MICRO-SCALE COMBUSTION ISSUES AND APPROACHES
A Thesis
Presented to the faculty of the Department of Mechanical Engineering
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
Mechanical Engineering
by
Betty Bui
FALL
2013
© 2013
Betty Bui
ALL RIGHTS RESERVED
ii
MICRO-SCALE COMBUSTION ISSUES AND APPROACHES
A Thesis
by
Betty Bui
Approved by:
__________________________________, Committee Chair
Timothy Marbach
__________________________________, Second Reader
Akihiko Kumagai
____________________________
Date
iii
Student: Betty Bui
I certify that this student has met the requirements for format contained in the University format
manual, and that this thesis is suitable for shelving in the Library and credit is to be awarded for
the thesis.
__________________________, Graduate Coordinator ___________________
Akihiko Kumagai
Date
Department of Mechanical Engineering
iv
Abstract
of
MICRO-SCALE COMBUSTION ISSUES AND APPROACHES
by
Betty Bui
Keeping up with the rapid growing technology and meeting its power demands, compact and
portable devices are desired. Electrochemical batteries currently satisfy these standards.
However, micro-combustion has advantages over lithium-ion batteries. Micro-combustion can
produce a higher power density, higher heat and mass transfer coefficients, as well as shorter
recharge duration. Utilizing hydrocarbons as a fuel in micro-combustion could lead to the
possibility of applying this technology towards aerospace and/or defense. The reduction in size
and its components would greatly benefit areas of weight and cost.
With the decrease in size of micro-combustion offers a larger surface-to-volume ratio but also
leads to flame quenching and short residence time. Sustaining combustion requires additional
methods such as heat-recirculation and porous inert media.
Micro-combustor design with a total volume of 1188 mm3 was validated. Mass flow rate of
premixed fuel/air entered the system at an axial velocity of 2.0 m/s. This design was set forth
with power production of 100 Watts. Computational fluid dynamic studies with ANSYS 13.0
Workbench help simulate the fluid flow in the proposed models. The numerical methods and
algorithm calculated fluid dynamics and heat transfer. By varying the inner annulus wall to
converge, power increase as much 13% was simulated. The pressure, temperature, and velocity
also increased as the heat loss of the total system decreased by sixth of a fraction.
v
With the variants of the angle draft annulus wall creating a compressor affect could lead to further
research to be applied to aerospace and defense technologies.
_______________________, Committee Chair
Timothy Marbach
_______________________
Date
vi
ACKNOWLEDGEMENTS
I would like to express my great appreciation to Dr. Timothy Marbach for his valuable and
constructive suggestions during the planning and development of this research work. I would
also like to extend my thanks to Dr. Dongmei Zhou and Dr. Akihiko Kumagai for their support
and guidance.
Furthermore, I would like to express my gratitude to my husband, Duy, and my family for their
support and encouragement to finalize this thesis.
vii
TABLE OF CONTENTS
Page
Acknowledgements ................................................................................................................ vii
List of Tables ........................................................................................................................... xi
List of Figures ........................................................................................................................ xii
Chapter
1. INTRODUCTION .............................................................................................................. 1
2. BACKGROUND OF STUDY ............................................................................................ 2
2.1 Micro-electromechanical Systems .............................................................................. 2
2.2 Hydrocarbons ............................................................................................................... 2
2.3 Applications ................................................................................................................. 5
3. MICRO-SCALE COMBUSTION ...................................................................................... 7
3.1 Basic Physics of Combustor ........................................................................................ 8
3.2 Physical Description of Combustor ............................................................................. 9
3.3 Combustion Process ................................................................................................... 10
4. CHALLENGES AND CONCEPT ................................................................................... 11
4.1 Approaches to Achieve Combustion in Micro-scale ................................................. 11
4.2 Meso-scale Combustion ............................................................................................. 13
4.3 Heat Recirculation ..................................................................................................... 15
4.4 Catalytic Combustion ................................................................................................ 16
4.5 Porous Inert Media Combustion ................................................................................ 17
5. COMPUTATIONAL PROCEDURES ............................................................................. 19
5.1 Introduction................................................................................................................ 19
viii
5.2 Governing Equations ................................................................................................. 19
5.3 Boundary Conditions .................................................................................................. 20
5.4 Standard Equations .................................................................................................... 22
6. VALIDITY OF MODEL .................................................................................................. 24
6.1 Baseline Combustor ................................................................................................... 24
6.2 Fluid Control Zones ................................................................................................... 24
6.3 Validation................................................................................................................... 27
6.4 Results........................................................................................................................ 29
7. MODEL PARAMETER OF STUDY ............................................................................... 36
7.1 Geometry Parameter Study ........................................................................................ 36
7.2 85° Draft Angle.......................................................................................................... 37
7.3 87° Draft Angle........................................................................................................... 42
7.4 93° Draft Angle.......................................................................................................... 47
8. FINDINGS AND INTERPRETATIONS ......................................................................... 52
8.1 Analysis of Data......................................................................................................... 52
8.2 Future Research ......................................................................................................... 56
Appendix A. Nomenclature ................................................................................................... 57
Appendix B. User Defined Function ..................................................................................... 59
Appendix C. Gas-phase reaction mechanism of hydrogen oxidation .................................... 60
Appendix D. Heat Flux at variable velocities at specified draft angles ................................. 61
Appendix E. Heat Flux along walls ....................................................................................... 62
Appendix F. Pressure distribution along converging nozzle ................................................. 63
Bibliography ........................................................................................................................... 64
ix
LIST OF TABLES
Tables
Page
1.
Table 2-1: Fuel Properties............................................................................................. 4
2.
Table 2-2: Issues of various fuel types for DoD fuel cell applications ........................ 6
3.
Table 3-1: Comparison between a conventional and micro-combustor [MIT]............. 7
4.
Table 6-1: Baseline areas and volumes ....................................................................... 25
5.
Table 6-2: Baseline Heat Transfer.……… ........................ …………………………. 31
6.
Table 6-3: Baseline Heat Losses ................................................................................. 31
7.
Table 7-1: Variation Angle Areas and Volumes ......................................................... 37
8.
Table 8-1: Heat Flux Comparison................................................................................ 53
x
LIST OF FIGURES
Figures
Page
1.
Figure 2-1: Energy Densities of Specific Fuels ............................................................ 3
2.
Figure 3-1: MIT Baseline Combustor ........................................................................... 8
3.
Figure 3-2: Cross Section of Combustor .................................................................... 10
4.
Figure 4-1: Example of computed temperatures in a Swiss roll combustion ............ 15
5.
Figure 4-2: Spiral Swiss roll temperature ................................................................... 16
6.
Figure 6-1: Baseline Combustor (millimeters) ........................................................... 26
7.
Figure 6-2: Isotropic Sectional View .......................................................................... 26
8.
Figure 6-3: Combustion process ................................................................................. 27
9.
Figure 6-4: Mesh division ........................................................................................... 28
10.
Figure 6-5: Combustor Wall Designations ................................................................. 30
11.
Figure 6-6: Baseline Pressure Contour ....................................................................... 32
12.
Figure 6-7: Baseline Temperature Contour ................................................................ 33
13.
Figure 6-8: Baseline Velocity Contour ....................................................................... 34
14.
Figure 6-9: Baseline Velocity Vector ......................................................................... 35
15.
Figure 7-1: 85° Draft Pressure Contour ...................................................................... 38
16.
Figure 7-2: 85° Draft Temperature Contour ............................................................... 39
17.
Figure 7-3: 85° Draft Velocity Contour ...................................................................... 40
18.
Figure 7-4: 85° Draft Velocity Vector ........................................................................ 41
19.
Figure 7-5: Swirl velocity patterns 87° (Left) and 85° (Right) ................................. 42
20.
Figure 7-6: 87° Draft Pressure Contour ...................................................................... 43
xi
21.
Figure 7-7: 87° Draft Temperature Contour ............................................................... 44
22.
Figure 7-8: 87° Draft Velocity Contour ...................................................................... 45
23.
Figure 7-9: 87° Draft Velocity Vector ........................................................................ 46
24.
Figure 7-10: 93° Draft Pressure Contour .................................................................... 48
25.
Figure 7-11: 93° Draft Temperature Contour ............................................................. 49
26.
Figure 7-12: 93° Draft Velocity Contour .................................................................... 50
27.
Figure 7-13: 93° Draft Velocity Vector ...................................................................... 51
28.
Figure 8-1: Pressure Comparison................................................................................. 54
29.
Figure 8-2: Velocity Comparison ................................................................................ 55
30.
Figure 8-3: Temperature Comparison .......................................................................... 56
xii
1
CHAPTER 1
Introduction
Within the past decade, small-scale combustions have made significant and encouraging progress
and development. It has proven worthy of further research contributing its efforts to
miniaturizing portable devices for many applications. Government funded agencies, such as
Defense Advanced Research Projects Agency (DARPA), National Science Foundation (NSF),
and Department of Defense (DoD) have attributed a majority of the advanced small-scale
combustions concepts and technologies.
Combustions provide an immense potential of energy source. Currently, batteries are vastly used
to provide daily demands of portable small-scale energy, such as laptops, cellular phones, etc.
However, hydrocarbon fuels have the greater potential to provide a higher amount of energy and
be more efficient than the common household batteries due to its higher energy density.
Numerous micro-engineered devices have been developed almost invisible to the naked eye [1].
DARPA has experimented with transducers to be used in commercial applications. From
accelerometers, inertial guidance systems, to chemical sensors; these macro systems are being
replaced by micro-components. The micro-components are becoming increasingly essential to
the operation of engines, transmissions, suspensions, fire-control systems, and other military
vehicle subsystems [1]. Aerospace technologies rely on micro-electromechanical systems
(MEMS). Its focus is to reduce spacecraft life-cycle cost while still delivering a spacecraft that
can perform useful science or commercial service [6]. With the size reduction not only lowers
cost, but also increases fuel efficiency.
2
CHAPTER 2
Background of Study
2.1 Micro-electromechanical Systems
Micro-eletromechanical systems, or MEMS, are chip-sized semiconductors that are used in
technologies such as GPS devices and aircraft inertial guidance units [2]. MEMS technologies
have been applied to many areas of micospacecraft. In microspacecraft, micro-propulsion system
requires for high-accuracy station keeping, altitude control, and orbit adjustment. However, the
need to reduce weight, cost, and increase operational lifetimes, MEMS can no longer compete in
the field of micro-power generation or high-specific energy power. The microscopic moving part
that acts as a sensor is considered a disadvantage. The low Reynolds number combined with the
planar nature of MEMS devices makes it more difficult to mix the reactants. Though the small
diameter of the channels may help to diffusive mixing, the residence time of the fluids in the
channels is also small and may be insufficient to ensure complete mixing [10].
With the accelerated need for a compact, long lifetime, more readily power supply, and the desire
to provide higher thermal efficiency and longevity for targeted applications, research has been
redirected towards small-scale combustion utilizing hydrocarbons.
2.2 Hydrocarbons
Conventional batteries, such as lithium ions, currently satisfy the demand for small, portable
devices, which include laptops and cellular phones. However, it can support only a few hours of
power and require several hours to charge. Compared with conventional batteries, combustion
can produce a much higher power density. Batteries have low specific energy while liquid
hydrocarbon fuels have a very high specific energy. A miniaturized power-generating lifetime
3
device, even with a relatively inefficient conversion of hydrocarbon fuels to power, would result
in increased lifetime and/or reduced weight of an electronic or mechanical system [6]. For
example, a micro-scale combustion used as a propulsion system for smaller satellites can provide
longer operational cycles and reduce the mass and volume fraction of the power systems [5].
Figure 2-1 represents the energy densities to those of common fuels. Hydrogen demonstrates the
remarkable advantage of sustaining the flame in smaller micro-combustors, despite some
disadvantages such as its storage requirements [6]. Furthermore, the advantages of hydrocarbon
fuels include low cost, improved voltage stability, no memory effect and instant recharge.
140
Energy Density (MJ/kg)
120
100
80
60
40
20
0
Fuel
Figure 2-1: Energy Densities of Specific Fuels
4
Table 2-1: Fuel Properties
Fuel Property (in air at STP unless
otherwise specified)
Hydrogen-Air
Mixture
Hydrocarbon-Air
Mixture
H2
120 kJ/g
2 cm/s
4% - 75%
2.5 - 5 cm/min
0.02 mJ
858 K
CH1.8
42.8 kJ/g
0.2 cm/s
0.6% - 4%
0.05 - 0.5 cm/min
0.25 mJ
500 K
Characteristic Reaction Time (@ 5 atm)
Flame Propagation Velocity
1 X 10-6 s
300 cm/s
1 X 10-5 s
20 cm/s
Stoichiometric Adiabatic
Flame Temperature
Fraction of Thermal Energy Radiated
2318 K
17% - 25%
2200 K
30% - 42%
Nominal Composition
Fuel Specific Heating Value
Diffusion Velocity
Flammability Limits (by volume)
Vaporization Rate w/o Burning
Minimum Ignition Energy
Auto-ignition Temperature
Table 2-1 compares the fuel properties between hydrogen-air to a common hydrocarbon-air
mixture. Hydrogen-air mixtures have been successfully burned in small volumes for micro-gas
turbines applications; however, storable hydrocarbon fuels will not combust at the desired mass
flow rates within the desired combustor volumes [17]. The rate of a hydrocarbon–air reaction is
typically 5–50 times slower than that of a hydrogen–air reaction [15]. The constant mass flow
rate and volume affects the decrease in power density. For hydrocarbon combustion, fuels such
as methane, propane, and ethylene requires the power densities decrease by a factor of 10 due to
primarily the increased reaction time. To utilize hydrocarbon fuels for practical devices,
heterogeneous catalytic processes were implemented to increase reaction rates and improve
stability.
Hydrocarbon fuels can provide a greater energy supply and be more efficient than the common
household batteries compared with its higher energy density as much as 90 percent.
Liquid hydrocarbons have an extremely high specific energy (typically 45 MJ/kg) are easily
transportable and are quite safe [10] while lithium ion batteries have an energy density of 1.2
5
MJ/kg (0.5 MJ/kg for alkaline battery). Even at 10% energy conversion efficiency, hydrocarbons
fuels can provide 10 times the energy density of even the most advanced batteries. In addition,
recharging is simply refueling, which can be done very quickly [9].
The environmental issue concerns of emissions are also beneficial in small-scale combustions.
Given the small size of the devices, the emissions and heat release of nitric oxides (NOx), carbon
monoxide (CO), and unburned hydrocarbons (UHCs) would decrease in relation to size of the
combustion.
2.3 Applications
With its size to compact ratio, it can be applied in many applications such as aerospace,
automotive, and biomedical. Research and development within different fields of studies all have
a common goal intended which is to reduce emission and provide clean and stable combustion in
a portable and compact device.
One of the greatest constraints for small spacecraft is its volume. Restriction with volume
dictates its propulsion and power capacity. To date, series of combustion-based micro power
systems have been successful. These micro-engines include micro-gas turbines, microthermoelectric devices, and the micro thermo-photovoltaic (TPV) systems. Power generation is
broken into four subcategories: micro-combustors, heat engines, rockets, and fuel cells. Although
combustors and rockets are not power generators by themselves, they can be used in conjunction
with power devices, such as thermoelectric, piezoelectric, inert fluid cycles, to produce electrical
power and are therefore included here because of their combustion component [10]. Fuel cells
are not necessarily a combustion device; however, the catalytic combustion within the cell
classifies it as a fuel cell. Currently, DARPA are working to develop thermoelectric power
generator, and a single-chamber solid-oxide fuel cell, micro-scale jet or rocket engine.
6
Micro-gas turbine applied in propulsion is capable of producing 10-100 Watts of electrical power
while occupying less than 1 cm3 and consuming approximately 7 grams of jet fuel per hour [19].
Furthermore, propulsion systems are expected to perform multiple functions ranging from high
thrust and ΔV, change in velocity, to fine impulse bits. Generally, low-impulse bit functions are a
good fit for electric propulsion while high thrust missions are a good fit for chemical systems
[21]. Another advantage of a micro-engine approach to propulsion is that thrust is truly modular,
so one engine design can be used over a wide range of vehicles and thus be produced in large
quantities [9]. As such, a miniaturized device even with a moderately efficient conversion of
hydrocarbon fuels to power would result in increased lifetime and/or reduced weight of an
electronic or mechanical system that are currently most often powered by electrochemical cells
[20]. Table 2-2 lists the fuel along with its challenges associated with it. Hydrogen works well as
a base fuel in fuel cell applications.
Table 2-2: Issues of various fuel types for DoD fuel cell applications
Fuel Type
Challenges for DoD Applications
JP-8, JP-5
Required removal of sulfur and reforming for fuel cells
Diesel
Aromatic hydrocarbon content
Gasoline
Flammable
Hydrogen
Low volumetric density; Tactical distribution issues
Methanol
Flammable; Toxic
Ethanol
Flammable; Requires reforming for fuel cells
Propane
Flammable; Requires high temperature fuel cell
Butanol
Relatively safe; Requires reforming
Biodiesel
Low sulfur content, but sulfur still needs to be removed; Requires
high temperature fuel cell; Cold temperature start up issues.
7
CHAPTER 3
Micro-scale Combustion
Similar to conventional gas turbine combustor modeled after the thermodynamic Brayton cycle,
the functional requirements of a micro-scale combustion involves the efficiency conversion of
chemical energy to fluid thermal and kinetic energy with low total pressure loss, reliable ignition,
and wide flammability limits [15]. However, satisfying these requirements is much more difficult
on a micro-scale. MIT researchers have compared several parameters of the conventional
combustor against the micro-combustor in Table 3-1.
Length
Conventional Combustor
0.2 m
Micro-combustor
0.001 m
Volume
0.073 m3
6.6 x 10-8 m3
Cross-sectional area
Inlet total pressure
Inlet total temperature
Mass flow rate
Residence time
Efficiency
Pressure ratio
Exit temperature
0.36 m2
37.5 atm
870 K
140 kg/s
7 ms
> 99%
> 0.95
1800 K
6.0 x 10-5 m2
4 atm
500 K
1.8 x 10-4 kg/s
5 ms
> 0.9
> 0.95
1600 K
Power density
1960 MW/m3
3000 MW/m3
Table 3-1: Comparison between a conventional and micro-combustor [MIT]
Shown in Figure 3-1 is MIT’s baseline engine schematic that was modeled after its larger
counterpart. The combustion process will be covered in the next section.
8
Figure 3-1: MIT Baseline Combustor
Although there is no universal definition of small-scale combustion, it can be defined within three
categories: macro, meso, and micro. Macro-scale includes characteristic geometry larger than 1.0
centimeters; micro-scale is less than 1.0 millimeters, and meso-scale covering the range between
macro and micro, where the parameters are in the combustion chamber, not device.
3.1 Basic Physics of Combustor
Small-scale combustion device utilizes the combustion and transforms the chemical energy into a
usable energy by directing the energy towards the combustion zone. Fuel-air mixture is
introduced into the device and ignites to reach its lower flammability limit. Chemical reaction
occurs within the reactants and energy is released. Once the combustion is initialized, the
reaction of the products increases the energy and temperatures approach equilibrium. The release
of energy transitions from the combustor to the exhaust port. The energy can then be collected
and harnessed with a power conversion device. Convective heat energy is also transferred
through the exterior walls by conducting through the interior walls, all while radiating across the
annulus or by convection across the annulus.
9
The advantage of micro-combustors is that the devices do not have moving parts, which
simplifies its complexity. However, the tradeoff lies in “low efficiency, suffer from the difficulty
of maintaining a large temperature drop across the thermoelectric material, because of small scale
of devices and because of good electrical conductors [10].” However, challenges of
manufacturing small-scale power generators can be difficult as well as material failure and flame
stability. Scaled-down systems properties are not linear and will require modifications.
3.2 Physical Description of Combustor
The basic layout of the combustor is shown in Figure 3-2. The cylindrical design has been
proven to maximize heat transfer to and from the combustion zone.
1. Location of reactants, fuels and air enter combustor.
2. Location of reaction mixture enters the combustion zone.
3. Location of porous inert medium.
4. Direction of heat transfer via conduction through the walls.
5. Location of products exiting the combustor.
10
Figure 3-2: Cross Section of Combustor
3.3 Combustion Process
Combustion is the sequence of exothermic chemical reaction between a fuel and an oxidant
accompanied by the production of heat and conversion of chemical species [14]. Heat is
generated volumetrically and it is lost to the surroundings via conduction, convection and
radiation. In macro-scale combustion, the heat losses to the chamber walls are usually small
relative to the heat generated by the chemical reaction so quenching is not a problem. However,
special consideration must be made for the small scale of a micro-combustion chamber because
so much of a higher proportion of the combustor volume is in contact with the combustor’s walls
at the micro-scale, heat losses must be included in any combustion model [14].
11
CHAPTER 4
Challenges and Concept
For micro-scale combustions, reducing the size of the combustor affects many areas such as fluid
mechanics, heat transfer, and chemical reaction significantly. As the size decreases, the surfaceto-volume ratio increases which can also lead to Reynolds number and flame dimensions to
become too small, and can lead to incomplete combustion. The timing of the combustion is also
very important. The stability in the combustion relies on the chemical reaction and residence
time. Maintaining the reaction becomes a challenge. Thus, additional measures are required to
sustain combustion. Factors as such heat recirculation, reactant preheating, catalytic combustion,
and/or porous medium can improve and assist with micro-scale combustion.
The surface-to-volume ratio increases, which combined with the enhanced heat flux, results in
heat transfer effects becoming very important at the surface or boundary of the device. Heat
transfer by natural convection decreases due to the induced buoyant flow decreasing. If the heat
transfer out of the system is greater than the heat released from the chemical reaction, the
combustion is considered “quenched”, the heat release cannot keep up with the heat loss, and the
energy source begins to diminish.
4.1 Approaches to Achieve Combustion in Micro-scale
Understanding the physics and concepts related to micro-scale combustion, and implementing
heat transfer principles and qualitative fluid dynamics; micro-scale combustion is feasible. The
objective of these studies are to develop a portable and sustainable combustion. Compared to a
conventional combustor, a micro-combustor is more highly constrained by inadequate residence
time for complete combustion and high rates of heat transfer from the combustor [18].
12
Damkohler number, Da , given in equation 4.l, is the fundamental time constraint for the ratio
between the fluid dynamic time, which defines how much time the fluid takes to get to the
combustion chamber (τresidence), and the chemical reaction time (τreaction).
𝐷𝑎 =
𝜏𝑟𝑒𝑠𝑖𝑑𝑒𝑛𝑐𝑒
𝜏𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛
(4.1),
For a complete reaction, Da should be greater than one. Residence time is determined by the size
of the combustion chamber and the flow rate of the reactant stream through the chamber as
expressed in equation 4.2. Reaction time is primarily a function of fuel properties and the
mixture temperature and pressure expressed in equation 4.3.
𝜏𝑟𝑒𝑠𝑖𝑑𝑒𝑛𝑐𝑒 ≈
𝑣𝑜𝑙𝑢𝑚𝑒
𝑉𝑃
(4.2)
=
𝑣𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 𝑚̇𝑅𝑇
[𝑓𝑢𝑒𝑙]𝑜
𝜏𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 ≈
𝐴[𝑓𝑢𝑒𝑙]𝑎 [𝑂2 ]𝑏 𝑒
−𝐸𝑎
⁄𝑅𝑇
0
(4.3)
Where V is the volume, P the pressure, 𝑚̇ the mass flow, T the temperature, and R the gas
constant. A chemical reaction time can be approximated by an Arrhenius type expression. Ea is
the activation energy while A, a, and b are empirically determined. In order to sustain
combustion, fluid dynamic times will need to increase, while chemical times will need to be
reduced. Refer to Appendix C for common gas-phase constants. NASA has also developed a
software, CEA (Chemical Equilibrium with Applications), to calculate chemical equilibrium
compositions and properties of complex mixtures.
The Peclet number, equation 4.4, is defined as the ratio of the diffusion time to the residence
time.
𝑃𝑒 =
𝜏𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑣𝑏 𝑑ℎ
=
(4.4)
𝜏𝑟𝑒𝑠𝑖𝑑𝑒𝑛𝑐𝑒
𝐷𝐴,𝐵
𝑅𝑒 =
𝜌𝑈𝐿
(4.5)
𝜇
13
In addition, the fluid mechanic effects in terms of the Peclet number and Reynolds number,
equation 4.5, will play certain roles in the mixing and combustion in the micro-combustor. The
terms in Reynolds numbers are represented as ρ as density, U as the velocity scale, L as the length
of flow, and µ as the dynamic viscosity. With the micro-combustor, laminar flow usually
dominates the flow field and molecular diffusion becomes the major mixing mechanism [11].
Surface-to-volume ratio, which characterizes the comparison of heat loss from the surface relative
to heat generation due to combustion in the volume, is proportional to the inverse of the hydraulic
diameter. The hydraulic diameter, 𝐷ℎ , is defined in equation 4.6.
𝐷ℎ = 4
𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎
(4.6)
𝑤𝑒𝑡𝑡𝑒𝑑 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟
It also effects the residence time, diffusion time, and chemical reaction timescales. These scale
dependencies determine the importance placed on different parameters within the structural
design process.
4.2 Meso-scale Combustion
By reducing the scale of combustion, the residence time and the diffusion timescales may
decrease as well. However, the chemical reaction time scale may increase as the surface-tovolume ratio is increased, therefore the reaction inside the combustor may be suppressed or
incomplete. Mehra and Waitz (1998) were the first to successfully develop a hydrogen-air
mixture combustor of 0.066 cubic centimeters compatible for an engine geometry. Waitz
supported that a micro-scale combustor is more highly constrained by inadequate residence time
for complete combustion and high rates of heat transfer from the combustor [17].
There is a tradeoff between flow residence time and power density. High power density requires
high mass flow rates through small chamber volumes. And thereby mass flow rate per volume,
𝑚̇, cannot be reduced without affecting the power density in the device, equation 4.7.
14
𝑃𝑜𝑤𝑒𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 ∝
̇
𝑚̇ 𝑚𝑓 𝐿𝐻𝑉
𝜌
∝
∝
(4.7)
𝑉
𝑉
𝜏𝑟𝑒𝑠𝑖𝑑𝑒𝑛𝑐𝑒
Where LHV is the lower heating value of the fuel and ρ the fluid density.
Considering heat transfer, Biot numbers associated with microstructures will generally be
uniform body temperatures, unless boundary heat transfer coefficient is large enough for Bi >0.1,
which is unlikely. The Biot number, Bi, is a dimensionless number in heat transfer that gives the
ratio of heat transfer resistances inside of and at the surface of the body, equation 4.8.
𝐵𝑖𝑜𝑡 𝑁𝑢𝑚𝑒𝑟 =
ℎ𝐿𝑐
(4.8)
𝑘𝑏
where h is the film coefficient, heat transfer coefficient, or convective heat transfer coefficient,
LC is the characteristic length, which is commonly defined as the volume of the body divided by
the surface area of the body, such that 𝐿𝑐 =
𝑉𝑏𝑜𝑑𝑦
𝐴𝑠𝑢𝑟𝑓𝑎𝑐𝑒
, and kb is the thermal conductivity of the
body.
The gas temperature in a micro-combustor is much higher due to the larger micro fluidic channel
and as a result, the mean free path of the gases in the micro-combustor becomes large. The
combustion flow in a micro-combustor is still regarded as continuum flow. Therefore, the
governing equations for conventional combustion still apply. The Knudsen number, Kn, shown
in equation 4.9, effects on the temperature and flow field in micro-combustion.
𝐾𝑛 =
𝜆
(4.9)
𝐿
Where λ is the mean free path, L is the representative physical length scale. Research concludes
that the first effects of the non-continuity appear for values of Kn = 0.1, while the continuous
model loses its validity at Kn = 0.3.
15
4.3 Heat Recirculation
Compared with conventional combustor, micro-scale combustions heavily rely on heat
recirculation. Heat is transferred from the flame source through upstream conduction preheating
the unburned mixture, which may lead to increasing the reaction zone in micro-combustors [6].
Weinberg developed a combustor design to recycle gas energy with a Swiss roll geometry. The
Swiss roll combustor geometry contains a combustion chamber in the center with a path of long
channels wrapped. Its simple geometry of no moving parts and spiral design minimized the heat
loss to the environment by utilizing the combustor walls. This design utilized heat recirculation
within parallel channels in opposite flow rate of the reactants and the products. This method
creates large excess enthalpy with high combustion efficiency. Steady combustion was achieved
with mixtures well below the normal flammability limits. In addition, the flame temperature is
higher than the adiabatic flame temperature of the reactants at inlet conditions. Figure 4-1
displays the temperature contours, blue at the inlet with initial temperatures, while red being the
combustion chamber with high temperatures.
Figure 4-1: Example of computed temperatures in a Swiss roll combustion
16
Ronney and Ahn applied heat recirculation to a micro-scale Swiss roll design. The reactants and
products in separate spiraling counterflow passages upstream and downstream of the reaction
zone are shown in Figure 4-2. Combustion was achieved over a wide range of flow velocities and
equivalence ratios using both gas phase and catalytic combustion. These studies demonstrated
that heat recirculation is a viable method of achieving and sustaining combustion in small
volumes. [13].
Figure 4-2: Spiral Swiss roll temperature
4.4 Catalytic Combustion
The increase of the surface-to-volume ratio of the combustor presents a problem for gas-phase
reaction, and surface heat loss is a problem that also affects the catalytic reaction. By applying a
proper catalyst, the activation energy of the reaction can be lowered significantly to enhance the
reaction rate in low-temperature. Combustion can be initiated and sustained with only pure gasphase reactions. Unlike the gas-phase reactions, surface reactions are not very sensitive to the
reduced size of micro-combustors, which can subject to further shrinking of micro-combustors.
17
Anh studied both the gas-phase and catalytic combustion in a Swiss roll and concluded that the
catalytic combustion increased the reaction rates, which made it more favorable over the gasphase reaction. The high surface-to-volume ratio and small length scales suits well with catalytic
combustion. A catalyst lowers the reaction’s activation energy. At lower temperatures, catalytic
combustion would also be faster than gas-phase combustion [21].
4.5 Porous Inert Media Combustion
Another technique to stabilizing micro-scale combustion is use of porous media. Porous
materials are utilized in many applications to function as a filter, sieve, membrane, heat
insulators, catalyst supports, radiant burners, etc. The porous material has a skeletal structure
containing voids or pores, called a matrix. In a porous inert media (PIM), combustion takes place
“three dimensional solid porous matrix having interconnected pores [6].” The porous surface
material offers high combustion efficiencies with low emissions. The conventional combustion
has properties of a free flame, thin reaction zone and high temperature gradients leads to gaseous
products and have a low thermal conductivity.
Apart from convection, the conduction and radiation modes of heat transfer are also activated [6].
PIM allows the local temperature in a combustor to increase above adiabatic flame temperature
through preheating incoming reactants using thermal energy from combustion products. The
flame in the combustion chamber convectively heats up the porous medium, which then transfers
upstream to preheat the inert mixture via radiation. Stabilization is achieved, as the effective
flame is equal to that of the incoming velocity. These characteristics seem favorable to microcombustion because the pre-heating is useful in increasing the flame temperature, and therefore
sustaining flames in a smaller space.
18
Chou et al. simulated the combustion process in a micro-cylindrical combustor filled with porous
media and found that a higher and more uniform temperature distribution can be achieved along
the wall of the micro-combustor. Recently, Marbach and Agrawal integrated heat recuperation
with PIM, for a methane combustion [12].
Marbach and Agrawal used silicon-carbon (SiC) coated carbon foam as PIM. PIM inside the
combustor rather than on the surface extended the lean blowoff (LBO) limit, which also improved
fuel prevaporization and premixing with air for liquid fuel applications.
Combinations of these methods have been experimented analytically to support micro-scale
combustion are feasible and realistic. Within this thesis, studies are conducted through
computational fluid dynamic modeling.
19
CHAPTER 5
Computational Procedures
5.1 Introduction
This section will cover the fundamental governing equations of fluid dynamics, thermodynamics,
and heat transfer computations associated with micro-scale combustions.
5.2 Governing Equations
To model the combustor as accurately to scale, the design has to follow a few basic principles.
The governing equations for multiphase thermo-fluid problems are the mass, momentum and
energy conservation equations. For Newtonian and incompressible fluids with constant physical
properties, the governing equations in conservative forms are continuity, momentum, and energy
equations 5.1 – 5.5.
Conservation of mass:
𝜕
𝜕
𝜌𝑣𝑟
(𝜌𝑣𝑧 ) + (𝜌𝑣𝑟 ) +
= 𝑆𝑚 (5.1)
𝜕𝑧
𝜕𝑟
𝑟
where 𝜌 is the density, 𝑣𝑧 is the axial velocity, 𝑣𝑟 is the radial velocity, and 𝑆𝑚 is a mass source.
Conservation of momentum in axial:
1 𝜕
1 𝜕
(𝑟𝜌𝑣𝑧 𝑣𝑧 ) +
(𝑟𝜌𝑣𝑟 𝑣𝑧 )
𝑟 𝜕𝑧
𝑟 𝜕𝑟
=−
𝜕𝑃 1 𝜕
𝜕𝑣𝑧
2
1 𝜕
𝜕𝑣𝑧 𝜕𝑣𝑟
+
) − ⃗∇ ∙ 𝑣 ] +
+
)] + 𝑆𝑧 (5.2)
[𝑟𝜇 (2
[𝑟𝜇 (
𝜕𝑧 𝑟 𝜕𝑧
𝜕𝑧
3
𝑟 𝜕𝑟
𝜕𝑟
𝜕𝑧
20
Conservation of momentum in radial direction:
1 𝜕
1 𝜕
(𝑟𝜌𝑣𝑧 𝑣𝑟 ) +
(𝑟𝜌𝑣𝑟 𝑣𝑟 )
𝑟 𝜕𝑧
𝑟 𝜕𝑟
=−
+
⃗ ∙𝑣 =
Where: ∇
𝜕𝑣𝑧
𝜕𝑧
𝜕𝑃 1 𝜕
𝜕𝑣𝑟
𝜕𝑣𝑟
1 𝜕
𝜕𝑣𝑟 2
𝑣
⃗ ∙ 𝑣 ))] − 2𝜇 𝑟
+
)+
− (∇
[𝑟𝜇 (2
]+
[𝑟𝜇 (2
𝜕𝑟 𝑟 𝜕𝑧
𝜕𝑧
𝜕𝑧
𝑟 𝜕𝑟
𝜕𝑟 3
𝑟2
2𝜇
𝑣2
⃗ ∙ 𝑣 ) + 𝜌 𝑧 + 𝑆𝑧 (5.3)
(∇
3𝑟
𝑟
+
𝜕𝑣𝑟
𝜕𝑟
+
𝑣𝑟
𝑟
(5.4)
Conservation of Energy:
𝜕
𝜌𝑣𝑟2
𝜕
𝜌𝑣𝑧2
1 𝜕
𝜕𝑇
(𝑟𝑘 )) + 𝑆𝐸 (5.5)
(𝜌𝑐𝑝 𝑣𝑟 𝜕𝑇 +
) + (𝜌𝑐𝑝 𝑣𝑧 𝜕𝑇 +
)=(
𝜕𝑟
2
𝜕𝑧
2
𝑟 𝜕𝑟
𝜕𝑟
𝑆𝐸 is the energy source.
5.3 Boundary Conditions
For the cylindrical design, the boundary conditions for axial and radial are symmetric, for which
was assumed to be zero due to the normal diffusive fluxes for temperature and velocity in the
axial and radial direction equation 5.6.
𝜕2𝑇
𝜕 2 𝑣𝑧
𝜕 2 𝑣𝑟
=
0,
=
0,
= 0,
𝜕𝑧 2
𝜕𝑧 2
𝜕𝑧 2
(5.6)
Wall boundary conditions were applied at the exterior surfaces with no-slip conditions for
velocity calculations.
Convective Heat Flux between exterior surfaces and ambient are shown in equation 5.7:
𝑞 = ℎ∞ (𝑇𝑤 − 𝑇𝑓 ) + 𝜀𝑒𝑥𝑡 𝜎(𝑇𝑤4 − 𝑇𝑓4 )
(5.7)
21
ℎ∞ as convective heat transfer coefficient, 𝑇𝑤 as temperature at wall, 𝑇𝑓 as temperature of fluid,
𝜀𝑒𝑥𝑡 as emissivity at the surface, and 𝜎 as Stefan-Boltzmann coefficient.
To incorporate the mass source zone volume, 𝑆𝑚 , was calculated by dividing the total mass flow
rate, 𝑚̇, by the volume of the source zone, equation 5.8 to represent the uniform injection of fuel
and air.
𝑆𝑚 =
𝑚̇𝑠𝑜𝑢𝑟𝑐𝑒
(5.8)
∀𝑠𝑜𝑢𝑟𝑐𝑒𝑧𝑜𝑛𝑒
The PIM zone was challenging to model. The energy source and sink terms accounted for the
complexness. In order to closely replicate flame behavior, a scaling factor was added to the
energy source zone equation 5.9. The magnitude of the heat generation in each cell was equal to
the local mass flow rate (axial velocity multiplied by density) in the cell, divided by the average
mass flow rate through the heat source zone [13].
The heat source mass flow rate equation:
𝑆𝑚 =
𝑚̇𝑠𝑜𝑢𝑟𝑐𝑒
𝑣𝑙𝑜𝑐 ∙ 𝜌𝑙𝑜𝑐
∙
(5.9)
∀𝑠𝑜𝑢𝑟𝑐𝑒𝑧𝑜𝑛𝑒 𝑣𝑎𝑣𝑔 ∙ 𝜌𝑎𝑣𝑔
The Sink Term, 𝑆𝑖 , calculates the radiation heat exchange between inner wall of outer chamber.
By adding the sink term to the conservation of momentum equations and an effective thermal
conductivity was used in the conservation of energy. Simplifies to the power law correlation
equation 5.10.
𝑆𝑖 = −𝐶𝑜 ∙ |𝑣|𝐶1 (5.10)
The thermal conductivity porosity was based on conductivities of the solid and fluid and the
porosity using 𝑘𝑒𝑓𝑓 shown in equation 5.11.
𝑘𝑒𝑓𝑓 = 𝜙 ∙ 𝑘𝑓 + (1 − 𝜙) ∙ 𝑘𝑠 (5.11)
22
Where, keff is the effective thermal conductivity, 𝜙 is the porosity, kf is the thermal conductivity
of the fluid and ks is the thermal conductivity of the solid. The porosity of silicon carbide was
0.80 based on manufacturer specifications.
5.4 Standard Equations
The ideal gas laws for standard mass flow rate and density are shown in equations 5.12 and 5.13.
𝑚̇ = 𝜌𝐴𝑣 (5.12)
𝜌=
𝑚𝑃
𝑅𝑇
(5.13)
Since the dependence of Nusselt number on Reynolds number differs between the flow regimes,
laminar flow was assumed throughout the combustion process. Reynolds number, in the laminar
case provides Nusselt number shown in equation 5.14.
5
𝑁𝑢𝑑 ∝ √𝑅𝑒𝑑4 (5.14)
As a result, the convective heat transfer coefficient is provided in equation 5.15.
ℎ∞ =
𝑘 ∙ 𝑁𝑢𝑑
(5.15)
𝑑ℎ
is inversely proportional to the fifth root of the hydraulic diameter, 𝐷ℎ .
The ideal combustion process in which the fuel is burned completely with theoretical air is called
stoichiometric. The equation for combustion for methane and air is expressed as equation 5.16:
𝐶𝐻4 +
2
2
2
(𝑂2 + 3.76𝑁2 ) → 𝐶𝑂2 + 2𝐻2 𝑂 + ( ) (3.76)𝑁2 + (( ) − 2) 𝑂2 (5.16)
𝜙
𝜙
𝜙
To quantify the amounts of fuel and air is given in equation 5.17, the air-fuel ratio, AF, which is
usually expressed on a mass basis.
𝐴𝐹 =
𝑚𝑎𝑖𝑟
(5.17)
𝑚𝑓𝑢𝑒𝑙
23
The amount of air used in combustion process can also be expressed as an equivalence ratio in
equation 5.18:
𝜙=
(𝑚̇𝑓 ⁄𝑚̇𝑎 )𝑎𝑐𝑡𝑢𝑎𝑙
(𝑚̇𝑓 ⁄𝑚̇𝑎 )𝑠𝑡𝑜𝑖𝑐ℎ𝑖𝑜𝑚𝑒𝑡𝑟𝑖𝑐
(5.18)
Flame stability is dependent on fuel lean mixtures, small lower heating value fuel and heat loss,
etc. As fuel/air equivalence ratio gradually decreases, the flame will nearly reach blow-off point,
LBO. Flame temperature can be calculated with NASA CEA for adiabatic flame temperature. In
reality, combustion processes are never perfect or complete.
24
CHAPTER 6
Validity of Model
6.1 Baseline Combustor
The baseline model was developed and verified with previous research under specified
parameters from Marbach and Deal. The baseline combustor consists of four parts: two
concentric cylinders, an outer chamber, and a combustion chamber; lid, and porous inert media.
The diameter of the outer chamber is 11 millimeters (mm), with a shell thickness 0.5 mm and
height of 12.5 mm. The combustion chamber has an inside diameter of 6.5 mm and 10 mm in
length. The physical dimensions are also outlined in Figure 6-1. The PIM is located at the
entrance of the combustion chamber. The material for the PIM is silicon carbide coated carbon
foam. Table 6-1 lists volumes and areas for the baseline combustor. An isotropic sectional view
of the assembly is shown in Figure 6-2.
The combustion process, previously described in Chapter 3.2, is modeled in Figure 6-3, with the
white arrows showing the fuel/air mixture flow, while the smaller black arrows shows the heat
transfer within the system. The combustor design here was set to optimize power production of
100 Watts of electricity.
6.2 Fluid Control Zones
The combustor was compiled of five volume fluid control regions: mass source zone, annulus
zone, porous zone, energy source zone, and exhaust zone. The mass source zone is where the
fuel and air is premixed prior to entering the combustor, shown as the blue disk in figure 6.1 and
figure 6.2. The mass source is determined by equation 6.1,
𝑀𝑎𝑠𝑠 𝑆𝑜𝑢𝑟𝑐𝑒 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 =
𝑚𝑎𝑠𝑠 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒
(6.1)
𝑠𝑜𝑢𝑟𝑐𝑒 𝑣𝑜𝑙𝑢𝑚𝑒
25
where the mass flow rate is calculated equation 6.2.
𝑀𝑎𝑠𝑠 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 = 𝜌𝜈𝐴 (6.2).
The fuel and air mixture enters at an axially velocity of 2.0m/s downstream, towards the base of
the combustor, along the annulus. Air was chosen as the working fluid because it accounted for
approximately 95% of the reactant mass in experiments and nitrogen, the main constituent of air,
accounted for over 70% of the product mass [14]. The reactants then travel up towards the
porous inert media shown in red. The porous zone employs the power law in equation 5.10 with
the constant values of CO = 10,000 and C1 = 1.2 and with a porosity of 0.8.
The energy source was modeled as a sustained flame with varying heat release with its velocity
and modified heat source mass flow equation 5.9 within the cell zone. The thickness of the
energy source was 2.0e-4 mm. Due to the unsteady state and its dynamic conditions of the
energy source, a user defined function (UDF) was compiled in C language and used to express
the region more accurately as referenced in Appendix B. The exhaust zone was modeled as an
open fluid with no conditions or limits applied.
Table 6-1: Baseline areas and volumes
Baseline Combustor Volumes and Surface Areas
Mass Source Volume
mm3
17.18
Mass Source Area
mm2
34.36
Annulus Volume
3
mm
483.51
PIM Volume
mm3
82.96
PIM Inlet Surface Area
mm2
33.18
PIM Exit Surface Area
2
mm
33.18
PIM Contact Area
mm2
51.05
Exhaust Volume
mm3
248.87
Exhaust Surface Area
2
mm
331.83
Exterior Wall Surface Area
mm2
274.89
3
1187.91
Total Combustor Volume
mm
26
Figure 6-1: Baseline Combustor (millimeters)
Figure 6-2: Isotropic Sectional View
27
Figure 6-3: Combustion process
6.3 Validation
Software simulation cuts cost in building a prototype, however, the tradeoff in simulations can
present some errors. To simulate the results, computational fluid dynamics (CFD) software,
ANSYS 13.0 Workbench was utilized to create the geometry, mesh, and setup of the boundary
conditions to validate the models. Its capabilities can compute various fluid properties and
demonstrate the heat effects within the geometry. A uniform grid with 5593 nodes and 5332
elements was best fitted for the combustor geometry. Figure 6-4 shows the mesh division.
For a pressure-velocity based method, ANSYS Fluent SIMPLE algorithm along with first-order
upwind scheme was used to converged results. Additional general solver options of steady and
axisymmetric were applied. The energy equation was activated in the models. Ideal-gas air fluid
28
properties were Cp = 1005 J/kg·K, thermal Conductivity, 𝑘𝑎𝑖𝑟 =0.0266 W/ m·K, viscosity, υ =
1.787e-05, and molecular weight of air M =28.966 kg/kmol.
The combustion chamber, outer walls, and lid were made of stainless steel. Physical stainless
steel properties are in the Fluent library as ρ = 8030 kg/m3, Cp = 502 J/kg·K and 𝑘𝑠𝑡𝑒𝑒𝑙 = 16.27
W/m·K. A constant convective heat transfer coefficient of h∞ 12.0 W/m2K was assumed along
with emissivity of 0.8 for stainless steel, and h = 12 W/ m2·K.
Multiple cell fluid zones were connected and formed as one continuous working fluid. The
operating conditions of the combustor were 𝑇∞ surrounding of 300 Kelvin and 𝑃∞ of 101,325
Pascal. Radiation was neglected since the exterior surface temperatures were less than 600 K.
The appropriate mass flow rate according to equations 6.1 and 6.2 were applied to determine the
amount of reactants entering the system from the reactant inlet zone of a specific volume.
Figure 6-4: Mesh division
29
6.4 Results
Studies were conducted varying the velocities of 1.0 m/s, 1.5 m/s, and 2.0 m/s for the baseline
combustor as outlined in Table 6-2 in relation to wall designations outlined in Figure 6-5.
As previous studies showed, total heat transfer rate increased as velocity increased. At Vin = 2.0
m/s, heat input in the annulus raised the reactant bulk temperature of 300 K at the inlet plane to
1460 K at the exit plane. In addition, the heat loss increased as velocity decreased. Heat loss was
1.85% for Vin = 2.0 m/s, 2.44% for Vin = 1.5 m/s, and 3.60% for Vin = 1.0 m/s as listed in Table
6-3. Therefore, a higher reactant flow velocity is most suitable to reduce fractional heat loss as
well as to achieve the high energy density. The preheated reactants enter the PIM, which
provides additional preheating as well as fuel-air mixing. Heat flux with its wall designations
labeled in Figure 6-5 are calculated as well. A majority of the heat flux occurs in the outlet
region, while a small fraction is absorbed in exhaust wall 5. This design intent was to preheating
of the reactants by heat recirculation from the products.
ANSYS Workbench automatically detects boundaries interior and external walls with inlet,
outlet, and axis. Pressure contours are displayed in Figure 6-6. Initial pressures at 101,325 Pa
expand within the annulus to dissipate uniformly before the pressure flow is developed and
releases to open atmosphere. Figure 6-7 shows the temperature flow is uniform in the annulus
and steadily increase at the combustion zone where a spike occurs at the energy source. The
velocity contour flow of the combustor is shown in Figure 6-8. Figure 6-9 displays the velocity
vector of the fluid mixture. Uniform velocity patterns occur along the annulus followed by a
180° bend into the PIM to distribute evenly. At the combustion zone, velocities reach up to 12.78
m/s.
30
Figure 6-5: Combustor Wall Designations
31
Table 6-2: Baseline Heat Transfer
Velocity (m/s)
1 - Outlet
2 - Inlet
3 - Exterior
4 - Interior
5 - Exhaust
2.0
98.15
0.00
-0.01
0.00
1.86
Baseline
1.5
96.23
0.00
-0.01
0.00
3.60
Total Heat
Transfer Rate (W)
100.00
99.83
1.0
96.70
0.00
-0.01
0.00
2.43
99.12
Table 6-3: Baseline Heat Losses
Velocity
(m/s)
2.0
1.5
1.0
Exhaust
Flux
(W)
98.15
96.70
96.23
Wall
Flux
(W)
1.85
2.42
3.60
Total
Flux
(W)
100.00
99.12
99.83
Heat
Loss
(%)
1.85%
2.44%
3.60%
32
Figure 6-6: Baseline Pressure Contour
33
Figure 6-7: Baseline Temperature Contour
34
Figure 6-8: Baseline Velocity Contour
35
Figure 6-9: Baseline Velocity Vector
36
CHAPTER 7
Model Parameter of Study
7.1 Geometry Parameter Study
The proposed geometry modification to the Baseline design to improve heat flux is to vary the
angles between the combustor wall to the outer chamber wall. The concept is to study the
behavior of the fluid with converging throat along the annulus.
The micro-gas turbine combustor share similarities with the Brayton cycle. The compression
aspect of Brayton cycle draws ambient air conditions into the compressed zone where
temperature and pressure are raised. The high-pressure air continues into the combustion
chamber, where the fuel is burned at constant pressure.
Comparison studies applied in the Baseline combustor were kept constant while varying the angle
between the outer chamber and combustion chamber. The combustor length and wall thickness
remained respectively 10.0 mm and 0.5 mm. The relative mass source to correlate with the
affected area and volume adjustments are provided in Table 7-1. Pressure, temperature, velocity,
and heat flux behaviors were examined.
The maximum converging throat angle was calculated with basic trigonometry of right angle
triangle to avoid constricting flow completely. The angle between the Baseline combustor wall
and the lid is defaulted at 90°. Tangent inverse angle was calculated as 7.125° with its throat area
as zero. By setting limits and ranging the degree between the two perpendicular walls, 87° Draft
Angle were selected at increments of two degrees. The experimental angles are 85°, 87°, and the
diverging expansion angle 93° for supplementary fluid dynamics studies.
37
Table 7-1: Variation Angle Areas and Volumes
Draft Variation
Mass Source
Volume
85°
87°
93°
mm3
16.92
17.03
17.33
Mass Source Area
2
mm
95.29
95.65
96.80
PIM Volume
mm3
77.50
79.66
86.35
PIM Inlet Area
mm2
37.83
35.89
30.58
PIM Outlet Area
2
mm
33.21
33.16
33.20
Annulus Volume
mm3
389.61
436.07
559.56
Annulus Area
mm2
821.20
799.71
742.04
Exhaust Volume
3
mm
255.63
239.09
193.87
Exhaust Area
mm2
223.89
213.57
185.72
7.2 85° Draft Angle
Comparing the pressure contour, Figure 7-1 with the Baseline pressure contour Figure 6-6, the
converging annulus in the 85° Draft Angle experiences a greater pressure gradient difference with
a swirl pattern at the exit to the base of the combustor. At the inlet, pressures start out at 145 Pa
decreasing to 100 Pa along the annulus wall. The pressure distribute more uniformly after
entering the PIM. The pressures approach zero as the fluid exits. The temperatures shown in
Figure 7-2 displayed no drastic contour change from the Baseline temperature contours.
Velocity, in turn, followed the converging trend as predicted, with an increase at the throat
creating a larger velocity entering the PIM shown in Figure 7-3. Maximum velocity vector
reached was 13.87 m/s. Figure 7-4 shows the high concentration of velocity vector flow to be in
the combustion zone. The combustion velocity profile develops and increases as it exits the
combustor.
38
Figure 7-1: 85° Draft Pressure Contour
39
Figure 7-2: 85° Draft Temperature Contour
40
Figure 7-3: 85° Draft Velocity Contour
41
Figure 7-4: 85° Draft Velocity Vector
42
7.3 87° Draft Angle
The next experimental parameter is to study the fluid behavior with a less aggressive draft angle
of 87°. With a 3% angle difference compared against the Baseline combustor, the pressure
contours in Figure 7-6 mediates between the Baseline and 85° Draft Angle combustors. The
pressure decreases less incremental than 85° Draft Angle. Pressures starting at 110 Pa decrease
to 83 Pa at the throat. The swirl pressure bubble at the end of the annulus throat flows is much
smoother into the PIM region. The temperatures in Figure 7-7 showed no drastic changes. The
velocity transitioning from the throat to the PIM alleviated the velocity vortex occurring beyond
the annulus prior to entering the PIM. Figure 7-5 enlarges the velocity patterns side by side.
With a lower velocity concentration, the maximum velocity achieved here was 13.36 m/s. The
velocity contour and vector is shown in Figure 7-8 and Figure 7-9.
Figure 7-5: Swirl velocity patterns 87° (Left) and 85° (Right)
43
Figure 7-6: 87° Draft Pressure Contour
44
Figure 7-7: 87° Draft Temperature Contour
45
Figure 7-8: 87° Draft Velocity Contour
46
Figure 7-9: 87° Draft Velocity Vector
47
7.4 93° Draft Angle
The diverging 93° draft angle was introduced to view the behaviors of a diverging annulus wall.
The pressures carried more consistent values along the annulus into the base of the combustor
compared to Baseline design shown in Figure 7-9. Initial maximum pressures increased to 135
Pa compared to that of 114 Pa in the Baseline combustor although the constant pressures entering
the PIM are carried further into the PIM. The temperature contours showed similar patterns as
the Baseline combustor in Figure 7-10. With the exhaust chamber flaring open, heat was not
effectively recirculated through the walls. Combustion was only carried out on the surface of the
PIM outlet. The maximum velocity was 13.76 m/s, where its concentration of vectors expanded
on the face of the PIM outlet area.
48
Figure 7-10: 93° Draft Pressure Contour
49
Figure 7-11: 93° Draft Temperature Contour
50
Figure 7-12: 93° Draft Velocity Contour
51
Figure 7-13: 93° Draft Velocity Vector
52
CHAPTER 8
Findings and Interpretations
8.1 Analysis of Data
Converging-diverging nozzles are found in many engineering applications including steam and
gas turbines, aircraft and spacecraft propulsion systems, and even industrial blasting nozzles and
torch nozzles. The effects of backpressure on the exit velocity, the mass flow rate, and the
pressure distribution along the nozzle were expressed within this study.
Since converging combustor chamber wall is sufficiently long, inlet velocity is negligible. With
fluid velocity in the reservoir being negligible and the flow through the annulus approximated is
isentropic, the stagnation pressure and stagnation temperature of the fluid at any cross section
through the nozzle are equal to the reservoir pressure and temperature, respectively [4].
Appendix F shows the pressure distribution along a converging nozzle. If the backpressure, Pb is
equal to P1, there is no flow and the pressure distribution is uniform along the nozzle. When the
backpressure is reduced to P2, the exit plane pressure P3 also drops to P2. This causes the pressure
along the nozzle to decrease in the flow direction [4]. Backpressure is greatly expressed in the
converging draft angles of 85° and 87°.
The comparisons of pressure, velocity and temperature are graphed in Figures 8-1, 8-2, and 8-3
respectively. The horizontal axis follows points along the fluid flow generated. Starting at point
0 being the inlet, the length of the annulus ends at point 40. Points 41 to 172 represent the
midpoint of the base to the annulus with a constant y-axis value. Points 173 to 286 continue from
the midpoint to the centerline in the negative x-direction. The data points generated with ANSYS
on a cell center location basis results the plots to be abrupt at certain points. The graphical
representation would not to be best to express the parameters.
53
The heat flux amongst the Baseline and three geometries follow the similar trend in heat loss
percentage. As the velocity decreased, the heat loss increased, to reiterate a higher reactant flow
velocity is desirable to reduce fractional heat loss as well as to achieve the high energy density.
Total heat flux generated with the 85° Draft Angle increased by 15 Watts. Its heat loss was
1.79% compared with the Baseline combustor of 1.85% as shown in Table 8-1. Additional heat
fluxes at variable velocities at specified draft angles were also conducted and included in
Appendix D.
Table 8-1: Heat Flux Comparison
Exhaust Wall
Total
Heat
Flux
Flux
Flux
Loss
(W)
(W)
(W)
(%)
Baseline
98.15
1.85
100.00
1.85%
85°
113.39
2.07
115.46
1.79%
87°
107.00
1.98
108.98
1.81%
93°
89.36
1.72
91.08
1.89%
54
Pressure
1.60E+02
1.40E+02
1.20E+02
Pressure (Pa)
1.00E+02
85° Draft Angle
8.00E+01
87° Draft Angle
6.00E+01
93° Draft Angle
Baseline Draft Angle
4.00E+01
2.00E+01
0.00E+00
0
-2.00E+01
50
100
150
200
250
Pathline of Fluid Flow
Figure 8-1: Pressure Comparison
300
350
55
Velocity
1.60E+01
1.40E+01
1.20E+01
Velocity (m/s)
1.00E+01
85° Draft Angle
8.00E+00
87° Draft Angle
6.00E+00
93° Draft Angle
Baseline Draft Angle
4.00E+00
2.00E+00
0.00E+00
0
-2.00E+00
50
100
150
200
250
Pathline of Fluid Flow
Figure 8-2: Velocity Comparison
300
350
56
Temperature
1.60E+03
1.40E+03
Temperature (K)
1.20E+03
1.00E+03
85° Draft Angle
8.00E+02
87° Draft Angle
93° Draft Angle
6.00E+02
Baseline Draft Angle
4.00E+02
2.00E+02
0.00E+00
0
50
100
150
200
250
300
350
Pathline of Fluid Flow
Figure 8-3: Temperature Comparison
8.2 Future Research
The Baseline combustor was designed to output the optimal range of 100 Watts. The
backpressure in the converging walls of 85° can generate up to 115 Watts, which is an increase of
13%. Refer to Appendix E for additional details of studies at various velocities. Convergence of
the combustor wall to the outer chamber in this recirculating combustor design is a potential area
of further research for improving the heat flux to generate more power at same volumes. These
projected parameters would be beneficial to aerospace and/or defense technologies by reducing
weight and deceasing cost. Constructing a prototype could verify these results closely as outlined
in this thesis.
57
APPENDIX A
Nomenclature
A
Arrhenius pre-exponential factor
a,b
Arrhenius exponents
atm
Atmospheric pressure
CP
Specific heat capacity [J/kg·K]
d
Diameter [m]
Da
Damkohler number
Dh
Hydraulic diameter
Ea
Activation energy
h
Convective heat transfer coefficient [W/m2·K]
k
Thermal conductivity [W/m·K]
Kn
Knudsen number
L
Length [m]
ṁ
Reactant mass flow rate [kg/s]
ṁf
Fuel mass flow rate [kg/s]
M
Molecular weight [g/mol]
Nu
Nusselt number
P
Pressure [N/m2]
Pe
Peclet number
Re
Reynolds number
Sm
Mass source [kg/m3·s]
SE
Energy source
T
Temperature
58
V
Volume [m3]
vr
Radial velocity [m/s]
vZ
Axial Velocity [m/s]
ε
Surface emissivity
λ
Mean free path
φ
Porosity
ρ
Density[kg/m3]
μ
Dynamic viscosity [kg·m/s]
σ
Stefan-Boltzmann coefficient [W/m2·K4]
Φ
Combustion equivalence ratio
Greeks
59
APPENDIX B
User Defined Function
#include "udf.h"
DEFINE_SOURCE(energy_source, c, t, dS, eqn)
{
real source, Qdot, r, length, Vavg, rho;
real Vin = 2.0;
Qdot = 100;
r = 0.0325;
length = 0.002;
rho = 1.25;
source = -(Qdot/(3.1415*r*r*length))*C_U(c,t)*C_R(c,t)/(rho*Vin);
dS[eqn] = 0;
return source;
}
60
APPENDIX C
Gas-phase reaction mechanism of hydrogen oxidation22
Reactions
A
β
Ea
O2 + H = OH + O
H2 + O = OH + H
5.13E+16
1.18E+10
-0.816
1.00
16507.0
8842.7
H2 + OH = H2O + H
OH + OH = H2O + O
H2 + O2 = OH + OH
1.17E+09
6.00E+08
1.70E+13
1.30
1.30
0.00
3626.0
0.0
47780.0
H + OH + M = H2O + Ma
O2 + M = O + O + M
7.50E+23
1.85E+11
-2.60
0.50
0.0
95560.0
H2 + M = H + H + Mb
2.23E+12
0.50
92600.0
2.10E+18
6.70E+19
6.70E+19
2.50E+14
2.50E+13
4.80E+13
5.00E+13
2.00E+12
1.30E+17
1.60E+12
1.00E+13
-1.00
-1.42
-1.42
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.0
0.0
0.0
1900.0
700.0
1000.0
1000.0
0.0
45500.0
3800.0
1800.0
c
H + O2 + M = HO2 + M
H + O2 + O2 = HO2 + O2
H + O2 + N2 = HO2 + N2
HO2 + H = H2 + O2
HO2 + H = OH + OH
HO2 + O = OH + O2
HO2 + OH = H2O + O2
HO2 + HO2 = H2O2 + O2
H2O2 + M = OH + OH + M
H2O2 + H = H2 + HO2
H2O2 + OH = H2O + HO2
Rate constants are given in the form of k = ATβexp(-Ea/T).
a
Enhancement factors: H2O = 20.0.
b
Enhancement factors: H2O = 6.0, H = 2.0, H2 = 3.0.
c
Enhancement factors: H2O = 21.0, H2 = 3.3, O2 = 0.0, N2 = 0.0.
61
APPENDIX D
Heat Flux at variable velocities at specified draft angles.
Velocity
(m/s)
2.0
1.5
1.0
85° Draft Angle
Exhaust
Wall
Total
Flux
Flux
Flux
(W)
(W)
(W)
113.39
2.07
115.46
112.32
2.73
115.05
112.61
4.14
116.75
Heat
Loss
(%)
1.79%
2.37%
3.55%
Velocity
(m/s)
2.0
1.5
1.0
87° Draft Angle
Exhaust
Wall
Total
Flux
Flux
Flux
(W)
(W)
(W)
107.00
1.98
108.98
105.77
2.60
108.37
105.75
3.91
109.66
Heat
Loss
(%)
1.81%
2.40%
3.57%
Velocity
(m/s)
2.0
1.5
1.0
93° Draft Angle
Exhaust
Wall
Total
Flux
Flux
Flux
(W)
(W)
(W)
89.36
1.72
91.08
87.68
2.23
89.91
86.73
3.28
90.01
Heat
Loss
(%)
1.89%
2.48%
3.65%
62
APPENDIX E
Heat Flux along walls
Velocity (m/s)
1 - Outlet
2 - Inlet
3 - Exterior
4 - Interior
5 - Exhaust
2.0
113.39
0.00
-0.01
0.00
2.08
85°
1.5
112.32
0.00
-0.01
0.00
2.74
Total Heat Transfer Rate (W)
115.46
115.05
116.75
Velocity (m/s)
1 - Outlet
2 - Inlet
3 - Exterior
4 - Interior
5 - Exhaust
2.0
107.00
0.00
-0.01
0.00
1.99
87°
1.5
105.77
0.00
-0.01
0.00
2.61
1.0
105.75
0.00
-0.01
0.00
3.92
Total Heat Transfer Rate (W)
108.98
108.37
109.66
2.0
89.36
0.00
-0.01
0.00
1.73
93°
1.5
87.68
0.00
-0.01
0.00
2.24
1.0
86.73
0.00
-0.01
0.00
3.30
91.08
89.91
90.01
Velocity (m/s)
1 - Outlet
2 - Inlet
3 - Exterior
4 - Interior
5 - Exhaust
Total Heat Transfer Rate (W)
1.0
112.61
0.00
-0.01
0.01
4.14
63
APPENDIX F
Pressure distribution along converging nozzle4
64
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