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Mesoscale SOFC-based power generator system: modeling and experiments

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Mesoscale SOFC-based power generator system: modeling and experiments

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Content Mesoscale SOFC-Based
Power Generator System:
Modeling and Experiments

By

Jakrapop Wongwiwat

A Dissertation Presented to the
Faculty of the USC Graduate School
University of Southern California
in Partial Fulfillment of the
Requirements for the Degree
Doctor of Philosophy
(MECHANICAL ENGINEERING)

August 2019

Table of Contents
List of Figures i
List of Tables iii
Abstract 1
Chapter 1 Introduction 2
1.1 Why do We Still Use Batteries for Portable Electronic Devices? 2
1.2 Research Objectives 5
Chapter 2 Background 8
2.1 Thermal Transpiration Membrane 8
2.2 Catalytic Combustion 12
2.3 Solid Oxide Fuel Cell Modeling 18
Chapter 3 Methods 25
3.1 Thermal Transpiration Membrane 25
3.2 Catalytic Combustion 27
3.3 Self-Sustaining and Self-Pressurizing Combustion Chamber 29
3.4 Solid Oxide Fuel Cell Modeling 31
Chapter 4 Results 33
4.1 Thermal Transpiration Membrane 33
4.2 Catalytic Combustion 37
4.3 Self-Sustaining and Self-Pressurizing Combustion Chamber 41
4.4 Solid Oxide Fuel Cell Modeling 43
Chapter 5 Conclusion 47
5.1 Thermal Transpiration Membrane 47
5.2 Catalytic Combustion 48
5.3 Self-Sustaining and Self-Pressurizing Combustion Chamber 49
5.4 Solid Oxide Fuel Cell Modeling 50
References 51
Appendix UDF for ANSYS-Fluent 55
i

List of Figures
Figure 1 – Energy densities of various energy storage materials illustrating the respective
volumetric and gravimetric densities 2
Figure 2 – Small-scale rotary engine and microscale gas turbine blades 3
Figure 3 – The schematic of small-scale power generator: assembled view and exploded view 5
Figure 4 – Bouncing gas molecules driven by temperature gradient across a micro-scale
channel 9
Figure 5 – Flow coefficient vs. Knudsen number for circular capillary channel and therma
transpiration membrane diagram and parameter 10
Figure 6 – Catalytic combustion diagram for C 3H 8-air reaction on platinum surface 13
Figure 7 – Dual chamber solid oxide fuel cell diagram and Single chamber solid oxide fuel cell
diagram 18
Figure 8 – Reactions that occur around the SOFC 19
Figure 9 – Electrochemical reactions that occur inside the SOFC 20
Figure 10 – Macroscopic view and microscopic view of glass microfiber membrane 26
Figure 11 – Macroscopic view and microscopic view of Hydrophilic polyethersulfone membrane 26
Figure 12 – The thermal transpiration membrane apparatus 26
Figure 13 – Schematic of thermal transpiration membrane experimental setup 27
Figure 14 – Gas flow diagram and electrical circuit for catalytic combustion experimental
setup 28
Figure 15 – Experimental setup for catalytic combsution on plantinum foil 29
Figure 16 – Cross-section of the simulation model in ANSYS-Fluent and boundary conditions 29
Figure 17 – The diagram of self-sustaining thermally driven cylindrical combustion chamber 30
Figure 18 – The self-sustaining thermally driven cylindrical combustion chamber, the model
and boundary conditions for the simulation 31
Figure 19 – Boundary conditions of mT-SOFC in ANSYS-Fluent 32
Figure 20 – The relation of flow rate and pressure drop from the leak of the system and Darcy
backflow through the membrane 34
ii

Figure 21 – The performance curve running on air at various temperature gradients across
Whatman membrane from experiments and modified Muntz equation 35
Figure 22 – The performance curve running on air at various temperature gradients across
Whatman membrane from experiments and modified Muntz equation 35
Figure 23 – The performance curve in various temperature gradients across the membrane
for two sheets of membrane and three sheets of membrane 36
Figure 24 – An example of simulation result from C 4H 10-air mixture at 1.5 equivalence ratio
and 12 cm/s flow speed 37
Figure 25 – The product compositions of experimental results and simulation results of C 3H 8-
air mixture at 16 cm/s constant flow speed and 2.5 constant equivalence ratio 38
Figure 26 – The product compositions of experimental results and simulation results of C 4H 10-
air mixture on platinum foil at 12 cm/s constant flow speed and 1.5 constant equivalence
ratio 39
Figure 27 – The product compositions of experimental results and simulation results of C 4H 10-
air mixture on platinum mesh at 12 cm/s constant flow speed and 1.5 constant
equivalence ratio 40
Figure 28 – Extinction curves of C 3H 8 and C 4H 10 on platinum foil 41
Figure 29 – An example of the simulation result at 0.48 cm/s C 4H 10 flow speed 42
Figure 30 – The product compositions from the self-sustaining thermally driven combustion
chamber at various C 4H 10 flow rate 42
Figure 31 – Polarization curve of experimental results and simulation results from mT-SOFC
running H 2 at various operating temperature 44
Figure 32 – Polarization curve of experimental results and simulation results from mT-SOFC
running C 4H 10 at various operating temperature 45

iii

List of Tables
Table 1 Detailed surface reaction mechanism for catalytic combustion on platinum
surface [22] 14
Table 2 Parameters for the one-step rate expression for catalytic combustion on platinum
surface from Zhong et al.’s [23] and Deshmukh et al.’s [24] work. 17
1

Abstract
Batteries have at most 2% of the energy density of hydrocarbon fuels, but internal
combustion engine have never been successfully built to power handheld application neither. It
is due to difficulties in minimizing heat and friction losses. An alternative approach is a
micro-tubular solid oxide fuel cell (mT-SOFC) running on butane that does not require any moving
parts to generate power. The mT-SOFC is integrated with a thermal transpiration membrane, a
nanoporous medium operating as a gas pump with applied temperature gradient. Catalytic
combustion on a platinum surface generates heat for the mT-SOFC and thermal transpiration
membrane.
The thermal transpiration membrane, catalytic combustion and mT-SOFC were each
modeled separately. ANSYS-Fluent simulation results of all three components were compared
with respective experimental results. Then, the transpiration membrane and catalytic
combustion were integrated into a mesoscale self-sustaining and self-pressurizing combustion
chamber running on butane without moving parts. The combustion chamber can supply an
appropriate temperature and fuel-air mixture equivalence ratio for the mT-SOFC. The model of
mT-SOFC was also developed to estimate the power generation at various operating
temperatures for hydrogen and butane.

Keywords: thermal transpiration membrane, catalytic combustion, solid oxide fuel cell

2

Chapter 1 Introduction

1.1 Why do We Still Use Batteries for Portable Devices?
Portable electronic devices have an ever-growing need for electrical power sources, yet
batteries have a vastly less specific energy than hydrocarbon fuels. Typically, hydrocarbon fuels
contain energy up to 12,000 Wh/kg, but commercial batteries such as lithium ion contain only
200 Wh/kg which is only 1.6% of the energy stored in hydrocarbon fuels as shown in Figure 1 [1].
Although energy density of batteries has been increasing more than doubling in the last decade,
battery weight is still a major concern for mobile applications such as wheel chairs, mobile robots
and portable military devices. For example, ASIMO, Honda’s humanoid robot [2], weighs about
50 kg and its lithium-ion battery weighs about 6 kg which is 12% of the total body weight, yet it
can only run 1 hour still last. Another example is Boston Dynamics’ RHex military mobile robot
[3] which can operate up to 6 hours, but has to carry lithium-ion batteries up to 18% of its weight.
Due to these issues, batteries have to be recharged or replaced frequently, unlike hydrocarbon
fuel that can be stored in a container and filled up easily.

Figure 1 – Energy densities of various energy storage materials
illustrating the respective volumetric and gravimetric densities

3

The scaling down of internal combustion engines and electrical generators for handheld
portable devices has been unsuccessful, due to issues with heat loss, friction loss and the
difficulty of manufacturing parts at such a small scale with sufficient precision. A small aircraft
engine is an example of small scale power generator using hydrocarbon fuel. Menon et al. [4]
provided data from a 2.45-cc engine with 8% maximum efficiency at 8,000 rpm, but this type of
engine creates unacceptable noise even for outdoor applications. The engine cannot be scaled
down further, due to too many moving parts, e.g. a piston, valves and a crankshaft. Wankel rotary
engine with fewer moving parts, as shown in Figure 2, was studied by Walther et al. [5], but with
this small-scale mechanism, the manufacturing process and heat loss have become problems.
This rotary engine to be powered by hydrogen which also becomes a storage problem. Generally,
hydrogen can be stored in a pressurized tank, but it puts a lot of weight of the power generator.
Dessornes et al. [6] have developed a 55W-microscale gas turbine that must operate at 840,000
rpm to achieve a 55 W power output, so friction loss and heat loss were still major problems.
Manufacturing tolerances were also difficult to deal with due to the extremely high rotational
speed.

Figure 2 – (Left) small-scale rotary engine and
(Right) microscale gas turbine blades

Small-scale power generators with no moving parts have been investigated by several
research groups, due to a concern with friction. Hsu et al. [7] has proposed an idea of using
thermoelectric plates to generate electricity from hydrocarbon combustion without any moving
parts. However, the efficiency of thermoelectric power generator itself was too low to generate
enough power to handheld devices. Another simple power generator for small scale devices is
4

Proton Exchange Membrane (PEM) fuel cell. The fuel cell decomposes oxygen on the cathode
side and fuel on the anode side and hydrogen ions are conducted through its membrane. Then,
electricity is generated from the net change in Gibb’s free energy. Typically, PEM fuel cells uses
pure hydrogen as an energy source; otherwise, the fuel cell may become contaminated from
impurities. These impurities have been discussed in Shan et al.’s work [8] which shows that cell
performance was reduced. Even hydrogen for PEM fuel cell can be stored in a high-pressure tank
with a graphene nanostructure [9] or extracted from chemical hydride such as sodium
borohydride [10] as in Rajuara et al.’s and Li et al.’s work, respectively. These techniques still
require more study on sophisticated systems. Another type of fuel cells is the Direct Methanol
Fuel Cell (DMFC) using ethanol as an energy source, but the power density of electricity
generation is too low compared to PEM fuel cells which have been discussed in Li et al.’s work
[11]. One more type of fuel cell is the Solid Oxide Fuel Cell (SOFC), a robust fuel cell that can
operate with various types of hydrocarbon fuels, but it must operate under a high temperature
of at least 800 K. SOFC provides higher power density than DMFC and can produce electricity in
a single chamber [12-13-14] as in Hibino et al.’s, Shao et al.’s and Milcarek et al.’s work,
respectively. There is also no energy storage issue for SOFC, if propane or butane is used as fuel.
Each type of fuel cell has different advantages and limitations, but if the high operating
temperature environment can be provided from the fuel, SOFC could be a feasible solution for a
small-scale portable electrical power generator.
To store energy in liquid fuels seems to be a reasonable solution; however, to extract
energy from hydrocarbon fuel, oxygen as an oxidizer must be continuously driven into the
combustion chamber to maintain the reaction. If a small fan which consumes electricity is used,
friction loss and energy supplied will be huge problems at the small scale. To avoid these
problems, using a thermal transpiration pump from nanoporous membranes can eliminate losses
due to friction from moving parts and electricity supplied. The pumping power is generated from
a temperature gradient across the membrane, inducing air or gas from the cold side to the hot
side of the membrane. The temperature gradient can be provided from catalytic combustion on
a platinum surface placed inside the combustion chamber. Our solution for a small-scale power
generator is to use thermal transpiration membranes and catalytic combustion from butane,
5

combining with a micro-tubular solid-oxide fuel cell (mT-SOFC) to generate electricity. This mT-
SOFC can operate with hydrocarbon fuels, but it requires high temperature operating conditions
up to 600 K.
These three components can be combined together as a small-scale power generator.
The thermal transpiration membrane provides air pumping power into the combustion chamber
from the temperature gradient across the membrane. Catalytic combustion on a platinum
surface from the hydrocarbon fuel provides heat for the hot side of the membrane and for mT-
SOFC. Then the fuel cells consume unburned fuel and oxidizer from the catalytic combustion to
generate electricity. This concept of self-sustaining power generation without moving parts was
previously introduced by Wang et.al. [15] as shown in Figure 3. Their work achieved only 0.092%
of efficiency due to heat loss and unburned fuel at the exhaust; however, they showed the
promising solution for a small-scale power generator.

Figure 3 – The schematic of small-scale power generator:
(Left) assembled view and (Right) exploded view

1.2 Research Objectives
Based on the addressed issues, a small-scale power generator can be constructed from
the combination of a mT-SOFC to generate electricity, catalytic combustion on platinum surfaces
to generate heat for the mT-SOFC and thermal transpiration membranes as a thermal energy
harvester which can pump the external air for the mT-SOFC and catalytic combustion and works
as a heat insulator at the same time.

6

This work is split into 4 sections as:
1. The study of thermal transpiration membrane
To achieve the maximum air pumping power, i.e. maximum flow rate with enough
pressure, various membrane pore sizes have to be investigated by 1D flow
experimental setup. The larger pore size provides the greater flow rate, but provides
less pressure gradient across the membrane; therefore, an appropriate membrane
must be selected based on maximum pumping flow rate. A uniform heating wire in
the experimental setup will supply heat to the hot side of the membrane instead of
using heat from catalytic combustion. The numerical model of the membrane has
been studied to estimate the flow rate and pressure rise from the membrane for the
further design.

2. The study of catalytic combustion on platinum surface
Platinum catalyst inside the combustion chamber have to be investigated to utilize
all supplied fuel effectively. The fuel is used for generating heat from the platinum
and generate electricity from mT-SOFC. Catalytic combustion models for propane-air
mixture and butane-air mixture were investigated and compared with experiments in
various equivalence ratios and mixture flow speeds.

3. The study of self-sustaining and self-pressurizing combustion chamber
The integrated system of catalytic combustion and the thermal transpiration
membrane with the maximum pumping performance have to be built to study the
combustion chamber performance and compare to the simulation in ANSYS-Fluent.
The performance of combustion chamber was also explored to demonstrate the wide
range control and operating condition of the chamber which is applicable for mT-
SOFC.

7

4. The study of micro-tubular solid-oxide fuel cells (mT-SOFC)
A micro-tubular solid-oxide fuel cell (mT-SOFC) has to be investigated in this study,
because a lot of fuel cell parameter are still unknown. The modeling of mT-SOFC was
studied and compared with experimental results at various different operating
conditions such as different fuels and different operating temperature.

8

Chapter 2 Background

2.1 Thermal Transpiration Membrane
Thermal transpiration is a rarefied gas dynamics phenomenon describing the gas flow
through a narrow channel with an imposed temperature gradient. When gas molecules hit a wall
that has temperature gradient, these gas molecules tend to bounce to the hot side of the wall at
the higher speed than to the cold side of the wall, because gas molecules get kinetic energy from
the hot wall. Therefore, the net number of molecules of the gas flows toward the hotter end of
the wall. As gas flow from cold end to the hot end, a pressure gradient is created across the
channel. The concept of thermal transpiration has been studied since Osborne Reynolds since
1879 [16] with high thermal conductivity porous media causing high thermal energy input for
pumping power. For more recent research, Han et al. [17] have introduced an experimental study
of thermal transpiration pump using aerogel as a membrane to decrease thermal power input
and increase temperature gradient across the membrane. However, aerogel is a fragile material
that may not be compatible for our application as a portable power generation device. To predict
thermal transpiration membrane pumping performance, rarefied gas dynamics theory has to be
used for this work.
The theory of rarefied gas dynamics through a micro-scale channel provides the relation
of pressure across the membrane and temperature gradient. This phenomenon can be explained
by bouncing molecules in the channel with higher possibility of bouncing toward higher
temperature end rather than toward lower temperature end as shown in Figure 4. The channel
has to be as small as the scale of mean free path of gas molecule (𝜆 ) which is the distance travel
of molecules before they hit other molecules. The ratio between the molecule mean free path
and the characteristic length of flow is usually defined as Knudsen number (𝐾𝑛 ). The
characteristic length of thermal transpiration membrane is defined as pore radius (𝐿 𝑟 ). In general,
if 𝐾𝑛 is greater than 0.1, the concept of rarefied gas dynamics exists. Sone et al. [18], Vargo et al.
[19] and Muntz et al. [20] have also studied about the mass flow rate (𝑀 ̇ ) induced by thermal
transpiration membrane. The relation of all related parameters is shown as:
9

Figure 4 – Bouncing gas molecules driven by temperature gradient across a micro-scale channel

𝑀 ̇ = 𝑃 𝑎𝑣𝑔 √
𝑚 2𝑘 𝑇 𝑎𝑣𝑔 𝐴 𝑇𝑇
𝐿 𝑟 𝐿 𝑥 [
∆𝑇 𝑇 𝑎𝑣𝑔 𝑄 𝑇 −
∆𝑃 𝑃 𝑎𝑣𝑔 𝑄 𝑃 ] (1)
and can be rearranged as
∆𝑃 =
[

∆𝑇 𝑇 𝑎𝑣𝑔 𝑄 𝑇 −
𝑀 ̇ 𝑃 𝑎𝑣𝑔 √
𝑚 2𝑘 𝑇 𝑎𝑣𝑔 𝐴 𝑇𝑇
𝐿 𝑟 𝐿 𝑥 ]

𝑃 𝑎𝑣𝑔 𝑄 𝑃 (2)
where ∆𝑃 is the pressure difference between both side of the membrane, 𝑃 𝑎𝑣𝑔 is the average
pressure across the membrane, ∆𝑇 is the temperature difference across the membrane, 𝑇 𝑎𝑣𝑔 is
the membrane average temperature, 𝑄 𝑇 is the thermally driven flow coefficient, 𝑄 𝑃 is the
pressure driven return flow coefficient, A
𝑇𝑇
is the channel cross-section area behaving as thermal
transpiration membrane, 𝐿 𝑟 is the pore size radius, 𝐿 𝑥 is the capillary channel length, 𝑚 is the
weight of a gas molecule and 𝑘 is Boltzmann’s constant. The relation of 𝑄 𝑇 and 𝑄 𝑃 as a function
of Knudsen number, 𝐾 𝑛 ≡ 𝜆 /𝐿 𝑟 (Knudsen number is the ratio of gas mean free path to channel
radius) is shown in Figure 5 (Left) and the thermal transpiration diagram and parameters are
shown in Figure 5 (Right)
Two operating conditions of thermal transpiration membrane can be considered. The first
condition is zero mass flow rate, 𝑀 ̇ = 0 or the outlet is blocked. When the mass flow rate is zero,
pressure goes to maximum and pressure drop across the system is expressed as

∆𝑃 = [
∆𝑇 𝑇 𝑎𝑣𝑔 𝑄 𝑇 ]
𝑃 𝑎𝑣𝑔 𝑄 𝑃 (3)
High
temperature
end
Low
temperature
end
10

Figure 5 – (Left) Flow coefficient vs. Knudsen number for circular capillary channel
(Right) Thermal transpiration membrane diagram and parameters

The temperature average, the temperature difference, the pressure average and the
pressure difference can be measured from experiments and
𝑄 𝑇 𝑄 𝑃 can be solved. From Knudsen
Number relation in Figure 5 (Left), 𝐾 𝑛 ≡ 𝜆 /𝐿 𝑟 , effective pore radius can also be determined
subsequently. Another operating condition is maximum flow rate or when the air outlet is widely
open. Pressure drop in the air path is approximately zero and can be expressed as

𝑀 ̇ 𝑃 𝑎𝑣𝑔 √
𝑚 2𝑘 𝑇 𝑎𝑣𝑔 𝐴 𝑅 𝐿 𝑟 𝐿 𝑥 =
∆𝑇 𝑇 𝑎𝑣𝑔 𝑄 𝑇
(4)
It is similar to zero mass flow condition that all variables can be substituted into
Equation (4) and effective area 𝐴 𝑅 can be solved. Unknown thermal transpiration properties can
be determined and used for further combustion chamber design.
If Knudsen number is smaller than 0.1, gas flow through the thermal transpiration
membrane can be considered as continuum flow through porous media. The flow rate can be
estimated by using Darcy’s law
𝑀 ̇ = −𝜌 𝜅 𝐴 𝐷 ( 𝛥𝑃 )
𝜇 𝐿 𝑥 (5)
Porous membrane
Driven Flow
High temperature (T
2
)
High pressure (P
2
)
Low temperature (T
1
)
Low pressure (P
1
)
Area (A)
Thickness (L
x
)
Pore size radius
(L
r
)
11

when 𝜌 is the density of gas, 𝜅 is permeability of membrane, 𝐴 𝐷 is the cross-section area
that Darcy’s law applies, 𝛥𝑃 is the pressure difference across membrane, 𝜇 is dynamic viscosity
of membrane and 𝐿 𝑥 is the membrane thickness.
The thermal transpiration membrane in this study is made up of fiber glass which is not
uniform material in microscale. Some regions on the membrane behave as thermal transpiration
pump while some region behave as back flow through porous media expressed by Darcy’s law.
Therefore, Equation (1) has to be modified by including Darcy term into the equation as

𝑀 ̇ = 𝑃 𝑎𝑣𝑔 √
𝑚 2𝑘 𝑇 𝑎𝑣𝑔 𝐴 𝑡𝑜𝑡 ( 𝐴𝐹
𝑇𝑇
)
𝐿 𝑟 𝐿 𝑥 [
∆𝑇 𝑇 𝑎𝑣𝑔 𝑄 𝑇 −
∆𝑃 𝑃 𝑎𝑣𝑔 𝑄 𝑃 ] − 𝜌 𝑎𝑣𝑔 𝑘 𝐷𝑎𝑟𝑐𝑦 ( 𝐴 𝑡𝑜𝑡 ( 1− 𝐴𝐹
𝑇𝑇
) ) 𝛥𝑃
𝜇 𝐿 𝑥
(6)
where 𝐴 𝑡𝑜𝑡 is the total area of the membrane, 𝐴𝐹
𝑇𝑇
is the area factor of the thermal transpiration
membrane, 𝜌 𝑎𝑣𝑔 is the avergae air density, 𝑘 𝐷𝑎𝑟𝑐𝑦 is the permeability of the membrane which
can be defined from the experiment.
Furthermore, if multiple layers of thermal transpiration membrane are stacked together,
the transpiration area increases due to the probability of stacking transpiration areas from
different layers. The relation between the area factor and the number of layers can be estimate
by proability as
𝐴𝐹
𝑇𝑇 ,𝑡𝑜𝑡 = 1− ( 1 − 𝐴 𝐹 𝑇𝑇
)
𝑁 (7)
where 𝐴𝐹
𝑇𝑇 ,𝑡𝑜𝑡 is the area factor when all layers of the membrane combined, 𝐴 𝐹 𝑇𝑇
is the area
factor of each membrane and 𝑁 is the number of membrane layers. Then Equation (6) is
substituted into Equation (5) as

𝑀 ̇ = 𝑃 𝑎𝑣𝑔 √
𝑚 2𝑘 𝑇 𝑎𝑣𝑔 𝐴 𝑡𝑜𝑡 ( 𝐴𝐹
𝑇𝑇 ,𝑡𝑜𝑡 )
𝐿 𝑟 𝐿 𝑥 ,𝑡𝑜𝑡 [
∆𝑇 𝑇 𝑎𝑣𝑔 𝑄 𝑇 −
∆𝑃 𝑃 𝑎𝑣𝑔 𝑄 𝑃 ] − 𝜌 𝑎𝑣𝑔 𝜅 ( 𝐴 𝑡𝑜𝑡 ( 1 − 𝐴𝐹
𝑇𝑇 ,𝑡𝑜𝑡 ) ) 𝛥𝑃
𝜇 𝐿 𝑥
(8)
when 𝐿 𝑥 ,𝑡𝑜𝑡 is the total thickness of all layers combined. The mass flow rate of the gas flowing
through the thermal transpiration membrane can be estimated under various operating
conditions and membrane properties as in Equation (8).

12

2.2 Catalytic Combustion
In this study, the catalytic combustion provides heat for two purposes. One is to generate
enough heat for thermal transpiration membrane to generate pressure difference and pump the
external air into the combustion chamber for mT-SOFC. Another purpose is to provide heat for
mT-SOFC to operate at high temperature and generate electricity.
There are two types of combustion, i.e. homogeneous combustion which is gas phase
combustion and heterogeneous combustion which is catalytic combustion occurring only on
catalytic surface. Both types of combustion are a chemical reaction process between oxidizer and
fuel but for the catalytic combustion the catalyst decreases activation energy of the reaction so
that the surface combustion can sustain at lower temperature than gas phase combustion. Well-
known catalyst is a noble metal i.e. platinum which has been used in this study because platinum
is one of the most reactive catalysts.
Combustion reaction happens in many steps, called elementary reactions but they can be
expressed in one global reaction step as
𝐴 + 𝐵 ⇄ 𝐶 + 𝐷 (9)
When 𝐴 and 𝐵 are combustion reactants and 𝐶 and 𝐷 are combustion products. Elementary
reactions of simple hydrocarbon reaction, typically more than ten steps. The speed of reaction is
expressed by reaction rate which can be considered either elementary reactions or global
reaction for overall reaction rate.
Langmuir-Hinshelwood (LH) proposed adsorption rate model that is commonly used to
express reaction rate for catalytic combustion as

𝑟 𝑎𝑑𝑠 = 𝑘 𝐴 𝑎𝑑𝑠 𝐶 𝑠 ,𝐴 𝜃 ( 𝑠 )− 𝑘 𝐴 𝑑𝑒𝑠 𝜃 𝐴 (10)
when 𝑘 𝐴 𝑎𝑑𝑠 is rate constant for adsorption, 𝑘 𝐴 𝑑𝑒𝑠 is rate constant for desorption, 𝜃 ( 𝑠 ) is empty
space on the surface, 𝜃 𝐴 is number of molecule adsorbed and 𝐶 𝑠 ,𝐶 3
𝐻 8
gas phase concentrations
adjacent to the surface and the relation of adsorption and desorption can be expressed as

𝑘 𝐴 𝑎𝑑𝑠 𝐶 𝑠 ,𝐴 𝜃 ( 𝑠 )= 𝑘 𝐴 𝑑𝑒𝑠 𝜃 𝐴 (11)
which can be rearranged as
13

𝜃 𝐴 =
𝑘 𝐴 𝑎𝑑𝑠 𝐶 𝑠 ,𝐴 𝜃 ( 𝑠 )
𝑘 𝐴 𝑑𝑒𝑠
(12)
The rate constant of adsorption and the rate constant of desorption for each molecule
are different described by modified Arrhenius expression as

𝑘 𝑎𝑑𝑠 =
𝑠 𝛤 √
𝑅𝑇
2𝜋𝑀
𝑒 −
𝐸 𝐴 𝑎𝑑𝑠 𝑅𝑇
(
𝑇 𝑇 𝑟𝑒𝑓 )
𝛽 𝑎𝑑𝑠
(13)

and
𝑘 𝑑𝑒𝑠 = 𝐴 𝑒 −
𝐸 𝐴 𝑑𝑒𝑠 𝑅𝑇
(
𝑇 𝑇 𝑟𝑒𝑓 )
𝛽 𝑑𝑒𝑠
(14)
when 𝑠 is sticking coefficient, Γ is site density (2.5 10
-9

𝑚𝑜𝑙 𝑐 𝑚 2
for platinum), 𝑅 is universal gas
constant, 𝑇 is catalyst surface temperature, 𝑇 𝑟𝑒𝑓 is reference temperature at 300 K, 𝐸 𝐴 is
activation energy of adsorption and desorption, 𝛽 is temperature exponent and 𝐴 is desorption
coefficient. Generally, high temperature increases rate constant of adsorption and desorption
which tend to increase global reaction rate of catalytic combustion.
In this study, when fuel-air mixture flows over platinum active site, some fuel molecules,
which is propane (C 3H 8) for example, and oxygen (O 2) get adsorbed on the platinum surface as in
Figure 6. C 3H 8 and O 2 molecules that sit next to each other have probability to get reaction and
stay on the surface until the reaction complete. Then combustion products which are water (H 2O)
and carbon dioxide (CO 2) desorb from surface. Because activation energy of desorption of H 2O
and CO
2
are lower than C
3
H
8
and O
2
, they have higher probability of leaving the catalyst surface
rather than staying on the surface comparing to C 3H 8 and O 2.

Figure 6 – Catalytic combustion diagram for C
3
H
8
-air reaction on platinum surface
C
3
H
8
O
2
H
2
O CO
2

adsorption
desorption
Premixed
gas
Combustion
products
Platinum active site
14

During the reaction, radicles have existed and disappeared all the time and a lot of
researchers have tried to calculate the detailed mechanism for elementary reactions on the
surface such as Chatterjee et al. [21], Koop et.al [22] and Zhong et.al [23] expressing detailed
surface reaction mechanism on platinum surface in their work. Adsorption coefficients, pre-
exponential factors and activation energies of detail mechanisms are shown in Table 1.
Table 1 Detailed surface reaction mechanism for catalytic combustion on platinum surface [22]
Reaction S 0 [∙] or A [mol, cm, s] E a [kJ/mol]
Adsorption
C 3H 8 + Pt(s) → C 3H 8(s) 1.5  10
-2
0.0
C 3H 6 + Pt(s) + Pt(s) → C 3H 6(s) 9.8  10
-1
0.0
C 3H 6 + O(s) + Pt(s) → C 3H 5(s) + OH(s) 5.0  10
-2
0.0
O 2 + Pt(s) + Pt(s) → O(s) + O(s) 7.0  10
-2
0.0
CO 2 + Pt(s) → CO 2(s) 5.0  10
-3
0.0
CO + Pt(s) → CO(s) 8.4  10
-1
0.0
H 2O + Pt(s) → H 2O(s) 7.5  10
-1
0.0
H 2 + Pt(s) + Pt(s) → H(s) + H(s) 4.6  10
-2
0.0
Desorption
C 3H 8(s) → C 3H 8 + Pt(s) 1.0  10
13
20.9
C 3H 6(s) → C 3H 6 + Pt(s) + Pt(s) 3.7  10
12
74.4
C 3H 5(s) + OH(s) → C 3H 6 + O(s) + Pt(s) 3.7  10
21
31.0
O(s) + O(s) → O 2 + Pt(s) + Pt(s) 3.7  10
21
232.2+90 (s)
CO 2(s) → CO 2 + Pt(s) 3.6  10
10
23.7
CO(s) → CO + Pt(s) 2.1  10
13
136.2-33  CO(s)
H 2O(s) → H 2O + Pt(s) 5.0  10
13
49.2
H(s) + H(s) → H 2 + Pt(s) + Pt(s) 2.1  10
21
69.1-6  H(s)
The detail mechanism model is still complicated and computational time consuming;
therefore, Deshmukh et al. [24] and Kaisare et.al. [25] provided simpler simulation modeling with
one-step mechanism to estimate fuel-lean catalytic combustion of propane on platinum surface
by global reaction as

𝐶 3
𝐻 8
+ 5𝑂 2
→ 3𝐶 𝑂 2
+ 4𝐻 2
𝑂 (15)
and there is an assumption that the platinum surface is covered by O 2 and empty space as

𝜃 𝑂 ( 𝑠 )+ 𝜃 ( 𝑠 )= 1 (16)
15

which 𝜃 𝑂 ( 𝑠 ) is the coverage of O and 𝜃 ( 𝑠 ) is the empty space on the platinum surface. There is
no C 3H 8 covering the surface because when a C 3H 8 molecule adsorb on the surface, reaction
occurs immediately. Combustion products which are CO 2 and H 2O desorb from the surface
immediately as well. Reaction rate limits are the empty space, C 3H 8 adsorption rate and C 3H 8 gas
phase concentration described as

𝑟 = 𝛤 𝑘 𝐶 3
𝐻 8
𝑎𝑑𝑠 𝐶 𝑠 ,𝐶 3
𝐻 8
𝜃 2
( 𝑠 )
(17)
when 𝑟 is the reaction rate, 𝛤 is the site density (2.5 10
-9

mol
cm
2
for platinum), 𝑘 𝐶 3
𝐻 8
𝑎𝑑𝑠 is the rate of
adsorption and C
s,C
3
H
8
is the concentration of C 3H 8 adjacent to the platinum surface. Relation
between O 2 and O(s) under partial equilibrium assumption is that
𝑂 2
+ 2( 𝑠 )↔ 2𝑂 ( 𝑠 ) (18)
when O(s) is an oxygen atom attached to the surface and it implies that

𝑘 𝑂 𝑎𝑑𝑠 𝐶 𝑠 ,𝑂 2
𝜃 2
( 𝑠 )= 𝑘 𝑂 𝑑𝑒𝑠 𝜃 𝑂 2
(19)
The empty space depends on the rate of adsorption and desorption as

𝜃 ( 𝑠 )=
1
1+ √
𝑘 𝑂 𝑑𝑒𝑠 𝑘 𝑂 𝑎𝑑𝑠 𝐶 𝑠 ,𝑂 2

(20)
The reaction rate can be expressed as

𝑟 =
𝛤 𝑘 𝐶 3
𝐻 8
𝑎𝑑𝑠 𝐶 𝑠 ,𝐶 3
𝐻 8
(1 + √
𝑘 𝑂 𝑑𝑒𝑠 𝑘 𝑂 𝑎𝑑𝑠 𝐶 𝑠 ,𝑂 2
)
2

(21)
However, fuel-lean mixture is difficult to sustain in room temperature due to heat losses, even in
experimental study from Wierzba et al.’s work [26], an electrical heater was wrapped around
combustion catalytic reactor to maintain the reactor temperature. Moreover, a mT-SOFC
produces more power when it operates under fuel-rich mixture conditions; therefore, fuel-rich
mixture is more favorable to the fuel cell.
In fuel-rich mixture, the model that was proposed by Deshmukh and Kaisare has to be
modified because when the concentration of O 2 decreases, the reaction rate goes to infinity
16

which is impossible for surface combustion. Other reaction rate limits need to be considered
including H 2O and CO 2. Assumptions of fuel-rich mixture catalytic combustion are C 3H 8, CO 2 and
H 2O are covering the surface and only the rest is an empty space. When an O 2 molecule adsorbs
on the surface, reaction occurs immediately. The relation of surface coverage can be expressed
as

𝜃 𝑐 3
𝐻 8
( 𝑠 )+ 𝜃 𝐶 𝑂 2
( 𝑠 )+ 𝜃 𝐻 2
𝑂 ( 𝑠 )+ 𝜃 ( 𝑠 )= 1 (22)
The rate constant for adsorption and the rate constant for desorption are still as same as what
are shown in fuel-lean mixture. The reaction rate has to be modified as

𝑟 𝑠𝑢𝑟 = 𝛤 𝑘 𝑂 2
𝑎𝑑𝑠 𝐶 𝑠 ,𝑂 2
𝜃 2
( 𝑠 ) (23)
The relation of rate constants for adsorption, rate constants for desorption, gas phase
concentrations and the empty space for C 3H 8, CO 2 and H 2O becomes

𝜃 𝐶 3
𝐻 8
= (
𝑘 𝐶 3
𝐻 8
𝑎𝑑𝑠 𝐶 𝑠 ,𝐶 3
𝐻 8
𝑘 𝐶 3
𝐻 8
𝑑𝑒𝑠 )𝜃 ( 𝑠 )
(24)

𝜃 𝐶 𝑂 2
= (
𝑘 𝐶 𝑂 2
𝑎𝑑𝑠 𝐶 𝑠 ,𝐶 𝑂 2
𝑘 𝐶 𝑂 2
𝑑𝑒𝑠 )𝜃 ( 𝑠 )
(25)

𝜃 𝐻 2
𝑂 = (
𝑘 𝐻 2
𝑂 𝑎𝑑𝑠 𝐶 𝑠 ,𝐻 2
𝑂 𝑘 𝐻 2
𝑂 𝑑𝑒𝑠 )𝜃 ( 𝑠 )
(26)
respectively. Finally, the reaction rate in fuel-rich condition is

𝑟 = 𝛤 𝑘 𝑂 2
𝑎𝑑𝑠 𝐶 𝑠 ,𝑂 2
[

1
𝑘 𝐶 3
𝐻 8
𝑎𝑑𝑠 𝐶 𝑠 ,𝐶 3
𝐻 8
𝑘 𝐶 3
𝐻 8
𝑑𝑒𝑠 +
𝑘 𝐶 𝑂 2
𝑎𝑑𝑠 𝐶 𝑠 ,𝐶 𝑂 2
𝑘 𝐶 𝑂 2
𝑑𝑒𝑠 +
𝑘 𝐻 2
𝑂 𝑎𝑑𝑠 𝐶 𝑠 ,𝐻 2
𝑂 𝑘 𝐻 2
𝑂 𝑑𝑒𝑠 + 1
]

2

(27)
From this modified reaction rate, it is clearly seen that CO 2 and H 2O become factors for surface
coverage and O 2 adsorption rate becomes an important factor because O 2 is deficient molecule
for the surface reaction in fuel-rich mixture. Deshmukh et al. [24] also introduced reduced
parameters for the rate of adsorption and the rate of desorption of C
3
H
8
, O
2
, CO
2
and H
2
O as in
Table 2.
17

Table 2 Parameters for the one-step rate expression for catalytic combustion on platinum surface
from Zhong et al.’s [23] and Deshmukh et al.’s [24] work.
Reaction
S 0 [∙] or
A [mol, cm, s]

 E a [kJ/mol]
C 3H 8 + Pt(s) → C 3H 8(s) 1.5  10
-2
0.0 0.0
[23]

C 3H 8(s) → C 3H 8 + Pt(s) 1.0  10
13
0.0 20.9
[23]

C 4H 10 + 2Pt(s) → C 4H 10(s) 9.5  10
-1
0.0 0.0
[23]

C 4H 10(s) → C 4H 10 + 2Pt(s) 1.0  10
13
0.0 10.71
[23]

O 2 + 2Pt(s) → 2O(s) 6.86  10
-4
0.766 0.0
[24]

2O(s) → O 2 + 2Pt(s) 9.04  10
18
1.039 49.5-32.0  O
[24]

CO 2 + Pt(s) → CO 2(s) 4.69  10
-2
0.250 0.0
[24]

CO 2(s) → CO 2 + Pt(s) 1.83  10
11
0.523 13.0
[24]

H 2O + Pt(s) → H 2O(s) 1.43  10
-4
1.162 0.0
[24]

H 2O(s) → H 2O + Pt(s) 7.87  10
5
2.589 40.2
[24]

Besides propane, butane (C 4H 10) is another interesting fuel for small-scale power
generator. Energy density of n-C 4H 10 is 45.7 MJ/kg almost as same as C 3H 8 and both of them can
be stored in liquid phase easily. One-step reaction for C 4H 10 can be under the same assumption
of C 3H 8 that is

𝐶 4
𝐻 10
+ 6.5𝑂 2
→ 4𝐶 𝑂 2
+ 5𝐻 2
𝑂 (28)
In fuel-rich mixture, the platinum surface is covered by 3 types of molecule that are n-C 4H 10, CO 2
and H 2O. When an O 2 molecule adsorbs on the surface reaction occurs immediately. Moreover
Zhong et.al. [23] introduced C 4H 10 molecule that is taking two spots on platinum active site.
Relation between n-C 4H 10 and n-C 4H 10(s) under partial equilibrium assumption is
𝐶 4
𝐻 10
+ 2( 𝑠 )↔ 2𝐶 4
𝐻 10
( 𝑠 ) (29)
The relation of rate constants for adsorption, rate constants for desorption, gas phase
concentrations and the empty space for C 4H 10 becomes

𝜃 𝐶 4
𝐻 10
= (
𝑘 𝐶 4
𝐻 10
𝑎𝑑𝑠 𝐶 𝑠 ,𝐶 4
𝐻 10
𝑘 𝐶 4
𝐻 10
𝑑𝑒𝑠 )[𝜃 ( 𝑠 ) ]
2

(30)
Substitute the relation of C 4H 10 coverage into reaction rate for fuel-rich condition including CO 2
and H 2O. Finally, reaction rate on the platinum surface of C 4H 10 can be rearranged and becomes
18

𝑟 = 𝛤 𝑘 𝑂 2
𝑎𝑑𝑠 𝐶 𝑠 ,𝑂 2
[

−[(
𝑘 𝐶 𝑂 2
𝑎𝑑𝑠 𝐶 𝑠 ,𝐶 𝑂 2
𝑘 𝐶 𝑂 2
𝑑𝑒𝑠 )+ (
𝑘 𝐻 2 𝑂 𝑎𝑑𝑠 𝐶 𝑠 ,𝐻 2
𝑂 𝑘 𝐻 2 𝑂 𝑑𝑒𝑠 )+ 1] ± √[(
𝑘 𝐶 𝑂 2
𝑎𝑑𝑠 𝐶 𝑠 ,𝐶 𝑂 2
𝑘 𝐶 𝑂 2
𝑑𝑒𝑠 )+ (
𝑘 𝐻 2
𝑂 𝑎𝑑𝑠 𝐶 𝑠 ,𝐻 2
𝑂 𝑘 𝐻 2 𝑂 𝑑𝑒𝑠 )+ 1]
2
− 4(
𝑘 𝐶 4
𝐻 10
𝑎𝑑𝑠 𝐶 𝑠 ,𝐶 4
𝐻 10
𝑘 𝐶 4 𝐻 10
𝑑𝑒𝑠 )( −1)
2(
𝑘 𝐶 4
𝐻 10
𝑎𝑑𝑠 𝐶 𝑠 ,𝐶 4
𝐻 10
𝑘 𝐶 4 𝐻 10
𝑑𝑒𝑠 )
]

2

(31)
The modified reaction rate of C 4H 10 on platinum surface can be solved similarly to C 3H 8 by
considering only the positive root. O 2 adsorption rate and concentration of O 2 are still an
important factor because O 2 is a deficient reactant for surface reaction in fuel-rich mixture for
both C 3H 8 and C 4H 10 cases.

2.3 Solid Oxide Fuel Cell Modeling
A solid oxide fuel cell (SOFC) is an electrochemical conversion device that can generate
electricity from fuel e.g. butane and oxidizer which is O 2. Advantages of this type of fuel cell are
high efficiency, fuel flexibility and long-term stability comparing to PEM fuel cells. However, a
limitation of using this solid-oxide fuel cell is the requirement of high operating temperature at
least 550 C. An SOFC is made up of three layers, anode cathode and electrolyte, as depicted in
Figure 7 by dual chamber type and single chamber type. The process of SOFC starts from oxygen
molecules passing through the cathode and recharge electrons to generate oxygen ions. When
these ions go through electrolyte and reach the anode side, they react with fuel and generate
electrons. The electrolyte works as one-way gate to prevent these electrons from coming back
to the cathode side. If the anode and the cathode are connected to an external load, electrons
will go through the load to combine with oxygen molecules on another side.

Figure 7 – (Left) Dual chamber solid oxide fuel cell diagram and
(Right) Single chamber solid oxide fuel cell diagram
Cathode
Anode
Electrolyte
O
2
+N
2

fuel CO
2
+H
2
O
N
2

O
2-

e
-

O
2-
O
2-

Cathode
Anode
Electrolyte
Fuel-air
mixture
Reaction
products
O
2-

e
-

O
2-
O
2-

19

To design the proper size of SOFC for the maximum performance and efficiency, the
numerical model of SOFC have to be studied and compared with experimental results. Some
works have been done for the SOFC running on hydrogen (H 2) and methane (CH 4) as shown in
Gupta et al.’s, Xie et al., and Ferrero et al. works [27, 28, 29] including fuel reforming model and
water gas shift reaction (WGSR). To design SOFC running on C 4H 10 for a meso scale power
generator, the numerical model of SOFC will be investigated in this study by extending fuel
reforming model and WGSR model of CH 4 on SOFC anode surface to one-step reforming model
for C 4H 10 which is shown in Figure 8. This study will also include electrochemistry and power
generation of SOFC as in Figure 9 to estimate its performance and efficiency, related to the study
of Hao et. al. [30, 31, 32].

Figure 8 – Reactions that occur around the SOFC
Cathode (LSCF)
Anode (NiO-GDC)
Electrolyte (GDC)
e
-

O
2

C
4
H
10

O
2

air N
2

O
2-

O
2-

O
2-

O
2-

C
4
H
10
-air
mixture
CO
2

N
2

H 2O
2

O
2

Fuel reformer (surface)
𝐶 4
𝐻 10
+ 2𝑂 2
→ 4𝐶𝑂 + 5𝐻 2

Reaction rate
𝑟 𝑓𝑟
= 𝑘 𝑓𝑟 [𝐶 4
𝐻 10
][𝑂 2
]
2

Water gas shift reaction (gas phase)
𝐶𝑂 + 𝐻 2
𝑂 ↔ 𝐶 𝑂 2
+ 𝐻 2

Reaction rate
𝑟 𝑊𝐺𝑆𝑅 = 𝑘 1
൬𝑃 𝐶𝑂
𝑃 𝐻 2
𝑂 −
𝑃 𝐶 𝑂 2
𝑃 𝐻 2
𝑘 2
൰
Exchange current density
𝑖 0,𝑎 = 𝑖 𝐻 2
∗
൫𝑃 𝐻 2
,𝑎 / 𝑃 𝐻 2
∗
൯
1/4
൫𝑃 𝐻 2
𝑂 ,𝑎 ൯
3/4
1 + ൫𝑃 𝐻 2
,𝑎 / 𝑃 𝐻 2
∗
൯
1/2

Exchange current density
𝑖 0,𝑐 = 𝑖 𝑂 2
∗
ቀ𝑃 𝑂 2
,𝑐 / 𝑃 𝑂 2
∗
ቁ
1/4

1+ቀ𝑃 𝑂 2
,𝑐 / 𝑃 𝑂 2
∗
ቁ
1/2

20

Figure 9 – Electrochemical reactions that occur inside the SOFC

Internal fuel reforming process modeling
Internal fuel reforming process is the reaction that occurs when a molecule of
hydrocarbon fuel is broken down by catalyst on the anode of SOFC with oxygen. In general, nickel
is used as catalyst for the reaction. Carbon monoxide (CO) and hydrogen (H 2) is generated from
this reaction. The fuel reforming has been investigated and proposed by Xu and Ni et. al. [33, 34,
35] for their fuel cell modeling. They only focused on the reforming of CH 4. For our application,
C 4H 10 is used as a fuel source; therefore, the reforming of C 4H 10 has to be investigated as a part
of mT-SOFC modeling. Sumi et. al. [36] has studied the performance of fuel reforming on an
anode supported GDC cell running on C 4H 10. Their work did not include modeling, yet the reaction
rate has been estimated based on their experimental results. The 1-step reaction of C 4H 10
reforming is expressed as
𝐶 4
𝐻 10
+ 2𝑂 2
→ 4𝐶𝑂 + 5𝐻 2
(32)

H 2
Exchange current density
𝑖 0,𝑐 = 𝑖 𝑂 2
∗
൫𝑃 𝑂 2
,𝑐 / 𝑃 𝑂 2
∗
൯
1/4

1+ ൫𝑃 𝑂 2
,𝑐 / 𝑃 𝑂 2
∗
൯
1/2

O 2
Exchange current density
𝑖 0,𝑎 = 𝑖 𝐻 2
∗
൫𝑃 𝐻 2
,𝑎 / 𝑃 𝐻 2
∗
൯
1/4
൫𝑃 𝐻 2
,𝑎 ൯
3/4
1 + ൫𝑃 𝐻 2
,𝑐 / 𝑃 𝐻 2
∗
൯
1/2

Butler-Volmer eq. (Ionic current)
𝑖 𝑖 = 𝑖 0,𝑎 ( 𝑒 𝛼 𝜂 𝑎𝑐𝑡 ,𝑎 𝑓 − 𝑒 −𝛼 𝜂 𝑎𝑐𝑡 ,𝑐 𝑓 )
Electronic current
𝑖 𝑒 = −𝑖 𝑖 𝜎 𝑒 𝜎 𝑖 𝑒 𝜂 𝑐 𝑓 𝑒 𝐸𝑓
− 1
1 − 𝑒 −
𝑖 𝑖 𝐿 𝑒 𝑓 𝜎 𝑖
Anode
Cathode
Nernst potential
𝐸 𝑜 = −
𝛥 𝐺 𝑜 2𝐹 +
𝑅𝑇
2𝐹 𝑙𝑛
𝑝 𝐻 2
𝑝 𝑂 2
1/2
𝑝 𝐻 2
𝑂
O
2-

O
2-

e
-

H 2O
CO 2
CO
21

and the reaction rate is

𝑟 𝑓𝑟
= 𝐴 𝑓𝑟
𝑒 𝐸 𝑎 ,𝑓𝑟
𝑅𝑇 [𝑃 𝐶 4
𝐻 10
][𝑃 𝑂 2
]
2

(33)
which 𝐴 𝑓𝑟
and 𝐸 𝑎 ,𝑓𝑟
are left as free-fitted parameters in the SOFC model.

Water gas shift reaction modeling
Water gas shift reaction (WGSR) is the reaction that occurs on the anode surface when
carbon dioxide (CO 2), water vapor (H 2O), carbon monoxide (CO) and hydrogen (H 2) present on
the anode surface at high temperature. The well-known reaction is expressed as
𝐶𝑂 + 𝐻 2
𝑂 ↔ 𝐶 𝑂 2
+ 𝐻 2
(34)
Since WGSR is two-way reaction, the reaction rate in SOFC was investigated by Lehnert et. al.
[37] and more recent research, M. Ni and Haberman et. al. [38-39] has modified the reaction rate
of WGSR at any gas concentrations and temperature from M.V. Twigg’s work [40] as
𝑅 𝑊𝐺𝑆𝑅 = 𝑘 𝑠𝑓
(𝑃 𝐶𝑂
𝑃 𝐻 2
𝑂 −
𝑃 𝐶 𝑂 2
𝑃 𝐻 2
𝑘 𝑝𝑠
) (35)

𝑘 𝑠𝑓
= 0.0171exp ൬−
103191
𝑅𝑇
൰
(36)
𝑘 𝑝𝑠
= exp( −0.2935𝑍 3
+ 0.6351𝑍 2
+ 4.1788𝑍 + 0.3169) (37)
𝑍 =
1000
𝑇 ( 𝐾 )
− 1 (38)

Electrochemistry modeling
The performance of electrical power generation from mT-SOFC can be estimated based
on electrochemistry on the cell and the partial pressure of fuel and oxidizer adjacent to the anode
and cathode surface. Mathematical model was introduced by Hao et.al. [30, 31, 32] to determine
the current and voltage generation from SCFC. The ionic current density can be estimated from
Butler-Volmer equation as
𝑖 𝑖 = 𝑖 0
( 𝑒 𝛼 𝜂 𝑎𝑐𝑡 𝑓 − 𝑒 −𝛼 𝜂 𝑎𝑐𝑡 𝑓 ) (39)
where 𝑖 0
is the exchange current density at the anode- and cathode-electrolyte interface, 𝛼 𝑎 is
anodic charge transfer coefficient, 𝛼 𝑐 is cathodic charge transfer coefficient, 𝜂 𝑎𝑐𝑡 is the activation
overpotential and 𝑓 =
𝐹 𝑅𝑇
which 𝐹 is Faraday constant (96485 C/mol), 𝑅 is the universal gas
22

constant (8.314 J/molK) and 𝑇 is the temperature of the fuel cell. The exchange current density
on the anode is expressed as

𝑖 0,𝑎 = 𝑖 𝐻 2
∗
൫𝑃 𝐻 2
,𝑎 / 𝑃 𝐻 2
∗
൯
1/4
൫𝑃 𝐻 2
,𝑎 ൯
3/4
1 + ൫𝑃 𝐻 2
,𝑐 / 𝑃 𝐻 2
∗
൯
1/2

(40)
where 𝑖 𝐻 2
∗
= 8.5
𝐴 𝑐 𝑚 2
, 𝑃 𝐻 2
,𝑎 is the partial pressure of hydrogen adjacent to the anode, 𝑃 𝐻 2
∗
is
expressed as

𝑃 𝐻 2
∗
=
𝐴 𝑑𝑒𝑠 𝛤 2
√
2𝜋𝑅𝑇 𝑊 𝐻 2
𝛾 0
𝑒 −
𝐸 𝑑𝑒𝑠 𝑅𝑇

(41)
where 𝐴 𝑑𝑒𝑠 = 5.59 × 10
15
𝑚 2
𝑠 ∙𝑚𝑜𝑙 , 𝛤 = 2.6 × 10
−5
𝑚𝑜𝑙 𝑚 2
, 𝐸 𝑑𝑒𝑠 = 88.12
𝑘𝐽
𝑚𝑜𝑙 , 𝛾 0
= 0.01 and 𝑊 𝐻 2
is
the molecular weight of hydrogen. The exchange current density on the cathode is also expressed
as

𝑖 0,𝑐 = 𝑖 𝑂 2
∗
൫𝑃 𝑂 2
,𝑐 / 𝑃 𝑂 2
∗
൯
1/4

1 + ൫𝑃 𝑂 2
,𝑐 / 𝑃 𝑂 2
∗
൯
1/2

(42)
where 𝑖 𝑂 2
∗
= 28000
𝐴 𝑚 2
, 𝑃 𝑂 2
,𝑐 is the partial pressure of oxygen adjacent to the cathode surface,
𝑃 𝑂 2
∗
is expressed as

𝑃 𝑂 2
∗
= 𝐴 𝑂 2
𝑒 −
𝐸 𝑂 2
𝑅𝑇

(43)
where 𝐴 𝑂 2
= 4.8× 10
8
𝑎𝑡𝑚 and 𝐸 𝑂 2
= 200
𝑘𝐽
𝑚𝑜𝑙
The relation between cell potential and current density can be describe as the voltage
potential from the Nernst potential and the voltage drop across the anode, the cathode and
electrolyte. The cell potential can be calculated from

𝐸 𝑐𝑒𝑙𝑙 = 𝐸 𝑜 −
𝐿 𝑒 𝑖 𝑖 𝜎 𝑖 ( 𝑇 )
− 𝜂 𝑎𝑐𝑡 ( 𝑖 𝑖 )− 𝜂 𝑎𝑐𝑡 ( 𝑖 𝑖 )
(44)
where 𝐿 𝑒 is the electrolyte thickness, 𝑖 𝑖 is the ionic current density, 𝜂 𝑎𝑐𝑡 is the overpotential at
anode- and cathode-electrolyte, 𝐸 𝑜 is the Nernst potential for 𝐻 2
reaction defined as
23

𝐸 𝑜 = −
Δ𝐺 𝑜 2𝐹 +
𝑅𝑇
2𝐹 𝑙𝑛 (
𝑝 𝐻 2
𝑝 𝑂 2
1/2
𝑝 𝐻 2
𝑂 )
(45)
where Δ𝐺 𝑜 is the Gibbs free energy of the reaction 𝐻 2
+
1
2
𝑂 2
↔ 𝐻 2
𝑂 and for 𝐶𝑂 reaction defined
as

𝐸 𝑜 = −
Δ𝐺 𝑜 2𝐹 +
𝑅𝑇
2𝐹 𝑙𝑛 (
𝑝 𝐶𝑂
𝑝 𝑂 2
1/2
𝑝 𝐶 𝑂 2
)
(46)
where Δ𝐺 𝑜 is the Gibbs free energy of the reaction 𝐶𝑂 +
1
2
𝑂 2
↔ 𝐶𝑂 and 𝜎 𝑖 ( 𝑇 ) is the electrolyte
ionic conductivity defined as

𝜎 𝑖 ( 𝑇 )=
𝜎 0,𝑖 𝑇 𝑒 −
𝐸 𝑎 ,𝑖 𝑅𝑇

(47)
The relation between the ionic current density and the cell potential has already defined;
however, the electronic current density has to be also defined from the cell potential and the
ionic current density as

𝑖 𝑒 ( 𝑥 )= −𝑖 𝑖 𝜎 𝑒 𝜎 𝑖 𝑒 𝜂 𝑐 𝑓 𝑒 𝐸𝑓
− 1
1 − 𝑒 −
𝑖 𝑖 𝐿 𝑒 𝑓 𝜎 𝑖
(48)
which 𝜎 𝑒 is the electronic conductivity defined as

𝜎 𝑒 = 𝑘 𝑝 𝑂 2
−1/4

(49)
which 𝑘 = 𝜎 0,𝑒 𝑇 −1
𝑒 −
𝐸 𝑎 ,𝑒 𝑇 and 𝜎 0,𝑒 and 𝐸 𝑎 ,𝑒 are left as free-fitted parameters.
The total current density generation from the fuel cell is the sum of the ionic current and
the electronic current that have already calculated previously in this section. The total current
output to the circuit is

𝑖 𝑡𝑜𝑡 = 𝑖 𝑖 + 𝑖 𝑒
(50)
If the anode and cathode of the fuel cell are connected to an external load 𝑅 𝑙𝑜𝑎𝑑 , the
power generation will be estimated as
24

𝑃 𝑐𝑒𝑙𝑙 = 𝑖 𝑡𝑜𝑡 2
𝑅 𝑐𝑒𝑙𝑙
(51)
As shown from Eq. 39 to Eq. 48, the total current flow through the fuel cell depends on
the cell voltage and the cell voltage is also a function of the current flow. Iterative method has to
be used to calculate the current flow and the cell voltage.

25

Chapter 3 Methods

3.1 Thermal Transpiration Membrane
To design a portable power generator for mobile devices and make it perform at the
highest performane and efficiency, each section including thermal traspiration membrane has to
be studied and modeled carefully. One dimensional flow experiment for the thermal
transpiration membrane has been setup in order to specify the properties of porous membrane.
Multiple porous membranes were tested in this study. One membrane is microfiber filters which
has larger pore radius than aerogel which has been studied previously by Han et al. [17], but it is
not as fragile as the aerogel.
Macroscopic views and microscopic views of glass microfiber filter in Figure 10 and Figure
11 obviously show that filters do not have cylindrical flow channels with zero wall thickness. Then
effective pore radius, effective area and permeability have to be identified from experiments.
Whatman
TM
1825-090 glass microfiber filter with 0.35 µm advertised pore radius and 420 µm
advertised thickness, was selected for this work because of sufficient flow and pressure. Another
membrane was Supor (hydrophilic polyethersulfone) from Pall Corporation with 0.05 µm
advertised pore radius and 132 µm advertised thickness. A nickel-chromium 17 /m wire was
used to supply heat to one side of the membrane. A varibale electical power supply was used to
supply power to the heating wire which can vary from 0-20V/0-3A to control temperature
gradient across the membrane. Thermal guards were applied on each side of the membrane to
make the temperature on each side of the membrane uniform. The thermal guards were made
up of perforated aluminum sheets providing high thermal conductivity compared to the
membrane. Two K-type thermocouples were placed on each side of the membrane and
connected to AD597 thermocouple conditioners. All holes were sealed by Ceramabond 552-VFG
from Aremco Products, Inc. A bubble flow meter and two piezoeletric differential pressure
sensors, 223BD-00001, were used to measure flow rate and pressure difference acoss the
membrane and the ambient pressure, respectively. A control valve was used to control the
pressure inside the buffer tank to raise up the line pressure of the system. When other gases
26

were tested, such as argon and carbon monoxide, the line pressure had to be incresed to avoid
the external air leaking into the system. The diagram for the apparatus and the schematic are
shown in Figure 12 and Figure 13, respectively.

Figure 10 - (Left) Macroscopic view and
(Right) microscopic view of glass microfiber membrane

Figure 11 - (Left) Macroscopic view and
(Right) microscopic view of Hydrophilic polyethersulfone membrane

Figure 12 – The thermal transpiration membrane apparatus
Inlet flow
Outlet flow
Heating wire
Membrane
Thermocouple
27

Figure 13 – Schematic of thermal transpiration membrane experimental setup
3.2 Catalytic Combustion
To optimized fuel consumption and power generation from SOFC, catalytic combustion
characteristic has to be studied and compared with experimental results for simulation purposes.
Two Hastings 202 flow controllers were used to supply premixed C 3H 8-air mixture or C 4H 10-air
mixture at various equivalence ratio and flow speed. A 15VDC power supply was connected to
the flow controllers. A datalogger, NI 9610 with Labview programming, was used to control and
record fuel and air flow rate. A K-type thermocouple was connected to a thermocouple
0-20 V/0-3 A
Datalogger
NI 6008
Pressure
Transducer
Heating wire
Bubble flow meter
Gas outlet
Gas tank
Membrane
Thermocouple
Thermocouple
Control valve
Buffer
chamber
Pressure
Transducer
Gas inlet
Control signal
Thermocouple
conditioner
AD597
28

conditioner AD597 with ice point compensation integration to record exhaust temperature and
a gas chromatography was used to analyze the concentration of compositions. The schematic
diagram of the experimental setup is shown in Figure 14.
The catalytic combustion was setup in a 7-mm diameter quartz tube tube with 1-cm long
plain platinum foil as shown in Figure 15. C 3H 8-air mixture with various equivalence ratios ( )
from 1.5 to 3.4 and various flow speed from 10 cm/s to 22 cm/s were supplied through the glass
tube from flow controllers. A thermocouple was used to measure gas temperature after
combustion and combustion product compositions were analyzed by gas chromatograph.
Catalytic combustion with C 4H 10-air mixture was tested in the same setup with various
equivalence ratio from 0.8 to 4.0 and various flow speed from 4 cm/s to 20 cm/s on platinum foil.
Platinum mesh was also tested to study reaction performance and flame extinction curve.
Typically, platinum mesh provides less reaction because the reaction area of platinum mesh is
less than platinum foil but the combustion on platinum mesh can sustain at lower temperature
due to less heat loss. The results from different fuel and geometry will be discussed in the
following chapter.

Figure 14 – Gas flow diagram and electrical circuit for catalytic combustion experimental setup

Flame
arrester
15 VDC supply +15 V
-15 V
Datalogger
NI 6211
Setpoint
Feedback
Thermocouple
conditioner
AD597
Gas chromatograph
SRI 8610C
Flow controller
Flow controller
Platinum foil
C 3H 8 or C 4H 10
Air
Feedback
Setpoint
Thermocouple
Quartz tube
29

Figure 15 – Experimental setup for catalytic combsution on plantinum foil

Additionally, ANSYS Fluent has been used to simulate catalytic reaction, heat generation
from the catalyte surface, heat transfer and flow in 3D solver. User-defined function (UDF) coding
for one-step mechanism for fuel-rich mixture was implemented to solve reaction rate on the
catalyst surface. Two UDF files were modified for C
3
H
8
-air mixture and C
4
H
10
-air mixture. Heat
radiation model was included in the calculation and heat transfer coefficient to the surrounding
was set to 10 W/m
2
K. Material properties for platinum and quartz tube were also considered in
this simulation as shown in Figure 16.

Figure 16 – Cross-section of the simulation model in ANSYS-Fluent and boundary conditions

Platinum foil
(or platinum mesh)
Thermocouple
Quartz tube
Fuel-air mixture
Flow controllers
outlet
(products)
s
inlet
(reactants)
Platinum
(surface reaction)
Quartz wall
(h = 10 W/m
2
K)
30

3.3 Self-Sustaining and Self-Pressurizing Combustion Chamber
Experimental results and simulation results have to be compared when thermal
transpiration membrane and catalytic combustion on platinum are integrated together for the
further design. The goal of this setup is to have a self-sustaining thermal driven flow combustion
chamber which is able to provide appropriately high temperature, flow speed and equivalence
ratio of fuel-air mixture for solid-oxide fuel cells (SOFC). A cylindrical chamber is designed to
induce external air into the chamber and sustain combustion on platinum surface. The thermal
transpiration membrane, Whatman
TM
1825-090 glass microfiber filter, was wrapped around the
cylinder to pump air along the cylinder. The cylindrical structure was made up of aluminum to
make the temperature of the membrane spread uniformly. Aluminum has high thermal
conductivity and easy to be fabricated comparing to other materials. The setup has to start from
supplying C 4H 10 at the center of the chamber and the platinum has to be heated up by a heating
wire that is inserted to the center of the chamber. The heat from heating wire induces external
air into the combustion chamber to react with C 4H 10 on platinum surface. After few seconds, the
combustion will be able to sustain on its own from the external air and heat generated from
catalytic combustion. This combustion chamber shows that the membrane can provide enough
air for the combustion and sustain by itself. The higher temperature, the higher air is driven and
the higher heat transfer out from the combustion chamber. To achieve the most appropriate
operating condition and design of the combustion chamber, all parameters such as fuel flow rate,
position of the platinum, the membrane area have to be varied. The diagram of the cylindrical
chamber is shown in Figure 17 and the ANSYS-Fluent model is shown in Figure 18 which is only
one quarter of the cylinder to reduce the simulation time.

Figure 17 – The diagram of self-sustaining thermally driven cylindrical combustion chamber
Platinum foil
Products
Fuel
(C 4H 10)
Aluminum cylinder
Thermally driven air
Thermally driven air
Membrane
31

Figure 18 – The self-sustaining thermally driven cylindrical combustion chamber, the model and
boundary conditions for the simulation

The simulation on the self-sustaining thermal driven cylindrical combustion chamber is
also studied by using ANSYS-Fluent. UDF files for the thermal transpiration membrane and C 4H 10
catlytic combution were integrated into UDF libraries. Radiation model was also included in the
calculation. The platinum surface temperature has to be initialized upto 600 K. After multiple
iterations, external air will be pumped into the chamber by the thermal transpiration membrane
and the combustion will be able to sustain by itself from the external air and the supplied C 4H 10
at the inlet.

3.4 Solid Oxide Fuel Cell Modeling
To reduce the computational time, only 1/48 or 7.5 degree of a cylindrical fuel cell was
made in Solidworks and imported to ANSYS-Fluent for mT-SOFC modeling. The center of fuel cell
was supplied by H 2 or C 4H 10-air mixture to expose to the anode and the cathode was exposed to
the surrounding air. Both sides along the fuel cell were set to symmetric surfaces to simulate the
Aluminum tube
Platinum foil
(surface reaction)
Transpiration membrane
As-built combustion chamber Aluminum structure
Cross-section of combustion chamber
32

entire fuel cell. The air inlet temperature was set to maintain the temperature as a furnace.
Multiple user-defined function (UDF) files were made and imported to the simulator to calculate
H 2 or C 4H 10 and O 2 consumption rate, H 2O and CO 2 production rate, heat release and power
generation from fuel cell. Two mT-SOFC geometries were made based on Suzuki et.al.’s work [41]
for mT-SOFC running on H 2 and Sumi et.al.’s work [42] running on C 4H 10. The geometry and
boundary conditions of mT-SOFC are depicted in Figure 19.
The first geometry of Ni-GDC mT-SOFC running on H 2 was made by following Suzuki’s work
which the fuel cell was 0.8 mm in diameter with the active area of 0.13 cm
2
. The thickness of the
anode, electrolyte and cathode were 175 m, 10 m and 15 m, respective. H 2 flow rate inside
the fuel cell was at 5 mL/min
-1
H 2O flow rate from the humidifier was at 30% of H 2 flow rate and
N 2 flow rate was at 10 mL/min
-1
. The total flow speed of premixed gas was at 16.5 mL/min
-1
. The
surrounding air was set to 773 K and 823 K according to the temperature of the furnace in Suzuki’s
work.
The second geometry of Ni-GDC mT-SOFC running on C 4H 10 was made by following Sumi’s
work. The fuel cell diameter was 2.8 mm and the active area was 2.6 cm
2
. The thickness of the
anode, electrolyte and cathode were 640 m, 10 m and 20 m, respective. The flow rate of 10%
C 4H 10, 3% H 2O from humidifier and 87% N 2 was supplied into the center of the fuel cell at the
flow rate of 100 mL/min
-1
. The surrounding air was set to 923 K as following the furnace
temperature in Sumi’s study.

Figure 19 – Boundary conditions of mT-SOFC in ANSYS-Fluent

anode
cathode
electrolyte
air
fuel
fuel
products
air
air
33

Chapter 4 Results

4.1 Thermal Transpiration Membrane
The pore radius of glass microfiber membrane and hydrophilic polyethersulfone have
been provided by manufacturers, but the flow channels are different from what was studied;
therefore, experiments on thermal transpiration membrane must be investigated. From multiple
times of running the experiment, it was found that Equation (2) cannot be used to predict the
flow rate pumpped by the membrane. Simplier experiments have to be run to measure the
leakage of the system and the back flow through the membrane. One more leak term has to been
predicted by the leakage through a small hole by pressure drop across the hole as

𝑀 ̇ 𝐿𝑒𝑎𝑘𝑎𝑔𝑒 = 𝜌 𝑘 𝑙𝑒𝑎𝑘 ( ∆𝑃 )
𝑛
(52)
Therefore, the total gas flow rate through the membrane is estimated as

𝑀 ̇ = 𝑃 𝑎𝑣𝑔 √
𝑚 2𝑘 𝑇 𝑎𝑣𝑔 𝐴 𝑡𝑜𝑡 ( 𝐴𝐹
𝑇𝑇
)
𝐿 𝑟 𝐿 𝑥 [
∆𝑇 𝑇 𝑎𝑣𝑔 𝑄 𝑇 −
∆𝑃 𝑃 𝑎𝑣𝑔 𝑄 𝑃 ] − 𝜌 𝑎𝑣𝑔 𝑘 𝐷𝑎𝑟𝑐𝑦 ൫𝐴 𝑡𝑜𝑡 ( 1− 𝐴𝐹
𝑇𝑇
) ൯𝛥𝑃
𝜇 𝐿 𝑥 − 𝜌 𝑎𝑣𝑔 𝑘 𝑙𝑒𝑎𝑘 ( ∆𝑃 )
𝑛
(53)
where the first term is the flow from thermal transpiration membrane, the second term is the
Darcy backflow through porous media and the last term is the leakage of the apparatus. The first
test was run by pressure rising the apparatus and block the flow right before the membrane, then
measure the flow rate of the gas by a bubble flow meter. The second test is when gas was allowed
to flow through the membrane without any heat supply on one side of the membrane. An
example of the flow rate through a Whatmann membrane and the leakage of the system were
measured and shown in Figure 20.
34

Figure 20 – The relation of flow rate and pressure drop from the leak of the system and the
Darcy backflow through the membrane
From the graph above, the leak constant and Darcy constant of the setup and the
membrane were found as 𝑘 𝑙𝑒𝑎𝑘 = 7.720× 10
−11
𝑚 4
𝑠 𝑘𝑔
for 𝑛 = 1 and 𝑘 𝐷 𝑎𝑟𝑐𝑦 = 3.814× 10
−13
𝑚 2

which can be used in Equation (53) to estimate the total flow rate. An effective pore radius (𝐿 𝑟 )
and an effective capillary’s cross-sectional area (𝐴𝐹
𝑇𝑇
) have to be fitted from the experimental
data compared with results as shown in the performance curve, Figure 21, and Equation (53).
The temperature gradient across the membrane was controlled by electrical power supply to
heating wire for three cases of temperature difference. Volume flow rate was controlled by
varying a valve at the exit. The smaller outlet generates higher pressure drop across the
membrane which reduces volume flow rate. At no flow condition, the relation between pressure
drop over average pressure and temperature gradient over average temperature. From Equation
(53), the trend of the performance cureve is supposted to be linear at the specific temperature
gradient across the membrane which agrees with the experimental results.
The membrane thickness was measured as 360- m. The fitted properties of this
membrane were 0.8- m effective pore radius and 0.36 thermal transpiration area factor, while
the leak constant and Darcy constant were mentioned above. The measured and fitted
parameters are in the possible range and can be used to estimate the flow rate through the
membrane for the further design.

P = 215.4Flow P = 23.99Flow
0
10
20
30
40
50
60
70
0.0 0.5 1.0 1.5 2.0 2.5
Pressure Difference [Pa]
Darcy or leakage Flowrate [cc/min]
Leakage
Darcy Backflow
35

Figure 21 – The performance curve running on air at various temperature gradients across
Whatmann membrane from experiments ( •) and modified Muntz equation ( −)

Figure 22 – The performance curve running on air at various temperature gradients across
Whatmann membrane from experiments ( •) and modified Muntz equation ( −)

Another membrane from Pall Corporation was tested in the same apparatus and
procedure which the result is shown in Figure 22. The membrane thickness was measured as 190-
m. The fitted properties of this membrane were 0.2- m effective pore radius and 0.18 thermal
transpiration area factor, while the Darcy constant was 1.90 × 10
−14
𝑚 2
. The measured and
fitted parameters are in the possible region that the advertised pore radius is 0.1 m. The
0
5
10
15
20
25
30
0.0 0.2 0.4 0.6 0.8 1.0
Pressure Difference [Pa]
Volume Flow Rate [ml/min]
dT13K Tavg334K
dT18K Tavg341K
dT22K Tavg351K
dT28K Tavg360K
dT33K Tavg371K
0
10
20
30
40
50
60
70
80
0.0 0.1 0.2 0.3 0.4 0.5
Pressure Difference [Pa]
Volume Flow Rate [ml/min]
dT12K Tavg341K
dT15K Tavg351K
dT19K Tavg365K
dT22K Tavg374K
dT26K Tavg384K
T = 12K, Tavg = 341K
T = 15K, Tavg = 351K
T = 19K, Tavg = 365K
T = 22K, Tavg = 374K
T = 26K, Tavg = 384K
T = 13K, Tavg = 334K
T = 18K, Tavg = 341K
T = 22K, Tavg = 351K
T = 28K, Tavg = 360K
T = 33K, Tavg = 371K
36

performance curve of Pall membrane shows the higher shut-off pressure because of the smaller
pore radius; however, the volume flow rate is about a half of Whatmann membrane.
The experiment was also done with varying membrane thickness by stacking mulitple
membrane together upto 3 layers. The effective pore radius and membrane permeability of each
experiment had significantly small variation. The membrane thickness was measured directly
from the membrane after the experiment was done. For two layer case, the effective thermal
transpiration area was 0.15 and for three layer case, the effective thermal transpiration area was
0.23. The performance curves of these two conditions are shown in Figure 23. From the result,
the area factor increased if the number of layers increased, because the back flow leak areas
were blocked by thermal transpiration areas. The relation between the area factor and the
number of layers can be estimate by proability as
𝐴𝐹
𝑇𝑇 ,𝑡𝑜𝑡 = 1− ( 1 − 𝐴 𝐹 𝑇𝑇
)
𝑁 (54)
where 𝐴𝐹
𝑇𝑇 ,𝑡𝑜𝑡 is the area factor when all membrane combined, 𝐴 𝐹 𝑇𝑇
is the area factor of each
membrane and 𝑁 is the number of membrane layers. Equation (54) can be substituted into
Equation (53) as

M
̇ = 𝑃 𝑎𝑣𝑔 √
𝑚 2𝑘 𝑇 𝑎𝑣𝑔 𝐴 𝑡𝑜𝑡 ( 1− ( 1 − 𝐴 𝐹 𝑇𝑇
)
𝑁 )
𝐿 𝑟 𝐿 𝑥 ,𝑡𝑜𝑡 [
∆𝑇 𝑇 𝑎𝑣𝑔 𝑄 𝑇 −
∆𝑃 𝑃 𝑎𝑣𝑔 𝑄 𝑃 ] − 𝜌 𝑎𝑣𝑔 𝜅 ( 𝐴 𝑡𝑜𝑡 ( 1− 𝐴 𝐹 𝑇𝑇
)
𝑁 ) 𝛥𝑃
𝜇 𝐿 𝑥 − 𝜌 𝑎𝑣𝑔 𝑘 𝑙𝑒𝑎𝑘 ( ∆𝑃 )
𝑛
(55)
when 𝐿 𝑥 ,𝑡𝑜𝑡
is the total thickness of all layers combined.

Figure 23 – The performance curve in various temperature gradients across the membrane for
(left) two layer membrane and (rigth) three layer membrane
0
10
20
30
40
50
60
70
0.0 1.0 2.0 3.0 4.0 5.0
Pressure Difference [Pa]
Volume Flow Rate [cc/min]
dT 62K, Tavg 374K
dT 79K, Tavg 393K
dT 98K, Tavg 413K
dT 119K, Tavg 435K
dT 143K, Tavg 460K
T = 62K, T
avg
= 374K
T = 79K, T
avg
= 393K
T = 98K, T
avg
= 413K
T = 119K, T
avg
= 435K
T = 143K, T
avg
= 460K
0
10
20
30
40
50
60
70
0.0 1.0 2.0 3.0 4.0 5.0
Pressure Difference [Pa]
Volume Flow Rate [cc/min]
dT 57K, Tavg 370K
dT 74K, Tavg 390K
dT 94K, Tavg 409K
dT 113K, Tavg 428K
dT 143K, Tavg 460K
T = 57K, T
avg
= 370K
T = 74K, T
avg
= 390K
T = 94K, T
avg
= 409K
T = 113K, T
avg
= 428K
T = 143K, T
avg
= 460K
37

4.2 Catalytic Combustion
To have an optimal design power generator, the simulation for catalytic combustion on
platinum surface has to be done in ANSYS-Fluent to compare with experimental results in various
equivalence ratio and fuel-air mixture flow speed. If results are comparable, catalytic combustion
modeling can be used to design the power generator. The simulation results in fuel-rich region,
considering O 2 as a deficient reactant and the catalytic surface is covered by hydrocarbon fuel
which is C 3H 8 or C 4H 10, CO 2 and H 2O. An example of the contour of temperature, C 4H 10, O 2 and
CO 2 mole fractions at 1.5 equivalence ratio and 12 cm/s flow speed are shown in Figure 24. The
simulation result indicates the higher temperature and more reaction rate occur on the leading
edge of the platinum, because of more fuel and oxygen concentration.

Figure 24 – An example of simulation result from C 4H 10-air mixture at 1.5 equivalence ratio
and 12 cm/s flow speed
The concentration for each exhaust product coming out from the glass tube is shown in
Figure 25. The upper figures are fixed flow speed at 16 cm/s with varying equivalence ratio. The
lower figures are fix equivalence at 2.5 with varying flow speed. The results show the higher
Contours of static temperature (K) Contours of C
4
H
10
mole fraction
Contours of O
2
mole fraction Contours of CO
2
mole fraction
38

equivalence ratio the more C 4H 10 coming out from the glass tube. The simulation results seem to
have slightly higher reaction rate which can be seen from more combustion products coming out
and more oxygen being consumed in the reaction. When flow speed was increases, more C 4H 10
and O 2 came out and less CO 2 and H 2O, because the residue time decreased.

Figure 25 – The product compositions of experimental results and simulation results of C 3H 8-air
mixture at (upper) 16 cm/s constant flow speed and (lower) 2.5 constant equivalence ratio
Additionally, experimental results and simulation results from C 4H 10 on platinum foil and
platinum mesh were also compared. The experimental setup was kept the same as C 3H 8-air
mixture, but C 4H 10-air mixture flow speed was extended to the lower flow speed to explore the
0
2
4
6
8
10
12
1.0 1.5 2.0 2.5 3.0 3.5 4.0
Product Composition [%]
Equivalence Ratio
O2 Experiment
O2 Simulation
C3H8 Experiment
C3H8 Simulation
0
2
4
6
8
10
12
1.0 1.5 2.0 2.5 3.0 3.5 4.0
Product Composition [%]
Equivalence Ratio
CO2 Experiment
CO2 Simulation
H2O Experiment
H2O Simulation
0
2
4
6
8
10
12
7 10 13 16 19 22 25
Product Composition [%]
Flow speed [cm/s]
O2 Experiment
O2 Simulation
C3H8 Experiment
C3H8 Simulation
0
2
4
6
8
10
12
7 10 13 16 19 22 25
Product Composition [%]
Flow speed [cm/s]
CO2 Experiment
CO2 Simulation
H2O Experiment
H2O Simulation
39

region near extinction. The experiment was done from 4.0 to 22.0 cm/s flow speed to provide
more residue time for the surface combustion and the equivalence ratio was also extended to
the lean mixture. The results from both experiment and simulation on platinum foil are shown in
Figure 26 and on platinum mesh are shown in Figure 27. They show reasonable trends for all
exhaust gases on fuel-lean and fuel-rich mixture that when the flow speed increases, more fuel
comes out from the outlet and results also agree on the lean and stoichiometric region.

Figure 26 – The product compositions of experimental results and simulation results of C 4H 10-air
mixture on platinum foil at (upper) 12 cm/s constant flow speed
and (lower) 1.5 constant equivalence ratio
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5
Product Composition [%]
Equivalence Ratio
O2 Experiment
O2 Simulation
C4H10 Experiment
C4H10 Simulation
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5
Product Composition [%]
Equivalence Ratio
CO2 Experiment
CO2 Simulation
H2O Experiment
H2O Simulation
0
2
4
6
8
10
12
14
2 6 10 14 18 22
Product Composition [%]
Flow Speed [cm/s]
O2 Experiment
O2 Simulation
C4H10 Experiment
C4H10 Simulation
0
2
4
6
8
10
12
14
2 6 10 14 18 22
Product Composition [%]
Flow Speed [cm/s]
CO2 Experiment
CO2 Simulation
H2O Experiment
H2O Simulation
40

Figure 27 – The product compositions of experimental results and simulation results of C 4H 10-air
mixture on platinum mesh at (upper) 12 cm/s constant flow speed
and (lower) 1.5 constant equivalence ratio

Extinction curves of C 3H 8 on platinum foil and C 4H 10 on platinum foil were also studied to
explore the effect of heat losses on the setup and the simulation. The extinction curves are shown
in Figure 28. The experiment and simulation were started by igniting combustion in the self-
sustaining region and the equivalence ratio was slowly decreased until the combustion could not
sustain. The temperature of the platinum surface dropped significantly. On the low Reynolds
number side, the flow speed of fuel-air mixture was also slowly decreased until the combustion
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5
Product Composition [%]
Equivalence Ratio
O2 Experiment
O2 Simulation
C4H10 Experiment
C4H10 Simulation
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5
Product Composition [%]
Equivalence Ratio
CO2 Experiment
CO2 Simulation
H2O Experiment
H2O Simulation
0
2
4
6
8
10
12
14
16
2 4 6 8 10 12 14 16 18 20
Product Composition [%]
Flow Speed [cm/s]
O2 Experiment
O2 Simulation
C4H10 Experiment
C4H10 Simulation
0
2
4
6
8
10
12
14
16
2 4 6 8 10 12 14 16 18 20
Product Composition [%]
Flow Speed [cm/s]
CO2 Experiment
CO2 Simulation
H2O Experiment
H2O Simulation
41

could not sustain as well. The experiment of C 3H 8-air mixture seems to be more sustainable at
the low Reynolds number side than the simulation. However, both C 3H 8-air mixture and C 4H 10-air
mixture show reasonable trends of equivalence ratio down to 0.6 and up to 8 which cover the
operating region of SOFCs. The catalytic combustion modeling can be used to design a
combustion chamber for the optimal condition for SOFCs.

Figure 28 – Extinction curves of C 3H 8 and C 4H 10 on platinum foil

4.3 Self-Sustaining and Self-Pressurizing Combustion Chamber
The thermal transpiration membrane and catalytic combustion were combined in order
to demonstrate the feasibility of self-sustaining and self-pressurizing combustion chamber. Then
a simulation model in ANSYS Fluent was made as illustrated in the previous chapter. The
combustion in the simulation can sustain without supplying any air to the inlet. Air was only
pumped by the transpiration membrane from temperature gradient across the membrane. The
cylindrical chamber in the simulation was able to provide the appropriate equivalence ratio for a
SOFC to operate at the optimum operating condition. The simulation results including
temperature gradient and mole fraction of CO 2 and H 2O are shown in Figure 29. It shows that the
self-sustaining thermally driven combustion chamber is feasible. Furthermore, the product
compositions at the outlet were measured by a gas chromatograph by varying C 4H 10 flow speed.
The comparison between experimental results and computational results are shown in Figure 30.
0.1
1.0
10.0
0 10 20 30 40 50 60 70 80
Equivalence Ratio at Extinction
Reynolds Number
C3H8 foil experiment
C3H8 foil simulation
0.1
1.0
10.0
0 10 20 30 40 50 60 70 80
Equivalence Ratio at Extinction
Reynolds Number
C4H10 foil experiment
C4H10 foil simulation
42

Figure 29 – An example of the simulation result at 0.48 cm/s C 4H 10 flow speed

Figure 30 – The product compositions from the self-sustaining thermally driven combustion
chamber at various C 4H 10 flow rate
0
5
10
15
20
0 10 20 30 40 50
Product Concentration at outlet [%]
C
4
H
10
flow rate at inlet [ml/min]
O2 Experiment
O2 Simulation
C4H10 Experiment
C4H10 Simulation
0
5
10
15
20
0 10 20 30 40 50
Product Concentration at outlet [%]
C
4
H
10
flow rate at inlet [ml/min]
CO2 Experiment
CO2 Simulation
H2O Experiment
H2O Simulation
Contours of C
4
H
10
mole fraction Contours of Static Temperature
Contours of O 2 mole fraction Contours of CO 2 mole fraction
Platinum foil
43

The integration of thermal transpiration membrane and catalytic combustion
demonstrates that product compositions or equivalence ratio at the outlet are adjustable by
varying fuel flow rate. The target of this design is to utilize all fuel and maximize power
generation. This cylindrical combustion chamber can be simply integrated with a mT-SOFC to
supply fuel at the center on the anode side and induce the external air to the cathode side of the
fuel cell. Platinum can be placed around the fuel cell near the surface of the transpiration
membrane to generate heat for the fuel cell and the membrane at the same time.

4.4 Solid Oxide Fuel Cell Modeling
The last component of the power generation system is micro-tubular solid oxide fuel cell
(mT-SOFC). There are multiple parameters of mT-SOFC that have to be fitted to estimate the
power generation and fuel utilization of the fuel cell. Ionic conductivity and electronic
conductivity contain parameters which were mentioned in Chapter 2. The electrochemistry part
has to be fitted with the mT-SOFC running on H 2 from Sumi et.al.’s work [41] with 4 unknowns in
ionic conductivity, Equation (47), and electronic conductivity, Equation (49). However, it was
found that each parameter was varied depending on the fuel cell manufacturing process. The
pre-exponential factor (𝜎 0,𝑒 ) and the activation energy (𝐸 𝑎 ,𝑒 ) in electronic conductivity for
electronic conductivity were fitted first to match the open-circuit voltage (OCV) of the model with
the experimental results of the fuel cell running on H 2. The larger Variable 𝑘 , the more electronic
current flows back occurring in the SOFC which reduces OCV of the cell. The pre-exponential
factor (𝜎 0,𝑒 ) of 1.2× 10
7

𝐾𝑎𝑡 𝑚 0.25
Ω−𝑐𝑚
was found and the activation energy (𝐸 𝑎 ,𝑒 ) was taken from the
original value of 220
𝑘𝐽
𝑚𝑜𝑙 from [31], respectively. The activation energy (𝐸 𝑎 ,𝑖 ) in the ionic
conductivity was held constant from the typical value from various literature of 120
𝑘𝐽
𝑚𝑜𝑙 . Then
pre-exponential factor (𝜎 0,𝑖 ) of the ionic conductivity was adjusted to fit the maximum power
density. However, the maximum power generation from SOFC still can’t be fitted without
adjusting Butler-Volmer equation coefficient (𝛼 ). This coefficient is the common value that most
literature left it as a free-fitted parameter which the value is between 0 to 1. If the coefficient
increases, the different of maximum power will increase. The pre-exponential factor (𝜎 0,𝑖 ) and
44

coefficient (𝛼 ) were fitted to 7.2 × 10
8
𝑆 /𝑚 and 0.25 respectively. The fitted results are shown
in Figure 31. The sensitivity of adjustable parameters will be discussed in the following section.

Figure 31 – Polarization curve of experimental results and simulation results from mT-SOFC
running on H 2 at various operating temperature

After the electrochemistry part was fitted, Constant 𝑘 𝑓𝑟
in Equation (33) which represent
the pre-exponential factor of internal fuel reforming process of mT-SOFC was adjusted to match
the power generation curve of the fuel cell. The activation energy, 𝐸 𝑎 ,𝑓𝑟
= 166
𝑘𝐽
𝑚𝑜𝑙 , of the direct
internal fuel reformer used the typical value of hydrocarbon fuel which also mentioned in Xu
et.al.’s work [33]. The pre-exponential factor 𝑘 𝑓𝑟
was fitted to 3.1 × 10
8
𝑚 10
𝑚𝑜𝑙 −𝑠 for mT-SOFC
running on C 4H 10. The experimental results and simulation results from the fuel cell were
compared in Figure 32.

Sensitivity Analysis
In the electrochemistry model of SOFC, there are 5 variable parameters, 𝜎 0,𝑒 , 𝐸 𝑎 ,𝑒 , 𝜎 0,𝑖 ,
𝐸 𝑎 ,𝑖 and 𝛼 that can be adjusted, because they depend on SOFC material properties. Each
parameter was also varied from different literature, but some of them were determined in the
comparable value. Sensitivity analysis is one way to study how sensitive the result is, if some
0
200
400
600
800
1000
1200
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 1000 2000 3000
Power
(mW/cm
2
)
Volt (V)
Current (mA/cm
2
)
H
2
• Simulation results from
ANSYS-Fluent
⎯ Experiment by Suzuki et.al.
running on H 2

45

parameters have changed. The best fit values of all adjustable parameters were used and the
maximum power and open-circuit voltage of SOFC running on H 2 were set as a baseline condition.
The first parameter, for example 𝜎 0,𝑒 , was increased by 10%, then the open-circuit voltage and
the maximum power were record to compare with the baseline condition. The results of
sensitivity analysis of electrochemistry model of SOFC running on H 2 were shown in Table 3.

Figure 32 – Polarization curve of experimental results and simulation results from mT-SOFC
running on C 4H 10 at various operating temperature
Table 3 Sensitivity of open-circuit voltage and maximum power at various adjustable parameters
Adjustable
parameters
Sensitivity of
open-circuit Voltage
Sensitivity of
maximum power
Reason to adjust
𝜎 0,𝑒 -0.851 -0.089 Wide range of published values
𝐸 𝑎 ,𝑒 1.483 0.009 Use a typical value
𝜎 0,𝑖 0.016 0.0013 Wide range of published values
𝐸 𝑎 ,𝑖 -2.115 -0.404 Use a typical value
𝛼 -0.128 0.841 Non-measurable value
𝑘 𝑓𝑟
0.042 0.581 One data set available

To minimize free fitted parameter, only some parameters were chosen to adjusted to fit
the electrochemistry model with experimental results of SOFC running on H 2 based on each
parameter sensitivity results. First, the activation energy of ionic conductivity and electronic
0
100
200
300
400
500
600
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 200 400 600 800
Power
(mW/cm2)
Voltage
(V)
Current (mA/cm2)
C
4
H
10
-air
• Simulation results from
ANSYS-Fluent
⎯ Experiment by Suzuki et.al.
running on C 4H 10

46

conductivity (𝐸 𝑎 ,𝑖 and 𝐸 𝑎 ,𝑒 ) were chosen to be held constant or in the typical values comparing to
other literature; even though, they change the maximum power a lot when operating
temperature changes. Pre-exponential terms of ionic conductivity and electronic conductivity
(𝜎 0,𝑖 and 𝜎 0,𝑒 ) were chosen to be adjusted, because the ionic conductivity term can modify the
maximum power and the electronic conductivity term can modify the open-circuit voltage. From
the simulation results, it was found that at zero current flow condition, electronic current flow is
equal to ionic current flow, so the pre-exponential term of electronic conductivity has a major
control on the results. For the maximum power conditions, the electronic current flow becomes
a small relative to the ionic current flow, because the voltage generation across the fuel cell is
also minimized. The coefficient of Butler-Volmer equation (𝛼 ) was also chosen to be adjusted.
The coefficient, determining the relation of potential of the fuel cell related to the current flow,
is not measurable by any device, so it is usually left as a free-fitted parameter in many literatures.
The maximum power decreases when the coefficient decreases. This parameter is also related to
the fuel cell operating temperature; therefore, the decrease of this coefficient makes the
maximum power different decrease when temperature decreases.
The sensitivity of fuel reforming process modeling was also compared with the baseline
condition, but only the pre-exponential term (𝑘 𝑓𝑟 ) can be studied because of the limiting
experimental results. However, the results in Table 3 shows that the increase of 𝑘 𝑓𝑟 can increase
the maximum power, but increase the open-circuit voltage slightly. When the simulation result
was observed, it was found that the limiting step of the reaction is the fuel reforming process.
The faster rate of reforming, the more power can be generated from the fuel cell.

47

Chapter 5 Conclusion

5.1 Thermal Transpiration Membrane
In this work, a thermal transpiration membrane was used as an air pump for catalytic
combustion and a solid oxide fuel cell. The modeling of thermal transpiration membranes has to
be studied based on Muntz et. al.’s work from the temperature gradient across the membrane
by introducing the concept of rarefield gas dynamic. In that previous work, the relation between
gas flow rate, pressure generated from the membrane and the temperature gradient was
introduced based on membrane properties such as pore radius and affective area of the
membrane. However, for more accurate estimation of the membrane performance, the equation
of flow through porous media from Darcy’s law had to be included to predict the back flow that
occur on the membrane.
Two membranes were studied in this work, Whatman
TM
1825-090 glass microfiber filter
and Supor (hydrophilic polyethersulfone) from Pall Corporation. The experiment was done by
squeezing each membrane between perforated aluminum sheet to make the temperature on
one side of the membrane uniform. A heating wire was used to supply heat on one side of the
membrane. The temperature on each side of the membrane and pressure drop were measured
by thermocouples and pressure sensors. Performance curves from each temperature gradient
across the membrane were plotted and membrane properties which are pore radius, effective
area and permeability were estimated as constants of each membrane.
Membrane properties were consistense at various conditions, such as different
temperture gradient and higher average pressure. The model from this work demonsrates that
it can be used to extimate the performance of thermal transpiration membrane by fitting only
pore radius and effective area of the membrane. Both membranes perform differently, but the
performance curves and the higher operating temperature of borosilicate glass microfiber filter
show that Whatman
TM
1825-090 can produce higher maximum flow rate at zero pressure which
is more appropriate for self-sustaining and self-pressuring combustion chamber.

48

5.2 Catalytic Combustion
Catalytic combustion on platinum surface was used to release heat to the SOFC to
generate electricity and release heat to the thermal transpiration membrane to pump external
air to the cathode side of the fuel cell. Catalytic combustion on platinum surface was previously
introduced by Deshmukh et al. [24]; however, the model can only predict the reaction on the
lean C 3H 8-air mixture and lean C 4H 10-air mixture. The reaction rate of the catalytic combustion
had to be modified to estimate the reaction rate on rich mixture. On the lean mixture condition,
C 3H 8 or C 4H 10 was considered as the deficient reactant and when it adsorbs on the catalyst
surface, the reaction occurs immediately. On the other hand of rich mixture condition, O 2 was
considered as the deficient reactant and the reaction occurs immediately after O 2 molecules
adsorb on the surface.
The experiment of catalytic combustion on platinum surface was done in a quartz glass
tube. Flow controllers were used to control the flow rate of fuel and air separately. Equivalence
ratio and reactant flow speed can be varied near the operating condition of SOFC by the flow
controllers via Labview program. A thermocouple was placed on platinum surface to measure
the temperature and the experiment was done under atmospheric pressure. Product
concentrations which are C 3H 8 or C 4H 10, O 2 and CO 2 were measured by gas chromatograph to
compare with simulation results in ANSYS-Fluent. Between lean mixture and rich mixture, an
error function was used to smooth out the reaction rate and make the model applicable the
operating range of the fuel cell.
Product concentrations from the simulation at various equivalence ratio and flow speed
can estimate the reaction rate of catalytic combustion from the experiment over the wide range
of SOFC operating conditions. The extinction curves of C 3H 8 and C 4H 10 at various Reynolds number
and equivalence ratio were also measured and the simulation was also able to predict the
extinction curve from equivalence ratio 0.7 to equivalence ratio 8.0. This model can be used to
estimate the catalytic combustion on platinum surface from C 3H 8 or C 4H 10 to generate heat for
the SOFC and the thermal transpiration membrane.

49

5.3 Self-Sustaining and Self-Pressurizing Combustion Chamber
Catalytic combustion on platinum surface and the thermal transpiration membrane were
integrated for a self-sustaining and self-pressurizing combustion chamber for mT-SOFC. An
aluminum cylinder was built with 4 sloth holes along the cylinder. Platinum mesh was placed
inside the cylinder and around the cylinder was wrapped by thermal transpiration membrane.
The platinum was used as catalyst to generate heat from C 4H 10 and air for the membrane. At the
same time the membrane can pump the external air into the chamber for the catalytic
combustion because of the temperature gradient from the combustion inside. One side of the
cylinder was made for a C 4H 10 inlet port and another side of the cylinder is the exhaust outlet.
The inlet flow speed of C
4
H
10
can be controlled by a flow controller.
The combustion can be started by supplying C 4H 10 into the chamber and a heating wire
was used to initial the heat. After few seconds, the external air would be pumped into the
chamber by the transpiration membrane and sustain the catalytic combustion on platinum
surface. The transpiration membrane works as a heat insulator and a pump at the same time
which make the combustion chamber sustain on its own.
The maximum temperature near the platinum mesh could go up to 600 C which is
applicable for mT-SOFC operation. The exhaust equivalence ratio coming out from the
combustion chamber can also be controlled by adjusting flow speed. The higher the C
4
H
10
flow
speed, the higher equivalence ratio of the exhaust.
The simulation in ANSYS-Fluent was also made to compare with the experimental results.
It shows that the combined modeling of thermal transpiration membrane and catalytic
combustion can be used to predict the exhaust concentration and the maximum temperature in
the simulation was in the reasonable range. This self-sustaining and self-pressurizing combustion
chamber is not the prove of concept that this type of combustion chamber works at the small
scale, but also the thermal transpiration membrane model and catalytic combustion model work
in the simulation and can be used to design other self-sustaining combustion chamber.

50

5.4 Solid Oxide Fuel Cell Modeling
A micro-tubular solid-oxide fuel cell was used to generate electricity in this study. A fuel
cell is a device that can generate electricity from fuel which can be H 2 and C 4H 10 and O 2. The
tubular type SOFC was chosen, because of the structure of the fuel cell is applicable for the self-
sustaining and self-pressurizing combustion chamber. There are a lot of research about mT-SOFC,
yet the modeling of mT-SOFC operating on C 4H 10 has not well-established. Internal fuel reformer
model, water gas shift reaction model and electrochemistry model of mT-SOFC were studied.
Most of the parameters of fuel cell were taken from literatures; however, there were still some
adjustable parameters which had to be determined based on experimental results.
Some experimental results of Ni-GDC based mT-SOFC running on H
2
and C
4
H
10
have been
done at various operating temperature; therefore, these results can be used to compare with the
simulation in ANSYS-Fluent. A user-defined function was built to calculate the current density,
fuel and O 2 consumption of the fuel cell. The calculation based on the operating temperature,
fuel and O 2 concentration and the operating voltage of the fuel cell.
Adjustable parameters, which are ionic conductivity, electronic conductivity and fuel
reformer pre-exponential term, were adjusted to fit the simulation result with experimental
results. The model of internal fuel reformer and electrochemistry were coupling together;
therefore, the simulation on fuel cell running on H
2
has to be studied and the pre-exponential
term of conductivities were adjusted. Then the simulation results from fuel cell running on C 4H 10
were fitted to experimental results by adjusting only pre-exponential term of the fuel reformer
model. The sensitivity analysis of the fuel was also done to decide which parameters could be
adjusted.
The modeling of mT-SOFC at various operating temperature and fuels shows the
agreement between experimental results and simulation results which is able to be used to
integrate with thermal transpiration membrane and catalytic combustion for self-sustaining
power generation without any moving parts for portable devices.
51

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55

Appendix UDF for ANSYS-Fluent

1. Thermal Transpiration Membrane
User-defined function (UDF) for ANSYS-Fluent to simulate the thermal transpiration
membrane pumping performance was implement in C programming. The UDF is based on
Equation 1 which calculates total air mass flow from the temperature different and pressure
generation across the membrane. The fan model in ANSYS-Fluent was chosen to generate
pressure for the flow calculation. If the actual mass flow is not equal to the calculated mass flow,
the pressure would be slightly adjusted for the next iteration.

#include "udf.h"
#include "math.h"

float CalP = 0.0;
float DelP = 0.0;
float DelP1 = 0.0;
float DelP2 = 0.0;
float Mflow_act = 0.0;
int firstcal = 0;
float kOverM = 286.9; //[m^2 per s^2*K]
float Rair = 287.0; //[J/kgK]
float rhoamb = 1.17659; //[kg/m3]
float Pamb = 101325.0; //[Pa]
float mfpath = 68.0; //[nm]
float Lr = 1250.0; //[nm]
float Lx = 470000.0; //[nm]
float permea = 0.00000000000019325; //[m2]
float dynvis = 0.0000213826; //[kg/ms]
float AFTT = 0.28;
float Atot = 0.00006482; //[m2]
float Mflow2 = 0.0; //[kg/s]
float Mflow_cal = 0.0; //[kg/s]
float Ki = 10000.0;

DEFINE_PROFILE(KnudsenPump, t1, index)
{
float effmfpath = 68.0; //[nm]
float rhoavg = 1.17659; //[kg/m3]
float Kn = 0.0;
float QT = 0.0;
float QP = 53.0;
float a = 0.0; //Grouping term, temporary variable
float b = 0.0; //Grouping term, temporary variable
float Pavg = 101325.0; //[Pa]
float Tavg = 300.0; //[K]
int i = 0;

//Set the domain ID for cold side of the membrane
Domain *d2 = Get_Domain(1);
int id2 = 75;
Thread *t2 = Lookup_Thread(d2, id2);
face_t f2;
float Tc = 0.0;
56

float Pc = 0.0;

//Set the domain ID for hot side of the membrane
Domain *d3 = Get_Domain(1);
int id3 = 71;
Thread *t3 = Lookup_Thread(d3, id3);
face_t f3;
float Th = 0;
float Ph = 0;

float x[3];
float y;
face_t f1;

//Get T and P from the inlet side
begin_f_loop(f2, t2)
{
i = i+1;
Tc = Tc + F_T(f2,t2); //Read temperature from the surface
Pc = Pc + F_P(f2, t2); //Read pressure from the surface
}
end_f_loop(f2, t2)
Tc = Tc/i; //Average the temperature
Pc = Pc/i + Pamb; //Average the pressure

//Get T and P from the outlet side
i = 0;
Mflow_act = 0.0;
begin_f_loop(f3, t3)
{
i = i + 1;
Th = Th + F_T(f3, t3); //Reading temperature from the surface
Ph = Ph + F_P(f3, t3); //Reading pressure from the surface
Mflow_act = Mflow_act + F_FLUX(f3, t3); //Read mass flow [kg/s]
}
end_f_loop(f3, t3)
Th = Th/i; //Average the temperature
Ph = Ph/i + Pamb; //Average the pressure
//Calculate gas properties
Tavg = (Tc+Th)/2.0;
Pavg = (Pc+Ph)/2.0;
rhoavg = Pavg/(Rair*Tavg);
effmfpath = mfpath/(rhoavg/rhoamb);
Kn = effmfpath/Lr;
QT = -0.3877*pow(Kn,2.0)+0.6153*Kn+0.0035; //Curve fitting the value of QT
QP = QT/(Kn-0.03459)*3.84535; //Curve fitting the value of QP
a = Pavg*pow((1.0/2.0/kOverM),0.5)*Atot*AFTT*Lr/Lx; //Temporary Variable a
b = permea*Atot*(1-AFTT)/dynvis/(Lx*0.000000001); //Temporary Variable b

Mflow_cal = a*( (Th-Tc)/pow(Tavg,1.5)*QT - (Ph-Pc)/Pavg/pow(Tavg,0.5)*QP ) - rhoavg*b*(Ph-Pc);
if (Mflow_cal < 0)
Mflow_cal = 0.0;

DelP1 = 336370617201472.0*Mflow_cal*Mflow_cal+335509811.63*Mflow_cal-0.046019;
DelP2 = DelP2 - Ki*(Mflow_act - Mflow_cal); //Adjust the next DelP until Mflow matches
DelP = DelP1 + DelP2;

begin_f_loop(f1, t1)
{
F_CENTROID(x, f1, t1);
y=x[1];
F_PROFILE(f1, t1, index) = DelP; //Output pressure for the fan model in Fluent
}
end_f_loop(f1,t1)
}

57

2. Catalytic Combustion
The reduced mechanism of catalytic combustion on platinum surface was implement in
user-defined function (UDF) for the simulation. Prebuilt surface reaction platform was used to
calculate the reaction rate of C 4H 10 and O 2 which generate CO 2 and H 2O. The combustion model
can estimate the reaction rate from the lean mixture (Vlachos’ model) to the rich mixture
(Modified Vlachos’ model) by using an error function to gradually connect the calculated rate at
equivalence ratio around 1.

#include "stdio.h"
#include "udf.h"
#include "math.h"
// Species numbers. Must match order in ANSYS FLUENT dialog box
#define C4H10 0
#define O2 1
#define CO2 2
#define H2O 3

int loop = 0;

//------------ Define Constants ---------------//
double max_rr = 0.1; //[mol/cm2-s]
double area_factor = 1.0;
double gamma = 2.5e-9; //[mol/cm2]
double R = 1.987; //[cal/mol-K]
double Tref = 300.0; //[K]
double Tavg = 300.0;
//O2
double x_o2 = 0.0;
double Cs_o2_avg = 0.0; //[mol/cm3]
double Cs_o2 = 0.0; //[mol/cm3]
double s_o2 = 6.86e-4; //[]
double M_o2 = 0.032; //[kg/mol]
double Eads_o2 = 0.0; //[kcal/mol]
double Bads_o2 = 0.766; //[]
double kads_o2 = 0.0; //[cm3/mol-s]
double A_o2 = 9.04e18; //[1/s]
double Bdes_o2 = 1.039; //[]
double ttha_o = 0.6; //[initial value]
double Edes_o2 = 27.1; //[kcal/mol]
double kdes_o2 = 0.0; //[1/s]
//C4H10
double x_c4h10 = 0.0;
double Cs_c4h10_avg = 0.0; //[mol/cm3]
double Cs_c4h10 = 0.0; //[mol/cm3]
double s_c4h10 = 0.95; //[]
double M_c4h10 = 0.058; //[kg/mol]
double Eads_c4h10 = 0.0; //[kcal/mol]
double Bads_c4h10 = 0.0; //[]
double kads_c4h10 = 0.0; //[cm3/mol-s]
double A_c4h10 = 1.0e13; //[1/s]
double Bdes_c4h10 = 0.0; //[]
double Edes_c4h10 = 45.0/4.184; //[kcal/mol]
double kdes_c4h10 = 0.0; //[1/s]
//CO2
double x_co2 = 0.0;
double Cs_co2_avg = 0.0; //[mol/cm3]
double Cs_co2 = 0.0; //[mol/cm3]
double s_co2 = 4.69e-2; //[]
58

double M_co2 = 0.044; //[kg/mol]
double Eads_co2 = 0.0; //[kcal/mol]
double Bads_co2 = 0.25; //[]
double kads_co2 = 0.0; //[cm3/mol-s]
double A_co2 = 1.83e11; //[1/s]
double Bdes_co2 = 0.523;
double Edes_co2 = 3.1; //[kcal/mol]
double kdes_co2 = 0.0; //[1/s]
//H2O
double x_h2o = 0.0;
double Cs_h2o_avg = 0.0; //[mol/cm3]
double Cs_h2o = 0.0; //[mol/cm3]
double s_h2o = 1.43e-4; //[]
double M_h2o = 0.018; //[kg/mol]
double Eads_h2o = 0.0; //[kcal/mol]
double Bads_h2o = 1.162; //[]
double kads_h2o = 0.0; //[cm3/mol-s]
double A_h2o = 7.87e5; //[1/s]
double Bdes_h2o = 2.589;
double Edes_h2o = 9.6; //[kcal/mol]
double kdes_h2o = 0.0; //[1/s]

double k_o2 = 0.0;
double k_c4h10 = 0.0;
double k_co2 = 0.0;
double k_h2o = 0.0;
double k_sum = 0.0;
double Eq_ratio = 0.0;
double Eq_ratio_avg = 0.0;
double reaction = 0.0;
double reaction_avg = 0.0;

//1 is fuel-rich mixture
double a_term1 = 0.0;
double b_term1 = 0.0;
double c_term1 = 0.0;
double determinant1 = 0.0;
double det21 = 0.0;
double pt_s1 = 0.0;
double root11 = 0.0;
double root21 = 0.0;
double fwdfctr1 = 1.0;
double reaction1 = 0.0;
double reaction_avg1 = 0.0;
double reaction_old1 = 0.0;

//2 is fuel-lean mixture
double a_term2 = 0.0;
double b_term2 = 0.0;
double c_term2 = 0.0;
double determinant2 = 0.0;
double det22 = 0.0;
double pt_s2 = 0.0;
double root12 = 0.0;
double root22 = 0.0;
double fwdfctr2 = 1.0;
double reaction2 = 0.0;
double reaction_avg2 = 0.0;
double reaction_old2 = 0.0;
double sigmoida = 25.0;
double rrratio = 0.0;

DEFINE_SR_RATE(arrhenius, f, fthread, r, mw, xi, rr)
{
double Tsur = F_T(f,fthread); //[K]
double rho = C_R(F_C0(f,fthread),THREAD_T0(fthread)); //[kg/m3]

x_o2 = xi[O2]; // import mole fractions of species O2
if (x_o2 < 0)
59

x_o2 = 0.0;
x_c4h10 = xi[C4H10]; // import mole fractions of species C3H8
if (x_c4h10 < 0)
x_c4h10 = 0.0;
x_co2 = xi[CO2]; // import mole fractions of species CO2
if (x_co2 < 0)
x_co2 = 0.0;
x_h2o = xi[H2O]; // import mole fractions of species H2O
if (x_h2o < 0)
x_h2o = 0.0;
if (Tsur < 295)
Tsur = 300.0;
if (rho < 0)
rho = 1.12;

reaction1 = 0.0;
reaction2 = 0.0;

if ((x_o2 > 0)&&(x_c4h10 > 0))
{
Eq_ratio = (x_c4h10/x_o2)*6.5;
Cs_o2 = x_o2*101325.0/1.987/4.184/Tsur/1000000.0;
Cs_c4h10 = x_c4h10*101325.0/1.987/4.184/Tsur/1000000.0;
Cs_co2 = x_co2*101325.0/1.987/4.184/Tsur/1000000.0;
Cs_h2o = x_h2o*101325.0/1.987/4.184/Tsur/1000000.0;

kads_c4h10 = s_c4h10/gamma*pow(4.184*R*Tsur/2/M_PI/M_c4h10,0.5)*100.0*exp(-
Eads_c4h10*1000.0/R/Tsur)*pow(Tsur/Tref,Bads_c4h10);
kdes_c4h10 = A_c4h10*exp(-Edes_c4h10*1000.0/R/Tsur)*pow(Tsur/Tref,Bdes_c4h10);
kads_co2 = s_co2/gamma*pow(4.184*R*Tsur/2/M_PI/M_co2,0.5)*100.0*exp(-
Eads_co2*1000.0/R/Tsur)*pow(Tsur/Tref,Bads_co2);
kdes_co2 = A_co2*exp(-Edes_co2*1000.0/R/Tsur)*pow(Tsur/Tref,Bdes_co2);
kads_h2o = s_h2o/gamma*pow(4.184*R*Tsur/2/M_PI/M_h2o,0.5)*100.0*exp(-
Eads_h2o*1000.0/R/Tsur)*pow(Tsur/Tref,Bads_h2o);
kdes_h2o = A_h2o*exp(-Edes_h2o*1000.0/R/Tsur)*pow(Tsur/Tref,Bdes_h2o);
kads_o2 = s_o2/gamma*pow(4.184*R*Tsur/2/M_PI/M_o2,0.5)*100.0*exp(-
Eads_o2*1000.0/R/Tsur)*pow(Tsur/Tref,Bads_o2);

ttha_o = 0.6; // initialize ttha_o
do
{
Edes_o2 = 49.5-32.0*ttha_o;
kdes_o2 = A_o2*exp(-Edes_o2*1000.0/R/Tsur)*pow(Tsur/Tref,Bdes_o2);
k_o2 = kads_o2*Cs_o2/kdes_o2;
ttha_o = pow(k_o2,0.5)/(1.0+pow(k_o2,0.5));
loop += 1;
} while (loop < 30);
loop = 0;

k_c4h10 = kads_c4h10*Cs_c4h10/kdes_c4h10;
k_co2 = kads_co2*Cs_co2/kdes_co2;
k_h2o = kads_h2o*Cs_h2o/kdes_h2o;

//fuel-rich condition
k_sum = k_c4h10 + k_co2 + k_h2o;
reaction1 = area_factor*gamma*kads_o2*Cs_o2*pow(1.0/(k_sum+1.0),2.0); //[mol/cm2-s]

//fuel-lean condition
reaction2 = area_factor*gamma*kads_c4h10*Cs_c4h10/pow(1+pow(kdes_o2/kads_o2/Cs_o2,0.5),2.0);

//An error function to smooth out the reaction rate near 1.0 equivalence ratio
rrratio = 1/( pow(2.71828,-sigmoida*(Eq_ratio-1))+1);
reaction = reaction1*(rrratio) + reaction2*(1-rrratio);
}
Eq_ratio_avg = (Eq_ratio_avg + Eq_ratio)/2.0;
*rr = reaction*10.0; //multiply by 10 to convert the unit to [kgmol/m2-s];
}

60

3. Solid Oxide Fuel Cell running on H
2

The solid oxide fuel cell can on H 2 and releases H 2O from the anode side and consumes
O 2 at the cathode side. Sink and source module cannot be implemented to calculate the reaction
rate for each single cell separately; therefore, surface reaction module was modified to estimate
the reaction rate on the fuel cell instead. A UDF file was implemented to estimate the different
reaction rate of H 2 and the setup in ANSYS-Fluent has to match with reactant species which is
“hydrogen-air”. After the calculation for the anode side is done, the O 2 consumption rate on the
cathode side is also calculated for another UDF file to consume O 2.

// UDF for the anode
#include "stdio.h"
#include "udf.h"
#include "math.h"
#include "mem.h"

// Species numbers. Must match order in ANSYS FLUENT dialog box
#define H2 0
#define O2 1
#define H2O 2
#define N2 3

int loop = 0;

//------------ Define Constants ---------------//
double time_step = 10.0; //[s]
double max_rr = 0.1; //[mol/cm2-s]
double gamma = 2.5e-9; //[mol/cm2]
double Tref = 300.0; //[K]
double Tavg = 300.0; //[K]
double Tfactor = 1.0; //[]
double reaction = 0.0; //[mol/s]
double volume_ano = 0.33502e-9; //[m3]
double volume_cat = 0.03490e-9; //[m3]
double Aano = 2.2973e-6; //[m2]
double Acat = 2.2973e-6; //[m2]

//H2
double xano_h2 = 0.0001; //mole fraction on the anode side
double yano_h2 = 0.0; //mass fraction on the anode side
double molano_h2 = 0.0; //[mol]
double Csano_h2 = 0.0; //[mol/m3]
double xcat_h2 = 0.0; //mole fraction on the cathode side
double ycat_h2 = 0.0; //mass fraction on the cathode side
double molcat_h2 = 0.0; //[mol]
double Cscat_h2 = 0.0; //[mol/m3]
double M_h2 = 0.002; //[kg/mol]
double LHV_h2 = 120.0e+6; //[J/kg]

//O2
double xano_o2 = 0.0;
double yano_o2 = 0.0;
double molano_o2 = 0.0; //[mol]
double Csano_o2 = 0.0; //[mol/m3]
double xcat_o2 = 0.0;
double ycat_o2 = 0.0;
double molcat_o2 = 0.0; //[mol]
61

double Cscat_o2 = 0.0; //[mol/m3]
double M_o2 = 0.032; //[kg/mol]
double n_o2 = 1.0;

//H2O
double xano_h2o = 0.0001;
double yano_h2o = 0.0;
double molano_h2o = 0.0;
double Csano_h2o = 0.0; //[mol/m3]
double xcat_h2o = 0.0;
double ycat_h2o = 0.0;
double molcat_h2o = 0.0;
double Cscat_h2o = 0.0; //[mol/m3]
double M_h2o = 0.018; //[kg/mol]

//N2
double xano_n2 = 0.0;
double yano_n2 = 0.0;
double molano_n2 = 0.0;
double Csano_n2 = 0.0; //[mol/m3]
double xcat_n2 = 0.0;
double ycat_n2 = 0.0;
double molcat_n2 = 0.0;
double Cscat_n2 = 0.0; //[mol/m3]
double M_n2 = 0.028; //[kg/mol]

double molano_tot = 0.0;
double molcat_tot = 0.0;

double rateh2 = 0.0; //[mol/s]
double rateh2_old = 0.0; //[mol/s] to prevent rateh2 to jump
double rateh2o = 0.0; //[mol/s]

extern float rateo2 = 0.0; //[W/m3] O2 consumption rate for the cathode side

//fuel cell electron calculation
double Ru = 8.314; //[J/molK] = Ru = R*4.184
double F = 96485.33; //[C/mol]
double Le = 0.000006; //[m] Electrolyte thickness

double Ades = 5.59e+15; //[1/s m2/mol]
double Gamma = 0.000026; //[mol/m2]
double gamma0 = 0.01; //[-]
double Edes = 88120.0; //[J/mol]
double Ps_h2 = 0.0; //[Pa]
double is_h2 = 85000.0; //[A/m2]
double i_0a = 0.0; //[A/m2]
double ii0a = 0.0; //temporary parameter for ii/2/i_0a

double Ao2 = 4.96493e+13; //[Pa]
double Eo2 = 200000.0; //[J/mol]
double Ps_o2 = 0.0; //[Pa]
double is_o2 = 28000.0; //[A/m2]
double i_0c = 0.0; //[A/cm2]
double ii0c = 0.0; //temporary parameter for ii/2/i_0c

//Variable
double sigma0 = 720000000.0; //[S/m]
double Ea = 120000.0; //[J/mol]
double a = 12000000.0; //[K atm^0.25/Ohm-cm]
double b = 26500.0; //[K]
double alpha_ano = 0.25;
double alpha_cat = 0.25;
double Edefine = 0.4; //[V]
double kp_fc = 2000.0; //[-]

double DelG0 = -228610.0; //[J/mol]
double E0 = 0.0; //[V]
double ff = 0.0; //[1/V]
62

double sigmai = 0.0; //[1/Ohm-m]
double k = 0.0; //[Pa^0.25/Ohm-cm]
double sigmae = 0.0; //[1/Ohm-m]
double i0 = 0.0; //[A/m2]
double ie = 0.0; //[A/m2]
double ii = 10000.0; //[A/m2] 4000.0 is just an initial value
double erfratio = 0.0;
double eta_acta = 0.0; //[V]
double eta_actc = 0.0; //[V]
double eta_actc1 = 0.0; //[V]
double eta_actc2 = 0.0; //[V]

double Ecell = 0.0; //[V]
double Rload = 0.3; //[Ohm]
double itot = 0.0; //[A]
double rateh2ec = 0.0; //[mol/s]
double rateo2ec = 0.0; //[mol/s]
double powerdens = 0.0; //[mW/cm2]

DEFINE_SR_RATE(sofc_h2, f, fthread, r, mw, xi, rr)
{
double Tano = Tfactor*F_T(f,fthread); //[K]
double rho = C_R(F_C0(f,fthread),THREAD_T0(fthread)); //[kg/m3]
int i = 0;

//Define the surface ID number of the interface of electrolyte and cathode for O2 mole fraction
Domain *d2 = Get_Domain(1);
int id2 = 58;
Thread *t2 = Lookup_Thread(d2, id2);
face_t f2;
ycat_o2 = 0.0;
ycat_n2 = 0.0;

ycat_o2 = 0.0;
ycat_n2 = 0.0;
begin_f_loop(f2, t2)
{
i = i+1;
ycat_o2 = ycat_o2 + F_YI(f2,t2,O2);
ycat_n2 = ycat_n2 + F_YI(f2,t2,N2);
}
end_f_loop(f2, t2)
ycat_o2 = ycat_o2/i;
ycat_n2 = ycat_n2/i;
molcat_o2 = ycat_o2/M_o2;
molcat_n2 = ycat_n2/M_n2;
molcat_tot = molcat_o2+molcat_n2;
xcat_o2 = molcat_o2/molcat_tot;

xano_o2 = xi[O2]; //import mole fractions of species O2
if (xano_o2 < 0)
{ xano_o2 = 0.0;
error = 1; }
xano_h2 = xi[H2]; //import mole fractions of species C3H8
if (xano_h2 < 0)
{ xano_h2 = 0.0;
error = 2; }
xano_h2o = xi[H2O]; //import mole fractions of species H2O
if (xano_h2o < 0)
{ xano_h2o = 0.0; }
if (Tano < 295)
{ Tano = 300.0;
error = 3; }
if (rho < 0)
{ rho = 1.12;
error = 4; }
if ((xano_h2 > 0.0001)&&(xcat_o2 > 0.0001)&&(xano_h2o > 0.0001)&&(Tano>700))
{
Ps_h2 = Ades*pow(Gamma,2.0)*pow( 2.0*M_PI*Ru*Tano*M_h2 , 0.5)/gamma0 * exp(-Edes/Ru/Tano);
63

0.25 )*pow( xano_h2o, 0.75 )/( 1+pow((xano_h2*101325.0/Ps_h2),0.5) ));
Ps_o2 = Ao2*exp(-Eo2/Ru/Tano);
i_0c = is_o2*(pow( (xcat_o2*101325.0/Ps_o2),0.25 )/( 1+pow((xcat_o2*101325.0/Ps_o2),0.5) ));

ff = F/Ru/Tano;
E0 = -DelG0/2.0/F+Ru*Tano/2.0/F*log( xano_h2*pow(xcat_o2,0.5)/xano_h2o ); //[V]
k = a/Tano*exp(-b/Tano);
sigmae = k*pow( xcat_o2, -0.25)*100.0;
sigmai = sigma0/Tano*exp(-Ea/Ru/Tano);

loop = 0;
do
{
ii0a = ii/2.0/i_0a;
eta_acta = log( ii0a + sqrt(ii0a*ii0a+1.0) ) /alpha_ano/ff;
ii0c = ii/2.0/i_0c;
eta_actc = log( ii0c + sqrt(ii0c*ii0c+1.0) ) /alpha_cat/ff;
if ((eta_acta > 0.0)&&(eta_acta < 1.0))
eta_acta = eta_acta;
else if (eta_acta > 1.0)
eta_acta = 1.0;
else eta_acta = 0.0;
Ecell = E0 - Le/sigmai*i0-eta_acta-eta_actc;
ii = kp_fc*(Ecell - Edefine) + ii;

if (fabs(Ecell - Edefine) < 0.001)
loop = 120;
loop += 1;
} while (loop < 20);

ie = -ii*sigmae/sigmai*exp(eta_actc/2.0*ff)*(( exp(Ecell*ff)-1.0 )/( 1.0-exp(-ii*Le*ff/sigmai) ));
itot = ii+ie;
}
else
{
itot = 0.0;
ii = 0.0;
Ecell = -150.0;
rateh2_old = 0.0;
}
Pgen_factor = xano_h2/xinlet_h2*1.0;
Pgen_factor = 1.0;
if (Pgen_factor > 1.0)
Pgen_factor = 1.0;
powerdens = Pgen_factor*Ecell*itot/10.0; //[mW/cm2] 10.0 is to convert the unit.

//sum all rate
rateh2 = Pgen_factor*(1.03645e-5)*ii/2.0/10000.0;

if (rateh2 > (rateh2_old+(1.e-7)))
rateh2 = rateh2_old+(1.e-7);
else if (rateh2 < (rateh2_old-(1.e-7)))
rateh2 = rateh2_old-(1.e-7);
rateh2_old = rateh2;

if (xano_h2 < 0.001)
rateh2 = 0.0;
rateo2 = rateh2/2.0; //[mol/s]

*rr = rateh2*10.0; //[multiply by 10 to be kgmol/m2-s];
}

64

// UDF for the cathode
#include "stdio.h"
#include "udf.h"
#include "math.h"
#include "mem.h"

extern float rateo2;
double Vcat2 = 0.03490e-9; //[m3]
double Acat2 = 2.2973e-6; //[m2]

DEFINE_SOURCE(O2cat_source,f,fthread,dS,eqn)
{
float rateo2_rr1 = -rateo2*Acat2/Vcat2*10000.0; //10000.0 is the unit conversion.
return rateo2_rr1;
}

65

4. Solid Oxide Fuel Cell running on C
4
H
10

The solid oxide fuel cell running on C 4H 10 consumes C 4H 10-O 2 and releases CO 2 and H 2O
from the anode side and consumes O 2 at the cathode side. The surface reaction module was also
modified to estimate the reaction rate on the fuel cell similar to the solid oxide fuel cell running
on H 2. However, the modeling of fuel cell is slightly different, because it has to include fuel
reforming process and water gas shift reaction in the anode side and H 2 is consumed by the
interface surface between anode and electrolyte.

#include "stdio.h"
#include "udf.h"
#include "math.h"
#include "mem.h"

#define C4H10 0
#define O2 1
#define CO2 2
#define H2O 3
#define N2 4

int error = 0;
int loop = 0;

//------------ Define Constants ---------------//
double Pavg = 10.0;
double time_step_area = 0.05; //[s-m2] 0.0005 //0.0000001 //0.01 works
double max_rr = 0.1; //[mol/cm2-s]
double gamma = 2.5e-9; //[mol/cm2]
double Tref = 300.0; //[K]
double Tavg = 300.0; //[K]
double Tfactor = 1.0; //[]
double reaction = 0.0; //[mol/s]
double volume_ano = 0.33502e-9; //[m3] 1.5524 mm3
double volume_cat = 0.03490e-9; //[m3] 0.05846 mm3
double Aano = 2.2973e-6; //[m2] 3.868 mm2
double Acat = 2.2973e-6; //[m2] 3.868 mm2
double Hano = 0.64e-3; //Anode height [m2] = 0.64 mm

//powergen factor
double Pgen_factor = 0.0;

//C4H10
double xano_c4h10 = 0.00001; //mole fraction on the anode side
double yano_c4h10 = 0.0; //mass fraction on the anode side
double molano_c4h10 = 0.001; //[mol]
double Csano_c4h10 = 0.0; //[mol/m3]
double xcat_c4h10 = 0.0; //mole fraction on the cathode side
double ycat_c4h10 = 0.0; //mass fraction on the cathode side
double molcat_c4h10 = 0.0; //[mol]
double Cscat_c4h10 = 0.0; //[mol/m3]
double M_c4h10 = 0.058; //[kg/mol]
double LHV_c4h10 = 45.27e+6; //[J/kg]

//O2
double xano_o2 = 0.00001;
double yano_o2 = 0.0;
double molano_o2 = 0.0; //[mol]
double Csano_o2 = 0.0; //[mol/m3]
double xcat_o2 = 0.0;
66

double ycat_o2 = 0.0;
double molcat_o2 = 0.0; //[mol]
double Cscat_o2 = 0.0; //[mol/m3]
double M_o2 = 0.032; //[kg/mol]
double n_o2 = 1.0;

//CO2
double xano_co2 = 0.00001;
double yano_co2 = 0.0;
double molano_co2 = 0.0;
double Csano_co2 = 0.0; //[mol/m3]
double xcat_co2 = 0.0;
double ycat_co2 = 0.0;
double molcat_co2 = 0.0;
double Cscat_co2 = 0.0; //[mol/m3]
double M_co2 = 0.044; //[kg/mol]

//H2O
double xano_h2o = 0.00001;
double yano_h2o = 0.0;
double molano_h2o = 0.0;
double Csano_h2o = 0.0; //[mol/m3]
double xcat_h2o = 0.0;
double ycat_h2o = 0.0;
double molcat_h2o = 0.0;
double Cscat_h2o = 0.0; //[mol/m3]
double M_h2o = 0.018; //[kg/mol]

//H2
double xano_h2 = 0.01; //mole fraction on the anode side
double yano_h2 = 0.0; //mass fraction on the anode side
double molano_h2 = 0.0; //[mol]
double Csano_h2 = 0.0; //[mol/m3]
double xcat_h2 = 0.0; //mole fraction on the cathode side
double ycat_h2 = 0.0; //mass fraction on the cathode side
double molcat_h2 = 0.0; //[mol]
double Cscat_h2 = 0.0; //[mol/m3]
double M_h2 = 0.002; //[kg/mol]
double LHV_h2 = 120.0e+6; //[J/kg]

//CO
double xano_co = 0.01;
double yano_co = 0.0;
double molano_co = 0.00001; //[mol]
double Csano_co = 0.0; //[mol/m3]
double M_co = 0.028; //[kg/mol]

//N2
double xano_n2 = 0.00001;
double yano_n2 = 0.0;
double molano_n2 = 0.0;
double Csano_n2 = 0.0; //[mol/m3]
double xcat_n2 = 0.0;
double ycat_n2 = 0.0;
double molcat_n2 = 0.0;
double Cscat_n2 = 0.0; //[mol/m3]
double M_n2 = 0.028; //[kg/mol]

double molano_tot = 0.0;
double molcat_tot = 0.0;

double ratec4h10 = 0.0; //[mol/s]
double rateh2 = 0.0; //[mol/s]
double rateh2_old = 0.0; //[mol/s] to prevent rateh2 to jump
double rateh2o = 0.0; //[mol/s]
double rateo2ano = 0.0; //[mol/s]
double rateo2cat = 0.0; //[mol/s]
double rateco2 = 0.0; //[mol/s]
double rateco = 0.0; //[mol/s]
67

extern float rateo2 = 0.0; //[W/m3]

//Fuel reformer
double kfr = 7.0e+4; //[m6/mol2-s]
double Ea_fr = 166000.0; //[J/mol] from M.Ni 2018
double rfr = 0.0; //[mol/m2-s] reaction rate of fuel reformer per anode area
double rfr_old = 0.0; //[mol/m2-s] reaction rate of fuel reformer per anode area
double rfra = 0.0; //[mol/s] reaction rate of fuel reformer total area
double rfra_old = 0.0; //rfra from the previous roung
double ratec4h10fr = 0.0; //[mol/s]
double ratec4h10fr_old = 0.0; //[mol/s]
double ratec4h10fr_damp = 1.0e-7;
double rateo2fr = 0.0; //[mol/s]
double rateco2fr = 0.0; //[mol/s]
double rateh2ofr = 0.0; //[mol/s]
double ratecofr = 0.0; //[mol/s]
double rateh2fr = 0.0; //[mol/s]

//water-gas shift reaction
double Pco = 0.0; //[Pa]
double Ph2o = 0.0; //[Pa]
double Pco2 = 0.0; //[Pa]
double Ph2 = 0.0; //[Pa]
double rwg = 0.0; //[mol/m3-s]
double rwg_old = 0.0; //rwg from the previous round
double rateco2wg = 0.0; //[mol/s]
double rateh2owg = 0.0; //[mol/s]
double ratecowg = 0.0; //[mol/s]
double rateh2wg = 0.0; //[mol/s]

double Z = 0.0;
double Kps = 0.0;

//fuel cell electron calculation
double Ru = 8.314; //[J/molK] = Ru = R*4.184
double F = 96485.33; //[C/mol]
double Le = 0.000006; //[m] //Electrolyte thickness

double Ades = 5.59e+15; //[1/s m2/mol]
double Gamma = 0.000026; //[mol/m2]
double gamma0 = 0.01; //[-]
double Edes = 88120.0; //[J/mol]
double Ps_h2 = 0.0; //[Pa]
// temporary change
double is_h2 = 85000.0; //[A/m2]
double i_0a = 0.0; //[A/m2]
double ii0a = 0.0; //temporary parameter for ii/2/i_0a

double Ao2 = 4.96493e+13; //[Pa]
double Eo2 = 200000.0; //[J/mol]
double Ps_o2 = 0.0; //[Pa]
double is_o2 = 28000.0; //[A/m2]
double i_0c = 0.0; //[A/cm2]
double ii0c = 0.0; //temporary parameter for ii/2/i_0c

//Variable
double sigma0 = 720000000.0; //[S/m]
double Ea = 120000.0; //[J/mol]
double a = 12000000.0; //[K atm^0.25/Ohm-cm]
double b = 26500.0; //[K]
double alpha_ano = 0.25;
double alpha_cat = 0.25;
double Edefine = 0.7; //[V]
double kp_fc = 10000.0; //[-]

double DelG0h2 = -228610.0; //[J/mol]
double DelG0co = -257230.0; //[J/mol]
double E0h2 = 0.0; //[V]
68

double E0co = 0.0; //[V]
double E0 = 0.0; //[V]
double ff = 0.0; //[1/V]
double sigmai = 0.0; //[1/Ohm-m]
double k = 0.0; //[Pa^0.25/Ohm-cm]
double sigmae = 0.0; //[1/Ohm-m]
double i0 = 0.0; //[A/m2]
double ie = 0.0; //[A/m2]
double ii = 5000.0; //[A/m2] 4000.0 is just an initial value
double erfratio = 0.0;
double eta_acta = 0.0; //[V]
double eta_actc = 0.0; //[V]
double eta_actc1 = 0.0; //[V]
double eta_actc2 = 0.0; //[V]

double Ecell = 0.0; //[V]
double Rload = 0.3; //[Ohm]
double itot = 0.0; //[A]
double rateh2ec = 0.0; //[mol/s]
double rateh2ec_old = 0.0; //[mol/s] to prevent rateh2 to jump
double ratecoec = 0.0; //[mol/s]
double ratecoec_old = 0.0; //[mol/s] to prevent rateco to jump
double rateo2ec = 0.0; //[mol/s]
double rateh2oec = 0.0; //[mol/s]
double rateh2ec_cal = 0.0; //[mol/s]
double rateco2ec = 0.0; //[mol/s]
double rateec_damp = 1.0e-6; //damp, don't allow rateec jump to much
double rwg_damp = 1.0e-7; //damp, don't allow rwg jump to much
double powerdens = 0.0; //[mW/cm2]

double rrout = 0.0;

DEFINE_SR_RATE(sofc_c4h10, f, fthread, r, mw, xi, rr)
{
double Tano = Tfactor*F_T(f,fthread); // K
double rho = C_R(F_C0(f,fthread),THREAD_T0(fthread)); //kg/m3
int i = 0;

//Get O2 concentration on the cathode side
Domain *d2 = Get_Domain(1);
int id2 = 51;
//electrolyte-cat-wall1-shadow
Thread *t2 = Lookup_Thread(d2, id2);
face_t f2;
ycat_o2 = 0.0;
ycat_n2 = 0.0;

ycat_o2 = 0.0;
ycat_n2 = 0.0;
begin_f_loop(f2, t2)
{
i = i+1;
ycat_o2 = ycat_o2 + F_YI(f2,t2,O2);
ycat_n2 = ycat_n2 + F_YI(f2,t2,N2);
}
end_f_loop(f2, t2)
ycat_o2 = ycat_o2/i;
ycat_n2 = ycat_n2/i;
molcat_o2 = ycat_o2/M_o2;
molcat_n2 = ycat_n2/M_n2;
molcat_tot = molcat_o2+molcat_n2;
xcat_o2 = molcat_o2/molcat_tot;

xano_o2 = xi[O2]; // import mole fractions of species O2
if (xano_o2 < 0.000001)
{ xano_o2 = 0.000001;
error = 1; }
xano_c4h10 = xi[C4H10]; // import mole fractions of species C4H10
if (xano_c4h10 < 0.000001)
69

{ xano_c4h10 = 0.000001;
error = 2; }
xano_h2o = xi[H2O]; // import mole fractions of species H2O
if (xano_h2o < 0.000001)
{ xano_h2o = 0.000001; }
xano_co2 = xi[CO2]; // import mole fractions of species H2O
if (xano_co2 < 0.000001)
{ xano_co2 = 0.000001; }
if (Tano < 295)
{ Tano = 300.0;
error = 3; }
if (rho < 0.5)
{ rho = 1.12;
error = 4; }

Csano_c4h10 = xano_c4h10*101325.0/8.314/Tano;
Csano_o2 = xano_o2*101325.0/8.314/Tano;
if ((Csano_c4h10>0.0)&&(Csano_o2>0.0))
rfr = kfr*exp(-Ea_fr/Ru/Tano)*Csano_c4h10*pow(Csano_o2,2.0)*Hano*(1-xano_c4h10);
//[mol/m2-s]
else rfr = 0.000000000;
rrout = rfr*10.0; // [multiply by 10 to be kgmol/m2-s]

ratec4h10fr = -rfr; //[mol/m2-s]
rateo2fr = -rfr*2.0; //[mol/m2-s]
ratecofr = rfr*4.0; //[mol/m2-s]
rateh2fr = rfr*5.0; //[mol/m2-s]

//Adjusting the mol fraction
molano_c4h10 = xano_c4h10; //mol_c4h10 = x_c4h10/x_tot -> x_tot is 1
molano_o2 = xano_o2;
molano_co2 = xano_co2;
molano_h2o = xano_h2o;
molano_n2 = xano_n2;
molano_co = rateco*time_step_area + molano_co; //mol_co [mol]
molano_h2 = rateh2*time_step_area + molano_h2;

molano_tot = molano_c4h10 + molano_o2 + molano_co2 + molano_h2o + molano_n2 + molano_co +
molano_h2;
xano_c4h10 = molano_c4h10/molano_tot;
xano_o2 = molano_o2/molano_tot;
xano_co2 = molano_co2/molano_tot;
xano_h2o = molano_h2o/molano_tot;
xano_co = molano_co/molano_tot;
xano_h2 = molano_h2/molano_tot;

Csano_c4h10 = xano_c4h10*101325.0/8.314/Tano;
Csano_o2 = xano_o2*101325.0/8.314/Tano;
Csano_co2 = xano_co2*101325.0/8.314/Tano;
Csano_h2o = xano_h2o*101325.0/8.314/Tano;
Csano_co = xano_co*101325.0/8.314/Tano;
Csano_h2 = xano_h2*101325.0/8.314/Tano;

Pco = xano_co*101325.0; //[Pa]
Ph2o = xano_h2o*101325.0; //[Pa]
Pco2 = xano_co2*101325.0; //[Pa]
Ph2 = xano_h2*101325.0; //[Pa]
Z = 1000.0/Tano-1.0;
Kps = exp(-0.2935*pow(Z,3.0) + 0.6351*pow(Z,2.0) + 4.1788*Z + 0.3169 );
if ((Pco > 0.0)&&(Ph2o > 0.0)&&(Pco2 > 0.0)&&(Ph2 > 0.0))
rwg = ( 0.0171*exp(-103191.0/Ru/Tano) )*( Pco*Ph2o - Pco2*Ph2/Kps )*Hano; //[mol/m2-s]
else rwg = 0.0;

if (rwg > (rwg_old+(rwg_damp)))
rwg = rwg_old+(rwg_damp);
if (rwg < (rwg_old-(rwg_damp)))
rwg = rwg_old-(rwg_damp);
rwg_old = rwg;
rateco2wg = rwg; //[mol/m2-s]
70

rateh2owg = -rwg; //[mol/m2-s]
ratecowg = -rwg; //[mol/m2-s]
rateh2wg = rwg; //[mol/m2-s]

if ((xano_h2 > 0.000001)&&(xano_co > 0.000001)&&(xcat_o2 > 0.000001)&&(xano_h2o >
0.000001)&&(xano_co2 > 0.000001)&&(Tano>700))
{
Ps_h2 = Ades*pow(Gamma,2.0)*pow( 2.0*M_PI*Ru*Tano*M_h2 , 0.5)/gamma0 * exp(-Edes/Ru/Tano);
i_0a = is_h2*(pow( (xano_h2*101325.0/Ps_h2), 0.25 )*pow( xano_h2o, 0.75 )/(
1+pow((xano_h2*101325.0/Ps_h2),0.5) ));
Ps_o2 = Ao2*exp(-Eo2/Ru/Tano);
i_0c = is_o2*(pow( (xcat_o2*101325.0/Ps_o2),0.25 )/( 1+pow((xcat_o2*101325.0/Ps_o2),0.5) ));

ff = F/Ru/Tano;
E0h2 = -DelG0h2/2.0/F+Ru*Tano/2.0/F*log( xano_h2*pow(xcat_o2,0.5)/xano_h2o ); //[V]
E0co = -DelG0co/2.0/F+Ru*Tano/2.0/F*log( xano_co*pow(xcat_o2,0.5)/xano_co2 ); //[V]
E0 = (E0h2*xano_h2 + E0co*xano_co)/(xano_h2+xano_co); //[V]
k = a/Tano*exp(-b/Tano);
sigmae = k*pow( xcat_o2, -0.25)*100.0;
sigmai = sigma0/Tano*exp(-Ea/Ru/Tano);

loop = 0;
do
{
ii0a = ii/2.0/i_0a;
eta_acta = log( ii0a + sqrt(ii0a*ii0a+1.0) ) /alpha_ano/ff;
ii0c = ii/2.0/i_0c;
eta_actc = log( ii0c + sqrt(ii0c*ii0c+1.0) ) /alpha_cat/ff;

if ((eta_acta > 0.0)&&(eta_acta < 1.0))
eta_acta = eta_acta;
else if (eta_acta > 1.0)
eta_acta = 1.0;
else eta_acta = 0.0;

Ecell = E0 - Le/sigmai*i0-eta_acta-eta_actc;
ii = kp_fc*(Ecell - Edefine) + ii;

if (fabs(Ecell - Edefine) < 0.001)
loop = 120;
loop += 1;
} while (loop < 20);

ie = -ii*sigmae/sigmai*exp(eta_actc/2.0*ff)*(( exp(Ecell*ff)-1.0 )/( 1.0-exp(-ii*Le*ff/sigmai) ));
itot = ii+ie;
}
else
{
itot = 0.0;
ii = 0.0;
Ecell = -150.0;
//rateh2_old = 0.0;
}
Pgen_factor = xano_c4h10;
if (Pgen_factor > 1.0)
Pgen_factor = 1.0;
powerdens = Ecell*itot/10.0*(xano_h2+xano_co); //[mW/cm2]
Pavg = Pavg*0.999995 + powerdens*0.000005;
//sum all rate
rateh2ec = -(1.0364e-5)*ii/2.0*xano_h2/(xano_h2+xano_co)/2.0/10000.0*(xano_h2+xano_co);//[mol/m2-s]
ratecoec = -(1.0364e-5)*ii/2.0*xano_co/(xano_h2+xano_co)/2.0/10000.0*(xano_h2+xano_co);//[mol/m2-s]
rateh2ec_cal = rateh2ec;

if (rateh2ec > (rateh2ec_old+(rateec_damp)))
rateh2ec = rateh2ec_old+(rateec_damp);
else if (rateh2ec < (rateh2ec_old-(rateec_damp)))
rateh2ec = rateh2ec_old-(rateec_damp);
rateh2ec_old = rateh2ec;
if (ratecoec > (ratecoec_old+(rateec_damp)))
71

ratecoec = ratecoec_old+(rateec_damp);
else if (ratecoec < (ratecoec_old-(rateec_damp)))
ratecoec = ratecoec_old-(rateec_damp);
ratecoec_old = ratecoec;

if (xano_h2 < 0.000000001)
rateh2ec = 0.0;
if (xano_co < 0.000000001)
ratecoec = 0.0;

ratec4h10 = ratec4h10fr; //[mol/m2-s]
rateo2ano = rateo2fr; //[mol/m2-s]
rateo2cat = rateo2ec; //[mol/m2-s]
rateco2 = rateco2ec + rateco2fr + rateco2wg; //[mol/m2-s]
rateh2o = rateh2ofr + rateh2owg + rateh2oec; //[mol/m2-s]
rateco = ratecoec + ratecofr + ratecowg; //[mol/m2-s]
rateh2 = rateh2ec + rateh2fr + rateh2wg; //[mol/m2-s]

*rr = rrout;
}

Abstract (if available)

Abstract Batteries have at most 2% of the energy density of hydrocarbon fuels, but internal combustion engine have never been successfully built to power handheld application neither. It is due to difficulties in minimizing heat and friction losses. An alternative approach is a micro-tubular solid oxide fuel cell (mT-SOFC) running on butane that does not require any moving parts to generate power. The mT-SOFC is integrated with a thermal transpiration membrane, a nanoporous medium operating as a gas pump with applied temperature gradient. Catalytic combustion on a platinum surface generates heat for the mT-SOFC and thermal transpiration membrane. ❧ The thermal transpiration membrane, catalytic combustion and mT-SOFC were each modeled separately. ANSYS-Fluent simulation results of all three components were compared with respective experimental results. Then, the transpiration membrane and catalytic combustion were integrated into a mesoscale self-sustaining and self-pressurizing combustion chamber running on butane without moving parts. The combustion chamber can supply an appropriate temperature and fuel-air mixture equivalence ratio for the mT-SOFC. The model of mT-SOFC was also developed to estimate the power generation at various operating temperatures for hydrogen and butane.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Wongwiwat, Jakrapop (author)

Core Title Mesoscale SOFC-based power generator system: modeling and experiments

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Mechanical Engineering

Publication Date 07/28/2019

Defense Date 06/17/2019

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag catalytic combustion,OAI-PMH Harvest,solid oxide fuel cell,thermal transpiration membrane

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ronney, Paul D. (committee chair), Egolfopoulos, Fokion N. (committee member), Tsotsis, Theodore T. (committee member)

Creator Email jakrapop.won@gmail.com,wongwiwa@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-198589

Unique identifier UC11663597

Identifier etd-WongwiwatJ-7659.pdf (filename),usctheses-c89-198589 (legacy record id)

Legacy Identifier etd-WongwiwatJ-7659.pdf

Dmrecord 198589

Document Type Dissertation

Format application/pdf (imt)

Rights Wongwiwat, Jakrapop

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA