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Studies of Swiss-roll combustors for incineration and reforming applications

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Studies of Swiss-roll combustors for incineration and reforming applications

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Content Studies of Swiss-roll Combustors for
Incineration and Reforming Applications
by
Patharapong Bhuripanyo
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(AEROSPACE ENGINEERING)
August 2024

ii
Dedication
This dissertation is dedicated to my loving family & partner.

iii
Table of Contents
Dedication ……….......................................................................................................................... ii
List of Tables .................................................................................................................................. v
List of Figures................................................................................................................................ vi
Abstract........................................................................................................................................... x
Chapter 1: Introduction................................................................................................................... 1
1.1 Background ........................................................................................................................... 1
1.2 Motivations and Applications ............................................................................................... 3
1.2.1 Fuel-Lean (Incineration) Applications ........................................................................... 3
1.2.2 Fuel-Rich (Reforming) Applications.............................................................................. 6
1.3 Literature Reviews ................................................................................................................ 9
1.3.1 General Behaviors of Swiss-roll Combustors ................................................................ 9
1.3.2 Turbulence Effects and Scaling.................................................................................... 11
1.3.3 Comparison to Linear Combustors and Geometrical Effects....................................... 12
1.3.4 Catalytic Effects ........................................................................................................... 14
1.3.5 Materials and Designs .................................................................................................. 15
1.4 Scopes of Present Studies.................................................................................................... 15
Chapter 2: Experimental and Numerical Methods........................................................................ 17
2.1 Experimental Setup ............................................................................................................. 17
2.2 Numerical Modeling ........................................................................................................... 20
2.2.1 Overview ...................................................................................................................... 20
2.2.2 General, Turbulence, and Heat Loss Submodels.......................................................... 21
2.2.3 Flame and Kinetic Models............................................................................................ 22
2.2.4 Mesh and Solution Methods......................................................................................... 24
Chapter 3: Results – Performance Tradeoff Studies..................................................................... 26
3.1 Effects of Turns................................................................................................................... 29
3.2 Effects of Fins ..................................................................................................................... 32
3.3 Effects of Inlet-to-Outlet Channel Size Ratios.................................................................... 38
Chapter 4: Results – Fuel Reforming............................................................................................ 42
4.1 Hydrocarbon Reforming ..................................................................................................... 44
4.1.1 PSR Analysis................................................................................................................ 44

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4.1.2 Two-dimensional CFD Predictions and Experimental Results.................................... 47
4.2 Ammonia Reforming........................................................................................................... 51
4.2.1 PSR Analysis................................................................................................................ 51
4.2.2 Qualitative Design Space.............................................................................................. 53
4.2.3 Two-dimensional CFD Predictions.............................................................................. 55
4.2.4 Alternative Designs ...................................................................................................... 61
4.2.5 Reformate Analysis ...................................................................................................... 66
Chapter 5: Results – Flare Performance Studies........................................................................... 71
5.1 Oscillating Flowrate Study.................................................................................................. 72
5.2 Fuel Surge Study ................................................................................................................. 73
Chapter 6: Results – Catalytic Effects.......................................................................................... 80
Chapter 7: Conclusions & Future Works...................................................................................... 83
7.1 Conclusions......................................................................................................................... 83
7.2 Future Works....................................................................................................................... 85
References..................................................................................................................................... 88
Appendices: CFD Model Supplementary Details......................................................................... 95
Appendix A: Governing Equations........................................................................................... 95
Appendix B: Turbulence Model.............................................................................................. 100
Appendix B1: Wall Function - Standard Wall Function ..................................................... 105
Appendix B2: Wall Function - Enhanced Wall Treatment ................................................. 106
Appendix C: Radiation Model ................................................................................................ 106
Appendix D: Kinetic Models .................................................................................................. 107
Appendix E: Out-of-Plane Heat Loss Model .......................................................................... 110
Appendix F: Solution Methods............................................................................................... 112

v
List of Tables
Table 1: List of notable geometries for baseline ¼-ft, 3.5-turns Swiss-roll in geometrical
studies. .................................................................................................................................. 28
Table 2: Notable dimensions of different turns combustors......................................................... 30
Table 3: Notable dimensions of varying finned combustors. ....................................................... 33
Table 4: Notable dimensions of varying inlet-to-outlet channel width ratio combustors............. 39
Table 5: Summary of key conditions used in the 3D half-core simplified model. ....................... 87
Table 6: Kinetic Models Overview............................................................................................. 108
Table 7: C3H8/C4H10-Pt Catalytic Combustion Model Summary (𝐸𝑎′ in kJoules/Mole)........... 109

vi
List of Figures
Figure 1: (Left) Swiss-roll combustor and (Right) superadiabatic combustion sustained with
heat-recirculation concepts. .................................................................................................... 2
Figure 2: (Left) 11” diameter, 12” tall Swiss-roll VOC incinerator (Crawmer, 2017) and
(Right) flare gas incinerator concept. (Chen, 2022) ............................................................... 5
Figure 3: Swiss-roll combustor-based micropower generator concepts incorporated with
(Top) thermoelectric (Merotto, 2016) and (Bottom) piezoelectric (Cho, 2009) engines. ...... 6
Figure 4: Comparisons of hydrogen’s energy density to (Left) fuel alternatives (DOE, 2017)
and (Right) other miscellaneous fuels (Ganzer, 2020). .......................................................... 7
Figure 5: (Left) Computational domain and reaction zone at Re ≈ 103 and (Right) fuel mol
percentage at extinction limits of 3.5 turns combustor, compared between experiments
and simulation with turbulence model active/suppressed (Kuo, 2006). ............................... 10
Figure 6: (Left) Swiss-roll extinction limits with turbulence, radiation, and out-of-plane heat
loss individually suppressed and (Right) maximum thermocouple temperatures and
combustion temperature comparisons at limit points between models and experiments
(Kuo, 2007)........................................................................................................................... 10
Figure 7: Computed extinction limits of varying scale combustors (Left) without property
values adjusted and (Right) with values adjusted to obtain constant α, Da and R (Chen,
2013). .................................................................................................................................... 12
Figure 8: Dimensionless excess enthalpy vs number of transfer units (NTU) for (Left) linear
heat exchanger and (Right) spiral heat exchanger at varying heat loss coefficients (α)
(Ronney 2015). ..................................................................................................................... 13
Figure 9: Extinction limits of multi-turns combustors with varying overall size with and
without* out-of-plane heat loss (Chen, 2011)....................................................................... 13
Figure 10: (Left) Surface and gas phase limits of 7.5cm x 7.5cm x 5cm, 3.5-turns combustor
and (Right) limit temperatures (Ahn, 2005). ........................................................................ 14
Figure 11: Swiss-roll design (Left) with injector for JP-8 reforming (Chen, 2018) and
(Right)3D-printed Inconel-718 combustor with fins. ........................................................... 15
Figure 12: Simplified experimental setup diagram....................................................................... 17
Figure 13: Combustor housing and flow straightener during experiment. ................................... 18
Figure 14: Flow controller box. .................................................................................................... 18
Figure 15: LabVIEW software interface....................................................................................... 19
Figure 16: Out-of-plane simplified resistance heat loss model schematic. .................................. 22
Figure 17: Propane-air extinction limits comparison between 1-step model, detailed
chemistry and experiment for 3.5-turns baseline ¼-ft scale Inconel 718 Swiss-roll............ 28
Figure 18: Geometries for 2.5-turns and 5.5-turns combustors.................................................... 29
Figure 19: Simulated extinction limits comparison between varying-turns ¼-ft scale
combustors working with C3H8-air combustor at 1 atm with the same overall, core and
feature sizes........................................................................................................................... 31

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Figure 20: Simulated EE vs ΔP tradeoff between varying-turns ¼-ft scale combustors
working with C3H8-air combustor at 1 atm with the same overall, core and feature
sizes....................................................................................................................................... 32
Figure 21: Geometries for area ratio-1.2 and area ratio-2.0 combustors...................................... 33
Figure 22: Simulated extinction limits comparison between varying-fins ¼-ft scale
combustors working with C3H8-air combustor at 1 atm with the same overall, core and
feature sizes........................................................................................................................... 34
Figure 23: Fluid zone’s average turbulence kinetic energy for each fin configuration ................ 35
Figure 24: Simulated EE vs ΔP tradeoff between varying-fins ¼-ft scale combustors
working with C3H8-air combustor at 1 atm with the same overall, core and feature
sizes....................................................................................................................................... 36
Figure 25: 1/lean ϕ limit vs channel length-to-combustor diameter ratios for two different
area-based enhancement methods (turns vs fins).................................................................. 37
Figure 26: Geometries for I25%O75% and I75%O25% channel sizes-adjusted combustors,
showing inlet halves.............................................................................................................. 38
Figure 27: Simulated extinction limits comparison between inlet-to-outlet ratios-adjusted ¼-
ft scale combustors working with C3H8-air combustor at 1 atm with the same overall,
core and feature sizes. ........................................................................................................... 40
Figure 28: Simulated EE vs ΔP tradeoff between inlet-to-outlet ratios-adjusted ¼-ft scale
combustors working with C3H8-air combustor at 1 atm with the same overall, core and
feature sizes........................................................................................................................... 41
Figure 29: Adiabatic equilibrium compositions of (Left) CH4-air and (Right) C3H8-air
mixtures at 1 atm................................................................................................................... 42
Figure 30: Adiabatic equilibrium compositions of NH3-air mixtures at 10 atm........................... 43
Figure 31: 0D PSR outlet species results for (Top) CH4-air and (Bottom) C3H8-air mixtures
at ϕ = 3 and 𝑇0 = 600 K computed with GRI-Mech III........................................................ 44
Figure 32: Major species outlet composition comparison for ¼-ft scale plain-wall Swiss-roll
combustor (operating at 𝑅𝑒 ≈ 619) between simulation (line) and experiments for
(Top) CH4-air and (Bottom) C3H8-air mixtures at 1 atm...................................................... 48
Figure 33: Outlet (Left) compositions and (Right) H and C atoms to H2 and CO conversion
ratios at fixed equivalence ratio (ϕ = 3) for ¼-ft scale, 3.5 turns Swiss-roll operating
with 300K inlet C3H8-air mixture. ........................................................................................ 49
Figure 34: Outlet (Left) mol fractions and (Right) reformed products conversion ratios at
high Re conditions and varying mixtures (Top) ϕ = 1.5, (Center) ϕ = 2.0, and (Right) ϕ
= 2.5. ..................................................................................................................................... 50
Figure 35: 0D PSR H2 yield sensitivity map of NH3-air mixtures in fixed-temperature
reactor at 10 atm.................................................................................................................... 52
Figure 36: Qualitative design space of simple-design Swiss-roll reformer for NH3 reforming. .. 54
Figure 37: Outlet H2 yield percentages of simulated 1-ft scale, 3.5-turns combustors
operating with NH3-air mixtures at 10 atm between (Top) plain-wall and (Bottom)
finned (doubled internal area) Swiss-rolls without any artificial constraints. ...................... 57
Figure 38: Outlet H2 yield percentages of simulated 1-ft scale, 3.5-turns combustors
operating with NH3-air mixtures at 10 atm between (Top) plain-wall and (Bottom)

viii
finned (doubled internal area) Swiss-rolls with flames artificially suppressed from inlet
channels................................................................................................................................. 59
Figure 39: Maximum gas temperatures for plain-wall combustors operating with (Top)
natural flame and (Bottom) artificially core-constrained flames.......................................... 60
Figure 40: Outlet H2 yields of NH3-air mixtures with NH3 (also at 300 K) directly injected at
the core’s entry (perpendicular to air stream). ..................................................................... 61
Figure 41: Flame index (non-premixed vs premixed burn) contours of 1-ft combustor at 𝑅𝑒
= 6.0x103
, ϕ = 2 operating at 10 atm across two different 300 K NH3 injection
locations. ............................................................................................................................... 63
Figure 42: Outlet H2 yield percentages of NH3-air mixtures with double-inlets, 3.5-turns,
plain-wall combustor coupled with mixing section prior to the core operating at 10 atm. .. 64
Figure 43: Outlet compositions and temperatures at varying flowrates of double-inlet
combustor coupled with mixing section prior to the core operating at 10 atm. ................... 65
Figure 44: NOx concentrations across four Re cases of double-inlet, 3.5-turns reformer with
half-turn mixing section at 10 atm........................................................................................ 66
Figure 45: Simplified zero-dimensional gas-turbine reformate analysis schematic..................... 66
Figure 46: Laminar flame speeds of outlet reformate mixtures stoichiometrically-mixed with
600 K, 10 atm compressed air, calculated with Otomo’s mechanism. ................................. 67
Figure 47: Ignition delay times of outlet reformate mixtures stoichiometrically-mixed with
600 K, 10 atm compressed air, calculated with Otomo’s mechanism. ................................. 67
Figure 48: Simplified zero-dimensional stand-alone reformer analysis with upstream fixed ϕ... 68
Figure 49: Resulting reformate mixture’s 𝑆𝐿 at varying 𝐵𝐹 and ϕ for the same original ϕ=1
NH3-air mixture at 300K, 10 atm (assumed reformer is operating at 𝑅𝑒 = 3.49x104
). ........ 69
Figure 50: Effective extinction limits for high flowrate (𝑅𝑒 = 2577) case under steady mass
flow oscillations of varying amplitude factors and frequencies for ¼-ft scale SwissRoll combustor with CH4 detailed methane GRI-Mech III chemistry. ................................ 72
Figure 51: Simulated fuel surge profile for 𝜙𝑝𝑒𝑎𝑘 = 2, 𝑇𝑠𝑢𝑟𝑔𝑒 = 8 s applied to simulatedsteady initial conditions 𝑅𝑒0 = 1546, 𝜙0 = 0.22 condition in a baseline premixed ¼-ft
combustor in 2D.................................................................................................................... 74
Figure 52: Simulated transient and steady-state comparisons between maximum gas and
solid temperature responses of ¼-ft scale Swiss-roll combustor in 2D operating at leanlimit exposed to 8-seconds methane surges with (Top) 𝜙𝑝𝑒𝑎𝑘 = 1 and (Bottom) 𝜙𝑝𝑒𝑎𝑘
= 3 under constant air mass flow at baseline 𝑅𝑒0 = 1546, 𝜙0 = 0.22. ................................. 75
Figure 53: Species response profile with 𝑇𝑆𝑢𝑟𝑔𝑒 = 8s for (Top) 𝜙𝑝𝑒𝑎𝑘 = 1 and (Middle)
𝜙𝑝𝑒𝑎𝑘 = 3 with (Bottom) comparison of CH4 and H2 to steady-state conditions. .............. 76
Figure 54: (Left) Transient temperature profiles at four RB-SiC wall locations for 𝜙𝑝𝑒𝑎𝑘 =
2, 𝑇𝑆𝑢𝑟𝑔𝑒 = 32 s case and (Right) surge duration-dependent qualitative viable
operating space...................................................................................................................... 77
Figure 55: DRE performance (time-averaged across slug duration) under different methane
surge profiles (𝜙𝑝𝑒𝑎𝑘, 𝑇𝑠𝑢𝑟𝑔𝑒) for 3.5 turns ¼-ft scale combustor operating initially at
lean-limit conditions (𝑅𝑒0 = 1546, 𝜙𝑝𝑒𝑎𝑘 = 0.22).............................................................. 79
Figure 56: Total duration which solid domain (any point) exceeds threshold 1400 K
temperature under different methane surge profiles (𝜙𝑝𝑒𝑎𝑘, 𝑇𝑠𝑢𝑟𝑔𝑒) for 3.5 turns ¼-ft

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scale combustor operating initially at lean-limit conditions (𝑅𝑒0 = 1546, 𝜙𝑝𝑒𝑎𝑘 =
0.22). ..................................................................................................................................... 79
Figure 57: (Left) Experimental configuration of ¼-ft scale rectangular Swiss-roll with
catalyst placed in the core (Ahn, 2005) and (Right) baseline mesh used in the study.......... 80
Figure 58: Extinction and transition limits comparison between 2D simulation results and
experiments (experimental data taken from (Ahn, 2005)) for ¼-ft scale rectangular
combustor with Pt catalyst.................................................................................................... 81
Figure 59: Temperature contours for three different near-extinction points (Top-Left) 𝑅𝑒 =
4, ϕ = 1.0, (Top-Right) 𝑅𝑒 = 41, ϕ = 0.26 and (Bottom) 𝑅𝑒 = 619, ϕ = 0.30....................... 82
Figure 60: Temperature contours of reduced core section (with half-turn inlet/outlet
channels) of ¼-ft scale combustor operating with single-step C3H8-air chemistry
achieved through matching of outermost core wall heat loss conditions, core outlet
pressure and core inlet temperature (same mass flowrate). .................................................. 86
Figure 61: Pressure-based COUPLED algorithm flowchart....................................................... 112

x
Abstract
This work explores the potential of heat-recirculating, thermally-efficient, “Swiss-roll”
reactors in the context of various energy-transition applications at varying scales. Without
involving any mass transfer, the simple device comprising of combustion core enclosed with builtin spiral heat exchanger allows combustion to be sustained far outside of conventional
flammability limits, both lean and rich, without any external energy input. Such “excess
enthalpy/superadiabatic” combustion mode enables (1) more efficient destruction of methane as
well as reducing susceptibility to fluctuations typical in flaring applications and (2) hydrogen
production through fuel reforming of hydrocarbons for portable-scale power generation and
ammonia for decarbonized gas-turbine applications.
The first set of contribution focuses on fuel-reforming, where corresponding detailed
kinetics were analyzed to determine yield favorability, in which design spaces for Swiss-roll
devices were subsequently inferred. Various reactor designs were explored through twodimensional computational fluid dynamics (CFD) calculations, providing insights into
mechanisms influencing hydrogen yield and highlighting key limitations of conventional singlestream Swiss-roll designs. For ammonia fuel, a promising design was proposed and the properties
of the produced high-temperature, hydrogen-rich reformates were analyzed, demonstrating
viability of Swiss-roll as fuel-reformers. The second include two different transient analyses to
determine changes in methane destruction efficiency and extinction limits in context of flares when
subjected to upstream fluctuations. Lastly, various performance improvement methods
(geometrical and catalysts) were explored, each with unique thermohydraulic performance tradeoff behaviors capable of further expanding operational limits in pursuit for more efficient
combustion and reforming.

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Chapter 1: Introduction
1.1 Background
Globally, demands for innovative energy transition technology has greatly increased over
the recent decade from the combined challenges of climate change and sustainability. Despite
commendable efforts in shifting reliance on fossil fuels towards cleaner, more renewable energy
sources (such as solar, wind, hydro and geothermal power), each with its own advantages and
shortcomings, current projections signal inescapable dependency on the former over the next
several decades (IEA, 2023; IRENA, 2023). This underscores the need for technological progress
in carbon-based technologies in short-to-medium term in order to meet 2050 Net Zero Emissions
Target per Paris Agreement in attempt to limit global temperature increase to below 1.5 ℃. In
addition to energy production, infrastructural advancements in storage, conversion and transport
technologies are also considered critical in reaching the emission target. Hydrogen (H2) storage
and reforming technologies seek to recover H2 based on ammonia (NH3), or heavier hydrocarbons
can reduce overall costs toward mass adoption of hydrogen fuels.
On a tangent note, the potential net-positive impacts from improving existing carbon-based
processes, either through increasing combustion efficiency or reduction of unnecessary greenhouse
gas (GHGs) and nitrogen oxides (NOx) emissions, are often understated. Industrial and electrical
productions-related GHG emissions currently make up just short of 50% of United States total
contributions (EPA, 2024). Globally, it is estimated that 139 billion cubic meters of natural gases
was flared in 2022 alone, very commonly with unacceptable destruction efficiency (GGFR, 2023).
Cutting down methane (CH4) emissions from such sources is considered one of the most effective
ways to slow down the rate of climate change in the short term.

2
In the mid-1970s, Weinberg and Lloyd first proposed a concept of heat-recirculating
combustion system without involving any mass transfer through single-stream Inconel 600 spiral
burners capable of extending the flammability limit of lean methane-air mixture to 1.5% fuel from
5.3% conventional limit (Lloyd 1974; Lloyd 1975). The concept was conceived to facilitate
increasing demands for low-grade fuels and tackle unneeded inefficiency in wide-range of
combustion applications. The working principles rely on multi-layered counter-current heatexchanger arranged in a spiral configuration enclosing a combusting section in the centermost core
region, per Figure 1, which effectively enables internal heat-recirculation between hightemperature products and incoming colder reactants while also largely mitigating heat losses in
conjunction. The addition of recycled thermal enthalpy from the working mixture’s heat release,
commonly referred to as “excess enthalpy” (Chen, 2011), raises overall effective enthalpy (thermal
+ chemical) of working mixture. Such a system can drastically reduce the amount of chemical
enthalpy, hence the amount of fuel required to sustain chemical reaction. Despite the
straightforward concept and wide-range of benefits which Swiss-roll devices offer, prior early
applications were only constrained to small scale power generation (Kuo, 2006) and gas mask
systems (Chen, 2011) until recent years.
Figure 1: (Left) Swiss-roll combustor and (Right) superadiabatic combustion sustained with
heat-recirculation concepts.

3
1.2 Motivations and Applications
In most industrial premixed combustion applications, the flame temperature, hence the
flame speed and other flammability indicators, are too often considered to be solely dependent on
the fuel-air composition of working mixture. However, such dependency is severed by simply
facilitating finite amount of excess enthalpy, greatly expanding operational limits. Swiss-roll
reactors are capable of providing such benefits in a thermally efficient manner without any external
power source or mechanical complexity, making the device extremely economical and versatile.
Overall, it has recently been considered in wide-range of applications such as fuel reforming
(Schoegl, 2009; Crawmer, 2018; Chen, 2018; Chen, 2015), active gas mask (Chen, 2011), waste
gas/volatile organic compounds (VOCs) incinerators (Crawmer, 2017; Crawmer, 2018), in
addition to microscale power generation (Cho, 2009; Vican, 2002; Ochoa, 2003) from earlier
years. The device is also extremely scalable in nature, translating to exceptionally wide flow rate
turndown ratio (up to 1:10,000 with catalysts), hence also has potential in high flowrate
applications such as flare incineration systems (Chen, 2022) and gas turbine fuel-reforming
applications (Radyjowski, 2022). The bulk of this work primarily focuses on incineration and fuelreforming applications, as well as performance tradeoff studies.
1.2.1 Fuel-Lean (Incineration) Applications
Sustaining combustion in the extended lean flammability limits include increased
combustion efficiency, reducing fuel consumption and emissions. Swiss-roll combustors
previously demonstrated exceptionally low extinction limits (ϕ ≈ 0.058) working with propane-air
mixtures with a 9-turns, 12 cm diameter combustor without any external energy source or catalysts
(Chen, 2011). The processing of such ultra-lean mixture made possible through extreme heat-

4
recirculation results in breathable outlet gas in both composition (CO2 < 0.75 %) and temperature.
The ability to sustain the presence of flame with a very low fuel heat content is remarkable and is
particularly useful in detoxification applications, leveraging reaction zone’s high temperature and
active radicals in destroying harmful chemical and biological agents. Such concept can be
potentially advantageous compared to conventional filtration-based methods where the challenges
associated with filter’s toxin-compatibility, saturation and poisoning can be circumvented entirely.
With remarkable scalability demonstrated in preceding studies (Chen, 2013; Crawmer,
2017), it had naturally been considered for large-scale incineration applications. Especially for
flaring applications, known as the process of burning natural gases either due to environmental
(CH4 slips) economical (inadequate exothermicity) or safety reasons (pipeline blowdown
applications). For conventional flares, maintaining acceptable destructive efficiency (DRE) (>
98%) level is generally deemed as a critical challenge. Large fluctuations in upstream flowrates
and/or composition often result in incomplete combustion or disrupted flares, which translates to
≈ 95.2% actual DRE (Tran, 2024; Plant, 2022). Even under normal stable operations, “good” fuels
are often required to be further added to improve the enthalpy content to keep the flame alight.
The examples Swiss of larger-scale purification (Crawmer, 2017) and flare applications (Chen,
2022) are shown in Figure 2. The latter was designed specifically for natural gas and biogas
extraction operations, in which the waste gas can be economically processed at practically very
close to 100% DRE without the need for any supplemental fuels or other form of energy input.
Extremely wide turndown ratio facilitated by heat-recirculation can potentially provide transient
stability needed to maintain the flame’s presence. Additionally, due to ultra-lean and enclosed
operations, very low NOx emissions were also demonstrated, as well as advantages in lower
expected thermal radiation, both far less susceptible to environmental conditions.

5
Figure 2: (Left) 11” diameter, 12” tall Swiss-roll VOC incinerator (Crawmer, 2017)
and (Right) flare gas incinerator concept. (Chen, 2022)
Other key advantage of employing a Swiss-roll combustor for incineration applications is
its economical nature due to its straightforward, single-body designs and absence of moving parts.
Hence, the device can be inexpensive to fabricate, with the channels can easily be implanted
through milling machines for smaller-scale devices. Additionally, metal 3D additive
manufacturing methods can be employed to produce larger devices and potentially incorporating
more complex geometries.
Swiss-roll’s capability to mitigate energy losses combined with hydrocarbon fuels’
remarkably high energy densities potentially enable the concept to be used as microscale power
generation systems for microelectromechanical (MEMS) devices (Walther, 2011). Compatibility
of several thermal-to-electrical energy conversion solutions with Swiss-roll or linear heatexchanger devices were explored, namely thermoelectric generators (TEG) (Vican, 2002; Merotto,
2016; Yadav, 2014; Cohen, 2003) and piezoelectric generators (PEG) (Cho, 2009) per Figure 3
for external devices, as well as single-chamber fuel cells (SCFC) (Hibino, 2000; Ahn, 2009) for
internal devices. Such designs often incorporate catalytic combustion to reduce the impact of heat

6
losses and increase temperature concentration at the power-generation surfaces. Despite the
efforts, the thermal-to-electrical power conversion efficiency unremarkably remains below 4%.
Figure 3: Swiss-roll combustor-based micropower generator concepts incorporated with (Top)
thermoelectric (Merotto, 2016) and (Bottom) piezoelectric (Cho, 2009) engines.
1.2.2 Fuel-Rich (Reforming) Applications
As decarbonized fuel, H2 possesses many favorable attributes such as having high
gravimetric energy density (Peter, 2021), remarkable flame speed (Yu, 1986), and elevated
autoignition temperature (Huth, 2013). However, several critical intrinsic limitations exist for H2
concerning storage, safety, and transportation, forestalling the prospects of H2-based economy
despite increasing popularity over recent years. Due to its low volumetric energy density (Ganzer,
2020; DOE, 2017) per Figure 4, either relatively heavy storage vessels, liquification, or cryogenic
solutions are required to store practical amount of energy (Eberle, 2009; Usman, 2022).

7
Figure 4: Comparisons of hydrogen’s energy density to (Left) fuel alternatives (DOE, 2017)
and (Right) other miscellaneous fuels (Ganzer, 2020).
To achieve 300-miles driving range, it is estimated that fuel cell electric vehicles (FCEVs)
will require approximately 5 kg of H2, which translates to ≈ 200 liters at ≈ 10,000 psi (DOE, 2017).
More concerningly on weight basis, for each 1 kg of compressed H2 gas weight, roughly 12.5 – 25
kg of tank is expected to ensure operational safety (Cheng, 2024). This provides an opportunity
for Swiss-roll devices to potentially be deployed as a portable fuel reformer (Chen, 2015), instead
operating on other more conveniently-stored H2-carrier fuels which would then be converted to
synthesis gas, reverting fuel into H2, either partly or in full. The method also eliminates the need
for, hence the associated issues with the use of, catalysts (such as coking, sulfur tolerance,
deactivation, etc.) and external energy sources. The method is especially advantageous for fuel
sources with longer hydrocarbon chains or higher impurities, such as JP-8 (Chen, 2018), which
are far less compatible with catalysts. With the higher reaction temperature and reduction in heat
losses provided by Swiss-roll combustors, higher reforming efficiency can be achieved in addition
to providing fuel flexibility.

8
More specifically, in recent years, NH3 has been heavily considered as a non-carbon H2
carrier attributing to its respectable volumetric and gravimetric energy densities (Chatterjee, 2021).
NH3 can also be easily liquefied through simple compression to 145 psi at room temperature,
allowing existing infrastructures to be leveraged. However, as fuel, it is only constrained to low
flowrate applications due to its extremely low laminar flame speed (𝑆𝐿
) and narrow flammability
range (Kobayashi, 2019; Valera-Medina, 2021). To address this, H2 or other hydrocarbon fuels are
typically added to produce NH3 fuel-blends to enhance flame speed and ignition delay time,
improving operational stability (Kobayashi, 2019; Honzawa, 2019; Liu, 2019; Ichikawa, 2019).
Other hydrocarbon fuels are also viable as H2 carriers, offering more chemically-stable, noncorrosive alternatives. One distinct advantage of NH3 over typical hydrocarbons as fuel, is that the
exothermicity and composition of products are practically independent of pressure (Ronney 1988)
at temperature above 1000 K, potentially enabling larger throughput applications. For catalystbased methods, namely Ruthenium (Ru) and Nickel (Ni), the temperature range falls in the region
of ~ 650 – 800 K where the pressure dependency has significant effect on the reforming efficiency
(Radyjowski, 2022). Hence, Swiss-roll reformers are more compatible for high-pressure
applications such as gas-turbines, where ammonia cracking is preferred to occur at similar
operating pressure of 10 bar – 25 bar to avoid compression losses of pumping gaseous reformate
compared to pumping liquid ammonia. Additionally, volumetric-based thermal reformers generate
less pumping losses and have lower minimum-size restrictions compared to surface-based catalytic
cracking reformers where flow obstructions are present. Note that the theoretical operating limit
for autothermal reforming reaction is ϕ ≈ 6.5 where the process becomes endothermic, producing
colder products than incoming reactants.

9
1.3 Literature Reviews
1.3.1 General Behaviors of Swiss-roll Combustors
Earliest modeling works on Swiss-roll heat-recirculating combustors started in 1978 with
a proposed simple global energy balance model for the three separated zones of incoming
reactants, outgoing products, and fixed-temperature combustion (Jones, 1978), which exhibited
duo extinction limits behavior. One-dimensional energy balance analysis for a linear counter-flow
heat-exchanging combustor with well-stirred reactor (WSR) reaction zone and finite wall thickness
was proposed was later proposed (Ronney 2003), which expanded on the coupled effects between
finite-rate chemistry (𝐷𝑎), stream-wise wall conduction (𝐵𝑖), external heat losses (𝛼), as well as
flowrate. First attempt of two-dimensional CFD model with simplified out-of-plane heat loss and
experimentally-adjusted (single-point at high flowrate where the effects of heat loss is presumed
unimportant) 1-step chemistry models were conducted by Kuo and Ronney (Kuo, 2007; Kuo,
2006) per Figure 5. The results in Figure 6 emphasize the importance of radiative heat transfer
(Ronney 2003; Chen, 2004) and external heat loss effects at low Reynolds Number (𝑅𝑒) where
enthalpy supply is relatively small, and the favorable effects of turbulence on reaction zone
temperature at high 𝑅𝑒. At high flowrate, the extinction limit was found to be practically solely
dependent on reaction zone temperature regardless of how such temperature is attained (either due
to chemical enthalpy or turbulence enhancements). Sensitivity analysis here also revealed
performance favorability towards lower thermal conductivity practical solid materials as the too
much heat conduction translates to suboptimal perpendicular (with respect to the flow stream)
temperature profiles across the wall. The reaction zone profile inside Swiss-roll combustor is
broadened, attributing to the reliance on heat transfer from adjacent channel walls as opposed to
sole heat diffusion from heat release zone to unburned reactants. It is also worth noting that

10
working with excessively strong enthalpy flux causes the flame to propagate outward toward
upstream inlet channel turns as the flame becomes less dependent on heat-recirculation. This is
contrary to non-heat-recirculating combustion devices where flashback occurs at low 𝑅𝑒.
Figure 5: (Left) Computational domain and reaction zone at Re ≈ 103 and (Right) fuel mol
percentage at extinction limits of 3.5 turns combustor, compared between experiments and
simulation with turbulence model active/suppressed (Kuo, 2006).
Figure 6: (Left) Swiss-roll extinction limits with turbulence, radiation, and out-of-plane heat loss
individually suppressed and (Right) maximum thermocouple temperatures and combustion
temperature comparisons at limit points between models and experiments (Kuo, 2007).

11
1.3.2 Turbulence Effects and Scaling
More thorough investigation of turbulence and other three-dimensional effects were later
discussed over comparisons between two-dimensional and three-dimensional CFD results (Chen,
2011). The results emphasizes that the inclusion of model is essential for two-dimensional
simulations, but less so for three-dimensional simulations where the presence of dean vortices
induced from curvatures enhance overall heat-recirculation by roughly the same amount as
turbulence does when turbulence model is disabled. The study also validated the applicability of
quasi-one-dimensional out-of-plane heat loss model as temperature gradient across the insulation
horizontal plane was found to be minimal with low thermal-conductivity insulation material used.
Also, 4-step propane mechanism (Hautman, 1981) was used, allowing Swiss-roll to be modeled
without any adjustable parameter.
Scaling analyses (Chen, 2013; Ronney 2015) extended towards multiple-turns devices up
to three-dimensional analyses determined that five dimensionless groups (number of transfer units
(𝑁𝑇𝑈), heat loss (𝛼), Damkohler number (𝐷𝑎), wall’s conduction (𝐵𝑖) and internal radiative heat
transfer (𝑅)) are sufficient to characterize the performance of Swiss-roll combustors for
geometrically similar devices at varying scales. In place of 𝑁𝑇𝑈, 𝑅𝑒 may be used as a substitute
scaling parameter for both laminar and turbulent flows as they were found to be distinctly
correlated in absence of influence of other parameters. Shown in Figure 7 is three-dimensional
simulation results comparing geometrically-similar device at different scales with and without 𝛼,
𝐷𝑎, and 𝑅 values adjustments. The wall conduction effect (Bi) is found to be independent of scale
and is insignificant compared to the effect of internal radiation. The effects of combustor height
and Lewis number were shown to be unimportant at higher flowrates.

12
Figure 7: Computed extinction limits of varying scale combustors (Left) without property values
adjusted and (Right) with values adjusted to obtain constant α, Da and R (Chen, 2013).
1.3.3 Comparison to Linear Combustors and Geometrical Effects
For a perfectly adiabatic system, linear combustors exhibit intrinsic linear relationship
between excess enthalpy performance and 𝑁𝑇𝑈, which is superior compared to spiral heat
exchangers attributing to drop in effectiveness as 𝑁𝑇𝑈 becomes too large as the incoming flow’s
temperature may be higher than that of adjacent outlet turns, reversing the direction of local heat
transfer (Ronney 2015). This also explains the natural duo-limit extinction behavior in spiral
combustors as effectiveness peaks at a specific flowrate. However, with finite in-plane heat losses,
spiral exchangers perform significantly better, especially in the case of extreme heat losses (𝛼 →
∞) where combustors still demonstrate respectable recirculation performance as outer turns act as
insulation for inner turns. Figure 8 summarizes the findings taken from the works of Targett
(Targett, 1992) and Ronney (Ronney 2015).
As for internal designs, the performance generally improves with increased number of turns
(for both 1) same channel and core size and 2) same overall size) (Chen, 2011). Which are
consistent with Targett’s predictions (Targett, 1992) where without out-of-plane heat losses,

13
increasing number of turns will always result in broader extinction limits. With out-of-plane heat
losses, the benefits become less apparent as, starting with the outermost turns, temperature
difference across channels will lessens due to third-dimension heat losses and will stop
contributing to heat-recirculation. This implies that for actual devices, there exist an optimal
number of turns for a given flowrate, in which adding further spirals will only unnecessarily
increase pressure drop and heat losses from increased presence of solid materials.
Figure 8: Dimensionless excess enthalpy vs number of transfer units (NTU) for (Left) linear heat
exchanger and (Right) spiral heat exchanger at varying heat loss coefficients (α) (Ronney 2015).
Figure 9: Extinction limits of multi-turns combustors with varying overall size with and without*
out-of-plane heat loss (Chen, 2011).

14
1.3.4 Catalytic Effects
Combustion catalysts, primarily Rhodium (Rh) and Platinum (Pt), provide alternative
lower-temperature pathway from reactants to products for applications where high reaction
temperatures are undesirable or unsustainable. Employing catalytic combustion can reduce the
impact of heat losses and thermal stresses, especially at small scales where surface-to-volume ratio
is sufficiently high for catalytic combustion to be beneficial. Pt is a popular catalyst due to its
ability to retain oxygen atoms on surface at low temperature and desorbs when activation
temperature is reached (Deshmukh, 2007; Deutschmann, 1996). Experimental results conducted
on Swiss-roll burner with Pt catalyst (Ahn, 2005), per Figure 10, shows extinction limit can be
extended from Re ≈ 40 down to Re ≈ 2, and significantly further with ammonia-treated Pt, with
combustion sustainable at temperature as low as 85 ℃. Composition-wise the result shows
asymmetrical extinction limits, where the effective fuel-“lean” extinction limit is rich of
stoichiometric due to the need for excess fuel to remove oxygen from catalyst surface.
Figure 10: (Left) Surface and gas phase limits of 7.5cm x 7.5cm x 5cm, 3.5-turns combustor
and (Right) limit temperatures (Ahn, 2005).

15
1.3.5 Materials and Designs
Remarkable pace of progress in additive manufacturing technologies (Duda, 2016; Gadagi,
2021) greatly increases accessibility and affordability of high-temperature-resistant metals
(Inconel, maraging steel, titanium, etc.) and ceramics (silicon infiltrated, reaction-bonded silicon
carbide (Si/SiC, RBSiC)) (Evans, 2003) over recent years. Silicon Carbide (SiC) based Swiss-rolls
exhibit higher temperature resistance even compared to superalloys (Chen, 2022; Radyjowski,
2021). The higher maximum service temperature and the ability to produce more complex
geometries, such that shown in Figure 11, open up larger design spaces for Swiss-rolls previously
unattainable with the limitations of traditional manufacturing capabilities (Shirsat, 2011; Ma,
2021; Chen, 2018), primarily through flashback mitigation and channels’ heat transfer
enhancements (through fins, etc.).
Figure 11: Swiss-roll design (Left) with injector for JP-8 reforming (Chen, 2018)
and (Right)3D-printed Inconel-718 combustor with fins.
1.4 Scopes of Present Studies
Key practical influences that directly limits the performance of Swiss-roll combustors for
the listed applications categorically include 1) material, 2) pressure drop and 3) fabrication
limitations. Firstly, material’s maximum service temperature directly limits the maximum

16
operating flowrate, mixture composition (which determines the range of reactions) a Swiss-roll
combustor can facilitate. Secondly, given the simple nature of Swiss-roll combustors, pressure
drop is practically the only intrinsic parameter that determines the operational cost through
pumping power requirements. Lastly, available fabrication techniques limit both the geometrical
designs that can be produced, and hence also the types of materials which can be used to produce
such design. The ability to fabricate and/or design geometrically more favorable Swiss-roll designs
can directly support higher recirculation at lower pressure drop.
In pursuit of commercialization, Swiss-roll technology must address several glaring
challenges. For incineration applications, where extreme transient fluctuations are extremely
common, it is currently unclear how Swiss-roll operations will be affected in current absence of
transient predictions. For reforming applications, the reforming nature of hydrocarbons and NH3
fuels are not currently well-described in heat-recirculating environments, and in absence of
catalysts. Unconventional designs such as the inclusion of heat-transfer fins to enhance heat
transfer or adjustment in local geometries to assist with flashback controls, both at the cost of
increased pressure drop, can be explored. Ultimately, the challenge in designing a highperformance heat-recirculating combustor lies in the capability to generate high amount of heatrecirculation working with limited pressure drop and device size.
The benefits of catalyst on Swiss-roll combustors have been demonstrated clearly through
experiments. However, no modeling studies have been carried out in prior to this work. A modeled
Swiss-roll combustion device with catalytic combustion included can further support future
attempts in designing microscale thermal-mechanical power-generation systems.

17
Chapter 2: Experimental and Numerical Methods
2.1 Experimental Setup
The simplified experimental setup diagram for the laboratory ¼-ft scale combustor studies
is provided in Figure 12. Upstream fuel and air cylinders were connected to four Teledyne Hastings
mass flow controllers housed in an enclosed, ventilated box which regulates the flowrate and
mixture composition of working mixture to the desired values. The premixed mixture then passes
through a flame arrestor, and then a flow straightener with similar internal dimensions compared
to the baseline 3.5-turns combustor’s channel to ensure fully-developed flow enters the chamber.
The controller box’s output flowrates were calibrated with MesaLabs Bios Defender 530+ mass
flow calibrator.
Figure 12: Simplified experimental setup diagram.

18
Figure 13: Combustor housing and flow straightener during experiment.
Figure 14: Flow controller box.

19
Nickel-Chromium heating coils were coupled to 30 V power supply and inserted into the
core region as ignition heat source. K-type thermocouple with signal amplifier and ceramic tube
shielding was also inserted into the core at approximately quarter-height to monitor the flame’s
presence. LabVIEW systems were used for controls and data acquisitions. Figure 13 and Figure
14 shows the actual experimental setup and flow controller box. Figure 15 shows the LabVIEW
interface used.
The Inconel-718 Swiss-roll specimens were manufactured through direct metal laser
sintering (DMLS) method courtesy of Protolabs. Each combustor in study was vertically-coupled
with ceramic insulation wafers of 1 cm thickness and outer aluminum plates of 0.5 cm thickness.
The combined structure was held together with nuts and bolts at four corners. Ceramic adhesives
(Aremco CERAMABOND 552) in combination with steel mesh was generally used to seal off
remaining open sections.
Figure 15: LabVIEW software interface.

20
Agilent 8890 Gas Chromatograph (GC) system equipped with thermal conductivity
detector (TCD) and flame ionization detector (FID) was used to analyze the flow sample gathered
from the reformer’s exhaust for the reforming studies. H2O concentrations at outlet were
determined through error minimization of atom-balance between cold-flow and hot-flow GC
results.
Prior to and after each hot-flow test, leakage tests were performed using mass flow
calibrator at the combustor’s outlet to ensure leakage is kept below ~5%. The working mixture
was systematically ignited at relatively strong mixture compositions/flowrates, in which the igniter
was then turned off and the flow was slowly adjusted to testing conditions. The extinction
behaviors were found to be clearly observable based on temperature signals from centered
thermocouple.
2.2 Numerical Modeling
2.2.1 Overview
Two-dimensional (2D) steady-state and transient numerical Finite-volume method (FVM)
models of varying internal designs and scales were modeled via ANSYS Fluent to capture key
physics required to accurately predict the performances of Swiss-roll reformers. Accurate
representation of combustor’s extinction limit behaviors requires correctly capturing the overall
thermal energy balance from various transfer contributions (heat release from the flame,
convective heat transfer, turbulence, heat losses, solid zone conduction, radiative heat transfer,
etc.) as well as kinetics (flame location, reaction rates), and hence deemed as the key validation
condition. The conjugate heat-transfer problems here included both gas-phase fluid zone and
solid-phase combustor walls which are interconnected. Further details regarding each submodels
and solver are summarized in
.

21
Geometrically, previous works have shown that 2D simulations are generally adequate
over broad range of flow rates, at least for geometries absent of notable three-dimensional features
(Chen, 2011). The channels’ height-to-width aspect ratio in this study is comparable to prior works,
where the flows were predominantly observed to be quasi-2D over the bulk section between two
vertical surfaces (Chen, 2011). The domain’s maximum dimension varies from ¼-ft scale to 1-ft
scale depending on the application and objectives of the specific study.
2.2.2 General, Turbulence, and Heat Loss Submodels
Generally, inlets employ mass flow inlet boundary while outlet is a specified pressure at
reference value. The solid zones’ thermal properties were modeled as temperature-dependent. The
fluid zones were cautiously modeled as compressible ideal-gas though prior works showed that
incompressible flow assumption where density is only a function of temperature (with respect to
reference pressure) suffices for low Mach number flows studied here.
The effects of turbulence in Swiss-roll combustors mainly concerns convective heat
transfer enhancements (Kuo, 2007) of the heat-exchanging section. Provided the reaction zone in
Swiss-roll reactors are typically broader compared to typical premixed flames due to increased
reliance of heat transfer from the walls in addition to thermal diffusion (Kuo, 2006; Kuo, 2007;
Ronney 2015). Reynolds-averaged (RANS) methods were used here as shown in prior works to
produce satisfactory agreements (Chen, 2011), especially with Reynolds Stress Model (RSM)
model. The choice of RSM here is mainly due to the abandonment of isotropic Reynolds stress
tensor assumption, considered generally more appropriate for internal swirling flows with
curvature effects. Wall function method was used to reduce computational load in resolving the
boundary layer, with either Enhanced Wall Treatment and Standard Wall Functions was used
depending on target mesh density and appropriateness.

22
At outermost wall surfaces, a mixed natural convection (ℎ𝑐𝑜𝑛𝑣 = 10 W/m2K) and radiation
loss (𝜀𝑎𝑖𝑟 = 0.8) contributions was modeled. As for the out-of-plane heat losses, a user-defined
function (UDF) extension was implemented, accounting for volumetric heat loss from mid-plane
of the combustor through the insulation layers to the outermost surface as used in the experiments.
The 1D thermal resistance model scheme, per Figure 16, shows the layers included, neglecting
thin Swiss-roll base/ceilings sections due to resistances there being relatively small. Ultimately,
the solid region’s heat loss only depends on the local temperature, while the fluid regions depend
also on the Nusselt number, hence other local fluid properties and dimension of the channel.
Figure 16: Out-of-plane simplified resistance heat loss model schematic.
Since key combustion products, namely CO2 and H2O, participates in radiation. Radiative
heat transfer was modeled via Discrete Ordinates (DO) model, which also accounts for fluid’s
participation in radiation in contrast to Surface-to-surface (S2S) model which only models
radiative transfer between solid surfaces.
2.2.3 Flame and Kinetic Models
Finite rate chemistry was used throughout this work as individual reaction rates needed to
be resolved. In principle, the model assumes that the chemistry rates are slow compared to mixing

23
rates and the effects of turbulence on flame itself are neglected (no turbulence-chemistry
interaction), hence appropriate for laminar flames. However, prior works have established that
given the larger flame thickness present inside Swiss-roll environments and the length scale of
turbulence eddies being much smaller, the effects of turbulence are only important in the context
of improving internal heat transfer, which raises the temperature and hence reaction rates (Kuo,
2007; Kuo, 2006).
The kinetic models used here varies greatly depending on the application and mixture
regime. The simplest gas-phase combustion model involves single-step chemistry of propane
mechanism based on Westbrook and Dryer’s work (Westbrook, 1981) but with experimentallyadjusted pre-exponential factor (9 x 109
in m-sec-kmol) under high flowrate condition (𝑅𝑒 ≈ 1000)
where reaction rates are presumed strongly dominant compared to other secondary effects (heat
losses, radiative heat transfer, etc.) (Kuo, 2006; Kuo, 2007; Chen, 2011). This model was used in
fuel-lean geometrical optimization studies where the composition of products and intermediates
are not of primary interest, mainly to reduce computational loads. For flare studies where methane
slips and NOx emissions are critical, generic detailed hydrocarbon chemistry model was used,
namely GRI-Mech III (Smith, n.d.) with 53 total species and 325 reactions. For hydrocarbon
reforming where minimal prior works (Schoegl, 2009; Toledo, 2009; Chen, 2015) exist, two other
detailed mechanisms, USC-Mech II (Wang, 2007) and San-Diego Mech (UC San Diego, n.d.)
were also used in the study.
For ammonia-reforming, the work of Otomo’s (Otomo, 2018), which extended from the
work of Song’s (Song, 2016) were used along with GRI-Mech III to investigate N-H-O chemistry
reforming at elevated pressure. The three models produce agreeable product composition and
laminar flame speeds despite the pathways of high-residence time chemistry differ significantly.

24
However, provided limited practical residence time of Swiss-roll combustors, such details were
deemed unimportant, which later were confirmed in the simulation results.
For all gas-phase chemistry models, overall exothermicity (quantified through laminar
flame speed), intermediate pathways and product compositions were verified with literature values
via 0D analyses (laminar flame speed and perfectly-stirred reactor (PSR) modules) through
CHEMKIN over mixture’s temperature and composition ranges of interest.
As for catalytic combustion models of propane-air and butane-air on Platinum (Pt), the
base mechanism from Deutschmann’s group (Koop, 2009; Chatterjee, 2001) were used in
conjunction with partial oxidation extension model of Zhong’s (Xiong, 2011; Zhong, 2016).
Overall, the model includes 14 gas-phase species with 21 site species. The total of 84 reactions
includes 32 adsorption/desorption reactions, 40 reactions representing fuel breakdown processes
through presence of empty sites Pt(s) and/or radical-occupied sites (O(s), H(s) and OH(s)) and
remaining 12 reactions describing final combustion products formation on the surface. The
reactions are modeled as both site coverage-dependent and temperature-dependent. The butane
model produces decent agreements with the experimental and modeling data reported in Zhong’s
work (Zhong, 2016). The propane model yields slightly higher activation temperature close to
500K, slightly higher than the expected reported values in Ahn’s (Ahn, 2005), nonetheless
produces the overall behaviors as expected compared to the butane model.
2.2.4 Mesh and Solution Methods
Steady-state results were obtained interchangeably from steady-state and/or transient
solvers depending on the complexity of chemistry set involved, computational stability, and ease
of convergence in each specific case. Since the flowrate ranges studied here are within

25
incompressible range, pressure-based solvers were used throughout this work, which decouples
momentum and energy equations. For simpler chemistry models, steady-state analysis with
COUPLED P-V solver was generally preferred as the governing equations are simultaneously
solved instead of requiring pressure-correction step which potentially introduce source of errors in
pressure field. However, for more complex chemistry models and applications where high-fidelity
of pressure field is not of interest, SIMPLE algorithm was used to reduce computational costs.
Sensitivity analyses between the two revealed the general flame location and overall heat balance
are practically the same at convergence.
The mesh configurations of the walls and the channels are structured rectangles-dominant,
while for the middle section of the channel and core are triangles-dominant. Inflation layers were
applied near the wall and the first layer thickness was sized based on the choice of wall function
and flow’s velocity. The mesh width (parallel to the flow) was determined based on sensitivity
analysis balanced with computational load considerations. Mild adaptive grid refinement method
based on reaction rate’s gradient to improve resolution of reaction zone. Convergence was
determined based on combinations of sensitivity tests (grid & acceleration parameters),
convergence of key properties of interest, global heat and mass flux balances, and residuals.

26
Chapter 3: Results – Performance Tradeoff Studies
The heat-recirculation capability of Swiss-roll combustor is typically quantified through
demonstrated extinction limit where the flame sits in the core region, allowing for maximized
effective heat-recirculation. This performance is strongly dependent on the working flowrate (𝑅𝑒)
regime and is usually expressed in terms of excess enthalpy (𝐸𝐸), where the definition for
premixed mixture is given by:
𝐸𝐸 ≡
𝑇𝑚𝑎𝑥 − 𝑇𝑖𝑛𝑙𝑒𝑡
𝑇𝑎𝑑 − 𝑇𝑖𝑛𝑙𝑒𝑡
− 1
This is simply based off the definition of enthalpy assuming comparable specific heat (𝐶𝑃),
measuring the effective working enthalpy (chemical contribution + thermal contribution from
heat-recirculation) with respect to the inlet mixture’s total adiabatic heat content. The term can
conveniently be determined from experiments. The definition is also applicable to non-premixed
Swiss-rolls assuming the amount of fuel is sufficiently small. At near extinction point, the value
of 𝐸𝐸 naturally reaches maximum. While using stronger mixtures and/or adjusting the flowrates
(increasing for low 𝑅𝑒 regime, decreasing for high 𝑅𝑒) would result in flashback operational mode,
reducing 𝐸𝐸 as the full-span of recirculation channels would not be utilized.
Despite the small pressure drop across combustor generally needed to achieve recirculation
(Chen, 2011), it is the only sole operating cost parameter here.
∆𝑃 = 𝑃𝑖𝑛𝑙𝑒𝑡 − 𝑃𝑜𝑢𝑡𝑙𝑒𝑡
The specific scope of this section hence focuses on the tradeoff between 𝐸𝐸 and ∆𝑃 across
varying designs. Despite material’s maximum service temperature generally dictates the maximum

27
attainable heat-recirculation level, the performance tradeoff can be investigated especially for the
heat-exchanging sections. For a particular heat-recirculation design requirement, it is naturally
more optimal to scale up the combustor (Ronney 2015). From practical design and application
viewpoints, the available space is often limited, hence the size of the reactor (Radyjowski, 2022).
More recent variations of Swiss-roll combustors employ vertical flow section for the core region
to allow for increased residence time (with fuel injected directly into the core) (Chen, 2018),
increasing resistance to blow-off extinctions while also providing sufficient boundary layer
thickness to ensure sufficient thermal protection to the wall materials. Per these considerations, the
core size should also be treated as a limiting design factor in a design-tradeoff study. Fabrication
limitations of additive manufacturing methods (ex. minimum feature size, wall thickness, etc.) also
impose limits to the design space. Ultimately, the performance 𝐸𝐸 vs ∆𝑃 tradeoff study was
conducted across varying geometrical channel designs spread over ranges of flowrates, however
under the same overall size, core size, and fabrication constraints.
More specifically, extending from prior investigations focused on smaller-scale
applications at 1 atm, a ¼-ft scale, 3.5-turns cylindrical single-stream Swiss-roll design was used
as the baseline reactor (Chen, 2011). With the same overall size (~7.5 cm overall diameter, 5 cm
simulated height) and core size (2.35 cm core diameter) and manufacturing constraints (0.5 mm
wall thickness, 0.5 mm minimum feature size), three different design methods were explored for
the channels. The working inlet mixture is lean propane-air at 300 K over 𝑅𝑒 range of (100 < 𝑅𝑒
< 2600), covering both extinction mechanisms (heat loss and blow-off limits). 𝑅𝑒 values here are
defined with respect to the 2D baseline channel width (3 mm) and flow properties at inlet.
Table 1 summarizes the key geometrical parameters used in the baseline study, which directly
resembles the experimental setup.

28
Table 1: List of notable geometries for baseline ¼-ft, 3.5-turns Swiss-roll in geometrical studies.
Baseline Geometry Summary
Largest x-Dimension 77.0 mm
Largest y-Dimension 74.0 mm
Largest z-Dimension (Simulated) 50.0 mm
Largest Core x-Dimension 28.4 mm
Largest Core y-Dimension 23.6 mm
Number of Turns 3.5
Channel Width 3.0 mm
Wall Thickness 0.5 mm
Ceramic Insulation Thickness (Simulated) 1.0 cm
Aluminum Thickness (Simulated) 0.5 cm
Figure 17: Propane-air extinction limits comparison between 1-step model, detailed chemistry
and experiment for 3.5-turns baseline ¼-ft scale Inconel 718 Swiss-roll.
Similar validation procedures based on prior works were followed. Figure 17 shows the
general agreements between extinction limits observed in experiments with the baseline Inconel718 combustor and simulations using 1-step and GRI-Mech III detailed chemistry models. The

29
extinction limits were found to be noticeably abrupt and well-defined. The results expectedly
exhibit duo-limits behaviors, and the agreement justifies and reaffirms the use of 1-step chemistry
in for trade-off studies in this section conducted over lean-limit cases at comparable 𝑅𝑒.
3.1 Effects of Turns
Prior works focused on extinction limits expansion for combustors of varying turns but
with channel width and core area kept the same (varying overall size) (Chen, 2011). Naturally,
without size constraints, increasing the number of turns directly increases heat transfer area,
increasing Swiss-roll’s excess enthalpy capability, especially at high 𝑅𝑒 where the effects of heat
losses become unimportant (Chen, 2011). It is worth noting that having too many turns can lead
to excessive heat losses, where Ronney (Ronney 2015) has shown faint transition behavior at
extreme number of turns (𝑛 > 10) for a fixed-size combustor but varying core size. To respect all
three constraints (overall, core, and minimum feature sizes), this study introduces 2.5-turns and
5.5-turns combustors as shown in Figure 18, with resulting channel widths and effective heat
transfer wall lengths summarized in in Table 2.
Figure 18: Geometries for 2.5-turns and 5.5-turns combustors.

30
Table 2: Notable dimensions of different turns combustors.
2.5 turns 3.5 turns 5.5 turns
Channel Width 4.26 mm 3.00 mm 1.78 mm
Est. Total Channel Length 1.36 m 1.93 m 3.24 m
Wall Thickness 0.5 mm 0.5 mm 0.5 mm
The 𝑅𝑒 values here are based on the baseline 3.5-turns combustor’s inlet such that same
𝑅𝑒 corresponds to identical total inlet flowrates among the three combustors. Figure 19 shows the
resulting extinction limits between the three combustors. Consistent with prior works, the limits
were shown to improve significantly across all flowrates within these bounds, with benefits more
apparent at higher 𝑅𝑒. The number of turns in this study is not as extreme compared prior
investigation with varying overall size (Chen, 2011), hence the converging behavior in limits at
low 𝑅𝑒 in Figure 9 (where 3-turns and 6-turns combustors were shown to produce the same limit
ϕ at 𝑅𝑒 ≲ 200) is not as pronounced. The slight gap in limit ϕ values between 3.5-turns and 5.5-
turns at similar 𝑅𝑒 here can be mainly attributed to heat loss scaling with combustor size (Ronney
2015). Since the dimensionless heat loss parameter scales according to 𝛼 ~ 𝑑
1
, hence smaller
combustors in this study are less susceptible to heat losses (Ronney 2015), hence wider limits.
As number of turns increases, the transitional 𝑅𝑒 values (between heat loss-dominated and
residence time-limited regimes) also shifts toward higher 𝑅𝑒. The behavior was also noted in the
same prior study (Chen, 2011). Going towards higher 𝑅𝑒 values, the larger heat-recirculation
section in higher-turns combustors enable higher temperature to be reached for the same mixture,
hence the limit is greatly expanded here.
Intuitively, pressure increases exponentially with added turns as channels become longer
and narrower. Figure 20 shows the tradeoff between maximum 𝐸𝐸 (at extinction limit) and ∆𝑃.
The values of pressure drop here fall close to 0D estimates (not shown). At any fixed pressure

31
values (treated as operating pressure drop budget from design perspective), there exists a
combination of working flowrate and number of turns which yield highest value of 𝐸𝐸. Going
from low pressure budget to high pressure budget, the results suggest both flowrate and number
of turns (channel length) should be correspondingly increased in order to efficiently achieve
maximum 𝐸𝐸 values.
Figure 19: Simulated extinction limits comparison between varying-turns ¼-ft scale combustors
working with C3H8-air combustor at 1 atm with the same overall, core and feature sizes.
From practical and design point of views, the tradeoff plot is potentially useful in
correlating desired outputs (amount of heat-recirculation and working pressure drop) and design
parameter inputs (geometry and flowrate). Or alternatively, if a specific value of 𝐸𝐸 needs to be
attained under some baseline operating pressure, an optimal number of turns can also be implied.

32
Figure 20: Simulated EE vs ΔP tradeoff between varying-turns ¼-ft scale combustors working
with C3H8-air combustor at 1 atm with the same overall, core and feature sizes.
3.2 Effects of Fins
Alike to adding number of turns, including heat-transfer fins into channels increases
internal heat transfer area at the tradeoff of increasing pressure drop. For this study, the fins’
geometry in each reactor were kept identical throughout channels. Across different finned
combustors, the fins’ heights and gap spacing were adjusted such that the effective flow width is
virtually uniform throughout flow channels, as shown in Figure 21. The fins on the outermost walls
in the first and last half-turns are omitted, and the fins on opposing walls in the same section were
also omitted to preserve channel/feature uniformity.

33
Area ratio (𝐴𝑅) is defined as the ratio between total effective internal heat transfer wall
area (length) compared to the baseline case without fins. The features are summarized in Table 3.
Figure 21: Geometries for area ratio-1.2 and area ratio-2.0 combustors
Table 3: Notable dimensions of varying finned combustors.
Baseline AR 1.2 AR 1.5 AR 2.0
Total Fins Count 0 240 372 536
Fin Width - 0.5 mm 0.5 mm 0.5 mm
Fin Height - 0.8 mm 1.3 mm 1.8 mm
Est. Total Channel Length 1.93m 2.32 m 2.90 m 3.86 m
As shown in Figure 22, the resulting extinction limits for the four combustors are provided.
At high 𝑅𝑒, adding fins to channel walls greatly widens extinction limits, and the effect becomes
progressively at very high 𝑅𝑒. The improvements going from having no fins to having minimal
number of fins (AR 1.2) is remarkable but increasing the number of fins further (AR 1.5 and AR
2.0) yields diminishing added improvements. On the contrary, the added fins have adverse effects
at low 𝑅𝑒 region, below the transition 𝑅𝑒 of 412, where the increased mass from fins contribute to
increased heat losses and the extinction limits worsen.

34
Figure 22: Simulated extinction limits comparison between varying-fins ¼-ft scale combustors
working with C3H8-air combustor at 1 atm with the same overall, core and feature sizes.
The results suggest including fins primarily as a source of turbulence would be a more
effective method for the purpose of promoting heat transfer as opposed to implementing to increase
the wall’s bulk heat-transfer area. Also, other simple 2D fin geometries (center/forward/backwardleaning triangular shapes of equal 0.5 mm height) were explored in straight-channel tube of 3mm
diameter with fixed-temperature boundary, but no notable improvements were observed between
the designs. These results were expected for gaseous heat-exchangers where Prandtl number (𝑃𝑟)
is close to unity. Despite this, the overall heat transfer coefficient still increases with increasing
flowrate as 𝑁𝑢 ~ 𝑅𝑒0.8𝑃𝑟0.3
.

35
Figure 23 shows the domain-averaged turbulence kinetic energy trends with respect to 𝑅𝑒
for these combustors. At high flowrate, a peak exists at intermediate number of fins (AR 2.0),
where either removing or adding further bodies of fins will result in reduced amount of turbulence.
The inclusion of turbulence model at laminar, low 𝑅𝑒, regime may not result in appropriate K.E.
values here. Nonetheless, sensitivity tests showed that laminar and turbulence models produce
practically the same extinction limits.
Figure 23: Fluid zone’s average turbulence kinetic energy for each fin configuration
Figure 24 shows the trade-off slope between excess enthalpy and pressure drop becomes
progressively more favorable at high 𝑅𝑒, as suggested earlier in Figure 22. At low Re, adding fins
result in reduced excess enthalpy due to added heat losses from higher presence of solid zones.

36
Note that excess enthalpy can be increased approximately two-folds at the cost of a magnitude
increase in pressure drop through adding small fins at highest 𝑅𝑒 studied here going from plainwall baseline combustor to slightly-finned AR 1.2 combustor. Comparatively to increasing turns,
the 𝐸𝐸 vs ∆𝑃 tradeoffs for finned series slightly underperforms, naturally attributing to blockage
presence of fins, resulting in more pressure drop compared to plain-wall counterparts.
Figure 24: Simulated EE vs ΔP tradeoff between varying-fins ¼-ft scale combustors working
with C3H8-air combustor at 1 atm with the same overall, core and feature sizes.
Very early heat-recirculating combustor results (Burmeister, 2006; Chen, 2011) explicitly
showed linear relationship between the inverse of lean ϕ limit (which is inversely proportional to
maximum 𝐸 capable of being produced from combustor) and dimensionless channel path (𝐿/𝐷)

37
without considering the impact of heat losses (an assumption which generally holds true for Swissroll combustors as opposed to conventional heat-recirculating reactors (ex. linear)). The linear
relationship at limits is emphasized here in Figure 25. Note that the performances are slightly
worse at very high (𝐿/𝐷) compared to prior data reported in varying turns (but scaling overall size)
study by Chen (Chen, 2011) as larger combustors intrinsically have wider extinction limits for
high 𝑅𝑒 cases due to scaling of available residence time (as 𝐷𝑎 ~ 𝑑
2
, improving with size)
(Ronney 2015). Here, if overall size were constrained, the limit ϕ values expectedly become less
lean at the same (𝐿/𝐷). The plot here suggests, for the same (𝐿/𝐷) ratios and under the same three
key constraints, increasing internal area from incorporating fins is a slightly preferable
enhancement method (without considering pressure drop) compared to increasing turns for
sufficiently high (𝐿/𝐷). Nonetheless, the plot is a useful predictive tool in extrapolating expected
performance (limit ϕ, maximum 𝐸) of combustors with larger internal areas (Chen, 2011).
Figure 25: 1/lean ϕ limit vs channel length-to-combustor diameter ratios for two different areabased enhancement methods (turns vs fins).

38
3.3 Effects of Inlet-to-Outlet Channel Size Ratios
Two prior methods in increasing internal heat recirculation are both primarily based on
increasing internal wall surface area available for heat transfer. This section proposes a method
oriented around manipulating channels’ overall heat transfer coefficients through channel width
ratio adjustments. Since the favorable heat-transfer bottleneck (from hot channel, through the wall,
and into the cold gas) is the convective part as conduction step is orders of magnitude faster.
Particularly, the wall-to-cold gas is presumably the slowest (for conventional Swiss-rolls with
uniform channel with) due to lower thermal conductivity of colder gases. Previous work has shown
that optimal wall’s thermal conductivity is, in principle, smaller than the thermal conductivity of
air (𝑘𝑎𝑖𝑟 ≈ 0.026 W/mK) (Kuo, 2007) and having walls with higher 𝑘 results in suboptimal
streamwise wall’s temperature profiles for heat recirculation.
Figure 26: Geometries for I25%O75% and I75%O25% channel sizes-adjusted combustors,
showing inlet halves.
In order to mitigate this influence, overall impedance-balancing between two convection
steps were investigated with two combustors shown in Figure 26 and parameters displayed in the

39
following Table 4. Note that the 𝑅𝑒 values in this section are also based on baseline combustor
to provide a fair comparison similarly to the study of varying turns in prior section.
Table 4: Notable dimensions of varying inlet-to-outlet channel width ratio combustors.
I-25%,O-75% I-50%,O-50% I-75%,O-25%
Inlet Channel Width 1.5 mm 3.0 mm 4.5 mm
Outlet Channel Width 4.5 mm 3.0 mm 1.5 mm
Wall Thickness 0.5 mm 0.5 mm 0.5 mm
Figure 27 has shown that, redistributing the channel width toward smaller inlet/larger outlet
channel results in mildly broader extinction limits at high 𝑅𝑒. The trend was also observed
experimentally. The trend is rather unexpected considering in turbulent regime, the overall heat
transfer coefficient ℎ scales with 𝑁𝑢 (and hence 𝑅𝑒) and the inverse of channel width (∆𝑥).
𝑅𝑇𝑢𝑟𝑏𝑢𝑙𝑒𝑛𝑡 =
1
ℎ𝐴
=
∆𝑥
𝑁𝑢 𝑘𝐴 ~
∆𝑥
𝑅𝑒0.8 𝑘𝐴 ~ (
𝜇
𝜌𝑢∆𝑥
)
0.8 ∆𝑥
𝑘𝐴 ≈ (
𝜇
𝜌𝑢𝐻∆𝑥
)
1 𝐻∆𝑥
𝑘𝐴
~
𝜇
𝑚̇
𝐻∆𝑥
𝑘𝐴 ~
𝜇(𝑇
0.7
)
𝑘(𝑇
0.7)
∆𝑥 ~ ∆𝑥
Ultimately which, under the same mass flowrate, the convective heat transfer resistance
only scales with thickness and is not temperature dependent. Implying having differing ∆𝑥 should
not result in any increase in performance. This is in contrast to laminar cases where
𝑁𝑢 ~ 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡.
𝑅𝐿𝑎𝑚𝑖𝑛𝑎𝑟 =
1
ℎ𝐴
=
∆𝑥
𝑁𝑢 𝑘𝐴 ~
∆𝑥
𝑘(𝑇
0.7)
Which suggests channel width ∆𝑥 should be changed corresponding with flow’s
temperature. More specifically, the cold channel should be made smaller relative to the hot
channel. Yet, this was not observed neither in simulation nor experiments.

40
Figure 27: Simulated extinction limits comparison between inlet-to-outlet ratios-adjusted ¼-ft
scale combustors working with C3H8-air combustor at 1 atm with the same overall, core and
feature sizes.
Similar tradeoff plot is also provided in Figure 28. Despite the internal area being the same,
overall pressure drop unsurprisingly still increases as the narrowed sections increase pressure drop
significantly more than the decrease from the widened sections. Towards larger 𝑅𝑒, total pressure
drop is higher for I-25%O-75% compared to I-75%O-25% primarily due to the dependency on
𝜌𝑉
2
, the term which is higher for outgoing hot products than cold incoming reactants. From 𝐸𝐸
vs ∆𝑃 tradeoff perspective, at smaller flowrates the larger-inlet I-75%O-25% combustor is favored,
while for higher flowrates the smaller-inlet I-25%O-75% instead becomes favored. Most
noticeably, at highest 𝑅𝑒 the value of 𝐸𝐸 increases by ~60%. The transitional 𝑅𝑒 value here is

41
between 206 < 𝑅𝑒 < 412. Despite total pressure drop always increases from the baseline design
with this method, it is still particularly useful in applications where fuels are required to be injected
at the center due to limited working pressure head as discussed in the flare study section. By
making inlet smaller while still keeping the combined overall width the same, fuel can be injected
at lower pressure while still being able to not just maintain the original heat-recirculation level,
but also reaps some minor additional increase in 𝐸𝐸.
Figure 28: Simulated EE vs ΔP tradeoff between inlet-to-outlet ratios-adjusted ¼-ft scale
combustors working with C3H8-air combustor at 1 atm with the same overall, core and
feature sizes.

42
Chapter 4: Results – Fuel Reforming
This chapter explores the prospects of H2 production from hydrocarbons (C3H8, CH4) and
ammonia (NH3) using Swiss-roll devices. Simple thermodynamic equilibrium calculations for
hydrocarbon fuel-air mixtures show syngas-dominated products with maximum H2 mol fraction
located practically at ϕ ≈ 3.3 as per Figure 29. However, since the supply of H-atoms varies with
ϕ, it is important to consider the primary objective here for all fuels is to maximize hydrogen yield
of the following definition:
𝑅𝑒𝑓𝑜𝑟𝑚𝑖𝑛𝑔 𝑌𝑖𝑒𝑙𝑑 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛/𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 ≡
𝐻 𝑎𝑚𝑜𝑢𝑛𝑡 𝑟𝑒𝑠𝑢𝑙𝑡𝑖𝑛𝑔 𝑖𝑛 𝐻2
𝑇𝑜𝑡𝑎𝑙 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝐻 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 𝑎𝑠 𝑓𝑢𝑒𝑙
For CH4 and C3H8 fuels, the yield peaks at ϕ ≈ 3.0 (𝑌𝑖𝑒𝑙𝑑 ≈ 94% for C3H8), with small
traces of CO2 and H2O. The undesired “complete combustion” products become more favored for
leaner (ϕ < 3.0) mixtures and Soot formations become a concern for richer mixtures (ϕ > 3.0).
Nonetheless, the ϕ ≈ 3.0 condition is easily achievable in Swiss-roll combustors.
Figure 29: Adiabatic equilibrium compositions of (Left) CH4-air and
(Right) C3H8-air mixtures at 1 atm.

43
As for NH3 fuel, the two key advantages are the absence of coke and scalability with
pressure (in both products composition and flame speed) due to N-H kinetic pathways. These
properties make NH3 reforming ideal for high-throughput applications. Similarly, the equilibrium
compositions across varying ϕ at 10 atm is shown in Figure 30, which is practically the same at
1 atm. The yield monotonically increases with increasing ϕ, suggesting direct favorability of
reforming yield with increasing amount of heat-recirculation serviced by the reformer.
Figure 30: Adiabatic equilibrium compositions of NH3-air mixtures at 10 atm.
For both sets of fuels, preliminary zero-dimensional analyses were conducted to determine
the favorable conditions (temperature, pressure, composition, residence time, etc.) for reforming.
Then, two-dimensional CFD calculations with corresponding detailed chemistry sets were
performed to determine the effects unable to be accounted for in simplified zero-dimensional
studies (flow effects, thermal energy balance, flame location, etc.). Key limitations of employing
conventional single-stream Swiss-roll reformers were identified and the design space is also
discussed here, supplemented by proposed alternate solutions which were systematically explored.

44
4.1 Hydrocarbon Reforming
4.1.1 PSR Analysis
The analysis was conducted across ranges of ϕ and pre-heating levels (𝑇0). The series of
steady-state results at varying residence time at specific ϕ = 3.0 and 𝑇0 = 600 K for both fuels at
1 atm are displayed in Figure 31.
Figure 31: 0D PSR outlet species results for (Top) CH4-air and (Bottom) C3H8-air mixtures
at ϕ = 3 and 𝑇0 = 600 K computed with GRI-Mech III.

45
In contrast to lean or near-stoichiometric mixtures where the temperature and species
profile readily converges to the equilibrium values, initial partial-conversion were observed which
follows by very slow secondary conversion. USC 2.0 and San-Diego mechanisms also produce
practically similar results. The compositions of the initial spikes were found to contain significant
amount of H2O, as well as small portions of C2H2, C2H4 (and CH4 for propane fuel) in addition to
the desired H2 and CO. The results are consistent with other ultra-fuel rich investigations (Chen,
2015; Schoegl, 2009; Toledo, 2009).
Initially, CH4 breaks down through O, OH, and H radicals through common pathways (CH4
+ O → CH3 + OH, CH4 + OH → CH3 + H2O, and CH4 + H → CH3 + H2). Resulting bulk of CH3
combines into C2H6 which then reacts with H radicals (C2H6 + H → C2H5 + H2) which also
contribute significantly to production of H2 in addition to CH4 + H → CH3 + H2. Similar steps are
then repeated for C2H4, producing additional H2. Other key products from CH4 reduction, namely
OH and H2, gets reacted to form more H2O (H2 + OH → H2O + H) in addition to CH4 + OH →
CH3 + H2O, with both H2O formation reactions relying on OH radicals. Key reactions involved in
H2 productions, in summary, includes CH4 + H → CH3 + H2, C2H6 + H → C2H5 + H2, C2H4 + H
→ C2H3 + H2, as well as CH2O + H → HCO + H2 which are all predominantly dependent on
available H radicals. The H-atoms are supplied from C2H5 (+M) → C2H4 + H (+M), H2 + OH →
H2O + H, and CH2O-related pathways (originating from CH3 + O2 → CH2O + OH). As for slower
timescales where O and OH radicals have been mostly consumed and initial amount of H2O, CO
were formed, the remaining CH4 instead dominantly reduces to CH3 through CH4 + H → CH3 +
H2 and CH4 (+M) → CH3 + H (+M) reactions. CO2 slowly gets consumed reacting with singlet
state methylene (CO2 + CH2(s) → CO + CH2O). As for slow H2O consumptions, GRI-Mech 3.0

46
also attributes this to CH2(s) (H2O + CH2(s) (+M) → CH3OH (+M)) while for San-Diego Mech
this involves H2O + O → 2OH.
For C3H8 fuels, the reduction pathways do not directly produce CH4. Instead, the main
products consist of CH3, C2H5 and C3H7 through C3H8 (+M) → CH3 + C2H5 (+M) and C3H8 +H
→ C3H7 + H2. CH3 molecules would then combine to form C2H6, while C2H5 also decomposes into
C2H4 and H radical (both similar to CH4 chemistry). C3H7 gets reduced to CH3 and C2H4 (the latter
eventually gets reduced to C2H2, which eventually forms CH2CO directly responsible for slow CO
formations. The amount of CH4 produced initially are from CH3 reacting with H2 (CH3 + H2 →
CH4 + H) or individual H (CH3 + H (+M) → CH4 (+M)). The slow breakdown processes for CH4,
CO2, and H2O are practically the same with CH4-air case.
The H2 yield from an actual Swiss-roll is expected to follow the initial H2 spike as the
residence time of the reaction zone is limited. Sensitivity grid tests with inlet mixtures (1.5 ≤ ϕ ≤
4.0) and initial temperatures (300 K ≤ 𝑇0 ≤ 900 K) reveal the initial H2 spike yield peaking at ϕ ≈
3.3, which slightly increases with increasing 𝑇0. Despite unfavorable chemistry, this suggests H2
yield can be mildly increased if recirculation capability of Swiss-roll combustors can be improved.
The addition of H2O into the inlet working mixture was also done to determine if the kinetic
limitation which limits H2 yield can be mitigated. Ranges of C3H8-O2-H2O-N2 mixtures at the same
𝑇𝑎𝑑 = 1000-1800 K and 𝑇0 = 600 K were used; however, the improvements are only substantial at
high temperature (𝑇𝑎𝑑 = 1800 K, 10% H2O by mol) where the initial H2 spike increases by ~60%
compared to the C3H8 case in Figure 31. Nonetheless, such convoluted arrangement required
would be too impractical to implement especially for portable applications.

47
4.1.2 Two-dimensional CFD Predictions and Experimental Results
The two-dimensional CFD results for ¼-ft scale, 3.5-turns, plain wall, baseline combustor
across (2 ≤ ϕ ≤ 4) and comparisons with experiments for both fuels are shown in Figure 32 under
fixed moderate flowrate of ≈ 28 SLPM, corresponding to 𝑅𝑒 ≈ 619. The simulation results here
employed GRI-Mech 3.0 chemistry. The model does not include Soot formations hence the limits
comparison is not entirely appropriate here. Experimentally, the outlet concentration of H2
observed across ϕ ≈ 2.5-3.8 were found to be on the order of ≈ 22% for CH4 and ≈ 13-17% for
C3H8 fuel respectively. For CH4 cases, the model slightly under-predicts the H2 and CO amounts,
while mildly over-predicting H2O. Small traces of C2H2 (≈ 1-2%) and C2H4 (< 1%) were also
observed experimentally, consistent with 0D and 2D predictions. Soot particles were also noted in
the exhaust for very rich mixtures (ϕ > 3.5), presumed as the source of slight carbon imbalance in
the GC results there. In terms of H-atom conversion yield, for C3H8 fuel the value peaks at ϕ ≈ 2.5
at roughly 42% H2 conversion, an unimpressive number compared to the equilibrium amount of
83% at the same ϕ = 2.5, or 94% at the peak yield ϕ = 3, with H2O on similar percentage (≈ 38%)
and remaining ≈ 20% consisting of CH4, C2H2 and C2H4.

48
Figure 32: Major species outlet composition comparison for ¼-ft scale plain-wall Swiss-roll
combustor (operating at 𝑅𝑒 ≈ 619) between simulation (line) and experiments for
(Top) CH4-air and (Bottom) C3H8-air mixtures at 1 atm.

49
Sensitivity tests were also carried out to determine yield favorability across varying 𝑅𝑒
instead of ϕ, for the same fixed ¼-ft baseline combustor. Figure 33 depicts the outlet compositions
and yield percentages at fixed ϕ = 3 value. The yield improves slightly favoring higher flowrates
due to yield favorability with increasing temperature, but slightly drops toward very high flowrate
(𝑅𝑒 ≈ 2800) where near-extinction effects leaving unreacted portions of C3H8. The conversion
yield ranges only between 36% to 43%, not a significant increase compared to the compositionsensitivity results which favors leaner mixtures mentioned in prior paragraph.
Figure 33: Outlet (Left) compositions and (Right) H and C atoms to H2 and CO conversion
ratios at fixed equivalence ratio (ϕ = 3) for ¼-ft scale, 3.5 turns Swiss-roll operating with 300K
inlet C3H8-air mixture.
Further sensitivity tests were examined towards leaner (1.5 ≤ ϕ ≤ 2.5) and higher flowrate
cases (1100 < 𝑅𝑒 < 2900) where H2 yield was found to be slightly favored from prior sensitivity
tests. The two-dimensional CFD prediction results for major species (C2H2 and C2H4 not shown)
and H2, CO yields are shown in Figure 34. The maximum H2 yield across these conditions were
found to increase slightly to ≈ 52% for ϕ = 2.0 at intermediate 𝑅𝑒, with CH4, C2H2, and C2H4
becoming significant for ϕ > 2.0. Nonetheless, the yields here are seemingly monotonic,
highlighting the kinetic limitations of hydrocarbon reforming.

50
Figure 34: Outlet (Left) mol fractions and (Right) reformed products conversion ratios at high
Re conditions and varying mixtures (Top) ϕ = 1.5, (Center) ϕ = 2.0, and (Right) ϕ = 2.5.

51
4.2 Ammonia Reforming
4.2.1 PSR Analysis
Sensitivity analysis for NH3-air mixture at 10 atm fixed pressure was conducted over a
series of fixed-temperature reactor (1000 K ≤ 𝑇 ≤ 3000 K) at varying mixtures (2 ≤ ϕ ≤ 5) and
residence time (1x10-4 s ≤ 𝑡𝑟𝑒𝑠 ≤ 1 s). The primary outlet species were found contain H2, H2O,
unprocessed NH3, and N2. NOx was expectedly found to be significant only at near stoichiometric
mixtures and very high temperatures. The initial breakdown of O2 is largely associated with H +
O2 → O + OH reaction. The O and OH radicals then break down NH3 via NH3 + O → NH2 + OH
and NH3 + OH → NH2 + H2O. The latter reaction is rather dominant, readily forming the
equilibrium amount of H2O. As for longer timescales, the NH3 breakdown contribution from NH3
+ H → NH2 + H2 becomes relevant in relative absence of O and OH radicals provided sufficient
high-temperature residence time, in which the remaining portion of H2 is slowly recovered. Two
primary reactions, namely NH2 + H → NH + H2 and N2H2 + H → NNH + H2, also significantly
accounts for H2 formation independent of O-based radicals’ presences.
Figure 35 shows the combination of reactor temperature and residence time required to
attain certain yield of H2 in the outlet with Otomo’s mechanism. Song’s and GRI-Mech III
mechanisms also produced agreeable results. The results suggest net hydrogen production
monotonically favors increasing temperature and ϕ (provided the same temperature can be
maintained through increased heat-recirculation despite smaller heat content at higher ϕ).
Conversions become observable starting from ≈ 1500 K and eventually reaches maximum yield
with increasing temperature provided sufficient residence time. This is contrast to hydrocarbon
reforming where the slow H2O breakdown/SMR chemistry prevents the reforming yield to reach

52
equilibrium within practical residence time values. For timescales available inside Swiss-rolls
systems, the required temperature for decent yield is approximately ≈ 2000 K, which calls for
careful designs of Swiss-roll in preventing overheating of solid materials and also flame-holding
mechanisms to avoid out-of-center flame operations as the boundary layer thicknesses are smaller
in the channels.
Figure 35: 0D PSR H2 yield sensitivity map of NH3-air mixtures in fixed-temperature
reactor at 10 atm.
Ultimately, the yield dependency strongly depends on ϕ, temperature, and residence time
to high temperature. The yield function is therefore:
𝐻2 𝑌𝑖𝑒𝑙𝑑 = 𝑓{𝑇, ϕ, 𝑡𝑟𝑒𝑠}

53
The reaction zone temperature is directly tied to heat-recirculation capability of the
reformer, hence 𝐸𝐸. Therefore, pressure drop budget ∆𝑃 determines the maximum possible 𝐸𝐸
assuming best thermohydraulic design corresponding to operating 𝑅𝑒 is being considered. The
composition ϕ is technically an independent parameter, but ϕ𝑚𝑎𝑥 is also limited by 𝐸𝐸. The
available high-temperature residence time is dominantly tied to reformer’s scale (Ronney 2015).
From the design perspective, the yield function is qualitatively summarized as:
𝐻2 𝑌𝑖𝑒𝑙𝑑 = 𝑓{𝑇(~𝐸𝐸(~∆𝑃)), ϕ, 𝑡𝑟𝑒𝑠(~𝑠𝑐𝑎𝑙𝑒)}
4.2.2 Qualitative Design Space
As discussed in prior chapter, the reaction zone temperature can be increased by employing
higher 𝐸𝐸 potential reactors, through methods include but not limited to adding turns, adding fins,
etc. Per yield function, doing so would increase the expected yield. However, ϕ also influences the
yield favorability while also impose exothermicity limits. Working with higher ϕ implies working
with smaller temperature rise across reaction zone, therefore smaller overall temperature gradients
within the combustor, which in turn makes it more challenging to facilitate heat exchange,
potentially reducing 𝐸𝐸.
From design perspective, thermodynamically the three parameters 𝑇, ϕ, and 𝐸𝐸 are
straightforwardly linked. The combination of target temperature 𝑇 and mixture’s composition ϕ
sets the amount of 𝐸𝐸 needed from the reformer. The relationship can be mapped out as design
space where constraints can be visualized per Figure 36. The resulting 3D contour of positive
𝐸𝐸 = 𝑓(𝑇, ϕ) with 𝐸𝐸 on z-axis is an uphill contour with increasing slope towards the top-right
quadrant.

54
Figure 36: Qualitative design space of simple-design Swiss-roll reformer for NH3 reforming.
Firstly, the global ammonia-air reforming reaction turns endothermic at ϕ ≈ 6.5, hence
Swiss-roll solution cannot be used beyond such point. Secondly, reforming reaction cannot take
place if temperature drops too low, imposing a minimum temperature requirement on the design
space. For conventional single inlet/outlet Swiss-roll operating with premixed mixture, NOx
emission constraint can be clearly depicted near-stoichiometric mixtures, especially favoring
higher temperature. The remaining constraints are linked more strongly with the specific
combustor design, with the upper 𝐸𝐸 bound being linked to the pressure drop (visualized as
constant 𝐸𝐸 constraint line as one can assume an optimal design where 𝐸𝐸/∆𝑃 is maximized is
being deployed). Combustor’s temperature limit can also be represented here, with the exact
bounds for the two constraints being dependent on the specific design of the combustor.

55
Practically, the two boundaries can be extended by utilizing better designs. For instance, if
better designs that can achieve the same level of 𝐸𝐸 while keeping the same pressure drop cost
∆𝑃, then the upper bound would shift favorably upwards. Similarly, the core’s geometry can be
revised to potentially reduce high-temperature exposure to the core’s solid walls, allowing for
higher reaction temperature to be sustained at the core, which would shift the vertical-line rightside bound favorably further to the right.
However, the diagram does not account for the several effects. Primarily, the flashback
“out-of-center” constraint, which naturally occurs when working inlet flow contains excessive
enthalpy flux away from extinction limits. As a consequence, effective values of 𝐸𝐸 will inevitably
decrease from reformer’s full potential 𝐸𝐸𝑚𝑎𝑥 as the flame moves away from the core. When the
flame sits upstream the inlet channel operating in the “flashback” mode, the remaining inlet
channel section behind the flame would no longer contribute to heat recirculation as the
temperature gradients perpendicular to the wall are reversed, wastefully ejecting thermal energy
directly onto the adjacent outlet turns.
4.2.3 Two-dimensional CFD Predictions
Two-dimensional simulations were conducted on 3.5-turns Inconel-718 Swiss-rolls at 1-ft
scale, operating with NH3-air mixture at elevated 10 atm pressure to study reforming capabilities
for gas-turbine applications. The baseline combustor was directly scaled up, resulting in a channel
width of 1.25 cm, wall thickness of 0.25 cm, and the largest 2D core dimension is approximately
12 cm. Both plain-wall and finned Swiss-rolls were used in the study, with the latter having twice
effective internal heat-recirculation area compared to the plain-wall design. The fins’ widths were
uniformly sized to be the same as that of the wall’s thickness as minimum feature size is typically

56
the limiting manufacturing constraint. The choice of fins’ heights and spacings also ensured
uniform effective flow channel width. The range of Re values used here are relatively high
(≈ 6.0x103
- 3.5x104
), leveraging the pressure-scalability of NH3 chemistry.
The resulting outlet H2 yields, computed with Otomo’s mechanism, are shown as a function
of ϕ across four 𝑅𝑒 values in Figure 37. Only three major species, namely H2, H2O and NH3, were
noted in addition to extra N2 in the outlet reformate mixture, consistent with 0D results. The
amount of H2O formed corresponds precisely to the equilibrium yield as the timescales associated
with O and OH radicals’ consumptions which precede H2O formation reaction (NH3 + OH → NH2
+ H2O) are very fast. The remaining H-atoms were found to either remain in unreacted NH3 form
or get processed favorably into H2. The slower conversion pathway after O2 is used up here is tied
to NH3 + H → NH2 + H2 reaction, which favors H2 at sufficiently high temperature. Consequently,
the dependency of H2 yield on inlet value of ϕ is evident in the results. The yields generally exhibit
bell-shape figures, with the initial rises going from stoichiometric to slightly fuel-rich (1 ≤ ϕ ≤ 2)
are credited to the composition effects as temperatures are sufficiently high in this region. As the
amount of fuel is increased further, (ϕ > 2), the temperature effects (or lack thereof) dominate over
the composition effects and hence the yield decreases with increasing ϕ. Under normal
circumstances, as the results in Figure 37 for plain-combustor and finned combustor, the
favorability of H2 yield with increasing Re is associated with general increase in flame
temperatures as overall enthalpy supplies increase with increasing flowrate. For most of the cases
reported here, the flames are located sub-optimally upstream in the inlet channels, except for nearextinction cases toward very high ϕ where the flames retreated into the core region. The general
behavior was found to agree with experimental study at 6-inch scale conducted by our collaborator
(Radyjowski, 2023) despite lack of resources to conduct full-3D studies for direct comparison.

57
Figure 37: Outlet H2 yield percentages of simulated 1-ft scale, 3.5-turns combustors operating
with NH3-air mixtures at 10 atm between (Top) plain-wall and
(Bottom) finned (doubled internal area) Swiss-rolls without any artificial constraints.

58
Figure 38 shows the results from similar setup but with the flame artificially suppressed
from the inlet channels, allowing no reaction to occur there. These cases represent idealized
scenarios where the full heat-recirculation capabilities of the combustors were permitted to be
utilized. In principle, the analysis could have been conducted across series of individuallyoptimized (with respect to an arbitrary choice of geometrical dimension such as channel length,
fin, overall size, etc.) combustors with naturally-centered flame solutions for any given working
mixture. However, such method would be far less intuitive and much more computationally
intensive. The results here also show clear trends of bell-curve H2-yield, alike to natural-flame
cases. The H2-yields remarkably increase here as the synthetic increases in heat-recirculation
allows for higher temperatures to be reached prior to the reaction zone, while simultaneously
enabling richer mixtures to be effectively processed. Hence, the peak-yield ϕ values also shift
toward richer mixtures.
The maximum gas temperature values across the two plain-wall combustor cases are
provided in Figure 39. In contrast to free-flame cases where temperature naturally increases with
increasing Re, the trend is reversed for center-constrained flames cases. Such results were expected
as restricting the flame to the innermost core ensures favorable temperature gradients always exist
across the entire length of the wall dividing the hot and cold channels regardless of the working
mixture’s exothermicity. Additionally, the heat-recirculation residence time increases as 𝑅𝑒
decreases, translating into further increase in overall heat recovery. The combined effects greatly
raise the overall reaction zones’ temperatures and hence H2 yields. With this, the temperature
values become exceedingly high (1800 K ≲ 𝑇𝑚𝑎𝑥 ≲ 2900 K, for 𝑅𝑒 = 6.0x103
) compared to the
normal cases (1600 K ≲ 𝑇𝑚𝑎𝑥 ≲ 2000 K, also at same 𝑅𝑒), causing the composition effects to
become more apparent as temperature effects saturate.

59
Figure 38: Outlet H2 yield percentages of simulated 1-ft scale, 3.5-turns combustors operating
with NH3-air mixtures at 10 atm between (Top) plain-wall and (Bottom) finned
(doubled internal area) Swiss-rolls with flames artificially suppressed from inlet channels.

60
Figure 39: Maximum gas temperatures for plain-wall combustors operating with
(Top) natural flame and (Bottom) artificially core-constrained flames.
The maximum solid (Inconel718) zone temperature values predicted here (not shown) far
exceed material limitations, especially for 3D additive manufacturing materials. The temperature
rating of Inconel718 is only ≈ 1400 K, while for ceramic-based materials such as reaction-bonded
silicon carbide (RB-SiC) can potentially support up to ≈ 1700 K. For the conventional design used
here the maximum Inconel718 wall’s temperatures are generally on the similar order as that of the
flame temperature, except for scenarios where the flame sits in the core, where buffers of ≈ 200-
300 K were noted between the maximum gas and wall temperatures. This highlights the need for

61
designs with improved thermal management to keep the wall temperature below the materials’
limits.
4.2.4 Alternative Designs
The preceding section underlines key challenges associated with generating H2 from Swissroll reformer at high throughput. High reaction zone temperature threshold of ≈ 1800 K must be
achieved to produce decent yields while mitigating flashback and excessive heating of solid walls.
Various solutions have been considered and explored. Conventional single-stream premixed-flow
designs may remain viable provided the inlet channels are sufficiently scaled-down below
quenching distance while the core would consist of a decelerating flame-holding section. However,
such concept would be subjected to immense pressure drop which potentially eliminate large
portion of the design space. Other promising concept include separating the NH3 and air streams,
which then would meet at the core in a non-premixed manner, circumventing the flashback
entirely.
Figure 40: Outlet H2 yields of NH3-air mixtures with NH3 (also at 300 K) directly injected at the
core’s entry (perpendicular to air stream).

62
Extending from the study in prior section, performance of combustor variants with
separated fuel inlets placed at two different locations around the core were initially explored in 2D
simulations (the fuel at 300 K from inlet was simply removed and instead injected at the center).
Unfortunately, per Figure 40, severe reductions in extinction limits were observed but with very
small increase in H2 yield compared to the baseline free-flame plain reformer case. The combustor
notably failed to sustain the flame under the two higher 𝑅𝑒 values used in previous study. Per
energy balance check, the reduction was attributed to the decrease in recirculation as a significant
portion of mass have been omitted from the inlet turns. Unfortunately, for NH3-air mixture this is
a large concern as the relative amount of NH3 becomes significantly large compared to air,
especially for ultra fuel-rich mixtures. At ϕ = 3, NH3-to-total flowrate mass percentage is 33.1%
compared to 15.7% and 6.9% for methane-air and propane-air mixtures.
Moreover, inadequate mixing was found to be a major concern. Figure 41 shows qualitative
flame-index (𝜉), definition show below, (Yamashita, 1996) contours across two different injector
locations. The bulk of the flames observably are operating in a non-premixed fashion aside from
small regions of secondary recirculation zones. This explains the remarked increase in H2 yield as
the flame temperature becomes elevated from non-premixed operation. It is worth noting that the
use of 𝐸𝐸 parameter under these conditions would not be appropriate as the maximum flame
temperature no longer quantify the amount of heat being recycled. The results here underline the
need for 1) improved recirculation and 2) geometrical features which promote mixing at the
location where the two streams meet.
𝜉 ≡
𝛻𝑌𝐹,𝑚𝑎𝑥 ∙ 𝛻𝑌𝑂,𝑚𝑎𝑥
|𝛻𝑌𝐹,𝑚𝑎𝑥 ∙ 𝛻𝑌𝑂,𝑚𝑎𝑥|

63
Figure 41: Flame index (non-premixed vs premixed burn) contours of 1-ft combustor at
𝑅𝑒 = 6.0x103
, ϕ = 2 operating at 10 atm across two different 300 K NH3 injection locations.
Consequently, alternate design for separated-inlet variants introduced a separated channel
into the inlet spiral. This would allow partial amount of heat recirculation to be recovered. To
enhance mixing between the two streams pre-combustion, the dividing wall were made partially
porous at section close to the center. H2 yield was found to strikingly improved with the design.
For instance, at 𝑅𝑒 = 6.0x103
and ϕ = 3, H2 concentration increases to ~32% by mol compared to
~5% from original single-inlet stream design, driven by higher reaction zone temperatures
achieved without any artificial constraint. The improvements can be fully visualized through the
yield plot in Figure 42. The overall behavior promisingly resembles more toward centered flame
case in Figure 38, attributing to higher temperature overall. Across all designs studied here, NOx
levels were found to be very small (≤ 20 ppm) in the extended fuel-rich regime (ϕ ≳ 2.5) in relative
absence of O2.

64
Figure 42: Outlet H2 yield percentages of NH3-air mixtures with double-inlets, 3.5-turns, plainwall combustor coupled with mixing section prior to the core operating at 10 atm.
In terms of H-species, the outlet compositions here primarily consist of H2 and H2O for
ϕ < 2.5, with NH3 becoming progressively present as the flame temperature decreases with
increasing ϕ as shown in Figure 43. Expectedly, near stoichiometric the products are mostly H2O
and additional N2 at excessive temperature, even for values at outlet. H2 concentration peaks at
intermediate ϕ where reaction zone temperature is sufficient for reforming. Since operational
stability parameters such as flame speed (𝑆𝐿
) and ignition delay time (𝐼𝐷𝑇) are both strong function
of temperature, as well as H2 concentration, the reformer is expected to operate within 2 ≲ ϕ ≲ 4
regions where NOx is not too high (avoiding too low ϕ, shown in Figure 44) and 𝑆𝐿
, 𝐼𝐷𝑇
enhancements are insufficient (avoiding too high ϕ).

65
Figure 43: Outlet compositions and temperatures at varying flowrates of double-inlet combustor
coupled with mixing section prior to the core operating at 10 atm.

66
Figure 44: NOx concentrations across four Re cases of double-inlet, 3.5-turns reformer with
half-turn mixing section at 10 atm.
4.2.5 Reformate Analysis
From the perspective of gas-turbine application, if the high-temperature (≈ 800 K – 1300
K), H2-rich reformates here (Figure 43) were to be directly mixed with correspondinglystoichiometric amount of compressed air (assumed to be at 600 K, also at 10 atm) without any
further fuel addition (schematic depicted in Figure 45, mimicking actual use-case of gas turbine
despite reformer’s inlet temperature being at 300 K), the resulting reformate-air blends’
flammability would increase significantly compared to general NH3-air blends.
Figure 45: Simplified zero-dimensional gas-turbine reformate analysis schematic.

67
Figure 46: Laminar flame speeds of outlet reformate mixtures stoichiometrically-mixed with
600 K, 10 atm compressed air, calculated with Otomo’s mechanism.
Figure 47: Ignition delay times of outlet reformate mixtures stoichiometrically-mixed with
600 K, 10 atm compressed air, calculated with Otomo’s mechanism.

68
The H2 and temperature-driven enhancements can be quantified through changes in laminar
flame speed (𝑆𝐿
) and ignition delay time (𝐼𝐷𝑇), as shown in Figure 46 and Figure 47 respectively.
Neglecting moderately fuel-rich cases 1 < ϕ < 2.5 where autoignition occurs due to excessive
temperatures, the 𝑆𝐿 values here generally surpass that of typical hydrocarbon-air flames. Mainly
influenced by reformate’s temperature, the range of ignition delay times here are also very broad.
The integration of Swiss-roll reformer hence potentially allows the two key parameters to be
tailored to a specific gas-turbine requirement, enabling fuel-flexibility.
It is worth emphasizing that the increase in 𝑆𝐿
(as well as reduction in 𝐼𝐷𝑇) is a strong
function of both temperature and H2 content. To provide additional perspective, alternatively, the
upstream gas supplies were instead fixed by composition in configuration shown in Figure 48 for
ϕ = 1, starting at 10 atm and 300 K in the following analysis. An additional parameter, namely
“Bleed Factor (𝐵𝐹)”, is defined here which represents the portion of fuel which goes into the
reformer. The reformer’s actual operating ϕ is a free parameter, bringing corresponding amount of
air into the reformer to produce high-temperature, H2-rich, reformate. For simplification, the
reformer performance was assumed to be the same as that of 𝑅𝑒 = 3.49x104
cases (as profiles of
outlet species and temperature shown in Figure 43). The reformate is then mixed with the bypassed
amount of fuel and then air where the enhancements in 𝑆𝐿
is evaluated.
Figure 48: Simplified zero-dimensional stand-alone reformer analysis with upstream fixed ϕ.

69
Figure 49 shows the resulting reformate mixture’s 𝑆𝐿 at varying 𝐵𝐹 and reformer’s
operating ϕ. Expectedly, 𝑆𝐿
increases very strongly from original stoichiometric mixture’s value
(≈ 3.7 cm/s) at 10 atm. Even for small fuel bleed portion of 𝐵𝐹 = 0.25, the value of 𝑆𝐿
increases
by factors range from 1.7-3.0 favoring low ϕ due to higher final mixtures’ temperatures (430 K –
730 K) as the bulk of the fuel still remains in NH3 form (as well as the bulk of air is not used).
Hence, the improvement in 𝑆𝐿
is quite uniform regardless of the reformer’s operating mixture.
Figure 49: Resulting reformate mixture’s 𝑆𝐿 at varying 𝐵𝐹 and ϕ for the same original ϕ=1
NH3-air mixture at 300K, 10 atm (assumed reformer is operating at 𝑅𝑒 = 3.49x104
).
As 𝐵𝐹 increases further (𝐵𝐹 > 0.25), increasing portion of the fixed original mass is being
reformed into high temperature reformate. Despite H2 profiles peaking at intermediate ϕ, the

70
temperature effect on 𝑆𝐿
still dominates here as 𝑆𝐿
is a much stronger function of temperature than
the effect of recovered traces of H2. Near stoichiometric, the dilution from secondary air and NH3
flows at 300 K becomes much smaller (at 𝐵𝐹 = 0.6, final mixtures’ temperature for ϕ = 1.0 is 1260
K as opposed to ϕ = 1.5 which is at 950 K). This temperature gap is much larger compared to
2.5 ≤ ϕ ≤ 3.5 where the final mixtures’ temperatures differ less than 120 K within this range (as
the variations in diverted amount of air is much smaller for extended fuel-rich regime compared
to that of near-stoichiometric regime).

71
Chapter 5: Results – Flare Performance Studies
For flaring applications, strong transient variations of upstream conditions (both in flowrate
and composition) are primary causes of DRE performance reductions compared to ideal
conditions. Despite prior works on Swiss-rolls have shown extended operating limits through
many steady-state simulations and experimental studies, time-dependent investigations which can
provide potentially useful insights have been generally lacking. Hence, this chapter consists of two
sets of time-dependent simulations which were carried out to examine the Swiss-rolls’ capabilities
to operate under unsteady conditions and to determine any key design considerations which may
influence the design space of Swiss-rolls.
In terms of size-scaling, steady-state simulations were conducted in 2D up to 1-ft scale
with detailed chemistry. The results (not shown) were generally consistent with scaling guidelines
provided in (Chen, 2013), primarily lean-extinction limits were broadened at larger scales at highflowrate limit branch as more residence time for combustion is permitted there. The behavior is
also agreeable with prior experimental results (Crawmer, 2018) and reforming simulation results
in prior chapter. The study here extends from ¼-ft scale baseline combustor (5 cm height, 3 mm
channel width, 0.5 mm wall thickness and 22 mm core diameter) results (primary to reduce
computational costs) with chemistry switched to detailed chemistry (GRI-Mech III) since DRE
performances are concerned (and in absence of 1-step methane model). In principle, the
exothermicity increase facilitated by heat-recirculation combined with rapid combustion reaction
timescales should allow transient behavior at any specific timeframe to be comparable to steadystate results at the same conditions.

72
5.1 Oscillating Flowrate Study
This subsection introduces steady sinusoidal oscillatory profile to the inlet mass flowrate
without any adjustments in the mixture composition (ϕ) to determine the potential change in
effective extinction limits due to disturbances. The profiles here were characterized through
amplitude factor (𝐴) representing the ratio between maximum flowrate to the mean flow and
oscillation frequency (𝑓). The scope here focuses on single high flowrate benchmark case (average
value 𝑅𝑒 = 2577).
Figure 50: Effective extinction limits for high flowrate (𝑅𝑒 = 2577) case
under steady mass flow oscillations of varying amplitude factors and frequencies for
¼-ft scale Swiss-Roll combustor with CH4 detailed methane GRI-Mech III chemistry.

73
Per Figure 50, the results showing lean extinction limits at varying oscillation 𝑓 across two
values of 𝐴 are provided. The steady-state limits corresponding to the mean flow and peak
flowrates (for each value of 𝐴) are shown for comparison. The limits vary significantly despite the
overall time-averaged enthalpy flux being the same (albeit differences are much larger when
considering smaller local timeframes). At sufficiently high 𝑓, the extinction limits were found to
be practically the same as the steady-state limit as the combustor’s thermal response is much
slower compared to the timescales of changes experienced by the flame. Towards lower 𝑓 values,
below 𝑓 ≈ 0.3, the limits become narrower as heat loss timescales become comparable. In contrast,
the limit values naturally coincide with the flowrates where flow is most susceptible to extinction
under steady-conditions.
For estimated typical quasi-steady flare profile with turndown ratio (maximum-tominimum flowrate ratio) of 3 (f = 0.0625 s-1
, A = 1.5), the results suggest an additional ~14.6% in
fuel mass compared to steady operations will be required to sustain combustion under such
oscillation. The limits difference at two different extremes of 𝑓 was also observed for low 𝑅𝑒 cases
as well in preliminary results (not shown), but instead with the limits plateau to the minimum
flowrate troughs at sufficiently low 𝑓.
5.2 Fuel Surge Study
Separated transient study were conducted with increasing (then decreasing) fuel mass flow
under constant air mass flowrate (hence overall flowrates are permitted to change), representing
more abrupt, extreme changes which combustor would experience without any air-adjustment
control responses (either by design limitations or due to response rates being too slow).

74
The methane mass flow surges were modeled via Gaussian-type functions:
𝑓(𝑡) = 𝑓0 + (𝑓𝑚𝑎𝑥 − 𝑓0) exp [−
(𝑡 − (𝑏 + 𝑡0))
2
2𝑐
2
]
Which were applied separately to the overall mass flow, CH4 mol and air mol which are
default inputs for ANSYS Fluent for single premixed inlet. 𝑏 and 𝑐 are adjustable constants which
were manually determined to achieve correct overall profile. The geometry and models used here
are the same as the prior oscillatory study. Different surge profiles, characterized with varying
amplitudes (ϕ𝑝𝑒𝑎𝑘) and surge periods (𝑇𝑠𝑢𝑟𝑔𝑒), were investigated to determine changes in DRE
performances. The transient profiles were applied to steady-state converged result near lean
extinction limit (𝑅𝑒 = 1546, ϕ = 0.22) where the flame is centered in the core. Example of surge
profile for ϕ𝑝𝑒𝑎𝑘 = 2 and 𝑇𝑠𝑢𝑟𝑔𝑒 = 8 s is provided in Figure 51. The surges’ start and end times
were defined with respect to 0.1% difference in total mass flow compared to baseline flow.
Figure 51: Simulated fuel surge profile for 𝜙𝑝𝑒𝑎𝑘 = 2, 𝑇𝑠𝑢𝑟𝑔𝑒 = 8 s applied to simulated-steady
initial conditions 𝑅𝑒0 = 1546, 𝜙0 = 0.22 condition in a baseline premixed ¼-ft combustor in 2D.

75
Figure 52 shows the global maximum temperatures in each fluid and solid zones and the
comparison with instantaneous steady-state results (correspond to calculations where the mixtures
at such points are kept constant and running until time-independent results are obtained). ϕ𝑝𝑒𝑎𝑘 =
1 and ϕ𝑝𝑒𝑎𝑘 = 3 amplitudes used here translates to peak CH4 of 5-folds and 14-folds increase from
initial lean limit condition. The temperature profile for rich mixture peak ϕ𝑝𝑒𝑎𝑘 = 3 displays two
separate temperature spikes as the device passes through stoichiometry on two separate occasions.
Note that the flame and its location respond extremely fast to upstream changes, which the solid
phase noticeably lags behind as to be expected from convection delay.
Figure 52: Simulated transient and steady-state comparisons between maximum gas and solid
temperature responses of ¼-ft scale Swiss-roll combustor in 2D operating at lean-limit exposed
to 8-seconds methane surges with (Top) 𝜙𝑝𝑒𝑎𝑘 = 1 and (Bottom) 𝜙𝑝𝑒𝑎𝑘 = 3 under constant air
mass flow at baseline 𝑅𝑒0 = 1546, 𝜙0 = 0.22.

76
Significant gaps exist between transient and steady-state maximum wall temperatures,
which can serve as buffer provided sufficiently short surge duration. Note that the very high
temperature values here are not physical as solid phase change models were not included and
RB-SiC material limit temperature is on the order of 1400 K.
Figure 53: Species response profile with 𝑇𝑆𝑢𝑟𝑔𝑒 = 8s for (Top) 𝜙𝑝𝑒𝑎𝑘 = 1 and
(Middle) 𝜙𝑝𝑒𝑎𝑘 = 3 with (Bottom) comparison of CH4 and H2 to steady-state conditions.

77
The species mass fraction profiles over the surge durations (same cases as Figure 52) are
shown in Figure 53, which are practically symmetrical. The values closely follow instantaneous
steady-state solutions even at such rapid surge durations (for anticipated flare profiles). For lean
and near-stoichiometric mixtures, DRE performances are promising with all CH4 contents were
consumed. For very rich mixtures, the results show slight amount of excess CH4 as well as
reformed H2 as products of fuel-rich kinetic pathways.
The wall’s temperature profiles at four different locations for ϕ𝑝𝑒𝑎𝑘 = 2 and 𝑇𝑆𝑢𝑟𝑔𝑒 = 32 s
are provided in Figure 54 along with qualitative limit considerations. Note that despite the flame
readily retreated far upstream into inlet channels during surge ascend period, the temperature still
increases at centered locations due to increasing mixture strength. For less rapid surge timescales,
the wall’s temperature profile is expected to shift such that highest wall’s temperature would
coincide with flame’s location and the center part of walls are expected to cool down.
Figure 54: (Left) Transient temperature profiles at four RB-SiC wall locations for 𝜙𝑝𝑒𝑎𝑘 = 2,
𝑇𝑆𝑢𝑟𝑔𝑒 = 32 s case and (Right) surge duration-dependent qualitative viable operating space.

78
The qualitative limits (primary concerning DRE and overheating limits) are provided in
Figure 55 and Figure 56 respectively across ranges of ϕpeak and 𝑇𝑆𝑢𝑟𝑔𝑒 combinations. Insufficient
DRE performance limit constraints can be visualized as a relatively narrower envelope compared
to conventional extinction limits. For lean to slightly rich mixtures, corresponding to up to tenfold
increase in fuel, the methane DRE performance holds very close to 99%, and is expected to
maintain the value for longer surge periods as suggested by the preceding oscillatory-response
study. Beyond ϕpeak = 2, unfortunately DRE generally drops below 98% as the reactor switches
from incineration mode to reforming mode. Much further away towards ultra-rich mixtures (ϕpeak
> 7), DRE greatly drops, and the flame eventually extinguishes. Nonetheless, the limits here are
quite impressive, with steady-state limit ϕ value up to ϕ ≈ 7. It is worth noting that that, for brief
surge durations of less than 16 seconds, the flames were able to survive through the steady-state
limit without perturbation and are able recover to original conditions despite being subjected to
more than factor of 36 increase in fuel. Beyond 𝑇𝑆𝑢𝑟𝑔𝑒 > 30 s, the limits with and without
perturbation merges, suggesting the reactor’s solid zone more resembles quasi-steady manner at
least for this reactor’s scale.

79
Figure 55: DRE performance (time-averaged across slug duration) under different methane
surge profiles (𝜙𝑝𝑒𝑎𝑘, 𝑇𝑠𝑢𝑟𝑔𝑒) for 3.5 turns ¼-ft scale combustor operating initially at lean-limit
conditions (𝑅𝑒0 = 1546, 𝜙𝑝𝑒𝑎𝑘 = 0.22).
Figure 56: Total duration which solid domain (any point) exceeds threshold 1400 K temperature
under different methane surge profiles (𝜙𝑝𝑒𝑎𝑘, 𝑇𝑠𝑢𝑟𝑔𝑒) for 3.5 turns ¼-ft scale combustor
operating initially at lean-limit conditions (𝑅𝑒0 = 1546, 𝜙𝑝𝑒𝑎𝑘 = 0.22).

80
Chapter 6: Results – Catalytic Effects
Employing platinum catalyst greatly expands operational range of Swiss-rolls since the
catalyst can facilitate alternative combustion pathway at significantly lower temperature and in
richer conditions. This section is based on previous experimental investigations by Ahn (Ahn,
2005) where asymmetric extinction limits behavior favoring fuel-rich branch was demonstrated
through a 7 cm x 7 cm rectangular Swiss-roll with two Pt sheets placed in the core region. The
configuration and baseline mesh used in this study is shown together in Figure 57. The working
mixture here is C3H8-air in which the details regarding chemistry set are provided in the method
and CFD reference sections. The chemistry model was verified through simulated 1 mm x 1 mm
square channel of 1.5 cm length (section of honeycomb reactor) for C4H10 fuel operating at ϕ = 3.0
and 0.55 m/s flow velocity (Zhong, 2016). For C3H8 fuel used here, the simulated behavior from
same validation setup is similar albeit with slightly higher activation temperature (𝑇𝑚𝑖𝑛 ≈ 500 K
instead of ≈ 400 K for C4H10 fuel). Other aspects of the setup (turbulence, radiation, heat loss,
etc.) is methodically the same as that of other studies.
Figure 57: (Left) Experimental configuration of ¼-ft scale rectangular Swiss-roll with catalyst
placed in the core (Ahn, 2005) and (Right) baseline mesh used in the study.

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The predictions with the detailed mechanism show very consistent asymmetric extinction
and transition behaviors. The comparisons are shown in Figure 58 below with simulation where
Pt foils were placed at small distance of 1.5 mm away from the wall. The maximum temperature
of Pt foil ranges between 600 K – 730 K near catalytic-extinction points. The minimum simulated
𝑅𝑒 is as low as 𝑅𝑒 = 2 (0.92 cm/s averaged inlet velocity) at most favorable ϕ ≈ 3, which differs
moderately from reported experimental data of ϕ ≈ 7. On fuel-rich branch, at most favorable 𝑅𝑒
value, the simulated limit ϕ is as high as ϕ ≈ 140. Figure 59 shows the temperature contours at
three different limit locations.
Figure 58: Extinction and transition limits comparison between 2D simulation results
and experiments (experimental data taken from (Ahn, 2005)) for ¼-ft scale rectangular
combustor with Pt catalyst.

82
GRI-Mech III chemistry was also included in the model to provide catalytic-to-gas-phase
transition bounds. Strictly, for direct comparison with gas-phase limits in presence of Pt foil the
simulation should have determined the limits starting from gas-phase combustion region with both
combustion models (catalytic and gas-phase) and working outward until gas-phase reaction zone
subsides. However, when both models are computationally active, troublesome computational
instabilities were noted hence the catalytic-to-gas-phase transition was instead simulated and
reported here. The minimum transition temperature to gas-phase combustion was found to be ≈
1100 K on the lean branch.
Figure 59: Temperature contours for three different near-extinction points
(Top-Left) 𝑅𝑒 = 4, ϕ = 1.0, (Top-Right) 𝑅𝑒 = 41, ϕ = 0.26 and (Bottom) 𝑅𝑒 = 619, ϕ = 0.30

83
Chapter 7: Conclusions & Future Works
7.1 Conclusions
In this work, the practical viability of multi-scale (1) fuel-reforming and (2) incineration
applications facilitated by heat-recirculation from Swiss-roll reactors were separately explored.
Fuel reforming studies focused on H2 production through partial oxidation from heavier H2-carrier
fuels, with methane and propane fuels explored in small-scale devices with emphasis on smallscale power generation whereas ammonia fuel was explored for scale-up, high-pressure devices in
context of eliminating additional H2 dependency of ammonia-fueled gas-turbines.
For hydrocarbon fuels, 0D PSR analysis and 2D CFD results reveal the fast formations of
H2O (initial exothermic reactions) prevents further breakdowns of CH4, C2H2, C2H4 (secondary
endothermic SMR reactions), preventing equilibrium amount of H2 yield from being reached
within practical Swiss-roll residence time. Nonetheless, both CFD models and laboratory-scale
experiments at 1 atm produced agreeable results, demonstrating ~23% peak H2 on mol basis for
CH4 fuel and ~17% for C3H8 fuel.
As for ammonia fuel, the kinetic limitation is not as pronounced, as the remaining portion
of H2 may be recovered provided sufficiently high temperature through N-H pathways. The
expected yield of NH3-Air reforming was found to be a strongly dependent on amount of fuel and
high-temperature exposure. Hence, bell-shape H2 yield behavior with respect to ϕ was observed
both numerically and experimentally for conventional single-stream reformer. For moderately-rich
mixtures (1 ≤ ϕ ≤ 2.5) showing increasing reforming yield with increasing ϕ as temperature is
sufficiently high there. Whereas for ultra-rich mixtures (ϕ ≥ 2.5), in which temperature
progressively drops due to combination of lower mixture strength and insufficient recirculation

84
(exacerbated by flashback), H2 yield consequently decreases with increasing ϕ. Alternative designs
were subsequently explored to improve the performance, with double-inlet two-dimensional
reformer coupled with mixing-induced half-turn section producing peak H2 yield of ≈ 63%, a
notable 70% increase from ≈ 37% yield demonstrated from conventional design. The resulting
trends and improvements in fuel stability properties (𝑆𝐿
, 𝐼𝐷𝑇) of H2-rich, high temperature
reformates were noteworthy, highlighting viability of Swiss-roll as thermal fuel-reformers.
Extending from prior fuel-lean incineration-focused applications, this work focuses on
DRE performances of methane (CH4) for flaring applications through Swiss-rolls subjected to
transient upstream fluctuations. Under steady mass-flow oscillation (without composition change),
at sufficiently high oscillation frequencies (𝑓 > 0.5 s-1
) the extinction limits follow that of meanflow while for very slow frequencies (𝑓 < 0.01 s-1
), the limits expectedly follow that of the peak
flowrate (for high 𝑅𝑒, residence time-determined extinction regime). Steady-state results show
broader limits (both lean and rich) at larger scales operating at high flowrates, which are consistent
with prior scaling investigations. For Swiss-rolls subjected to fuel surges (keeping airflow
constant) of varying amplitudes and duration, the time-averaged DRE performances were found
to be acceptable (> 98%) within lean-to-moderately rich mixtures (0.22 ≤ ϕ ≤ 2). For surge
duration longer than 30 s, the reactor’s solid zone resembles quasi-steady manner at least for the
¼-ft scale studied.
Additionally, thermohydraulic performance improvement mechanisms of Swiss-roll
reactors were explored across different internal geometrical designs under the same set of practical
constraints (overall, core, feature sizes). For both two area-based methods (adding fins, turns), the
improvements in extinction limits, as well as 𝐸𝐸 vs ∆𝑃 relations at limits, were quantified at ¼-ft
scale. Similarly, thermal resistance-matching method (adjusting channel width ratios) was also

85
explored. Most notably, adding turns is generally favored from 𝐸𝐸 vs ∆𝑃 tradeoff perspective
while adding small fins also improve the tradeoff from turbulences effects.
Modeling efforts of Pt combustion catalyst-incorporated Swiss-roll was successfully
carried out, producing agreeable overall performance with prior experimental works where
extinction limits were greatly extended toward very low 𝑅𝑒 (𝑅𝑒 ≈ 2) and ultra fuel-rich regime
(ϕ ≈ 140). These behaviors enable Swiss-rolls to potentially be used in scaled-down applications.
7.2 Future Works
To fully-realize Swiss-roll heat-recirculating reactors for the targeted industrial-scale
applications, several design challenges which must be addressed. Regardless of the design concept
(premixed vs non-premixed), material’s maximum service temperature is the key design limitation
which determines performance limits for both incineration (high-temperature exposure limits from
exothermicity surges) and reforming (reaction zone temperature limits for reforming) uses. Further
efforts toward thermally improving Swiss-roll designs with three-dimensional features could go a
long way toward commercially-viable Swiss-roll products. In addition, upstream pressure budget
is uniquely critical to flare applications and future design efforts focusing on reducing outlet turns
pressure drop could address such challenge as well.
Extending from geometrical design study here, size-scaling analysis as well as
experimental efforts could provide further insights if high-temperature deformation-resistant
specimens become available (such as RB-SiC). For scaling, particularly in aspects of detailed
kinetics should also be more systematically investigated.

86
Figure 60: Temperature contours of reduced core section (with half-turn inlet/outlet channels) of
¼-ft scale combustor operating with single-step C3H8-air chemistry achieved through matching
of outermost core wall heat loss conditions, core outlet pressure and core inlet temperature
(same mass flowrate).
Further works can also be looked into reducing computational efforts required from 3D
simulations. The problem and domain can be simplified into heat-recirculating section and the
center region, especially for non-premixed designs where fuel is injected directly into the core,
hence the CFD domain needed to resolve the flame (for emission performances, DRE, etc.) can be
reduced to only the core section (coupled with simplified 0D energy balance or 2D CFD simplified
representations of the heat-exchanging channels to determine the pre-heating temperature).
Figure 60 shows preliminary simulated results for the vertically-symmetric domain ¼-ft size
conventional combustor with domain reduced to the core-section (still with insulation layers
included) for near-limit case where flame locates in the core per 2D predictions. This was achieved
by assuming constant temperature (taken from 2D results), mass flow core-inlet with matching
core-outlet pressure (also taken from 2D results). The outermost wall heat transfer coefficient was
iterated until results agree with 2D full-reactor simulation. The loss-reference temperatures (of

87
both hot and cold channels) were also directly taken from 2D results to complete the convective
heat loss description, hence energy balance for the core. The parameters used and resulting
agreements between 2D full model, simplified 2D and 3D cores are summarized in Table 5
provided below.
Table 5: Summary of key conditions used in the 3D half-core simplified model.
𝑅𝑒 = 619, ϕ = 0.17
2D Full 2D Core Only 3D Half Core
Cold Channel Loss Ref. Temperature (K) 1189 1189 1189
Hot Channel Loss Ref. Temperature (K) 1022 1022 1022
Half-Turn Inlet Pressure (Pa) 521.8 537.1 541.0
Half-Turn Outlet Velocity (m/s) 14.4 14.3 14.1
Fluid Max Temperature (K) 1279.6 1320.5 1321.2
Half-Turn Outlet Temperature (K) 1228.3 1240.3 1224.4
Half-Turn Outlet CO2 Mol (-) 0.0179 0.0191 0.0188

88
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95
Appendices: CFD Model Supplementary Details
As mentioned in the method chapter, all CFD works reported here employed Finite Volume
Method (FVM) approach in solving the Navier-Stokes equations. The method discretizes the
computational domain into a finite set of control volume where conservation laws are enforced
through flux conservations in algebraic forms, making up a system to be numerically solved in
order to render the flow field. Averaged physical quantities are stored at the center of each
individual volume and are spatially-extrapolated to obtain flux values at the boundaries.
Appendix A: Governing Equations
The flows inside Swiss-roll combustors are weakly-compressible, reacting flow with
intense energy release. Conservation equations for mass, momentum, energy, and species were
solved, as well as additional transport equations from turbulence and radiation models. Note that
ultimately, the RANS version of Navier-Stokes equation was used.
The single mass-conservation equation with no source term is given by:
𝜕𝜌
𝜕𝑡 + ∇ ∙ (𝜌𝑣⃗) = 0
Where the unknowns are density and two velocity vector components for 2D problems.
The general momentum-conservation equations without gravitational (𝜌𝑔⃗) and external (𝐹⃗)
body forces source terms reduce to:
𝜕
𝜕𝑡 (𝜌𝑣⃗) + ∇ ∙ (𝜌𝑣⃗𝑣⃗) = −∇𝑝 + ∇ ∙ (𝜏̿)

96
The static pressure is an added unknown scalar and additional equations are needed to
close the system.
The stress tensor (𝜏̿) = 𝑓(𝜇, 𝑣⃗) is expressed as:
𝜏̿= 𝜇 [(∇𝑣⃗ + ∇𝑣⃗
𝑇
) −
2
3
∇ ∙ 𝑣⃗𝐼]
Where 𝜇 is the molecular viscosity, I tensor is the unit tensor and the second term on the
right represents the effect of volume dilation, or the change in volume.
The general conservation of energy is described as:
𝜕
𝜕𝑡 (𝜌𝐸) + ∇ ∙ (𝑣⃗(𝜌𝐸 + 𝑝)) = −∇ ∙ [𝑘𝑒𝑓𝑓∇𝑇 − ∑ℎ𝑗
𝐽𝑗
𝑗
+ 𝜏𝑒𝑓𝑓 ∙ 𝑣⃗] + 𝑆ℎ
Or more specifically if Reynolds Stress Model (RSM) turbulence model, typically used in
throughout this work, is deployed.
𝜕
𝜕𝑡 (𝜌𝐸) +
𝜕
𝜕𝑥𝑖
[𝑢𝑖
(𝜌𝐸 + 𝑝)] =
𝜕
𝜕𝑥𝑗
[(𝑘 +
𝑐𝑝𝜇𝑡
𝑃𝑟𝑡
)
𝜕𝑇
𝜕𝑥𝑗
+ 𝑢𝑖(𝜏𝑖𝑗)
𝑒𝑓𝑓] + 𝑆ℎ
The equation enables the temperature of the fluid to be included, which adds another
unknown into the system. Total energy (𝐸) is comprised of three components, representing the
internal, kinetic, and potential contributions. The expression with the components in energy per
unit mass without gravitational potential is given as:
𝐸 = ∭𝜌𝑒𝑡 𝑑𝛺 = ∭𝜌 [𝑒(𝑇) +
1
2
𝑉
2
] 𝑑𝛺

97
The internal energy is a function of fluid temperature. The kinetic energy scales with fluid
velocity. The time rate of change of total energy (𝐸) depends on heat and work transfer per First
Law formulation:
𝑑𝐸
𝑑𝑡 = 𝑄̇ − 𝑊̇ + 𝑆̇
𝑔
The heat transfer (𝑄̇) and work transfer (𝑊̇ ) depends on fluid’s interactions with
surroundings. For Swiss-roll combustors, the heat transfer contributions come in various natures
(Ex. conduction, convection to/from internal walls, radiative heat transfer, and miscellaneous
losses to ambient, etc.). The two primary mechanisms of work done by a system, namely pressure
work and viscous work, categorically depends on the direction of the velocity component with
respect to the surrounding boundary.
𝑊̇
𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = ∯𝑝(𝑣⃗ ∙ 𝑛̂) 𝑑𝐴
𝑊̇
𝑣𝑖𝑠𝑐𝑜𝑢𝑠 = ∯(𝜏̿∙ 𝑣⃗) ∙ 𝑛̂ 𝑑𝐴
To close the system of equations, an equation of state is invoked. Ideal gas model was used
to correlate pressure, temperature, and density.
𝜌 =
𝑃
𝑅𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑇
Even though the flows here are considered incompressible (𝑀 < 0.1) where flow density
is unaffected by flow velocity and hence can be modeled as primary functions of temperature and
reference pressure, this work employed ideal-gas model throughout for caution. The density values
of solids were modeled as constants.

98
Thermal conductivity and specific heat capacity were modeled as temperature-dependent
polynomials over range of temperature values between 300 K to 3000 K, where constant values
were applied outside of these bounds. For fluid zones, kinetic theory-based models were used to
determine the values for thermal conductivity as well as viscosity of each individual species.
𝜇𝑠𝑝𝑒𝑐𝑖𝑒𝑠 = 2.67 × 10−6 √𝑀𝑠𝑝𝑒𝑐𝑖𝑒𝑠𝑇
𝜎
2Ω𝜇(𝑇
∗)
𝑇
∗ =
𝑇
(
𝜖
𝑘𝐵
)
𝑘𝑠𝑝𝑒𝑐𝑖𝑒𝑠 =
15
4
𝑅𝑢𝑛𝑖𝑣
𝑀𝑠𝑝𝑒𝑐𝑖𝑒𝑠
𝜇𝑠𝑝𝑒𝑐𝑖𝑒𝑠 (
4
15
𝐶𝑝𝑠𝑝𝑒𝑐𝑖𝑒𝑠
𝑀𝑠𝑝𝑒𝑐𝑖𝑒𝑠
𝑅𝑢𝑛𝑖𝑣
+
1
3
)
The Lennard-Jones parameters, namely particle diameter (𝜎) and potential well depth (
𝜖
𝑘𝐵
)
are inputs specific to each species. The viscosity collision integral (Ω𝜇) is a function of nondimensionalized temperature (𝑇
∗
). The values for the mixture were then computed from ideal-gas
mixing law.
𝜇𝑚𝑖𝑥𝑡𝑢𝑟𝑒 = ∑
𝑋𝑖𝜇𝑖
∑𝑗 𝑋𝑗∅𝑖,𝑗
𝑖
𝑘𝑚𝑖𝑥𝑡𝑢𝑟𝑒 = ∑
𝑋𝑖𝑘𝑖
∑𝑗 𝑋𝑗∅𝑖,𝑗
𝑖
∅𝑖,𝑗 =
[1 + (
𝜇𝑖
𝜇𝑗
)
1
2
(
𝑀𝑖
𝑀𝑗
)
1
4
]
2
[8 (1 + (
𝑀𝑖
𝑀𝑗
))]
1
2

99
As for the specific heat values of individual species, similar to the solid zone, these were
modeled as polynomial temperature fit based on values provided by CHEMKIN/Mechanism files
(also with temperature bounds on both extremes). For the mixture, the averaging is instead massfraction based:
𝐶𝑃𝑚𝑖𝑥𝑡𝑢𝑟𝑒 = ∑𝑌𝑖𝐶𝑃,𝑖
𝑖
The kinetic theory option for diffusivity computes the coefficient of each species-pair
(𝐷𝑖,𝑗
), which then would be used to calculate the diffusivity of each species with respect to the
mixture (𝐷𝑖,𝑚). Potential well depth value used in this expression is the geometric average of two
species (
𝜖
𝑘𝐵
)
𝑖,𝑗
.
𝐷𝑖,𝑗 = 0.0188
[𝑇
3 (
1
𝑀𝑖
+
1
𝑀𝑗
)]
2
𝑃𝑎𝑏𝑠 (
1
2
(𝜎𝑖 + 𝜎𝑗))Ω𝐷(𝑇
∗)
𝐷𝑖,𝑚 =
1 − 𝑋𝑖
∑ (
𝑋𝑗
𝐷𝑖,𝑗
𝑗,𝑗≠1 )
𝑇
∗
𝐷 =
𝑇
(
𝜖
𝑘𝐵
)
𝑖,𝑗
(
𝜖
𝑘𝐵
)
𝑖,𝑗
= √(
𝜖
𝑘𝐵
)
𝑖
(
𝜖
𝑘𝐵
)
𝑗

100
Appendix B: Turbulence Model
All the computational studies in this work employed Reynolds Averaged Navier-Stokes
(RANS) approach in resolving turbulence, which decomposes the flow velocity and other key
properties into mean and fluctuating components:
∅𝑖 = ∅̅
𝑖 + ∅𝑖
′
In which after such expressions of velocity terms are substituted into the governing
equations and some rearrangements, the resulting emergence of Reynolds Stress tensor 𝜏𝑖𝑗
′ ≡
𝜌𝑢𝑖
′𝑢𝑗
̅̅̅̅̅̅′
, representing added stresses due to turbulence motions, combination of mixing due to
turbulence fluctuations and smoothing through averaging, which requires simplified model for
closure for RANS-based methods.
𝜏𝑖𝑗
′ ≡ 𝜌 (
𝑢𝑥
′ 𝑢𝑥
̅̅̅̅̅̅′̅ 𝑢𝑥
′ 𝑢𝑦
̅̅̅̅̅̅′̅ 𝑢𝑥
′ 𝑢𝑧
̅̅̅̅̅̅′
𝑢𝑦
′ 𝑢𝑥
̅̅̅̅̅̅′̅ 𝑢𝑦
′ 𝑢𝑦
̅̅̅̅̅̅′̅ 𝑢𝑦
′ 𝑢𝑧
̅̅̅̅̅̅′
𝑢𝑧
′ 𝑢𝑥
̅̅̅̅̅′̅ 𝑢𝑧
′ 𝑢𝑦
̅̅̅̅̅′̅ 𝑢𝑧
′ 𝑢𝑧
̅̅̅̅̅̅′
)
Simpler RANS models (such as 𝑘-𝜀) works with Boussinesq hypothesis assuming that
Reynolds Stress 𝜌𝑢𝑖
′𝑢𝑗
̅̅̅̅̅̅′
is proportional to strain rates of mean (time-averaged) velocity in addition
to isotropic tensor assumption. Two additional unknowns present in turbulent viscosity
proportionality constant (𝜇𝑡
) expression 𝜇𝑡 = 𝜌𝐶𝜇(𝑘
2
/𝜀) (where 𝐶𝜇 = 0.09), namely turbulent
kinetic energy (k) and the dissipation rate (ε), results in two additional corresponding transport
equations required. However, despite prior works with 𝑘-𝜀 model showing promising agreements
(Kuo, 2007), the isotropic eddy viscosity assumption is perhaps innately not appropriate for
swirling confined flows. Consequently, Reynolds Stress Model (RSM) was mainly used
throughout this work, instead solving Reynolds stress transport equations and energy dissipation

101
equations. For 2D flows, this requires a total of five additional transport equations (four
components of tensor and dissipation rate) instead of two in the case of 𝑘-𝜀.
The full general transport equation of Reynolds stresses is provided as follows:
𝜕
𝜕𝑡 (𝜌𝑢𝑖
′𝑢𝑗
̅̅̅̅̅̅′) + 𝐶𝑖𝑗 = 𝐷𝑇,𝑖𝑗 + 𝐷𝐿,𝑖𝑗 + 𝑃𝑖𝑗 + 𝐺𝑖𝑗 + ∅𝑖𝑗 + 𝜀𝑖𝑗 + 𝐹𝑖𝑗 + 𝑆𝑢𝑠𝑒𝑟
𝐶𝑖𝑗 ≡
𝜕
𝜕𝑥𝑘
(𝜌𝑢𝑘𝑢𝑖
′𝑢𝑗
̅̅̅̅̅̅′
)
𝐷𝑇,𝑖𝑗 ≡ −
𝜕
𝜕𝑥𝑘
[𝜌𝑢𝑖
′𝑢𝑗
′𝑢𝑘
̅̅̅̅̅̅̅̅′̅ + 𝑝
′(𝛿𝑘𝑗𝑢𝑖
′ + 𝛿𝑖𝑘𝑢𝑗
′
)
̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
]
𝐷𝐿,𝑖𝑗 ≡
𝜕
𝜕𝑥𝑘
[𝜇
𝜕
𝜕𝑥𝑘
(𝑢𝑖
′𝑢𝑗
̅̅̅̅̅̅′
)]
𝑃𝑖𝑗 ≡ −𝜌 (𝑢𝑖
′𝑢𝑘
̅̅̅̅̅′̅
𝜕𝑢𝑗
𝜕𝑥𝑘
+ 𝑢𝑗
′𝑢𝑘
̅̅̅̅̅′̅ 𝜕𝑢𝑖
𝜕𝑥𝑘
)
𝐺𝑖𝑗 ≡ −𝜌𝛽 (𝑔𝑖𝑢𝑗
′𝜃
̅̅̅̅̅ + 𝑔𝑗𝑢𝑖
′𝜃
̅̅̅̅̅
)
∅𝑖𝑗 ≡ 𝑝
′ (
𝜕𝑢𝑖
′
𝜕𝑥𝑗
+
𝜕𝑢𝑗
′
𝜕𝑥𝑖
)
𝜀𝑖𝑗 ≡ −2𝜇
𝜕𝑢𝑖
′
𝜕𝑥𝑘
𝜕𝑢𝑗
′
𝜕𝑥𝑘
̅̅̅̅̅̅̅̅̅̅̅
𝐹𝑖𝑗 ≡ 2𝜌Ω𝑘 (𝑢𝑗
′𝑢𝑚
̅̅̅̅̅̅′̅
𝜀𝑖𝑘𝑚 + 𝑢𝑖
′𝑢𝑚
̅̅̅̅̅̅′̅
𝜀𝑗𝑘𝑚)
Note that only four of these terms (𝐷𝑇,𝑖𝑗, ∅𝑖𝑗, 𝐺𝑖𝑗, and 𝜀𝑖𝑗) require additional model to close
the equations. The other terms (𝐶𝑖𝑗, 𝐷𝐿,𝑖𝑗, 𝑃𝑖𝑗, and 𝐹𝑖𝑗) do not require any modeling.
For Turbulent Diffusive Transport term (𝐷𝑇,𝑖𝑗), the model is based on Daly and Harlow
(Daly, 1970), but with simplified version that uses scalar turbulent diffusivity:

102
𝐷𝑇,𝑖𝑗 ≡
𝜕
𝜕𝑥𝑘
(
𝜇𝑡
𝜎𝑘
𝜕𝑢𝑖
′𝑢𝑗
̅̅̅̅̅̅′
𝜕𝑥𝑘
)
The empirical constant 𝜎𝑘 was taken as 0.82 per commonly-used Lien and Leschziner
reference derived from a planar homogeneous shear flow case.
The Pressure-Strain term (∅𝑖𝑗) redistributes energy among the members of Reynolds
Stresses. For this work, a classic representation of pressure strain involving linear decomposition
comprising of three separate terms (Gibson, 1978; Fu, 1987; Launder, 1989) was used throughout.
More complex representations of pressure-strain such as the quadratic variation and stress-omega
models are theoretically more appropriate for Swiss-roll internal flows with curved surfaces and
swirls. However, based on good agreements with experiments in both prior and current work, the
switch to more descriptive models was deemed unnecessary.
∅𝑖𝑗 ≡ ∅𝑖𝑗,1 + ∅𝑖𝑗,2 + ∅𝑖𝑗,𝑤
The first contribution (∅𝑖𝑗,1) represents the return-to-isotropy decay term. The second
(∅𝑖𝑗,2) represents the rapid pressure-strain term. The last term (∅𝑖𝑗,𝑤) is the wall reflection term
which accounts for the redistribution of normal stresses within the wall’s vicinity. Primarily
reducing the perpendicular-to-wall normal stress and enhancing the stresses parallel to the wall.
∅𝑖𝑗,1 ≡ −𝐶1𝜌
𝜀
𝑘
[𝑢𝑖
′𝑢𝑗
̅̅̅̅̅̅′ −
2
3
𝛿𝑖𝑗𝑘]
∅𝑖𝑗,2 ≡ −𝐶2 [(𝑃𝑖𝑗 + 𝐹𝑖𝑗 +
5
6
𝐺𝑖𝑗 − 𝐶𝑖𝑗) −
2
3
𝛿𝑖𝑗(𝑃 +
5
6
𝐺 − 𝐶)]

103
∅𝑖𝑗,𝑤 ≡ 𝐶1
′
𝜀
𝑘
(𝑢𝑘
′ 𝑢𝑚
̅̅̅̅̅̅′̅
𝑛𝑘𝑛𝑚𝛿𝑖𝑗 −
3
2
𝑢𝑖
′𝑢𝑘
̅̅̅̅̅′̅
𝑛𝑗𝑛𝑘 −
3
2
𝑢𝑗
′𝑢𝑘
̅̅̅̅̅′̅
𝑛𝑖𝑛𝑘)
𝐶𝑙𝑘
3
2
𝜀𝑑
+ 𝐶2
′ (∅𝑘𝑚,2𝑛𝑘𝑛𝑚𝛿𝑖𝑗 −
3
2
∅𝑖𝑘,2𝑛𝑗𝑛𝑘 −
3
2
∅𝑗𝑘,2𝑛𝑖𝑛𝑘)
𝐶𝑙𝑘
3
2
𝜀𝑑
Gravitational term (𝐺𝑖𝑗) was not included in the 2D results reported here.
Finally, the dissipation rate (𝜀𝑖𝑗) was modeled as:
𝜀𝑖𝑗 =
2
3
𝛿𝑖𝑗(𝜌𝜀 + 𝑌𝑀)
𝑌𝑀 = 2𝜌𝜀𝑀𝑡
2
𝑀𝑡 = √
𝑘
𝑎
2
The additional term (𝑌𝑀) is called “Dilatation Dissipation” term based on Sarkar model in
which 𝑀𝑡
is the turbulent Mach number based on the sound speed. Computationally, the turbulence
kinetic energy (k) is obtained by taking the trace of the Reynolds Stress tensor. The scalar term of
dissipation (𝜀) is computed from a separate transport equation.
𝜕
𝜕𝑡 (𝜌𝜀) +
𝜕
𝜕𝑥𝑖
(𝜌𝜀𝑢𝑖
) =
𝜕
𝜕𝑥𝑗
[(𝜇 +
𝜇𝑡
𝜎𝜔
)
𝜕𝜀
𝜕𝑥𝑗
] + 𝐶𝜀1
1
2
(𝑃𝑖𝑖 + 𝐶𝜀3𝐺𝑖𝑖)
𝜀
𝑘
− 𝐶𝜀2𝜌
𝜀
2
𝑘
+ 𝑆𝜀
Each individual Reynolds stresses transport equation require, in addition to turbulence
dissipation rate 𝜀𝑖𝑗, boundary conditions that require a wall function to compute such values. A
separate transport equation for turbulence kinetic energy (𝑘) was solved to facilitate the k value,
which was then multiplied with different empirical constants to obtain the localnormal/tangential/binormal Reynolds stresses at the wall-adjacent cells.

104
(𝑢𝜏
′ )
̅̅̅̅̅̅2̅
𝑘
= 1.098
(𝑢𝜂
′ )
̅̅̅̅̅̅2̅
𝑘
= 0.247
(𝑢𝜆
′
)
̅̅̅̅̅̅2̅
𝑘
= 0.655
−
𝑢𝜏
′𝑢𝜂
̅̅̅̅̅′̅
𝑘
= 0.255
Since the dominance presence of walls inside Swiss-roll combustors impose no-slip
condition which need to be satisfied at the wall-gas contact surfaces, in addition to the wall being
the primary source of vorticity and turbulence, the spatial-transition of solution variables going
from the wall to the far-field fluid needs to be resolved methodically. Particularly, in computing
pressure drop from the wall shear stress (and channel dimensions), latter which is the product of
viscosity and velocity gradient at wall surface:
𝜏𝑤 = 𝜇
𝜕𝑢
𝜕𝑦|
𝑦=0
The two traditional approaches involve either 1) directly resolving the viscosity-affected
region down to the viscous sublayer through modifying the turbulence model or 2) using a semiempirical model to bridge the near-wall behaviors to the fully-turbulent region. The latter method,
typically referred to as “wall function method”, removes the need to modify the turbulence model
to account for the wall’s presence and was used throughout this work due to reduced computational
cost requirements.
The non-dimensionalized velocity (𝑢
+) and distance from the wall (𝑦
+), which is a function
of shear velocity (𝑢𝜏
) are given by:

105
𝑢
+ =
𝑢
𝑢𝜏
𝑦
+ = 𝑦
𝑢𝜏
𝜌
𝑢𝜏 = √
𝜏
𝜌
In the viscous sublayer very close to the wall (𝑦
+ < 5), the viscous stress dominates and
the relationship between 𝑢
+ and 𝑦
+ is linear. Far away from the wall, the turbulent Reynolds stress
dominates (𝑦
+ > 30) and the velocity profile is a logarithmic function. In summary:
𝑢
+
𝑙𝑎𝑚 = 𝑦
+ for 𝑦
+ < 5
𝑢
+
𝑡𝑢𝑟𝑏 =
1
𝜅
ln(𝑦
+) + 𝐶
+ for 𝑦
+ > 30
𝜅 is the von Karman constant. The transitional buffer layer in between where the two stress
contributions are comparable, the velocity profile is generally not well-defined there.
Standard wall function and enhanced wall treatments are two models mainly used in this
work. For larger flowrate and other computationally-demanding cases where pressure drop is of
secondary interest, standard wall function was mainly used due to coarser 𝑦
+ requirement for the
first layer thickness. Otherwise, the enhanced wall treatment approach was used due to better
resolution of viscous sublayers in addition to smoothing connection to outer logarithmic profile.
Appendix B1: Wall Function - Standard Wall Function
Standard Wall Function approach places the first cell centroid thickness covering the entire
viscous sublayer and utilizes models based on Launder and Spalding (Launder, 1974). In addition
to the velocity profile, similar laws based on Reynolds’ analogy was similarly used for temperature
(𝑓(𝑃𝑟)) and species (𝑓(𝑆𝑐)) profiles.

106
Appendix B2: Wall Function - Enhanced Wall Treatment
Enhanced wall treatment (Kader, 1981) is particularly advantageous as it is generally
adaptive to the mesh resolution being used. This is achieved by the introduction of blending
function (𝛤) with two empirically fitted constants to bridge the two linear and logarithmic wall
models:
𝑢
+ = e
𝛤𝑢𝑙𝑎𝑚
+ + 𝑒
1
𝛤
⁄ 𝑢𝑡𝑢𝑟𝑏
+
𝛤 = −
0.01(𝑦
+)
4
1 + 5𝑦
+
Reynolds’ analogy was also used for temperature (𝑓(𝑃𝑟)) and species (𝑓(𝑆𝑐)) profiles.
Appendix C: Radiation Model
In addition to the surface-to-surface transfer between combustor wall surfaces, gas-phase
combustion products also absorbs and scatter radiation, particularly CO2 and H2O. Consequently,
instead of a S2S model, this work employed DO radiation model which solves the governing
equation of radiative heat transfer for a selected finite number of discrete solid angles. The
radiative heat transfer equation (RTE) is given as:
𝑑𝐼(𝑟⃗, 𝑠⃗)
𝑑𝑠 + (𝑎 + 𝜎𝑠
)𝐼(𝑟⃗, 𝑠⃗) = 𝑎𝑛
2
𝜎𝑇
4
𝜋
+
𝜎𝑠
4𝜋
∫ 𝐼(𝑟⃗, 𝑠⃗
′
)𝛹(𝑠⃗, 𝑠⃗
′
)
4𝜋
0
𝑑𝛺
′
The equation solves for the radiation intensity 𝐼(𝑟⃗, 𝑠⃗), which is also a function of straightline beam direction 𝑠⃗, in addition to the spatial coordinate 𝑟⃗. The subscript (𝑠⃗
′
) denotes the
scattering direction and corresponding solid angle (𝛺
′
). The scattering coefficient (𝜎𝑠
) is a physical
property quantifying the tendency of particles to scatter incident radiation in different directions.

107
The DO model transforms the preceding equation into a transport equation solving for
radiation intensity in the spatial coordinates. The number of transport equations solved are the
same as the number of configured directions. The solution method used is identical to that used in
the fluid flow and energy equations. The energy-coupling method was not used as strong
correlation between energy and directional intensities are not expected. Hence, the equations for
the energy and radiation intensities were solved individually.
Appendix D: Kinetic Models
Finite rate chemistry was used throughout this work, solving individual reaction rates
through Arrhenius rate expressions. Except for surface reactions where adsorption and desorption
rate expressions were used. The general expressions for each of the two steps are:
𝑘𝑎𝑑𝑠 =
𝑠
𝛤𝑛 √
𝑅𝑢𝑛𝑖𝑣𝑇
2𝜋𝑀𝑠𝑝𝑒𝑐𝑖𝑒𝑠 (
𝑇
𝑇𝑟𝑒𝑓)
𝛽
′
𝑒
(
−𝐸𝑎′
𝑅𝑢𝑛𝑖𝑣𝑇
)
𝑘𝑑𝑒𝑠 =
𝐴
𝛤𝑛−1
(
𝑇
𝑇𝑟𝑒𝑓)
𝛽
′
𝑒
(
−𝐸𝑎′
𝑅𝑢𝑛𝑖𝑣𝑇
)
Where 𝑠 and 𝐴 are sticking probability and desorption pre-exponential factor. 𝛤 is the site
density, taken as 2.72 x 10-9 mol/cm2
per literatures cited. The remaining parts of the expressions
also contain temperature-exponential dependent and activation energy terms similar to Arrhenius
form.
As mentioned in the earlier section, prior works have shown that turbulence effects mainly
concern the heat-transfer enhancements of circulating channels hence no turbulence-chemistry
interaction was included. As for the chemistry sets, Table 6 provides a more descriptive summary.

108
Table 6: Kinetic Models Overview
Mechanism Description Reference(s)
Single-Step C3H8 1 reaction, 4 reactive species
C3H8 + 5O2 → 3CO2 + 4H2O
9 x 109
(m-s-kmole), 40 kcal/mole,
rate = k[C3H8]
m[O2]
n
, m = 0.1, n = 1.65
Adjusted at 𝑅𝑒 ≈ 1,000 for 3.5-turns
combustor at 0.25-ft scale
(Chen, 2011)
(Kuo, 2007)
GRI-Mech III 325 reactions, 53 species
Optimized for natural gas (CH4) combustion,
including NOx formations, no Soot model.
Skeletal propane model included.
(Smith, n.d.)
USC Mech II 784 reactions, 111 species
C1-C4 combustion mechanism, validated
across wide-rage ignition delay, shock-tube
species profiles, flame speed experiments.
NOx model not included.
(Wang, 2007)
(Davis, 1999)
San Diego Mech 270 reactions, 58 species
Minimized C1-C4 chemistry, no NOx model
(UC San Diego, n.d.)
C3H8/C4H10 Catalytic 84 reactions, 21 site + 14 gas-phase species
Validated with Zhong’s 2016 data.
(Zhong, 2016)
(Koop, 2009)
(Deutschmann, 1996)
(Zerkle, 2000)
(Chatterjee, 2001)
Otomo’s Mech 204 reactions, 32 species
NH3/H2/Air mechanism, validated with
ignition delay times, flame speed and species
flame structure across ranges of mixtures,
temperatures and pressure up to 30 atm.
NOx models included.
(Otomo, 2018)
(Song, 2016)
All gas-phase mechanisms were used without any modifications. Despite the ranges of
mixtures used in this work contain both extremely lean and rich mixtures, the key chemistry
pathways are expected to be sufficiently represented here. No Soot chemistry is present in the
listed hydrocarbon kinetic models, which warrants caution in working with extremely rich
(ϕ ≳ 3.5) mixtures. As for the surface chemistry, the C3H8/C4H10-Pt catalytic model is from a
combination of several sources from Deutschmann’s and Zhong’s groups hence a separate table
(Table 7) summarizing reactions and rate parameters used.

109
Table 7: C3H8/C4H10-Pt Catalytic Combustion Model Summary (𝐸𝑎′
in kJoules/Mole)
# Reaction s/A 𝛽
′ 𝐸𝑎′ Modifiers References
1 C4H10 + 2PT(S) => C4H10(S) 0.95 0 0 STICK (Zhong, 2016)
2 C4H10(S) => C4H10 + 2PT(S) 1.0E+13 0 45 (Zhong, 2016)
3 C4H10 + OH(S) + PT(S) => C4H9(S) + H2O(S) 1.0 0 0 STICK (Zhong, 2016)
4 C4H9(S) + H2O(S) => C4H10 + OH(S) + PT(S) 2.5E+20 0 23 (Zhong, 2016)
5 C3H8 + PT(S) => C3H8(S) 0.015 0 0 STICK (Zhong, 2016)
6 C3H8(S) => C3H8 + PT(S) 1.0E+13 0 20.9 (Zhong, 2016)
7 O2 + 2PT(S) => 2O(S) 0.07 0 0 STICK (Koop, 2009)
8 2O(S) => O2 + 2PT(S) 3.7E+21 0 227.4 COV/O(S) 0.0 0.0 -188.28/ (Zerkle, 2000)
9 CO2 + PT(S) => CO2(S) 0.005 0 0 STICK (Koop, 2009)
10 CO2(S) => CO2 + PT(S) 1.0E+13 0 27.1 (Zerkle, 2000)
11 CO + PT(S) => CO(S) 0.84 0 0 STICK (Koop, 2009)
12 CO(S) => CO + PT(S) 2.5E+16 0 125.5 COV/CO(S) 0.0 0.0 -33.0/ (Zerkle, 2000)
13 H2 + 2PT(S) => 2H(S) 4.46E+10 0.5 0.0 FORD/PT(S) 1/ (Deutschmann, 1996)
14 H2 + C(S) => CH2(S) 0.04 0 29.7 STICK (Zerkle, 2000)
15 2H(S) => H2 + 2PT(S) 3.7E+21 0 67.4 COV/H(S) 0.0 0.0 -10.0/ (Deutschmann, 1996)
16 H + PT(S) => H(S) 1.0 0 0 STICK (Zerkle, 2000)
17 H(S) => H + PT(S) 6.0E+13 0 254.4 COV/H(S) 0.0 0.0 -5.0/ (Quiceno, 2006)
18 O + PT(S) => O(S) 1.0 0 0 STICK (Zerkle, 2000)
19 O(S) => O + PT(S) 1.0E+13 0 358.8 COV/O(S) 0.0 0.0 -94.14/ (Zerkle, 2000)
20 OH + PT(S) => OH(S) 1.0 0 0 STICK (Zerkle, 2000)
21 OH(S) => OH + PT(S) 5.0E+13 0 251.1 COV/O(S) 0.0 0.0 -167.36/ (Zerkle, 2000)
22 H2O + PT(S) => H2O(S) 0.75 0 0 STICK (Koop, 2009)
23 H2O(S) => H2O + PT(S) 4.5E+12 0 41.8 (Koop, 2009)
24 CH3 + PT(S) => CH3(S) 1.0 0 0 STICK (Koop, 2009)
25 CH3(S) => CH3 + PT(S) 1.0E+13 0 163.0 (Koop, 2009)
26 CH4 + 2PT(S) => CH3(S) + H(S) 0.0009 0 72.2 STICK (Koop, 2009)
27 CH3(S) + H(S) => CH4 + 2PT(S) 1.5E+20 0 50.0 COV/H(S) 0.0 0.0 -2.8/ (Koop, 2009)
28 CH4 + O(S) + PT(S) => CH3(S) + OH(S) 5.0E+18 0.7 42.0 COV/O(S) 0.0 0.0 8.0/ (Koop, 2009)
29 CH3(S) + OH(S) => CH4 + O(S) + PT(S) 3.7E+21 0 85.9 (Koop, 2009)
30 CH4 + OH(S) + PT(S) => CH3(S) + H2O(S) 1 0 10 STICK (Koop, 2009)
31 C2H2 + PT(S) => C2H2(S)1 0.05 0 0 STICK (Koop, 2009)
32 C2H2(S)1 => C2H2 + PT(S) 1.0E+12 0 58.6 (Koop, 2009)
33 C4H10(S) => C4H9(S) + H(S) 7.0E+12 0 103.9 (Zhong, 2016)
34 C4H9(S) + H(S) => C4H10(S) 3.7E+21 0 41.8 (Zhong, 2016)
35 C4H10(S) + O(S) => C4H9(S) + OH(S) + PT(S) 9.9E+23 0 57.7 (Xiong, 2011)
36 C4H9(S) + OH(S) + PT(S) => C4H10(S) + O(S) 3.7E+21 0 41.8 (Xiong, 2011)
37 C4H9(S) + Pt(S) => C3H7(S) + CH2(S) 3.7E+24 0 68.7 (Zhong, 2016)
38 C3H7(S) + CH2(S) => C4H9(S) + Pt(S) 3.7E+21 0 55.8 (Zhong, 2016)
39 C3H8(S) + PT(S) => C3H7(S) + H(S) 3.7E+21 0 108.1 (Zhong, 2016)
40 C3H7(S) + H(S) => C3H8(S) + PT(S) 3.7E+21 0 56.6 (Zhong, 2016)
41 C3H8(S) + O(S) => C3H7(S) + OH(S) 1.7E+24 0 69.0 (Zhong, 2016)
42 C3H7(S) + OH(S) => C3H8(S) + O(S) 3.7E+21 0 31.3 (Zhong, 2016)
43 C3H7(S) + PT(S) => C3H6(S) + H(S) 3.7E+24 0 109.8 (Zhong, 2016)
44 C3H6(S) + H(S) => C3H7(S) + PT(S) 3.7E+21 0 75.9 (Zhong, 2016)
45 C3H7(S) + O(S) => C3H6(S) + OH(S) 3.7E+24 0 70.0 (Zhong, 2016)
46 C3H6(S) + OH(S) => C3H7(S) + O(S) 3.7E+21 0 45.3 (Zhong, 2016)
47 C3H6(S) + PT(S) => C2H3(S)1 + CH3(S) 3.7E+24 0 97.3 (Zhong, 2016)
48 C2H3(S)1 + CH3(S) => C3H6(S) + PT(S) 3.7E+21 0 55.8 (Zhong, 2016)
49 C2H3(S)1 => C2H3(S)2 1.0E+13 0 176.0 (Zerkle, 2000)
50 C2H3(S)2 => C2H3(S)1 1.0E+13 0 128.6 (Zerkle, 2000)
51 C2H3(S)2 + PT(S) => C2H2(S)2 + H(S) 3.7E+21 0 121.3 (Zerkle, 2000)
52 C2H2(S)2 + H(S) => C2H3(S)2 + PT(S) 3.7E+21 0 51.7 (Zerkle, 2000)
53 C2H2(S)1 => C2H2(S)2 1.0E+13 0 61.5 (Zerkle, 2000)
54 C2H2(S)2 => C2H2(S)1 1.0E+13 0 4.2 (Zerkle, 2000)
55 C2H3(S)1 + PT(S) => CH3(S) + C(S) 3.7E+21 0 46.9 COV/C(S) 0.0 0.0 50.0/ (Zerkle, 2000)
56 CH3(S) + C(S) => C2H3(S)1 + PT(S) 3.7E+21 0 46.0 (Zerkle, 2000)
57 C2H2(S)1 + PT(S) => C2H(S) + H(S) 3.7E+21 0 133.5 (Zerkle, 2000)
58 C2H(S) + H(S) => C2H2(S)1 + PT(S) 3.7E+21 0 66.9 (Zerkle, 2000)
59 C2H(S) + PT(S) => CH(S) + C(S) 3.7E+21 0 125.1 (Zerkle, 2000)
60 CH(S) + C(S) => C2H(S) + PT(S) 3.7E+21 0 121.3 (Zerkle, 2000)
61 CH3(S) + PT(S) => CH2(S) + H(S) 1.26E+22 0 70.3 (Zerkle, 2000)
62 CH2(S) + H(S) => CH3(S) + PT(S) 3.09E+22 0 0 COV/H(S) 0.0 0.0 -2.8/ (Zerkle, 2000)
63 CH2(S) + PT(S) => CH(S) + H(S) 7.31E+22 0 58.9 COV/C(S) 0.0 0.0 50.0/ (Zerkle, 2000)
64 CH(S) + H(S) => CH2(S) + PT(S) 3.09E+22 0 0 COV/H(S) 0.0 0.0 -2.8/ (Zerkle, 2000)

110
65 CH(S) + PT(S) => C(S) + H(S) 3.09E+22 0 0 COV/H(S) 0.0 0.0 -2.8/ (Koop, 2009)
66 C(S) + H(S) => CH(S) + PT(S) 1.25E+22 0 138.0 (Zerkle, 2000)
67 CH3(S) + O(S) => CH2(S) + OH(S) 3.7E+21 0 36.6 (Zerkle, 2000)
68 CH2(S) + OH(S) => CH3(S) + O(S) 3.7E+21 0 25.1 (Zerkle, 2000)
69 CH2(S) + O(S) => CH(S) + OH(S) 3.7E+21 0 25.1 (Zerkle, 2000)
70 CH(S) + OH(S) => CH2(S) + O(S) 3.7E+21 0 25.2 (Zerkle, 2000)
71 CH(S) + O(S) => C(S) + OH(S) 3.7E+21 0 25.1 (Zerkle, 2000)
72 C(S) + OH(S) => CH(S) + O(S) 3.7E+21 0 224.8 (Zerkle, 2000)
73 H(S) + O(S) => OH(S) + PT(S) 1.28E+21 0 11.2 (Koop, 2009)
74 OH(S) + PT(S) => H(S) + O(S) 7.39E+19 0 77.3 COV/O(S) 0.0 0.0 -73.22/ (Zerkle, 2000)
75 2OH(S) => H2O(S) + O(S) 7.4E+20 0 74.0 (Zerkle, 2000)
76 H2O(S) + O(S) => 2OH(S) 1.0E+20 0 43.1 COV/O(S) 0.0 0.0 240.58/ (Zerkle, 2000)
77 H(S) + OH(S) => H2O(S) + PT(S) 3.7E+21 0 17.4 (Zerkle, 2000)
78 H2O(S) + PT(S) => H(S) + OH(S) 1.15E+19 0 101.4 COV/O(S) 0.0 0.0 167.36/ (Chatterjee, 2001)
79 C(S) + O(S) => CO(S) + PT(S) 3.7E+19 0 0.0 (Koop, 2009)
80 CO(S) + PT(S) => C(S) + O(S) 3.7E+19 0 236.5 COV/CO(S) 0.0 0.0 -33.0/ (Koop, 2009)
81 CO(S) + O(S) => CO2(S) + PT(S) 3.7E+19 0 117.6 COV/CO(S) 0.0 0.0 -33.0/ (Koop, 2009)
82 CO2(S) + PT(S) => CO(S) + O(S) 3.7E+19 0 173.3 COV/O(S) 0.0 0.0 94.14/ (Koop, 2009)
83 CO(S) + OH(S) => CO2(S) + H(S) 2.0E+19 0 38.7 COV/CO(S) 0.0 0.0 -30.0/ (Koop, 2009)
84 CO2(S) + H(S) => CO(S) + OH(S) 2.0E+19 0 28.3 (Chatterjee, 2001)
Appendix E: Out-of-Plane Heat Loss Model
The applicability of out-of-plane resistance heat loss model was validated in prior work
(Chen, 2011) where temperature gradient profile along z-direction within the combustor section is
very small compared to external insulation sections due to relatively higher overall conductivity
of Swiss-roll materials and the gas-phase compared that of insulating materials. The validity is
expected to remain valid for geometrically similar devices at larger scales.
The principle of resistance heat transfer model preserves the heat flux per unit area across
each layer. The temperature values at each node aside from the first (𝑇1) (at combustor’s midplane) and last (𝑇∞) (ambient) are unknowns with corresponding number of equations equating
fluxes between each layer. The volumetric heat loss which was applied to each cell (assume
symmetry) is:
(
𝑄
𝑉
̇
) = −2 [(
𝑄
𝐴
̇
) ×
1
𝐻1
2
−𝐶𝑜𝑚𝑏𝑢𝑠𝑡𝑜𝑟]

111
For standard ¼-ft scale combustor with 5 cm height, the ceramic wafer insulation applied
at each end is 1 cm (𝑡𝑐𝑒𝑟𝑎𝑚𝑖𝑐) in thickness, coupled with 0.5 cm (𝑡𝑎𝑙𝑢𝑚𝑖𝑛𝑢𝑚) aluminum. The
outermost layer is a mixed free convection and radiative heat loss boundary. The schematic is
provided in Figure 16.
For solid zones, the following chain of equations was solved:
(
𝑄
𝐴
̇
) =
𝑘𝑖𝑛𝑐𝑜𝑛𝑒𝑙−718
𝐻1
2
−𝐶𝑜𝑚𝑏𝑢𝑠𝑡𝑜𝑟
(𝑇1 − 𝑇2
) =
𝑘𝑐𝑒𝑟𝑎𝑚𝑖𝑐
𝑡𝑐𝑒𝑟𝑎𝑚𝑖𝑐
(𝑇2 − 𝑇3
) =
𝑘𝑎𝑙𝑢𝑚𝑖𝑛𝑢𝑚
𝑡𝑎𝑙𝑢𝑚𝑖𝑛𝑢𝑚
(𝑇3 − 𝑇4
)
= 𝜀𝜎(𝑇4
4 − 𝑇∞
4
) + ℎ𝑓𝑟𝑒𝑒 𝑐𝑜𝑛𝑣(𝑇4 − 𝑇∞)
The heat loss per unit area terms were iteratively guessed until the solution is obtained for
any given mid-plane temperature (300 K < 𝑇1 < 3500 K). 𝑘𝑖𝑛𝑐𝑜𝑛𝑒𝑙−718 was assumed to be a
function of temperature 𝑇1. 𝑘𝑐𝑒𝑟𝑎𝑚𝑖𝑐 (0.2 W/mK) and 𝑘𝑎𝑙𝑢𝑚𝑖𝑛𝑢𝑚 (200 W/mK) were treated as
constants in the model. External surface emissivity 𝜀 was taken as 0.25 and ℎ𝑓𝑟𝑒𝑒 𝑐𝑜𝑛𝑣 was taken
as 10 W/m2K. The solutions were then fitted as a third-order polynomial function based on 𝑇1.
For fluid zones, the first resistance layer resistance was replaced by the inverse of heat
transfer coefficient (ℎ𝑒𝑓𝑓), which is a function of local Nusselt number (𝑁𝑢). For laminar flows,
𝑁𝑢 is a constant while for turbulent flow, it is a function of both 𝑅𝑒 and Prandtl number (𝑃𝑟)
(Ronney 2015), more specifically 𝑁𝑢 = 0.023𝑅𝑒0.8𝑃𝑟0.3
. For gases 𝑃𝑟 is close to unity and hence
𝑃𝑟0.3
term was assumed to be 0.9. The two functions were simply bridged at the 𝑅𝑒 value which
matches the 𝑁𝑢 values.
(
𝑄
𝐴
̇
) = ℎ𝑒𝑓𝑓(𝑇1 − 𝑇2
) =
𝑘𝑐𝑒𝑟𝑎𝑚𝑖𝑐
𝑡𝑐𝑒𝑟𝑎𝑚𝑖𝑐
(𝑇2 − 𝑇3
) =
𝑘𝑎𝑙𝑢𝑚𝑖𝑛𝑢𝑚
𝑡𝑎𝑙𝑢𝑚𝑖𝑛𝑢𝑚
(𝑇3 − 𝑇4
)
= 𝜀𝜎(𝑇4
4 − 𝑇∞
4
) + ℎ𝑓𝑟𝑒𝑒 𝑐𝑜𝑛𝑣(𝑇4 − 𝑇∞)

112
Unlike the solid zone, the solution here depends on other fluid properties (𝜌, 𝑉, 𝑘, 𝜇) in
addition to the temperature. The UDF model first determines if the cell belongs to a solid zone or
fluid zone based on the density value, then for fluid zone it determines which ℎ𝑒𝑓𝑓 model to use
based on the 𝑅𝑒 value. As a result, built-in iterative scheme was included to determine heat loss
per unit area for fluid zone. Since this work includes Swiss-rolls of various channel designs,
materials, and scales, geometrical parameters (both channels and insulation thicknesses) as well as
material properties had to be updated and validated prior to each setup. For simulations at different
scales, the thickness of insulations and supports were also linearly-scaled.
Appendix F: Solution Methods
Pressure-based solver was used throughout this work, which employs a projection method,
the mass conservation of the velocity field is satisfied by solving a pressure correction equation.
The pressure correction equation is derived from the continuity and momentum equations.
Figure 61: Pressure-based COUPLED algorithm flowchart
The COUPLED treatment of P-V relations of pressure-based solver was mainly used aside
from high computational cost cases where accuracy of pressure is a secondary concern where

113
SIMPLE option was used. The SIMPLE method sequentially solves for each velocity component
follows by the pressure-correction continuity equation. For COUPLED, the two steps are replaced
by a single step process where the coupled system of equations are solved Figure 61. Naturally,
absolute velocity formulation was used for all cases. Both steady-state and transient solvers were
both used depending on the specific study. Mixed-order upwind discretization schemes were used
and adjusted based on the convergence behaviors. For transient studies, both fixed and CFL-based
adaptive time-stepping were used depending on the type of study. Courant numbers were generally
kept below unity. The mesh sizing and sensitivity tests were discussed in prior section.
Conservation of mass, energy, and species were checked in all results.

Abstract (if available)

Abstract This work explores the potential of heat-recirculating, thermally-efficient, “Swiss-roll” reactors in the context of various energy-transition applications at varying scales. Without involving any mass transfer, the simple device comprising of combustion core enclosed with built-in spiral heat exchanger allows combustion to be sustained far outside of conventional flammability limits, both lean and rich, without any external energy input. Such “excess enthalpy/superadiabatic” combustion mode enables (1) more efficient destruction of methane as well as reducing susceptibility to fluctuations typical in flaring applications and (2) hydrogen production through fuel reforming of hydrocarbons for portable-scale power generation and ammonia for decarbonized gas-turbine applications.
The first set of contribution focuses on fuel-reforming, where corresponding detailed kinetics were analyzed to determine yield favorability, in which design spaces for Swiss-roll devices were subsequently inferred. Various reactor designs were explored through two-dimensional computational fluid dynamics (CFD) calculations, providing insights into mechanisms influencing hydrogen yield and highlighting key limitations of conventional single-stream Swiss-roll designs. For ammonia fuel, a promising design was proposed and the properties of the produced high-temperature, hydrogen-rich reformates were analyzed, demonstrating viability of Swiss-roll as fuel-reformers. The second include two different transient analyses to determine changes in methane destruction efficiency and extinction limits in context of flares when subjected to upstream fluctuations. Lastly, various performance improvement methods (geometrical and catalysts) were explored, each with unique thermohydraulic performance trade-off behaviors capable of further expanding operational limits in pursuit for more efficient combustion and reforming.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Bhuripanyo, Patharapong (author)

Core Title Studies of Swiss-roll combustors for incineration and reforming applications

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Aerospace Engineering

Degree Conferral Date 2024-08

Publication Date 08/26/2024

Defense Date 08/19/2024

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

Tag combustion,fuel reforming,heat-recirculation,incineration,OAI-PMH Harvest

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ronney, Paul (committee chair), Egolfopoulos, Fokion (committee member), Tsotsis, Theodore (committee member)

Creator Email patharap@usc.edu;patharapong.b@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113999JME

Unique identifier UC113999JME

Identifier etd-Bhuripanyo-13430.pdf (filename)

Legacy Identifier etd-Bhuripanyo-13430

Document Type Dissertation

Format theses (aat)

Rights Bhuripanyo, Patharapong

Internet Media Type application/pdf

Type texts

Source 20240827-usctheses-batch-1202 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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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

Repository Email cisadmin@lib.usc.edu