Close
About
FAQ
Home
Collections
Login
USC Login
Register
0
Selected
Invert selection
Deselect all
Deselect all
Click here to refresh results
Click here to refresh results
USC
/
Digital Library
/
University of Southern California Dissertations and Theses
/
CFD design of jet-stirred chambers for turbulent flame and chemical kinetics experiments
(USC Thesis Other)
CFD design of jet-stirred chambers for turbulent flame and chemical kinetics experiments
PDF
Download
Share
Open document
Flip pages
Contact Us
Contact Us
Copy asset link
Request this asset
Transcript (if available)
Content
CFD DESIGN OF JET-STIRRED CHAMBERS FOR TURBULENT
FLAME AND CHEMICAL KINETICS EXPERIMENTS
BY
ASHKAN DAVANI
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(AEROSPACE AND MECHANICAL ENGINEERING)
MAY 2019
ii
TABLE OF CONTENTS
Table of Figures iv
CHAPTER 1: INTRODUCTION 1
1.1. Why Combustion? 4
1.2. Literature review 9
1.3. Proposal 20
CHAPTER 2: BACKGROUND 23
2.1. Turbulence Basics 24
2.2. Combustion Regimes 29
2.3. Turbulent Burning Velocity 32
2.4. Perfectly Stirred Reactor (PSR) Model 34
CHAPTER 3: METHODS 37
3.1. Non-Reacting Turbulence 38
3.2. Performance Metrics 41
3.2.1. Turbulence Homogeneity, Intensity and Mean Flow Indices 41
3.2.2. Tracer Mixing Response 43
3.2.3. Chemical Composition Accuracy Index 43
CHAPTER 4: RESULTS 44
4.1. Turbulent Flame Studies 45
4.1.1. Simulation of Polyhedral Jet Stirred Reactors 45
4.1.2. Comparison with Fan-Stirred Chambers 52
iii
4.1.2.1. FSC-I: Ravi et al. 52
4.1.2.2. FSC-II: Chaudhuri et al. 55
4.1.3. Comparison of FSC and JSC 58
4.1.4. CIAO: Robustness to Imperfections 54
4.1.5. Simulated Flame Propagation 61
4.2. . Well-Stirred Reactor Studies 68
4.2.1. Tracer Mixing 70
4.2.2. Stoichiometric single-step and two-step kinetic models with no dilution 71
4.2.2.1. Case I: No heat release and activation energy 73
4.2.2.2. Case II: Effects of heat release and activation energy 76
4.2.3. Non-stoichiometric single-step reaction with dilution 78
4.2.4. Detailed H 2-O 2 reaction 81
4.2.4.1. Case I: τ res=0.12 s; Φ=0.2; P=1 atm 81
4.2.4.2. Case II: τ res=1 s; Φ=0.1; P=10 atm 85
4.2.4.3. Case III: τ res=0.01 s; Φ=0.2; P=1 atm 86
4.2.5. Performance comparison 87
4.2.6. Effects of design parameters 92
4.3. Experiment 94
CHAPTER 5: CONCLUSION 99
APPENDIX A: DETAILED ANALYSIS OF WSR THEORY 101
APPENDIX B: USC II DETAILED H2-O2 MECHANISM 102
APPENDIX C: DETAILS OF THE FLUORESCENCE EXPERIMENT 105
APPENDIX D: PRINCETON PLUG FLOW REACTOR 107
REFERENCES 110
iv
Table of Figures
Figure 1. Fuel shares of global total primary energy supply (TPES) in 1973 and 2013 reported in [12]. 5
Figure 2. World energy consumption history and projections between 1990 and 2040 [13].
CPP stands for clean power plant. 5
Figure 3. Global electricity generation (TWh) by fuel from 1971 to 2013 [12].
Other includes solar, wind, heat, etc. 6
Figure 4. Worldwide fossil fuel related CO 2 emissions in billion metric tons [13]. 7
Figure 5. Comparison between various theoretical and computational studies.
T
S ,
L
S ,
and
f
are turbulent burning velocity, laminar burning velocity, unburnt
and burnt density respectively.
t
Re is integral scale Reynolds number which is
defined as
v l u
t t
/ ' Re
. These parameters will be defined in next chapter. 11
Figure 6. Left: schematic of FSC developed by Sokolik et al. from [46];
1- motor, 2- paddle, 3- ignition electrodes 4- valves, 5- ionization probe, 6- glass.
Right: CAD representation 13
Figure 7. Left: Schematic of cylindrical FSC from [47]; right:
picture of the Leeds Mk II combustion vessel [33]. 13
Figure 8. Geometry of JSR proposed by Longwell and Weiss [55] in 1965.
Left: side view from [55], middle: the 3D CAD model and right: section view. 16
Figure 9. Geometry of JSR proposed by Bush [57] in 1965. Left: side view from [46],
middle: the 3D CAD model and right: top view. A, B, C and D are inlets, outlet,
nozzles and thermocouple glands respectively. 17
Figure 10. Geometry of the proposed 4JIPP JSR by Matras and Villermaux.
Left: schematics from [59]; right: CAD representation used in current work. 18
Figure 11. Dagaut et al. [54] reactor. Left two images: schematics from the original paper;
right two images: CAD model used in simulations in this study.
Overall diameter is 4 cm and the jets have diameter of 0.1 cm. 19
Figure 12. CAD representation of proposed IOS JSR in [61]. 19
Figure 13. Turbulent flames regime diagram also known as Borghi-Peters diagram [24]. 31
Figure 14. Schematic of an idealized propagating premixed turbulent flame. 32
Figure 15. Schematics of a Perfectly Stirred Reactor. Y, T, P, V, ṁ are mass fraction,
temperature, pressure, volume, and mass flow rate respectively and subscript
R denotes the reactor. 34
Figure 16. Dimensionless reactor temperature results for varying values of ṁ at
Da=1 for three different unrealistic (left) and one realistic (right) activation
energy values from PSR model. 36
Figure 17. Algorithm of PISO scheme for solving discretized pressure velocity equations 39
Figure 18. Schematic of the counter flow jets arrangement used by Pettit et al. in [87]. 40
Figure 19. Comparison of axial (left) and radial (right) velocity fluctuations in the gap
between a pair of counterflowing turbulent jets. Experiments and LES predictions
from Pettit et al. [87]; RSM simulations from the current study. The radial velocity
fluctuations are along the axis between the nozzle exits, relative to the stagnation
plane located at z = 0. 41
v
Figure 20. Jet-stirred chambers studied. Top row: wire-frame models showing the polyhedral
configurations of inlets and outlets; second row: locations of inlets (blue) and
outlets (red); third row: contours of turbulence intensity u’ i (m/s) (see Eq. (51)
fourth row: contours of mean velocity magnitude u
i
(m/s). The nominal diameter
of all JSCs is 30 cm. 48
Figure 21. Calculated Mean Flow Index (MFI, Eq. (53)), Homogeneity Index (HI, Eq. (54))
and Isotropicity Index (II, Eq. (55)) as a function of distance from the chamber
center (r) scaled by the chamber radius (R) for various jet-stirred chambers
(refer to Figure 20 and Figure 22). 49
Figure 22. Concentric Inlet And Outlet (CIAO) jet-stirred chamber. Left: geometrical
configuration; center: contours of mean velocity magnitude u
i
(m/s); right: contours of
turbulence intensity u'
i
(m/s). 50
Figure 23. Profiles of mean velocity magnitude u
i
( x) , u
i
( y) , u
i
( z)
(left) and turbulence
intensity u'
i
( x), u'
i
( y), u'
i
( z) (right) in the CIAO jet-stirred chamber. 50
Figure 24. Mean velocity vectors in the CIAO jet-stirred chamber. 50
Figure 25. Performance metrics of the CIAO reactor as function of the jet exit Reynolds
number for the spherical volume 0 ≤ r ≤ 0.5R. 51
Figure 26. Computational model of the Ravi et al. [34] Fan-Stirred Chamber. 53
Figure 27. Profiles of computed mean velocity u
x, i
, u
y, i
, u
z, i
(left) and turbulence intensity
components u'
x, i
, u'
y, i
, u'
z, i
(right) in the simulated Ravi et al.[34] fan-stirred chamber. 54
Figure 28. Computed mean velocity vectors colored by velocity magnitude (m/s) for
the Ravi et al. [34] fan-stirred chamber in the x-z plane. The width of the
measurement plane used by Ravi et al. for Particle Image Velocimetry
measurements is between the 2 black lines at the chamber center, but in
the x-y plane, i.e., in the plane of the 4 fans. 54
Figure 29. Experimental setup (left) and computational model (right) of the
Chaudhuri et al. [35] fan-stirred chamber. 56
Figure 30. Comparison of measured and computed radial mean velocity (
r
u )
and turbulence intensity ( ' u ) as a function of distance (radius in the
PIV measurement plane) from the center of the Chaudhuri et al. FSC [35]
at 2000 RPM. Both and ' u refer to the radial component of velocity
in the measurement plane only. 56
Figure 31. Profiles of computed mean velocity components u
x, i
, u
y, i
, u
z, i
(left)
and turbulence intensity components u'
x, i
, u'
y, i
, u'
z, i
(right) in the simulated
Chaudhuri et al. [35] fan-stirred chamber at 2000 RPM. 57
Figure 32. Computed mean velocity vectors colored by velocity magnitude (m/s)
for the Chaudhuri et al. [35] fan-stirred chamber in the x-z plane. The width
of the measurement plane used by Chaudhuri et al. for Particle Image Velocimetry
measurements is between the 2 black lines at the chamber center, but in th
e x-y plane, i.e. in the plane of the 4 fans. 57
r
u
vi
Figure 33. Calculated Mean Flow Index (MFI), Homogeneity Index (HI) and Isotropicity
Index (II) (Eqs.(53-55)) as a function of distance from the chamber center (r) scaled by
the chamber radius (R) for fan-stirred and jet-stirred chambers. “CIAO”: current CIAO
reactor; “TI”: truncated icosadehron; “Ravi et al.”: fan-stirred chamber [34];
“Chaudhuri et al.”: fan-stirred chamber [35]. 59
Figure 34. Contours of integral length scale (m) for the CIAO jet-stirred (left), Ravi et al.
fan-stirred chamber [34] (middle) and Chaudhuri et al. fan-stirred chamber [35] (right). 60
Figure 35. Computational domain of the combustion chamber from Griebel et al. [92].
The colors shown represent the computed values of mean progress variable c
for
the case = 0.5 (see Table 6) 63
Figure 36. Images of simulated expanding flame kernels (for the surface corresponding
to mean progress variable c = 0.5) in the Ravi et al. [34] FSC (upper row) and the
CIAO JSC (lower row). The 4 fans are shown in the FSC and the 8 concentric inlet/outlet
ports are shown in the JSC. Videos of these simulations are included in the
Supplemental Data. 65
Figure 37. Plots of flame radius r f vs. time t for different values of the mean progress
variable c in the Ravi et al. [34] FSC and the CIAO JSC. (a) Ravi et al., x-z plane;
(b) Ravi et al., x-y plane; (c) CIAO, x-z plane; (d) Ravi et al. and CIAO for full 3D flame
surface for c = 0.1 and 0.5 only. 67
Figure 38. Selection of various designed and modeled JSR chambers. Top row from left:
4JIPP-A exit at center, 4JIPP-A 2 exits, CIAO V2, inverted (Beach ball); bottom row
from left: V6, V8, V14, V16, Cubic. 69
Figure 39. Comparison of computed rates of decay of a passive tracer in the CIAO,
4JIPP-A,4JIPP-B and Cubic reactors and comparison with the exact solution for
a perfectly-stirred reactor. 70
Figure 40. Computed pathlines in JSRs. Left: CIAO reactor; right: 4JIPP-A reactor. 73
Figure 41. Computed product C mole fractions (X C) fields as a function of Da for the
test problem (Eq. (59)) with = 0 (i.e., single-step reaction) at Da = 2.5. Left:
4JIPP-A; right: proposed CIAO reactor. The exact solution for these conditions is X C = 0.268. 74
Figure 42. Left: Volume-averaged mole fraction of product C (X C) as a function of Da for
the test problem (Eq. (59)) with Δ = 0 (i.e., single-step reaction) predicted by the
FLUENT/RANS simulations for the various chambers along with comparison to the
exact theory (Eq. (65)) assuming perfect mixing. Right: comparison of inferred
(from Eq. (65)) rate constants using the volume-averaged product mole fraction
(relative to the actual prescribed k 1) as a function of Da. 74
Figure 43. RMS values of inferred over true k calculated for various chambers for different
Da numbers. 75
Figure 44. Comparison of computed values (solid symbols: CIAO; open symbols: 4JIPP-A)
to the exact solution (curves) for the two-step reaction (Eq. (66)) as a function of the
Damköhler number of reaction 1 (Da) and the ratio of Damköhler numbers of reaction
2 to 1 (Δ). Left: mole fraction of intermediate species (X C); right: mole fraction of
final product species (X D). 76
Figure 45. Comparison of computed product mole fractions (X C) for single-step reaction in
the CIAO to theoretical predictions for WSRs in under isothermal and non-isothermal
vii
conditions; for the latter case with E = 30 kcal/mole, T i = 900K, T f = 939K, resulting in
(T f)/ (T i) = 2. 78
Figure 46. Comparison of calculated values of reactant A mole fraction for 4JIPP-A and
CIAO JSRs and the exact solution obtained from the extended single-step reaction model. 80
Figure 47. Comparison of reactant mole fraction for extended single-step and detailed
reaction mechanisms which is discussed in following section. The single-step
values are obtained analytically, and the detailed mechanism values are predictions
from PSR model in CHEMKIN. 81
Figure 48. Comparison of H 2 mole fraction as a function of reactor temperature for 4JIPP
and CIAO jet-stirred reactors for an ideal Perfectly Stirred Reactor, the 4JIPP reactor
(volume-averaged and at specific locations averaged over a 2 mm radius spherical
volume: center (r/R=0), half-way toward the outlet and at the outlet plane (r/R=-0.5),
and halfway between center and top of the chamber (r/R=0.5), CIAO reactor
(volume-averaged; location-specific predictions are nearly identical) and experimental
results by LeCong and Dagaut [97]. 82
Figure 49. Comparison of averaged mole fractions of H 2 for both 4JIPP-A and CIAO reactors as
function of Da. 83
Figure 50. Computed temperature and species maps for 4JIPP (left column) and CIAO
(right column) jet stirred reactors. Mixture H 2 : O 2 : N 2 = 1 : 2.5 : 96.5 (equivalence
ratio = 0.2), wall temperature 925K, inlet temperature of 900K, inlet pressure
1 atm, residence time R = 0.12 s. 85
Figure 51. Comparison of H 2 mole fraction as a function of reactor temperature for
4JIPP-A and CIAO JSRs for an ideal Perfectly Stirred Reactor, the 4JIPP reactor
(volume-averaged and at specific locations averaged over a 2 mm radius
spherical volume: center (r/R=0), half-way toward the outlet and at the outlet
plane (r/R=-0.5), and halfway between center and top of the chamber (r/R=0.5),
CIAO reactor (volume-averaged; location-specific predictions are nearly identical)
and experimental results by LeCong and Dagaut in [97]. 86
Figure 52. Comparison of H 2 mole fraction as a function of reactor temperature for
4JIPP-A and CIAO JSRs for an ideal Perfectly Stirred Reactor, the 4JIPP-A and CIAO reactors
(volume-averaged and at specific locations averaged over a 2 mm radius spherical
volume: center, half-way toward the outlet and half-way between outlet and inlet). 87
Figure 53. Comparison of calculated CAI in CIAO and 4JIPP-A reactors for both detailed
and single-step chemistry at three different Da numbers for φ=0.2, P=1 atm and τ res=0.12 s. 88
Figure 54. Comparison of calculated CAI for CIAO and 4JIPP-A JSRs for two different Da.
Top row: case II of detailed mechanism with φ=0.1, p=10 atm and τ res=1 s
(left: T w=925 K, right: T w=1000K); bottom row: case III of detailed mechanism
with φ=0.2, p=1 atm and τ res=0.01 s (left: T w=950 K, right: T w=1000K). 89
Figure 55. CAI comparison for various chambers for the extended single-step reaction
with 1% A, φ=0.2, P=1 atm, and τ res=0.12 s. 90
Figure 56. Effects of turbulence model on CAI for three different chambers of CIAO,
4JIPP-A, and CIAO V2. 91
Figure 57. Plots of CAI comparison for various Da for CIAO (left) and 4JIPP-A (right) reactors. 92
viii
Figure 58. CAI comparison for various CIAO JSRs. Top: Effects of number of jets; bottom: effects of
chamber and inlet and outlet sizes. 93
Figure 59. Experimental setup for studying of mixing homogeneity in 3D printer CIAO. 95
Figure 60. CAD representation of CIAO chamber with built-in outlet manifolds. 96
Figure 61. Successive PLIF images (interval 0.008 s) of fluorescein concentration in a
CIAO JSR. Chamber diameter 15 cm, field of view of images 7.62 x 5.71 cm.
Top row: raw images from camera; middle row: outlined structures from dilated
images; bottom row: inverted outlines of smoothed images. 98
Description of the graphic on the cover page:
Tetrahedron, graphical representation of fire as one of the four classical elements in Plato’s
Timaeus. It is the polyherdon with smallest number of sides which has the largest ratio of surface
area to volume and was deemed appropiate to represent heat and sharpness of fire.
ix
"When the Evil Spirit assailed the creation of Good Truth; Good Thought and Fire came to be and
crushed the evil"
(Yasht 13.77)
x
TO MY PARENTS KHALIL AND SHAHNAZ
AND MY BROTHERS ARASH AND AMIR
WHOSE UNWAVERING SUPPORT NEVER CEASED
TO ENCOURAGE ME THROUGH ALL THE YEARS
DESPITE THE UNBEARABLE PHYSICAL DISTANCE
TO THE ONE WHO ALWAYS BELIEVED IN ME
FROM THE BEGINNING OF THE JOURNEY
TO MY FAMILY WHO HELPED ME THROUGH ALL THE HARDSHIPS
Chapter 1: Introduction
A golden coin from Sasanian Empire in Iran (224 CE) with depiction of Holy Fire.
2
Once upon a time there was a …
Fire, a phenomenon that is the cornerstone of human civilization. Occurrence of fire on
the Earth goes back to appearance of oxygen in atmosphere (oxidizer) and plants on terrain
(fuel). Study of the fossil record shows the very first evidence of fire during Silurian period
(around 440 million years ago) in early Paleozoic Era (540 to 300 million years ago) when both
oxygen and plants were sufficient to support fire [1, 2]. Some researchers estimate occurrence of
fire as early as 470 million years ago in Ordovician period during which formation of the land-
flora took place [3].
Origins of anthropogenic fire are highly debated. Archeologists estimate that the ability
of early humanoid to control fire developed in middle Pleistocene period (1.4 to 0.2 million years
ago) in late Cenozoic Era, however, the evidence for earliest use of controlled fire by homo
erectus (around 1.4 million years ago) is inconclusive and unequivocal consensus is that early
homo sapiens were able to create and control fire between 400,000 to 250,00 years ago [4, 5, 6].
Recent analyses of intact remains from Wonderwerk Cave in South Africa using more advanced
techniques show homo erectus controlled burning happened in the cave about 1 million years
ago [7]. Regardless of the origin, fire remains a significant process that is responsible for shaping
the ecosystem and ability to control it was a vital milestone in human progress. Importance of
fire in human life is widely reflected in mythology, cultural activities and traditional beliefs in
every major civilization throughout history. Understanding the cause and behavior of fire have
always been the focus of human curiosity and trying to come up with viable explanations have
been a continuous attempt. Before development of scientific method, like other natural
phenomena, origin of fire was associated with a metaphysical being and had mythological roots.
Some cultures referred to it as an element and some as a moving force. In Greek mythology, a
Titan named Prometheus stole the fire from gods and gave it to humanity for their protection
[8]. In Indian mythology, fire is represented by a god named Agni (which means fire in Sanskrit
and is the root for the word ignition) which is still a significant part of Hindu culture [9]. In Olmec
(oldest Mesoamerican civilization) mythology, the first god i.e. the Olmec Dragon, has eyebrows
of fire and it is believed to be the origin of Aztec’s god of fire Xiuhtecuhtli [10].
3
In Persian folklore, there are multiple accounts regarding origins of fire. However, there is
one which could be attributed more to a rather phenomenological description. According to a
legend in the Shahnameh (The Book of Kings), written by Ferdowsi around 1000 years ago,
Houshang (grandson of Keyumars, the First Man also known as The First King of the World) saw a
monstrous black serpent in a mountain and throwed a piece of rock (probably a flint stone) to kill
it. The stone missed the serpent and struck another rock which ignited a spark and started a fire.
He then prayed God for this discovery and after getting back gathered people and taught them
how to make fire. He made a big fire at night using the same technique in honor and admiration
of this gift from God and they celebrated the whole night around it. This became a festival called
Sadeh (meaning hundred), also known as festival of fire, which to this date is still celebrated in
winter in the night when there are fifty day and fifty nights left to the first day of spring [11]. Due
to its light and warmth, fire is highly respected in Persian culture. It symbolizes purity, life,
fighting all the dark forces and maladies and is considered sacred in Zoroastrianism, the ancient
monolithic religion in Iran and one of the oldest in the world which started about 1500 BCE and
is still practiced. The holy fire is the theophany of God and the divine fire should be burning all
the time. It should be purified throughout the year and only high rank priests (Magi) with a
special clothing and mask are responsible for the task.
Parsi Wedding, Chuck Marshall.
Zoroastrian priests (Mobed or
Magi) performing fire rituals.
4
Holy fire, Atar (which through time changed to Azar and is now Atash the Farsi word for
fire), is sometimes regarded as an angel or the messenger and sometimes as son of the God.
Holy fire is classified into three grades: lowest grade is Dadgah, then Adaran, and the highest
grade is Bahram which is comprised of sixteen different fires and its consecration ceremony
requires thirty-two priests. The fire It is kept in special flame holders called Atashdan which is
placed at center of special cubic or octagonal temples called Atashkadeh (place of fire). There
are still some active temples of fire across Iran, but majority of them were destroyed or
transformed after fall of Sasanian Empire at 651 CE.
Kahle Sheykh Aali (also known as
tomb of Allamah Davani), village
of Davan, Fars, Iran. This place
used to be a temple of fire and is
still considered a holy place
among local people.
1.1. Why Combustion?
Advancement of human civilization is directly related to energy supply and consumption.
According to the International Energy Agency (IEA) total primary energy supply (TPES) has
increased from 6100 Million Tons of Oil Equivalent (Mtoe) in 1973 to 13541 Mtoe (or 536.9
quadrillion Btu) in 2013 [12]. Fuel shares of TPES are shown in Figure 1. The worldwide energy
demand is anticipated to have a significant fast-paced growth from 2012 to 2040 according to
the International Energy Outlook 2016 (IEO2016) prepared by the U.S. Energy Information
Administration (EIA). Global energy consumption will have an increase of 266 quadrillion Btu
5
from 549 quadrillion Btu in 2012 to 815 quadrillion Btu in 2040 which is near 1.4% increase per
year [13].
Figure 1. Fuel shares of global total primary energy supply (TPES) in 1973 and 2013 reported in
[12].
It can be seen from Figure 1 that fossil fuels account for 81.4% of TPES in 2013 and it is projected
that fossil fuels still remain the major energy supply with more than 75% of global energy use in
2040 [13]. Global energy consumption projection is shown in Figure 2. It is worth noting that
although oil sustains its leading share by 2030, natural gas consumption will surpass coal.
Figure 2. World energy consumption history and projections between 1990 and 2040 [13]. CPP
stands for clean power plant.
The fastest growing form of end-use energy consumption in the world is electrical power
generation. Global energy consumption used for electricity generation increased from 8.6% in
6
1973 to 14.8% in 2013 [12]. Fuel share of world electricity generation from 1971 to 2013 is
shown in Figure 3.
Figure 3. Global electricity generation (TWh) by fuel from 1971 to 2013 [12]. Other includes
solar, wind, heat, etc.
Electricity demand is driven by economic growth and it is projected that the net
electricity generation increases by 69% by 2040 [13] as it can be seen in Table 1.
Energy source (PWh) 2012 2020 2025 2030 2035 2040 Averaged annual change %
Total World
21.6
25.8 28.4 30.8 33.6 33.6 1.9
Petroleum and other liquids
1.1
0.9 0.7 0.6 0.6 0.6 -2.2
Natural gas
4.8
5.3 6.3 7.5 8.8 10.1 2.7
Coal
8.6
9.7 10.1 10.1 10.3 10.6 0.8
Nuclear
2.3
3.1 3.4 .3.9 4.3 4.5 2.4
Renewables
4.7
6.9 7.9 8.7 9.6 10.6 2.9
Table 1. Net electricity generation by energy source for 2012-2014 [13]. (1 PWh =1000 TWh
=85.98 Mtoe)
It can also be seen that fossil fuels continue to be the principal energy source of
electricity generation providing 63% of net global electricity generation in 2040. However, due to
environmental concerns of greenhouse gas (GHG) emissions there is a significant interest to use
natural gas which emits far less carbon dioxide (CO 2) per KWh electricity generated compared to
other types of fossil fuels i.e. oil or coal. Natural gas which is the least carbon-intensive form of
fossil fuel will contribute to 26% of net global electricity generation in 2040 [13]. Nonetheless,
7
since anthropogenic emissions of CO 2 are a primary consequence of the combustion of fossil
fuels, climate change debate mainly encompasses energy consumption. Although coal will
remain the largest source of global energy-related CO 2 emissions with 39% of total fossil fuel
emissions by 2040, the natural gas share of CO 2 emissions projected to be 26% which is a 7%
increase from relatively small amount of 19% of total greenhouse gases in 1990 [13]. Global
energy-related CO2 emissions from 1990 to 2040 are shown in Figure 4.
Figure 4. Worldwide fossil fuel related CO 2 emissions in billion metric tons [13].
As mentioned earlier, the least carbon-intensive fossil fuel is natural gas. It emits CO 2 at
about half the rate of coal and it could help in reduction of CO 2 emissions in many countries.
Consequently, there is a considerable interest in using natural gas-fueled power generation
method due to lower emissions CO 2 emissions of various fuels are shown in Table 2.
Fuel lb CO2
per unit of mass or volume
Kg CO 2
per unit of mass or volume
lb CO 2
Million Btu
Kg CO 2
Million Btu
Coal (all types) 4631.50/short ton 2100.82/short ton 210.20 95.35
Diesel fuel and heating oil 22.40/gallon 10.16/gallon 161.30 73.16
Gasoline 19.60/gallon 8.89/gallon 157.20 71.30
Propane 12.70/gallon 5.76/gallon 139.05 63.07
Natural gas 117.10/thousand cubic feet 53.12/thousand cubic feet 117.0 53.07
Table 2. CO 2 emissions of various fuels according to [14].
8
Another major GHG after natural gas itself and CO 2 is Nitrogen Oxides (NO x) which
accounts for nearly 16% of total GHG emissions [15]. Most of produced NO x is from
anthropogenic sources with more than half of the emissions produced by transportation (road
and non-road) and power generation combined which are considered undesired consequences
of combustion [16-17].
There are three primary combustion related sources of NO x :
Thermal (or Zeldovich)
Prompt (or Fenimore)
Fuel
Thermal NO x is product of an enormously high activation energy reaction due to strong
N=N bond (≈220 kcal/mole) and consists of three principal reactions which were introduced by
Zeldovich [18] and are known as Zeldovich mechanism:
N 2 + O → NO + N (E 1 = 76.5 kcal/mole)
N + O 2 → NO + O (E 2 = 6.3 kcal/mole)
N + OH → NO + H
Due to the high activation energy and long characteristic time scale (τ NO~0.59 s for typical
stoichiometric hydrocarbon-air mixtures at 1 atm compared to τflame ~ 0.0006 s) Zeldovich NO is
not produced in the flame and it occurs in the burned gas downstream of it. Note that τflame is
the characteristic reaction time during which reaction occurs. However, there are some NO
produced inside the flame with the reaction paths proposed by Fenimore in 1971 [19] as:
CH + N 2 → HCN + N followed by N + O 2 → NO + O
C 2 + N 2 → 2CN followed by CN + O 2 → CO + NO
Since CH radical is present in the flame front only prompt NO is more prevalent in
hydrocarbon flames and it happens more for rich flames. The last source of NO x is oxidation of
nitrogen-bearing fuels such as coal and oil which is known as fuel NO x.
9
Most of the undesired consequences and environmental concerns of hydrocarbon
combustion could be minimized using Hydrogen (H 2) as a fuel. For instance, Internal Combustion
(IC) engines with H 2 as fuel would have no prompt and NO x. Furthermore, using H 2 enables the
engine to run extremely fuel-lean (since lean H 2-air mixtures have same burning velocity as
stoichiometric hydrocarbon-air mixture) which in turn leads to lower adiabatic flame
temperature and effectively eliminates thermal NO x. Using H 2 also eliminates hydrocarbon
emissions such as CO and CO 2.
Lean H 2-air combustion has unique properties that are different from hydrocarbon
combustion. For example, the lean flammability and minimum flame temperatures of H 2-air
flames are much lower than hydrocarbon-air flames for a given flame temperature (T f) since they
have higher characteristic reaction rates. Lower T f causes weaker flame wrinkling via thermal
expansion compared to hydrocarbon-air flames and since H 2-air mixtures have smaller Lewis
number (Le) (defined as ratio of thermal diffusivity of the bulk mixture α to mass diffusivity of
the stoichiometrially limiting reactant D) compared to hydrocarbon-air mixtures, flame fronts are
inherently unstable and wrinkle spontaneously due to diffusive-thermal instabilities [20-21-22].
Although effects of lower flame temperature have been studied widely, effects of other
characteristics of H 2-air mixture on behavior of flame are not well understood. For example,
effects of flame wrinkling on burning rate, quenching limits, emissions of NO x, unburned
hydrogen (UH 2), and H 2O 2 are not studied. Furthermore, the interactions of turbulence and
flames with such characteristics are not well investigated.
Although effects of thermal expansion and stability properties of flames will not be
studied in this proposal, effects of turbulence on flame propagation will be investigated
systematically in current work. After all, better understanding of combustion science is a key to
reduce undesired consequences and to improve the efficiency of combustion processes.
1.2. Literature review
Combustion processes are comprised of various physical and chemical phenomena. They
include physical transport, chemical reactions, and heat transfer. Hence, it is common and
10
essential to gather and form dimensionless groups based on different parameters from fluid
dynamics, chemistry, and thermodynamics to describe such processes. One of the extensively
used dimensionless numbers is Damköhler number (Da) which compares the turbulent mixing
( t) and chemical reaction ( c) time scales:
c
t
Da
(1)
t can be computed from turbulent integral scale properties (integral length scale
t
l and
turbulent intensity ' u ) such that:
' u
l
t
t
(2)
and c can be computed from laminar flame properties such that:
L
c
S
(3)
S L and δ are laminar burning velocity and flame thickness respectively. S L is considered to be the
most important quantity in premixed flames and is defined as the velocity at which the flame
front is propagating normal to itself and relative to the flow into the unburnt mixture and it
depends on both thermal and chemical properties of the mixture [24]:
2 / 1
) ( ~
L
S (4)
is thermal diffusivity and
is the reaction rate. A consequence of defining a velocity scale is
definition of a length scale i.e. flame thickness δ is defined as:
L
S
(5)
Combining Eqs. (2-5) Da number (also known as turbulent Da) can be rewritten as [23, 24]:
' u
S l
Da
L t
c
t
(6)
11
High Da number (Da >> 1) means turbulent mixing happens on scales faster than chemical
reaction. This is known as Propagating Turbulent Flame limit in which reaction rate is limited by
turbulent mixing. It is well known that turbulence increases the propagation rates (S T) of
premixed-gas flames by wrinkling the flame front and increasing its surface area, thereby leading
to higher rates of thermal enthalpy production per unit volume [23, 24, 25]. For this reason,
turbulence is used in essentially all power generation devices which employ premixed
combustion, e.g., spark ignition internal combustion engines and premixed gas turbines.
Although reaction rate constant (k) can be obtained from Arrhenius law directly, burning rate
cannot be calculated directly for turbulent combustion. However, possible turbulent combustion
models could be derived by performing physical analysis based on comparing turbulent flow and
chemical reaction characteristics [23]. It can be concluded from numerous turbulent combustion
models that increasing turbulence leads to faster burning rate without any limits [26, 27, 28, 29,
30, 31] however, this is not the case in practice as increasing turbulence leads to flame extinction
at certain intensity [32]. Comparison between various models and experiment is shown in Figure
5.
Figure 5. Comparison between various theoretical and computational studies.
T
S ,
L
S ,
and
f
are turbulent burning velocity, laminar burning velocity, unburnt and burnt density
respectively.
t
Re is integral scale Reynolds number which is defined as
v l u
t t
/ ' Re
. These
parameters will be defined in next chapter.
12
Many experimental apparatuses have been used to study premixed turbulent
combustion including Fan-Stirred Chambers (FSCs) [33, 34, 35, 36], Bunsen flames [37, 38, 39],
slot-jet generated turbulence [40], rod-stabilized V-shaped flames anchored downstream of a jet
employing fractal grids to generate turbulence [41] and opposed-jet counterflows [42, 43]. Many
models of premixed turbulent combustion typically make several assumptions like:
- Adiabatic reaction
- Thin reaction zones
- Constant turbulence intensity ' u
- Unity Lewis number
which might be acceptable, but they also assume:
- Homogeneous and isotropic turbulence over many integral scales of turbulence (l t)
with zero (or at least a constant) uniform mean flow
- Isotropicity and homogeneity is not affected by heat release
- Constant density across the flame
which are problematic and raise several concerns. A persistent issue with such apparatuses is
how nearly the turbulence generated by such apparatuses conforms to the simplifying
assumptions made by these models. In fact, the disagreement in predictions and experiments
which can be noted in Figure 5 could be due to these assumptions. For instance, to what extent
claims of isotropicity and homogeneity of FSCs in [34, 35] are valid? what causes the large scatter
in experimental data for S T? could it be because of the methodology (e.g. using fans for
generating turbulence) and dependency of experiments on numerous parameters (like
geometry, turbulence scales, etc.) since it has been shown [44] that turbulent transport
properties are geometry dependent?. perhaps, the most important question is what is the
“proper” definition of S T? these questions will be addressed in future chapters.
The first proposed FSC dates to 1961. Karpov and Sokolik [45] used fans to generate
turbulence in an enclosed chamber. Unfortunately, there are no geometrical details about their
chamber. Later in 1967, Sokolik, Karpov and Semenov [46] proposed another spherical FSC with
13
four fans (paddles) and studied turbulent burning velocities. The schematic of their FSC is shown
in Figure 6. It should be noted that geometrical data in this case could not be found as well.
Figure 6. Left: schematic of FSC developed by Sokolik et al. from [46]; 1- motor, 2- paddle, 3-
ignition electrodes 4- valves, 5- ionization probe, 6- glass. Right: CAD representation
Several years later in 1984, Abdel-Gayed, AI-Khishali, and Bradley [47] proposed a
cylindrical FSC with internal diameter (ID) of 305 mm and height of 150 mm which had 4 eight-
bladed fans with mean diameter of 147 mm each and the fans placed in a planar configuration.
The same group later proposed another spherical FSC [33] with ID of 380 mm with 4 eight-
bladed fans placed in a tetrahedral configuration which is still being used (known as Leeds Mk II
combustion vessel). Both geometries of the old FSC and the modified chamber are illustrated in
Figure 7.
Figure 7. Left: Schematic of cylindrical FSC from [47]; right: picture of the Leeds Mk II combustion
vessel [33].
Ever since its debut in 1961, numerous modified FSCs with various shapes and different
numbers of fans are proposed. A summary of various FSCs are shown in Table 3.
14
Year Authors Chamber type (ID mm) # Fans # Blades Fan ID (mm) Orientation
1961 Karpov and Sokolik [45] ? 4 ? ? Planar?
1967 Sokolik et al. [46] Sphere (ID ?) 4 8 ? Planar
1984 Abdel-Gayed et al. [47] Cylinder (ID 305) 4 8 147 Planar
1990 Flanser and Gloff [48] Cylinder (ID 260) 4 8 135 Planar
2000 Shy et al. [49] Cylinder (ID 225) 2 8 116 Linear
2001 Sick et al. [50] Sphere (ID 58) 4 ? 48 Planar
2003 Bradley et al. [33] Sphere (ID 380) 4 8 ? Tetrahedral
2008 Kitagawa et al. [51] Sphere (ID 406) 2 ? ? Linear
2008 Weiß et al. [52] Sphere (ID 118) 8 6 45 Cuboidal
2012 Ravi et al [34] Cylinder (ID 305) 4 Various 76.2 Planar
2013 Chaudhuri et al. [35] Cylinder (ID 114) 4 6 68.5 Planar
2013 Galmiche et al. [53] Sphere (ID 200) 6 4 40 Octahedral
Table 3. Summary of proposed FSCs over time. Question marks indicate lack of information.
In this study, two FSCs of Ravi et al [34] and Chaudhuri et al. [35] will be simulated and
further details are discussed in Chapter 4.
So far, the discussion was about high Da combustion regime. Another end of the Da
spectrum is when Da<<1, meaning that chemical reaction time scale is much longer than the
turbulent mixing time scale. Because of the slow chemical reaction, reactants and products are
presumably well-mixed within the chamber, through turbulent structures. This is known as
Perfectly Stirred Reactor (PSR) limit and the ideal chamber in which this condition is guaranteed
is called Well Stirred Reactor (WSR).
The Jet-Stirred Reactor (JSR) [54] is a classical apparatus for studying the chemical
kinetics of combustion reactions. In JSRs, several jets of combustible reactants are fed into a
mixing chamber maintained at elevated temperatures and reacted. Analysis of the products of
15
reaction as a function of reactant composition and residence time is used to infer the rates and
pathways of reaction. The key assumption required to interpret the data is that mixing of
reactants and products is complete and instantaneous, i.e. that the mixing time scale t is much
smaller than either the residence time scale r or the chemical time scale c so that no gradients
of composition or temperature occur. The JSR has one compelling advantage for chemical
kinetics experiments over shock tubes and laminar or turbulent tubular flow reactors which
greatly simplifies data interpretation: the JSR is ideally zero-dimensional in both space and time
whereas shock tubes are ideally zero-dimensional only in space and one-dimensional time and
flow reactors are ideally zero-dimensional only in time and one-dimensional in space. Notice that
dimensionality here means variance of sample to location or time of sampling, hence, zero-
dimensional in time and space means sample is invariance of location or time of sampling.
Additionally, JSRs have an inherent advantage over tubular flow reactors: the residence time r is
almost completely decoupled from the mixing time m, the latter potentially being far smaller
whereas in tubular flow reactors the mixing time and residence time both scales inversely with
the mean velocity and thus cannot be decoupled. Another problem with tubular flow reactors is
axial dispersion; that is, since the velocity profile is not purely plug-flow, reactants along the
centerline will be convected downstream more rapidly than material near the tube wall, which
renders the apparatus two-dimensional in space to some extent. Both issues can potentially be
avoided with a well-designed JSR.
Of course, there are challenges associated with JSR design and operation, the foremost of
which are:
1- ensuring rapid mixing of incoming reactants with the material already in the JSR,
specifically to ensure m << r and m << c
2- avoiding pre-reaction before the reactants enter the JSR.
The very first JSR to study chemical rates was proposed in 1955 by Longwell and Weiss
[55]. It was a spherical chamber with ID of 3 inches with a feeding tube that goes to the center
and is connected to a perforated sphere with ID of 5/8 inches. Reactants then issue from this
central perforated sphere through 68 jets with diameter of 0.047 inches each. There are 60
16
outlet ports (ID of ¼ inches) symmetrically bored into the chamber walls. The geometry of this
chamber is shown in Figure 8. There are neither reports nor measurements of actual level of
composition homogeneity in the paper and authors idealized such condition in their chamber.
Nonetheless, the chamber was designed to operate at temperatures exceeding 2000K at wide
range of pressures and residence times as short as 10
-4
second which is (as it will be discussed)
orders of magnitude smaller than common range of residence times in conventional JSRs (which
is on the order of 10
-2
s).
Figure 8. Geometry of JSR proposed by Longwell and Weiss [55] in 1965. Left: side view from
[55], middle: the 3D CAD model and right: section view.
Stainthorp and Clegg proposed a simple cylindrical chamber with only one inlet and one
outlet later in 1965 [56]. They studied effects of the jet and chamber diameter on level of “good
mixing” for a second order homogenous aqueous reaction and investigated advantages of fluid
mixing in a reactor compared to mixing through mechanical agitation.
Later in 1969, Bush [57] developed a set of rules to design JSRs and performed
experiments with gaseous reactions in a cylindrical JSR with diameter of 4 inches and height of 2
inches with only 2 internal jets with nozzles of 1/32 inches diameter. The geometry of his JSR is
shown in Figure 9. The author proposed a set of criteria and claimed that when satisfied
simultaneously, perfect mixing is ensured. The proposed criteria are:
1-Jets should be turbulent (so that internal mixing in tubes is maintained).
2-Jet velocity at the nozzle exit should not exceed sonic conditions.
17
3-The internal rate of recycling, defined as the ratio of flow rates (Q) at the jet exit and at
location x, (
= 0.3
[58]) is larger than 30 which is used to correlate jet diameter d with
chamber diameter D for “effective” mixing.
It should be noted that these rules have been used for designing JSRs to this date even
though there are many idealizations and simplifying assumptions made in the model. For
example, although the chamber is cylindrical, the mathematical analysis is carried out for a
toroidal shape [57]. It is also worth noting that the chamber was designed based on residence
times of 4-25 s, which are orders of magnitude larger compared to time scales of desired
reactions.
Figure 9. Geometry of JSR proposed by Bush [57] in 1965. Left: side view from [46], middle:
the 3D CAD model and right: top view. A, B, C and D are inlets, outlet, nozzles and
thermocouple glands respectively.
Using these rules, Matras and Villermaux designed a spherical JSR with 4 Jets In Plus Pattern
(4JIPP) in 1973 [59] with specifications as follows:
- Chamber diameter (D) :140 mm
- Jet diameter (d): 1 mm
- Inlet diameter: 4 mm
- Outlet diameter: 6 mmm
- The jet curve: the axis of the jets blends with a radius equal to half the radius of the sphere
D/4 = 35 mm.
18
According to [59], the jets are placed in a cross configuration so that two perpendicular
streams are produced, and it is assumed that the mixing occurs via generated turbulence from
the crossing of the two streams. It should be noted that David and Matras [60] also claimed that
when the 3 constraints in designing JSRs developed by Bush [57] are verified simultaneously, the
mixing would be “perfect” inside the chamber. Geometry of M-V 4 JIPP is presented in Figure 10.
Figure 10. Geometry of the proposed 4JIPP JSR by Matras and Villermaux. Left: schematics
from [59]; right: CAD representation used in current work.
Later in 1986, Dagaut et al. [54], proposed a modified version of 4JIPP reactor in which the jets
are separate from the entrance of the chamber. The reason to separate the jets from the
beginning is to avoid early unwanted reactions that might happen in the inlet tube from the
previous 4JIPP. The geometry of the Dagaut’s 4JIPP is presented in Figure 11.
19
Figure 11. Dagaut et al. [54] reactor. Left two images: schematics from the original paper; right
two images: CAD model used in simulations in this study. Overall diameter is 4 cm and the jets
have diameter of 0.1 cm.
Recently, another JSR is proposed by Zhang et al. [61]; a spherical chamber with ID of 50 with 8
inward off-center jets with diameter of 1 mm an and 4 outlets with diameter of 3 mm and after
performing numerical investigation, authors claimed that the performance of their proposed
chamber is better than previous JSRs. The geometry of proposed Inwardly Off-Center Shearing
(IOS) is shown in Figure 12.
Figure 12. CAD representation of proposed IOS JSR in [61].
Further details of some of the above-mentioned chambers will be discussed in Chapter 4. These
JSRs have been industry standard for decades and while many studies, e.g. [62], have addressed
the consequences of an assumed level of imperfect mixing, the prediction and characterization
of unmixedness has received very little attention. In fact, in a recent review paper Herbinet and
Battin-Leclerc [63] state that, “…no work on this topic has been performed since 1986, and new
work with up-to-date experimental techniques could bring valuable information to the subject.”
We shall show that existing reactors used for obtaining chemical kinetic data for combustion
20
reactions may lead to significant discrepancies between inferred reaction rate constants and the
actual values even for an extremely simple test problem. Therefore, a new reactor design that
promises to provide much smaller discrepancies and addresses the pre-reaction issue is needed.
1.3. Proposal
Based on the addressed issues prevail in current techniques in the studies of both
turbulent combustion and chemical kinetics, new apparatuses are designed in current work and
quantitative method for characterizing turbulence properties as well as uniformity of chemical
composition of species in chambers are developed. The performances of chambers are then
compared to FSCs and study of turbulent burning velocity will be carried out. The proposed
chambers create more nearly homogeneous and isotropic turbulence with small mean flow and
are motivated as follows. It is well known that a pair of counter-flowing turbulent jets produces
a nearly constant turbulence intensity ( ' u ) along the jet axis [43, 64, 65, 66]. While this provides
homogeneity only in the axial coordinate direction, multiple pairs of impinging jets aimed
towards a central location could in principle provide nearly homogeneous, isotropic, zero-mean
turbulence in all coordinate directions. Of course, the jet inflows necessitate a set of outlet ports
if the test section is to be is contained within a combustion chamber; in practice the chamber
inlets and outlets would need to be coupled to a recirculating-flow system or operated in a blow-
down mode. While jet-stirred chambers (JSCs) are widely used in chemical kinetics studies, they
are not typically employed for studying propagating turbulent premixed flames Nevertheless,
compared to the traditional FSCs and other apparatuses; the proposed JSC approach has several
potential advantages:
1. Any number and configuration of jets and outlet ports can be used to create a more
nearly homogenous, isotropic, zero-mean flow
2. A single pump or blowdown system, external to the combustion chamber, can be used to
drive the flow
3. There are no shafts penetrating the chamber wall that need to be sealed, only static jets
and ports breach the chamber wall
4. There is no flow bias due to swirl created by fans
21
5. Any desired amount of swirl can be deliberately introduced in a well-controlled manner
6. Since there are no moving parts, complicated geometries with multiple sets of jets and
ports are readily designed using CAD software and constructed using 3D printing
techniques
In addition, JSCs retain many of the advantages of FSCs over Bunsen flames, grid-generated
turbulence and other apparatuses with an appreciable mean flow, e.g.
1. ' u is nearly independent of the mean flow
2. The walls are remote; thus, conductive heat losses are negligible
3. The flames are freely propagating as opposed to conforming their shape in response to
being stabilized in the presence of a mean flow field
4. S T is readily inferred from the expansion rate of the quasi-spherical flame front (if in fact
the quasi-sphericity could be ensured)
5. The flames are not subject to a mean strain (as in a counterflow) or mean shear
6. The effects of ambient pressure are readily assessed
In the second part of this study, the feasibility of the proposed apparatus with best
homogeneity and Isotropicity performance will be tested as a mixing chamber for chemical
kinetics experiments and it will be compared to the widely accepted JSRs [54, 63]. The proposed
JSC is employed to overcome the limitations of current JSRs and it will be shown that conditions
under which WSR is defined i.e. homogeneity of species and rapid mixing time compared to
residence time are justified in proposed chamber. All of the JSR experiments, particularly,
measurement of the concentrations of large alkenes, cyclic ethers, ketones and aldehydes
(which are key compounds observed in JSR experiments at lower temperatures, c. 750K [63])
could be done in the proposed reactor. It should be emphasized that the objective of this study
is not to determine the reaction rates and mechanisms of a particular fuel, but rather to
ascertain the viability of proposed apparatuses as an improved apparatus for conducting
chemical kinetics studies and determine the range of conditions for which data obtained in such
an apparatus can be considered accurate and reliable.
22
Consequently, the objectives of current study are to:
1. Examine computationally the flow properties of a variety of JSCs using multiple impinging
jet configurations.
2. Determine the JSC configuration that provides most nearly homogeneous and isotropic
turbulence with large turbulence intensity compared to the mean velocity.
3. Determine how imperfections in the manufacturing and operation of the preferred JSC
affect its performance
4. Compare this JSC to other common turbulent combustion apparatuses, in particular FSCs,
with respect to both cold-flow properties and simulated propagating turbulent flames.
5. Use this JSC as an alternative to existing JSRs for chemical kinetic experiments.
23
Chapter 2: Theoretical Background
The oldest (dated 40,000-52,000 years old) known figurative painting, Lubang Jeriji Saléh cave,
Borneo, Indonesia [67].
24
2.1. Turbulence Basics
Turbulent flow field is described by several scales like time, length and velocity. Velocity
in a turbulent flow field can be decomposed into a mean flow and a random fluctuating
component such that:
) , ( ' ) ( ) , ( t x u x u t x u (7)
u and is called mean velocity and is defined as:
T
T
dt t x u
T
u
0
) , (
1
lim (8)
and ' u is called turbulence intensity which is a measure of strength of turbulence and can be
measured by defining RMS fluctuations of instantaneous velocity ) ( t u about u such that:
T
T
d t x u t x u
T
u
0
2
)) ( ) , ( (
1
lim '
(9)
The chaotic nature of turbulence comes from nonlinearity of convective term in the
Navier-Stokes equation which is derived from applying Newton’s second law to a fluid element in
an incompressible flow and is presented below:
u v p u u
t
u
2
) . (
(10)
the terms on the right-hand side of Eq. (10) characterize convective, pressure, and viscous forces
respectively and Eq. (10) could be written as [68]:
) ( u F
t
u
(11)
although Eq. (11) can be integrated to find ) , ( t x u , since u is chaotic and quite complex, such
integration needs enormous computation capacity. Furthermore, since generally understanding
of statistical properties of u i.e., u and ' u are rather desired, Eq. (11) should be rewritten for
25
these statistical properties. As it turns out Eq. (11) could be worked into set of statistical
equations, however, it would be such that [68]:
) ( ) ( u of pr op er ties l s tatis tica oth er F u of pr op er ties l s tatis tica certa in
t
(12)
As it can be seen from Eq. (12) that there are different knowns and unknowns in the system and
it turns out that regardless of number of manipulations, number of statistical unknowns are
always more than equations. This is known as the closure problem of turbulence which is a
consequent of non-linearity and is intrinsic property of any non-linear dynamical system [68-69-
70].
If the Navier-Stokes equation is written for the Reynolds decomposition, i.e. Eq. (7), and then
averaged over time Reynolds Averaged Navier Stokes (RANS) are formed as:
] [ ) . (
R
ij ij
i
i
i
xj x
p
u u
t
u
(13)
in which
ij
represents the stresses associated with the viscosity and is written as:
i
j
j
i
ij
x
u
x
u
v 2 (14)
and
R
ij
is called Reynolds Stress (RS) and is written as:
' '
j i
R
ij
u u (15)
Reynolds Stresses represent the flux of momentum in and out of a volume caused by turbulence
fluctuations even though they act like stresses and if the behavior of mean flow ought to be
predicted RS should also be determined. The problem however, is that as mentioned earlier no
matter how many times averaging is performed new unknown correlations will emerge.
Many of the closure “Turbulence Models” are in essence attempting to close the RS term in
RANS equations. Boussinesq in 1877 based on experimental observations proposed that RS could
be related to the mean rate of deformation such that:
26
) )( (
i
j
j
i
t
R
ij ij
x
u
x
u
v v
(16)
where
t
v is called turbulent viscosity also known as the eddy viscosity. A generalization of Eq.
(15) is known as Boussinesq equation and is written as:
ij k k
i
j
j
i
t
R
ij
u u
x
u
x
u
v
' '
3
) (
(17)
Turbulent flow is consisted of broad range of eddies with different length scales. The
largest of these eddies is bounded by the size of flow field and the smallest survives right before
the energy dissipation through molecular diffusivity becomes significant. Notice that henceforth,
the analysis is restricted to an isotropic, homogeneous turbulence. The largest length scale
corresponding to size of the largest eddy is called integral length scale (
t
l ) which is defined as
[68]:
o
t
dr r f l ) ( (18)
f(r) is called longitudinal velocity correlation function and is defined as [68-69-70]:
() ≡
'
()'
( )
'()
(19)
notice that brackets represent spatial averaging here. It’s also worth noting that f(r) is an
exponentially decaying dimensionless function and f (0) =1. Eq. (18) provides the size of the
largest eddy,
t
l , which shows the extent of the region over which velocities are significantly
correlated.
Since instantaneous velocity fields in experiments are generally measured as function of time
and not space, time autocorrelation function could be defined as [70]:
2
) ( '
) ( ' ) ( '
t u
t u t u
(20)
27
with the brackets denoting temporal averaging here. Turbulent integral time scale (
t
) is then
defined as:
o
t
d ) ( (21)
Using dimensional analysis, it can be shown that:
t t
u C l '
1
(22)
and with suitable assumptions,
2 / 1
1
)
8
(
C
.
Turbulent kinetic energy is generated at largest scales and is defined as:
2
'
2
3
' '
2
1
u u u k
i i
(23)
this energy is then cascaded to smaller scales through non-linear chaotic interactions which are
driven by convective forces in which viscosity plays no role (since Re=ul/ν is large, ratio of viscous
to convective force is negligible). When the energy reaches small enough scales in which viscous
and convective forces are comparable, it dissipates through viscosity at a rate called energy
dissipation rate ( ) which is defined as:
t
l
u
C
3
2
'
(24)
and with suitable assumptions, C 2 ≈ 3.1. has units of Watts/Kg (or m
2
/s
3
).
Kolmogorov [71] showed that kinetic energy is dissipated at smallest eddies with characteristic
length , time η , and velocity
u scales that depend only on and . These scales are
formed through dimensional analysis and are known as Kolmogorov microscales:
4 / 1
3
) (
(25)
4 / 1
) (
u (26)
28
2 / 1
) (
(27)
Another important length scale at which average strain rate occurs is known as is Taylor scale
(λ g) which is defined as:
t
g
u
'
(28)
Mean turbulent strain rate Σ t is defined as:
1
~
t
(29)
Plugging back Eqs. (24, 20), Σ t is written:
2 / 1
3
2 / 1
Re )
'
( ) ( ~
1
~
L
t
t
l
u
C
v
(30)
and with suitable assumptions [32], C 3 ≈ 0.157. Re L is turbulent Reynolds number and is defined
based on integral scale properties:
v
l u
t
L
'
Re (31)
Therefore, Taylor scale would become:
) 2 / 1 ( ) 2 / 1 (
3
Re 37 . 6 Re )
'
1
( '
'
L t L
t
t
g
l
u
l
C
u
u
(32)
Even though the physical interpretation is not clear, Taylor scale can be considered an
intermediate scale between integral scale and Kolmogorov microscale and it is usually observed
that the timescale of the small eddies is characterized by [70]:
15 ) 15 (
'
2 / 1
v
u
g
(33)
29
Turbulence enhance the mixing and thus changes the apparent fluid properties like viscosity and
thermal diffusivity. Total effect of turbulence on viscosity is:
2
4
' ~
k
C l u v
t T
(34)
T
v is turbulence viscosity. Using Eqs. (23, 24) and C 4 ≈ 0.084 from experiments it can be
concluded that:
L
T
v
v
Re 061 . 0 (35)
a similar relation for the turbulence thermal diffusivity α T can be obtained [72]:
L L
T
as Re Re 061 . 0
(36)
2.2. Combustion Regimes
As mentioned before, for Da >> 1 chemical reaction time is shorter than turbulent mixing
time. This leads to thin flame front in which the structures are not affected by turbulence and
flame surface is wrinkled by eddies. Thin front means the eddies are not fast enough to disturb
the flame structure. This is known as Huygens propagation or Flamelet regime and depending on
the ratio of turbulent intensity to laminar burning velocity is sub-categorized to two regimes:
- 1
'
L
S
u
: weakly wrinkled laminar flamelets: laminar propagation is predominant.
- 1
'
L
S
u
: strongly corrugated flame: pockets of flame induced by larger structures.
The categorization could also be described by comparing the smallest turbulent time scale i.e.
Kolmogorov scale and chemical time scale. This comparison leads to the definition of Karlovitz
number (Ka):
30
c
K a (37)
using Eqs. (3,27) and then substituting Eqs. (19, 26) this becomes:
2 / 3 2 / 1
)
'
( ) (
L
t c
S
u l
K a
(38)
and this can be expressed in terms of Re L using Eq. (31):
2 2 / 1
)
'
( Re 157 . 0
L
L
c
S
u
K a
(39)
A useful relation between Re L, Da, and Ka numbers can be obtained by combining Eqs. (6, 31)
and above definitions such that:
2 2
Re Da Ka
L
(40)
Ka number can be also utilized to compare the length instead of time scales of the flame. It can
be shown that [23, 24] reaction zone Ka is:
100
~ ~ ) ( ~
2 2
Ka
Ka Ka
(41)
Therefore, based on various values of Ka (or Da), different regimes of turbulent
combustion could be proposed. For example, previously described flamelet regime for which Da
>>1 means Ka <<1. The other combustion regimes proposed for turbulent premixed flames are
[73]:
- Da >> 1 ( 100 1 Ka ): Thin reaction zone or Broadened flame regime [74]: flame
preheat zone is thickened by turbulence, but the reaction zone remains intact.
- Da << 1 ( 100 Ka ): Well-Stirred Reactor zone or thickened flame regime: turbulence
is strong enough to penetrate the reaction zone and there’s no laminar flame
structure.
31
All of the above-mentioned regimes are commonly shown together on a diagram known
as regime diagram for premixed turbulent combustion as function of velocity and length scale
ratios
L
S u / ' and
t
l / which could be expressed in terms of Re and Ka numbers:
) (
'
Re
'
3 / 2
1
t
L
L
L
l
Ka
S
u
S
u
(42)
This diagram was first introduced by Borghi [75] and then modified by others [73,76,77]
and is shown in Figure 13 .
Figure 13. Turbulent flames regime diagram also known as Borghi-Peters diagram [24].
It is significant to keep in mind that such analyses and categorization are only qualitative
and are based on many assumptions (like heat release not affecting homogeneous and isotropic
turbulence, single step irreversible reaction analyses, etc.) and therefore the limits are subject to
change. For instance, Ka=1 for flamelet limit could change to Ka=0.1 or Ka=10 [23]. Also, it has
been shown both numerically [78] and experimentally [79] that the effect of small turbulent
scales on flames are not as substantial as it was presumed in classical theories due to their short
lifetime. Hence, the above analyses should be used vigilantly.
32
2.3. Turbulent Burning Velocity
The first theoretical expression for calculating turbulent burning velocity was introduced
by Damköhler in 1940 [80]. He proposed his expression for the flamelet regime (which he called
small scale turbulence) by writing continuity equation across the flame i.e. equating the mass
flux m through the cross-sectional area A with the flux through instantaneous turbulent flame
surface A T with velocity of S L such that:
A S A S m
T u T L u
(43)
The propagation of turbulent premixed flame for which Eq. (43) is written is schematically
presented in Figure 14.
Figure 14. Schematic of an idealized propagating premixed turbulent flame.
Notice that in Damköhler formulation
u
is considered constant and S T and S L are defined with
respect to unburn gas. It could be concluded from Eq. (43) that turbulent burning rate S T is only
due to area increase via wrinkling as:
A
A
S
S
T
L
T
(44)
33
Damköhler argued that for the small-scale turbulence the only thing that is modified is the
transport between the unburnt gas and the reaction zone. The assumption that chemical time
scale is not affected by turbulence leads to the writing the ratio of turbulent to the laminar
burning velocity such that:
2 / 1 2 / 1
)
'
( ~ ) ( ~
f
t
L
t
L
T
l
S
u
D
D
S
S
(45)
Damköhler assumed a purely kinematic interaction between turbulent flow field and wrinkled
flame front in the limit of large-scale turbulence ( 1
'
L
S
u
, i.e. corrugated flame zone) and
related the area increase of wrinkled flame as:
L
T
S
u
A
A '
~ (46)
which by comparing to Eq. (44) leads to:
' ~ u S
T
(47)
Ever since Damköhler introduced the analysis for calculating turbulent burning velocity, there
has been a significant effort to modify his equation and derive expressions for predicting S T and
various formulations have been proposed. By combining Eqs. (45, 47) an expression is emerged
[24]:
n
L L
T
S
u
C
S
S
)
'
( 1 (48)
In which n is an adjustable exponent where, 0.5 < n < 2.0 and C is a constant dependent on the
length scale ratio (
f
t
l
). Even tough n=2 and c=1 had been accepted widely for years [81] it was
later proposed n=0.7 [82]. A summary of various turbulent speed models is presented in Figure
5.
34
2.4. Perfectly Stirred Reactor (PSR) Model
As mentioned in earlier, Da<<1 (or Ka>>100) corresponds to a regime in which turbulent
mixing time scale is much smaller than chemical reaction time scale. This means reactants and
products are instantaneously mixed and species concentrations are uniform and homogeneous.
This regime is known as Perfectly Stirred Reactor (PSR) and the ideal chamber that provides such
condition is called Well-Stirred Reactor (WSR) which is also known as Continuously Stirred
Reactor (CSTR). The fundamental assumption here is constant T, P, and composition throughout
the chamber which means as soon as the reactants flow into the reactor they instantaneously
mix with everything else, hence the chamber is perfectly stirred.
Figure 15. Schematics of a Perfectly Stirred Reactor. Y, T, P, V, ṁ are mass fraction,
temperature, pressure, volume, and mass flow rate respectively and subscript R denotes the
reactor.
Suppose a single-step reaction of form A+B C+D occurs in a steady fixed volume WSR,
shown in Figure 15, with a fixed flow rate in and out of the system. The following simple analysis
could be written assuming that there is excess of one of the reactants, here B, starting by
calculating the thermal enthalpy rise in the chamber due to burned mass of A per unit time:
( )
= ̇
(
−
) →
,
= ̇
(
−
)
(49)
35
in which Q R is heating value of specie A, T ∞ is reactant temperature, T ad is adiabatic flame
temperature, T R is the reactor temperature, C P is heat capacity, Y A is mass fraction of A, and ṁ is
mass flow rate. Mass of A burned per unit time can be written as:
= ̇
,
(50)
Also,
=
×
Therefore, writing the reaction rate of A:
[]
|
=
[]
[ ]
exp
ℜ
= ̇
,
(51)
in the above equation M A is molar mass of A, Z is pre-exponential factor in Arrhenius relation, E is
activation energy, ℜ is universal gas constant, and values in brackets [ ] are molar concentration
of species. Note that:
[]
=
=
=
̇
,
; [ ]
=
̇
,
(52)
By writing the mass balance for A and B and combining the equations, the reactor temperature
T R equation is derived as a function of changing values of heat release, reference mass flow rate
(ṁ ref), and dimensionless activation energy (β=E/(ℜ T ad)):
̇ ̇
=
−
exp (
)
(53)
is dimensionless reactor temperature (T R/T ad) and ε is dimensionless inlet temperature (T ∞/
T ad) and φ is equivalence ratio. The detailed analysis connecting above equations are presented
in Appendix A. The dimensionless reactor temperature,
, for four different values of β are
plotted in Figure 16.
36
Figure 16. Dimensionless reactor temperature results for varying values of ṁ at Da=1 for three
different unrealistic (left) and one realistic (right) activation energy values from PSR model.
Effects of flow rate (or residence time) as well as activation energy are clearly shown in in
Figure 16. When the flow rate is small, the residence time is large and nearly complete reaction
occurs in the reactor (T R ≈ T ad) and if the flow rate is large there is not enough time for reaction,
hence little reaction occurs (T R ≈ T ∞). It is important to point out that when the activation energy
is not zero the response is classical Z-shaped curve which occurs for homogenous reactions.
Therefore, the upper branch, when mass flow is increased excessively, is extinction branch as the
reaction extinguishes and the lower branch, when the mass flow is sufficiently decreased and
residence time is adequate for reaction to occur, is ignition branch. It can be seen from Figure 16
that results are very sensitive to activation energy. As activation energy, thus β, is increased,
extinction point rises to higher T, i.e. closer to T ad. Furthermore, the curve spans many decades
of ṁ at realistic values of β (for hydrocarbons: β ≥ 10). As mentioned earlier, WSR could be used
to obtain estimates of reaction rate parameters Z and E specially by measuring extinction mass
flow rate. The PSR model is used to obtain analytical results for various single and multi-step
reactions in proceeding chapters.
37
Chapter 3: Methods
Jackson Pollock Making one of his drip paintings. Photographed by Hans Namuth in 1950.
Courtesy of Center for Creative Photography, University of Arizona.
38
3.1 Non-Reacting Turbulence
Simulations were performed using the Reynolds Averaged Navier-Stokes (RANS) approach
with the Reynolds Stress Model (RSM) for turbulent transport. In the RSM, transport equations
(with source and sink terms) for the turbulent kinetic energy dissipation rate and each of the
six independent Reynolds Stress terms are solved, resulting in seven equations for the
turbulence properties in 3D simulations. These turbulence properties provide the required
turbulent transport rates for use in the momentum and energy conservation equations [83].
Although RSM is a second order closure method and is generally considered less accurate than
more advanced techniques such as Large Eddy Simulation (LES) or Direct Numerical Simulation, it
requires far less computational effort and is considered to be the most elaborate RANS model
since the isotropic eddy-viscosity hypothesis is not assumed anymore. However, since there are
assumptions made for closing the various terms in the RANS equation the fidelity of RSM is still
limited. In particular, it is challenging to model the dissipation-rate and pressure-strain. Although
and the detailed discussion on the closure models and details of RSM method is beyond the
scope of current proposal, the general equations are mentioned here for brevity. The exact
equation for the transport of Reynolds Stresses can be written as:
∂
∂
(
'
') +
∂
∂
(
'
') = −
∂
∂
'
'
' + '(
' +
')+
∂
∂
∂
∂
(
'
')
−(
'
'
∂
∂
+
'
'
∂
∂
) − (
' +
') + '(
∂'
∂
+
∂'
∂
)
−2
∂'
∂
+
∂'
∂
− 2Ω
(
'
'
+
'
'
)
(54)
This equation can also be written in a simplified form:
ij ij ij ij ij ij L ij T ij k
k
ij
F G P D D R u
x
R
t
, ,
) ( ) ( (55)
in which
ij
R is the Reynolds Stress,
ij T
D
,
is turbulent diffusion,
ij L
D
,
is molecular diffusion,
ij
P is
stress production,
ij
G is buoyancy production,
ij
is pressure strain,
ij
is dissipation, and
ij
F is
production by system rotation. It should be noted that in order to close the Eq. (54), turbulent
39
diffusion, buoyancy, pressure strain and dissipation terms are required to be modeled. For this
work ANSYS-FLUENT computational fluid dynamics software versions 14 to 19 were used to solve
the RANS-RSM equations. By comparison with experiments it will be shown that this RANS-RSM
/ FLUENT approach likely provides sufficient accuracy for the class of problems investigated in
this work. The Pressure-Implicit with Splitting of Operators (PISO) scheme with second order
upwind spatial discretization and first order implicit time discretization for transient simulations
was used to solve the Navier-Stokes equations. In the PISO scheme, the governing equations are
solved in a segregated manner and to obtain a converged solution, iterations for solution are
carried out in a loop. In this method, after the boundary conditions are set the velocity gradients
are calculated and the velocity field is solved from discretized momentum equation followed by
calculating the mass fluxes at cell faces. Then, pressure correction equation is used, and mass
fluxes are updated so that constraint of the continuity equation is achieved. PISO scheme uses
two corrector steps per each predictor step and since the discretized equations are stored one at
a time the scheme is memory-efficient. The algorithm for solving the discretized equations is as
shown below [84, 85, 86]:
Figure 17. Algorithm of PISO scheme for solving discretized pressure velocity equations
40
Grid independence was confirmed by comparing results with different grid resolutions.
Between 2 x 10
6
and 5 x 10
6
volume hexagonal and tetrahedral elements were used for the
various JSCs and FSCs modeled in this work. The steady-state flow solver was employed where
applicable and spot-checked by using the results of converged steady solutions as starting
conditions for transient simulations. In such cases the steady solutions did not diverge; this
indicates a measure of stability of the results obtained although it does not represent a formal
stability analysis.
A relevant test of the viability of our simulations for the current purposes is the flow between a
pair or multiple pairs of impinging turbulent jets. No prior studies of multiple pairs of impinging
jets could be found, and Pettit et al. [87] provides the only well-characterized experimental study
of a single pair of impinging turbulent jets known to us. The schematics of experimental set up
used in [87] is shown in Figure 18.
Figure 18. Schematic of the counter flow jets arrangement used by Pettit et al. in [87].
The reported properties Pettit et al.’s experiment are as follows: jet and co-flow mean
outlet velocity 6.58 m/s, turbulence intensity 1.97 m/s, jet inner diameter 12.7 mm, jet wall
thickness 1.65 mm, annular co-flow outer diameter 29.5 mm and jet spacing 19 mm. All of these
features were incorporated into the simulations. The stated accuracy of Petit et al.’s Particle
Image Velocimetry (PIV) measurements of turbulent intensity was better than ± 10%. Figure 19
shows a comparison of the RSM simulations with the experiments and LES predictions of Pettit et
al. All of the key features of the flow are captured well by the RSM simulations, both with
41
regards to the differences between the axial ( ' u ) and radial ( ' v ) velocity fluctuation
characteristics and their magnitudes. In particular note that ' u (z) (where z is the axial
coordinate) is inhomogeneous, reaching a peak at the stagnation plane (z = 0), whereas ' v (z) is
nearly homogenous and of smaller magnitude than ' u . Mean-flow properties (not shown)
exhibited similar agreement.
Figure 19. Comparison of axial (left) and radial (right) velocity fluctuations in the
gap between a pair of counterflowing turbulent jets. Experiments and LES
predictions from Pettit et al. [87]; RSM simulations from the current study. The
radial velocity fluctuations are along the axis between the nozzle exits, relative to
the stagnation plane located at z = 0.
3.2. Performance Metrics
3.2.1. Turbulence Homogeneity, Intensity and Mean Flow
Indices
To be able to compare performance of various configurations with different conditions
(like number of inlets, orientation of inlets, imperfections in design, etc.) on production of
homogenous and isotropic turbulence a quantitative measure of these properties is needed.
Toward this objective, first recall that for RANS modeling the flow velocity at any location i is
divided into time-averaged mean-velocity components u
x, i
, u
y, i
and u
z, i
, and time-averaged
42
fluctuating components
u'
x, i
,
u'
y, i
, and
u'
z, i
. From these components we can define the mean
velocity magnitude u
i
and direction-averaged turbulence intensity u'
i
at any location (x, y, z) as
follows:
2
,
2
,
2
,
2
,
2
,
2
,
' ' '
3
1
' ;
z i y i x i i i z i y i x i
u u u u u u u u (56)
For a volume V comprised of n individual cells having volumes v i we can define a mean
turbulence intensity u'
V
volume-averaged over V:
V
v u u u
u
n
i
i i z i y i x
V
3
' ' '
'
1
2
,
2
,
2
,
(57)
From these definitions a Mean Flow Index (MFI) can now be defined, representing the volume-
averaged RMS mean flow divided by u'
V
averaged over the same volume V:
V
n
i
i i
u
v u
V
MF I
'
1
1
2
(58)
as well as a Homogeneity Index (HI), which represents the degree to which the turbulence
intensity within the volume V is homogeneous (i.e., constant) within that volume:
V
n
i
i V i z V i y V i x
u
v u u u u u u
V
HI
'
' ' ' ' ' '
3
1
1
2
,
2
,
2
,
(59)
and finally, an Isotropicity Index (II), which represents the degree to which the turbulence
intensity within the volume V is isotropic within that volume:
I I
1
3 V
u'
x, i
u'
i
2
u'
y, i
u'
i
2
u'
z, i
u'
i
2
v
i
i 1
n
u'
V
(60)
43
3.2.2. Tracer Mixing Response
It is frequently claimed [54,56 , 57, 63] that a sufficient criterion for adequate mixing in a JSR
is agreement with the exact solution for the decay of a tracer in a perfectly-stirred reactor when
the supply of tracer is suddenly stopped. This criterion was developed in 1951 by McDonald and
Piret [88] for aqueous solutions in which a small volume of dye was introduced to the chamber
and then the time for visual uniformity was measured.
The tracer decay is written in an exponential form of:
( )
(0)
= 1 − exp (
)
(61)
where C(t) is the tracer concentration, C(0) is initial concentration, τres is residence time and t is
time. This method will be used as a legacy tool to test PSR behavior of JSRs and it will be shown
that it is not a sufficient criterion to conclude that the apparatus will behave as a PSR in the
presence of chemical reactions.
3.2.3. Chemical Composition Accuracy Index
To evaluate the uniformity or lack thereof of products in the chambers, a Composition
Accuracy Index (CAI) is defined and calculated as follow:
=
1
,
,
− 1
(62)
In the above equation X is mole fraction, V is the chamber volume, v is cell volume, n is number
of cells in computation, r is the radius in which CAI is computed in and PSR values obtained from
Perfectly Stirred Reactor model. PSR values are computed directly from exact analytical solution
in case of single-step and two-step reactions and CHEMKIN software is used to get PSR values
when multi-step reaction is modeled.
44
Chapter 4: Results
Vassily Kandinsky (1913) Color Study, Squares with Concentric Circles
45
4.1. Turbulent Flame Studies
Jackson Pollock, Mural 1943
4.1.1. Simulations of Polyhedral Jet Stirred Reactors
With the initial test of the viability of the numerical model providing a level confidence in
its predictive capability, five spherical chambers of 30 cm diameter with the inlet jets and outlet
ports flush with the surface of the sphere arranged in accordance with the geometries of the
faces of Platonic solids were simulated (Figure 20, top and 2
nd
rows). For each geometry, each
inlet jet diameter is 2 cm and the annular outlet diameters are chosen to obtain the same total
outlet area as inlet area. For these 5 configurations the total volume inflow rate is held fixed at
0.0502 m
3
/s, corresponding to a mean jet exit velocity of 40 m/s and a Reynolds number of 5.33
x 10
4
for the 4-jet tetrahedral case with proportionally lower values for the cases with more inlet
jets. In all cases the turbulence intensity at the jet exits was fixed at 20% of the mean jet exit
velocity. Inlet boundary conditions were plug-flow with the specified inlet velocity and
turbulence intensity and ambient pressure outflow conditions were prescribed at all outlets and
no-slip condition is selected for all walls. Figure 20 shows that as the number of jets is increased,
to some extent the homogeneity of the turbulence intensity (3
rd
row) increases and the
magnitude of the mean flow (bottom row) relative to the turbulence intensity decreases.
46
These indices are plotted in Figure 21 for spherical volumes of radius r scaled by the
overall nominal chamber radius (R = 15 cm) for various polyhedral JSCs. Results are shown up to
a maximum radius of r/R = 0.5 because beyond that radius, a flame propagating in such a
chamber would cause a significant pressure rise leading to difficulty in interpreting flame
propagation speed data. It can be seen that overall the polyhedral geometries that perform well
in terms of mean flow (e.g. the rhombicosidodecahedron) do not perform as well in terms of
homogeneity and isotropicity and vice versa, with the rhombicosidodecahedron and the snub-
dodecahedron performing best in terms of MFI and the dodecahedron performing best in terms
of HI and II.
Although we will show that the performance parameters of these polyhedral designs are
comparable or superior to FSCs, they are still not as close to the ideal case of homogeneous,
isotropic, zero-mean turbulence as is desirable for some applications. In our examination of the
computed flow properties, we noted that any configuration of inlet jets and outlet ports
necessarily results in some mean flow from the former to the latter, just as stirring by fans
generates some mean flow and swirl. This led us to consider the possibility of locating the inlet
jets and outlet ports closer to each other than the locations corresponding to the centers of the
faces of polyhedrons. In this context we were inspired by the work of Hwang and Eaton [89],
who employed a set of 8 acoustically-forced “synthetic jets” at the corners of cube (equivalently,
a double-tetrahedral configuration) to obtain nearly homogeneous, isotropic, zero-mean
turbulence for the purpose of studying settling of particles in turbulent flows. The disadvantage
of this approach is the relatively low turbulence intensities attainable with acoustic forcing. Also,
although their cube dimension was 410 mm on a side, Hwang and Eaton measured flow
properties only in a central 40 mm x 40 mm region. (Chang et al. [90] extended Hwang and
Eaton’s work to a truncated icosahedral geometry, but measured flow properties only in the
region 0 ≤ r ≤ 50 mm in a chamber with R = 495 mm). Nevertheless, applying Hwang and Eaton’s
approach to JSCs, we tested a configuration of 8 jets at the corners of an imaginary cube
circumscribed by the spherical chamber surface, with each inlet jet surrounded by a concentric
outlet port having the same cross-section area. This configuration, which we have termed the
Concentric Inlet And Outlet (CIAO) geometry, is shown in Figure 22 (left). Computations of flow
47
properties in the CIAO geometry were performed with the same model as for the polyhedral
chambers, with the same total volumetric inflow rate and the same boundary conditions. Figure
22 (center and right) shows that compared to the polyhedral chambers, the turbulence in the
CIAO geometry is remarkably more homogeneous with substantially larger ratios of turbulent
intensity to mean flow. Profiles of mean velocity magnitude u
i
( x) , u
i
( y) , u
i
( z) and turbulence
intensity u'
i
( x), u'
i
( y), u'
i
( z) passing through the geometric center of the chamber are shown
in Figure 23, which again show the high degree homogeneity and small mean flow attainable in
this configuration. The MFI, HI and II indices of the CIAO configuration (Figure 21) show that this
behavior is obtained throughout the volume of interest within the chamber (r/R ≤ 0.5), i.e., that
the idealized homogeneous, isotropic and zero-mean-flow turbulence is very nearly obtained in
the CIAO jet-stirred chamber. Figure 24 shows the velocity vectors in the plane of 4 of the jets,
which again illustrates that the bulk of the chamber has very little mean flow.
48
Tetrahedron
(Tetra)
Dodecahedron
(Dodec)
Truncated Icosadehron
(TI)
Rhombicosidodecahedron
(Rhombi)
Snub-dodecahedron
(Snub)
4 inlets, 4 outlets 6 inlets, 6 outlets 20 inlets, 20 outlets 50 inlets, 12 outlets 80 inlets, 12 outlets
Figure 20. Jet-stirred chambers studied. Top row: wire-frame models showing the polyhedral configurations of inlets
and outlets; second row: locations of inlets (blue) and outlets (red); third row: contours of turbulence intensity u’ i (m/s)
(see Eq. (51) fourth row: contours of mean velocity magnitude u
i
(m/s). The nominal diameter of all JSCs is 30 cm.
49
Figure 21. Calculated Mean Flow Index (MFI, Eq. (53)), Homogeneity Index (HI,
Eq. (54)) and Isotropicity Index (II, Eq. (55)) as a function of distance from the
chamber center (r) scaled by the chamber radius (R) for various jet-stirred
chambers (refer to Figure 20 and Figure 22).
50
Figure 22. Concentric Inlet And Outlet (CIAO) jet-stirred chamber. Left: geometrical
configuration; center: contours of mean velocity magnitude u
i
(m/s); right:
contours of turbulence intensity u'
i
(m/s).
Figure 23. Profiles of mean velocity magnitude u
i
( x) , u
i
( y) , u
i
( z)
(left) and
turbulence intensity u'
i
( x), u'
i
( y), u'
i
( z) (right) in the CIAO jet-stirred chamber.
Figure 24. Mean velocity vectors in the CIAO jet-stirred chamber.
51
The effect of jet exit velocity on CIAO performance over the range 1 - 50 m/s
(corresponding to jet exit Reynolds numbers of 1.33 x 10
3
to 6.67 x 10
4
, compared to the
nominal value of 2.67 x 10
4
employed to obtain the data in Figure 21-Figure 24) are shown in
Figure 25. For compactness, only the performance indices at r/R = 0.5 are shown. The HI and II
parameters are noticeably affected by Re and are better (lower) at higher Re whereas the MFI is
hardly affected by Re. Figure 25 also shows that the turbulence intensity u'
V
scales linearly with
Re on this log-log plot with a slope close to unit and thus jet exit velocity, which might have been
anticipated considering that u'
V
scales almost linearly with fan rotation speed in FSCs [34, 35].
Figure 25. Performance metrics of the CIAO reactor as function of the jet exit
Reynolds number for the spherical volume 0 ≤ r ≤ 0.5R.
52
4.1.2. Comparison with Fan-Stirred Chambers
4.1.2.1. FSC-I: Ravi et al.
To compare the performance of the CIAO JSC design to conventional turbulent premixed
combustion apparatuses, numerical modeling of two different FSCs was conducted using a
sliding moving mesh method for modeling the interface between the gas and the fans. One
apparatus modeled was that reported by Ravi et al. [34], who used a cylindrical chamber of
diameter 305 mm and length 356 mm having four 3-bladed fans with 20˚ blade pitch mounted
around the circumference of the cylinder at its midplane. The field of view for their PIV
measurements was in the plane of the fan axes with dimensions 36 mm x 26 mm, thus
representing only a small portion of the chamber cross-section area. Their reported uncertainty
of the mean velocities was ± 0.1 m/s at a 95% confidence level; no uncertainty value for
turbulence intensities were reported. The computational model for this FSC (Figure 26) matched
the geometry of the chamber and their “Prototype 1” fan as precisely as possible given the
information presented by Ravi et al. Time-dependent computations were run at a fan rotation
speed of 8300 RPM until a nearly statistically steady-state condition was obtained. Ravi et al.
reported extensive velocity vector maps but provided very little tabulated or plotted velocity
data that could readily be compared quantitatively with computations. A comparison (Table 4)
of the reported mean velocities and turbulence intensities (averaged over the PIV measurement
plane) shows moderate agreement. Figure 27 shows line plots of the computed mean and
fluctuating velocity components for this FSC. It can be seen that while ' u is nearly constant
across much of the chamber (even well outside the PIV measurement region) in all 3 coordinate
directions (i.e., the turbulence is nearly homogeneous and isotropic), there is a substantial mean
flow (comparable to ' u ) over much of the chamber outside the relatively small measurement
region. This mean flow would compromise the validity of turbulent burning velocity data in this
apparatus since flame motion in the laboratory frame due to self-propagation cannot readily be
distinguished from motion due to convection of the flame by the mean flow. This point is
further illustrated by the velocity vector map shown in Figure 28, which shows that in the plane
of the fans, there is a significant outward flow (the fans, by Ravi et al.’s intention, were rotated
53
to obtain outward flow in the plane of the fan axes) whereas in the third dimension there is a
strong inflow. Consequently, flames imaged in the plane of the fans would appear circular, thus
implying spherical symmetry, whereas the actual shape would be that of an oblate spheroid.
This assertion will be confirmed by simulated flame propagation in this apparatus reported in
following sections.
u
x
u
y
u'
x
u'
y
Experiment 0.03 -0.01 1.48 1.49
Simulation 0.037 -0.051 0.94 0.98
Table 4. Comparison of measured [34] and predicted flow velocities (m/s) averaged over
the experimental PIV measurement plane.
Figure 26. Computational model of the Ravi et al. [34] Fan-Stirred Chamber.
54
Figure 27. Profiles of computed mean velocity u
x, i
, u
y, i
, u
z, i
(left) and turbulence
intensity components u'
x, i
, u'
y, i
, u'
z, i
(right) in the simulated Ravi et al.[34] fan-stirred
chamber.
Figure 28. Computed mean velocity vectors colored by velocity magnitude (m/s)
for the Ravi et al. [34] fan-stirred chamber in the x-z plane. The width of the
measurement plane used by Ravi et al. for Particle Image Velocimetry
measurements is between the 2 black lines at the chamber center, but in the x-y
plane, i.e., in the plane of the 4 fans.
55
4.1.2.2. FSC-II: Chaudhuri et al.
The second FSC we modeled was that of Chaudhuri et al. [35], who employed a
cylindrical chamber of diameter 11.4 cm and length 12.7 cm having four 6-bladed fans with 90˚
blade pitch mounted around the circumference of the cylinder at its midplane. The field of view
for the PIV measurements was in the plane of the fan axes with dimensions 20 mm x 20 mm. No
information on the uncertainty of the PIV measurements was provided. The computational
model (Figure 29) matched the geometry of the chamber as precisely as possible given the
information presented by Chaudhuri et al. Time-dependent computations were run at a fan
rotation speed of 2000 RPM until a nearly statistically steady-state condition was obtained.
Figure 30 shows a comparison of Chaudhuri et al.’s measurements of mean (
r
u ) and fluctuating
( ' u ) components of radial velocity in the measurement plane, averaged over all azimuthal
angles at a particular radius, and the corresponding flow properties extracted from our
computations. It can be seen that the agreement is very favorable in terms in terms of both
r
u
and . The
r
u data show a mean inflow (thus negative velocities as shown) comparable to the
turbulence intensity. Figure 31 shows line plots of the computed mean and fluctuating Cartesian
velocity components in this chamber. In this chamber ' u is reasonably constant across the
middle part of the chamber in all 3 coordinate directions (i.e., the turbulence is nearly
homogeneous and isotropic) but, as with Ravi et al. [34], there is a substantial mean flow
(comparable to ' u ) over much of the chamber. This point is further illustrated by the velocity
vector map shown in Figure 32, which shows that in the plane of the fans, there is a significant
outward flow whereas in the third dimension there is a strong inflow. Consequently, flames
imaged in the plane of the fans would appear circular, thus implying spherical symmetry,
whereas the actual shape would be that of a prolate spheroid.
' u
56
Figure 29. Experimental setup (left) and computational model (right) of the
Chaudhuri et al. [35] fan-stirred chamber.
Figure 30. Comparison of measured and computed radial mean velocity (
r
u ) and
turbulence intensity ( ' u ) as a function of distance (radius in the PIV
57
measurement plane) from the center of the Chaudhuri et al. FSC [35] at 2000
RPM. Both and ' u refer to the radial component of velocity in the
measurement plane only.
Figure 31. Profiles of computed mean velocity components u
x, i
, u
y, i
, u
z, i
(left) and turbulence intensity components u'
x, i
, u'
y, i
, u'
z, i
(right) in the
simulated Chaudhuri et al. [35] fan-stirred chamber at 2000 RPM.
Figure 32. Computed mean velocity vectors colored by velocity magnitude (m/s)
r
u
58
for the Chaudhuri et al. [35] fan-stirred chamber in the x-z plane. The width of the
measurement plane used by Chaudhuri et al. for Particle Image Velocimetry
measurements is between the 2 black lines at the chamber center, but in the x-y
plane, i.e. in the plane of the 4 fans.
4.1.3. Comparison of FSC and JSC
A comparison of the mean flow, homogeneity and isotropicity indices for one polyhedral
jet-stirred reactor (truncated icosadehron), CIAO and both fan-stirred chambers are shown in
Figure 34. It can be seen that all perform reasonably well in terms of homogeneity and
isotropicity across the middle half of the chamber (HI and II both less than 0.1) but show much
more variation in terms of mean-flow (MFI) performance. The jet-stirred chambers perform
better than the fan-stirred chambers, with the CIAO again performing exceptionally well.
Contours of the turbulence integral length scale L I (defined as
0.164 u'
i
3
[73]), for the CIAO
jet-stirred chamber and both FSCs are shown in Figure 34. As with the turbulence intensities, the
turbulence length scales are much more uniform in the CIAO chamber than in the FSCs.
59
Figure 33. Calculated Mean Flow Index (MFI), Homogeneity Index (HI) and
Isotropicity Index (II) (Eqs. (53-55)) as a function of distance from the chamber
center (r) scaled by the chamber radius (R) for fan-stirred and jet-stirred
chambers. “CIAO”: current CIAO reactor; “TI”: truncated icosadehron; “Ravi et
al.”: fan-stirred chamber [34]; “Chaudhuri et al.”: fan-stirred chamber [35].
60
Figure 34. Contours of integral length scale (m) for the CIAO jet-stirred (left), Ravi
et al. fan-stirred chamber [34] (middle) and Chaudhuri et al. fan-stirred chamber
[35] (right).
These results show that jet-stirred chambers, particularly the CIAO configuration, are
promising alternatives to fan-stirred chambers.
4.1.4. CIAO: Robustness to Imperfections
Complex jet-stirred geometries can be fabricated using 3D printing techniques, but some
degree of imperfections must be anticipated. To determine the effect of inaccuracies in the
fabricated process, the performance of the CIAO configuration was simulated in which the 8 jets
were intentionally misaligned by 2 degrees in random directions. Note that 2 degrees
misalignment translates to more than 1 cm deviation across the 30 cm chamber diameter and
thus represents a severe case of fabrication imperfection. Another envisioned scenario is
variations in jet exit velocities due to mismatched inlet manifold flow restrictions. To test
scenario a set of computations was performed in which the jet exit velocities were randomly
varied with a standard deviation of 10% of the mean value. Comparisons of these non-ideal
scenarios to the ideal case with respect to their effects on the performance indices MFI, HI and II
at r/R = 0.5 are shown in Table 5, along with the corresponding results for ideal FSCs having fans
perfectly aligned and speed-matched. It can be seen that, as expected, for the CIAO
configuration the nonideal cases show higher values of these indices than the ideal cases, but
nevertheless they are still much lower than the ideal polyhedral jet-stirred chamber or the fan-
stirred chambers. Consequently, we conclude that the performance of the CIAO design is
61
sufficiently robust to imperfections in the fabrication and operation that they provide a viable
alternative to fan-stirred chambers.
TI CIAO CIAO-M CIAO-V FSC1 FSC2
Mean Flow Index (MFI) 1.058 0.061 0.071 0.095 1.170 2.458
Homogeneity Index (HI) 0.092 0.011 0.025 0.017 0.205 0.081
Isotropicity Index (II) 0.077 0.010 0.018 0.0134 0.134 0.040
Table 5. Comparison of performance indices at r/R=0.5 for jet-stirred and fan-
stirred chambers. TI: Truncated Icosahedron; CIAO: perfectly-aligned CIAO with
equal velocities at all inlets; CIAO-M: with random 2˚ misalignments of all 8 jets;
CIAO-V: with 10% RMS variation in jet exit velocities; FSC1: ideal fan-stirred
chamber of Ravi et al. [35]; FSC2: ideal fan-stirred chamber of Chaudhuri et al.
[34].
4.1.5. Simulated Flame Propagation
The ultimate purpose of the jet-stirred and fan-stirred chambers examined in this work is
to measure the propagation rates of turbulent premixed flames. While a detailed comparison of
simulated premixed combustion in CIAO jet-stirred chambers and FSCs is beyond the scope of
the current work, a simulation of a stoichiometric methane-air mixture is presented here. It must
be emphasized that the purpose of these simulations is a comparison of the behavior of
simulated flame propagation in JSCs and FSCs; we do not claim that the flame propagation
model we used is the most accurate available or should be used for quantitative predictions. The
FSC employed for this comparison is that of Ravi et al. [34] because their nominal chamber
diameter is very similar to our baseline CIAO chamber. The jet exit velocity for the CIAO
simulation is chosen to be 8.75 m/s in order to produce the same volume-averaged turbulence
intensity u'
V
over the region 0 ≤ r ≤ 0.5R as in the Ravi et al simulation (1.25 m/s), resulting in a
scaled turbulence intensity u’/S L = 3.13, where S L is the laminar burning velocity, for both
chambers. For these conditions, the turbulent Karlovitz number is estimated using Eq. (39):
62
018 . 0 )
'
( Re 157 . 0
2 2 / 1
L
L
S
u
Ka
where Re L is the integral scale turbulent Reynolds number
defined in Eq. (31). Since Ka << 1 for this case, combustion occurs in the flamelet regime as
discussed in Section 2.2, thus a standard G-equation formulation [24] was employed using the
Peters turbulent flame speed formula [91]. The performance of this RSM – G-equation
simulation was first tested by comparison with an experiment with a well-defined geometry and
boundary conditions. We chose the work by Griebel et al. [92], who studied enclosed turbulent
lean methane-air Bunsen flames. Figure 35 shows the configuration and dimensions of their
experiment. The reported inlet conditions were pressure 5 atm, temperature 673K, u = 40 m/s,
' u = 2.03 m/s and L I = 3.1 mm. For three equivalence ratios these authors reported the
turbulent burning velocity S T which they defined by:
S
T
A
j e t
A
f l a m e,c 0.05
u
j e t
(63)
where A jet is the Bunsen jet cross-section area, A
f l a m e, c 0.05
is the flame surface area where the
flame position is defined as the location where the mean progress variable, c , is 0.05 and u jet is
the Bunsen jet exit velocity. Progress variable is a scalar quantity used to describe the flame such
that c = 0 in the unburnt mixture and c =1 in the fully burnt gas. Progress variable is regarded
as a normalized temperature or as a normalized product mass fraction [24]:
u
F
b
F
u
F F
u b
u
Y Y
Y Y
c or
T T
T T
c
(64)
T is mixture temperature and Y F is fuel mass fraction and scripts u and b denote unburnt and
burnt mixtures respectively.
Griebel et al. [92] also reported the flame length X P, defined as axial distance
downstream of the jet exit where c = 0.5. Table 6 shows that our computed results compare
favorably to the experimental data (average discrepancy 13% for all 6 properties compared),
thus encouraging us to employ the RSM – G-equation approach for a comparative study of
turbulent flame propagation in jet-stirred and fan-stirred chambers. Yasari et al. [93] also
63
modeled this experiment using FLUENT-RANS but a different flame speed model; surprisingly,
the agreement between model and experiment was better when using a two-equation isotropic
k- model was employed than when the seven-equation RSM model was employed that can
account for flow anisotropicity. LES simulations [94] of this experiment using a fractal model for
subgrid-scale flame propagation show better agreement with experiments than Yasari et al.’s
computations, but our work has shown that the RSM – G-equation model is adequate for the
task.
Figure 35. Computational domain of the combustion chamber from Griebel et al.
[92]. The colors shown represent the computed values of mean progress variable
c
for the case = 0.5 (see Table 6)
Property
Equivalence ratio ( )
0.43 0.5 0.56
S T (experiment) (m/s) 1.12 1.73 2.25
S T (computed) (m/s) 1.50 1.71 1.95
X P (experiment) (mm) 267.3 199.2 164.3
X P (computed) (mm) 257.9 188.1 146.1
Table 6. Comparison of measured [92] and computed (this work) values of turbulent burning
velocity (S T, Eq. (56) and flame length (X P) in enclosed turbulent methane-air Bunsen flames.
It should be noted that for FSCs and for the JSCs with combustion, the phenomena of
interest are inherently unsteady and, in these cases, fully transient simulations were conducted
with time steps ranging from 10 to 100 μs. For our comparative study of expanding spherical
64
flames in JSCs and FSCs, combustion was initiated by instantaneously “patching” a central region
of radius 1 cm with products of complete combustion (̅ = 1.0). This is analogous to an
instantaneous deposition of about 1 J of energy in the form of an electric or laser spark, without
the gasdynamic expansion wave that would result from such a spark.
Figure 36 shows images of simulated expanding flame fronts at several different times in the Ravi
et al. [34] FSC and the CIAO JSC. It can be seen that, as might be expected based on a
comparison of their MFI characteristics (Figure 33) the fronts are much more nearly spherical in
the CIAO chamber. Moreover, as anticipated based on the mean velocity characteristics in the
Ravi et al. FSC (Figure 28) the flame shape is similar to an oblate spheroid due to the outflow in
the plate of the 4 fans.
Plots of computed mean flame radius (r f) vs. t for several values of c are shown in Figure 37.
Two definitions of flame radius are employed: (1) mean radius inferred based on 2D planar slices
through the expanding quasi-spherical flame (i.e., the radius of a circle having the same area of
reacted material as the 2D slice) in the x-y and x-z planes (r f,xy and r f,xz, Figure 37 a-c) that would
correspond to tomographic images of the flame (obtained, for example, via Planar Laser Induced
Fluorescence of OH molecules) and (2) mean radius inferred based on the entire 3D flame
surface (r f,xyz, Figure 37d) (i.e., the radius of a sphere having the same volume of reacted material
as the volume enclosed by the 3D surface). For the FSC, the x-y plane corresponds to the plane
containing the axes of the 4 fans. Results are shown only for 0 ≤ r f ≤ 0.5R since larger r f lead to
significant pressure and temperature rise within the FSC (a constant-volume apparatus) due to
adiabatic compression caused by the expanding flame front. In the CIAO JSC there are outlets to
remove some of the volume of gas generated by thermal expansion of the burned gas but there
is also inflow that increases the volume of gas in the chamber, hence, it is not clear a priori which
apparatus, FSC or JSC, would have more significant pressure rise effects. A comparison (not
shown) was made and it was found that at the same mean flame radius the pressure rise in the
FSC and JSC was nearly identical.
For the CIAO jet-stirred chamber, only r xz data are shown because the r xy data are nearly
identical, whereas for the FSC, both r f,xy and r f,xz are shown because these data are significantly
different.
65
t = 0.0060 s t = 0.01385 s t = 0.01815 s t = 0.01631 s
t = 0.0060 s t = 0.01015 s t = 0.01470 s t = 0.0190 s
Figure 36. Images of simulated expanding flame kernels (for the surface
corresponding to mean progress variable c = 0.5) in the Ravi et al. [34] FSC
(upper row) and the CIAO JSC (lower row). The 4 fans are shown in the FSC and
the 8 concentric inlet/outlet ports are shown in the JSC. Videos of these
simulations are included in the Supplemental Data.
For the CIAO JSC, Figure 37 shows that both the 2D (r f,xz) and 3D (r f,xyz) vs. t plots are
nearly straight lines with similar slopes for flame radii defined based on all values of c , thus the
apparent turbulent flame speed S T is nearly constant for all t and c (no smoothing has been
applied to these data). This is in distinct contrast to the FSC where r f,xy and r f,xz vs. t plots are
much noisier and the slopes of these plots vary considerably depending on r f and c . Note that in
Ravi et al.’s FSC, the apparent flame propagation speeds are higher in the x-y than the x-z plane
because of the radial outflow in the x-y plane (see Figure 28) and thus as viewed in this plane,
the mean flow convects the flame front outward at a rate faster than self-propagation alone
66
would cause, whereas in the x-z plane there is outflow in only the x direction and inflow in the z
direction. In contrast, for the fully 3D flame surface, both the FSC and CIAO JSC yield practically
steady and nearly identical propagation speeds for differing choices of c . Thus, while the
presence of the mean flow in the FSC (radially outward in the plane of the fans and inward in the
direction orthogonal to this plane) leads to significant distortion of the flame shape from that of
a perfect sphere toward that of an oblate spheroid, apparently it does not have a significant
effect on the overall reactant consumption rate. This might be expected for constant-density
flows since these mean flows could not cause a change in fluid volume, but the combustion
products have much lower density than the reactants and thus an interaction between the mean
flow in the cold gas and the dilatation-induced flow caused by the flame might have been
expected. Consequently the results shown in Figure 37d suggests that while the choice of c
used to define flame position in 2D LIF or (path-integrated) schlieren images of spherically
expanding turbulent flames is known to affect the inferred S T [95], if the entire 3D flame surface
were imaged (e.g., via Volume Laser-Induced Fluorescence [96]), the inferred S T is more nearly
independent of (1) r f, (2) the choice of c used to define r f and (3) the presence of mean flow in
the unburned gas and its interaction with dilatation-induced flow. Two measures of turbulent
burning velocity S T for expanding spherical flames are (1) the displacement speed, i.e., the
difference between the local propagation speed of the flame front dr f,xyz/dt and the local radial
convection speed u r (averaged over the surface at radius r f,xyz) and (2) the consumption speed,
i.e. the mass burning rate per unit area divided by the average gas density downstream of the
front (i.e., inside the sphere of radius r f. Table 7 shows a comparison of these two definitions of
S T along with theoretical predictions from the Peters model [91] used by FLUENT to determine
the local S T which in turn is an input to the G-equation used to determine the flame front
propagation. It can be seen that these 3 values agree reasonably well throughout the relevant
part of the simulation, i.e., during the quasi-steady propagation phase, indicating that the CIAO
JSC may be a useful apparatus for measuring turbulent burning velocities. A similar table for the
Ravi et al.’s FSC could not be generated because the flame shape was too far from spherical to
extract meaningful data on u r.
67
Figure 37. Plots of flame radius r f vs. time t for different values of the mean progress variable c in the
Ravi et al. [34] FSC and the CIAO JSC. (a) Ravi et al., x-z plane; (b) Ravi et al., x-y plane; (c) CIAO, x-z
plane; (d) Ravi et al. and CIAO for full 3D flame surface for c = 0.1 and 0.5 only.
Time
(s)
rf
(m)
drf/dt
(m/s)
Ur
(m/s)
ST,D
(m/s)
ST,C
(m/s)
ST,Peters
(m/s)
0.0120 0.0379 6.806 4.700 2.106 1.800 1.936
0.0165 0.0702 7.111 3.852 3.325 2.280 1.843
0.0200 0.0992 6.811 4.213 2.597 2.104 1.822
Table 7. Comparison of computed values of turbulent burning velocity in the CIAO JSC based on
displacement speed (ST,D) and consumption speed (ST,C) for c = 0.05 along with the corresponding
theoretical predictions by Peters [91] based on the local flow and transport properties at c = 0.05.
(c)
(a)
(b)
(d)
68
4.2. Well-Stirred Reactor Studies
Jackson Pollock, Number 1, 1949
As mentioned in Chapters 1 and 2, Da<<1 (or Ka>>100) corresponds to a regime in which
turbulent mixing time scale is much smaller than chemical reaction time scale. This means
reactants and products are instantaneously mixed and species concentrations are uniform and
homogeneous. This regime is known as Perfectly Stirred Reactor (PSR) and the ideal chamber
that provides such condition is called Well-Stirred Reactor (WSR). This chamber is used to study
the rates and pathways of reactions and hence is significant in chemical kinetics studies. Since it
has been shown already that CIAO reactor provides effective mixing of turbulent kinetic energy
within the chamber, it may be a viable alternative to existing techniques for this purpose. As
previously mentioned, JSR [54] is a classical apparatus extensively used for this purpose.
However, certain concerns with such apparatus (like ensuring rapid mixing of incoming reactants
and avoiding pre-reaction in reactants before entering the chamber) have not been investigated
rigorously. Specifically, prediction and characterization of unmixedness has not been done
thoroughly. To address these issues, a systematic approach has been taken to test the exiting JSR
and assess the feasibility of CIAO as an alternative apparatus in chemical kinetics investigations.
The original design of JSR as well as the other common JSRs are shown in Chapter 1. Henceforth,
the Dagaut type JSR [54] shown in Figure 11 is referred to as 4JIPP-A and Matras-Villemaux type
JSR [63] shown in Figure 10 is referred to as 4JIPP-B. To find a configuration that provides ideal
69
composition predicted by WSR theory, many different chambers are designed and numerically
modeled. For brevity, results from only seven of the chambers are shown here:
1- Modified CIAO (called CIAO-V2) with 4 inlets instead of 8 that are placed tangent to the
surface of the chamber (Another CIAO-V2 with 8 jets is also designed, but not shown here).
2- Non-concentric chamber with 4 inlets and 4 outlets placed adjacently (called AIAO),
3- Inverted inlet and outlet (called Beach ball) in which 4 inlets and outlets are placed at the
center of the chamber,
4- V6 with 62 concentric inlets and outlets,
5- V8 with 6 inverted inlets and outlets at center located at faces of a double tetrahedron,
6-V14 with 12 inlets and 1 outlet in which 2 inlets are inverted and the outlet is located at
center,
7- V16 with 4 inverted inlets and 4 outlets in which inlets and outlets are placed at corners of a
cube.
These configurations are shown in Figure 38.
Figure 38. Selection of various designed and modeled JSR chambers. Top row from left: 4JIPP-A
exit at center, 4JIPP-A 2 exits, CIAO V2, inverted (Beach ball); bottom row from left: V6, V8, V14,
V16, Cubic.
70
4.2.1. Tracer Mixing
As mentioned in Chapter 3, a sufficient criterion for adequate mixing in a JSR is
agreement with the exact solution for the decay of a tracer in a perfectly-stirred reactor when
the supply of tracer is suddenly stopped. With this motivation, test of a small concentration of
CO 2 (mole fraction of 0.2) tracer in N 2 was conducted for 4JIPP-A, 4JIPP-B, CIAO, and a trivial
cubic reactor (shown in Figure 38) with the same mean residence time R. Results are shown in
Figure 39 for tracer concentrations averaged at the exit planes of the reactors to simulate the
experimental measurements. All of these cases show nearly ideal behavior, i.e. they follow Eq.
(61), yet it will be demonstrated that the behavior of the JSR configurations under reacting-flow
conditions is far from that of a PSR. Consequently, we conclude that exponential decay of a non-
reactive tracer that closely follows the exact solution is not a sufficient criterion to conclude that
the apparatus will behave as a PSR in the presence of chemical reactions.
Figure 39. Comparison of computed rates of decay of a passive tracer in the CIAO, 4JIPP-
A,4JIPP-B and Cubic reactors and comparison with the exact solution for a perfectly-stirred
reactor.
71
4.2.2. Stoichiometric ingle-step and two-step kinetic models
with no dilution
To evaluate the viability of the proposed chambers for JSR problems, a very simple test
problem is employed, consisting of a one-step or two-step reaction between reactants A and B,
in the 2-step case with an intermediate species C and final product D. Following the PSR model
discussed in Chapter 2, exact analytical solution of the reactions could be carried out. The single-
step reaction with no intermediate species is given by:
1 1
1
2
1
2
1
B A k
dt
D d
dt
C d
dt
B d
dt
A d
D C B A (65)
And the two-step reaction is given by:
2) (Step
) 1 (Step
2
1
2
1
2
1 1
1
C k
d t
D d
d t
C d
D C
B A k
d t
C d
d t
B d
d t
A d
C B A
(66)
If the mixture at the inlets is an equimolar mixture of A and B (i.e. their mole fractions X i
are both 0.5) with no inert, the molar concentrations of A and B ([A] and [B] respectively, units of
moles/m
3
) are the same for all time since any reaction of A also causes a reaction of B. For this
case, assuming perfect mixing, within the reactor the concentrations are [A] R = [B] R thus the
decrease in [A] due to chemical reaction within the reactor is given by:
V
V
A k t A k A
R R
2
1
2
1
(67)
V and are the reactor volume and volume flow rate respectively (note V / is the residence
time res), Here we are assuming that there is no change in density due to reaction. Therefore,
the concentration of A within the reactor is given by
72
V
V
A k A A A A
R o o R
2
1
(68)
where [A] o is the initial concentration of reactant A at the inlet. Non-dimensionalizing:
V
V
A k
A
A
V
V
A k
A
A
A
A
o
o
R
o
o
R
o
R
1
2
1
2
1 1
(69)
It can be noticed immediately that
V
V
A k
o
1
is ratio of residence and reaction time scales and is
therefore Damköhler number. Substituting ξ for scaled reactant concentration, Eq. (62) can be
rewritten as:
V
V
A k Da
A
A
Da
o
o
R
1
2
, ; 1
(70)
Solving this quadratic equation for ξ and retaining only the physically meaningful root:
Da
Da
2
1 4 1
(71)
The scaled reactant concentration ξ will vary from 1 for pure reactants (when the reaction rate is
low, i.e. low Da) to zero for pure products (when the reaction rate is high, i.e. high Da). The
scaled product mole fraction [C] R/[A] o will vary oppositely, i.e. from 0 for pure reactants to 1 for
pure products. The mole fractions X i in the reactor for the single-step reaction is then given by:
1 1
2
1
;
1 1
Da
Da
X X
Da
Da
X X
D C B A
(72)
Similarly, for the two-step reaction:
o
D C B A
A k
k
Da
Da Da
X
Da Da
Da Da
X
Da
Da
X X
1
2
4
1
1 2 2
;
1
1 2 2
;
1 1
(73)
where is the ratio of the Damköhler numbers for reaction step (2) to step (1).
73
FLUENT / RANS modeling with this simple reaction scheme has been conducted for Dagaut et
al.’s [54] (also referred to as 4JIPP-A) reactor (shown in Figure 11) and the CIAO reactor with the
same V and res. In these computations, by intent no model of turbulence-chemistry interaction
is used so that a direct comparison of the performance of the reactors can be made. Moreover,
if a model of turbulence-chemistry interaction is needed the key assumption of JSRs – uniform
composition, thus no variance in reaction – is already violated. Results are shown in Figure 40-
Figure 42.
4.2.2.1. Case I: No heat release and activation energy
Figure 42 shows that the CIAO reactor provides much more uniform composition than
Dagaut-type arrangement. Particularly, as it can be seen in Figure 40 the Dagaut geometry
results in a central region of nearly solid-body rotation with limited mixing and thus long
residence times which in turn lead to high product concentrations in this region. This uniformity
(or lack thereof) is reflected in Figure 42 (left) which shows that for the single-step reaction ( =
0) the volume-averaged product mole fraction X C in the CIAO reactor is much closer to the exact
solution than in the Dagaut-type reactor. Perhaps more significantly is the inverse way of
evaluating performance, i.e., the way JSR data are used to obtain kinetic data: when the volume-
averaged product mole fraction X C is inserted into Eq. (66), Da and thus the kinetic constant k 1 is
inferred.
Figure 40. Computed pathlines in JSRs. Left: CIAO reactor; right: 4JIPP-A reactor.
74
Figure 42 (right) shows that the simulated volume-averaged values of X C in the CIAO reactor
result in inferred values of k 1 that are much closer to the actual values than those obtained in
the 4JIPP-A reactor.
Figure 41. Computed product C mole fractions (X C) fields as a function of Da for the test problem
(Eq. (59)) with = 0 (i.e., single-step reaction) at Da = 2.5. Left: 4JIPP-A; right: proposed CIAO
reactor. The exact solution for these conditions is X C = 0.268.
Figure 42. Left: Volume-averaged mole fraction of product C (X C) as a function of Da for the test
problem (Eq. (59)) with Δ = 0 (i.e., single-step reaction) predicted by the FLUENT/RANS
simulations for the various chambers along with comparison to the exact theory (Eq. (65))
assuming perfect mixing. Right: comparison of inferred (from Eq. (65)) rate constants using the
volume-averaged product mole fraction (relative to the actual prescribed k 1) as a function of Da.
75
to facilitate comparisons between the 4JIPP and CIAO reactors, the aforementioned
simulations have of necessity employed premixed reactants with the presumption of no reaction
before entering the chamber. This was necessary because the 4JIPP reactor has one high mass
flow inlet path for air (or other oxidant) and a different low-mass-flow, low-residence-time inlet
path for fuel to minimize potential fuel pyrolysis. This is not directly compatible with the
symmetrical inlets of the CIAO reactor, hence the use of premixed reactants for comparison. Of
course, premixing of reactants is not a practical technique for real experiments because heated
premixed reactants will begin to react before entering the “reactor.” Consequently, simulations
of the CIAO reactor were performed using non-premixed reactants (4 jets with reactant A, 4 jets
with reactant B). Figure 42 shows that the results with non-premixed reactants are nearly the
same as those of premixed reactants up to Da ≈ 10. Fundamentally this is possible because the
CIAO reactor has effectively decoupled the residence time res from the mixing time m, the latter
being much smaller. As it can be seen in Figure 42 , the CIAO V2 and AIAO provides slightly
better uniformity compared to CIAO, but the Beach ball chamber provides perfect results as the
X c and inferred over true k values are same as predicted values in WSR. Although the non-
ideality of the chambers could be seen from averaged mole fraction and inferred k results,
another metrics could be used to evaluate the uniformity or lack thereof of products in the
chambers. For this reason, RMS values of inferred k is calculated and is shown in Figure 43.
Figure 43. RMS values of inferred over true k calculated for various chambers for different Da
numbers.
76
Figure 44 shows that for the two-step model ( > 0) the CIAO reactor predicts volume-
averaged values of the intermediate [C] and product [D] mole fractions that are closer to the
exact solutions than the 4JIPP reactor extends to the two-step model. It may be noted in
particular that the concentrations of [C] are predicted reasonably well for conditions of Da and
resulting in a nearly 4-decade range of [C] whereas for the 4JIPP-A configuration there is
substantially more difference between the computed and exact solutions.
Figure 44. Comparison of computed values (solid symbols: CIAO; open symbols: 4JIPP-A) to the exact
solution (curves) for the two-step reaction (Eq. (66)) as a function of the Damköhler number of
reaction 1 (Da) and the ratio of Damköhler numbers of reaction 2 to 1 (Δ). Left: mole fraction of
intermediate species (X C); right: mole fraction of final product species (X D).
4.2.2.2. Case II: Effects of heat release and activation energy
Most chemical reaction rates of relevance to combustion are far more sensitive to temperature
(due to the Arrhenius term) than composition. Consequently, in JSRs, by intention the reactant
concentrations are usually limited to values that are sufficiently small that the heat release does not
cause a significant enough temperature rise to have a substantial effect on reaction rates. The drawback
of low reactant concentrations (and thus low product concentrations) is that chemical analysis (e.g. gas
chromatography and mass spectrometry) and optical diagnostics will be less accurate due to
lower signal-to-noise ratios. For an Arrhenius temperature dependence, the ratio of reaction
77
rate at the initial temperature T i to that at the adiabatic (complete reaction) temperature T f is
given by
i f
i f
i
f
RT
E
T
T T
T
T
; exp (74)
where E is the effective activation energy for the reaction and R the gas constant. The issue lies
in the fact that the non-dimensional activation energy is typically large for the reactions of
relevance to combustion and thus T f – T i must be small if the variation in due to temperature
fluctuations is to be kept small. For example, for a typical overall activation energy of 30
kcal/mole, with T i = 900K, to limit (T f)/ (T i) ≤ 2 requires T f ≤ 1.043 T i = 939K, which in turn for a
lean propane-air mixture limits the fuel concentration to 1.5% of stoichiometric. The key
question for modeling to address is, do the apparent advantages of the CIAO configuration
compared to existing JSR designs still apply for systems with finite heat release and if so, what is
the maximum heat release or more specifically (T f-T i)/T f for which the well-stirred
approximation can be employed? An analysis for a single-step reaction similar to the isothermal
analysis above, including an enthalpy balance between the degree of reaction and the
temperature with the reactor T R leads to a typical WSR relation of the form
D a
*
D aexp
E
R T
i
T
R
T
i
2
T
R
T
i
T
f
T
i
T
f
T
R
2
exp
1
T
R
1
T
i
(75)
where Da has been scaled so that the reaction rate with finite activation energy but zero heat
release is the same as that with zero activation energy as in Eq (66). The isothermal and non-
isothermal predictions and comparison to computed results in the CIAO reactor with the
conditions are shown in Figure 45. As a direct consequence of the scaling chosen, with heat
release the mean reaction rate increases and thus more product is formed at a given Da. In the
limit of low Da there is little heat release (T R ≈ T i) and thus the results are the same for zero and
finite activation energy. Figure 45 shows that the CIAO reactor is able to reproduce the effects of
heat release and finite activation energy reasonably well, at least for the case (T f)/ (T i) ≤ 2.
78
Figure 45. Comparison of computed product mole fractions (X C) for single-step
reaction in the CIAO to theoretical predictions for WSRs in under isothermal and non-
isothermal conditions; for the latter case with E = 30 kcal/mole, T i = 900K, T f = 939K,
resulting in (T f)/ (T i) = 2.
4.2.3. Non-stoichiometric single-step reaction with dilution
Even though a single-step reaction is employed to assess the viability of the CIAO
configuration for JSR problems in section 4.2.2, direct comparison of results to detailed
chemistry cases cannot be made. Single-step reactions have two important advantages over the
detailed mechanisms: 1-exact solutions are obtained by solving the model analytically and there
are no concerns about uncertainties unlike detailed mechanisms, and 2-they are computationally
much less expensive since there is only 1 reaction with very few species. Thus, to investigate the
feasibility of utilizing a simple single-step reaction as a JSR design tool another single-step
reaction model based on the global reaction of 2H 2+O 2 2H 2O in the detailed chemistry is
written between reactants A and B with final products of C, no heat release and no activation
energy of the form:
2A+B 2C
For which the rate of consumption of each specie is written as:
79
[]
= 2
[ ]
= −
[]
= −2[]
[ ]
(76)
And assuming perfect mixing, similar to previous case the decrease in [A] due to chemical
reaction within the reactor is given by:
[]
− []
= −
[ ]
(77)
Combining the Eqs. (76-(77):
[]
− []
= 2[]
[ ]
(78)
Similarly, for [B]:s
[ ]
− [ ]
= −
[ ]
= []
[ ]
(79)
And,
[ ]
= [ ]
− []
[ ]
(80)
Which can be rearranged as:
[ ]
(1 + 2[]
) = [ ]
[ ]
=
[ ]
[ ]
(81)
Therefore Eq. (78) can be rewritten as:
[]
− []
=
2[]
[ ]
1 + 2[]
(82)
Rearranging the above equation and dividing by []
:
−
[]
[]
−
[]
[]
[]
+
[]
[]
+
[]
[]
+
2[]
[ ]
[]
= 0 →
[]
[]
+
2[ ]
− []
[]
[]
[]
+
1
[]
[]
[]
−
1
[]
= 0
(83)
80
Now if we define normalized mole fractions of species A and B as =
[]
[]
and =
[ ]
[]
=
and
define Damköhle number as = []
then, Eq. (83) can be written as:
+ (2 − 1)
+ − 1 = 0 (84)
in which k, and τ are reaction rate and residence time. Hence, by solving Eq. (76) exact mole
fractions of A in reactor as a function of Da can be calculated. This single-step model with
conditions of 1% A, 2.5% B and 96.5% diluent at 1 atm and with τ res=0.12 s is employed in
simulations for various JSRs and results are presented in Figure 46. These conditions are chosen
because experimental data from reaction of H 2-O 2 are available which will be modeled using the
detailed chemistry mechanism in the following section.
Figure 46. Comparison of calculated values of reactant A mole fraction for 4JIPP-A and CIAO
JSRs and the exact solution obtained from the extended single-step reaction model.
It can be seen from Figure 46 that the predicted volume-averaged results for both
chambers are very close to exact computed PSR solution. Even though the single-step reaction is
developed based on the global reaction of H 2-O 2 mechanism, to verify its viability reactant mole
fractions as a function of Da are plotted for both single-step and detailed mechanism (details of
which is discussed in next section) in a single plot. Figure 47 shows that the two lines cross at
Da=1 which means the single-step reaction can be used confidently at least for Da values near
unity in simulating the JSRs.
81
Figure 47. Comparison of reactant mole fraction for extended single-step and detailed
reaction mechanisms which is discussed in following section. The single-step values are
obtained analytically, and the detailed mechanism values are predictions from PSR model in
CHEMKIN.
4.2.4. Detailed H
2
-O
2
reaction
Following the aforementioned results that employed simple model chemistries having exact
solutions for all properties, simulations were performed in CIAO and 4JIPP-A reactors using detailed H 2-O 2
chemistry for two different cases in [97]: 1- 1% H 2 with Φ (equivalence ratio) = 0.2 at 1 atm pressure and
residence time of 0.12 s and 2- 1% H 2 with Φ=0.1 at 10 atm pressure and residence time of 1 s. After
comparing the results with the experimental data in [97], another case with 1% H 2 and Φ=0.2 at 1 atm
pressure and residence time of 0.01 s is simulated since characteristic residences time of phenomena of
interest like knocking is only a few milliseconds which is orders of magnitude smaller than typical
residence times studied in common JSRs. Detailed H 2-O 2 reaction mechanism of USC mech II [98] with 9
species and 28 reactions is used in to get the PSR values from CHEMKIN and is imported to FLUENT to
model the reactions inside the JSRs. (The reaction mechanism is shown in Appendix B)
4.2.4.1. Case I: τ
res
=0.12 s; Φ=0.2; P=1 atm
The first with case with available experimental data for comparison from [97] is oxidation
of H 2 with mole fractions of 0.01 H 2, 0.025 O 2, and 0.965 N 2 for various temperatures. It is not
mentioned in the paper that reported temperatures are for walls or measured by the
thermocouples. Since during the experiment the 4JIPP JSR is placed in a furnace, we believe the
82
temperatures are wall temperature therefore, computations are carried out with the changing
the wall temperatures and results are shown in Figure 48.
Figure 48. Comparison of H 2 mole fraction as a function of reactor temperature for
4JIPP and CIAO jet-stirred reactors for an ideal Perfectly Stirred Reactor, the 4JIPP
reactor (volume-averaged and at specific locations averaged over a 2 mm radius
spherical volume: center (r/R=0), half-way toward the outlet and at the outlet plane
(r/R=-0.5), and halfway between center and top of the chamber (r/R=0.5), CIAO reactor
(volume-averaged; location-specific predictions are nearly identical) and experimental
results by LeCong and Dagaut [97].
It was also found (Figure 48) that in the 4JIPP reactor, the predicted compositions were quite
different between local and volume-averaged values whereas in CIAO the composition was much
more uniform over the chamber volume. Somewhat surprisingly, the volume averaged 4JIPP-
RANS predictions of mole fractions are close to PSR predictions even though the local mole
fractions vary widely. The presence of sample probe in the 4JIPP reactor was found to have a
significant effect on the results. 4JIPP experiments for these conditions [97] show large
difference from PSR prediction and in fact agree fairly well with predictions at a sample location
half-way between chamber center and outlet. It should be mentioned that the sampling at
center using the suction of 1 cm
3
/s over extended period compared to the residence time
(around 60 s) is also modeled and even though the results do not differ from averaged values for
83
CIAO they are quite different for 4JIPP-A. Now the question that remains is how exactly the
experimental data are measured since the reported data are not volume averaged values.
A more common way of presenting the results in the literature is to plot the mole fraction
values as function of Da which is a dimensionless quantity instead of temperature. Unlike the
single-step model, the Da for detailed mechanism does not have a unique definition, however
we think it should be defined based on consumption of the major specie, i.e. H 2 here. Hence, Da
for detailed reaction mechanism is defined as:
=
(85)
in which τ50 is the time it takes for 50% of H 2 to consume in zero-dimensional, constant T and P
simulation is obtained from CHEMKIN. The Da values are calculated, and the results are shown in
Figure 49.
Figure 49. Comparison of averaged mole fractions of H 2 for both 4JIPP-A and CIAO
reactors as function of Da.
Figure 50 shows contours of temperature, H 2 and HO 2 radical mole fractions at wall
temperature of 925K for both 4JIPP-A and CIAO reactors. It can be seen that results in the CIAO
reactor more nearly matches PSR predictions than does the 4JIPP reactor. In particular, again
84
the 4JIPP reactor exhibits long residence times and thus more reaction progress near the reactor
center where samples are typically extracted, and thus may lead to overestimates of overall
reaction rates.
Temperature
H 2 mole fraction (PSR prediction )
85
HO 2 mole fraction
Figure 50. Computed temperature and species maps for 4JIPP (left column) and CIAO (right
column) jet stirred reactors. Mixture H 2 : O 2 : N 2 = 1 : 2.5 : 96.5 (equivalence ratio = 0.2), wall
temperature 925K, inlet temperature of 900K, inlet pressure 1 atm, residence time R = 0.12 s.
To investigate the effects of wall surface reaction on the results, another set of
computations with reactive walls are carried out. For this case, Platinum, which is widely used for
catalytic reactions due to its high reactivity, is selected for walls. The mechanism used for the
surface reaction is shown in Table 8 which consists of adsorption and desorption reactions.
Reaction A n E (joules/mole)
H 2(g) + 2Pt(s) => 2H-Pt(s) 4.4579E+10 0.5 0.0
H(g) + Pt(s) => H-Pt (s) 1.00 0 0
2H-Pt(s) => H 2(g) +2Pt(s) 3.70E+21 0 67400.0
Table 8. Surface reaction mechanism of H 2-Pt with the coefficients of the
Arrhenius relation (k=AT
n
exp(-E/RT)) taken from [99].
4.2.4.2. Case II: τ
res
=1 s; Φ=0.1; P=10 atm
The second case modeled in JSRs is the longer residence time at larger reactor pressure. The
mixture is 1% H 2, 5% O 2, and 94% N 2 (φ=0.1). Like the previous case, mole fractions of H 2 as a
86
function of reactor temperature are measured and compared to the experiment. Results are
shown in Figure 51.
Figure 51. Comparison of H 2 mole fraction as a function of reactor temperature for 4JIPP-A
and CIAO JSRs for an ideal Perfectly Stirred Reactor, the 4JIPP reactor (volume-averaged and at
specific locations averaged over a 2 mm radius spherical volume: center (r/R=0), half-way
toward the outlet and at the outlet plane (r/R=-0.5), and halfway between center and top of
the chamber (r/R=0.5), CIAO reactor (volume-averaged; location-specific predictions are
nearly identical) and experimental results by LeCong and Dagaut in [97].
As it can be seen from Figure 51, CIAO predictions more nearly match the PSR values similar to
previous case and there are no substantial differences between volume averaged and local
measurements, however, this is not the case for 4JIPP-A reactor since the local measurements
vary significantly as location of probe is changed.
4.2.4.3. Case III: τ
res
=0.01 s; Φ=0.2; P=1 atm
To assess viability of using CIAO JSR for smaller residence times computations with τres of
10 ms with atmospheric pressure and φ=0.2 are carried out and results are shown in Figure 52.
87
Figure 52. Comparison of H 2 mole fraction as a function of reactor temperature for 4JIPP-A
and CIAO JSRs for an ideal Perfectly Stirred Reactor, the 4JIPP-A and CIAO reactors (volume-
averaged and at specific locations averaged over a 2 mm radius spherical volume: center, half-
way toward the outlet and half-way between outlet and inlet).
Like both previous cases, the dependency of results to location in 4JIPP-A reactor is much
more significant as it can be seen in Figure 52 even though the volume averaged values are
similar for both chambers.
4.2.5. Performance comparison
It is shown throughout previous sections that volume-averaged results cannot be used
alone to evaluate uniformity or lack thereof in the chamber and although the RMS values for the
ratio of inferred/true values of k somewhat shows performance of the chambers, we have
developed a better performance metrics which shows the behavior of any given JSR across the
chamber in an improved fashion and it could be used to compare the uniformity of chambers.
The definition of this new metrics, CAI is shown in Eq. (62) and it is discussed in Chapter 3. CAI is
calculated for the aforementioned cases and results are presented in Figure 53-Figure 57.
88
Figure 53. Comparison of calculated CAI in CIAO and 4JIPP-A reactors for both detailed and
single-step chemistry at three different Da numbers for φ=0.2, P=1 atm and τ res=0.12 s.
89
It is worth noting that the Da numbers correspond to wall temperatures and the relations
are shown in Table 9.
T w Time to 50% H 2 (s) Da
900 0.009038 0.028
925 0. 006965 1.76
950 0.005931 18.8
Table 9. Computed Da numbers corresponding to wall
temperatures for detailed mechanism case I: φ=0.2, P=1 atm and
τ res=0.12 s.
Figure 54. Comparison of calculated CAI for CIAO and 4JIPP-A JSRs for two different Da. Top row:
case II of detailed mechanism with φ=0.1, p=10 atm and τ res=1 s (left: T w=925 K, right: T w=1000K);
bottom row: case III of detailed mechanism with φ=0.2, p=1 atm and τ res=0.01 s (left: T w=950 K,
right: T w=1000K).
90
Several observations could be made from Figure 53-Figure 54. It is obvious that as Da
approaches unity the agreement between CAI values for both detailed mechanism and extended
single-step reaction is significantly better. This reiterates that the designed single-step reaction
can successfully be employed instead of the detailed chemistry as also shown in Figure 47 .
Another important remark is that if only the RMS values of reactant composition for whole
chamber is to be the criterion for uniformity, 4JIPP-A reactor performs better than CIAO,
however, it is evident that a single value does not represent the behavior of JSR and going from
center toward walls CIAO shows enhanced performance over more than half of the chamber.
The other important observation is that at center where the samples are taken, CIAO performs
the best and this is quite opposite for the 4JIPP-A reactor since CAI is the highest at that point
which is believed to be caused by the long local residence time due to the flow pattern inside the
chamber. To evaluate the performance of other designed JSRs, computations for Da=1 are
carried out using the extended single-step reaction and CAI results are shown in Figure 55.
Figure 55. CAI comparison for various chambers for the extended single-step reaction with 1%
A, φ=0.2, P=1 atm, and τ res=0.12 s.
91
It is clear from Figure 55 that the orientation and number of jets considerably affect the
mixedness of the mixture inside the chamber. Perhaps, the most discernable remark from the
above plot is that placing the jets inside the chamber and shooting outwardly causes the CAI to
be large at center and the inner half of the chamber but placing them on the circumference and
shooting inwardly leads to lower CAI at center and inner half of the chamber and higher near
walls. Hence, CAI is generally the largest close to jets where the mean flow is substantial.
Furthermore, it can be seen when the concentric jets are entering to chamber tangentially as in
CIAO-V2 JSR, the uniformity is enhanced significantly throughout the chamber.
To investigate effects of turbulence model on the results, simulations for three chambers
of CIAO, 4JIPP-A, and CIAO V2 with three different turbulence models of k-ε, RSM, and LES are
carried out for the single-step case at Da=1 and results are presented in Figure 56.
Figure 56. Effects of turbulence model on CAI for three different chambers of CIAO, 4JIPP-A, and
CIAO V2.
To distinguish the behaviors of CIAO and 4JIPP-A reactors better, CAI are calculated for a
wide range of Da for the single-step reaction and results are plotted in Figure 57.
92
Figure 57. Plots of CAI comparison for various Da for CIAO (left) and 4JIPP-A (right) reactors.
It is evident that the uniformity of both chambers at very low Da are comparable.
However, very low Da means the chamber is filled mostly with reactants since little reaction
occurs hence, it is out of the range of interest and more attention should be paid to the middle
range of Da far from both limits of very little and very large reaction rates. Therefore, it can be
seen from Figure 57 that the mixedness condition in 4JIPP-A reactor deteriorates rapidly as the
Da is increased. For example, when Da=0.5 which according to Figure 46 is about 50%
completion of reaction, CAI for CIAO is less than 0.1 for whole chamber, but it is starting from 0.2
and goes stays more than 0.1 for 4JIPP-A. This shows improved mixedness in CIAO as the mixture
is much more uniform than 4JIPP-A reactor specifically at the range of interest for kinetics
studies.
4.2.6. Effects of design parameters
There are four different dimensional parameters at play in each chamber: chamber
diameter, jet diameter, residence time, and chemical time. In this section, to investigate the
effects of the chamber size as well as the jet diameter and number of jets on the uniformity of
CIAO chamber, a design parameter study is carried out. For this purpose, the non-stoichiometric
single-step reaction with dilution with 1% of A (φ=0.2) at 1 atm and τ res=0.12 s for Da=1 is
employed. First, CIAO chambers with 1, 2, 4 and 62 jets are simulated, and results are compared
with baseline CIAO with 8 jets. Next, chamber diameter is doubled, and calculations are carried
93
out in 80 mm diameter chamber. Then, for the baseline CIAO jet diameter is changed and finally,
at the nominal jet diameter of 1 mm, the outlet area is increased and decreased by 50%. Results
are shown in Figure 58.
Figure 58. CAI comparison for various CIAO JSRs. Top: Effects of number of jets; bottom:
effects of chamber and inlet and outlet sizes.
It is evident that decreasing number of jets, and consequently increasing jet velocity at
constant jet diameter, enhances the mixing on the average, but worsens the mixing at center. In
the limit of having minimum number of jets, i.e. only one, CAI is highest at center. This is due to
the large concentration of reactants issued from the high velocity jet which remains unperturbed
until it hits the wall on the other side and since there is no other jet, the mean flow remains large
inside the chamber across the jet axis. However, increase in velocity means higher Re and Re L
94
which in turn means faster mixing and thus lower CAI away from the region of large
concentration. As the number of jets are increased, the uniformity at center is enhances since
the mean flow is lowered (as shown by MFI in Section 4.1.1) while CAI for the rest of chamber
doesn’t change significantly. In the other limit, i.e. having many jets, the jet diameter is reduced
to 0.3 mm diameter so that the overall jet Re is same as the baseline CIAO and it can be seen
except near walls where effect of jets is strong, performance is enhanced compared to baseline
CIAO. It is important to note that even for non-premixed jets, akin to the practical technique for
real experiments, the performance of CIAO is still very good from center to r/R=0.25. Effects of
chamber and jet size are visible in Figure 58. Decreasing the jet size enhances the mixing but
reaches a limit since going from 0.5 mm to 0.4 mm jets have virtually the same CIA across the
chamber. As the chamber diameter is doubled and the jet diameter is kept constant (1mm), it
can be seen that the performance is only enhanced a little compared to the baseline CIAO even
though the jet Re is increased by 8 times (r 2=2r 1 V 2=8V 1 u jet,2=8u jet,1). Re jet is calculated to
be 915.5 for the 0.5 mm jet in 40 mm chamber, therefore to see if there is a unique Re jet
corresponding to specific CAI respond, jet diameter is increased to 4 mm for the 80 mm chamber
so that the Re jet is the same as 40 mm chamber with 0.5 mm jets. Results show that even though
CAI is improved from center to r/R=0.5, it drastically increases as the performances suffers at
larger radii. The last design parameter that significantly affects the mixedness is the outlet area.
For the CIAO baseline the ratio of outlet to inlet area is one; thus, two different outlet-to-inlet
ratios are modeled to investigate whether changing this ratio has any effects on mixing or not
and it was found (Figure 58) that while increasing the outlet area slightly deteriorates the mixing,
decreasing the outlet area improves the CAI significantly for most of the chamber. Similar to
decreasing the inlet area, the increased level of shear induced turbulence is believed to be
reason.
4.3. Experiment
To assess the viability of the CIAO design for study of chemical kinetics experimentally, a
3D printed chamber was built and tested in cold-flow mixing experiments using fluorescein +
water solutions and Laser Induced Fluorescence imaging to quantify the mixing levels. The
95
spherical CIAO with built-in manifolds has a diameter of 150 mm and the jets have diameter of
10 mm and thus, the chamber is half of the nominal size in the Turbulent Flame simulations
discussed in previous chapters. The entire experimental setup is shown Figure 59 in and CAD
representation of the chamber is depicted in Figure 60.
Figure 59. Experimental setup for studying of mixing homogeneity in 3D printer CIAO.
96
Figure 60. CAD representation of CIAO chamber with built-in outlet manifolds.
In the experiments, fluorescein-water solution flows from one of the buckets and the
other bucket is filled just with water. The reason for which fluorescein is used is as follows: The
Schmidt number, Sc, is ratio of kinematic viscosity to molecular diffusivity defined as:
D
v
Sc (86)
and it is much larger than unity for fluorescein in water which on first glance should significantly
affect mixing behavior compared to gases with Sc ≈ 1, however, simulations [100] show that
when the Peclet number which is defined as:
P e R e
2
S c (87)
exceeds about 10
4
, the turbulent Schmidt number is about 1.3, independent of Sc or
R e
.Using standard turbulence scaling laws the criterion P e R e
2
S c 10
4
can be expressed as
R e
L
10
3
S c , where R e
L
is the integral-scale Reynolds number, a requirement easily met by
fluorescent aqueous tracers, even at relatively low R e
L
. Consequently, under the conditions of
interest it can be expected that the behavior of high-Sc tracers will be similar to that of gaseous
reactants with Sc ≈ 1. It is also possible to visualize mixing properties of gases with Sc ≈ 1 using
PLIF of acetone vapor [101] with a quadrupled YAG laser, however it is anticipated that gas
97
sampling + simple visualization of aqueous tracers will be adequate to characterize the mixing
uniformity. Consistent with the computational predictions, the initial experimental results
indicate much more uniform mixing than 4JIPP type chambers. For these cases the residence
time R = 0.83 s and the time between successive frames is 0.008 s (video is recorded at 125 fps).
It can be seen from Figure 61 that the images are not well correlated, thus even over time
period 1/100 of the residence time there is substantial mixing, indicating that near-PSR
conditions exist. The quantification of mixing from image processing has not been done yet since
optical system used lacks the necessary quality.
98
Frame # 1 Frame # 2 Frame # 3 Frame # 4 Frame # 5
Figure 61. Successive PLIF images (interval 0.008 s) of fluorescein concentration in a CIAO JSR. Chamber diameter 15 cm, field of view of images 7.62 x
5.71 cm. Top row: raw images from camera; middle row: outlined structures from dilated images; bottom row: inverted outlines of smoothed images.
99
Chapter 5: Conclusion
A computational study of jet-stirred chambers (JSCs) as an apparatus for studying
spherically expanding turbulent premixed flames reveals that a configuration of 8 inlets with
concentric outlets at the corners of an imaginary cube circumscribed by a sphere may produce
nearly homogeneous and isotropic turbulence with a very high ratio of turbulence intensity to
mean velocity throughout much of the chamber. Quantitative metrics for mean velocity,
homogeneity and isotropicity in this Concentric Inlet And Outlet (CIAO) JSC were shown to be far
superior to those in Fan-Stirred Chambers (FSCs). These metrics were not substantially
diminished by intentionally misaligning the jets or mismatching jet exit velocities. An initial
comparison of simulated flame propagation in the CIAO JSC and an FSC showed more nearly
steady and quasi-spherical flame propagation in the former, with less dependence of the
inferred flame propagation rate on the choice of definition. Our results indicate that the CIAO
JSC provides effective mixing of turbulent kinetic energy within the chamber. Since JSCs are
frequently employed in chemical kinetics studies at low Da under the assumption (sometimes
not fully justified) that reactants and products within the JSC are well-mixed, the CIAO JSC may
be a viable alternative to existing JSCs for this purpose. To evaluate the viability of CIAO and to
study mixture uniformity systematically, various reaction models for different scenarios are
employed. A quantitative metrics for mixedness is developed and used to compare various
chambers. CFD computations for simple reaction and detailed chemistry models demonstrate
that even for very simple chemical scenarios, the non-uniformity of mixing in widely-used JSRs
results in inferred reaction rate constants that are significantly different from the true values and
CIAO apparatus provides an improved performance and shows promising results in study of
chemical. Effects of geometrical parameters of CIAO on uniformity of chamber are also
investigated and it was found that for a given chamber diameter, decreasing either inlet or outlet
areas improves the uniformity. Increasing numbers of jets also enhances the mixedness. Finally,
it was found that a modified version of CIAO (called CIAO-V2) where the concentric inlet and
100
outlets are tangentially entering the chamber show a substantial improvement of composition
uniformity across the chamber.
101
Appendix A: Detailed analysis of WSR theory
Continuing from (52) in Section 2.4:
Mass A burned per unit time= (total mass flow) (change in mass fraction A) = ̇ (
,
− ̇
,
)
,
− ̇
,
=
(
−
)
=
(
−
)
,
(
−
)
=
,
−
−
→
,
=
,
−
−
Then since []
=
,
[]
=
,
(1)
Mass balance on B: since one B molecule is consumed for every A
̇
,
− ̇
,
= ( ̇
,
− ̇
,
); v is stoichiometric oxygen to fuel mass ratio
,
=
,
,
=
,
− ̇
,
− ̇
,
→
,
=
(
)
−
(
)
,
=
(
−
) − (
−
)= ̇
,
[ ]
=
,
−
(2)
Finally combining Equations:
̇ =
,
[]
[ ]
exp (−
ℜ
)
̇ =
,
,
,
−
exp (−
ℜ
)
̇ =
,
−
exp (−
ℜ
)
̇ =
,
−
exp (−
ℜ
)
Eq. ((53) emerges as:
̇ ̇
=
−
exp (
)
With: ̇
≡
,
;
≡
; ≡
; ≡
ℜ
;
102
Appendix B: USC II detailed H
2
-O
2
mechanism
!! USC Mech ver 2.0
! Release date: May 2007
!!****************************************************************************
!! Please contact Hai Wang at haiw@usc.edu for questions and comments
!****************************************************************************
!! Reference sources can be found at the end of the file.
!============================================================================
ELEMENTS
O H C N
END
SPECIES
!
O2 H2
H O OH HO2 H2O H2O2 N2
END
!!
REACTIONS
! ---- Optimized H2/O2 mechanism ----
H+O2 = O+OH 2.644E+16 -0.6707 17041.00 !GRI3.0 * 1.00
O+H2 = H+OH 4.589E+04 2.700 6260.00 !GRI3.0 * 1.19
OH+H2 = H+H2O 1.734E+08 1.510 3430.00 !GRI3.0 * 0.80
OH+OH = O+H2O 3.973E+04 2.400 -2110.00 !GRI3.0 * 1.11
H+H+M = H2+M 1.780E+18 -1.000 0.00 !GRI3.0 * 1.78
H2/0.0/ H2O/0.0/
H+H+H2 = H2+H2 9.000E+16 -0.600 0.00 !GRI3.0
H+H+H2O = H2+H2O 5.624E+19 -1.250 0.00 !GRI3.0 * 0.94
H+OH+M = H2O+M 4.400E+22 -2.000 0.00 !GRI3.0 * 2.00
H2/2.0/ H2O/6.30/
103
O+H+M = OH+M 9.428E+18 -1.000 0.00 !86TSA/HAM * 2.00
H2/2.0/ H2O/12.0/
O+O+M = O2+M 1.200E+17 -1.000 0.00 !GRI3.0
H2/2.4/ H2O/15.4/
H+O2(+M) = HO2(+M) 5.116E+12 0.440 0.00 !00 TROE - Based on M=N2 * 1.10
LOW / 6.328E+19 -1.400 0.00 /
TROE/ 0.5 1E-30 1E+30 /
O2/0.85/ H2O/11.89/
H2+O2 = HO2+H 5.916E+05 2.433 53502.00 !00MIC/SUT * 0.80
OH+OH(+M) = H2O2(+M) 1.110E+14 -0.370 0.00 !88ZEL/EWI * 1.50
LOW / 2.010E+17 -0.584 -2293.00 /!Fit 88ZEL/EWI and 92BAU/COB
TROE / 0.7346 94. 1756.00 5182.0 /!H2O=6xN2 88ZEL/EWI
H2/2.0/ H2O/6.00/
!
! Reactions of HO2
!
HO2+H = O+H2O 3.970E+12 0.000 671.00 !GRI3.0
HO2+H = OH+OH 7.485E+13 0.000 295.00 !99MUE/KIM * 1.06
HO2+O = OH+O2 4.000E+13 0.000 0.00 !GRI3.0 * 2.00
HO2+HO2 = O2+H2O2 1.300E+11 0.000 -1630.00 !90HIP/TRO
DUPLICATE
HO2+HO2 = O2+H2O2 3.658E+14 0.000 12000.00 !90HIP/TRO * 0.87
DUPLICATE
OH+HO2=H2O+O2 1.41E+18 -1.760 60.0 ! Wang07
Duplicate
OH+HO2=H2O+O2 1.12E+85 -22.300 26900.0 ! Wang07
Duplicate
OH+HO2=H2O+O2 5.37E+70 -16.720 32900.0 ! Wang07
Duplicate
OH+HO2=H2O+O2 2.51E+12 2.000 40000.0 ! Wang07
104
Duplicate
OH+HO2=H2O+O2 1.00E+136 -40.000 34800.0 ! Wang07
Duplicate
!
! Reactions of H2O2
!
H2O2+H = HO2+H2 6.050E+06 2.000 5200.00 !GRI3.0 * 0.50
H2O2+H = OH+H2O 2.410E+13 0.000 3970.00 !86TSA/HAM
H2O2+O = OH+HO2 9.630E+06 2.000 3970.00 !86TSA/HAM
H2O2+OH = HO2+H2O 2.000E+12 0.000 427.00 !95HIP/NEU
DUPLICATE
H2O2+OH = HO2+H2O 2.670E+41 -7.000 37600.00 !Refit95HIP/NEU
DUPLICATE !2.2E14 MAX K
!
END
105
Appendix C: Details of the fluorescence experiment
Fluorescence involves two processes: absorption and emission. The laser light must be
absorbed by the fluorescent dye and excite the molecules of fluorescent material, then it can
emit fluorescent light at a longer wavelength (lower energy photon going out than coming in).
The right wavelength for the laser is selected based on the peak absorption of fluorescein which
according to [102] and as it can be seen is around 490 nm.
Figure: Absorption spectra of fluorescein in 5mM buffer in the presence of various ionic
strength from 0 to 1000 mM NaCl (from [102]).
Next, a concentration of fluorescein such that there isn’t much absorption over the length of the
test section, let’s say not more than 20% is picked. According to Beer’s Law, the beam intensity
at a location x is lower than that at x = 0 according to the formula:
() = (0)
Where is the absorption coefficient (units 1/length). Of course will depend on the
concentration of fluorescein, so the specification for for fluorescein or any other dye is in units
of (1/length)(1/concentration), then Beer’s Law becomes
() = (0)
Where now has units of (1/length)(1/concentration) and m is the molarity of the solution.
106
For fluorescein, a typical value of (called in the above plot) is used from [102].
If we use 50000 M
-1
cm
-1
as a typical value (M = moles per liter), then if we want I(x)/I(0) = 0.5
(50% absorption) over a path length (x) of 15 cm, then:
() = (0)
→ 0.5 exp (50000 M
cm
)( )(15 cm)] → = 2.97 × 10
(
)
The molecular mass of fluorescein is 332 g/mole, thus the concentration needed in grams per
liter is
2.97 × 10
332
= 9.89 × 10
For 7 gallons of solution (as used in the experiment):
9.89 × 10
.
(5 ) = 2.63 × 10
This prevents significant attenuation of the beam by absorption. However, this low
concentration may or may not provide enough intensity of fluorescent to be able to image the
fluorescence. Therefore, the key is then to have enough laser power to provide a bright enough
image for the camera to detect clearly.
107
Appendix D: Princeton Plug Flow Reactor
Atmospheric Pressure Flow Reactor (PFR) Introduced by Crocco, Glassman and Smith in 1959
Later Variable PFR by Vermeersch and Dryer in 1991[103]: Princeton VPFR consisted of 4 parts:
Air inlet
Jet injector
Diffuser
Test tube
Geometrical parameters are:
Oxidizer
inlet radius (m) 0.0508
Diffuser
half angle (deg) 5
baffle plate radius (m) 0.04445
in radius (m) 0.0127
gap (m) 0.0064
out radius (m) 0.058
Fuel inlet
tube radius (m) 0.003175
Tube
radius (m) 0.0508
injector holes # 8
length (m) 1.73
hole radius (m) 0.000125
probe 0.00635
Simulations for various cases from [103] are carried out and results are shown in following
illustrations.
Figure: CAD representation of VPFR in [103].
108
It is not clear where the sampling begins, so based on numerous iterations of different
neck (between injection and diffuser) sizes it is believed that the neck is about 3 inches. 2D
axisymmetric computations with RSM are carried out for cold flow first and flow field is
“validated” against the experiment [103]. The results for Re=10000 are illustrated in next page:
Then, H2-O2 reaction with 0.82% H2 and 0.41% O2 and 99.87% N2 at P=6 atm and T=945
corresponding to Re=3830 is modeled [103]. Profiles of temperature (K) and H 2O mole fractions
for various axial lines are plotted below:
109
Figure: Contour of temperature for the case with reaction mentioned earlier (T=945
corresponding to Re=3830)
It can be concluded from figures that:
% variation in H 2O mole fraction from r=0
to r=R
x=60 cm 65
x=100 cm 48
X=150 cm 17
x=190 cm 4.6
110
References
[1] J.G. Pausas, J.E. Keeley, A Burning Story: The Role of Fire in the History of Life, BioScience, 59 (2009)
593–601.
[2] I.J. Glasspool, D. Edwards, L. Axe, Charcoal in the Silurian as evidence for the earliest wildfire, Geology
32 (2004) 381–383.
[3] C.H. Wellman, J. Gray, The microfossil record of early land plants, Philos. Trans. R. Soc. Lond. B Biol.
Sci., 355 (2000) 717–3.
[4] S.R. James, Hominid use of fire in the lower and middle Pleistocene. A review of the evidence, Current
Anthropology, 30 (1989) 1-26.
[5] C. Organ, C.L. Nunn, Z. Machanda, R.W. Wrangham, Phylogenetic rate shifts in feeding time during the
evolution of Homo, Proc. Natl. Acad. Sci. USA, 108 (2011) 14555–14559.
[6] W. Roebroeks, P. Villa, On the earliest evidence for habitual use of fire in Europe, Proc. Natl. Acad. Sci.
USA 108:5209–5214
[7] F. Berna, P. Goldberg, L.K. Horwitz, J. Brink, S. Holt, M. Bamford et al., Microstratigraphic evidence of
in situ fire in the Acheulean strata of Wonderwerk Cave, Northern Cape province, South Africa., Proc.
Natl. Acad. Sci. 109 (2012)1215-1220.
[8] E.F. Beall, Hesiod's Prometheus and Development in Myth, Journal of the History of Ideas, 52 (1991)
355–371.
[9] S.W. Jamison, J.P. Brereton, The Rigveda: 3-Volume Set, Oxford University Press (2014).
[10] M.D. Coe, R. Koontz, Mexico: From the Olmecs to the Aztecs, 6th ed., Thames and Hudson (2008)
[11] E. Yarshater (Ed.), The Cambridge History of Iran, Cambridge University Press (1983).
[12] International Energy Agency, Key World Energy Statistics 2015.
[13] U.S. Energy Information Administration (EIA), International Energy Outlook 2016, (May 2016).
[14] https://www.eia.gov/environment/emissions/co2_vol_mass.cfm
[15] Intergovernmental Panel On Climate Change (IPCC), Climate Change 2014: Mitigation of Climate
Change Summary for Policymakers and Technical Summary
[16] European Environment Agency: http://www.eea.europa.eu/data-and-maps/indicators/eea-32-
nitrogen-oxides-nox-emissions-1/assessment.2010-08-19.0140149032-3
[17] US Environmental Protection Agency (EPA): https://www3.epa.gov/cgi-
bin/broker?polchoice=NOX&_debug=0&_service=data&_program=dataprog.national_1.sas
111
[18] Y.B. Zel'dovich, The Oxidation of Nitrogen in Combustion Explosions, Acta Physicochimica U.S.S.R.
(1946) 21: 577–628.
[19] C.P. Fenimore, Formation of nitric oxide in premixed hydrocarbon flames, Symp. (Int.) Combust. 13
(1971) 373–380.
[20 ] J. Daou, A. Liñán, Ignition and extinction fronts in counterflowing premixed reactive gases, Combust.
Flame 118 (1999) 479-488.
[21] F. A. Williams, Combustion Theory, 2nd ed., Benjamin-Cummings (1985).
[22] J. D. Buckmaster, M. Short, Cellular instabilities, sublimit structures and edge-flames in premixed
counterflows, Combust. Theory and Modelling 3 (1999) 199-214.
[23] D. Veynante, L. Vervisch, Turbulent combustion modeling, Prog. Energy Combust. Sci. 28 (2002) 193–
266.
[24] N. Peters, Turbulent Combustion, Cambridge University Press (2000).
[25] R. Borghi, Turbulent combustion modelling, Prog. Energy Combust. Sci. 14 (1988) 245–292.
[26] G. I. Sivashinsky, Cascade Model for Turbulent Flame Propagation, Dissipative Structures in Transport
Processes and Combustion (D. Meinköhn, ed.), Springer Series in Synergetics, 48 (1990) 30.
[27] K. N C. Bray, Studies of the turbulent burning velocity, Proc. Roy, Soc. Lond A.341 (1990) 315-335.
[28] S. B. Pope, M. S. Anand, Flamelet and distributed combustion in premixed turbulent flames,
Proceedings of the Combustion Institute, 20 (1985) 403-410.
[29] F. C. Goldin, An Application of Fractious to Modeling Premixed Turbulent Flames, Combust. Flame 68
(1987) 249.
[30] V. Yakhot , Propagation Velocity of Premixed Turbulent Flames, Combustion Science and Technology,
60 (1988) 191-214.
[31] V. Bychkov, Velocity of Turbulent Flamelets with Realistic Fuel Expansion. Phys. Rev. Lett. 84 (2000)
6122–6125.
[32] D. Bradley, A.K.C. Lau, M. Lawes, Flame Stretch Rate as a Determinant of Turbulent Burning Velocity,
Philos. Trans R Soc. London Ser. A Phys Eng. Sci., 338 (1992) 359-387.
[33] D. Bradley, M.Z. Haq, R.A. Hicks, T. Kitagawa, M. Lawes, C.G.W. Sheppard, R. Woolley, Turbulent
burning velocity, burned gas distribution, and associated flame surface definition, Combust. Flame 133
(2003) 415–430.
[34] S. Ravi, S.J. Peltier, E.L. Petersen, Analysis of the impact of impeller geometry on the turbulent
statistics inside a fan-stirred, cylindrical flame speed vessel using PIV, Exp. Fluids 54 (2013) 1424.
[35] S. Chaudhuri, F. Wu, D. Zhu, C.K. Law, Flame speed and self-similar propagation of expanding
turbulent premixed flames, Phys. Rev. Lett. 108 (2012) 1–5.
[36] C.C. Liu, S.S. Shy, M.W. Peng, C.W. Chiu, Y.C. Dong, High-pressure burning velocities measurements
for centrally-ignited premixed methane/air flames interacting with intense near-isotropic turbulence at
constant Reynolds numbers, Combust. Flame 159 (2012) 2608–2619.
112
[37] H. Kobayashi, T. Tamura, K. Maruta, T. Niioka, F. Williams, Burning velocity of turbulent premixed
flames in a high-pressure environment, Symp. (Int.) Combust. 26 (1996) 389–396.
[38] S. Pfadler, M. Löffler, F. Dinkelacker, A. Leipertz, Measurement of the conditioned turbulence and
temperature field of a premixed Bunsen burner by planar laser Rayleigh scattering and stereo particle
image velocimetry, Exp. Fluids 39 (2005) 375–384.
[39] S.A. Filatyev, J.F. Driscoll, C.D. Carter, J.M. Donbar, Measured properties of turbulent premixed
flames for model assessment, including burning velocities, stretch rates, and surface densities, Combust.
Flame 14 (2005) 11–21.
[40] T.W. Lee, G.L. North, D.A. Santavicca. Surface properties of turbulent premixed propane/air flames at
various Lewis numbers, Combust. Flame 93 (1993) 445-456.
[41] T. Sponfeldner, N. Soulopoulos, F. Beyrau, Y. Hardalupas, A.M.K.P. Taylor, J.C. Vassilicos, The
structure of turbulent flames in fractal- and regular-grid-generated turbulence, Combust. Flame 162
(2014) 3379-3393.
[42] K.H.H. Goh, P. Geipe, R.P. Lindstedt, Lean premixed opposed jet flames in fractal grid generated
multiscale turbulence, Combust. Flame 161 (2014) 2419-2434.
[43] D. Geyer, A. Kempf, A. Dreizler, J. Janicka, Turbulent opposed-jet flames: A critical benchmark
experiment for combustion LES, Combust. Flame 143 (2005) 524–48.
[44] R.K Cheng, I.G. Shepherd, The influence of burner geometry on premixed turbulent flame
propagation, Combust. Flame 85 (1991) 7-26.
[45] V.P. Karpov, A.S. Sokolik, The relationship between the self-inflammation of paraffins and their rates
of laminar and turbulent burning, Dokl. Akad. Nauk SSSR 138 (4) (1961) 874–876.
[46] A.S. Sokolik, V.P. Karpov, E.S. Semenov, Turbulent combustion of gases, Fizika Goreniya i Vzryva 3 (1)
(1967) 61-76.
[47] R.G. Abdel-Gayed, K.J. Al-Khishali, D. Bradley, Turbulent burning velocities and flame straining in
explosions, Proc. R. Soc. Lond. A 391 (1984) 393-414.
[48] T.D. Fansler, E.G Groff, Turbulence characteristics of a fanstirred combustion vessel, Combust Flame
80 (1990) 350–354.
[49] S.S. Shy, K. IW, M.L. Lin, A new cruciform burner and its turbulence measurements for premixed
turbulent combustion study, Exp Thermal Fluid Sci 20 (2000) 105–114.
[50] V. Sick, M.R. Hartman, V.S. Arpaci, R.W. Anderson, Turbulent scales in a fan-stirred combustion
bomb. Combust. Flame 127 (2001) 2119–2123.
[51] T. Kitagawa, T. Nakahara, K. Maruyama, K. Kado, A. Hayakawa, S. Kobayashi (2008) Turbulent burning
velocity of hydrogen-air premixed propagating flames at elevated pressures, Int. J. Hydrogen Energy 33
(2008) 5842–5849.
[52] M. Weiß, N. Zarzalis, R. Suntz, Experimental study of Markstein number effects on laminar flamelet
velocity in turbulent premixed flames, Combust. Flame 154 (2008) 671–691.
113
[53] B. Galmiche, N. Mazellier, F. Halter, F. Foucher, Turbulence characterization of a high-pressure high-
temperature fan-stirred combustion vessel using LDV, PIV and TR-PIV measurements, Exp Fluids 55 (2014)
1636.
[54] P. Dagaut, M. Cathonnet, J.P. Rouan, R. Foulatier, A. Quilgars, J.C. Boettner, F. Gaillard, H. James, J.
Phys. E: Sci. Instrum. 19 (1986) 207 – 209.
[55] J.P. Longwell, M.A. Weiss, High Temperature Reaction Rates in Hydrocarbon Combustion, Ind. Eng.
Chem., 47 (1955) 1634–1643.
[56] F.P. Stainthorp, G.T. Clegg, Fluid stirring in continuous flow system, Chem. Eng. Sci. Suppl., 20 (1965)
167-172.
[57] S.F. Bush, The design and operation of single-phase jet-stirred reactors for chemical kinetic studies,
Trans. Inst. Chem. Eng. 47 (1969) 59–7.
[58] J.O. Hinze, B.G. Van Der Hegge Zijnen, Transfer of heat and matter in the turbulent mixing zone of an
axially symmetrical jet, Appl. Sci. Res. (1949) 1: 435.
[59] D. Matras, J. Villermaux, Un réacteur continu parfaitement agité par jets gazeux pour l'étude
cinétique de réactions chimiques rapides, Che. Eng. Sci. 28 (1973) 129-137.
[60] R. David, D. Matras, Règies de construction et d'extrapolation des réacteurs auto-agités par jets
gazeux, Can. Soc. Chem. Eng. 53 (1975) 297-300.
[61] T. Zhang, H. Zhao, Y. Ju, Numerical Studies of the Residence Time Distributions of an Inwardly Off-
center Shearing Jet Stirred Reactor (IOS-JSR), AIAA Journal 56 (9) (2018) 3388-3392.
[62] A. Nicolle, P. Dagaut, Fuel 85 (17-18) (2006) 2469–2478.
[63] O. Herbinet, F. Battin-Leclerc, International Journal of Chemical Kinetics 46 (10) (2014) 619-639.
[64] E. Mastorakos, A.M.K.P. Taylor, Whitelaw JH. Extinction of turbulent counterflow flames with
reactants diluted by hot products, Combust. Flame 102 (1995) 101–114.
[65] K. Sardi, A.M.K.P. Taylor, J.H. Whitelaw, Conditional scalar dissipation statistics in a turbulent
counterflow, J. Fluid Mech. 361 (1998) 1–24.
[66] A. Kempf, H. Forkel, J.Y. Chen, A. Sadiki, J. Janicka, Large-eddy simulation of a counterflow
configuration with and without combustion, Proc. Combust. Inst. 28 (2000) 35–40.
[67] Aubert M, Setiawan P, Oktaviana AA, Brumm A, Sulistyarto PH, Saptomo EW, et al, Palaeolithic cave
art in Borneo, Nature 564 (2018) 254–257.
[68] P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers, Oxford University Press
(2004).
[69] H. Tennekes, J.L. Lumley, A First Course in Turbulence, The MIT Press (1972).
[70] S. B. Pope, Turbulent Flows, Cambridge University Press (2000).
114
[71] A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large
Reynolds numbers, Proceed. of the USSR Academy of Sciences (in Russian) 30 (1941) 299–303.
[72] V. Yakhot, S.A. Orszag, renormalization group analysis of turbulence, Phys. Rev. Lett 57 (1986) 1722-
1724.
[73] N. Peters, the turbulent burning velocity for large scale and small-scale turbulence, J Fluid Mech., 384
(1999) 107-132.
[74] P.D. Ronney, V. Yakhot, Flame Broadening Effects on Premixed Turbulent Flame Speed, Combust. Sci.
Tech. 86 (1992) 31-43.
[75] R. Borghi, On the structure and morphology of turbulent premixed flames, Recent advances in the
Aerospace Sciences, (1985) 117-138.
[76] R.G. Abdel-Gayed, D. Bradley, and F.K.K Lung, Combustion regimes and the straining of turbulent
premixed flames 76 (1989) 213-218.
[77] T. Poinsot, D. Veyante, S. Candel, Diagrams of premixed turbulent combustion based on direct
simulation, Proc. Combust. Inst., 23 (1990) 613-619.
[78] T. Poinsot, D. Veynante, S. Candel, Quenching process and premixed turbulent combustion diagrams.
J. Fluid Mech. 228 (1991) 561-606.
[79] W.L. Roberts, J.F. Driscoll, M.C. Drake, L.P. Gross, Images of quenching of a flame by a vortex: to
quantify regimes of turbulent combustion, Combust. Flame 94 (1993) 58-69.
[80] G. Damköhler, "Der Einfluss der Turbulenz auf die Flammengeschwindigenkeit in Gasgemishcen", Z.
Elektrochem, 46 (1940) 601-652, English translation NASA Tech. Mem. 1112.
[81] P. Clavin, F.A. Williams, Theory of premixed-flame propagation in large-scale turbulence, J. Fluid
Mech 90 (1979) 589-604.
[82] F.A. Williams, Combustion Theory, Benjamin/Cummins, Menlo Park (1985a)
[83] B.E. Launder, G.J. Reece, W. Rodi, Progress in the development of a Reynolds-Stress turbulence
closure, J. Fluid Mech 68 (1975) 537-566.
[84] J. Chorin, Numerical solution of Navier-Stokes equations, Mathematics of computation, 22 (1968)
745-762.
[85] R.I. Issa, Solution of the implicitly discretized fluid flow equations by operator-splitting, J.
Computational Physics, 62 (1985) 62-40.
[86] H.M. Glaz, J.B. Bell, P. Colella, Second-order projection method for the incompressible Navier-Stokes
equations, J. Computational Physics, 85 (1989) 257.
[87] M.W.A. Pettit, B. Coriton, A. Gomez, A.M. Kempf, Large-Eddy Simulation and experiments on non-
premixed highly turbulent opposed jet flows, Proc. Combust. Inst. 33 (2011) 1391–1399.
[88] R.W. MacDonald, E.L. Piret, Continuous flow stirred tank reactor systems-agitation requirements,
Chem. Eng. Prog. 47 (1951) 363—369.
115
[89] Hwang, J.K. Eaton, Creating homogeneous and isotropic turbulence without a mean flow, Exp. Fluids
36 (2004) 444–454.
[90] K. Chang, G.P. Bewley, E. Bodenschatz, Experimental study of the influence of anisotropy on the
inertial scales of turbulence, J. Fluid Mech. 692 (2012) 464–481.
[91] N. Peters, The turbulent burning velocity for large-scale and small-scale turbulence, J. Fluid Mech.
384 (1999) 107–132.
[92] P. Griebel, P. Siewert, P. Jansohn, Flame characteristics of turbulent lean premixed methane/air
flames at high pressure: Turbulent flame speed and flame brush thickness, Proc. Combust. Inst. 31 (2007)
3083-3090.
[93] E. Yasari, S. Verma, A.N. Lipatnikov, RANS Simulations of Statistically Stationary Premixed Turbulent
Combustion Using Flame Speed Closure Model, Flow Turbulence Combust. 94 (2015) 381–414.
[94] R. Keppeler, E. Tangermann, U. Allaudin, M. Pfitzner, LES of Low to High Turbulent Combustion in an
Elevated Pressure Environment, Flow Turbulence Combust. 92 (2014) 767–802.
[95] D. Bradley, M. Lawes, M.S. Mansour, Correlation of turbulent burning velocities of ethanol–air,
measured in a fan-stirred bomb up to 1.2 MPa, Combust. Flame 159 (2012) 2608–2619.
[96] L. Ma, Q. Lei, J. Ikeda, W. Xu, Y. Wu, C. D. Carter, Single-shot 3D flame diagnostic based on volumetric
laser induced fluorescence (VLIF), Proceedings of the Combustion Institute, Vol. 36 (in press).
[97] T. Le Cong, P. Dagaut, Experimental and Detailed Modeling Study of the Effect of Water Vapor on the
Kinetics of Combustion of Hydrogen and Natural Gas, Impact on NO
x
, Energy and Fuels, 23 (2009)
725–734 (2009).
[98] H. Wang, X. You, A.V. Joshi, S.G. Davis, A. Laskin, F. Egolfopoulos, C.K. Law, USC Mech Version II. High-
Temperature Combustion Reaction Model of H2/CO/C1-C4 Compounds.
http://ignis.usc.edu/USC_Mech_II.htm, May 2007.
[99] O. Deutschmann, R. Schmidt, F. Behrendt, J. Warnatz. Proc. Combust. Inst. 26 (1996) 1747-1754.
[100] D. A. Donzis, K. Aditya, K. R. Sreenivasan, P. K. Yeung, J. Fluids Eng. 136 (6) (2014).
[101] A. Lozano, B. Yip, R. K. Hanson, Experiments in Fluids 13 (6) (1992) 369-376.
[102] R. Sjöback, J. Nygren, M. Kubista, Absorption and fluorescence properties of fluorescein,
Spectrochimica Acta. 51 (1995) L7-L21.
[103] M.L. Vermeersch, A variable pressure flow reactor for chemical kinetic studies: Hydrogen, methane
and butane oxidation at 1 to 10 atmospheres and 880 to 1040 K, Ph.D. Thesis Princeton Univ. (1991).
Abstract (if available)
Abstract
A series of jet-stirred chambers were designed to study combustion processes at high and low Damköhler numbers (Da, ratio of residence time to chemical time) corresponding to turbulent premixed flames and chemical kinetics respectively. In the first section, computations employing the RANS - Reynolds Stress Model were used to simulate the flows and identify an optimal configuration of jets and outlet ports providing the most nearly ideal flow, i.e. homogeneous and isotropic with large turbulence intensity compared to the mean velocity. Results showed that a configuration of 8 jets, each surrounded by a concentric annular outlet, at the corners of an imaginary cube circumscribed by a spherical chamber produced by far the most nearly optimal flow characteristics. The performance of this configuration, called Concentric Inlet And Outlet (CIAO), was also compared quantitatively to two popular fan-stirred chamber (FSC) designs and CIAO JSC was found to provide far more nearly ideal flow. A comparison of simulated turbulent premixed flames shows that CIAO enabled far more nearly spherical expanding flames with nearly the same inferred turbulent burning velocity regardless of the value of the mean progress variable used to define the flame location, whereas in the FSC there was considerable variation depending on the definition. In the second section, application of this chamber as well as other proposed chambers as a Jet-Stirred Reactor (JSR) for chemical kinetics experiments are studied. Computations carried out with simple and detailed mechanism reactions and their performance was compared to classical JSRs (4 Jets In Plus (+) Pattern (4JIPP) introduced by Matras & Villermaux 1973
Linked assets
University of Southern California Dissertations and Theses
Conceptually similar
PDF
Investigations of fuel effects on turbulent premixed jet flames
PDF
Studies of methane counterflow flames at low pressures
PDF
Re-assessing local structures of turbulent flames via vortex-flame interaction
PDF
Flame ignition studies of conventional and alternative jet fuels and surrogate components
PDF
Flame characteristics in quasi-2D channels: stability, rates and scaling
PDF
Modeling investigations of fundamental combustion phenomena in low-dimensional configurations
PDF
Experimental studies of high pressure combustion using spherically expanding flames
PDF
Experimental and kinetic modeling studies of flames of H₂, CO, and C₁-C₄ hydrocarbons
PDF
Investigations of fuel and hydrodynamic effects in highly turbulent premixed jet flames
PDF
Direct numerical simulation of mixing and combustion under canonical shock turbulence interaction
PDF
Studies of combustion characteristics of heavy hydrocarbons in simple and complex flows
PDF
Studies of siloxane decomposition in biomethane combustion
PDF
Kinetic modeling of high-temperature oxidation and pyrolysis of one-ringed aromatic and alkane compounds
PDF
Model based design of porous and patterned surfaces for passive turbulence control
PDF
Numerical study of shock-wave/turbulent boundary layer interactions on flexible and rigid panels with wall-modeled large-eddy simulations
PDF
Electrokinetic transport of Cr(VI) and integration with zero-valent iron nanoparticle and microbial fuel cell technologies for aquifer remediation
Asset Metadata
Creator
Davani, Abbasali (Ashkan)
(author)
Core Title
CFD design of jet-stirred chambers for turbulent flame and chemical kinetics experiments
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Mechanical Engineering
Publication Date
11/08/2019
Defense Date
03/01/2019
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
CFD,chemical kinetics,combustion,fan-stirred reactor,flame,homogeneous,isotropic,jet-stirred reactor,LES,OAI-PMH Harvest,perfectly-stirred reactor,RANS,turbulence,turbulent combustion,well-stirred reactor
Format
application/pdf
(imt)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Ronney, Paul David (
committee chair
), Egolfopoulos, Fokion N. (
committee member
), Lynett, Patrick Joseph (
committee member
)
Creator Email
addashkan@gmail.com,davanida@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c89-156701
Unique identifier
UC11659947
Identifier
etd-DavaniAbba-7420.pdf (filename),usctheses-c89-156701 (legacy record id)
Legacy Identifier
etd-DavaniAbba-7420.pdf
Dmrecord
156701
Document Type
Dissertation
Format
application/pdf (imt)
Rights
Davani, Abbasali (Ashkan)
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Tags
CFD
chemical kinetics
combustion
fan-stirred reactor
flame
homogeneous
isotropic
jet-stirred reactor
perfectly-stirred reactor
RANS
turbulence
turbulent combustion
well-stirred reactor