ADVANCING COMBUSTION TECHNOLOGY: A
FOCUS ON ALTERNATIVE LIQUID FUELS AND

INNOVATIVE DESIGNS OF POROUS MEDIA
BURNERS

A Dissertation

Presented to the Faculty of the Graduate School

of Cornell University

in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

by

Nicholas DiReda

May 2024



© 2024 Nicholas DiReda

ALL RIGHTS RESERVED



ADVANCING COMBUSTION TECHNOLOGY: A FOCUS ON

ALTERNATIVE LIQUID FUELS AND INNOVATIVE DESIGNS OF POROUS

MEDIA BURNERS

Nicholas DiReda, Ph.D.

Cornell University 2024

Increasing demands for energy efficiency and reduced emissions drive ongo-

ing advancements in combustion technology. Traditional combustion methods

face challenges related to efficiency, emissions, and fuel flexibility. Therefore, a

need exists for novel combustion technologies that innovate fuel utilization and

combustion processes. The exploration of alternative liquid fuels, replacing con-

ventional options like ethanol, holds considerable potential in enhancing over-

all energy consumption and expanding fuel options. Similarly, porous media

burners (PMBs) present a transformative approach, offering improved combus-

tion efficiency, leaner flammability limits, and reduced emissions. This thesis

ventures to explore and advance these novel combustion technologies, aiming

to enhance our understanding of the fundamental thermodynamic mechanisms

and provide practical insight into real world applications.

First, we present an experimental and computational analysis of the iso-

lated droplet burning of two furanic compounds, 2-methylfuran (MF) and

2,5 dimethylfuran (DMF), noted by the Department of Energy as prospec-

tive biomass derived additives into existing petroleum based fuels. Exper-

iments were performed in a reduced gravity environment, facilitating one-

dimensional burning amenable to numerical simulations with detailed chem-

istry. Further, the oxidative stability of stored samples was investigated. Gas



chromatography-mass spectrometry (GC-MS) revealed important considera-

tions when storing DMF due to the polyunsaturated chemical structure and a

susceptibility to oxidation and chemical breakdown. Nonetheless, these fuels

are considered ”top tier” alternatives because of the well established produc-

tion methods from biomass.

Second, we studied the effects of dynamic stability in a conventional SiC

PMB, motivated by the fluctuating fuel flow and composition in biomass gasi-

fication. Experiments involved varying sinusoidal equivalence ratios (Φ) while

maintaining constant flow rate to simulate volatility from the gasification pro-

cess. Tests across differentΦ amplitudes and forcing frequencies revealed a non-

monotonic relationship between mixture pore scale Reynolds number (Repore)

and dynamic stabilization. Notably, a Φ of 0.2 was sustained under specific ini-

tial conditions, corresponding to the widest flammability range on the steady

stability map. However, emissions data showed higher CO accumulation dur-

ing sinusoidal experiments compared to baseline, attributed to the convective

lag of fuel during a cycle. Additionally, a transfer function derived from stable

data predicted system response under different conditions. This study provides

insights into the dynamic thermal response of PMBs and the potential for con-

trolling combustion in bio-derived fuels from fluctuating sources.

Next, we employed additive manufacturing (AM) to create and analyze four

PMBs with internal morphology inspired by biological systems, such as butter-

fly wings and mitochondrial membranes. Specifically, we integrated the triply

periodic minimal surfaces (TPMS) architectures of diamond (D), gyroid (G), I-

WP (I), and Schwartz primitive (P) into PMBs. Each burner was designed to

a constant porosity of 0.75 and similar pore-size gradation scheme. Experi-

mental analyses cover lean stability, emissions, and temperature distribution.



A volume-averaged model utilizing correlations for Nusselt numbers specific

to each TPMS was used to predict stability regimes and temperature profiles.

Lastly, computational fluid dynamics (CFD) was performed to explore the pore-

scale hydrodynamic and heat transfer mechanisms underlying the experimental

observations. We found the I and D burners exhibited the widest stable opera-

tion ranges and highest temperatures. Additionally, the volumetric heat transfer

coefficient used within the model captured the trends seen experimentally. Fur-

thermore, pore-scale simulations revealed the existence of thermal ”pockets”

potentially explaining the enhanced interphase heat exchange unique to the I

burner at low flow rates. This study isolates morphologic effects on combustion

performance, highlighting interphase heat exchange as a dominant factor. Our

results underscore the importance of internal morphology and the influence on

combustion physics.

Finally, we studied the impact of porosity, morphology, and material compo-

sition on the mechanical performance of AM ceramic PMBs. Thermal-structural

simulations of five different TPMS-based PMBs were conducted to analyze

thermal-stress distributions. Alumina and mullite structures were 3D-printed

and tested in a methane-air combustion experiment, revealing superior dura-

bility in mullite compared to alumina. TPMS burners with higher specific

surface area, tortuosity, and moderate pore diameter, such as D and I, exhib-

ited lower thermal strain and reduced propensity for thermal-structural failure

while maintaining the ability to sustain a flame. X-ray imaging confirmed a

correlation between predicted stress regions and experimental crack formation.

These findings provide a foundation for future work in optimizing PMB perfor-

mance and longevity through AM techniques.



BIOGRAPHICAL SKETCH

Nicholas DiReda was born in Worcester, Massachusetts and grew up in a nearby

town called Oxford. He played hockey under the watchful eye of his father,

also named Nick, who was his coach until high school. At Saint John’s High

School, he played both hockey and golf, winning 3 state titles and matching the

school record for lowest 9 hole score (5 under par). After graduating from high

school in 2013, he went on to play Division 1 Men’s Golf at Central Connecticut

State University where he majored in Civil Engineering. Ironically, it was this

program that revealed an exceptional interest in the field of Thermodynamics.

After graduating in 2017, he went on to Worcester Polytechnic Institute to

pursue a Master of Science degree in Aerospace Engineering while working

full-time at General Dynamics Electric Boat and part-time as a bouncer at a local

night club. During this time, he began experimental supersonic combustion re-

search and was encouraged by his advisor to consider PhD programs. In 2020,

he began as a PhD student in the Mechanical and Aerospace Engineering pro-

gram at Cornell University. Here, he took advantage of the spectrum of oppor-

tunities uniquely offered by Cornell. Alongside his pursuit of a PhD in Ther-

mal Sciences, he relentlessly delved into biomedical research and completed

relevant coursework, both through Cornell and outside institutions, focusing

on bio-energetics, immunology, circadian biology, and nutrition in an effort to

identify the root cause of his own autoimmune diseases. The skills he learned

during his pursuit of a PhD in engineering provided a unique perspective on

approaching human health problems. He was successful, now dedicates the

remainder of his life to spreading the information he has learned and helping

others optimize their health.

iii



To my family:

Dad, Ma, Bella, Alex, the Aunts, Tim,

thank you for always picking up the phone

iv



ACKNOWLEDGEMENTS

This list could be as long as the main text. But the first person I’d like to thank

is my advisor, Dr. Sadaf Sobhani, for opening the doors to her lab and sup-

porting me as I navigated through this maze. Her understanding of Thermal

Science and academia in general has been indispensable. I’m also indebted to

my friends within the lab and department, who were passionate enough to care

about their work but down-to-earth enough to grab a drink or sing karaoke

whenever we felt like it.

I’d be remiss without mentioning the members and coaches at my local

CrossFit gym. I said I would have left Ithaca at one point if it weren’t for that

community, and I meant it. They’ve opened their arms to me as both a bother-

some member and now a coach, and I’ve gained lifelong friends and invaluable

experience because of it. Furthermore, I have to thank my band of ”dirtbags”

that has stuck together since high school. Despite some of us moving away and

getting married, we’ve remained close friends and always make a point to have

a fire or ride some horses when we’re all in the same area. Not to mention, the

endless laughs from sharing social media posts or phone calls because ”texting

is for children.”

Lastly, I owe everything to my family. I put 100,000 miles on my car over the

last 4 years traveling back home for one reason or another, ”but that’s how we

do it.” Thankful to my Ma for always checking in and letting me crash at her

house despite leaving a mess on the kitchen counter. Alex for texting or calling

just to say hi and ”see how it’s goin out there.” Isabella for chatting everyday

and being someone to look up to despite her being 8 years younger. Aunt An-

drea for listening when I needed to vent about some health issue. Aunt Debbie

for checking in on me frequently. Cousin Tim for the hours of phone calls airing

v



out our beef with the world and how we can escape this matrix. Sue-shi for

keeping an eye on my old man while I’ve been away. And finally, the old man

himself for setting the perfect example of what it looks like to be a man. His

leadership throughout my life has forged who I am today and his unshakable

support has made my doctorate possible.

vi



TABLE OF CONTENTS

Biographical Sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

1 Introduction 1
1.1 Isolated Droplet Combustion . . . . . . . . . . . . . . . . . . . . . 1
1.2 Porous Media Combustion . . . . . . . . . . . . . . . . . . . . . . . 3

2 Isolated droplet combustion of alkylated furans with an assessment of
oxidative stability 8
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Oxidative stability . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1 Burning rate . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2 Flame and soot behavior . . . . . . . . . . . . . . . . . . . . 20
2.3.3 Oxidative stability . . . . . . . . . . . . . . . . . . . . . . . 24

2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3 Dynamic stability of porous media burners and sensitivity to oscillat-
ing inlet conditions 29
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3.1 Steady operation . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.2 Dynamic operation . . . . . . . . . . . . . . . . . . . . . . . 37

3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4 Experimental and computational investigation of bio-inspired mor-
phologies in porous media burners 47
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Burner design and additive manufacturing . . . . . . . . . . . . . 49

4.2.1 Burner design . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.2 Additive manufacturing . . . . . . . . . . . . . . . . . . . . 50

4.3 Experimental and Computational Methods . . . . . . . . . . . . . 52
4.3.1 Experimental setup and procedure . . . . . . . . . . . . . . 52
4.3.2 Volume-averaged modeling . . . . . . . . . . . . . . . . . . 53
4.3.3 CFD simulations . . . . . . . . . . . . . . . . . . . . . . . . 54

vii



4.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.4.1 Stability and emissions . . . . . . . . . . . . . . . . . . . . . 56
4.4.2 Temperature distributions . . . . . . . . . . . . . . . . . . . 59
4.4.3 CFD results and discussion . . . . . . . . . . . . . . . . . . 62

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5 Thermal and structural performance of additively manufactured ce-
ramic porous media burners 70
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.2.1 TPMS structures . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2.2 Computational modeling . . . . . . . . . . . . . . . . . . . 75
5.2.3 Additive manufacturing . . . . . . . . . . . . . . . . . . . . 77
5.2.4 Characterization and testing . . . . . . . . . . . . . . . . . 78

5.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.3.1 Flexural bending and TMA tests . . . . . . . . . . . . . . . 81
5.3.2 Thermal-structural simulations . . . . . . . . . . . . . . . . 82
5.3.3 Combustion experiments . . . . . . . . . . . . . . . . . . . 87
5.3.4 Durability and X-ray image analysis . . . . . . . . . . . . . 88

5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6 Conclusions and Future Work 92
6.1 Main Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.2 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

A Additional Data 97
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
A.2 MF and DMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
A.3 Operation of the burner apparatus . . . . . . . . . . . . . . . . . . 100

Bibliography 105

viii



LIST OF TABLES

1.1 Assumptions for Droplet Combustion . . . . . . . . . . . . . . . . 2

2.1 Properties of MF and DMF . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Results from stability analysis . . . . . . . . . . . . . . . . . . . . 25

3.1 Limits of stable dynamic conditions. . . . . . . . . . . . . . . . . . 44

4.1 Parameters for experimental models. . . . . . . . . . . . . . . . . 50

5.1 Triply Periodic Minimal Surfaces (TPMS) studied and corre-
sponding implicit functions used to defined the structure. . . . . 73

5.2 Specific surface area (Sv), pore diameter (dpore), minimum sheet
thickness (tavg), and tortuosity for 1 mm 75% porosity unit cells
of each TPMS structure. . . . . . . . . . . . . . . . . . . . . . . . . 75

ix



LIST OF FIGURES

1.1 Heat transfer modes and temperature profile exhibited within a
conventional PMB . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Selected raw images of fuels discussed. Time corresponds to
time after spark. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Comparison between predicted and measured burning rates (a).
Sensitivity analysis (b)-(e) shows responses to changing initial
droplet temperature (Baseline: T = 293 K), or gas thermal con-
ductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Calculated burn rates (Kb) starting from estimated onset of
steady state burning

(
0.6 s/mm2

)
. . . . . . . . . . . . . . . . . . . 19

2.4 Temporal evaluations of soot volume fraction (a)-(f) as a function
of radial distance from droplet center acquired using the light
extinction method for three experiments of each fuel. Measured
SSR and FSR combined with numerical data (g) with quantifica-
tions of soot production by integrating SVF data (h) and averag-
ing the peaks of the SVF curves (i). . . . . . . . . . . . . . . . . . . 22

2.5 Visible residue formed after evaporation of 5 mL of DMF . . . . . 26

3.1 Foams used in the experiment include the 10 PPI SiC foam (a)
and 100 PPI SiC foam (b). P&ID diagram for the laboratory ex-
perimental setup (c). Schematic of the PMB setup, with the ther-
mocouple locations labeled (d). Example of unsteady flow for
a 30 s period and equivalence ratio amplitude of 0.15 at an ini-
tal condition of 0.6 (e) Oscillatory combustion within the PMB
ending in blow-off (f). . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Experimental stability and CO measurements (a) at steady state
operation. Experimental and computed solid (dashed line) and
gas (solid line) axial temperatures at equivalence ratios of 0.70
(b) and 0.55 (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Temperature and CO data as a function of time at Φ = 0.6 and
mass flux of 0.50 kg/m2/s (Repore = 158) for unstable failure by
blow-off at 1/60 Hz (a) and stabilization at 1/30 Hz (b). Normal-
ized T100-10 and CO responses shifting from unstable (c) to stable
(d) by reducing ∆Φ for a given frequency of 1/120 Hz. . . . . . . 37

3.4 Phase portraits of normalized system input-output signals com-
paring unstable (a) and stable (b). Fourier transforms of the in-
terface thermocouple response data (T100-10) with multiple modes
at unstable (c) and stable (d) conditions. . . . . . . . . . . . . . . 38

3.5 Transfer function predictions for three different cases compared
with experimental output data. . . . . . . . . . . . . . . . . . . . . 41

3.6 The maximum stable Pe for each frequency (splines) is plotted
against Repore. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

x



4.1 Geometric modeling and 3D printing of the mullite burners . . . 51
4.2 Experimental setup with instrumentation as labeled. Thermo-

couples are placed radially within shell, axial locations are shown. 51
4.3 Geometric model used in CFD with boundary conditons. . . . . 55
4.4 Surface flame at the outlet of the P burner (a). Initial heating pro-

files at start-up conditions,Φ = 0.95 and mass flux = 0.3 kg/m2/s,
for the four burner types. (b) . . . . . . . . . . . . . . . . . . . . . 57

4.5 Experimentally determined stability limits (a)-(c) compared with
VAM results (d)-(f). Shaded contours of experimental CO read-
ings are shown in (a)-(c). . . . . . . . . . . . . . . . . . . . . . . . 58

4.6 Experimental and computational axial temperature profiles de-
termined for the D, G, and I burners (a)-(c) at the flash-back (F-B)
and blow-off (B-O) limits. Shaded regions illustrate interphase
heat transfer between the gas and solid. . . . . . . . . . . . . . . . 60

4.7 Experimental axial temperature profiles for the D, G, and I burn-
ers at a common stable inlet condition. . . . . . . . . . . . . . . . 61

4.8 Velocity streamlines through the different TPMS models for an
inlet velocity of 0.5 m/s. . . . . . . . . . . . . . . . . . . . . . . . . 63

4.9 Mid-plane contours of velocity (a) and vorticity (b) for an inlet
velocity of 0.5 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.10 Estimated hydraulic tortuosity and particle residence time
within each model for an inlet velocity of 0.5 m/s. . . . . . . . . . 64

4.11 Mid-plane temperature contours (a) and volume rendering of
the I-type at Reh = 34 (b). . . . . . . . . . . . . . . . . . . . . . . . 65

4.12 Estimated interstitial heat transfer coefficients (a) and Nusselt
numbers (b) for each morphology (ε = 0.75) across a range of
laminar Reh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.13 Static pressure developed on the upstream faces of the models
(a) and corresponding mid-plane contours along the length (b)
for an inlet velocity of 0.5 m/s. . . . . . . . . . . . . . . . . . . . . 67

4.14 Predicted pressure drops in each morphology across a range of
laminar Reh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.1 (a) Computational results illustrating streamlines used to com-
pute tortuosity of 1 mm unit cells of the five TPMS structures
investigated. (b) Workflow for the geometry generation, experi-
mentation and computations. . . . . . . . . . . . . . . . . . . . . . 74

5.2 (a) PMB experimental setup with an embedded flame in the
alumina and mullite burners shown during operation. (b)
Schematic illustrating thermocouple arrangement. . . . . . . . . 79

xi



5.3 (a) Average flexural bending strength of alumina and mullite,
comparing ‘Z’ and ‘XY’ print orientation, and effects of thermal
shock at 400 °C and 700 °C. (b) Experimental TMA data for alu-
mina and mullite (solid lines) with logarithmic curve fits for each
(dashed lines). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.4 Failure Index FI based on maximum principal stresses of uni-
form cell size structures (4 mm cell size) and graded mullite
structures (4 mm - 2 mm). . . . . . . . . . . . . . . . . . . . . . . 83

5.5 Volume percentage of failure indices for uniform and graded
cell size alumina and mullite structures. . . . . . . . . . . . . . . . 84

5.6 (a) Thermocouple temperature measurements at steady-state
burner operation, dotted lines indicate unsuccessful non-
embedded flames. (b) Specific surface area (Sv), pore diameter,
and tortuosity of each 1 mm 0.75 porosity unit cell, with regions
of flame stability indicated. . . . . . . . . . . . . . . . . . . . . . 85

5.7 (a) Axial thermal strain for uniform and graded structures in
alumina and mullite at 75% porosity. (b) Thermal strain at 4 mm
cell size and variable porosity. . . . . . . . . . . . . . . . . . . . . 86

5.8 Failure Index FI based on maximum principal stresses of struc-
tures with 75% porosity and different cell size, and correspond-
ing thermal strain calculated at uniform temperature conditions. 87

5.9 (a) XCT isosurface of mullite ‘D’ burner, with longitudinal and
transverse cross sections from (b) XCT and (c) simulations. (d)
XCT isosurface of mullite ‘I’ burner, with longitudinal and trans-
verse cross sections from (e) XCT and (f) simulations. Minor
cracks in the are highlighted in red for clarity. . . . . . . . . . . . 89

A.1 Simulation of a droplet of DMF (initial diameter of 0.580 mm)
with and without a fiber (SiC, d=14 micron, cross) . . . . . . . . . 98

A.2 Numerical approach to initiating a spark. . . . . . . . . . . . . . . 99
A.3 Sensitivity to spark position and size . . . . . . . . . . . . . . . . 100

xii



CHAPTER 1

INTRODUCTION

This thesis presents advancements in various aspects of combustion. Several

projects are discussed with a common objective of improving state of the art

combustion technology amid global controversy around energy utilization. The

thermodynamic systems herein include the isolated droplet configuration and

porous media burner (PMB). Both are unique in their ability to capture funda-

mental multi-phase heat transfer effects found in real-world applications, such

as evaporation or solid-solid radiation feedback.

1.1 Isolated Droplet Combustion

Since the early 1950s, researchers have acknowledged the symmetrical burning

of isolated droplets as an optimal scenario for exploring the intricate dynam-

ics of chemical reactions and two-phase flow with phase change. Applications

where these physics emerge are ubiquitious at the time of this dissertation, such

as internal combustion engines and rocket engines [1, 2].

In this configuration, a single liquid droplet combusts within an infinite ox-

idizing medium. Fuel vaporizes at the droplet surface and diffuses outward,

while oxidizer diffuses inward. The resulting stoichiometric reaction generates

a zone of intense chemical reaction, manifesting as a diffusion flame. Heat ex-

change occurs via conduction and radiation, both outward from the flame and

inward back to the droplet surface. This heat flux is balanced by the evaporation

process at the vapor/liquid interface.

1



The ”classical” d2-law simplifies droplet combustion by assuming infinitely

fast gas-phase chemical reactions, thereby confining them to an infinitesimally

thin sheet [3]. The assumptions invoked are summarized below in Table 1.1.

Table 1.1: Assumptions for Droplet Combustion

No. Assumption
1 Spherical symmetry.
2 Isolated droplet in infinite medium.
3 Isobaric process.
4 Chemical reaction infinitely fast with respect to diffusion.
5 Constant gas phase transport properties and heat capacity.
6 Gas phase quasi-steadiness.
7 Constant, uniform droplet temperature (No droplet heating).
8 Neglects Soret effect, Dufour effect and radiation.
9 Unity Lewis number for all gaseous species.

10 Negligible buoyancy.
11 Negligible radiation.

In Chapter 2, the spherical droplet model is promoted through experiments

conducted under reduced gravity conditions, approximately 10-4 times Earth’s

gravity, produced by a free-fall environment. This experimental approach en-

ables a direct comparison with numerical models incorporating intricate chem-

istry to simulate crucial parameters such as burning rate, flame localization, and

soot generation [4]. The study focuses on assessing a novel set of furanic biofu-

els, namely 2-Methylfuran (MF) and 2,5-Dimethylfuran (DMF), both of which

are under consideration by the Department of Energy for potential scaled im-

plementation.

The primary findings indicate that DMF exhibits a prolonged initial heat-

ing period compared to MF, yet it demonstrates a slightly higher burning rate.

Additionally, DMF yields greater quantities of soot, in line with expectations

stemming from its elevated carbon concentration relative to oxygen content.

Furthermore, the research unveils a notable sensitivity to chemical degrada-

2



tion in DMF following exposure to ambient conditions, emphasizing the im-

portance of proper storage practices. Collectively, our findings present valuable

insights that should be taken into account by relevant agencies considering the

widespread adoption of these fuels.

1.2 Porous Media Combustion

A PMB is a multifaceted thermodynamic system that incorporates fluid-

structure interactions, heat transfer, and combustion science. The roots of

porous media combustion trace back to the early 20th century, with initial in-

vestigations focusing on combustion phenomena within porous solids [5, 6, 7],

such as coal beds and packed catalyst beds. However, systematic inquiries into

porous media combustion emerged more prominently in the latter half of the

century [8]. Early research endeavors aimed to elucidate flame propagation

characteristics through porous materials, particularly in contexts such as un-

derground coal fires and industrial processes involving packed beds [9, 10, 11].

At the core of porous media combustion, physical processes are governed

by fluid flow, heat transfer, and chemical reactions within a porous struc-

ture [12, 13]. In this porous medium, whether it be a ceramic foam or a packed

bed of particles, the interstitial voids create a complex environment where com-

bustion kinetics are profoundly influenced. The coupling of fluid flow through

the porous matrix with heat transfer processes generates complex thermody-

namic interactions, resulting in increased flame speeds, leaner flammability lim-

its, and reduced pollutant emissions [14, 15]. Central to this paradigm, are the

thermodynamic exchanges between the fluid and solid phases, delineating the

3



interplay from all modes of heat transfer, as depicted below in Figure 1.1.

Figure 1.1: Heat transfer modes and temperature profile exhibited within a con-
ventional PMB

The schematic presented in Figure 1.1 illustrates a traditional ”step” PMB,

featuring a downstream combustion section and an upstream arrestor region.

The combustion segment facilitates convective heat transfer from the high-

temperature products to the adjacent porous medium, characterized by larger

pore sizes and typically employing materials with enhanced thermal conductiv-

ity. Conversely, the arrestor section serves to convectively preheat incoming re-

actants while impeding the upstream propagation of flames through the utiliza-

tion of smaller pores and materials with reduced thermal conductivity [16]. Ef-

fective flame anchoring occurs at the interface between these two zones, where

heat transfer mechanisms encompass both solid-to-solid conduction and radia-

4



tion processes.

Historically, fabrication of porous media has predominantly been limited

to stochastic ceramic lattices, commonly employing materials such as Yttria-

stabilized Zirconia Alumina (YZA), Alumina (Al2O3), or Silicon Carbide (SiC).

For example, the creation of an SiC porous medium typically entails a sponge

replication process, wherein a polyurethane foam is impregnated with resin and

subsequently pyrolyzed to yield a reticulated vitreous carbon foam. While this

method exhibits control over bulk properties like nominal pore size, it lacks

precision in regulating microstructural attributes such as pore connectivity and

shape.

In the pursuit of improved performance, researchers have explored innova-

tive designs such as radial step distributions [17] or multiple step-wise layers

[18]. However, these approaches suffer from discontinuous interconnectivity

and dead zones, thereby impacting hydrodynamic uniformity, heat transfer, and

subsequent performance outcomes. Furthermore, the utilization of stochastic

lattices poses challenges for resolving pore-scale modeling endeavors [19]. Con-

sequently, researchers have increasingly proposed the adoption of well-defined

geometries to both improve modelling efforts and burner performance [20].

In recent years, there have been notable advancements in ceramic additive

manufacturing (AM) techniques, facilitating the precise fabrication of porous

ceramic structures with controlled geometric features. While studies have ac-

knowledged the potential for enhancing performance by tailoring PMB designs

with periodic geometries [21, 22, 23], this avenue remains largely unexplored.

Beyond geometric control, periodic structures offer benefits such as uniform

pore distributions, mitigation of cold spot formation, improved heat transfer,

5



and enhanced reproducibility.

Triply periodic minimal surfaces (TPMS) represent a distinct set of math-

ematical surfaces characterized by seamless traversal through space, devoid

of gaps or self-intersections. These structures exhibit intricate and repetitive

patterns, displaying a remarkable degree of symmetry. Found abundantly in

natural systems such as cellular membranes, skeletal tissue, lung alveoli, and

mitochondrial membranes [24, 25], TPMS morphologies are believed to have

emerged during evolution as nature’s mechanism for local operations with min-

imal entropy, hence, they can efficiently store and process information in re-

sponse to external stimuli. Inspired by this evolutionary design, researchers

have increasingly explored the adoption of such natural morphologies in their

work [26].

TPMS have attracted considerable attention across diverse fields, including

materials science and engineering, owing to their unique geometric characteris-

tics inspired by biological systems [27, 28, 29]. In the realm of AM and porous

media combustion, TPMS offer numerous advantages. For example, their intri-

cate structures provide a high specific surface area, facilitating enhanced heat

transfer capabilities. Moreover, the periodic arrangement of TPMS allows for

precise control over porosity and pore size distribution. As a result, the integra-

tion of TPMS morphologies into PMBs provides a platform for investigating the

influence of specific geometric properties on combustion characteristics such as

flame stability and recirculation efficiency.

Chapters 3-5 of this dissertation are dedicated to advancing the field of

porous media combustion technology. In Chapter 3, an investigation is con-

ducted on a conventional Silicon Carbide (SiC) step burner subjected to sinu-

6



soidal fluctuations of equivalence ratio at the inlet. The study reports on the ef-

fects of these fluctuations on stability, thermal output, and emissions. The find-

ings hold significant relevance for combustion applications fueled by biomass

gasification, characterized by inherent unsteadiness.

Chapter 4 presents a pioneering study examining the effects of integrat-

ing TPMS sheets morphologies on combustion performance metrics of stabil-

ity, temperature profiles, and emissions. By maintaining a consistent gradation

scheme and porosity, extraneous variables are minimized, allowing for the iso-

lation of heat transfer effects attributable to TPMS topology. Volume-averaged

simulations incorporating published correlations of Nusselt numbers (Nu) for

each TPMS unit cell provide valuable insights into characteristic differences that

influence combustion behavior. CFD is then used to augment the experiments

and volume-averaged model by providing pore-scale insight into the fluid dy-

namics and heat transfer properties of each TPMS.

Furthermore, Chapter 5 presents thermal-structural simulations conducted

on five TPMS PMBs. Each cylindrical burner was subjected to high temperature

conditions, while maintaining fixed radial constraints and free axial motion.

Consequently, each structure developed thermal stress and strain to varying de-

grees based on its internal morphology. These simulations were complemented

by X-ray imaging conducted post-experimental testing, leading to significant in-

sights into the thermo-mechanical performance of the PMBs. In accordance with

implications drawn from prior research, this study showcases the substantial in-

fluence of tailored internal morphology, achieved through AM techniques, on

porous media combustion. This dissertation concludes with recommendations

and directions for future research aimed at optimizing PMB performance.

7



CHAPTER 2

ISOLATED DROPLET COMBUSTION OF ALKYLATED FURANS WITH

AN ASSESSMENT OF OXIDATIVE STABILITY

2.1 Introduction

Progressively stringent fuel economy and emission standards are being legis-

lated worldwide to address the environmental impacts associated with fossil

fuel combustion. Despite these efforts, projections indicate a continued increase

in crude oil consumption in the coming years [30]. While ethanol has histori-

cally played a role in reducing harmful emissions when blended into crude oil

derivatives, impact analyses suggest that ethanol produced under the Renew-

able Fuel Standard may have a carbon intensity nearly 24% higher than that

of gasoline [31]. Consequently, there is growing interest in next-generation fu-

els derived from biomass, which are seen as promising candidates to replace

ethanol while simultaneously maximizing fuel efficiency and emissions perfor-

mance [32].

Among these alternatives, a mixture of furanic biofuels has been identified

as a top blendstock by the Co-Optimization of Fuels and Engines (Co-Optima)

initiative under the Department of Energy. This selection process highlighted

the attractive production pathways and fuel properties of 2-Methylfuran (MF)

and 2,5-Dimethylfuran (DMF) [33], both of which now considered viable candi-

dates as petroleum additives. Given their potential significance, it is imperative

to gain a thorough understanding of the fundamental combustion properties of

these fuels.

8



Table 2.1: Properties of MF and DMF

Description (units) MF DMF
Molecular formula C5H6O C6H8O
H/C ratio 1.2 1.33
O/C ratio 0.2 0.17
LHV(MJ/kg)[33] 31.2 32.9
Research octane number[33] 103 101
Motor octane number[33] 86 88.1
HoV(kJ/kg)[33] 358 332
Boiling point (K)[35] 337.9 365.2
Critical temperature (K)[35] 527 557
ρL@20◦C

(
kg/m3

)
[35] 910 903

λg@400◦C(W/(m · K))[35] 0.020 0.019
Cp,g@400◦C(J/(mol · K))[35] 116.9 146.7

Defining the Co-Optima “merit function” was a formula weighted by ther-

mal properties such as research octane number (RON), heat of vaporization

(HoV), laminar flame speed, and particle matter index (PMI) [34], see Table

2.1 for the relevant chemical properties. The higher the merit score, the more

attractive a blendstock would be for potential commercialization. Ultimately,

the furan mixture received a high merit score warranting further investigation

through engine tests and relevant experiments [33].

In engine models, extensive documentation exists regarding the reduction

in particle emissions achieved by blending MF or DMF with petroleum fuels

[36, 37, 38, 39]. Significant efforts have been dedicated to the development of un-

derlying oxidation mechanisms using various experimental techniques, includ-

ing standard methods with premixed flames [40, 41, 42], shock tubes [43, 44],

laminar burning velocities [45, 46], and flow reactors [47, 48]. While these fun-

damental configurations are invaluable for mechanism development, it is im-

portant to note that steps are often taken to pre-vaporize the fuel, thereby dis-

9



connecting it from the liquid phase and potentially influencing the chemistry

of ignition [49]. Isolated droplet studies offer a unique opportunity to employ

kinetic mechanisms while considering the liquid-vapor phase transition within

the context of a diffusion flame. This approach provides a comprehensive un-

derstanding of the combustion process, particularly regarding the interactions

between the liquid and vapor phases.

Previous research has investigated the influence of initial droplet diam-

eter on the evaporation and ignition of crude fast pyrolysis bio-oil (FPBO)

droplets [50]. The study utilized a surrogate fuel blend containing 5.5% DMF

and conducted comparisons with simulations, highlighting the increasing at-

tention directed towards droplet experiments in recent literature [51, 52, 53].

Zhou et al. [54] experimentally investigated the combustion behavior of DMF-

biodiesel blends at various compositions under buoyant convective conditions.

Their findings revealed distinct micro-explosive combustion stages and en-

hanced burning rates at higher DMF concentrations. Additionally, intriguing

bubbling behavior was observed during the combustion of pure DMF droplets,

possibly attributable to conduction effects from the surrounding fibers (0.1 mm

diameter). However, further investigation is warranted to elucidate the un-

derlying mechanism behind this phenomenon. To the best of our knowledge,

droplet studies focusing on MF or its blends have not been conducted, and ex-

isting studies on DMF have been limited to investigations under the influence

of a convective field. Therefore, there remains a notable gap in the literature

concerning isolated droplet combustion studies of MF and its blends.

Given the significant interest in furan derivatives, investigating their com-

bustion behavior under reduced convection provides valuable insight into the

10



fundamental differences between these fuels. This study aims to evaluate the

burning characteristics of pure MF and DMF, as well as a binary mixture of 50%

MF/DMF (by volume), through both experiments and simulations. Numerical

modeling was conducted using the OpenSMOKE++ framework, which assumes

spherical symmetry to enable the solution of mass species and energy conserva-

tion equations. Additional assumptions include constant pressure, equilibrium

conditions at the liquid/gas interface, and no chemical reactions in the liquid

phase. Similar equations are solved for both phases, with the main difference

being the consideration of chemistry in the gas phase. Further details on the

numerical model can be found in [55, 52]. Additionally, experimental quantifi-

cations of soot volume fraction (SVF) were performed using the Full-field Light

Extinction Method (FFLEM). Elucidating soot formation is crucial when evalu-

ating new fuels, and the simplified nature of isolated droplet studies allows for

a unique comparison of MF and DMF.

Lastly, concerns have been raised regarding the oxidative stability of furan-

derived fuels [33]. ASTM D873 methods were employed in a study by Chris-

tensen et al. [56], revealing levels of gum formation 10-100 times higher than

those observed in conventional gasoline. Wang et al. [57] investigated the ther-

mal oxidation and decomposition of DMF, highlighting safety concerns arising

from the presence of peroxides in the gum products. In parallel, a side study

conducted with Southwest Research Institute (SwRI) evaluated the potential

decomposition of DMF during storage. The scant mention of possible contam-

ination in the literature reviewed for kinetic development underscores the im-

portance of proper handling when studying these fuels. The findings presented

herein will provide valuable insights amidst considerations for commercial uti-

lization in the coming years.

11



2.2 Methods

2.2.1 Data acquisition

Experiments were performed in an environment promoting 1-D transport. This

was facilitated by eliminating the convective effects induced by buoyancy and

forced flow. Classically, the Rayleigh (Ra) and Reynolds (Re) numbers are

parameters used to characterize the effects of buoyancy and inertia. Spheri-

cal flames are promoted as Ra approaches zero and the variable leveraged to

achieve this was gravity. Experiments were completed in a drop-tower facil-

ity that provides 1.2 s total of free fall with an estimated reduction in gravity

to O
(
10−2 − 10−4

)
. Further, restricting droplet motion during free fall minimizes

inertial forces thus shrinking the Re. This was done by deploying a droplet onto

the intersection of two 14 µm SiC fibers in quiescent air within a sealed cham-

ber. After ignition, MF and DMF droplets burned to completion in under 0.7 s,

well within the 1.2 s facilitated by the 7.6 m drop tower. Further details of the

experimental design and procedures can be found in [58].

Two pairs of electrodes were positioned symmetrically on opposite sides of

the mounted droplet with a gap of approximately 2.0 mm. Spark discharge

was controlled to within 400 µs and the minimum energy to ignite a droplet

was found by lowering the voltage until no ignition occurred. This parameter

was controllable to a resolution of 1 V. Once these settings were determined, a

droplet was deployed onto the fibers where it was evaporated to the desired ini-

tial diameter with control to +/ − 0.01 mm. This method was performed for the

pure fuel systems only since preferential evaporation would skew the mixture

concentrations.

12



The chamber was secured to a drop package held in place by an electromag-

net and dropped upon trigger of a commensal circuit. A 150 ms delay time was

incorporated between trigger and spark discharge to minimize disturbances in-

duced by release. Raw burning data was recorded in the form of both color and

black and white (BW) images. The flame shape and luminosity were recorded

using a Hitachi HV-C20 camera ( 0.3MP; 30fps ). With a total burn time around

0.7 s, this frame rate was sufficient in providing enough frames to analyze tem-

poral changes in flame diameter. A Canadian Photonics MS-80K (3.9 MP; 200

fps) augmented by a single wavelength LED (Prizmatix Mic-LED with BLCC-

04; 630 nm ) captured BW images which were used to measure droplet burn

rates and assess soot formation.

Figure 2.1: Selected raw images of fuels discussed. Time corresponds to time
after spark.

Raw data was provided as shown in Figure 2.1. To ensure accuracy, a man-

ual and laborious process was employed to measure the droplet, flame, and soot

13



diameters throughout the burning history. Calibration was made by inserting

an object of known size into the focus of the camera where a 1.0 mm distance

was found to be 493 pixels in length. The ImagePro Plus (Rockville, MD, USA)

software with a Dell 4k HD monitor was then used to manually draw an ellipse

and record the major (’ a ’) and minor (’ b ’) dimensions. These values were

then used to calculate an equivalent diameter according to (a× b)1/2. The transi-

tion area from the background to a properly focused droplet was on average 6

pixels, equaling an uncertainty of approximately ±0.006 mm. Flame and soot di-

ameters were measured with the same method. However, operator skill was re-

quired to define where these regions exist. Therefore, multiple group members

contributed to measurements, ensuring consistency. These boundaries could be

determined within 8 pixels, limiting uncertainties to ±0.112 mm.

The collimated light provided by the Prizmatix MIC-630-LED in this work

facilitates the use of the Full Field Light Extinction Method (FFLEM) to quan-

titatively extract Soot Volume Fraction from BW images. This method is based

on the attenuation of light when a laser beam passes through the spherically

symmetric soot-containing region of the flame [59]. The data reduction process

uses an automated program to analyze sooting images and thus quantitatively

extract SVF from recorded BW images. The program automatically extracts gray

scales along each selected Ray of Interest (ROI) and computes the soot volume

fraction profile using a tomographic inversion technique based on three-point

Abel inversion [59]. Detailed discussions of this program can be found in [60].

14



2.2.2 Oxidative stability

MF was provided by Sigma Aldrich with a purity ≥ 98.5% and stabilized with

200 − 400 ppm of butylated hydroxytoluene (BHT) while DMF was purchased

from TCI Chemicals with a purity > 98% and no additives. The oxidative sta-

bility of the supplied DMF was a concern because of its unsaturated chemical

structure and lack of antioxidant additive. Therefore, a study was created with

SwRI to estimate the compositional changes after initial exposure to ambient air

and subsequent storage.

The first step was to define a protocol that mimics experimental conditions.

A typical set of experiments in the drop tower required about 20 mL of fuel

be stored in the sealed reservoir inside of the chamber. Pipettes were used to

transport fuel from the storage container (Fischerbrand clear 240 mL glass bot-

tle) to the reservoir, leaving the fuel exposed to ambient air for 30s on aver-

age per day. Therefore, the protocol determined with SwRI was the following:

test a 0.5µL sample with gas-chromatography-mass spectrometry (GC-MS) us-

ing upon breaking the seal, store 100 mL in the same glass bottle as used in the

lab for one business day (typ. 24-48 hr), and retest with GC-MS. An Agilent

6890 Plus GC System was used throughout the study. Samples were taken us-

ing 1.5 mL GC target vials for use in splitless and split (300:1) analyses. The

thought was to use a high split (small sample) injection to track the concentra-

tion of DMF and a splitless (full sample) injection to uncover impurities and by-

products. Total Ion Chromatograms (TICs) were overlayed to estimate species’

concentrations and their evolution. This process was repeated six times over 10

business days and the results are discussed in Section 2.3.3.

15



2.3 Results

2.3.1 Burning rate

Regression analysis of droplet diameters for MF and DMF is presented in Fig-

ure 2.2 (a). Results are shown for an average initial diameter of 0.58 mm. The

regression rate of a droplet (Kb) is defined as the slope within the linear region,

indicating steady-state burning. Prior to this stage, the time period is classi-

fied as the initial heating period, characterized by nonlinearity. Experimental

values during this period exceeded predictions, however, the overall trends

closely match the model. Predictions suggest a longer initial heating period

for DMF compared to MF, with a higher burning rate for DMF. It was antici-

pated that identically sized MF droplets would burn to completion faster than

DMF droplets, consistent with previous findings [61], which indicated a shorter

combustion duration for MF compared to DMF in a DISI engine. Trends in the

experimental data corroborate these observations, and a sensitivity analysis was

conducted to identify reasons for discrepancies between the model and experi-

ments.

Individually, the effects of thermal conductivity (liquid and gas), initial

droplet temperature, radiation, and fiber presence were investigated. Consid-

erable impacts were found with small changes in the initial droplet tempera-

ture and gasphase thermal conductivity, shown in Figure. 2.2 (b-e). A 10 K de-

crease in initial droplet temperature increased the droplet heating period with

negligible effect on Kb. This was anticipated since no changes are made to the

properties that govern steady state behavior when altering initial temperature

alone. Although this shifted the burning curve towards the experimental data,

16



Figure 2.2: Comparison between predicted and measured burning rates (a).
Sensitivity analysis (b)-(e) shows responses to changing initial droplet tempera-
ture (Baseline: T = 293 K), or gas thermal conductivity.

17



the baseline assumption of 293 K is a good representation of the lab environ-

ment. The physics influencing the initial heating period are complicated and

it is possible for the model to not completely capture experimental conditions.

Alternatively, a 20% decrease in λg significantly affected Kb, consistent with the

classical correlation: Kb ∝ λg/ρlCp,g. This is important since the model estimates

gas-phase properties according to the kinetic theory of gases, and upon liter-

ature review, no experimental data could be found to verify the correlations

made for λg of MF and DMF. Further sensitivity analyses are presented within

the Appendix of this dissertation.

Estimates for Kb are shown in Figure. 2.3 from the approximate start of

steady state burning
(
0.6 s/mm2

)
. The model predicted distinct third order be-

havior for DMF with less severe inflections for MF. Although the measured and

predicted Kb values differed slightly, this third order behavior was also seen in

the experimental data. An accelerated burning process could be attributed to

the cracking behavior of DMF observed in [54] near the end of burning, how-

ever no clear disruptions were seen in the images for DMF during this study.

Notably, the 20% reduction in λg followed experiments closely for the case of

DMF while MF data fell nicely between the baseline and 0.8λg curves. It is fair

to acknowledge the possibility of closer agreement between experiments and

the model upon experimental verification of the incorporated gas-phase prop-

erty data.

Concerning the 50/50vol blend, an unexplored question was the possibility of

a flash boiling or micro-explosive event when burning a mixture of these fuels.

This phenomenon is witnessed when a large enough difference in boiling points

exists within the blend. This behavior was noted in [54] when mixing DMF in

18



Figure 2.3: Calculated burn rates (Kb) starting from estimated onset of steady
state burning

(
0.6 s/mm2

)
biodiesel where the boiling point of DMF was much less than that of biodiesel.

MF exhibits a boiling point roughly 28 K less than DMF, not as severe as the case

of biodiesel so it was unclear whether disruptions would be witnessed or not.

Close examination of the images revealed a disrupted burning event occurring

at diameters between 0.11 mm − 0.14 mm for 3/3 experiments. Further investi-

gation uncovered disruptions at diameters between 0.16 mm − 0.22 mm for the

case of ”pure” MF. This interesting behavior occurred at diameters near twice

that of the 50/50 blend, suggesting the potential cause is associated with MF.

A possibility for the disruption is influence from the BHT additive, which is

classified as flammable with a boiling point around 538 K. A necessary condi-

tion to trigger flash boiling requires the temperature of the droplet correspond-

19



ing to the surface concentration to exceed the boiling point of one or more mix-

ture components inside the droplet [62]. It is possible for 400ppm of BHT to be

present in the initial 500 mL bottle of MF. Assuming an initial droplet diameter

of 0.58 mm, there could be roughly 1% volume concentration of BHT when the

droplet reaches a diameter of 0.18 mm. This is because MF will vaporize (lower

boiling point) while the BHT remains dissolved within the burning droplet. It

is conceivable for these dissolved additives to concentrate near the droplet sur-

face, raising the surface temperature to the boiling point of BHT. General criteria

for liquid superheating has been recognized as approximately 90% of its critical

point [62]. With a critical temperature of 527 K, it is possible for MF nucleation

to be triggered with subsequent flash boiling and ejection. Proving this theory

will require an ultra-pure (”neat”) sample of MF with no additives which at the

time of this study is difficult to obtain.

2.3.2 Flame and soot behavior

Evolutions of soot and flame diameters are illustrated in Figure. 2.1 with anal-

ysis summarized in Figure. 2.4. At first glance, colored images displayed strik-

ing luminosity, particularly right after ignition, indicative of high flame tem-

peratures and considerable soot production. The measured equivalent soot and

flame diameters are normalized by the droplet diameter at that instance in time.

The first two rows in Figure. 2.4 contain estimations of SVF using the light ex-

tinction method. Raw data is shown at three instances after spark (0.05 s−0.15 s)

as a function of the radial position normalized by the droplet diameter (r/ri). A

distinct spike exists for both fuels early in burning and the peak location for MF

was consistently farther than DMF. Around 0.15 s, aggregates form at various

20



radial positions causing intensity spikes. Manual measurements of flame and

soot diameters were completed per the discussion in section 2 for the entirety of

burning and these results are summarized with computations in Figure. 2.4g

Simulations predicted near identical behavior for the SSR and FSR of both

fuels. Calculations for the FSR were provided with consideration of soot and

did not differ discernably when soot was neglected, see the supplementary ma-

terials. Experimental results for FSR agreed well with calculations while SSR

data agreed respectably for the first half of burning. A slight divergence can be

seen for the remainder with MF soot shells consistently farther from the droplet

compared to DMF, and both higher than the computations.

An explanation for the underprediction of SSR is the model’s consideration

of particle size. The mechanism describes soot as a collection of pseudo-species

with different H/C ratios and sizes (mass). 25 BINs are used to sort the species

where the mass in each increases according to BIN(i + 1)/BIN(i) = 2. Aggre-

gate sizes up to 120 nm are included in the physics when calculating SSR. The

aggregates that defined the outer layer of the soot shell were measured to be ap-

proximately 20-50 µm in equivalent diameter, much larger than those included

in the model. Agglomeration occurs as unburnt precursors drift away from

the droplet surface, thus growing in the absence of oxidation. Therefore, the

model would underpredict the location of the soot shell relative to experiments.

Further work with a model incorporating a larger spectrum of observable ag-

gregates may agree closer with experimental data.

Soot formation was unique for MF and DMF compared to commonly stud-

ied fuels such as pump gasoline, diesel, their surrogates, or normal alkanes. As

the aggregates form, they can escape the shell, coalesce on the fibers, or reside

21



Figure 2.4: Temporal evaluations of soot volume fraction (a)-(f) as a function of
radial distance from droplet center acquired using the light extinction method
for three experiments of each fuel. Measured SSR and FSR combined with nu-
merical data (g) with quantifications of soot production by integrating SVF data
(h) and averaging the peaks of the SVF curves (i).

within the flame undergoing oxidation. This is different from petroleum fuels or

their surrogates where soot clusters form a dense shroud within the flame that

appears to encapsulate the droplet [52, 63]. They’re also different from alkanes,

such as n-hexadecane, which form small particles spherically positioned around

the droplet with minimal agglomeration [29]. The difference may be attributed

to the chemical structures of MF and DMF. The heterocyclic aromatic backbone

promotes the formation of large polycyclic aromatic hydrocarbons (PAHs), im-

portant precursor molecules for soot formation. However, the unsaturated fu-

ran ring contains a single oxygen atom which promotes soot oxidation. With an

22



extra methyl group, DMF has been shown to produce a larger number of soot

precursors [64] and less reductions in particle emissions when blended with

petroleum fuels compared to MF. The SSR is a complex relationship between

thermophoretic and Stefan drag forces, but the lower SSR observed for DMF is

either due to a lower Stefan effect, (evaporation away from droplet,) or stronger

thermophoretic effect, (force on particles toward the droplet). With ostensibly

identical FSRs and adiabatic temperature values [46], the lower SSR for DMF is

associated with longer residence times which favor soot production. A higher

tendency to form soot precursors could result in a lower Stefan velocity due to

increased small particle mass, thus increasing residence time and further pro-

moting soot coalescence.

To estimate the total soot produced by each fuel, the SVF data was integrated

over the radial range shown (r/ri = 0 : 5) for various time instances throughout

burning. The results are presented as a function of t/D0
2 in Figure. 2.4h and val-

ues were consistently higher for DMF. Figure. 2.4i presents fourth order poly-

nomial fits of the average peak SVF values for the three analyzed runs. At this

initial diameter ( 0.58 mm ), both fuels burned to completion in approximately

0.6 s and exhibited peak soot production around 25% of the total burn time.

The maximum SVF of MF was slightly earlier in burning and given the simi-

lar chemical structures and pathways for soot production, this is likely due to

lower total soot formed by MF combustion. Overall, the results in Figure. 2.4h

and Figure. 2.4i suggest a tendency for DMF to form larger quantities of soot.

23



2.3.3 Oxidative stability

This study of DMF oxidation was designed to identify the initial composition

of the supplied fuel and elucidate potential degradation during storage. By-

products and impurities were found by performing GC-MS methods at var-

ious times within the 10-day period. Results should be considered a semi-

quantitative assessment of fuel quality for the experiments completed herein,

but nonetheless highlight species that may be present in other studies using

DMF without antioxidant additives.

A high split (small sample) injection was used to track the DMF concen-

tration over the study duration. Tracking the parent peak on the TIC for a

300 : 1 split revealed a chromatographic area (∆) of 98.6%(±1%) at each testing

period and suggests the samples used within our experiments were consistent

in composition. However, splitless (entire sample) injections uncovered several

other species in trace amounts at both initial testing and end of testing (EOT).

Unknown species were identified using a library database search with match

factors and reverse match factors to indicate levels of confidence. High match

factors (>800) for species with furan rings were the most trusted as possible

oxidative by-products. Other common molecules with high confidence were

considered as potential impurities. Manual inspection of the scan results was

employed to filter out remaining artifacts such as column material. Without

the use of response factors and proper calibration to a ”neat” DMF (unavailable

at time), absolute concentrations are difficult to declare. However, the chro-

matographic areas of each chemical (∆chemical ) were used to measure relative

abundance within the fuel. For simplification, ∆chemical was normalized by the

value for 5-Methylfurfuryl acetate at initial testing, the chemical detected with

24



Table 2.2: Results from stability analysis

Chemical ID Formula αinitial αEot

2-Ethyl-5-methylfuran C7H10O 1.83 3.53
2-Acetyl-2-methyltetrahydrofuran C7H12O2 4.15 4.03
5-Methyl-2-furanmethanol C6H8O2 9.66 12.62
3-Hexene-2,5-dione (DAE) C6H8O2 8.18 11.82
N-(5-Methylfurfuryl) dimethylamine C8H13NO 2.52 4.76
2-(2-Furanylmethyl)-5-methylfuran C10H10O2 2.15 3.74
2,2-Isopropylidenebis(5-methylfuran) C13H16O2 2.90 4.76
5-Methylfurfuryl acetate C8H10O3 1.00 1.49

the lowest ∆ of 0.032%. A variable α was defined such that α = ∆chemical
∆hexadecane

. To give

a sense of species growth over the 10-day period, α values were calculated at

both initial testing and EOT. A summary of results is provided in Table 2.2.

The compounds listed above are possible by-products or impurities discov-

ered within the supplied fuel with a complete list of TICs and IDs detailed in

the supplementary materials. GC area %’s ( ∆ ) qualitatively suggest the concen-

trations of each compound are very small, which was expected given the stated

high purity. Long chain alkanes could be considered impurities from processing

and were amongst the lowest concentrations detected. However, 3Hexene-2,5-

dione and 5-Methyl-2-furanmethanol are main products of DMF oxidation [57].

These chemicals were detected in relatively large quantities at both initial test-

ing and EOT, indicative of low-level oxidation before and during the testing

performed herein. It is likely initial conception occurred during processing and

concentrations would grow as DMF is exposed to an oxygen containing envi-

ronment. The exposure protocol employed did not reveal a significant forma-

tion of impurities, but future work using response factors and calibration with

an ultrapure sample would better provide absolute conclusions.

To get an idea of the time scales for oxidation under ambient conditions, a 5

25



Figure 2.5: Visible residue formed after evaporation of 5 mL of DMF

mL sample was left to evaporate in a controlled setting of ambient air. Complete

evaporation occurred within four days leaving behind the residue (gum) visible

in Figure. 2.5. A 1 mL toluene/acetone mix was used as a solvent and GC-

MS attempted to identify dissolved gum products. As expected, 3-Hexene-2,5-

dione and 5-Methyl-2furanmethanol were detected, consistent with prior MS

results of DMF gum residue [56]. Other hits include compounds of similar

structure such as 2-(2-propenyl)-furan, 2-(2-Furanylmethyl)-5-Methylfuran, and

1-(2-furanyl)-1-Butanone. These findings reinforce concern of DMF degradation

without proper stabilizing agents.

Previous work severely stressed the fuel to characterize oxidation [56, 57],

therefore observing an accelerated degradation of DMF. In this study, MS results

imply the presence of impurities and by-products was extremely low (∼ 1%)

and the impact on the combustion data presented within is likely insignificant.

However, it is clear proper handling and storage of non-stabilized unsaturated

furans is paramount to ensure fuel quality and user safety. The use of antiox-

idant additives is recommended to inhibit fuel degradation and the effects of

26



additives on combustion behavior need to be thoroughly examined. To be cer-

tain of the influence of impurities, oxidative by-products, and antioxidants on

droplet burning behavior, comparisons should be made to ultra-pure samples

of fuel.

2.4 Conclusions

This study presents the first observations of MF and DMF combustion through

an isolated droplet configuration in a microgravity environment. Multiple

methodologies were employed to characterize the fundamental burning behav-

ior of each fuel. Image processing techniques exclusive to the isolated droplet

configuration were used to quantify sooting propensity and results were in en-

couraging agreement. Additionally, a study was completed with Southwest Re-

search Institute examining the possibility of fuel degradation during storage.

Results are summarized as follows:

• MF droplets burned to completion faster than identically sized DMF

droplets, both experimentally and computationally. DMF initial heating

periods were predicted longer than MF while the burning rate of DMF

was also predicted slightly higher with a marginal acceleration near ter-

mination. Experimental data verified these predicted trends and a con-

vergence of absolute values may be seen upon experimental validation of

gas-phase property data for MF and DMF. Literature review revealed no

experimental testing for the relevant property data.

• Flame diameters between the fuels were predicted to be near identical and

this was verified by experiments. SSR was observed to be higher in the

27



case of MF, suggestive of shorter residence times and greater soot oxida-

tion. A higher tendency for DMF to form soot was supported by employ-

ing the light extinction method and unique image segmentation of soot

agglomeration.

• The oxidation of MF and DMF during storage is a potential concern. MS

results of splitless injections indicated trace amounts ( ∼ 1%) of oxida-

tive by-products upon initial testing that remained minimal throughout

the 10 day duration. The presence of compounds such as 3-Hexene-2,5-

dione and 5Methyl-2-furanmethanol raises concerns about DMF stability

and emphasize the importance of strict protocol when handling these fu-

els. These products were also identified within the residue (gum) formed

after complete evaporation of a 5 mL sample, indicating a connection to

DMF oxidation.

28



CHAPTER 3

DYNAMIC STABILITY OF POROUS MEDIA BURNERS AND

SENSITIVITY TO OSCILLATING INLET CONDITIONS

3.1 Introduction

Porous media burners operate on the principle of an excess enthalpy flame.

Within the burner, a porous insert recirculates heat from the combustion prod-

ucts to the gas phase reactants, thus increasing the flammability limits, flame

speed, and thermal efficiency relative to a free flame [12, 14, 65, 66, 67, 68].

Furthermore, PMBs have been shown to reduce NOx and other harmful green-

house gas emissions, providing an enticing application in climate change mit-

igation [69]. Conventional applications of PMBs have predominantly focused

on steady operating conditions, however, potential renewable fuel sources have

been shown to possess dynamic chemical compositions [70]. Therefore, ana-

lyzing and understanding the thermal response to temporal inlet conditions is

important for the utilization of novel fuel sources by PMBs.

Historically, the standard PMB configuration consists of an interfaced-

stabilized design where an embedded flame is sustained at the interface of two

porous materials supplied by a steady hydrocarbon source [71, 72, 16, 73, 74, 75].

Ceramic foams with a high pore density act as an upstream flashback arrestor,

while foams with larger pore sizes are utilized downstream [65, 76]. Some re-

search, however, has shown the advanced ability of PMBs to burn low-carbon

and carbon-free fuels, such as bio-derived syngas and ammonia [77, 78]. While

these alternative fuels can support a low-carbon energy system, they exhibit a

narrow flammability range, low energy density, a propensity for pollutant for-

29



mation, and impurities that result in operational challenges for power genera-

tion and industrial combustors. Specifically, the products derived from biomass

gasification can exhibit time-evolving perturbations in species composition and

energy content. Dynamic fuel composition arises from the fundamental dual

gasification reaction processes: devolatilization and char reaction [70]. This bi-

nary gasification process results in a dynamic volumetric flow rate of syngas

from the gasifier, and thus generates a temporal dependence of (Φ.

If the adaptability of PMBs is to be extended to bio-derived fuels, opera-

tion under dynamic chemical composition needs to be fundamentally charac-

terized. Few investigations into the unsteady behavior of PMBs have been re-

ported to date. Recently, researchers have exploited the thermal mass of PMBs

to investigate the time scale over which supplied fuel can be interrupted and

reintroduced [79]. They remarked a dependency of flame relight on mass flux,

noting additional cooling due to higher flow velocities despite a pronounced

heat release rate. Others have employed simulations of sinusoidal convection

over obstacles within porous media, which revealed the existence of a frequency

threshold where the thermal system begins to experience non-linear effects [80].

Notably, as the forcing frequency decreases, the flow time scale grows and al-

lows for a stronger thermal response to the varying inlet conditions, whereas

higher frequencies can produce a system exhibiting linear time-invariant (LTI)

behavior. Experimentally, investigations of a PMB responding to fluctuations in

methane, bio-gas, and methane/hydrogen flow have been reported at ultra-lean

conditions (Φ below 0.3) [81, 82]. The flow of pure methane and mixtures includ-

ing carbon dioxide was varied sinusoidally up to 30% of the initial Φ value at

periods of either 60 s or 180 s, while the air flow rate was held constant. Flames

were found to destabilize by blow-off or flash-back within 10 cycles at a period

30



of 180 s, but could operate with minimal temperature disturbances over a 60

s period. Similarly, flows of methane and hydrogen were subjected to ampli-

tudes of 10-50% at a single period of 60 s. System performance was reported

to be stable at amplitudes up to 30% for a 70% methane 30% hydrogen blend.

These preliminary studies uncover a sensitivity of dynamic PMB operation to

the amplitude and frequency of inlet flow conditions. However, both the hydro-

dynamic and chemical temporal variations can affect burner stability, therefore,

there exists a need to isolate each of these effects and provide a more compre-

hensive investigation into dynamic flame stability in a PMB.

Here, we address this gap by analyzing the dynamic response of flame stabil-

ity, temperature profiles and emissions for an oscillatory operating interfaced-

stabilized PMB. The investigation begins with a characterization of the stabil-

ity regime for the burner under steady operating conditions. Eight mass flux

conditions within the steady stability limits were selected for oscillatory exper-

iments where sinusoidal fuel flow is imposed over frequencies from 1/180 Hz

- 1/30 Hz while holding the mixture flow rate constant. Amplitudes of equiv-

alence ratio are increased at each frequency until flame instability or extinction

occurs. Stabilization is defined by observing the temperature response, where

the linearity of the system is assessed. For conditions exhibiting LTI behavior, a

transfer function was generated from experimental data and used to predict the

system response at various dynamic conditions. These results provide novel in-

sights about oscillatory operation of PMBs, which are relevant for applications

involving the combustion of time-evolving fuel sources, such as from biomass

gasification.

31



Figure 3.1: Foams used in the experiment include the 10 PPI SiC foam (a) and
100 PPI SiC foam (b). P&ID diagram for the laboratory experimental setup (c).
Schematic of the PMB setup, with the thermocouple locations labeled (d). Ex-
ample of unsteady flow for a 30 s period and equivalence ratio amplitude of 0.15
at an inital condition of 0.6 (e) Oscillatory combustion within the PMB ending
in blow-off (f).

3.2 Experimental setup

For this work, an interfaced-stabilized PMB was constructed using Silicon Car-

bide (SiC). SiC is a high thermal conductivity ceramic that has previously been

demonstrated to yield enhanced combustion and durability performance com-

pared to zirconia or alumina burners [83]. 100 pores-per-inch (PPI) and 10 PPI

SiC foams were used in the PMB apparatus, as illustrated in Fig. 3.1 (a)-(d). Each

foam is 25.4 mm in diameter and 25.4 mm in height. As shown, the foams were

wrapped in ceramic insulation and encased inside a quartz tube. The temper-

ature response was measured via axial type K thermocouples, as positioned in

32



Fig. 3.1 (d). Thermocouple measurements record a junction temperature some-

where between that of the gas and surrounding solid [84] and for this study

serve the purpose of monitoring the flame location. The published uncertain-

ties in the thermocouple readings are ±0.4% of the measured value. Addition-

ally, combustion products were analyzed using the Testo 350 Portable Emission

Analyzer. The analyzer probe, as seen in Fig. 3.1 (d), was positioned 50 mm

from the exit plane of the burner to capture downstream emissions. The ranges

for O2, CO, NO, and NO2 are 0-25% (± 0.8% accuracy, 0.01% resolution), 0-500

ppm (±5% measured value accuracy, 0.1 ppm resolution) , 0 300 ppm (±5% mea-

sured value accuracy, 0.1 ppm resolution), and 0-500 ppm (±5% measured value

accuracy, 0.1 ppm resolution), respectively.

Premixed methane-air mixtures were supplied into the burner at user-

defined Φ and mass flux rates controlled by Alicat mass flow controllers (MFC).

Errors reported by the manufacturer were ±0.6% of the measured value for the

MFCs. For mapping steady operation, flame stability is inferred from compari-

son of the burner temperatures, whereby temperatures varied no more than ±5

K for 2 minutes. Supporting calculations of steady state temperature distribu-

tions were supplied by a volume-averaged model [85]. The flash-back limits

were found by decreasing mass flux at a constant Φ, causing the flame speed to

overcome the inlet velocity and travel slowly upstream into the 100 PPI foams.

Blow-off was triggered by increasing the mass flux for a given Φ until the flame

began to propagate downstream and eventually exit the burner. Extinction was

characterized by an insufficient heat release rate relative to the rate of heat rejec-

tion, causing temperatures to progressively decrease. These limits were identi-

fied by discernible temporal changes in flame position and intensity.

For unsteady experiments, fuel flow into the burners is prescribed by a sinu-

33



soidal flow of methane at a fixed mass flow rate for the mixture. The dynamics

are prescribed in LabVIEW via manipulation of sine waveforms by user defined

amplitudes (∆Φ) and frequencies (1/180 Hz - 1/30 Hz). Fig. 3.1 (e) exemplifies

the temporal changes in flow rate and corresponding Φ. To isolate the effects

of Reynolds number throughout the burner provided different levels of energy

content, eight initial conditions were chosen from the steady stability map, each

with a different pore scale Reynolds number, Repore, defined as:

Repore = Updp/ν, (3.1)

where Up is the pore scale velocity, dp is the nominal pore diameter, and ν is the

kinematic viscosity for a given Φ. To ensure repeatability, the process for reach-

ing each initial condition involved flame anchoring at a Φ of 0.8 and mass flux

of 0.7 kg/m2/s, followed by loweringΦ and mass flux to the desired steady val-

ues. Once temperature readings from all thermocouples stabilized, sinusoidal

operation within a prescribed ∆Φ and forcing frequency was initiated. Thermo-

couple placement remained identical to the illustration in Fig. 3.1 (d) and served

to identify flame location and destabilization. A ∆Φ = 0.05 was tested at peri-

ods of 180 s, 120 s, 90 s, 60 s, 45 s, and 30 s. After sweeping through all forcing

frequencies, ∆Φ was increased by 0.05. This process repeated until instabili-

ties were found at each condition. A condition was considered unstable when

the time derivative of the temperature response at the 100-10 PPI interface was

nonzero over the course of 10 cycles. See Fig. 3.1 (f) for the experimental setup

during sinusoidal operation and illustration of destabilization by blow-off.

34



3.3 Results and discussion

3.3.1 Steady operation

One primary benefit of porous media combustion is the ability to sustain em-

bedded flames at flow velocities above or below the laminar flame speed [12].

This section summarizes burner behavior during steady-state operation. Fig. 3.2

(a) presents the experimentally determined limits and corresponding CO mea-

surements at each stable condition. Throughout the stability map, temperatures

were not high enough to produce considerable NOx formation (< 20 ppm), how-

ever, CO emissions varied significantly. Lowering the mass flux at a fixed Φ or

lowering Φ at a mass flux < 0.4 kg/m2/s caused the maximum temperatures

to fall and the flame to shift slightly upstream and decay as the extinctino lim-

its were approached. This finding underscores the strong relationship between

reaction zone temperature and CO oxidation.

The measured and calculated axial temperature distributions for a range of

steady conditions are presented in Fig. 3.2 (b) and (c). Shaded regions repre-

sent the difference between the solid and gas temperatures computed from the

volume-averaged model. Since the experimental temperature measurements

correspond to a value between the gas and solid temperature, where the simu-

lation results highlight the effect of interphase heat exchange and the expected

variation between these temperatures [84]. A sharp increase in temperatures

was seen near the 100-10 PPI interface (T100-10), indicative of flame anchoring

at this location. Experiments confirmed that burner temperatures at the 10 PPI

foam would decline as mass flux was lowered due to lower rates of heat re-

lease. Hence, less oxidation of CO resulted in the higher quantities presented in

Fig. 3.2 (a). IncreasingΦ away from the lean limit produced an intensified flame,

35



illustrated by comparison of the 10 PPI temperatures in Fig. 3.2 (b) and (c). These

results reveal the range over which the coupled convective cooling and rate of

heat release is balanced such that a flame can be supported at steady-state.

Figure 3.2: Experimental stability and CO measurements (a) at steady state op-
eration. Experimental and computed solid (dashed line) and gas (solid line)
axial temperatures at equivalence ratios of 0.70 (b) and 0.55 (c).

36



Figure 3.3: Temperature and CO data as a function of time at Φ = 0.6 and mass
flux of 0.50 kg/m2/s (Repore = 158) for unstable failure by blow-off at 1/60 Hz (a)
and stabilization at 1/30 Hz (b). Normalized T100-10 and CO responses shifting
from unstable (c) to stable (d) by reducing ∆Φ for a given frequency of 1/120
Hz.

3.3.2 Dynamic operation

System response

Unsteady experiments were performed at eight initial conditions within the sta-

bility map in Fig. 3.2 (a). We selected Φ0 = 0.6 and 0.55, then four mass flux val-

ues for both. For a given steady condition, dynamic experiments began at the

lowest frequency (1/180 Hz) and continued to 1/30 Hz at a ∆Φ of 0.05. Then,

incremental changes in ∆Φ of 0.05 were tested across all frequencies until in-

stability was observed. This procedure produced a dynamic system where the

37



Figure 3.4: Phase portraits of normalized system input-output signals compar-
ing unstable (a) and stable (b). Fourier transforms of the interface thermocouple
response data (T100-10) with multiple modes at unstable (c) and stable (d) condi-
tions.

burner temperatures progressively declined until destabilization by blow-off or

extinction, or burner temperatures relaxed to a recurring pattern, see Fig. 3.3

(a) and (b). We found the corresponding detection of CO variations with ∆Φ

was feasible down to 5 ppm. Here, the rate of CO oxidation is dependant on

multiple factors, such as flame surface area, temperature, and Φ, therefore read-

ings displayed periodic but clear non-linear behavior for all cases. Additionally,

T100-10 reacted with the highest sensitivity to flow oscillations, see Fig. 3.3 (a) and

(b), therefore, readings at this location became the focus of classifying stability.

Fig. 3.3 (c) and (d) present visually unstable and stable conditions for the

initial case of Φ0 = 0.6 and mass flux of 0.36 kg/m2/s (Repore = 112). These il-

lustrations exemplify burner behavior at the threshold of stability regardless of

imposed conditions. Smaller ∆Φ can produce a highly repetitive temperature

response over the course of 10 cycles, depending on forcing frequency. As ∆Φ

was increased and destabilization began, the CO readings also increased due

38



to incomplete oxidation from a smaller reaction zone and lower temperatures.

Measurements were modulated for stable cases as presented in Fig. 3.3 (d), how-

ever, the increase in CO emissions was greater than the decrease below the base-

line value (t = 0). The observed accumulations of CO could be attributed to the

lag between the temperature response and convective ramping of fuel within

the system. Additionally, an increasing, time-variant phase shift between the

input and output from cycle to cycle is connected to the divergence of temper-

ature and CO data shown in Fig. 3.3 (c). This response delay is characteristic

of a thermal system experiencing flow instabilities [86] and can be minimized

by increasing the forcing frequency or decreasing ∆Φ. At a lower frequency, the

extended flow time scale enables a greater thermal response, therefore, lower

values in ∆Φ can be tolerated and higher amplitudes in the output response are

observed. As frequency is increased, a larger ∆Φ can be sustained along with

CO emissions oscillating closer to that of baseline.

Stability analysis

To better classify dynamic stability, phase portraits of the normalized Φ input

signal and output T100-10 response were developed, as shown in Fig. 3.4 (a) and

(b) where green and red represent the beginning and end of 10 cycles or desta-

bilization, respectively. Tracing the lines through time in Fig. 3.4 (a) reveals

non-linear behavior as the temperature response lags farther behind the input

signal and destabilizes via blow-off or extinction. Conversely, the trace shown

in Fig. 3.4 (b) features a slight decay initially but quickly approaches a mini-

mally phase shifted but periodic response consistent with that of an LTI system.

Fourier transforms of the response data reveal modes at integer multiples of

the forcing frequency for all cases, see examples in Fig. 3.4 (c) and (d). Multi-

39



ple modes were detected at both stable and unstable conditions, however, the

significance of the dominant mode shrinks and harmonics grow as an unstable

condition is approached, suggesting the burner can be approximated as a linear

system at stable conditions. The existence of less significant modes in the sta-

bles cases can be attributed to the initial response upon triggering the dynamic

phase. This is exemplified in Fig. 3.3 (b) around 100 s as the initial response

relaxes to a balanced state exhibiting periodicity.

Examining the linearity of each tested condition provided a straightforward

method for classifying stability. To predict the system response at various stable

conditions, a second order transfer function was generated from a set of stable

single-input single-output (SISO) data using the system identification toolbox in

Matlab. Fig. 3.5 presents experimental and predicted dynamic T100-10 responses

for stable cases at Φ0 = 0.6 and Repore = 158, where a second order transfer func-

tion, H(s), was produced from data corresponding to a frequency of 1/120 Hz

and ∆Φ = 0.1, general form given as:

H(s) =
as2 + bs + c
ds2 + es + f

(3.2)

where the coefficients a, b, c, d, e, and f were found to be 0.1325, 0.053, 0.0032,

1, 0.0843, and 0.0033 from this experimental condition. As shown, the pre-

dicted temperature responses are in good agreement with experimental data.

This finding suggests the response to inlet perturbations can be simulated us-

ing LTI approximations where appropriate, circumventing the need for a time-

dependent heat transfer model. However, as the conditions approached the

threshold of stability, predictions began to deviate from experimental data

which, as discussed, exhibits non-linear behavior. This is evidenced by Fig. 3.5

(c) where the predicted response slightly underestimated the experimental. Al-

40



Figure 3.5: Transfer function predictions for three different cases compared with
experimental output data.

though exhibiting stable behavior by our definition over 10 cycles, we found

an increase in ∆Φ over 0.15 at this forcing frequency resulted in destabilization.

This is an important finding for practical applications, since it suggests a con-

trol system could be implemented to sense such a deviation and implement the

41



appropriate feedback to prevent destabilization.

Physically, thermal inertia provided by the surrounding solid explains the

ability to sustain a flame outside of steady stable ranges until a time scale thresh-

old is reached. Stable combustion within porous media is often characterized by

the Peclet number, Pe [65], where a critical threshold exists separating propa-

gation and quenching regimes. Here, a definition of Pe is proposed to account

for the minimum energy content reached during a forced cycle, assuming an

initial temperature of 850 K. This value approximates the temperature slightly

upstream of the 10 PPI foam at steady conditions and allows for flame speed cal-

culations beyond the flammability limits at standard conditions. The modified

Pe accounting for the effects of excess enthalpy combustion is defined as:

Pe =
S a

Ldp

α
(3.3)

where S a
L is the laminar flame speed calculated for the mixture Φ0, dp is the

nominal pore diameter, and α is the thermal diffusivity of the gas mixture. Pe

was evaluated at the minimum equivalence ratio reached during an oscillation

(Pe(∆Φ)) using the freely propagating adiabatic 1-D flame model within Can-

tera [87] and the GRI.30 mechanism. The minimum stable Pe as a function of

Repore at each frequency are shown in Fig. 3.6.

As expected, the largest ∆Φ could be sustained at the highest forcing fre-

quency, however, the extension of lean flammability was not identical across all

mass flux values for Φ0 = 0.6. In fact, a non-monotonic relationship between

system linearity and mixture Repore was discovered. Normally, a lower Repore

implies a system will experience fewer chaotic responses and instabilities as

the inertial forces shrink, however, in the context of combustion, this can lead

to insufficient thermal mixing, reduced reaction rates, lower temperatures, and

42



Figure 3.6: The maximum stable Pe for each frequency (splines) is plotted
against Repore.

eventual extinction. Experiments for Repore below ≈ 110 destabilized by extinc-

tion at all limiting frequency and ∆Φ pairs, whereas conditions tested at Repore

above ≈ 110 destabilized by blow-off. Fig. 3.6 shows the second lowest mix-

ture mass flux for Φ0 = 0.6 can endure oscillations to the lowest Pe across the

eight conditions. Here, a ∆Φ of 0.4 was sustained at a frequency of 1/30 Hz, an

approximate 90% reduction in Pe compared to the limit at steady-state.

Table 3.1 summarizes the extension of Φ to which the burner can operate for

each Φ0. The maximum stable amplitude (∆Φmax) for a given Φ0 is seen at the

highest forcing frequency (1/30 Hz) and listed CO values represent the maxi-

mum detected during operation over the 10 cycles (rounded to the nearest 50

ppm). Similar to the steady CO map in Fig. 3.2 (a), an inverse trend between

mass flux and CO production is identified. Despite the ability to sustain a larger

43



Table 3.1: Limits of stable dynamic conditions.

Repore Φ0 ∆Φmax Pe CO (ppm)
94 0.55 0.15 27.4 1800
111 0.55 0.2 20.3 1050
122 0.55 0.2 20.3 950
145 0.55 0.05 42.5 400
88 0.6 0.25 20.3 3500
112 0.6 0.4 4.1 2250
158 0.6 0.25 20.3 450
188 0.6 0.15 35.1 150

∆Φmax at Repore ≈ 110, CO levels at larger ∆Φmax were considerably higher. Addi-

tionally, emissions near the extinction limit (Repore = 88 and 94) were relatively

increased, highlighting the dominant action of temperature on CO oxidation

rather than chemical composition. Upon closer inspection, the exceptional un-

steady stability limit found at Repore of 112 (mass flux = 0.36 kg/m2/s) corre-

sponds to the position within Fig. 3.2 (a) where the extinction/blow-off transi-

tion lies and the largest range of steady stable Φ is seen. Moreover, variations in

dynamic ∆Φ suggest steady conditions furthest within the flammability limits

can sustain the largest ∆Φmax.

These findings will help guide the design and control of thermal systems

operating under variable heat release conditions, such as those proposed for

porous burners fueled directly by biomass gasification products. Additionally,

the connection between linearity and stability can be leveraged in a systems

approach to enable fast predictions, in effect modeling the burner as a black box

experiencing an input signal and producing an output response.

44



3.4 Conclusions

This study presents dynamic system analysis of PMB operation. After steady

characterization of the interface-stabilized PMB, burner stability under sinu-

soidal variations in Φ at constant mass flux rates was investigated. Eight con-

ditions from the steady stability map were chosen for dynamic experiments.

Incremental changes in Φ were set at intervals of 0.05 over a range of frequen-

cies (1/180 Hz - 1/30 Hz). Stability was determined by assessing the linearity

of the system response to a sinusoidal input signal over the course of 10 cycles.

A transfer function derived from a single set of input-output data at a particu-

lar initial condition was found to adequately predict dynamic system response

with slight deviation at the threshold of stability.

Furthermore, a non-monotonic relationship between Repore and the exten-

sion of burner stability was found. A ∆Φ of 0.4 at an initial condition of Φ =

0.6 and Repore = 112 was sustained at a frequency of 1/30 Hz, while the greatest

stable ∆Φ for any other condition did not exceed 0.25. This location within the

steady stability map also features the widest range of operable Φ for that mass

flux, suggesting stable conditions lying deepest within the steady flammability

limits may possess greater resistance to flow perturbations than others. An in-

verse relationship between mass flux and CO levels was found for a constant

Φ, where stables levels around 2000 ppm were measured near the extinction

limits. A divergence between temperature and CO measurements was revealed

during dynamic experiments, while periodic formation of CO was modulated

for the stable cases. Quantities formed over the course of 10 cycles during a

single experiment totaled more than baseline levels at steady state, likely due to

convective lag between the ramping of fuel within the system and temperature

response. In conclusion, this study provides critical insights into the stability

45



and emissions behavior of PMBs operated under variable inlet conditions which

is relevant for application to combustion of non-conventional fuels, such as the

products of biomass gasification.

46



CHAPTER 4

EXPERIMENTAL AND COMPUTATIONAL INVESTIGATION OF

BIO-INSPIRED MORPHOLOGIES IN POROUS MEDIA BURNERS

4.1 Introduction

The integration of PMBs into conventional combustion applications has gar-

nered substantial attention by researchers [12, 71, 88, 89, 90, 91]. Leveraging heat

recirculation, PMBs offer a range of advantages including higher flame propaga-

tion speeds, broader flammability ranges, improved thermal power generation,

and reduced emission levels [68, 92, 65]. Flame stabilization in PMB designs typ-

ically involves segmented burners fabricated to uniform bulk properties, such

as porosity [93], pore size, and material. However, traditional manufacturing

methods have constrained PMB designs to a step-wise assembly of stochastic

foams, which can lead to challenges such as poor species mixing and dead zones

[94, 95]. With recent advancements in ceramic additive manufacturing (AM),

there are new opportunities to overcome these limitations and further enhance

combustion technology by integrating complex designs into PMB morphology.

For example, the implementation of periodic geometries through AM tech-

niques offers a means to enhance pore inter-connectivity and improve exper-

imental repeatability. Notably, triply periodic minimal surfaces (TPMS) have

emerged as a focus of interest due to their versatility in various engineering

applications [96, 97, 98]. Initially observed in biological systems such as mi-

tochondrial membranes [99], butterfly wings, and lung alveoli [100], TPMS

exhibit unique characteristics including high surface area, increased perme-

ability, continuous connectivity, and absence of sharp edges. It is speculated

that these morphologies evolved to fulfill specific physiological requirements,

47



leading to improved mechanical strength, mass transport, and energy conver-

sion [101, 102]. In the context of PMBs, the utilization of TPMS holds promise for

optimizing burner performance by enhancing interphase heat transfer between

the gas and surrounding solid.

Previously, numerous generalized investigations have documented correla-

tions for the flow characteristics and heat transfer properties of common TPMS

sheet and solid networks across a spectrum of Reh. Recent research by Yan et al.

[103] reported a comparative study of diamond and I-WP solid and sheet net-

works under turbulent conditions through CFD and supporting experiments.

They reported solid networks exhibit lower pressure drop and heat transfer co-

efficients than sheet networks, with the latter featuring a larger surface area

but fewer void spaces normal to the inlet flow field. Moreover, the extension of

TPMS application to PMBs has recently gained attention. Cheng et al. [104] con-

ducted pore-scale simulations of PMBs with uniform and graded morphologies

based on various TPMS architectures, including the diamond, gyroid, I-WP, and

primitive solid networks. Correlations for Nu from previous work [105] were

employed to calculate the volumetric heat transfer coefficient of each TPMS.

Their findings revealed a broad spectrum of stable operating conditions for gy-

roid, I-WP, and diamond configurations compared to primitive models. Addi-

tionally, their simulations of graded morphologies predicted superior stability

ranges over uniform pore networks. These predictions were corroborated ex-

perimentally by Sobhani et al. [21, 18], who performed volume-averaged mod-

eling and experimental testing of ceramic graded PMBs defined by the diamond

solid network. They showed increased stability over conventional step con-

figurations and highlighted the crucial role of enhancing heat recirculation in

PMB performance, particularly in facilitating the dynamic flame stabilization

48



observed in pore-size graded burners. Although the advantages of combining

AM and TPMS architectures in heat transfer applications are extensive, there

remains a need for a fundamental comparison of PMB morphology defined by

different sheet-based TPMS structures. Furthermore, the thermal-fluid charac-

teristics of the diamond, gyroid, I-WP, and primitive sheet networks need to be

investigated at Reh relevant to those typically seen during lean PMB operation

(Reh < 100).

In this work, we present an evaluation of PMB morphology through

combustion experiments, volume-averaged modeling, and laminar pore-scale

thermal-fluid analysis in Fluent. Specifically, PMB morphology is defined by

the diamond (D), gyroid (G), I-WP (I), and primitive (P) TPMS architectures

while porosity, cellular distribution, and material are held constant. Experimen-

tal data corresponding to flame stability, temperature distribution, and emis-

sions are reported. Pore-scale simulations focused on convection within the

laminar regime are performed to gain insight into the thermal-fluid and fluid-

structure interactions underlying the observed experimental results. Conclu-

sions are drawn regarding the key factors contributing to distinct PMB behavior

produced by each morphology.

4.2 Burner design and additive manufacturing

4.2.1 Burner design

The software MSLattice [106] was used to create structures and generate STL

files, see Equations (4.1) - (4.5) for the general definitions of each TPMS. A sheet

thickness is produced by solving −c ≤ F(x, y, z) ≥ c to achieve a set porosity or

49



cell size.

F(x, y, z) = c (4.1)

F(x, y, z)D = cos(x) cos(y) cos(z) − sin(x) sin(y) sin(z) (4.2)

F(x, y, z)G = sin(x) cos(y) + sin(y) cos(z) + sin(z) cos(x) (4.3)

F(x, y, z)I = 2(cos(x) cos(y) + cos(z) cos(x) + cos(y) cos(z)) − (cos(2x) + cos(2y) + cos(2z))

(4.4)

F(x, y, z)P = cos(x) + cos(y) + cos(z) (4.5)

After generation, models were imported into nTopology [107] where the

TPMS body was merged with a cylindrical shell. Holes within the shell were

defined to facilitate identical thermocouple placement across the three burners.

All burners were designed with a linear gradation scheme of 5 pores-per-inch

(PPI) at the inlet to 2.5 PPI at the outlet and a constant ε of 0.75. The length and

diameter were designed to 50 mm and 30 mm. See Table 4.1 for the parameters

of the experimental models, where Sv is the surface area to volume ratio.

Table 4.1: Parameters for experimental models.

TPMS Inlet PPI Outlet PPI ε Surface area (mm2) Sv (mm−1)
D 5 2.5 0.75 31,215 1.18
G 5 2.5 0.75 25,383 0.96
I 5 2.5 0.75 28,495 1.07
P 5 2.5 0.75 19,498 0.73

4.2.2 Additive manufacturing

STL files were printed using an Admaflex 130 digital light processing (DLP)

printer at a layer height of 30 µm and 50 µm mininum feature size. The printed

structures were first debound in a deionized water bath for 24 hours at 40°C to

remove a portion of the water-soluble resin, subsequently dried for 24-48 hours,

50



and then thermally debound in a muffle furnace over a 48 hour period. This

debinding process removes resin from the printing process in preparation for

sintering at a final temperature of 1625°C. The general fabrication process is

illustrated in Fig. 4.1. A mixture of mullite (11Al2O3–1SiO2) was chosen for the

experimental burners due to previous work showing increased durability over

pure alumina [108].

Figure 4.1: Geometric modeling and 3D printing of the mullite burners

Figure 4.2: Experimental setup with instrumentation as labeled. Thermocouples
are placed radially within shell, axial locations are shown.

51



4.3 Experimental and Computational Methods

4.3.1 Experimental setup and procedure

As shown in Fig. 4.2, the PMBs were wrapped in two layers of ceramic insu-

lation and encased inside a quartz tube. The temperature response served to

identify flame movement and was measured via seven type K thermocouples

within the shell at the axial locations shown. Uncertainties in the thermocouple

readings are ±0.4% of the measured value. Combustion products were analyzed

using the Testo 350 Portable Emission Analyzer. The analyzer was positioned

30 mm from the exit plane of the burner to capture downstream emissions. The

ranges for O2, CO, NO, and NO2 are 0-25% (± 0.8% accuracy, 0.01% resolution),

0-500 ppm (±5% measured value accuracy, 0.1 ppm resolution) , 0-300 ppm (±5%

measured value accuracy, 0.1 ppm resolution), and 0-500 ppm (±5% measured

value accuracy, 0.1 ppm resolution), respectively.

Premixed methane-air flow was supplied into the burner at user-defined

equivalence ratios (Φ) and mass flux rates controlled by Alicat mass flow con-

trollers (MFC). Errors reported by the manufacturer were ±0.6% of the mea-

sured value for the MFCs. Flame stability was inferred from thermocouple

readings, whereby temperatures varied no more than ±5 K for 2 minutes. The

blow-off limits were found by increasing the mass flux for a given Φ until the

flame began to propagate downstream and eventually exit the burner. Like-

wise, flash-back limits were found by decreasing mass flux and was declared

when the inlet thermocouple reached 1000 K. Extinction was characterized by a

constant decline in temperatures without discernible change in flame location.

52



4.3.2 Volume-averaged modeling

A volume-averaged model (VAM) utilizing the GRI3.0 mechanism was used to

study the effects of morphology on PMB stability. The assumptions used in

the formulation of the model are: (i) Dufour and Soret effects are neglected,

(ii) the burner is considered to be a gray body radiating to a black body at 298

K at the exit, (iii) radiative losses from the gas is neglected, and (iv) the solid

is chemically inert. The corresponding governing relationships are shown in

Equations (4.6)-(4.10) with further details described in [85]. Conservation of

mass:

∇̄ · ρgU = 0, (4.6)

Conservation of momentum:

ρg

[
∂

∂t
(U) + ∇̄ · (UU/ε)

]
= −∇̄(εp) + ρg∇̄ · [ν∇̄(U)], (4.7)

Conservation of energy (gas):

ρgcpg
∂(εT̄g)
∂t

+ ρcpg∇̄ · (UT̄g) = λg∇̄ · (ε∇̄T̄g) + hv

(
T̄s − T̄g

)
, (4.8)

Conservation of energy (solid):

ρscps (1 − ε)
∂T̄s

∂t
= ∇̄
(
λs,eff∇̄T̄s

)
− hv

(
T̄s − T̄g

)
, (4.9)

Conservation of species:

ερg
∂Yi

∂t
+ ερU · ∇Yi = ρg∇ · (εDim∇Yi) + εω̇, (4.10)

Specifically, the changes in TPMS morphology are captured by the volu-

metric heat transfer coefficient, hν, defined here as hν = λgNuS v/dh. Estima-

tions of Nu for each TPMS were taken from the literature [105], formulated as

53



Nu = (a+bε+cε2)Red
hPr1/3. The published correlations suggest that at Reh relevant

to PMB conditions, the order of hν follows I > D > G > P, thus, comparison of the

predicted and experimental stability regimes provides insight into influencing

convective heat transfer via morphology changes.

4.3.3 CFD simulations

Pore-scale simulations in Fluent were performed to investigate the flow charac-

teristics through the four sheet-based TPMS (Reh = 6-130). Here, the definition

of Reh and characteristic length are defined in Eq. (4.11) and (4.12).

Reh = Uddh/ν, (4.11)

dh = 4ε/S v, (4.12)

S v = S s/Vt, (4.13)

where Ud is the Darcy velocity, ν is the kinemtic viscosity of air, Ss is the surface

area of the TPMS and Vt is the volume of the TPMS channel.

STL files from MSLattice were converted to CAD bodies and meshed in AN-

SYS using poly-hex grids with 10 inflation layers near the TPMS wall. To re-

duce computational expense, six unit cells were arrange as shown in Fig. 4.3.

Air was selected as the working fluid with a reference temperature of T = 300

K. The steady laminar solver was employed in conjunction with the Coupled

scheme for pressure-velocity coupling and Second Order Upwind for energy

and momentum. The Darcy-Forcheimer relationship was employed to evaluate

pressure drop across each model [109]:

∆P
L
=

µ

K1
Ud +

ρ

K2
U2

d (4.14)

54



where K1 and K2 are the Forcheimer and Inertial permeability constants deter-

mined by polynomial fitting of the simulation data.

A mesh resolution study was conducted using ∆P as the target variable at an

inlet velocity of 1 m/s where the average static pressure in the inlet section was

compared to the outlet pressure (gauge = 0 atm). Meshes consisting of 4,707,952,

11,284,528, and 34,283,942 cells produced pressure drops of 87.7 Pa, 85.8 Pa, and

86.1 Pa, therefore the settings used to generate the cell count of 11,284,528 were

used in this study.

Figure 4.3: Geometric model used in CFD with boundary conditons.

Post processing was completed to estimate the hydraulic tortuosity and res-

idence time of a particle traveling through each TPMS model. To do this, we

considered 100 streamlines between the forward and aft faces of each mesh. Co-

ordinate and velocity data were exported and processed according to the Equa-

tion (4.15). The mass-weighted average velocity was computed along the TPMS

55



model and normalize by the length to approximate the residence time.

τi =

∑ni
j=1

√
∆x2

i, j + ∆y2
i, j + ∆z2

i, j√
(xi,ni − xi,1)2 + (yi,ni − yi,1)2 + (zi,ni − zi,1)2

(4.15)

To estimate the interstitial heat transfer coefficient (hsf), a constant heat flux

of 3000 W/m2 was applied to the walls of the TPMS. Equations 4.16 and 4.17

were then applied along the axis of the model.

hsf =
q′′

(T̄wall − T̄bulk)
(4.16)

Nu =
hsfdh

λg
(4.17)

Along 30 planes equally spaced from the forward face to aft end, we calculated

the area-weighted average surface temperature (T̄wall) and mass-weighted fluid

temperature (T̄bulk). It’s well known that hsf is high at the face of an object where

the fluid impinges, therefore, the mean value across all unit cells is reported.

4.4 Results and discussion

4.4.1 Stability and emissions

Distinctions in PMB behavior were immediately clear during experimental test-

ing. Of the four burners tested, the D, G, and I morphologies successfully sup-

ported anchored flames and operation across a range of conditions. Conversely,

the P operated solely with a surface flame, as shown in Fig. 4.4 (a). At similar

starting conditions, the evolution of temperature at TC 1 is shown in Fig. 4.4

(b). Clearly, the D and G burners swiftly transferred heat upstream through the

solid, whereas the I-type was slower, but anchoring was eventually achieved

56



by slightly reducing the inlet flow rate. However, lowering the flow rate or in-

creasing Φ within the P burner both resulted in flame quenching, indicative of

poor heat recirculation for this morphology. This finding is congruent with pre-

vious studies reporting low heat transfer performance of the P-type TPMS [104].

The underlying mechanism theorized to inhibit flame anchoring is discussed in

more detail in Section 4.4.3.

Figure 4.4: Surface flame at the outlet of the P burner (a). Initial heating profiles
at start-up conditions, Φ = 0.95 and mass flux = 0.3 kg/m2/s, for the four burner
types. (b)

Fig. 4.5 (a)-(c) illustrates the limits of extinction, blow-off, and flash-back in

addition to CO measurements at corresponding stable conditions for the D, G,

and I burners. Detected levels of CO did not exceed 600 ppm experimentally

and were found to increase near the extinction limits for all burners in a similar

fashion. This can be attributed to decreased temperatures as the mass flux was

lowered near the lean limits, emphasizing a fundamental role of temperature

in emissions rather than strictly morphologic changes. Regarding NOx forma-

tion, the temperature thresholds are higher than those seen in experiments, thus,

measurements were relatively low (< 20 ppm) at the lean conditions studied. It

57



should be noted however, detected NOx marginally increased from the extinc-

tion limits (low temperature) to the blow-off limits atΦ = 0.8 (high temperature)

as expected.

Figure 4.5: Experimentally determined stability limits (a)-(c) compared with
VAM results (d)-(f). Shaded contours of experimental CO readings are shown
in (a)-(c).

Experimental testing was limited to Φ ≤ 0.8 since conditions above this pro-

duced temperatures exceeding the thermocouple limit (1400 °C), inhibiting de-

tection of flame movement. However, within this range of Φ, each morphology

presented with distinct blow-off limits. Experimentally, blow-off was charac-

terized by flame propagation downstream until eventual departure from the

burner, indicating insufficient heat recirculation for the given inlet condition.

As shown in Figure 4.5 (d)-(f), the model is in good agreement with experimen-

tal data and confirms the heat recirculation capabilities of each morphology as

58



captured by hν can be used to predict the general breadth of stability within a

PMB. Both the D and I type burners operated with superior stable ranges of

flow rate for a given Φ compared to the G. From the correlations adopted, the

estimated Nu values of D and I are higher than the G. Coupled with slightly

higher surface areas, this combination explains the narrower range of stability

seen in the G burner and suggests modifications in cell size can be used to alter

dh and affect performance.

We also observed a notable change in the blow-off limits when comparing

solely the D and I type burners. It’s clear from published work that as Reh in-

creases through the turbulent regime the Nu of the D and G type grows to a

larger extent than the I and P types [110, 111]. However, at lean conditions

typically witnessed in PMB applications, Reh is confined to the laminar regime

where distinctions in heat transfer properties are more ambiguous. As dis-

cussed in Section 4.3.2, there is evidence to suggest the Nu of the D-type falls

below that of the I at sufficiently low Reh, implying the I-type may offer slightly

greater interphase heat exchange in this regime which is consistent with our

experiments. It should be noted, heat transfer properties of TPMS found in

the literature are highly sensitive to factors such as porosity and correlations

typically carry considerable margins of error. Furthermore, the morphologic ef-

fects on radiation and conduction are not accounted for in the model, however,

emphasizing the influence of interphase heat exchange resulted in qualitative

agreement between the predicted and experimental stability regimes.

4.4.2 Temperature distributions

Flame position within the PMBs can be approximated by the maximum TC

reading for experimental data and sharpest temperature gradient from com-

59



putations. Results from the volume-averaged model under-predict the longitu-

dinal distribution due to an inability to capture multi-dimensional effects from

hydrodynamic dispersion. Nevertheless, trends are consistent between exper-

iments and computations. Fig. 4.6 displays the axial temperature profiles at

stable conditions prior to the flash-back and blow-off limits for Φ = 0.8. As

shown, the I burner sustained an embedded flame over a slightly larger range

of mass flux and axial positions compared to the D and G. The D and G burners

featured a similar range of mass flux rates, however, the flame location within

the G burner responded with higher sensitivity to inlet conditions which can

largely be attributed to the lower surface area. Given the burners were of the

same height, greater sensitivity of flame position to inlet conditions led to earlier

flame departure for the G burner.

Figure 4.6: Experimental and computational axial temperature profiles deter-
mined for the D, G, and I burners (a)-(c) at the flash-back (F-B) and blow-off
(B-O) limits. Shaded regions illustrate interphase heat transfer between the gas
and solid.

The three burners all featured a common stable condition at Φ = 0.8 and a

mass flux of 0.6 kg/m2/s. For comparison, the experimental temperature pro-

60



Figure 4.7: Experimental axial temperature profiles for the D, G, and I burners
at a common stable inlet condition.

files are shown in Fig. 4.7. Although the theoretical power input is the same,

the G burner was not able to extract heat and preheat the reactants as effectively

as the D and I. This is clear when considering temperatures in the upstream

section where the gradient was the sharpest for the G burner. Taken together,

the experimental and computational data suggest the I and D morphologies of-

fer the widest range of stability due to enhanced convective heat recirculation

as captured by hν. It should be noted, ceramic materials are prone to cracking

at high temperatures and minor cracking was observed after 20 hours of test-

ing. This served as an unavoidable source of error since cracking can influence

permeability, surface area, and various heat transfer processes.

61



4.4.3 CFD results and discussion

Flow characterization

The flow characteristics through porous morphology are closely intertwined

with convective heat transfer. Thus, in this section, we present laminar hydro-

dynamic analysis of each TPMS and remark on connections to the PMB perfor-

mance observations previously discussed. Fig. 4.8 displays streamlines of the

fluid flowing through the four models at an inlet velocity of 0.5 m/s. It’s clear

the D and G models impose a greater disturbance to the flow compared to the

I and P where multiple streamlines traversed the matrix without contacting the

TPMS. Furthermore, mid-plane velocity and vorticity contours in Fig. 4.9 reveal

varying degrees of acceleration and structural interaction through the porous

networks. In the laminar regime, the formation of longitudinal vortices due to

sheer deformation of the fluid can improve the distribution of thermal energy

and enhance convective heat transfer significantly [112]. In theory, the high vor-

ticity seen in the D and G flows benefits convective heat transfer, however, the

velocity gradient responsible for the sheer deformation through the G channel

is high, suggesting the residence time within the burner is low. To quantify

these effects further, the hydraulic tortuosity and residence time are illustrated

in Fig. 4.10 for an inlet velocity of 0.5 m/s.

Compared to the others, flow through the P-type is notably the least tortu-

ous with the lowest residence time. Additionally, this morphology features low

surface area, therefore, flow accelerates through the unit cell with minimal struc-

tural interaction preventing the generation of vorticity. This ultimately leads to

low residence time, poor interphase heat exchange, and inadequate heat recircu-

lation upstream, thus, a mere surface flame was sustained during experimental

testing. Although the tortuosity is high in the G-type compared to the I-type,

62



Figure 4.8: Velocity streamlines through the different TPMS models for an inlet
velocity of 0.5 m/s.

Figure 4.9: Mid-plane contours of velocity (a) and vorticity (b) for an inlet ve-
locity of 0.5 m/s.

the residence times were similar. However, we theorize the inability to anchor a

flame at the same starting condition is largely explained by the number of voids

in a given unit cell. As shown in Fig. 4.10, a plane view of the I sheet TPMS

features four half circles on the edges whereas the G includes an additional two

full circles of smaller diameter. This increased the flame surface area close to

63



Figure 4.10: Estimated hydraulic tortuosity and particle residence time within
each model for an inlet velocity of 0.5 m/s.

the structure, thus, the flame anchored quicker in the G burner than the I. Inter-

estingly, Fig. 4.9 shows a unique feature of flow through the I-type model. As

illustrated, fluid acceleration near the edges of the unit cell surrounds pockets

of low velocity regions. It’s possible these cavities act as reservoirs for thermal

energy and contribute to the higher heat transfer seen at sufficiently low veloc-

ities.

Heat transfer simulations

Simulations were performed to investigate the convective heat transfer perfor-

mance within the laminar regime. Overlapping Fig. 4.11 (a) and 4.9 (b) confirms

the role of vorticity in enhancing heat transfer. The effect is most clearly shown

in the G model where the local temperature near the wall and vorticity are in-

creased. Concerning the I-type, further evidence was found to suggest the low

64



velocity regions served as thermal reservoirs, see Fig. 4.11 (b).

Figure 4.11: Mid-plane temperature contours (a) and volume rendering of the
I-type at Reh = 34 (b).

This finding was unique to the I-type model and appeared to diminish as

the inlet velocity increased and thermal mixing was promoted. However, for

PMB applications operating at lower flow velocities, these pockets indicate en-

hanced heat recirculation upstream and can contribute to the impressive stabil-

ity regime revealed by the I burner. To both validate the correlations from Cheng

et al. [105] and elaborate on this conjecture regarding the I-type, estimations of

hsf for each model were calculated, see Fig. 4.12

As shown, our estimations revealed the order of Nu followed I > D > G at

sufficiently low Reh. This is consistent with the reported correlations employed

in the VAM, and other reports of the superior heat transfer of the D-type as inlet

velocity increases. Moreover, the projected heat transfer coefficient of the G-type

increases similarly to the D-type, but to a lesser extent, while the P-type remains

low throughout. It should be noted, hsf has been shown to be highly sensitive

to ε, therefore a comprehensive heat transfer study of sheet-based TPMS across

a range of ε and low Reh would be beneficial to the combustion community.

65



Figure 4.12: Estimated interstitial heat transfer coefficients (a) and Nusselt num-
bers (b) for each morphology (ε = 0.75) across a range of laminar Reh

Furthermore, calculating the exact Reh in a PMB is difficult due to gradients in

species, temperature, and velocity, however, estimations of burner relevant Reh

are within the range of Reh = 3 - 40. Overall, the results presented herein suggest

both the I and D type TPMS offer the greatest benefits in terms of interphase

heat exchange in a PMB at low Reh, however, with modifications to cell size the

G-type may also confer advantages at higher flow rates.

Pressure drop

Simulations were concluded with calculations of the pressure drop across each

model. Unlike most heat exchanger applications, which can operate well within

the turbulent regime, the laminar ranges of Reh seen in PMB applications leads

to lower pressure drops. Nevertheless, minimizing ∆P is important for effi-

ciency, durability, and stability. It’s argued that periodic structures improve ∆P

through enhanced pore interconnectivity, avoiding the dead spots and random

pathways found in the conventional stochastic foams. Yet, varying the periodic

morphology influences ∆P to different degrees, as shown in Figs. 4.13 and 4.14.

When considering the disruption to particle path, it’s clear from Fig. 4.13

66



Figure 4.13: Static pressure developed on the upstream faces of the models (a)
and corresponding mid-plane contours along the length (b) for an inlet velocity
of 0.5 m/s.

Figure 4.14: Predicted pressure drops in each morphology across a range of
laminar Reh

(a) that the D-type imposes the greatest flow resistance. This morphology lacks

void spaces normal to the inlet flow field as seen in the G, I and P types which

67



enable some degree of linear transport through the matrix. Although this ge-

ometric distinction may account for the D-type’s favorable heat recirculation

abilities, excessive pressure drops warrants sustainability concerns. This find-

ing is consistent with reports at higher Reh where the D-type produces greater

∆P and friction factors compared to other common TPMS [111]. Interestingly,

although the I-type is predicted to exhibit a lower ∆P than G, the experimental

stability regime was much greater implying this TPMS may be superior to other

morphologies in PMB applications.

4.5 Conclusion

In conclusion, our investigations have shed light on the crucial role of TPMS

morphology in shaping burner behavior and performance. Through experimen-

tal testing, volume-averaged modeling, and CFD analysis, several key insights

have been uncovered regarding the impact of TPMS morphology on PMB sta-

bility, emissions, and flow characteristics. Key findings are as follows:

• TPMS morphology significantly influences PMB stability. Within their re-

spective stability regimes, emissions were similar and showed sensitivity

to temperature. The D and I morphologies exhibited superior stability

ranges compared to the G and P types, attributed to differences in heat re-

circulation capabilities and flame anchoring sensitivity to inlet conditions.

• Volume averaged modeling using hν unique to each TPMS captured trends

in stability regimes. Results suggest at low Reh, both the Nu and general

breadth of stability of a TPMS-based burner follows I > D > G > P.

• CFD analysis revealed distinct flow characteristics among different TPMS

morphologies, with the D and G models imposing greater flow distur-

68



bance compared to the I and P models. Hydraulic tortuosity and residence

time calculations further underscored the relationship between morphol-

ogy, flow acceleration, and mixing potential. The combination of low pres-

sure drop and high stability suggest the I-type TPMS confers the greatest

performance benefit in a PMB.

Overall, these findings highlight the intricate interplay between TPMS mor-

phology and PMB behavior, emphasizing the importance of morphology opti-

mization for enhancing burner efficiency, stability, and sustainability in various

industrial applications. Future research should continue to explore the nuanced

effects of TPMS morphology on PMB performance and develop advanced opti-

mization strategies to maximize burner effectiveness and longevity while mini-

mizing environmental impact.

69



CHAPTER 5

THERMAL AND STRUCTURAL PERFORMANCE OF ADDITIVELY

MANUFACTURED CERAMIC POROUS MEDIA BURNERS

5.1 Introduction

Ceramic materials are widely employed in various engineering applications

[113, 114, 115] due to their remarkable compressive strength, stiffness, and re-

silience in corrosive environments. In particular, porous ceramic structures have

been applied in high temperatures systems, including heat exchangers, injector

face plates, and catalytic converters to modulate thermal transport, reactivity,

and stability [116, 117]. However, creating complex yet durable ceramic struc-

tures that concurrently optimize thermal, fluidic, and structural performance

is challenging using conventional methods. Combining the potential for cus-

tomization from AM with the excellent thermal and corrosion resistance of ce-

ramic materials enables the construction of optimized structures that are robust

for application to extreme conditions.

Traditional fabrication techniques of ceramic foams consider bulk proper-

ties, such as pore density, and result in random strut orientations and pore dis-

tributions, which can significantly alter performance. AM methods, such as

DLP, allow for the fabrication of highly engineered structures generated from

computer-aided design (CAD) software, circumventing the limitations of tra-

ditional methods. Specifically, a series of formula-driven structures known

as TPMS are often used to generate CAD models. TPMS structures include

Schwarz primitive, gyroid, I-graph and Wrapped Package-graph or ‘I-WP’, dia-

mond, and PMY. Defining the porous matrix based on one of these TPMS allows

significant control over the topology, pore size, wall thickness, and functional

70



gradation. TPMS have been considered in a variety of thermofluidic applica-

tions [118, 119, 120]. However, the complexity of TPMS structures prohibits

manufacturing via conventional means beyond a small number of unit cells,

thus necessitating the use of AM.

Recently, multiple studies have examined the mechanical and thermal prop-

erties of additively manufactured TPMS structures [121, 122, 123, 124]. Com-

pression testing of TPMS across a range of porosities demonstrate Diamond

and I-WP as two of the strongest sheet-TPMS, whereas primitive is commonly

found to be among the weakest [122, 123, 125]. A similar trend was found for

polymeric TPMS structures where Gyroid has been reported to possess promis-

ing mechanical properties as well [126, 127]. Numerical simulations of residual

thermal stresses induced during fabrication via AM reported the effective me-

chanical properties of various TPMS geometries and noted reductions in proper-

ties such as stiffness. [128]. Interpenetrating phase composites reinforced with

thickened sheet-TPMS architectures were found to produce a lower effective

coefficient of thermal expansion (CTE) compared to conventional composites

leading to higher robustness [129]. Although previous studies have demon-

strated the differences in compressive strength among TPMS structures as well

as the effects of thermal stresses, the relationship between ceramic TPMS topol-

ogy and thermal-structural performance in high temperature systems has not

been investigated.

One application of interest for complex ceramic porous structures is a PMB.

Prior studies have shown that combustion in porous media offers significant ad-

vantages over traditional free-flame combustion in regards to emissions, flame

stability, and fuel efficiency [65, 66, 67, 68]. PMBs are comprised of an inert

porous infill inside solid burner walls, and are characterized by a large internal

71



surface area which promotes conductive and radiative heat transfer through-

out the burner. Heat recirculation to the reactants upstream results in excess

enthalpy burning and enables stable ultra-lean combustion [130, 131, 83, 132],

leading to improved fuel efficiency and decreased emissions of NOx and CO

byproducts [68]. However, a clear limitation of ceramic PMBs is the preser-

vation of structural integrity upon exposure to the temperature field created

by a flame. Multiple studies have noted the propagation of cracks within the

struts of the porous matrix and a loss of mass during experimental testing

[132, 83]. Large thermal gradients generated during flame anchoring and sys-

tem shutdown are implicated in the formation of excessive stress levels. Post-

experimental XCT images reveal fracture at various locations throughout the

PMB. Thermal performance is dependent on the retention of structural integrity,

thus, preserving PMB mechanical behavior is key to achieving a sustainable de-

sign. Therefore, characterizing the thermal-structural durability of additively

manufactured porous ceramic structures is highly relevant to addressing the

growing interest in such advanced clean combustion technologies as well as

other high temperature energy conversion and thermal management systems.

Here, coupled thermal-structural simulations and experiments of five dif-

ferent cylindrical ceramic TPMS structures were performed to investigate their

performance and durability at high temperatures. Variations in tensile stress

levels formed under thermal expansion were explored computationally. Tem-

perature measurements from experiments were used to define the thermal con-

ditions applied in computational analysis. For experimentation, structures were

fabricated using DLP 3D printing in mullite and alumina, two ceramic materi-

als that exhibit different CTE, which is known to contribute to thermal shock

resistance [133]. Flexural bending tests and thermomechanical analysis (TMA)

72



were performed on samples of both materials at elevated temperatures to com-

pare strength degradation, anisotropy and CTE. Furthermore, crack formation

in burners post-combustion were examined using X-ray Computed Tomogra-

phy and compared with high tensile regions predicted by simulations. The

methods used for finite element (FE) simulations, designing and manufactur-

ing of the porous structures, and combustion experimental setup are outlined

in Section 5.2, followed by the computational and experimental results in Sec-

tion 5.3. Finally, the conclusions and comments about future work are presented

in Section 5.4.

5.2 Methods

5.2.1 TPMS structures

Five TPMS structures were investigated, namely Schwarz primitive (SP), gyroid

(G), I-WP (I), diamond (D), and PMY (P). The TPMS implicit functions used for

each structure is shown in Table 5.1.

TPMS Implicit function
SP ψSP(x, y, z) = cos(x) + cos(y) + cos(z)
G ψG(x, y, z) = sin(x)cos(y) + sin(y)cos(z) + sin(z)cos(x)
I ψI(x, y, z) = 2(cos(x)cos(y)+cos(z)cos(x) + cos(y)cos(z))

- (cos(2x)+cos(2y)+cos(2z))
D ψD(x, y, z) = cos(x)cos(y)cos(z) - sin(x)sin(y)sin(z)
P ψP(x, y, z) = 2cos(x)cos(y)cos(z) + sin(2x)sin(y) + sin(x)sin(2z)

+ sin(2y)sin(z)

Table 5.1: Triply Periodic Minimal Surfaces (TPMS) studied and corresponding
implicit functions used to defined the structure.

In this work, sheet-TPMS structures were selected based on their favorable

mechanical properties as compared to skeletal-TPMS [134, 135]. Previous work

73



with alumina 3D printed TPMS structures demonstrated both higher strength

and stiffness for the case of sheet-gyroids as compared to skeletal-gyroids [136].

Additionally, sheet-TPMS offer a higher Sv, which is advantageous in ther-

mal applications where interphase heat exchange is critical. In the sheet-TPMS

framework, a thickness is applied to the minimal surface to achieve a target cell

size and relative density [106]. Porous structures studied were designed using

MSLattice software [106].

3D print

Debind

Sinter

Experiment

(b)

Generate geometry XCT

Mesh

Evaluate material 
properties Input 

thermocouple data
Compare

Simulate thermal-
structural behavior

Analyze thermal-stress 
distribution

T
PM

S 
un

it 
ce

lls

SP

G

I

D

P(a)

Figure 5.1: (a) Computational results illustrating streamlines used to compute
tortuosity of 1 mm unit cells of the five TPMS structures investigated. (b) Work-
flow for the geometry generation, experimentation and computations.

Figure 5.1 illustrates the unit cells of the five TPMS structures employed in

this study and workflows for simulations and experiments. For 1 mm cell size

and 75% porosity structures, the geometric properties of the TPMS structures

investigated are summarized in Table 5.2. The Sv, pore diameter, and minimum

sheet thickness were measured within nTopology. Hydraulic tortuosity is de-

74



TPMS Sv (mm−1) tavg (mm) dpore (mm) Tortuosity
SP 22.5 0.1 0.35 1.05
G 27.2 0.08 0.26 1.20
I 32.2 0.06 0.28 1.17
D 36.2 0.06 0.29 1.23
P 39.0 0.02 0.08 1.17

Table 5.2: Specific surface area (Sv), pore diameter (dpore), minimum sheet
thickness (tavg), and tortuosity for 1 mm 75% porosity unit cells of each TPMS
structure.

fined as the total length of a line divided by the euclidean distance from start

to finish; this was estimated using ANSYS Fluent by imposing laminar viscous

flow through each unit cell at a Reynolds number < 1. The total length of each

streamline was divided by the corresponding euclidean distance, then averaged

over the volume to give a characteristic tortuosity [102]. Figure 5.1 (a) shows

the streamlines through each structure, which illustrates tortuosity. The geo-

metric properties of each TPMS structure are later used to analyze combustion

and thermal-structural behavior from corresponding computational and exper-

imental results.

5.2.2 Computational modeling

Thermal-structural FE simulations were performed to evaluate the impact

of internal TPMS topology on thermal-stress formation and dissemina-

tion. Additionally, a comparison between pure alumina (Al2O3) and mullite

(11Al2O3–1SiO2) was made to explore the differences between two commonly

used AM ceramic materials that exhibit varying thermal properties. Geomet-

ric models featured both uniform and linearly graded pore distributions to in-

vestigate fundamental understanding of thermal-structural behavior as a func-

tion of topological features as well as to facilitate comparisons with the graded

75



experimental burners. The length and diameter of the computational porous

structures were 10 mm with a surrounding shell of 0.5 mm thickness. First,

computational designs were imported from MSLattice to software nTopology

[107] for meshing. Then, all meshes were constructed with quadratic tetrahe-

dral elements to adequately capture deformation at edge midpoints. A mesh

resolution study was conducted to establish convergence of results and an el-

ement edge length/pore diameter ratio of approximately 0.05 was found to be

satisfactory. Figure 5.1 (b) illustrates the resolution of an example solid mesh.

Meshes were then imported into ANSYS Mechanical where steady-state ther-

mal analysis was coupled with static-structural analysis. A radial constraint

boundary condition was imposed on the outer surface of the cylinder, which

represents experimentation conditions (see Sec 5.2.4) and other relevant practi-

cal applications. Experimental thermocouple measurements from combustion

testing were used for the temperature boundary conditions at the top and bot-

tom faces to facilitate comparisons between the simulations and experiments.

Averaged measurements from thermocouples 2 and 3, which were closest to

the flame, were imposed for the top and bottom boundary conditions, respec-

tively (see Figure. 5.2 (b) for thermocouple locations). Given a positive CTE,

this temperature condition induces thermal expansion and elastic strain since

free motion is restricted by structural boundary conditions. Stress and strain

develop according to the following relations for isotropic materials [137]:

ϵ thermal
i j = α(T − Tre f )δi j (5.1)

ϵelastic
i j = 1/E(σi j − ν(σkkδi j − σi j)) (5.2)

ϵ total
i j = ϵ thermal

i j + ϵelastic
i j (5.3)

σi j = 2µϵ total
i j + (λe − β(T − Tre f ))δi j (i,j = 1,2,3) (5.4)

76



Where α is the temperature dependent CTE, ν is the poisson ratio, E is the

Young’s Modulus for the material, λ and µ are the Lamé elastic constants, β is

the thermoelastic constant, e is the dilatation; T is the temperature at evaluation,

and Tre f is a reference temperature used to define zero-strain. The constants λ,

µ, and β are compact terms that are functions of α, ν, and E. Published litera-

ture was consulted for approximate E and ν values appropriate for this study

[138, 139]. For alumina and mullite, the reduction in E has been shown to be on

the order of 10% at a temperature of 1000°C. Ambient values for E were selected

as 400 GPa for standard alumina and 230 GPa for the mixture of mullite used

herein. These approximations were later verified from estimations using the de-

flection data obtained from bending tests discussed Section 5.2.4. Values for ν

were taken to be fixed at 0.23 and 0.25 for alumina and mullite, respectively. As

shown in equations 5.1-5.4, the magnitude of thermal strain is directly related

to the material’s CTE, therefore accurate property data as temperature increases

is paramount. Therefore experiments on printed samples were performed to

determine the CTE as a function of temperature.

5.2.3 Additive manufacturing

High-quality stereolithography files were generated of the burners and scaled

by a factor of 1.3 to account for shrinkage during sintering. Structures were

printed using an Admaflex 130 DLP printer at a layer height of 30 µm and 50

µm feature size. The printed structures were first debound in a deionized wa-

ter bath for 24 hours at 40°C to remove a portion of the water-soluble resin,

subsequently dried for 24–48 hours, and then thermally debound in a muffle

furnace over a 48 hour period. This debinding process removes resin from the

printing process in preparation for sintering at a final temperature of 1625°C.

77



The general design process is illustrated in Figure 5.1 (b). Previous additively

manufactured porous structures used in PMBs [132] were fabricated using only

alumina, which resulted in significant degradation of the structures due to ther-

mal cycling. In order to address this durability concern, silica was added to the

alumina slurry to create a mixture of mullite (11Al2O3–1SiO2). The addition of

silica lowers the mixture CTE, thus it is expected to exhibit improved resistance

to thermal shock while maintaining superior processing characteristics to the

alumina slurry. Additionally, one alumina diamond structure was printed for

comparison of material durability.

5.2.4 Characterization and testing

Flexural bending tests were conducted to compare the strength reductions of

thermally shocked and un-shocked samples of 3D printed mullite and alumina.

Criteria followed ASTM C1525-18 and C1161-18, utilizing a four-point bending

test with a loading span half that of the support span [140, 141]. Maximum

flexural stress was calculated using the formula:

σ f =
3FL
4bd2 (5.5)

where the flexural stress is given as a function of the load in N (F), length of the

support span (L), width of the test beam (b) and depth of the beam (d). In these

tests, a support span of 40 mm was utilized with a beam length of 45 mm, and

width and depth of 4 and 3 mm respectively. Three samples were printed and

tested for each reported condition.

Thermomechanical analysis was conducted via a TA Instruments Q400EM

wherein 5 mm sections of alumina and mullite flexural bending beams were

heated from 100 to 1000°C with a holding force of 1 N for the duration of the

78



experiment. The CTE was calculated based on the linear coefficient of thermal

expansion:

α =
1
L

dL
dT

(5.6)

where α is the CTE, dependent on the reciprocal of the original sample length,

L, and the change in length, dL, with respect to change in temperature, dT .

MFCs

Thermocouple 
data logger

(a)

Burner

(b)

1

2

3

4

Mullite 
‘D’ Burner

Alumina 
‘D’ Burner

Embedded 
flame

Figure 5.2: (a) PMB experimental setup with an embedded flame in the alumina
and mullite burners shown during operation. (b) Schematic illustrating thermo-
couple arrangement.

Experimental PMBs were designed as a cylinder with an outer shell thick-

ness of 1.5 mm, an outer diameter of 28 mm, and axial height of 50 mm. In each

case, the TPMS structure was linearly graded axially, from a cell size of 5 mm

at the entrance to 10 mm at the exit, at a constant 75% porosity. Prior research

has shown similar grading to support stable combustion over a wide range of

operating conditions [132, 18, 142]. The structures were created in MSLattice

and subsequently merged with a tubular structure generated in nTopology.

Figure 5.2 (a) and (b) illustrate the experimental setup and thermocouple

79



spacing in the burners. Three type K thermocouples (labelled as 1) were posi-

tioned at a height of 5 mm above the burner exit and spaced evenly across the

diameter, with the left and right thermocouples placed 2.5 mm inward from the

edge. Three additional type-K thermocouples (labeled 2–4) were inserted into

the sampling ports in the tube, one 10 mm upstream from the burner exit, one at

the middle point of the burner, and one 10 mm from the entrance to the burner.

All temperature data was captured with a Pico Technology TC-08 thermocouple

data logger. A mixture of methane gas and air was introduced to the PMBs via

two MKS mass flow controllers (MFCs) at a constant rate during the duration of

the experiment. In these experiments, flow rate and fuel-air equivalence ratios

were kept constant to isolate the effects of heat flux on porous microstructure.

The fuel-air equivalence ratio, ϕ, is defined as the ratio of mass flux of fuel to

that of air divided by the stoichiometric ratio of the fuel to air. Here, a fuel-

lean value of ϕ = 0.95 was targeted by setting a flow rate of 1400 standard cubic

centimeters per minute (SCCM) of air and 140 SCCM of methane. PMBs were

preheated with a heat gun to reach an internal temperature of at least 100°C at

all thermocouples in order to reduce the potential for thermal shock upon ig-

nition. After ignition, the flame stabilized at the surface of the PMB for up to

10 minutes. Next, a secondary external heat source was applied to move the

flame into the porous media. In most cases, this heat source was used until the

temperature of the top thermocouple was 300-400°C. At this point, the flame

moved upstream, embedding in the porous structure. The system was then al-

lowed to reach an equilibrium stabilization temperature defined to be the point

at which the temperature at the top burner thermocouple port did not fluctuate

more than 5°C over a 15 minute period.

X-ray computed tomography (XCT) imaging of burners after experiments

80



was conducted to determine the extent of material failure for each burner. Imag-

ing was performed using a Zeiss Versa 520, scanning at 120 kV with an exposure

time of 1.2 s, with a resulting 30-35 µm per pixel resolution. The digital imaging

files generated from the XCT scans were segmented in 3D Slicer [143, 144] to

produce high contrast images that highlight any cracks developed within the

fired burners.

5.3 Results and discussion

5.3.1 Flexural bending and TMA tests

Figure 5.3 illustrates the results from flexural bending and TMA tests of 3D

printed mullite and alumina bars printed perpendicular (‘Z’) and parallel (‘XY’)

to the printing plane. The results show that while mullite has lower flexural

strength than pure alumina, its strength degradation due to thermal shock is

less pronounced than that of alumina, as shown in Figure 5.3 (a). When heated

to 700 °C, strength in the XY plane exhibited a ∼ 90% strength reduction for

alumina and ∼77% for mullite as compared to room temperature strength. This

demonstrates that pure alumina suffers from greater material degradation at el-

evated temperatures. Bars printed in the ‘Z’ orientation had approximately 74%

lower strength than those in ‘XY’, thus illustrating significant anisotropy in the

strength of ceramic AM materials. Average strength values in the XY plane at

ambient conditions were used to evaluate the FI in the simulation analysis.

Figure 5.3 (b) illustrate the higher CTE of alumina compared to mullite over

the operating regime of the PMBs. The logarithmic curve fits for each experi-

mental run were used as inputs for the ANSYS thermal models to better char-

acterize the thermomechanical behavior of 3D printed ceramics.

81



(b)(a)

Alumina

Mullite

C
T

E
 (x

10
-6

 /
ºC

)

Temperature (ºC)

XYZ

Figure 5.3: (a) Average flexural bending strength of alumina and mullite, com-
paring ‘Z’ and ‘XY’ print orientation, and effects of thermal shock at 400 °C and
700 °C. (b) Experimental TMA data for alumina and mullite (solid lines) with
logarithmic curve fits for each (dashed lines).

5.3.2 Thermal-structural simulations

The computational results are presented using the failure index FI, which

is used to quantify regions of material failure based on maximum principal

stresses, σMPS, adapted from [145]. The material is likely to fail when FI is equal

to or greater than 1, defined as:

FI =
σMPS

σMAX
(5.7)

where σMAX is the maximum average strength of the material as determined

by flexural bending tests. Since the ultimate compressive strength of ceram-

ics is typically an order of magnitude higher than the ultimate tensile strength,

the structure promoting the highest states of tensile stress is assumed have the

highest propensity for crack formation. These states of tensile stress are cap-

tured by σMPS developed within each element. FI is calculated at each element

for the simulated uniform and graded TPMS structures, and results are shown

82



in Figures 5.4- 5.8. Regions shown in grey exhibit only principal stresses in com-

pression, where all others experience varying degrees of tensile stress.

Mullite  
4 mm

Alumina 
4 mm

FI: 1.0 0 Compression

I-WP (I) Diamond (D)Gyroid (G)Schwarz 
Primitive (SP) PMY (P)

Mullite 
4 mm - 2 mm

Figure 5.4: Failure Index FI based on maximum principal stresses of uniform cell
size structures (4 mm cell size) and graded mullite structures (4 mm - 2 mm).

Figure 5.4 correspond to structures with 75% porosity and either a linear

gradation in cell size from 4 mm to 2 mm or a uniform cell size of 4 mm. For

all structures tested, the highest stresses are seen near the center of the struc-

ture, which suggests that peak stress levels are most sensitive to the underlying

TPMS topology as opposed to the junction at the cylindrical wall. Significantly

more regions of failure (i.e. FI > 1) are predicted for structures made of alumina

as compared to mullite. Among the mullite structures, ’D’ and ’P’ have smaller

regions of failure.

Results shown in Figure 5.4 are further quantified by binning the nodes in

different FI categories. Since element edge lengths for each mesh were nearly

identical with less than 15% deviation from the mean for one standard devia-

tion, the number of nodes in each FI range are normalized by the total nodes

83



M
ul
lit
e

A
lu
m
in
a

Uniform Graded

Figure 5.5: Volume percentage of failure indices for uniform and graded cell
size alumina and mullite structures.

to approximate the percentage of elements under compression or at various de-

grees of tension approaching failure. These results are shown in Figure 5.5 for

uniform and graded structures, respectively. Results for uniform and graded

structures were consistent for each TPMS topology. This analysis confirms that

more elements in the alumina structures were found to have FI > 1 as compared

to mullite. This supports our experimental finding and can be attributed to the

lower CTE of mullite, as seen in Figure 5.3 (b) which produces lower thermal ex-

pansion given identical temperature conditions. The volume with FI > 0.8 for SP

structures was considerably higher for both graded and ungraded conditions.

This indication of lower strength is consistent with previous work examining

the compression testing of TPMS which concluded sheet-based SP samples had

lower ultimate strength than I and G structures [123]. SP stress distributions in-

dicate failure propensity due to a poor ability to mitigate thermal strain in forms

other than tensile stress.

Unrestricted and frictionless motion in the Z axis allows axial deformation

which can be used as a proxy for the stiffness of each structure. The geometric

84



(b)(a)

No embedded flame
Low thermal strain

No embedded flame
High thermal strain

Embedded flame
Moderate thermal strain

No embedded flame

Thermocouple location Pore diameter (mm)

S v

Figure 5.6: (a) Thermocouple temperature measurements at steady-state burner
operation, dotted lines indicate unsuccessful non-embedded flames. (b) Specific
surface area (Sv), pore diameter, and tortuosity of each 1 mm 0.75 porosity unit
cell, with regions of flame stability indicated.

characteristics from Table 5.2 are shown graphically in Figure 5.6 (b) to highlight

regions of low, moderate and high thermal strain. Figure 5.7 (a) illustrates axial

thermal strain (ϵ) calculated as the axial deformation normalized by the original

length for 75% structures. High Sv, low pore diameter, high tortuosity generally

correspond to low thermal strain and stress distribution. Here, the SP and P

structures were found to be the least and most stiff, respectively. SP has low Sv,

large pore diameter, and low tortuosity providing the freedom for expansion

under thermal loads. Greater deformation is shown to scale with stress severity

for each structure. The stiffer structures such as P have higher Sv, smaller pores,

and greater tortuosity, and thus lower stress and FI fields.

Simulations were also performed to understand the effects of porosity and

cell size changes on thermal-structural behavior. These simulations were con-

ducted from ambient to a uniform condition of 550 °C. Results shown in Fig-

ure 5.7 (b) represent uniform structures at three different porosities (68%, 75%,

82%) and 4 mm cell size. Cell size gradation and porosity within a given TPMS

85



(a)
Porosity

(b)

Figure 5.7: (a) Axial thermal strain for uniform and graded structures in alu-
mina and mullite at 75% porosity. (b) Thermal strain at 4 mm cell size and
variable porosity.

structure are found to have a weaker influence on stress development than in-

ternal topology and material properties. Results demonstrate that axial thermal

strain increases with porosity for all structures due to larger void space and

thinner struts. However, the trend in thermal strain between the structures is

mostly independent of porosity, with the exception of D and P structures at the

lowest porosity.

Results in Figure 5.8 correspond to uniform structures at 75% porosity and

three different cell sizes 4 mm, 3 mm, 2 mm. At smaller cell sizes within a

fixed dimension structure, the increased number of connections between adja-

cent cells improves lateral support and stiffness. Thus, there is a decrease in

thermal strain with decreasing cell size. As with porosity, the trend in thermal

strain between the structures is mostly independent of cell size (i.e. SP consis-

tently the largest).

86



4

3

2

U
ni

t c
el

l s
iz

e 
(m

m
)

FI: 1.0 0 Compression

Diamond (D)Gyroid (G)Schwarz 
Primitive (SP)

Figure 5.8: Failure Index FI based on maximum principal stresses of structures
with 75% porosity and different cell size, and corresponding thermal strain cal-
culated at uniform temperature conditions.

5.3.3 Combustion experiments

To thermally stress each burner, we exploited the high temperatures from com-

bustion in the PMB configuration as described in Section 5.2.4. The experiments

illustrated significant performance variations for burners of different internal

topology under constant operating conditions. Figure 5.6 (a) displays the av-

erage stabilization temperature measurements from all internal thermocouples

over the duration of operation, which was approximately 15 minutes for each

burner that sustained an embedded flame. These measurements did not fluctu-

ate more than 5°C over this time interval. Since the burners were not insulated,

radiative heat losses result in lower temperatures than reported in comparable

works with TPMS-based PMBs [142, 116]. The heat from combustion recircu-

lated upstream in all cases, as evidenced by preheated reactant temperatures.

For the burners that sustained an embedded flame, the temperature profiles

differed by approximately 10% within the solid, but followed similar trends in

regards to the gradient between thermocouples 2 and 4.

87



Of the five tested structures, only three were successful in maintaining an

embedded flame, or combustion within the porous media, namely D, G, and I.

In contrast, SP and P burners did not achieve embedded flames. As illustrated

in Figure 5.6 (b), the geometric properties of the SP and P structures are hy-

pothesized to prohibit embedded flames. Among the TPMS structures tested,

SP has the minimum Sv and tortuosity, which lead to shorter fuel residence time

within the burner and lower the interphase heat exchange. These characteristics

limit the heat release and recirculation needed in porous burners to sustain an

embedded flame. Conversely, as the structure with the maximum Sv and tor-

tuosity, the P structure enables excessive heat transfer from the gas to the solid

phase, thus acting as a flame arrestor.

5.3.4 Durability and X-ray image analysis

All burners exhibited noticeable wear in the regions experiencing the highest

heat flux with differing levels of crack severity. The D and I burners were found

more durable than the G. Furthermore, the mullite D burner was significantly

more durable than the alumina D burner. Considerable fracture exhibited by

the G burner precluded imaging by XCT, and the P and SP burners were dis-

regarded since embedded flames could not be sustained. Figure 5.9 illustrates

the cracking seen in the D and I burners after approximately one hour of steady

operation. Minor cracks are highlighted in red to improve visibility. Multiple

cracks can be seen to cross the D structure struts in the layer plane, which is re-

ported to be of lower strength compared to the layer-orthogonal direction when

considering results from the four point flexural bending tests, see Figure 5.3.

Altering the print orientation of future models may provide greater resilience if

weak points are identified and structures are printed so that they exhibit favor-

88



able mechanical properties in such loading direction.

5 mm

Diamond (D)
I-WP (I)

FI: 1.0 0 Compression

(a) (b) (c) (d) (e) (f)

FI: 1.0 0 Compression

Figure 5.9: (a) XCT isosurface of mullite ‘D’ burner, with longitudinal and trans-
verse cross sections from (b) XCT and (c) simulations. (d) XCT isosurface of
mullite ‘I’ burner, with longitudinal and transverse cross sections from (e) XCT
and (f) simulations. Minor cracks in the are highlighted in red for clarity.

The X-ray images show cracks in both longitudinal and transverse planes

for D and I mullite burners. Figure 5.9 (b) and (c) show comparison between

the X-ray images and the FE simulation for longitudinal and transverse cross-

sections of the D burner. Analogously, Figure 5.9 (e) and (f) show these results

for the I burner. For both structures, there is noticeable overlap between regions

of predicted high FI and the crack locations in the X-ray images, denoted by

the red arrows. It is likely that initiation occurred at such locations within a

unit cell then propagated throughout the structure as operation continued. Un-

like ductile materials, ceramics do not undergo plastic deformation, but rather

sudden planar fracture perpendicular to tensile loading directions. Minor crack

locations and high stress regions are shown to exhibit consistent spacing. High-

lights within a unit cell in Figure 5.9 (e) appeared approximately 90°apart as did

high FI regions in Figure 5.9 (f). These comparisons demonstrate the fidelity of

FE simulations in predicting regions of high stress and subsequently burner fail-

ure zones.

89



5.4 Conclusion

In this study, ceramic additive manufacturing was applied to print five different

TPMS porous structures, namely Schwarz primitive (SP), gyroid (G), I-WP (I),

diamond (D), and PMY (P). The structural and thermal performance of these

structures were investigated using FE simulations and combustion experimen-

tation. The main conclusions drawn from this work are summarized as follows:

• Axial thermal strain from simulations was used as a proxy for stiffness

and an indicator of potential failure. TPMS structures with high specific

surface area, high tortuosity, and low pore diameter were found to have

lower thermal strain and thus decrease failure index values.

• The combustion performance of porous burners is found to be sensitive

to geometric features of the TPMS structure. SP and P burners did not

facilitate an embedded flame at the same operating conditions as the D,

I and G burners, which is hypothesized to be a result of the extremes of

specific surface area and tortuosity characteristic of these structures.

• The mullite burner at a composition of 95% alumina and 5% silica had

much higher durability as compared to the pure alumina burner. This

finding was supported by simulations using experimentally derived ma-

terial properties for mullite and alumina.

• Comparisons between simulations and XCT imaging of burners after op-

eration showed strong correlation between the predicted tensile stress con-

centrations and experimental crack formation. Crack spacing patterns

were also identified, which supports the use of FE simulations to predict

thermal-structural performance.

These results demonstrate the potential for tailoring complex porous struc-

90



tures via ceramic AM in the application of high temperature systems, both to

augment thermofluidic behavior and for system durability. Future work is re-

quired to develop alternate ceramic slurries for DLP printing, which have more

favorable thermal shock performance as compared to alumina or mullite, to fur-

ther improve durability. Beyond porous burners, future work also includes the

application of this methodology to developing optimized ceramic heat exchang-

ers, heat pipes, and other complex ceramic structures in energy and thermal

management systems.

Acknowledgements

Imaging data was acquired through the Cornell Institute of Biotechnology’s

Imaging Facility, with NIH 1S10OD012287 funding for the Zeiss-Xradia Versa

520 X-ray microscope. This work made use of the Cornell Center for Materials

Research Facilities supported by the National Science Foundation under Award

Number DMR-1719875.

91



CHAPTER 6

CONCLUSIONS AND FUTURE WORK

6.1 Main Findings

This thesis represents a multifaceted investigation of various aspects of combus-

tion science, spanning from fundamental studies of combustion phenomena to

novel combustion technologies. Through rigorous experimentation, computa-

tional modeling, and theoretical analysis, we have addressed critical challenges

and advanced our understanding across diverse fronts of combustion research.

The first observations of potential 2-methylfuran (MF) and 2,5-dimethylfuran

(DMF) combustion in the isolated droplet configuration within a micrograv-

ity environment were performed. Through computations and experiments, the

fundamental burning behavior of each potential bio-fuel was analyzed, reveal-

ing that MF droplets burned faster than DMF droplets. While DMF had longer

initial heating periods, its burning rate was slightly higher with marginal ac-

celeration near termination. Additionally, MF demonstrated a larger SSR com-

pared to DMF, indicating greater soot oxidation. No discernable oxidation oc-

curred during storage of DMF samples used in the study. However, stability

analysis of opened and stored samples revealed the presence of compounds

like 3-Hexene-2,5-dione and 5 Methyl-2-furanmethanol raising concerns about

DMF stability and emphasizing the need for strict handling protocols. Overall,

this research provides valuable insights into the combustion characteristics of

MF and DMF droplets, two biofuels under careful considering as additives in

gasoline.

Second, we analyzed the dynamic behavior of PMBs, focusing on their stabil-

ity and emissions under variable conditions. We found that PMBs can maintain

92



stability even when subjected to fluctuations in fuel composition (equivalence

ratio) and mass flux. Intuitively, conditions farther from flammability limits

showed greater stability against flow perturbations. Additionally, we observed

an inverse relationship between mass flux and CO levels, with stable conditions

approaching 2000 ppm near extinction limits. Furthermore, we unveiled the ex-

istence of linearity and a threshold of transition to non-linearity when destabi-

lizing, suggesting the implementation of control systems into unsteady burner

applications could be straightforward. Our findings provide valuable insights

for optimizing PMB emissions and stability, especially in applications involving

unconventional fuels like those from biomass gasification.

Next, additively manufactured PMBs with bio-inspired TPMS morphologies

were studied. Mullite burners with a constant porosity of 0.75 were fabricated

with a linear cellular gradation from 2.5 PPI at the inlet to 5 PPI at the outlet.

A volume-averaged model incorporating empirically derived volumetric heat

transfer coefficients was employed to support experimental stability regimes

and temperature distributions, showing good agreement with experimental re-

sults. Of the four burners studied, three supported anchored flames and ex-

hibited stability in the order of I > D > G, with the I architecture reporting the

overall greatest heat recirculation and interphase heat exchange. CFD provided

insight into the underlying fluid-structure interactions and heat transfer prop-

erties at relevant flow rates, uncovering ”thermal pockets” within the I-type

which may explain the finding of increased stability at low Reh. In summary, the

study underscores the importance of internal morphology in PMB design, with

the I and D architectures showing superior flame stability and burner durability

compared to G and P.

Lastly, we specifically investigated the structural performance of five TPMS

93



based PMBs at elevated temperatures. High Sv, tortuosity, and low pore diame-

ter were predicted to reduce thermal strain, enhancing durability. Importantly,

the structure with the lowest pore diameter, PMY, was predicted to undergo the

least thermal strain but experimentally failed to support a flame, highlighting

the need to balance geometric properties in PMB design. We found the I, G, and

D burners supported flames with varying degrees of fracture. Mullite burners

showed superior durability compared to pure alumina. Finite element simu-

lations accurately predicted crack formation, validating their use in predicting

thermal-structural performance. Overall, these results suggest the I-WP and Di-

amond TPMS architectures have high potential as internal topologies to PMBs.

6.2 Final Remarks

This dissertation concludes with practical views of the novelties from each

study, along with directions for future work.

• MF and DMF droplets exhibit similar burning characteristics, with MF

producing slightly less soot. However, concerns are raised for the chemi-

cal breakdown of these fuels during storage once exposed to oxygen. Re-

searchers should consider antioxidant additives and examine the effects

on burning from their addition. Furthermore, the level of toxicity associ-

ated with MF raises the largest concern for scaled integration. Care should

be taken when evaluating the potential ecological impacts.

• Dynamic perturbations of inlet flow conditions appear to be sustainable to

a degree, depending on the flow velocity and magnitude of ∆Φ. Although

we found a maximum ∆Φ of 0.4 could be sustained, operation at this limit

produced significant levels of CO formation, attributed to the low temper-

94



atures at Φ = 0.2 and convective lag of fuel within the burner. Operation at

a higher flow velocity will result in a lower allowable ∆Φ, but the higher

power output at stable conditions resulted in higher temperature and thus,

less CO. Future work should consider fuels that more closely mimic those

derived from biomass gasification, along with new burner designs, mod-

eling efforts and materials since the heat transfer properties will impact

stability.

• The TPMS architectures employed, namely I-WP, gyroid, primitive, and

diamond, showed varying breadths of stable operating conditions. It was

clear the primitive suffers in terms of heat recirculation and specifically

interphase heat exchange at the same cell size as the others. For the ge-

ometries which supported embedded flames, gyroid was the lesser of the

three, however, this architecture was able to stabilize at a slightly lower

lean limit than the others which exhibited quenching, likly due to the

higher Sv of diamond and I-WP. Future work should exploit the exemplary

characteristics of each morphology, such as the exceptional blow-off limits

of I-WP at Φ = 0.8, to create custom structures for the desired applications.

Furthermore, there is great potential for generating custom periodic mor-

phologies by utilization of a cost function targeted at optimizing a variable

of interest, such as the volumetric heat transfer coefficient (interphase heat

exchange), tortuosity and residence time, or specific surface area.

• The first thermal-structural simulations of TPMS structures with fixed ra-

dial constraints were reported. Importantly, we showed a significant im-

pact on stress levels by altering internal topology. The Schwarz primitive

TPMS was predicted to have the highest degree of stress while experi-

ments showed no flame could be sustained despite varying Φ and mass

95



flux, therefore is not considered a potential candidate for PMB applica-

tions. Similarly, our experiments failed to sustain a flame inside the PMY

burner, however, it is possible a larger pore diameter will result in flame

stabilization while maintaining the expected high resilience thermal loads.

As mentioned in the previous point, there are likely periodic structures

that can be fabricated through AM techniques that outperform the archi-

tectures reported. Furthermore, new materials, such as aluminum nitride

or silicon nitride, should be experimentally tested in the burner configura-

tion. A low thermal expansion coefficient and elastic modulus can hinder

the magnitude of stress development from thermal loads. Materials with a

high conductivity will distribute thermal stresses more equally, leading to

a lower severity of cracking, however, experimental testing will uncover

the impact on flash-back and blow-off limits. There are many variables

of influence here, and researchers should focus on the ones that produce

PMBs with wide stability regimes and high thermal-structural durability.

96



APPENDIX A

ADDITIONAL DATA

A.1 Introduction

Each section within the Appendix provides additional data to support the cor-

responding chapter.

A.2 MF and DMF

Here, the aim was to explore how different numerical setups affect the vapor-

ization rates of various fuels. We observed a discrepancy between experimental

results and numerical simulations, particularly in the initial phase of droplet va-

porization. While experiments showed a prolonged initial phase with minimal

change in droplet diameter, simulations indicated a negligible duration for this

phase.

To address this inconsistency, we conducted initial investigations to pinpoint

potential causes. We examined numerical parameters such as grid points, dis-

cretization schemes, and simplifications/assumptions in the physical and chem-

ical models utilized in simulations. Factors considered included the Soret effect,

presence of fiber, kinetic mechanisms, and key transport properties.

We found that the inclusion of the fiber does not significantly change the

vaporization rate. More specifically, the effect is to slightly decrease the vapor-

ization rate in the initial phase and then to slightly accelerate the vaporization

during the final phase. Overall, it seems that the fiber plays a minor role, and

it is difficult to imagine that the discrepancy with the experimental data can be

explained on the basis of effects induced by the fiber

97



Figure A.1: Simulation of a droplet of DMF (initial diameter of 0.580 mm) with
and without a fiber (SiC, d=14 micron, cross)

We tried to investigate if the way we adopted to ignite the droplet can have

an impact on the numerical simulations. As we know, the conventional ap-

proach followed in the past is to simulate the spark through a non-uniform

initial temperature profile, having a trapezoidal shape, like the one reported

below.

The key-parameters for prescribing the temperature profile are its distance

from the droplet center (p0), its thickness (w0), and its peak temperature. Both

p0 and w0 variables are normalized on the initial droplet radius (R0). In other

words, p0 = 1.5 means that the distance between the spark and the droplet

center surface is equal to 1.5R0 (i.e., the distance from the spark and the droplet

surface is 0.5R0). The default values are p0 = 1.01, w0 = 3.0, and T0 = 2200 K.

As observed from the default value p0 = 1.01, the spark is positioned very

close to the droplet surface (a distance of just 0.1R0). Attempts to relocate the

spark to a significantly larger distance (for example, p0 = 3 or larger) result in

98



Figure A.2: Numerical approach to initiating a spark.

failed ignition. This is because the time for fuel evaporation and reaching the

hot spark region is much longer than the duration of the initially imposed tem-

perature profile. Ignition with a spark at a large distance is only achievable by

allowing for pre-vaporization of the droplet before the actual simulation begins.

The approach involves running an initial simulation of the droplet in a gaseous

environment with a temperature equal to ambient temperature (i.e., 292 K) for

a short duration (typically 1-10 seconds). During this phase, the fuel vapor-

izes and diffuses into the gaseous atmosphere, albeit at a very slow rate due to

the low temperature, maintaining the droplet diameter nearly constant. Con-

sequently, at the conclusion of this preliminary simulation, a small quantity of

fuel is already present in the gaseous phase. With this setup, the real simulation

can commence, with the initial temperature profile corresponding to the spark.

Since there is already a certain amount of fuel in the atmosphere, it becomes

feasible to position the spark at a larger distance.

As it turns out, for the same ignition temperature and spark size, moving the

spark away from the droplet shifted the curve in the direction of experiments,

see p0 = 2.0 (light blue line). This location closely resembled the actual position

99



Figure A.3: Sensitivity to spark position and size

of sparks in experiments. Thus, it is reasonable to associated the shifted burning

curve seen in Figure. 2.2. With this result, we were satisfied with our results

and concluded the study in preparation for publication.

A.3 Operation of the burner apparatus

1. Open the SteadyConsMdot.vi f ileonthelablaptop.

2. Note there are very similar .vi files on the desktop, but this one has

no ramped oscillations mid-testing.

Plug in gas MFC chord and select the COM port that pops up for the gas con-

troller BEFORE connecting the air MFC.

Open the block diagram and double click on the write to file sub vi. A dialog

box will pop up and you may select the filename and location you wish to write

100



to. Make sure that just below that you have selected to use the next available

filename each time the program runs so that you don’t overwrite your file!

a. Each time the program is run, a new file will be created. If you are testing

to make sure everything works, make sure you change the filename in the

sub vi to what you want and delete the tester file you have just created (just

so that you don’t get confused when looking through the data).

b. I have set it up so that the data currently gets written to a folder on the

desktop. The current data gathered so far was curated and put into another

subfolder titled something along the lines of “real PMC data”.

Select the combustible gas you are using BEFORE starting the program.

Picolog Setup

1. Plug in the Picolog data unit to the USB port on the right side of the laptop.

2. Open Picolog and check that all 8 “ports” are being used as inputs.

a. Ports 1 and 2 are the upstream and 100-100 ppi interface TCs.

b. 3 and 4 are the 10-100 PPI TCs.

c. 5 and 6 should be midway through the 10 ppi foam.

d. 7 and 8 should be at the exit.

3. Check that each thermocouple is set to type K and has a 1s sampling fre-

quency.

a. Note that this 1s frequency is chosen to align with the labview data

and to make things intuitive.

101



4. Before starting, check the temp data to see if any TCs are reading irregular

numbers and check for shorts.

5. Don’t start recording until you are ready to start the Labview program.

Gas Analyzer Setup

1. Open easyemission on the lab desktop, go to the testo 350 tab.

2. Connect the computer to the analyzer via USB if possible (slightly safer

for data seemingly) or set up with Bluetooth. (John knows the details).

3. Ensure the chart settings have all the relevant gases selected (e.g CO, NO,

NO2, O2, CO2).

4. Start collecting once rest of setup is complete.

a. Note that running for too long will make the sensors go over range

and possibly cause errors saving the data. Don’t run for more than a

few hours.

Procedure

1. Make sure all the setpoints on the MFCs are set to 0 before opening any

valves. You will accidentally start the experiment sooner than expected if

not.

2. First start collecting gas analyzer data, it takes a second to calibrate.

3. Start your Labview program with 12 SLPM air and 0 SLPM CH4, quickly

start the Picolog collection so that the data is “in phase”.

4. Once you are ready to start, set the CH4 to 1.25 SLPM and immediately

light the burner.

102



a. This is a near equivalence mixture to get the burner started / make it

easy to light. This will quickly be changed.

b. I typically start a stopwatch on my phone so that I generally know

how long it’s been since the experiment started. This is not essential

but helpful.

5. Once lit, lower the CH4 back to 1 SLPM.

a. Want equivalence ratio around 0.8, mass flux around 0.2.

6. After five or so minutes (once the temperature has risen significantly but

not leveled off), raise the mass flux to 0.3 kg/m2/s by increasing the CH4

to 1.25 SLPM and the air to 15 SLPM.

a. Note that Labview will switch these values immediately as you type

them so you may have a jump in equivalence ratio briefly as you

change things. This is why I typically change the CH4 first to make

sure the mixture doesn’t get too lean.

b. If the burner is flashing back, you may need to increase the mass flux/

decrease equiv ratio. I recommend trying 15.7 air, 1.25 CH4.

7. Wait for the burner to reach a temperature in the range 1000-1200 Celsius

and for the changes in temperature to become very small. I find that the

temperature rarely stops increasing, but it will essentially approach some

asymptote on the temp graph. This happens often around the 15 - 20 min

mark.

a. Note that at this point the burner acoustics should have died down

and the flame glow should be visibly towards the middle of the

burner.

103



8. Once you are confident the temperature of the interface has “leveled off”,

set the settings for the oscillations (Do this before turning it on!).

a. Set the phase to 0, period to X, amplitude to X.

9. Once you are confident these are all correct, flip the switch to start the

sinusoidal flow. There’s no need to change any of the ‘steady state’ flow

settings for the CH4 and make sure you keep the Air settings the same.

10. Monitor the temp data to see if the interface temp drops significantly be-

low the exit or 100-10 ppi interface temp. Consider that condition stable

after 2 cycles.

a. If the burner has flashed back / blown off by the above criteria. Turn

off sinusoidal flow and let it reheat to the temp it previously way.

11. If stable, turn off sinusoidal flow until temp has reached the baseline. Then

increase amplitude by 0.1 and rerun. Repeat until unstable (then change

the frequency and start over).

12. Once you are ready to stop the experiment, set the methane to 0 first, then

quickly after set the air to 0. Try to stop the Picolog and mass flow con-

trollers at the same time.

13. Turn off and save gas analyzer data.

104



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