e.g. up to ten).

Besides long-term operation tests, a main focus was set on the hydrogen deactivation

problem of the heat pipes. This mechanism was identified particularly challenging for SOC

application of planar heat pipes. Below atmospheric working pressure, thin wall thicknesses

and high external hydrogen pressure cause a rapid heat pipe deactivation, typically in less

than 1 hour. Motivated by this fast deactivation mechanism, several countermeasures are

discussed in an analytical study. Experimentally however, only the introduction of a thin

intermediate air barrier layer succeeded in a secure mitigation of the problem, at cost of

increased heat transfer resistance to the heat pipe.

The developed planar heat pipe interconnector prototypes were tested in real stack

operation. Therefore, in a first step, a test rig for planar solid oxide cells, capable of fuel cell

as well as electrolysis operation, was installed. A newly developed design for the short stack

evaluations based on 100 x 100 mm² ESC cells from Kerafol (NiO/GDC | 10Sc1CeSZ | LSCF)

and allowed the incorporation of heat pipe interconnectors. Due to the more state-of-the-

art processing, CROFER 22H was used as interconnector material, with a compressible

sealing concept (mica-glass hybrid gaskets).

Chapter 8: Summary and conclusion

160

Results clearly indicated that planar heat pipe interconnectors are capable of flattening stack

internal temperature profiles and that extraction of reaction heat from the stack is possible.

In SOFC operation, especially under internal reforming conditions, the heat pipes reduced

stack internal gradients from 43 K to 15 K even for the short stack with relevant ambient

temperature influence. Thermal influence on electrolysis operation was only small, in the

range of a few Kelvin and no significant impact of the HP interconnectors was detected.

Supplementary measurements of stack internal heat transfer properties identified thermal

contact resistance as main parameter that influences heat transfer into the planar heat pipe

structure. In particular for stack set-ups with low heat pipe frequencies (no direct

neighboring to every cell), this factor influences significantly the efficiency of the heat pipe

interconnectors.

Figure 8.1: Determination of maximum investment cost of planar heat pipe interconnectors on basis of an increase of stack power densities.

0 2 4 6 8 10 12

0

0.2

0.4

0.6

0.8

cost neutral price per heat pipe €/HP

1000 2000

po

wer

in

crea

se/

-H

P/ k

We

l

cells per HP

9 16 30 55 100

181

330

602

1098

stackinvestmentsavings in €

0 2 4 6 8 10 12

0

0.2

0.4

0.6

0.8


1000 2000

po

wer

in

crea

se/

-H

P/ k

We

l

cells per HP

9 16 30 55 100

181

330

602

1098

80 €/HP100 mm

100 mm 8000 €/kW

Example 1:small cells,high stack costs,6 cells per HP

0 2 4 6 8 10 12

0

0.2

0.4

0.6

0.8


1000 2000

po

wer

in

crea

se/

-H

P/ k

We

l

cells per HP

9 16 30 55 100

181

330

602

1098500 €/HP200 mm

200 mm 5000 €/kW

Example 2:medium cells,med stack costs,4 cells per HP

Summary and conclusion

161

The results of the experimental stack evaluation provided relevant data to a numerical

model implemented in commercial CFD software. The FLUENT model incorporates

electrochemical cell behavior, heat transfer properties and heat pipe description according

to experimental findings. The stack model is operational for full stack layouts including

kinetics and thermal impact of steam reforming reactions.

Simulation results build a basis for stack layout guidelines presented in the final chapter. It is

shown that heat pipe controlled stacks allow a strong decrease of air ratios and provide a

basis for power density increase. Even at low heat pipe frequencies of 10 SOCs per heat pipe

layer, a temperature neutral reduction of the air ratio from 5 to 1.5 for methane operated

stacks seems possible. Decreasing excess air mainly increases thermal efficiency, in

particular when the resulting dew point shift can be used due to low temperature CHP.

Increased power density, on the other hand, may be a direct approach to pay-off additional

heat pipe investment costs.

As a concluding message, Figure 8.1 shows an evaluation of cost reductions by increased

current densities due to higher average cell temperatures. Starting from HP frequencies and

stack sizes the diagram gives power density increases made possible by heat pipe

interconnectors. Including the conventional stack investment costs, the corresponding

savings due to the power density increase are calculated. As result, the color chart provides

an indication of the total cost neutral price of the planar heat pipe interconnector. As the

depicted example demonstrates, small cell sizes (100 mm) at a HP frequencies of 6 cells per

HP lead to only small investment savings of approx. 750 €/kW for the high investment cost

case. This corresponds to a maximum additional production cost per HP interconnector of

approx. 80 € in order to stay beneficial from an investment based viewpoint. For large cell

stacks, such as 200 x 200 mm² cells and medium specific stack investments, this permissible

costs may reach up to approx. 500 € per HP-Interconnector being used each 4 cells.

Compared to the rather low raw material costs below 50 € / HP these costs seem perfectly

feasible in relevant production scales.

Further work will have to focus on full stack demonstration of the planar heat pipes. An

important task on system level is the electrical insulation of the heat pipe interconnectors

that work on different electrical potential levels. In order to gain in-depth knowledge of

long-term behavior and in-stack degradation effects these prototypes should be

manufactured in close cooperation with a stack manufacturer. State-of-the-art stacks allow

the required thermal cyclability and operational stability in order to carry out reliable long-

term benefit evaluations. This thesis provides the necessary tools and impulses for the

corresponding stack layout and the heat pipe interconnector design.

163

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175

List of figures

Figure 1.1: Concept of SOC stacks with integrated planar heat pipe interconnector layers, designated to themperature gradient flattening and heat extraction from the stack. ....................................................................................................... 3

Figure 1.2: Scope of this work ................................................................................................. 5

Figure 2.1: The energy balance of a fuel cell ........................................................................... 8

Figure 2.2: Structure and functional principle of a solid oxide cell (here SOFC operation) .. 10

Figure 2.3: SOC stack set-ups and gas manifolding concepts, sealings and frames are not displayed. Left: cross-flow. Right: counter-flow (co-flow similar) ...................... 12

Figure 2.4: Local energy balance of a SOC in both operation modes at two operation voltage levels V1 and V2 of a SOC, i-V-curve calculated for typical ASC parameters [Dillig2012] at 800°C, fuel composition 80% H2, 20% H2O .............. 16

Figure 2.5: Energy balance under reversible fuel cell operation, thermodynamic data according to [Chase1998] .................................................................................... 18

Figure 2.6: Gas species evolution and energy balance in an isothermal co-flow SOFC cell (i = 0.4 A cm2, V = 0.75 V, 800°C) under full internal methane steam reforming conditions (S/C = 2 𝐸𝐴 = 95 kJ mol-1, 𝑘0 = 8542 mol s-1 bar-1 m², 𝛼𝐶𝐻4 = 0.85, 𝛼𝐻2𝑂 =-0.35, WGS in equilibrium) ........................................... 22

Figure 3.1: Left: Anode side of ruptured cell after operation (source: [Fleischhauer2014], reprinted with permission from Elsevier), right: electrolyte damage in cross section (source: [Malzbender2007], reprinted with permission from Elsevier) 25

Figure 3.2: Crack formation process according to [Fleischhauer2014]................................. 26

Figure 3.3: Right: SEM image of Ni/YSZ anode delamination from electrolyte; a gap (black area) results (source: [Hsiao1997], reprinted with permission from Elsevier), Left: delaminated LSM-cathode (source: [Ivers-Tiffée2001], reprinted with permission from Elsevier) ........................................................... 27

Figure 3.4: Exhaust gas temperature increase for adiabatic SOFC stack operation (heat transport only by gas flows); Stack operation at 800°C, U = 0.75 V per cell, fuel use FU = 0.8; Fuel: pure hydrogen operation, catalytic partial oxidation (CPOX) of methane with air ratio 0.27 and steam reforming (SR) with S/C=2 of methane. Both partial pre-reforming (approx. 50%) and full stack internal reforming are displayed. ..................................................................................... 29

Figure 3.5: Exhaust gas temperature change for adiabatic SOEC stack operation (heat transport only by gas flows); Stack operation at 800°C, steam use uf = 0.8. Both water and CO2 electrolysis are displayed. .................................................. 30

Figure 3.6: Integrated SOFC stack module (source: [Peters2014], reprinted with permission from Wiley) ....................................................................................... 31

Figure 3.7: Prototypes of cylindrical heat pipe integration to planar SOFC stacks (left) or tubular SOFCs (right) (Source: [Hesse2006]) ....................................................... 32

Figure 3.8: Flowchart of the combined SOFC/allothermal biomass gasification system (source: [Fryda2008], reprinted with permission from Elsevier) ........................ 33

List of figures

176

Figure 3.9: Advanced cooling concepts for HT-PEMs and the effect on temperature profiles. Thermal oil, air cooled interconnector plates and tubular heat pipes integrated to heat pipe interconnector (source: [Supra2014]) .......................... 34

Figure 3.10: Concepts for micro heat pipe integrated into DMFC stack structure (source: [Faghri2008], reprinted with permission from Taylor&Francis) ......................... 35

Figure 3.11: Set-up and functioning of a (planar) heat pipe ................................................... 36

Figure 3.12: Left: Axial grooves as capillary structure for planar heat pipes (source: [Chen2015], reprinted with permission from Elsevier). Right: Designs for micro heat pipes with less than 1mm width of edge (Source: [Reay2006]). ...... 38

Figure 3.13: Left: typical set-up for performance evaluation of low temperature heat pipes. Right: wall temperature profile along a low temperature two-phase heat spreader (TPHS) in horizontal orientation at different cooling loads (source: [Rullière2007], reprinted with permission from Elsevier) .................... 39

Figure 3.14: Left: Low temperature heat pipe open cell structure (source: [Queheillalt2008], reprinted with permission from Elsevier) Right: High temperature liquid metal honeycomb heat pipe (source: [Basiulis1982]) ......... 40

Figure 4.1: Schematic diagram of calculation scheme for SOEC /SOFC simulations ............ 43

Figure 4.2: Schematic of accessing variables in neighboring calculation threads ................ 44

Figure 4.3: Small excerpt of SOC stack meshing of a 2-cell shortstack. Different colors / arrows indicate cell threads that are separated by split walls and may be attributed thermal contact resistances ............................................................... 45

Figure 4.4: Calculated polarization curves for ESC cells, and linear approximation based on ASR .................................................................................................................. 51

Figure 4.5: Thermal resistance representation of heat transfer in planar heat pipe (left: detailed, right: as modeled in this work) ............................................................ 54

Figure 4.6: Left: schematic representation of heat transfer mechanisms perpendicular to cell plane in SOFC stacks; right: Representation with thermal resistances, colored according to relative contribution for a typical stack situation at 800°C (see Table 6.5) ........................................................................................... 55

Figure 5.1: Vapor pressure of different alkali metals suitable as heat pipe working fluid (data according to [Reay2006], [Ohse1985] and [Anderson1993]) and typical SOFC operation ranges for metal supported cells (MSC), anode supported cells (ASC) and electrolyte supported cells (ESC) as to [Tucker2010] ................. 60

Figure 5.2: Capillary heights in porous structures under evaluation for planar heat pipes, calculated for typical working fluids (Na, K, NaK) at 800°C and low temperature fluids (H2O, NH3) at 20°C for comparison ...................................... 63

Figure 5.3: Design concepts (A-E) for planar high temperature heat spreaders .................. 64

Figure 5.4: SEM-image of Design C, prototype 270 – 12. Left: view on capillary structure, right: cross section of casing with spot-welded screen mesh. ............................ 65

Figure 5.5: Prototypes for design concepts (A-E) of planar high temperature heat spreaders ............................................................................................................. 66

Figure 5.6: Left: Heat pipe filling set-up, mounted in glovebox. Right: Heat pipe evacuation set-up for heat pipe degassing and activation ................................. 68

List of figures

177

Figure 5.7: Planar heat pipe degassing and activation procedure in the sodium phase diagram ................................................................................................................ 69

Figure 5.8: Experimental set-up of planar heat pipe performance measurements (side view). ................................................................................................................... 70

Figure 5.9: Distribution of heat pipe zones (evaporator, adiabatic, condenser) and thermocouples in planar heat pipe test rig for HP270 measurements (top view). ................................................................................................................... 71

Figure 5.10: Distribution of heat pipe zones (evaporator, adiabatic, condenser) and thermocouples in planar heat pipe test rig for HP270 measurements. ............. 71

Figure 5.11: Temperature recordings (above image) and temperature profiles (down) of HP270-9 in horizontal operation under stepwise increasing cooling load until dry-out of evaporator .......................................................................................... 73

Figure 5.12: Temperature profiles of HP270-8 at varying tilt angles and constant cooling flows (2 sm³h-1 ( = 370 W) at 0° slightly decreasing with tilt angle to 310 W at -90°) ..................................................................................................................... 74

Figure 5.13: Cool-out of planar heat pipes (adapted from [Hoogeboom2014])..................... 75

Figure 5.14: HP 4 in horizontal position (𝜙 = 0°) with increased heating power and constant air coolant flow, showing a reduction of the non-condensable gas zone at the end of the cooler section for increased internal pressure levels..... 76

Figure 5.15: Heat transfer rates and temperature profiles for exemplary prototypes in horizontal position (𝜙 = 0°) at maximum heat transfer before dry-out. ............ 77

Figure 5.16: Temperature profiles for exemplary design E prototypes HP 15 and HP 16 with differing tilt angle at approx. 100 W transferred power............................. 78

Figure 5.17: Summary of wick structure analysis. Maximum measured heat transfer rates 𝑄𝐻𝑃,𝑚𝑎𝑥, temperature drops Δ𝑇 and calculated temperature differences in HP casing. Lower diagram indicates the resulting effective conductivities 𝑘𝐻𝑃 of the HP ..................................................................................................... 79

Figure 5.18: Performance measurement of Design C prototypes with different capillary structures and computed heat transfer limits. ................................................... 81

Figure 5.19: Performance evaluation of design C prototypes under different tilt angles. ..... 82

Figure 5.20: Left: Schematic start-up of liquid metal heat pipe from room temperature at constant heating rate (adapted from [Jang1995]). Tm = melting temperature, T* = transition temperature, Ts = stationary temperature, Right: own experimental measurements, T* calculated for design C prototype HP270-13 . 83

Figure 5.21: Maximum temperature gradient in condenser during start-up from different initial temperatures and with varying heat-up rates for HP similar to HP270-13. ........................................................................................................................ 84

Figure 5.22: Long-term operation (over 2100 h) behavior of HP 270-12 in horizontal operation at 550 W heat transfer and 800 °C adiabatic temperature. ............... 86

Figure 5.23: Temperature profiles during long-term test operation of a planar heat pipe HP 270-12 ............................................................................................................ 86

Figure 5.24: Post-mortem SEM analysis of HP270-12 capillary structure (from evaporator). ......................................................................................................... 87

List of figures

178

Figure 5.25: Comparison of degradation rates of planar heat pipes HP 6 and HP 270-12 per 1000 h ............................................................................................................ 88

Figure 5.26: Cross section SEM analysis of HP270-12 (evaporator) after 2100 h. EDX mapping of Fe (red dots) and Ni (yellow dots) .................................................... 88

Figure 5.27: Scheme of the inactivation of heat pipes due to hydrogen permeation with temperature and partial pressure profiles within heat pipe (compare [Leimert2016]) ..................................................................................................... 90

Figure 5.28: Numerical parameter study of hydrogen deactivation and its mitigation in planar high temperature heat pipes. Boundary conditions of base case (blue): working fluid: Na, casing: AISI 316 SS, scase = 1mm uncoated, lHP=270 mm, lH2

= 0.5 lHP, 𝑇𝐻𝑃, 𝑖𝑛𝑎𝑐𝑡 = 650°𝐶, transition zone temperature gradient: 𝜕𝑇𝐻𝑃, 𝑖𝑛𝑎𝑐𝑡/𝜕𝑥 = 5 K/mm, 𝑝𝐻2 = 0.5 bar .................................................... 92

Figure 5.29: Flow diagram for hydrogen degradation measurements of planar heat pipes .. 94

Figure 5.30: Deactivation and reactivation of HP 270-6 due to hydrogen permeation after 131 h constant horizontal operation. .................................................................. 95

Figure 5.31: HP270-16 with 100 µm Ag coating. Before(left) and after (right) operation in hydrogen atmosphere ......................................................................................... 96

Figure 5.32: Deactivation free operation of HP270-10 in hydrogen atmosphere (pH2=1 bar) due to intermediate layer. ........................................................................... 97

Figure 5.33: Deactivation free operation of HP270-16-2, casing of CROFER 22H, in hydrogen atmosphere (up to pH2=1 bar rest N2) at 800°C and 700°C . ............... 98

Figure 5.34: Chromium oxide and spinel layer formation on CROFER at 900°C in air (source: [Froitzheim2008], with permission from Elsevier) ................................ 99

Figure 5.35: Measurement set-up (left) and measurement cell (right) for hydrogen permeation measurements. ................................................................................ 99

Figure 5.36: Measured hydrogen permeabilities of CROFER 22H (1.4755), 1.4841 and 1.4301 in humidified hydrogen (standard deviations of measurement shown)100

Figure 5.37: Phase diagrams of binary alkali metal - hydrogen system in heat pipes – calculated with Factsage on basis of [Stull1985]. Exemplary determination of NaH formation limit (= approx. 400 °C) in coldfinger for HP operated at 800C in active zone. .................................................................................................... 101

Figure 5.38: Basic mechanism of metal hydride induced deactivation of high temperature heat pipes .......................................................................................................... 101

Figure 5.39: Dynamics of hydrogen deactivation with NaH formation after hydrogen environment at t=0. Left diagram: Solid black line shows cold end temperature of heat pipe, data points indicated inactive length of heat pipe in relation to entire heat pipe length. Right: Temperature profiles during initial heat pipe deactivation and starting of NaH formation. ............... 102

Figure 6.1: View of SOC short stack test rig at EVT ............................................................. 105

Figure 6.2: Flow sheet of SOFC / SOEC shortstack test rig .................................................. 107

Figure 6.3: Wiring scheme of SOC test rig designed by EBZ Dresden, providing fuel cell and electrolysis mode operation ....................................................................... 108

Figure 6.4: Stack design for 4-cell stack with planar heat pipe interconnector .................. 109

List of figures

179

Figure 6.5: Installed 3-cell short stack with heat pipe interconnector in SOC test rig ........ 110

Figure 6.6: Sealing concept of short stack based on compressible gaskets ........................ 111

Figure 6.7: Explosion view of the heat pipe interconnector ............................................... 112

Figure 6.8: Images of the heat pipe interconnector: a) open with capillary and mesh structure; b) cathode flow field; c) with SOFC placed ....................................... 112

Figure 6.9: Distribution of thermocouple groups in the different layers of a two cell stack113

Figure 6.10: Distribution of thermocouples in the intermediate interconnectors ............... 114

Figure 6.11: Comparision of iV-curves in SOFC and SOEC operation mode between manufacture’s data in ceramic housing and own measurements in 1-cell stack. .................................................................................................................. 116

Figure 6.12: Evaluation of stack gas tightness / leakage behavior and electric contact under varying temperatures in SOFC operation on H2/H2O mixture ................ 117

Figure 6.13: Individual TC temperatures compared to polarization curve (right) and averaged stack temperature difference to OCV operation compared with calculated cell heat production (left) of a 1-cell stack. Operation conditions: Tfurnace=850°C, mechanical load=0.5 kN, SOFC operation: VH2 = 0.5 SL / min, VN2 = 0.5 SL / min, SOEC operation: VH2 = 0.6 SL / min, mH2O = 30 g/h; Vair = 1 SL / min .............................................................................................................. 118

Figure 6.14: Reversible SOC operation of a 1-cell stack over 120 SOFC / SOEC cycles. Operation conditions: Tfurnace=850°C, mechanical load=0.5 kN, VH2 = 0.6 SL min-1, mH2O = 30 g h-1; Vair = 1 SL min-1; cycle time: 30 min ............................... 119

Figure 6.15: Voltage polarization curves for the two cell stacks with and without integrated heat pipe interconnectors (HP). Furnace temperature: 830°C, SOFC operation: 1.5 SL min-1 H2, 1.5 SL min-1 N2, 3.0 SL min-1 air, SOEC operation: 1.5 SL min-1 H2, 90 g h-1 H2O, 3.0 SL min-1 air, power densities averaged over both cells for each stack arrangement. ..................................... 120

Figure 6.16: Influence of current density on average in plane temperature for two cell stacks with and without integrated heat pipe interconnectors (HP). Furnace temperature: 830°C, SOFC operation: 1.5 SL min-1 H2, 1.5 SL min-1 N2, 3.0 SL min-1 Air, SOEC operation: 1.5 SL min-1 H2, 90 g h-1 H2O, 3.0 SL min-1 air, external temperatures of heat pipe averaged over the isothermal part of

heat pipe outside the stack. 𝛥𝑇𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝐻𝑃 indicates temperature increase without HP, while 𝛥𝑇𝑐. 𝐻𝑃 shows residual temperature increase for a temperature controlled HP. .............................................................................. 121

Figure 6.17: In cell plane temperature distributions for 2-cell stacks operated in SOFC operation under different current loads. Blue lines indicate air flow parallel temperature profiles, red lines fuel flow parallel temperature profiles. Left: Without heat pipe integration to the stack structure. Right: Heat pipe interconnector designed according to table 2 integrated into the stack structure between the two cells. ...................................................................... 122

Figure 6.18: Temperature profiles of fuel flow parallel measurements in 2-cell stacks operated on unreformed methane steam mixtures (S/C=2). Temperatures indicate difference to open circuit hydrogen operation with and without integrated heat pipe interconnectors (HP). Furnace temperature: 830°C, SOFC operation: 1 SL min-1 CH4, 3 SL min-1 air ................................................. 123

List of figures

180

Figure 6.19: Set-up of measurement cell for high temperature contact resistance measurements. .................................................................................................. 125

Figure 6.20: Thermal contact set-ups (explosion view) ........................................................ 126

Figure 6.21: Left: Calculation of interface temperatures and temperature differences for the contact resistance measurement of set-up 1 at 800°C contact temperature, Gaussian error bars of temperature measurements and inaccuracies of positioning are smaller than displayed markers; right: Geometry of test specimens for thermal contact measurements. ................... 129

Figure 6.22: Left: Uniformal heat transfer in contact interface according to numerical evaluations, Right: comparison with experimental validation via radial movement of the thermocouples with casing thickness t = 0.2 mm, small deviations from central temperature measurements can be almost completely explained by heat conduction in the thermocouple casing. .......... 130

Figure 6.23: Left: Heat transfer measurement (normalized to cylinder cross section) through full stack set-up, (set-up 1) for different load situations, blank steel or pre-oxidized steel, error bars are only shown for 32.8 kPa and 21.3 kPa measurement.Right: Resulting heat transfer rates (based on cylinder cross section) for different stack-relevant set-ups, pre-oxidized steel surfaces, 44.3 kPa contact pressure. ........................................................................................ 131

Figure 6.24: Heat transfer resistance of the different contact points within a repeating unit of the stack (Rc1: interconnector ribs – Ni-mesh; Rc2: Ni-mesh – anode; Rc3: cathode – interconnector ribs). ................................................................. 132

Figure 6.25: Heat transfer measurement through SOFC sealing materials (set-up 4) at constant contact compression of 83 kPa. ......................................................... 133

Figure 6.26: Comparison of measured and experimentally calculated SOFC polarization curves (ASR used in FLUENT model was fit to accord to experimentally determined cell performance according to equation (6.11)). Furnace temperature: 830°C, SOFC H2 operation: 1.5 SL min-1 H2, 1.5 SL min-1 N2, 3.0 SL min-1 Air, CH4 operation: 1 SL min-1 CH4, 96 g h-1 H2O, 3.0 SL min-1 air ......... 134

Figure 6.27: Comparison between numerical and experimental results of in plane temperature profiles 2 cell stacks operated on unreformed methane steam mixtures (S/C=2). Temperatures with (right) and without (left) integrated heat pipe interconnectors (HP) are shown. Furnace temperature: 830°C, SOFC operation: 1.0 SL min-1 CH4, 96 g h-1 H2O, 3.0 SL min-1 air, stack current: 20 A 135

Figure 6.28: Dry off-gas concentrations (after condensation) of the exhaust gas of 2-cell stacks operated on unreformed methane steam mixtures (S/C=2) at different stack currents. Filled column show values measured at the experimental set-up with gas analyzer, hatched column results of FLUENT model. Furnace temperature: 830°C, SOFC operation: 0.5 SL min-1 CH4, 48 g h-1 H2O, 1.5 SL min-1 N2, 3.0 SL min-1 air .................................................................................... 136

Figure 6.29: Temperature profiles of fuel flow parallel measurements in 2 - cell stacks operated on hydrogen (up) / unreformed methane steam mixtures at S/C=2 (down). Temperatures indicate difference to open circuit hydrogen operation with and without integrated heat pipe interconnectors (HP).

List of figures

181

Furnace temperature: 830°C, H2 operation: 1.5 SL min-1 H2, 1.5 SL min-1 N2, 3.0 SL min-1 Air, CH4 operation: 1.0 SL min-1 H2, 2.0 SL min-1 Air ..................... 137

Figure 7.1: In plane cell temperature profiles of SOFC stack (200mm cells/ CFY interconnector) on hydrogen operation. Min and max cell temperatures are tagged. Operation conditions: average stack operation voltage per cell: 0.75 V, current density: 0.4 A cm-1, fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5) ................................................................................................. 140

Figure 7.2: Maximum temperature differences at cell level for SOFC operation on hydrogen depending on number of cells per heat pipe interconnector for different solid oxide cell sizes and interconnector materials. Operation conditions: average stack operation voltage per cell: 0.75 V, current density: 0.4 A cm-1, fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5) ... 141

Figure 7.3: Left: Possible average stack temperature increase at constant maximum cell temperature, Right: Resulting current density increase. Operation conditions: average stack operation voltage per cell: 0.75 V, initial current density: 0.4 A cm-1, fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5) ............ 142

Figure 7.4: Representation of temperature profiles within a SOFC stack repeating unit operated on hydrogen and 10 cells per heat pipe interconnector layer. Stack size: 200 x 200 mm² cells, average 0.75 V per cell, 0.4 A cm-², fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5), CROFER 22H interconnector material .................................................................................... 143

Figure 7.5: Maximum average temperature difference between two neighboring cells in stack Operation conditions: Stack operation voltage per cell: 0.75V, current density: 0.4 A cm-2, fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5) ............................................................................................................... 144

Figure 7.6: Current density profiles under SOFC operation in a stack with 1 HP with 10 cell layers. Left: cell 1 (neighboring the HP interconnector), Right: cell 5 (maximum distance of HP) stack 200 x 200 mm² cells, 0.75 V, 0.4 A cm², fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5), CROFER 22H interconnector material .................................................................................... 144

Figure 7.7: Layout of heat pipe interconnectors for stacks based on CROFER 22 H depending on HP-aspect ratio = length / width. HP interconnectors designs as in Table 6.1 in horizontal operation. Operation conditions: Stack operation voltage per cell: 0.75V, current density: 0.4 A cm-2, fuel: 0.95 H2, 0.05 H2O, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5), .......................................................... 145

Figure 7.8: Influence of heat pipe interconnectors on SOEC stacks. Left: Temperature profiles at endothermal operation with varying air ratios. Left: Average cell current densities in SOEC operation with different HP-interconnector frequencies. SOFC stack: 200 x 200 mm² cells, 1.15 V, 0.4 A cm², cathode: 0.05 H2, 0.95 H2O, SU= 0.75 (Σ = 1.33), anode: air, CROFER 22H interconnector material .................................................................................... 146

Figure 7.9: Representation of temperature profiles within a SOFC stack repeating unit operated on unreformed methane / steam mixtures as fuel (S/C = 2) and 10 cells per heat pipe interconnector layer. Stack size: 200 x 200 mm² cells, average 0.75 V per cell, 0.4 A cm-², fuel: 0.34 CH4, 0.64 H2O, H2=0.02, FU= 0.75, cathode: air, AU= 0.2 (𝜆 = 5), CROFER 22H interconnector material ..... 147

List of figures

182

Figure 7.10: Left: Simplified heat balance of a stack repeating unit operated on full internal steam reforming of methane, indicating the recycle flow within the heat pipe structure. Right: heat ratio of heat pipe recycled heat to total reforming heat depending on HP frequency, degree of reforming and air ratio. Stack size: 200 x 200 mm² cells, average 0.75 V per cell, 0.4 A cm-², fuel: 0.34 CH4, 0.64 H2O, H2=0.02, FU= 0.75, cathode: air, CROFER 22H interconnector material .................................................................................... 149

Figure 7.11: Maximum cell temperature differences, depending on HP frequency, degree of reforming and air ratio. For the stack without HP a higher maximum air ratio is considered. Stack size: 200 x 200 mm² cells, average 0.75 V per cell, 0.4 A cm-², fuel: 0.34 CH4, 0.64 H2O, H2=0.02, FU= 0.75, cathode: air, AU= 0.2, CROFER 22H interconnector material ............................................................... 150

Figure 7.12: Standard natural gas fired SOFC-system in CHP configuration with exemplary temperatures and powers for parameter set according to Table 7.1 .............. 151

Figure 7.13: Sankey plot of a standard SOFC Process with (Pre-) Steam Reforming simulated with Aspen Plus - conditions: 50% Pre-reforming (at 560°C), 50% internal reforming in cell, air ratio =5, stack fuel use =0.8, avg. cell temperature 810°C, air blower efficiency= 0.5 ................................................. 152

Figure 7.14: Thermal efficiencies of SOFC-CHP systems depending on fuel type, air ratio and level of heat use (exhaust temperature). Standard SOFC process with (Pre-) Steam Reforming - conditions: 50% Pre-reforming (at 560°C) of methane, S/C = 2, 50% internal reforming in cell, stack fuel use =0.8, cell voltage 0.75 V, It is assumed perfect heat recuperation for pre-heating gases, no parasitic heat losses of stack and system. ................................................... 153

Figure 7.15: Improved system integration based on planar heat pipe technology for natural gas fired SOFC-system in CHP configuration. Left: full external reformer coupled by heat pipes. Right: One-step heat pipe preheater and fully internal reforming. .................................................................................... 155

Figure 7.16: SOFC with heat pipe process integration simulated with Aspen Plus - conditions: 50% anode off-gas recycling, 100% pre-reforming (at 800°C), no internal reforming in cell, air ratio 𝜆 = 1.5 (no high excess air required due to HP, stack fuel use =0.8, avg. cell temperature 840°C, air blower efficiency= 0.5, 4% parasitic losses ...................................................................................... 156

Figure 7.17: Thermal efficiencies depending on air ratio, exhaust temperature and fuel type. Standard SOFC process with pure hydrogen or (pre-) steam reforming – conditions (CH4): 50% pre-reforming (at 560°C) of methane, S/C = 2, 50% internal reforming in cell, stack fuel use = 0.8, cell voltage 0.75 V. It is assumed perfect heat recuperation for pre-heating gases, heat losses of stack and system to environment Qloss are set to 0 in the displayed lines. Heat capacities of off-gases assumed constant. ............................................... 157

Figure 8.1: Determination of maximum investment cost of planar heat pipe interconnectors on basis of an increase of stack power densities. .................. 160

183

List of tables

Table 2.1: Thermal expansion coefficients of typical cell and stack materials averaged in the stated temperature range ............................................................................. 13

Table 3.1: Degradation mechanism depending on cell temperature according to [Stehlík2009; Yokokawa2008] ............................................................................. 24

Table 3.2: Cell material strength .......................................................................................... 26

Table 3.3: Typical stack air ratios during operation ............................................................. 28

Table 3.4: Heat pipe heat transfer limits as defined by [Chi1976; Peterson1994; Reay2006]. x’ describes property x of liquid phase, x’’ of vapor phase at saturation point ................................................................................................... 37

Table 3.5: Exemplary prototypes of planar heat pipes ........................................................ 38

Table 4.1. Geometry and materials ...................................................................................... 42

Table 4.2. Input Parameters to electrochemical model ...................................................... 49

Table 4.3. Input parameters to homogenous gas reactions in anode flow channels for methane steam reforming and water gas shift reaction on SOFC anodes, adapted from [Mogensen2011], [Ahmed2000] .................................................. 53

Table 4.4: Thermal conductivity of typical stack materials .................................................. 56

Table 5.1: Effective curvature radius of capillary structure according to [Chi1976] ........... 62

Table 5.2: Typical wetting angles of alkali metals ................................................................ 62

Table 5.3: Excerpt of the fabricated planar heat pipe prototypes for design concept evaluation (further prototypes listed in Table 5.5) ............................................. 65

Table 5.4: Planar heat pipe cleaning procedure .................................................................. 67

Table 5.5: Excerpt of the fabricated planar heat pipe prototypes for performance evaluation and optimization of design C ............................................................. 80

Table 5.6: Specific surface to free volumes of planar and cylindrical heat pipes of equivalent capillary structures ............................................................................ 85

Table 5.7: Excerpt of the fabricated planar heat pipe prototypes for hydrogen deactivation tests (based on design type C) ....................................................... 94

Table 6.1: Heat pipe interconnector design parameters ................................................... 111

Table 6.2: Stack heat up and reduction program on basis of a 1-cell short stack ............. 115

Table 6.3: Experimental conditions applied during temperature profile evaluation for 2-cell short stacks ................................................................................................. 119

Table 6.4: Measurement set-up parameters ..................................................................... 125

Table 6.5: Resulting heat transfer resistances for stack repeating unit at different temperature levels (for graphic representation see Figure 4.6) ....................... 132

Table 7.1: Parameter set for standard system simulation ................................................. 151

Table 7.2: Simulated pressure loss and blower needs at reduced air flows (at constant stack geometry, design point air ratio = 5, isentropic efficiency of blower =0.5) ................................................................................................................... 152

185

Permissions

Part of the information (text, figures and tables) presented in chapter 4 and 6 was reprinted

from the Journal of Power Sources, Vol. 300: Dillig, M., Biedermann, T., & Karl, J., Thermal

contact resistance in solid oxide fuel cell stacks, 69-76, Copyright (2015) with permission

from Elsevier.

Part of the information (text, figures and tables) presented in chapter 6 was reprinted from

the Fuel Cells, Vol. 15: Dillig, M., Meyer, T., & Karl, J., Integration of Planar Heat Pipes to

Solid Oxide Cell Short Stacks, 742-748, Copyright (2015) with permission from John Wiley

and Sons.


the Journal of Heat and mass transfer, Vol. 92: Leimert, J., Dillig, M.,& Karl, J., Hydrogen

inactivation of liquid metal heat pipes, 920-928, Copyright (2016) with permission from

Elsevier.


the Fuel Cells, Vol. 14: Dillig, M., Leimert, J., & Karl, J., Planar high temperature Heat Pipes

for SOFC/SOEC Stack applications, 479-488, Copyright (2014) with permission from John

Wiley and Sons.


the Energy Procedia, Vol. 28: Dillig, M., & Karl, J., Thermal Management of High Temperature

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