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Studies of combustion characteristics of heavy hydrocarbons in simple and complex flows
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Studies of combustion characteristics of heavy hydrocarbons in simple and complex flows
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Content
STUDIES OF COMBUSTION CHARACTERISTICS OF HEAVY
HYDROCARBONS IN SIMPLE AND COMPLEX FLOWS
by
Runhua Zhao
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTERHN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MECHANICAL ENGINEERING)
May 2016
ii
Dedication
To my parents, Guanhou Zhao and Qin Tang for their love and support.
iii
Acknowledgments
The author wishes to thank Professor Fokion Egolfopoulos for his encouragement, support
and guidance throughout this doctoral work.
iv
Table of Contents
Dedication ...................................................................................................................... ii
Acknowledgments........................................................................................................ iii
List of Tables ............................................................................................................. viii
List of Figures ............................................................................................................... ix
Abstract .................................................................................................................... xviii
Chapter 1: Introduction ............................................................................................... 1
1.1 Background ...................................................................................................... 1
1.2 Basic Concepts ................................................................................................. 2
1.2.1 Laminar Flame Speed ............................................................................... 2
1.2.2 Flame Stretch ............................................................................................ 3
1.2.3 Flame Extinction ....................................................................................... 4
1.2.4 Lewis Number ........................................................................................... 5
1.2.5 Karlovitz Number ..................................................................................... 6
1.2.6 Markstein Number .................................................................................... 7
1.3 Objectives ........................................................................................................ 8
1.4 References ........................................................................................................ 8
Chapter 2: Experimental Approach .......................................................................... 10
2.1 Experimental Setup ........................................................................................ 10
2.2 Liquid and Solid Fuel Preparation Procedure ................................................ 12
2.3 Reference Flame Speed and Local Strain Rate .............................................. 14
2.4 Determination of Laminar Flame Speed ........................................................ 15
2.5 Determination of Extinction Strain Rate........................................................ 16
2.6 References ...................................................................................................... 21
Chapter 3: Numerical Approach ............................................................................... 23
3.1 One Dimensional Modeling ........................................................................... 23
3.1.1 Codes Description ................................................................................... 23
3.1.2 Mixture-Averaged and Multicomponent Transport Formulations ......... 23
v
3.1.3 Sensitivity Analysis Methodology .......................................................... 25
3.2 Three Dimensional Modeling ........................................................................ 27
3.2.1 Codes Description ................................................................................... 27
3.2.2 Mesh Generation Methodology .............................................................. 28
3.3 Kinetic Models ............................................................................................... 31
3.3.1 Models Used in Current Study ................................................................ 31
3.3.2 Kinetic Model Reduction Using Directed Relation Graph Method........ 32
3.4 References ...................................................................................................... 33
Chapter 4: Determination of Laminar Flame Speeds: Molecular Transport Effects 37
4.1 Introduction .................................................................................................... 37
4.2 Numerical Approach ...................................................................................... 43
4.3 Results and Discussion .................................................................................. 46
4.4 Concluding Remarks ...................................................................................... 65
4.5 References ...................................................................................................... 66
Chapter 5: An Experimental and Modeling Study of the Propagation and Extinction of
Neat Hydrocarbons, Practical Fuels and Jet Fuels ....................................................... 71
5.1 Introduction .................................................................................................... 71
5.2 Experimental Approach ................................................................................. 74
5.3 Numerical Approach ...................................................................................... 77
5.4 Results and Discussion .................................................................................. 79
5.4.1 Propagation and extinction of n-C
14
H
30
/air and n-C
16
H
34
/air flames...... 79
5.4.2 Propagation and extinction of Gasoline Ethanol Blends ........................ 83
5.4.3 Propagation and extinction of jet fuel flames ......................................... 88
5.5 Concluding Remarks ...................................................................................... 91
5.6 References ...................................................................................................... 92
Chapter 6: An Experimental and Modeling Study of the Propagation and Extinction of
Cyclopentadiene ........................................................................................................... 97
6.1 Introduction .................................................................................................... 97
vi
6.2 Experimental Approach ................................................................................. 99
6.3 Numerical Approach .................................................................................... 102
6.4 Results and Discussion ................................................................................ 103
6.5 Concluding Remarks .................................................................................... 113
6.6 References .................................................................................................... 114
Chapter 7: Determination of Extinction Strain Rate: Molecular Transport Effects 118
7.1 Introduction .................................................................................................. 118
7.2 Experimental Approach ............................................................................... 120
7.3 Numerical Approach .................................................................................... 122
7.4 Results and Discussion ................................................................................ 124
7.5 Concluding Remarks .................................................................................... 130
7.6 References .................................................................................................... 131
Chapter 8: Determination of Laminar Flame Speeds Using Axisymmetric Bunsen
Flames: Intricacies and Accuracy .............................................................................. 135
8.1 Introduction .................................................................................................. 135
8.2 Experimental Approach ............................................................................... 137
8.3 Numerical Approach .................................................................................... 141
8.4 Results and Discussion ................................................................................ 145
8.4.1 Non-ideal effects in Bunsen flames ...................................................... 146
8.4.2 Results of the parametric analysis......................................................... 157
8.4.3 Correction factors.................................................................................. 161
8.5 Concluding Remarks .................................................................................... 163
8.6 References .................................................................................................... 164
Chapter 9: Zimont Scale Vortex Interactions with Premixed Flames .................... 170
9.1 Introduction .................................................................................................. 170
9.2 Numerical Approach .................................................................................... 172
9.3 Results and Discussion ................................................................................ 174
9.3.1 Vortex-Flame Interaction ...................................................................... 174
vii
9.3.2 Fuel Decomposition .............................................................................. 179
9.4 Concluding Remarks .................................................................................... 182
9.5 References .................................................................................................... 183
Chapter 10: Conclusions and Recommendations ................................................... 185
10.1 Conclusions .................................................................................................. 185
10.2 Recommendations for Future Work............................................................. 187
Bibliography .............................................................................................................. 189
viii
List of Tables
Table 4.1 Lewis number, Le and ratio of fuel to O
2
diffusivities for the
mixtures used in the present study.
45
Table 5.1 Fuel specific properties. 77
Table 5.2 RD 387 Surrogate Molar Compositions 79
Table 7.1 Summary of computational cases. 124
Table 7.2 Effective LJ-12-6 potential parameters of n-alkane-N
2
interactions for calculating the binary diffusion coefficients of
n-alkane in N
2
.
125
Table 8.1 S
u
calculations using simulation results with and without the
presence of boundary layer in the inlet velocity profile for a
CH
4
/air flame at =1.0. The values in the brackets indicate the
percentage difference for each S
u
from S
u
0
.
149
ix
List of Figures
Figure 1.1 Variation of the ratio of oxygen diffusivity to fuel diffusivity
with carbon number for ϕ = 1.4 n-alkane/air mixtures at
p = 1 atm and T
u
= 298 K.
6
Figure 2.1 Representative example of the non-linear extrapolation
technique.
11
Figure 2.2 Schematic of the experiment configuration. 13
Figure. 2.3 Graphical definition of measurement points in counterflow. 14
Figure. 2.4 Representative example of the non-linear extrapolation
technique.
16
Figure 2.5 Experimental results comparison of uniform flow field using
screened burner (top) and non-uniform flow field using open
burners (bottom).
18
Figure 2.6 2D axisymmetric simulation results of open burner opposing jet
twin-flame configuration flame at high strain rate and low
strain rate condition. (a) high flow rate flame and (b) low flow
rate flame with adaptive grid resolution; (c) high flow rate
flame and (d) low flow rate flame radial velocity gradient in the
tangential direction.
19
Figure 2.7 Evolution of the extinction process for lean CH
4
/air flames
produced by open burner (a-d) and screened (e-h) burners.
20
Figure 3.1 Computational grid used in the numerical simulations overlaid
with boundary conditions applied for pressure, temperature,
velocity, and chemical species.
29
Figure 3.2 Temperature as a function of distance along a 1-D cut through
the flame front for a CH4/air mixture with =0.80 at the high
Re condition.
30
x
Figure 4.1
Deviation of experimental
o
S
u
’s of n-heptane/air mixtures at
p = 1 atm from that of Ji et al. [16] (T
u
= 353 K) represented by
the solid line. Data represented by symbols include: ( ●) Kelley
et al. [17] (T
u
= 353 K), ( ♦ ) Smallbone et al. [18] (T
u
= 350 K)
and (x) Kumar et al. [19] (T
u
= 360 K).
38
Figure 4.2 (a) Variation of Le with carbon number for n-alkane/air
mixtures at p = 1 atm and T
u
= 298 K, for ϕ = 0.7 (dashed line)
and ϕ = 1.4 (solid line). (b) Variation of the ratio of oxygen
diffusivity to fuel diffusivity with carbon number for ϕ = 1.4
n-alkane/air mixtures at p = 1 atm and T
u
= 298 K.
40
Figure 4.3
Computed
o
S
u
’s of CH
4
/air flames at p = 1 atm and T
u
= 298 K
using USC-Mech II. ( ─) OD; (---) DD; (-
.
-) ID.
47
Figure 4.4
Logarithmic sensitivity coefficients of
o
S
u
to the CH
4
-N
2
(red)
and O
2
-N
2
(blue) binary diffusion coefficients for CH
4
/air
flames at p = 1 atm, T
u
= 298 K, and various ϕ’s.
48
Figure 4.5
(a) Normalized mass fraction profiles of CH
4
( ┄) and O
2
( ─),
and CH
4
consumption rate profile ( ─) for a = 1.4 freely
propagating CH
4
/air flame at T
u
= 298 K and p = 1 atm,
computed using USC-Mech II and OD. (b) Normalized mass
fraction profiles of CH
4
( ┄ ) and O
2
( ─ ), and CH
4
consumption rate profile ( ─) for a freely propagating flame at
T
u
= 298 K, p = 1 atm, and = 1.4, computed using USC-Mech
II and DD.
49
Figure 4.6 Variation of ϕ
local
with temperature in a ϕ = 1.4 freely
propagating CH
4
/air flame at p = 1 atm, and T
u
= 298 K
computed using USC-Mech II with OD ( ●) and DD ( ■), and
variation of CH
4
consumption rate with temperature with OD
( ─) and DD (-
.
-).
50
xi
Figure 4.7
Variation of S
u,ref
/
o
S
u
with Ka of a ϕ = 0.7 CH
4
/air CFF at
p = 1 atm and T
u
= 298 K computed using USC-Mech II with
ID ( ■), OD ( ●), and DD ( ▲). ID (-
.
-), OD ( ─), and DD (---)
correspond to fitting using Eq. 1. The full range DNS results
are shown in hollow symbols, while the DNS results used for
fitting Eq. 1 are shown in solid symbols.
52
Figure 4.8
Variation of S
u,ref
/
o
S
u
with Ka of a ϕ = 1.0 CH
4
/air CFF at
p = 1 atm and T
u
= 298 K computed using USC-Mech II with
ID ( ■), OD ( ●), and DD ( ▲). ID (-
.
-), OD ( ─), and DD (---)
correspond to fitting using Eq. 1. The full range DNS results
are shown in hollow symbols, while the DNS results used for
fitting Eq. 1 are shown in solid symbols.
53
Figure 4.9
Variation of S
u,ref
/
o
S
u
with Ka of a ϕ = 1.4 CH
4
/air CFF at
p = 1 atm and T
u
= 298 K computed using USC-Mech II with
ID ( ■), OD ( ●), and DD ( ▲). ID (-
.
-), OD ( ─), and DD (---)
correspond to fitting using Eq. 1. The full range DNS results
are shown in hollow symbols, while the DNS results used for
fitting Eq. 1 are shown in solid symbols.
54
Figure 4.10 Variation of HRR
tot
with Ka of a ϕ = 0.7 CH
4
/air CFF at
p = 1 atm and T
u
= 298 K computed using USC-Mech II with
ID (-
.
-), OD ( ─), and DD (---).
56
Figure 4.11 Variation of HRR
tot
with Ka of a ϕ = 1.0 CH
4
/air CFF at
p = 1 atm and T
u
= 298 K computed using USC-Mech II with
ID (-
.
-), OD ( ─), and DD (---).
57
Figure 4.12 Variation of HRR
tot
with Ka of a ϕ = 1.4 CH
4
/air CFF at
p = 1 atm and T
u
= 298 K computed using USC-Mech II with
ID (-
.
-), OD ( ─), and DD (---).
58
xii
Figure 4.13 Variation of ϕ
local
with temperature in a ϕ = 1.4 CH
4
/air CFF at
p = 1 atm, T
u
= 298 K, and K = 30 s
-1
computed using
USC-Mech II with OD ( ●) and DD ( ■), and variation of CH
4
consumption rate with temperature with OD ( ─) and DD (-
.
-).
59
Figure 4.14 Variation of ϕ
local
with temperature in a ϕ = 1.4 CH
4
/air CFF at
p = 1 atm, T
u
= 298 K, and K = 200 s
-1
computed using
USC-Mech II with OD ( ●) and DD ( ■), and variation of CH
4
consumption rate with temperature with OD ( ─) and DD (-
.
-).
60
Figure 4.15
Variation of S
u,ref
/
o
S
u
with Ka of a ϕ = 0.7 n-C
12
H
26
/air CFF at
p = 1 atm and T
u
= 443 K computed using JetSurF 1.0 with ID
( ■) and OD ( ●). ID (-
.
-) and OD ( ─) correspond to fitting
using Eq. 1. The full range DNS results are shown in hollow
symbols, while the DNS results used for fitting Eq. 1 are shown
in solid symbols.
62
Figure 4.16
Variation of S
u,ref
/
o
S
u
with Ka of a ϕ = 1.4 n-C
12
H
26
/air CFF at
p = 1 atm and T
u
= 443 K computed using JetSurF 1.0 with ID
( ■) and OD ( ●). ID (-
.
-) and OD ( ─) correspond to fitting
using Eq. 1. The full range DNS results are shown in hollow
symbols, while the DNS results used for fitting Eq. 1 are shown
in solid symbols.
63
Figure 4.17 Variation of ( ϕ
local
)
peak
( ─) and HRR
tot
(--) with Ka of a ϕ = 1.4
n-C
12
H
26
/air CFF at p = 1 atm and T
u
= 443 K computed using
JetSurF 1.0 with OD.
64
Figure 5.1 (a) Experimental and computed laminar flame speeds of (a)
n-C
14
H
30
/air mixture, (b) n-C
16
H
34
/air mixtures at p = 1 atm and
T
u
= 443 K.
80
xiii
Figure 5.2 Ranked logarithmic sensitivity coefficients of laminar flame
speed with respect to kinetics computed using (a) Model I and
(b) Model II, for ϕ = 0.7, 1.0, and 1.4 n-C
14
H
30
/air mixture at
T
u
= 443 K.
81
Figure 5.3 (a) Experimental and computed extinction strain rate of (a)
n-C
14
H
30
/air mixture, (b) n-C
16
H
34
/air mixtures at p = 1 atm and
T
u
= 443 K.
82
Figure 5.4
Experimentally determined
o
S
u
’s at T
u
= 393 K of E100/air ( ●),
E85/air ( ■), E50/air (♦), E15/air ( ▲), and E0/air ( ○). The
error bars shown in the present experimental data are based on
the 2-𝜎 standard deviations.
85
Figure 5.5 Experimental and computed laminar flame speeds of ( ○)
E100/air mixture, ( □) E50/air mixtures, and ( ◇) E0/air
mixtures at p = 1 atm and T
u
= 393 K.
86
Figure 5.6 Experimentally determined K
ext
’s at T
u
= 393 K of E100/air
( ●), E85/air ( ■), E50/air (♦), E15/air ( ▲), and E0/air ( ○).
The error bars shown in the present experimental data are based
on the 2-𝜎 standard deviations.
87
Figure 5.7
Experimental and computed
o
S
u
’s at T
u
= 403 K of Jet A/air
( ▲), JP-8/air ( ●), and JP-5/air (♦). The error bars shown in the
present experimental data are based on the 2- 𝜎 standard
deviations.
89
Figure 5.8 Experimental and computed K
ext
’s at T
u
= 473 K of Jet A/air
( ▲), JP-8/air ( ●), and JP-5/air (♦). The error bars shown in the
present experimental data are based on the 2- 𝜎 standard
deviations.
90
Figure 6.1 Experimental and computed laminar flame speeds of
cyclopentadiene/air flames at T
u
= 353 K and p = 1 atm.
Symbols: present experimental data. Solid lines: simulations
using Model I. Dashed Lines: simulations using Model II.
Dashed-dot Lines: simulations provided by Lindstedt and Park
104
xiv
[35] using kinetic model in Ref. 16. The error bars shown in
the present experimental data are based on the 2-𝜎 standard
deviations.
Figure 6.2 Ranked logarithmic sensitivity coefficients of laminar flame
speeds with respect to kinetics, computed using Models I and II
for a = 0.7 cyclopentadiene/air flame at T
u
= 353 K and
p = 1 atm.
105
Figure 6.3 Reaction path analysis of a = 0.7 cyclopentadiene/air flame at
T
u
= 353 K, and p = 1 atm using (a) Model I, and (b) Model II.
The numbers indicate the conversion percentages.
106
Figure 6.4 Computed intermediate species profiles for a = 0.7
cyclopentadiene/air flame at T
u
= 353 K and p = 1 atm, using
Model I (solid lines) and Model II (dashed lines).
108
Figure 6.5 Experimental and computed extinction strain rates of
cyclopentadiene/air flames at T
u
= 353 K and p = 1 atm.
Symbols: present experimental data. Solid lines: simulations
using Model I. Dashed Lines: simulations using Model II.
The error bars shown in the present experimental data are based
on the 2- standard deviations.
109
Figure 6.6 Ranked logarithmic sensitivity coefficients of extinction strain
rates with respect to kinetics, computed using Models I and II
for a = 1.05 cyclopentadiene/air flame at T
u
= 353 K and
p = 1 atm.
110
Figure 6.7 Computed intermediate species profiles for a near-extinction
= 1.05 cyclopentadiene/air flame at T
u
= 353 K and p = 1 atm,
using Model I (solid lines) and Model II (dashed lines).
111
Figure 6.8 Concentration profiles during CPD oxidation in a plug flow
reactor with initial temperature of 1198 K, initial fuel
concentration of 2243 ppm, and = 1.03. Symbols:
experimental data from Butler and Glassman [15]; ( ○) C
5
H
6
,
( ●) CO, ( ■) C
2
H
2
, and ( ▲) C
4
H
6
; Lines: simulation with (a)
Model I (solid lines) time-shifted by -20 ms and (b) Model II
(dashed lines) time-shifted by -28 ms.
112
xv
Figure 6.9 Experimental and computed laminar flame speeds and
extinction strain rates of cyclopentadiene/air flames at
T
u
= 353 K and p = 1 atm. Symbols: present experimental
data. Solid lines: simulations using Model I. Dotted lines:
simulations using modified Model I by adding R8 from Model
II. The error bars shown in the present experimental data are
based on the 2- standard deviations.
113
Figure 7.1 Extinction strain rate of non-premixed n-C
12
H
26
/N
2
-O
2
flames
(T
u
= 473 K for the fuel jet and 300 K for the oxygen jet) with p
= 1 atm. Symbols: experimental data (this work); lines are
simulations (see Table 7.1).
127
Figure 7.2 Extinction strain rate of non-premixed n-C
12
H
26
/N
2
-O
2
flames
and n-C
10
H
22
/N
2
-O
2
flames all at T
u
= 403 K for the fuel jet and
300 K for the oxygen jet, with p = 1 atm. Experimental data
(symbols) were taken from Ref. [10]; lines are simulations (see
Table 7.1).
128
Figure 7.3 Structures of n-dodecane/N
2
(473 K) versus O
2
(300 K) near
extinction flames computed for (a) Case IV (full
multicomponent and thermal diffusion transport with updated
diffusion coefficients) and (b) Case III (mixture averaged
transport with the thermal diffusion ratio of Rosner et al. [39]).
The vertical dashed-dotted-dashed line indicates the position of
the stagnation surface.
130
Figure 8.1 S
u
o
’s as a function of as obtained from the full USC Mech II
kinetic model and the reduced models derived for CH
4
and
C
3
H
8
.
142
Figure 8.2 Computational grid used in the numerical simulations overlaid
with boundary conditions applied for pressure, temperature,
velocity, and chemical species.
143
Figure 8.3 Temperature as a function of distance along a 1-D cut through
the flame front for a CH
4
/air mixture with =0.80 at the high Re
condition.
144
xvi
Figure 8.4 Iso-contours of velocity (left) and density (right) for a CH
4
/air
flame at =1.0 with a high Re at the inlet for a) case with an
inlet boundary layer and b) case without an inlet boundary
layer. The black iso-surface represents the location of the flame
front.
147
Figure 8.5 Iso-contours of pressure (left) and radial velocity (right) for a
CH
4
/air flame at =1.0 for a) high Re case and b) low Re case.
Radial velocity is expressed as a percentage of the inlet
velocity.
150
Figure 8.6 Iso-surfaces of velocity overlaid on iso-contours of temperature
for a) CH
4
/air flame at =1.0 for high Re case and b) C
3
H
8
/air
flame at =1.0 for high Re case. Velocity values for
iso-surfaces are in units of m/s.
151
Figure 8.7 Iso-surfaces of temperature overlaid on iso-contours of density
for a CH
4
/air flame at =1.0 for high Re case.
153
Figure 8.8 S
u
estimates using different temperature iso-surfaces for a
CH
4
/air flame at =1.0 for high Re case. S
u
estimated using the
luminescence iso-surface is also presented for the same case.
153
Figure 8.9 (a) Fluid flow path highlighted by streamlines overlaid on
iso-contours of heat release rate for a CH
4
/air flame at =1.0 for
a high Re case. (b) Snapshot of experimental observation of a
CH
4
/air flame at =0.9 for a high Re case.
154
Figure 8.10 Iso-contours of total luminescence for a CH
4
/air flame at =1.0
for high Re case overlaid with iso-surfaces of total
luminescence having three different values; a)1e-9; b)1e-8;
c)1.5e-8.
155
Figure 8.11 S
u
estimates using different temperature iso-surfaces for a
CH
4
/air flame at =1.0 for high Re case. S
u
estimated using the
luminescence iso-surface is also presented for the same case.
155
Figure 8.12
Ratio of consumption speed to computed locally along the
flame surface plotted as a function of local stretch rate for three
different ’s for a) CH
4
/air flames and b) C
3
H
8
/air flames.
156
S
u
o
xvii
Figure 8.13 Experimental results for measured flame speeds using area and
angle methods at different inlet Re for CH
4
/air and C
3
H
8
/air
mixtures.
158
Figure 8.14 Simulation results for flame speeds estimated using area and
angle methods at different inlet Re for CH
4
/air and C
3
H
8
/air
mixtures.
160
Figure 8.15
Ratio of for CH
4
/air and C
3
H
8
/air mixtures from
experiments and literature.
162
Figure 9.1 Schematic view of the computation domain. 173
Figure 9.2 Velocity component in x-direction and Temperature as a
function of spatial location. (---) V
upc
; (−) V
pc
; (∙∙∙) T
upc
; (-∙-) T
pc
.
175
Figure 9.3 (a) Temperature contours for the UPC; (b) Streamlines for the
UPC; (c) Temperature contours for the PC; (d) Streamlines for
the PC.
176
Figure 9.4 (a) Streamlines ; (b) Path lines carrying particles depicted at
different times.
178
Figure 9.5 (a) The UPC Fuel Fraction and Temperature as functions of
time; (b) The PC Fuel Fraction and Temperature as functions of
time (-
.
-) CH
4
/Air mixure at 𝜙 = 1.0, T
u
= 300 K and P = 0.1
atm; ( ─) n-C
12
H
26
/Air mixure at 𝜙 = 1.0, T
u
= 300 K and P =
0.1 atm; (---) Temperature.
180
S
u
o
xviii
Abstract
The main focus of this dissertation was the experimental and numerical investigations of
laminar flames of heavy liquid and solid hydrocarbons under simple (one-dimensional,
steady state flow field using canonical configuration) and complex
(two/three-dimensional, transient flow at high Karlovitz number) flow conditions.
A number of theories that have developed based on simplified assumptions and
asymptotic analysis and more important for light fuels such as methane, were examined
both experimentally and numerically in two steady state and canonical configuration,
namely counter-flow configuration and Bunsen flame configuration. The counter-flow
configuration was used to determine laminar flame speeds and extinction strain rates
over a wide range of heavy hydrocarbons including normal alkanes (up to carbon
number 16), practical gasolines and jet fuels and aromatics (cyclopentadiene). The
analytical solution derived from asymptotic analysis provides good agreement for
laminar flame speeds for fuel lean conditions. However notable discrepancies have
been identified for fuel rich conditions due to lack of consideration of fuel-oxygen
differential diffusion especially for heavy fuels for which the molecular weight disparity
between oxygen and fuel is large.
For the Bunsen flame configuration, the area and angle methods were examined to
measure laminar flame speeds of methane/air flames (representative of light fuel) and
propane/air flames given that propane is the lightest hydrocarbon with distinctly higher
xix
molecular weight than oxygen. The results indicated that apart from issues raised from
inlet boundary condition, flame extinction induced complex flow distribution at burner
edge and flame tip effect, such configuration can’t produce quantitative results for fuels
heavier than methane due to lack of consideration of flame speed variation to stretch for
fuel/air mixtures with non-unity Lewis number.
Based on the understanding of the propagation of flames of heavy fuels, accurate
measurements of laminar flame speeds were carried out using the counter-flow
configuration at atmospheric pressure for a variety of complex fuel molecules for which
data are non-existing and which are of direct relevance to practical fuels.
The interaction between a flame and turbulence is a fundamental aspect of combustion.
To further illustrate the difference of flame behaviors between light and heavy fuels, the
vortex laminar flame interaction was studied numerically in a canonical
two-dimensional configuration for methane and n-dodecane flames. The n-dodecane
exhibits early decomposition prior entering the flame due to the local temperature rise
caused by the vortex, and such phenomenon is not observed in methane/air flames.
In summary, the main conclusion of this dissertation is that the fuel complexity that has
been frequently ignored in flame research needs to be accounted for in simple and
complex flows. It was shown that the fuel effects are both of physical and chemical
nature.
1
1 Chapter 1: Introduction
1.1 Background
In desire of heat and light, our modern civilization depends to great extent on
combustion of fuels. As such, its relevance as a field of study has never been of greater
importance. The prosperity and progress of mankind relies on utilizing such energy
source wisely. Developed countries, such as United States, accumulated wealth and
power largely based on fossil fuel utilization. The conflict between emerging
economies and the overwhelming evidence of global warming caused by greenhouse
gases requires burning fuels in a more efficient and environmental friendly way.
Despite the recent booming growth in hybrid and electric automobile market, liquid
fuel accounts for 97% of the energy consumption in the transportation sector. It
indicates that conventional fossil fuel is and will continue being the largest transportation
energy source in the foreseeable future. This is especially true in certain types of
transport mode where high energy density fuel sources are required.
To better achieve the increasing demand for higher energy efficiency and lower
emissions using liquid fuels, extensive research efforts have focused on the compilation
of chemical kinetic models, which serve as a tool in better engine design. Chemical
kinetic models have been investigated extensively for light hydrocarbons in the past and
the implication is to project the knowledge gained from these gaseous fuels onto heavy
2
hydrocarbons that are relevant to practical fuels. The analytical derivation of
combustion properties of gaseous fuels frequently requires approximations and
assumptions that have been established for gaseous fuels and which may not necessary
hold for large molecular weight hydrocarbons. In order to get quantitative results, the
strong coupling between chemical reaction and molecular transport requires detailed
numerical simulations to achieve the desired accuracy.
In light of these issues, the current work aims to quantify errors introduced when
knowledge gained for light hydrocarbon flames is extrapolated to heavy ones, both in
simple and complex canonical flows. The experiments reported in this dissertation were
conducted in idealized flow conditions that can be well controlled and reproduced,
allowing for the enhancement of the fundamental understanding of the chemical and
transport phenomenon that take place during combustion.
1.2 Basic Concepts
1.2.1 Laminar Flame Speed
The laminar flame speed,
o
S
u
, defined as the propagation speed of a steady, laminar,
one-dimensional, planar, adiabatic flame is a fundamental property of any combustible
mixture. It is a measure of the mixture’s reactivity, diffusivity, and exothermicity and
depends primarily on 𝜙 , the temperature of the unburned mixture, and the pressure.
The realization of flame stretch effects on flame propagation and its subsequent
subtraction from the measurements, allowed for the accurate knowledge of
o
S
u
becomes
3
possible and essential towards validating kinetic models [1] and constraining
uncertainties of rate constants [2].
1.2.2 Flame Stretch
Flame stretch, K, is a measure of the Lagrangian rate of flame surface “production”
resulting from its motion and nonuniformities in the underlying flow field. It is defined
at any point on the flame surface as the time derivative of the logarithm of the area, A, of
an infinitesimal element of the surface [3-5]:
dt
dA
A
K
1
K can be also expressed in terms of flow velocity [4]:
) )( V ( v
t
n n K
t t
Where
t
and v
t
are the tangential components of
and v evaluated at the
surface, and n is the unit normal vector of the surface, pointed in the direction of the
unburned gas. V is flame surface velocity, while the flow has a velocity v. The first
term represents the rate of change of the tangential velocity along the flame surface.
The second term represents the stretch by the movement of a curved flame.
For a flame established in the counterflow configuration, stabilization is via the
tangential component of K. For such flames this then reduces to:
r
K
r
v
2
4
where v
r
is the radial velocity and r is the radial coordinate. Using the continuity
equation this can then be related to the velocity gradient in the hydrodynamic zone i.e.:
x
K
x
v
where V
x
is the axial velocity and x is the axial coordinate, respectively.
1.2.3 Flame Extinction
Flame extinction occurs when the time available for chemical reaction becomes less
than the time required to generate sufficient heat for the fresh mixture to reach its ignition
temperature. Heat loss (convective, conductive, or radiative), radical quenching, and
flame stretch are the mechanisms that can cause extinction and they can be synergistic.
The value of K at which extinction occurs is defined as the extinction strain rate, K
ext
.
For premixed flame extinction, if the mixture Lewis number is greater than unity, the
flame temperature decreases as K increases. At certain point, the flame temperature is
not sufficient enough to support the fresh mixture to reach ignition temperature,
extinction occurs. On the other hand, for a mixture with Lewis number less than unity,
flame temperature increases as K increases. The flame is not extinguished until pushed
to the stagnation plane. As K increases even more, incomplete combustion and reactant
leakage results in a drop in the flame temperature and extinction occurs eventually.
For non-premixed flame extinction, the heat release rate is governed by diffusion
process, as stretch rate increases, the diffusion time scale decreases till the point
5
comparable to reaction time scale, and thus followed by incomplete combustion and
reactant leakage which eventually leads to extinction.
1.2.4 Lewis Number
The current state of the art definition for (effective) Lewis number is a weighted
average of the individual Lewis number, 𝐿𝑒
F
(fuel based Lewis number) and 𝐿𝑒
O
(oxidizer based Lewis number), defined as:
𝐿𝑒
eff
= {
(𝐿𝑒
O
+ (1 + 𝜙 ̅
)𝐿𝑒
F
) (2 + 𝜙 ̅
) ⁄ , lean mixture
(𝐿𝑒
F
+ (1 + 𝜙 ̅
)𝐿𝑒
O
) (1 + 𝜙 ̅
) ⁄ , rich mixture
where 𝜙 ̅
is always greater than zero, it is a measure of the mixture deviation from
stoichiometry, defined as:
𝜙 ̅
= {
𝛽 (𝜙 −1
− 1), lean mixture
𝛽 (𝜙 − 1), rich mixture
For a stoichiometric mixture, the Le
eff
is the average of 𝐿𝑒
F
and 𝐿𝑒
O
. For an
off-stoichiometric mixture, the deficient component is more heavily weighted such that
for very lean/rich mixtures the Le
eff
is practically that of the fuel/oxidizer, respectively.
While Le effects have been studied extensively in past pertinent studies, this is not the
case for reactant differential diffusion effect that can be rather important for large MW
fuels as evident from Fig. 1.1 in which the ratio of oxygen to fuel diffusivities is shown to
increase with the fuel carbon number for ϕ = 1.4 n-alkane/air mixtures, while the Le is
nearly unity and barely changed. The differential diffusion effect is generally
6
overlooked and considered secondary when dealing with small MW fuels, the following
chapter is to demonstrate its relative importance to fuels with large MW.
Figure 1.1 Variation of the ratio of oxygen diffusivity to fuel diffusivity with carbon
number for ϕ = 1.4 n-alkane/air mixtures at p = 1 atm and T
u
= 298 K.
1.2.5 Karlovitz Number
Stretch rate K can be often times deceiving when comparing flame speeds under
similar stretch conditions. A more appropriate approach is to use Karlovitz number, Ka,
which is a measure of the ratio of flame time scale, t
f
, respect to aerodynamic time scale,
defined as:
𝐾𝑎 = t
f
𝐾 =
l
f
S
u
0
𝐾 ≡
D
(S
u
0
)
2
𝐾
0
1
2
3
4
5
0 3 6 9 12 15
D
O
2
/ D
fuel
Carbon Number
7
For a fixed burning intensity flame, large Ka indicates that flame experiencing
stronger K and vice versa. Weakly burning flames exposed to the same K as strong
flames, since weak flames exhibit lower
o
S
u
and thus higher Ka, are experiencing more
profound hydrodynamic stretch effect than stronger flames.
1.2.6 Markstein Number
Markstein number, 𝜇 , (or Markstein Length, ℒ, which is the multiplication of
Markstein number and flame thickness, 𝑙 𝑓 = 𝐷 𝑡 ℎ
/S
u
0
) is a measure of sensitivity of
flame speed to stretch 𝑆 𝑓 = S
u
0
− ℒ𝐾 . It is defined as:
𝜇 =
𝜎 𝜎 − 1
∫
𝜆 (x)
x
dx
σ
1
+
𝛽 (Le − 1)
2(𝜎 − 1)
∫
𝜆 (x)
x
ln (
𝜎 − 1
x − 1
) dx
σ
1
in which, 𝜎 = 𝜌 𝑢 𝜌 𝑏 ⁄ is thermal expansion coefficient, 𝐿𝑒 is effective Lewis
number, 𝛽 = E(T
a
− T
u
)/R
o
T
a
2
is the Zeldovich number, 𝜆 (x) =
𝜆 ̃
(x)
𝜆 ̃
u
is scaled thermal
conductivity at given temperature condition.
It determines to what extent the flame speed varies with stretch. For most of the
hydrocarbons, 𝜇 is generally positive and decreases monotonically as the mixture varies
from lean to rich conditions. The large variations among the various fuels at lean
condition are due to the difference in their diffusive properties. For fuel rich conditions,
the effective Le is basically that of oxygen and the difference in 𝜇 mainly attributes to
different values of heat release rate for different mixtures.
8
It should be noted that the application of 𝜇 is only viable at sufficiently low Ka
condition due to the limitation of asymptotic approach where 𝑙 𝑓 is considered order of
magnitude smaller than hydrodynamic thickness. As will be discussed in the following
chapters, when the flow field is at the condition with relatively large Ka i.e. close to
extinction condition, the theoretical prediction is only in qualitatively agreement with the
experimental observations.
1.3 Objectives
The primary objective of this dissertation is to study fuel effects on a variety of
combustion phenomena in simple and complex flows. Among them are those
associated to the global combustion responses of premixed and non-premixed flames as
manifested by the laminar flame speed and extinction stretch rate. The effects of
molecular transport of practical fuels and their surrogate compounds such as
cyclopentadiene, n-dodedecane, n-tetradecane, and n-hexadecane on flame propagation
and extinction was investigated in simple one- and two-dimensional flow configurations.
Fuel effects were investigated also under realistic flow field conditions through direct
numerical simulations of the interactions of a laminar premixed flame and a single vortex
at the scale of the flame thickness during the course of this study.
1.4 References
[1] Law C. K., Sung, C. J., Wang, H., & Lu, T. F. AIAA Journal 41(9) (2003) 1629–1646.
[2] Sheen D. a., & Wang, H. Combustion and Flame 158 (2011) 2358–2374.
9
[3] Law C. K., Symposium (International) on Combustion (1989) 1381–1402.
[4] Matalon M., Combustion Science and Technology 31 (1983) 169-181.
[5] Williams F., Combustion Theory (2nd Editio) (1985).
10
2 Chapter 2: Experimental Approach
2.1 Experimental Setup
The experiments were carried out under atmospheric pressure in the counterflow
configuration [1-4] as schematically shown in Fig. 2.1 along with the details of a typical
burner. For flame propagation and premixed flame extinction measurements, the top
burner is injected with N
2
and bottom burner injected with fuel and air mixture. For
non-premixed flame extinction measurements, the top burner is injected with pure O
2
and
the bottom burner is injected with fuel and N
2
mixture. The top burner is kept at
ambient temperature, and the bottom burner is heated to the desired temperature for each
specific experiment. The burner is designed to include a N
2
co-flow channel
surrounding the nozzle to isolate the main jet. Two different types of burner, namely
contour nozzle and screened straight nozzle are implemented to make sure uniform
velocity profile coming out of the burner exit.
11
Figure 2.1 Representative example of the non-linear extrapolation technique.
The gaseous flow rates were metered using sonic nozzles, which were calibrated
using a dry-test meter with a reported accuracy of ± 0.21%. The upstream pressure of
each sonic nozzle was monitored by a pressure gauge with ± 0.25% precision. The
vaporization system included a precision syringe pump of ± 0.35% accuracy. All gas
lines were heated to prevent fuel vapor condensation. The temperature of the gas lines
was measured with K-type inline thermocouples. The temperature of the unburned
fuel/N
2
stream, T
u
, was measured at the center of the burner exit. The variation of this
temperature is within ± 5 K. Flow composition uncertainty has been determined to be less
than 0.5%. Flow velocity measurements were made by seeding the flow with
12
submicron size silicon oil droplets and by using particle image velocimetry (PIV). The
uncertainty associated with the PIV measurements is within 0.8 to 1.0%.
2.2 Liquid and Solid Fuel Preparation Procedure
The vaporization system included a high precision syringe pump (Harvard, PHD
22/2000) and a glass nebulizer (Meinhard, TR-50-A1) that injected fuel as fine droplets
into a cross-flow of heated air and heated nitrogen for premixed flames and
non-premixed flames respectively. It was determined that the cross-flow injection
configuration minimizes the fluctuations stemming from vaporization, and allows very
efficient mixing of the fuel with the heated gaseous stream. All tubes along the heating
path were wrapped with heating elements and insulation to eliminate cold spots. To
prevent fuel cracking, several inline K-type thermocouples were arranged along the
heating path to ensure that the temperature of fuel/air mixture was maintained below
490 K, which ensured also that the partial pressure of the fuel was lower than its vapor
pressure. The temperature of the unburned mixture, T
u
, was measured at the center of
the burner exit.
A major challenge with solid fuel experiments is that the fuel source is at solid state at
room temperature. Accurate fuel injection becomes difficult with current technology.
As a result, to better perform the experiments with solid fuel, modifications of the
experimental configuration had to be made and are shown schematically in Fig. 2.2.
13
Syringe Pump
Air
Glass Chamber
Preheated Air
Quartz
Nebulizer
Heating Tapes
DCPD
CPD/Air
35℃
200℃
250℃
Air
Air or N2
Glass Chamber
Preheated Air or N2
Quartz Nebulizer
Heating Elements
DCPD
CPD
Camera
Burners
Laser
Heating Tapes
DPIV System
N
2
Co-flow
Fuel/Air
Cooling water for top burner
Optics
Figure 2.2 Schematic of the experiment configuration.
The solid fuel is first melted within a heated oil bath and then injected into a
nebulizer by a high-precision syringe pump. The high-precision syringe pump was
heated at temperatures slightly higher than melting temperature to keep the fuel in the
liquid phase. Uniform size fuel droplets, ranging from 0.5 μm to 5 μm, were produced by
a nebulizer that were mixed and vaporized instantly with portion of the test air instantly
in a glass vaporization chamber heated at 490 K. The rest procedure is similar to those
in liquid fuel experiments with the exception that apart from monitoring system heating
temperature, liquefied fuel temperature lies within the syringe was recorded and the
14
density correction to the corresponding change in temperature was accounted for in the
final mixture composition calculation.
2.3 Reference Flame Speed and Local Strain Rate
In the counterflow configuration, a reference flame speed, 𝑆 u,ref
, is defined as the
minimum velocity upstream of the flame along the stagnation streamline. The imposed
𝐾 is defined upstream of 𝑆 u,ref
as the absolute value of the maximum gradient of the
flow velocity. These points are indicated in Fig. 2.3.
Figure. 2.3: Graphical definition of measurement points in counterflow.
15
There are two subtle and often times overlooked issues with this approach. First,
𝑆 u,ref
and K were obtained separately at adjacent locations close to the flame front.
Second, the choice of these two points in the flow field as markers of a given stretched
flame is mainly due to low level experimental complexity. A local velocity minimum
point and local velocity maximum gradient point are relatively easy to measure as
compared to other equally distinctive locations (i.e. maximum heat release rate point,
maximum H radical concentration point, 1% temperature rise point etc.) and the applied
stretch rate can be systematically extracted.
2.4 Determination of Laminar Flame Speed
o
S
u
’s could be determined, in principle, by plotting 𝑆 u,ref
vs K and extrapolating
linearly the 𝑆 u,ref
data to K = 0 using Markstein formula [5]. However, Tien and
Matalon [6] showed via asymptotic analysis that such relation is nonlinear due to the
presence of thermal expansion. More recently, a non-linear extrapolation using a
computationally assisted approach was developed by Egolfopoulos and coworkers [7-9]
to determine
o
S
u
’s as shown in Fig. 2.4.
16
Figure. 2.4: Representative example of the non-linear extrapolation technique.
As will be discussed in later chapters, by introducing linear or nonlinear extrapolation
to derive
o
S
u
will inherently increase the experimental uncertainty. The uncertainty
will be further augmented as fuel molecular weight deviates from that of air or mixture
equivalence ratio approaches richer condition. The reason for such phenomenon is due
to the assumption limit in deriving analytical solutions [10]. This particular source of
uncertainty could be avoided by comparing experimental data and detail numerical
simulation results directly without further extrapolation [11].
2.5 Determination of Extinction Strain Rate
For the determination of K
ext
of premixed and non-premixed flames, the single flame
configuration instead of twin flame configuration is used due to simplicity in system
40
45
50
55
60
65
70
0 100 200 300 400 500
Reference Flame Speed, S
u,ref
, cm/s
Stretch Rate, K, s
-1
0.02 0.04 0.06 0.08 Ka:
Experimental data
Linear extrapolation
Nonlinear extrapolation
using asymptotic equation
DNS
17
construction; lower fuel consumption rate which requires less heating elements and
controllers; lower Reynolds number and thus minimizing intrinsic flow instabilities; and
lower extinction strain rate for given equivalence ratio due to heat loss towards cold gas
instead of burnt gas. The difference between single flame configuration and twin flame
configuration can be modeled via 1D simulation, the results suggests that the extinction
strain rate is, to the first order, not affected by downstream flow condition [9, 12].
The absolute value of maximum axial velocity gradient in the center line of the flow
field just before flame extinguished is determined to be K
ext
. However, experimental
measurements and 2D simulation show that flow field non-uniformity can cause the
maximum strain rate occur at off center location and local measurements in the center
line are not the representative values of true extinction strain rates as shown in Fig 2.5.
and Fig 2.6. The non-uniform flow field exhibits higher strain rate at the edge of the
flame instead of at the center. This phenomenon is strengthened as the flow rate
increases [13].
18
Figure 2.5: Experimental results comparison of uniform flow field using screened burner
(top) and non-uniform flow field using open burners (bottom)
1
.
1
Open burner composites with screens ~5 Diameter upstream from the burner exit, burner with screens at the exit here
referred as screened burner.
19
(a) (b)
(c) (d)
Figure 2.6: 2D axisymmetric simulation results of open burner opposing jet twin-flame
configuration flame at high strain rate and low strain rate condition. (a) high flow rate
flame and (b) low flow rate flame with adaptive grid resolution; (c) high flow rate flame
and (d) low flow rate flame radial velocity gradient in the tangential direction.
The dynamic behavior of the extinction process can also be viewed with high-speed
camera and images are shown in Fig 2.7. Time t = 0 ms corresponds to the moment the
extinction process initiates. Extinction in open burner is found to initiate at a location
away from the centerline, followed by transition to a propagating edge flame surrounding
the still-burning flame core, and eventually resulting in global extinction at t = 70 ms;
note that unavoidable minor asymmetry in the burner alignment caused the initiation of
20
extinction on the right edge of the images. For screened burners on the other hand,
extinction initiates near the centerline before transitioning to an outwardly propagating
edge flame followed by global extinction at t = 30 ms. It should be noted that both
burners produced flat flame shapes, suggesting that a visual inspection of flame geometry
is not sufficient to ensure flow field quality.
Figure 2.7: Evolution of the extinction process for lean CH
4
/air flames produced by open
burner (a-d) and screened (e-h) burners.
Furthermore, as extinction initiates on the centerline, the direction of edge flame
propagation coincides with that of v
r
while for off-center extinction the edge flame
propagates opposite to v
r
. This results in the different time scales from initiation to
completion of the extinction process, e.g. 30 ms vs. 70 ms, of Fig. 2.7. The locally
off-center extinction transitioning to global extinction in open burner produces Kext
values that are systematically lower because the measured centerline velocity profiles are
not representative of the extinction state. Additionally, the magnitude of flow
non-uniformity has been shown [14] to scale with flow momentum and burner
separation distance as 𝜌 𝑣 𝑥 2
(
𝐷 𝐿 )
2
. For a fixed 𝐿 /𝐷 , extinction of stronger flames (higher
21
𝜙 ) necessitates greater 𝑣 𝑥 . As the stagnation pressure in counterflow is ellipsoidal in
shape [15], the centerline velocity is preferentially decelerated compared to the edges,
enhancing the exit velocity non-uniformity with increasing flow rate.
Based on these evidences, cautious must be taken to ensure uniform flow field
coming out of the burner exit at various temperature, burner diameter, separation distance
and pressure condition. On top of that, the burner exit axial velocity gradient can lead to
discrepancy between experimentally measured strain rate and numerical simulation
results. The reason for such difference is due to the implementation of plug flow
boundary condition in the 1D code [7] and hence updated code packages have been
applied to account for experimentally measured axial velocity gradient at the boundary.
2.6 References
[1] Davis S. G., & Law C. K. Combustion Science and Technology, 140 (1998) 427–449
[2] Law C. K. Symposium (International) on Combustion, (1989) 1381–1402.
[3] Vagelopoulos C. M., Egolfopoulos F. N., & Law C. K. Symposium (International) on
Combustion, 25 (1994) 1341–1347.
[4] Wu C., & Law C. Symposium (International) on Combustion, (1985) 1941–1949.
[5] Bechtold J. K., & Matalon M. Combustion and Flame, 127 (2001) 1906–1913.
[6] Tien J., & Matalon M. Combustion and Flame, 84 (1991) 238-248.
22
[7] Ji C., Dames E., Wang Y. L., Wang H., & Egolfopoulos F. N. Combustion and Flame, 157 (2010)
277–287.
[8] Veloo P. S., Wang Y. L., Egolfopoulos F. N., & Westbrook C. K. Combustion and Flame, 157
(2010) 1989–2004.
[9] Wang Y. L., Holley A. T., Ji C., Egolfopoulos F. N., Tsotsis T. T., & Curran H. J. Proc. Comb.
Inst, 32 (2009) 1035–1042.
[10] Jayachandran J., Zhao R., & Egolfopoulos F. N. Combustion and Flame, 161 (2014) 2305–
2316.
[11] Jayachandran J., Lefebvre A., Zhao R., Halter F., Varea E., Renou B., & Egolfopoulos F. N.
Proc. Comb. Inst, 35 (2015) 695–702.
[12] Wang Y. L., Feng Q., Egolfopoulos F. N., & Tsotsis T. T. Combustion and Flame, 158 (2011)
1507–1519.
[13] Burrel R., Zhao R., Lee D.J., Burbano H., & Egolfopoulos F.N. Proc. Comb. Inst, (2016) under
review.
[14] Niemann U., Seshadri K., & Williams F.A. Combustion and Flame, 162 (2015) 1540-1549.
[15] Sarnacki B. G., Esposito G., Krauss R. H., & Chelliah H. K. Combustion and Flame, 159 (2012)
1026–1043.
23
3 Chapter 3: Numerical Approach
3.1 One Dimensional Modeling
3.1.1 Codes Description
o
S
u
’s and K
ext
’s were computed using the PREMIX code [1,2] and an opposed-jet code
[3,4] respectively. Both are modified to account for thermal radiation of CH
4
, CO, CO
2
,
and H
2
O in the optically thin limit and are coupled with the Sandia CHEMKIN [5] and
Transport [6] subroutine libraries. The H and H
2
diffusion coefficients of several key
pairs are based on the recently updated set of Lennard–Jones parameters [7,8].
For K
ext
computations, a vigorously burning flame was established first, and then K
was increased to achieve extinction. At the extinction state, a two-point continuation
approach solves for K at the state of extinction [9,10]. The experimental values of the
axial velocity gradients at the burner exits, (du/dx)
exit
, burner separation distance, L, and
burner exit temperature, T
u
, were considered as the respective boundary conditions in the
simulation [11].
3.1.2 Mixture-Averaged and Multicomponent Transport Formulations
Both the PREMIX and the opposed-jet codes allow for the use of either
mixture-averaged or multicomponent formulations of transport coefficients. For the
mixture-averaged formulation, the diffusion velocity is assumed to be sum of the
ordinary diffusion velocity, thermal diffusion velocity (for low molecular weight species
24
H, H
2
and He), and a correction velocity. The ordinary diffusion velocity is determined
in the Curtiss-Hirschfelder approximation [12] by given the mixture-averaged diffusion
coefficient. The correction velocity is recommended by Coffee and Heimerl [13] to
insure the mass fraction sum to unity. For the multicomponent option, the transport
property evaluation follows the method described by Dixon-Lewis [14].
Multicomponent diffusion coefficients, thermal conductivities and thermal diffusion
coefficient are computed through the solution of a system of equations involving the
binary diffusion coefficients, the species mole fraction, and the thermodynamic and
molecular properties of the species [15]. The correction velocity is not required in the
multicomponent formulation.
As will be described in later chapters, a recent developed theory for binary diffusion
coefficient of long chain alkanes has been used to compare with experimental
measurements along with original theory which is based on Chapman-Enskog (CE)
expansion employing the Lennard-Jones (LJ) 12-6 potential function. In this new
theory, the drag force due to relative motion of a small cylinder in a dilute gas and in the
free molecule regime was obtained analytically from a rigorous gas-kinetic theory
analysis. The expression for the diffusion binary diffusion coefficient may be derived
from the Einstein relation (or the Einstein-Smoluchowski relation) via the drag
coefficient, that is, the diffusion coefficient is equal to the drag force divided by the drift
velocity [16].
25
It should also be noted that the mixture-averaged transport formulation of the original
Sandia PREMIX and OPPDIF codes does not consider the Soret effect of large/heavy
molecules even if the thermal diffusion is considered. To account for thermal diffusion
of heavy fuel molecules, the approximation of Rosner et al. [17] for the thermal diffusion
factor α
T
was implemented into the mixture-averaged formulation. The thermal
diffusion factor of species B in A takes the form of
𝛼 𝑇 = [0.454 ∙ 𝑑 (Λ + 0.261) + 0.116(Λ − 1)][1 − 𝐶 𝑇 ⁄ ],
where Λ is related to molecular size disparity, which may be evaluated by Λ ≅
1.31 Sc (1 + d)
−1/2
, Sc is the Schmidt number, d = (M
B
-M
A
)/(M
B
+M
A
) is the normalized
molecular mass disparity, and 𝐶 = 1.45[𝘀 𝐵𝐴
𝑘 𝐵 ⁄ − 85]
For the cases considered here, C/T ≪ 1 and thus the temperature correction is
unimportant.
3.1.3 Sensitivity Analysis Methodology
A logarithmic sensitivity function is defined as:
𝑑 (log𝐴 )
𝑑 (log𝐵 )
where A is the dependent variable and B is the perturbing variable. The advantage of
this approach is to allow comparisons between parameters i.e. 𝐵 𝑖 and 𝐵 𝑗 in a
dimensionless form and isolate the effect of one source from another. It also indicates
the relative “strength” of the influence of perturbing variable. The value greater than
26
unity is considered influential while value less than a fraction of unity is considered not
very important.
In combustion research, to assess the effects of chemical kinetics and molecular
diffusion on
o
S
u
and K
ext
. Sensitivity analysis is used to provide insight and help to
interpret the results from simulation, i.e.
𝑑 (log𝑆 𝑢 𝑜 )
𝑑 (log𝐴 𝑖 )
=
𝐴 𝑖 𝑆 𝑢 𝑜 𝜕 𝑆 𝑢 𝑜 𝜕 𝐴 𝑖
It calculates the logarithmic sensitivity coefficient of laminar flame speed with respect to
each individual reaction rate. Similar procedure can be done to analyze chemical and
transport effect with respect to K
ext
, which is originated by Dong and Holley [7, 18]
where the dependent variable is the maximum axial velocity gradient close to extinction
condition and the perturbing variable can be either chemical reaction rate or molecular
diffusivity of certain species.
As will be discussed in later chapters, a “brute force” approach is implemented to
determine the sensitivity of extinction strain rate with respect to thermal diffusion
coefficient in order to study the soret effect of heavy hydrocarbon in non-premixed
flames. It takes the form:
𝑑 (log𝐾 𝑒𝑥𝑡 )
𝑑 (log𝐷 𝑘 𝑇 )
=
𝐷 𝑘 𝑇 𝐾 𝑒𝑥𝑡 𝜕 𝐾 𝑒𝑥𝑡 𝜕 𝐷 𝑘 𝑇
where 𝐷 𝑘 𝑇 is the thermal diffusion coefficient of K
th
species.
27
3.2 Three Dimensional Modeling
3.2.1 Codes Description
The reduction of partial differential equations into algebraic equations still leaves
their method of solution an open question. Traditional 1-D and 0-D combustion codes
have employed non-linear techniques to great effect [19]. These principally involve
defining a residue for each algebraic equation and finding its roots via a modified Newton
method, retaining the coupling between all primitive variables during each iteration.
This approach cannot be easily extended to notably more complex geometries as the size
and number of operations of the matrices when using implicit methods very quickly
becomes prohibitive. An alternative is to linearize the algebraic equations such that
each is assumed to contain only one unknown while all others are substituted with
available guesses and iterated over until all the equations are satisfied [20]. This
linearized “predictor-corrector” approach is a widely used template in most finite volume
based solvers. Cuoci et al have released 'laminarSMOKE' [21] (A Cuoci et al. 2011), a
finite-volume based code built using the OpenFOAM [22] suite of CFD tools and the
OpenSMOKE library [23] of functions that handles detailed chemistry and transport
while offering an interface to various ODE solvers.
The stiff chemistry is handled by laminarSMOKE’s operator splitting algorithm, first
introduced by Strang [24]. The problem’s reaction step is thus a spatial array of
homogeneous reactors with appropriate initial conditions whose time integration is
28
handled by standard ODE solvers [25]. The momentum equation is solved via the PISO
algorithm (Pressure Implicit with Splitting of Operators) [26] - used for the
pressure-velocity coupling - to complete the algorithm for solving the discretized
conservation equations. Thermodynamic, transport and kinetic quantities were
evaluated using the OpenSMOKE library.
3.2.2 Mesh Generation Methodology
An example of grid generation is shown in Fig. 3.1, with axisymmetric grid layout
and a radius of 6 cm and height of 20 cm is used in the numerical simulations. The
approximate flame height and thickness are estimated using the 1-D calculations. The
initial grid is constructed to be uniform in the area where the flame is expected to reside.
The grid spacing in this region is set to be about 3 cells per flame thickness.
29
Figure 3.1. Computational grid used in the numerical simulations overlaid with
boundary conditions applied for pressure, temperature, velocity, and chemical species.
A stretched non-uniform grid is utilized outside of this refined area. An initial
non-reacting flow-field is established following which the mixture is ignited and the
simulation is carried on until a steady-state solution for the flame is reached.
Steady-state is established by ensuring that residuals for pressure, temperature, and
velocity have reached a constant value. Further, the flame position and height are
observed to be constant. At this point, an adaptive mesh refinement is performed at the
flame front to increase the grid resolution in that location. The location of the flame
30
front is determined by computing the gradient and curvature of the temperature field.
The simulation results from steady state are mapped on to the refined grid and
computations are performed till a new steady state is achieved. This sequence of steps
is carried out repeatedly till a highly refined flame region is established with an average
of 70-80 cells through the flame thickness for each condition investigated. This level of
refinement is considered adequate for the laminar conditions investigated in this work.
Figure 3.2 shows a plot of temperature as a function of distance along a 1-D cut through
the flame for a CH4-air mixture with =0.80 at the high Re condition. The data points in
Fig. 3.2 correspond to individual grid points illustrating the refinement achieved in the
solution through the flame thickness.
Figure 3.2. Temperature as a function of distance along a 1-D cut through the flame
front for a CH4/air mixture with =0.80 at the high Re condition.
31
3.3 Kinetic Models
3.3.1 Models Used in Current Study
In order to address the liquid and solid fuel molecule oxidation and pyrolysis
procedure, detail mechanism has been adopted in the current dissertation. The majority of
the simulation is conducted using USC Mech II consisting 111 species and 784 reactions
[27] and JetSurF 1.0 kinetic model consisting of 348 species and 163 reactions [28]. GRI
3.0 is used for natural gas related combustion simulation which consists 53 species and
325 reactions [29]. A skeletal mechanism based on a detailed C8-C16 n-alkane
high-temperature kinetic model developed by Westbrook et al. [30] for n-alkanes up to
n-C
16
H
34
is used, consisting of 157 species and 1161 reactions. For gasoline and its
surrogates simulation, a reduced 679 species and 3479 reaction mechanism by Westbrook
et al.[31] is used and followed by a further reduced 323 species version mechanism for
the Oppose-Jet simulation due to computation limitation. For solid fuel simulation, a
detailed kinetic model for jet fuel surrogates that include oxidation kinetics of toluene is
adopted [32] and compared with results from USC Mech II. A recent developed lump
model for jet fuel is used to validate against experiments regarding the assumption of
separation between pyrolysis process and combustion reaction in the vigorous burning
system.
32
3.3.2 Kinetic Model Reduction Using Directed Relation Graph Method
Detailed kinetic models for large hydrocarbons involve typically hundreds of species
and thousands of reactions to describe fuel oxidation and pyrolysis. However, as the
computational time scales with the square of number of species, it is desirable to produce
skeletal reduction with the elimination of unrelated species and reactions to the given
system. The method employed here to reduce chemical models is the Directed Relation
Graph (DRG) [33] which include solution sets from freely propagating flames, stretched
flames and close to extinction flames.
DRG seeks to resolve the coupling between major and minor species. Major species
are identified a priori and can be, for example, the fuel. The extent of the coupling is
quantified by:
𝑟 AB
≡
∑ |𝜈 A,i
𝜔 𝑖 𝛿 B,i
|
i=1,II
∑ |𝜈 A,i
𝜔 i
|
i=1,II
𝛿 B,i
= {
1 ,
0 ,
if the ith reaction involves species B
otherwise
where 𝜈 A
is the net stoiciometric coefficient of species A and 𝜔 is the net reaction rate.
Thus, r
AB
represents the relative error induced to A upon the elimination of B. The
user specifies an error tolerance, 𝘀 , defined such that B is considered important to A for
𝑟 AB
> 𝘀 . All species for which this relationship is not true are removed from the model,
generating a skeletal mechanism.
33
Recent modification includes the solution from both stretched flames and flames at
close to extinction condition [34]. The reason for such modification is due to the findings
of molecular differential diffusion phenomena in combustion process that the local
concentration of fuel to oxygen ratio may vary at close to the flame front location and
stretched flames may take drastically different reaction path than stretch-less flames.
3.4 References
[1] Grcar J. F., Kee R. J., Smooke M. D., & Miller J. A. Symposium (International) on Combustion,
21 (1988) 1773–1782.
[2] Kee R.J., Grcar J.F., Smooke M.D., & Miller J.A. Sandia Report SAND85-8240, Sandia
Natioanl Laboratories. (1985).
[3] Egolfopoulos F., & Campbell C. Combustion and Flame, 117 (1999) 206–226.
[4] Kee R.J., Rupley F.M., and Miller J.A. Sandia Report SAND89-8009, Sandia National
Laboratories. (1989).
[5] Kee R.J., & Miller J.A. Sandia Report SAND86-8841, Sandia National Laboratories. (1986).
[6] Kee R.J., Warnatz J., & Miller J.A. Sandia Report SAND83-8209, Sandia National Laboratories.
(1983).
[7] Dong Y., Holley A. T., Andac M. G., Egolfopoulos F. N., Davis S. G., Middha P., & Wang H.
Combustion and Flame, 142 (2005) 374–387.
34
[8] Middha P., & Wang H. Combustion Theory and Modelling, 9 (2005) 353–363.
[9] Egolfopoulos F. N., & Dimotakis P. E. Symposium (International) on Combustion, 27 (1998)
641–648.
[10] Nishioka M., Law C. K., & Takeno T. Combustion and Flame, 104 (1996) 328–342.
[11] Ji C., Dames, E., Wang Y. L., Wang H., & Egolfopoulos F. N. Combustion and Flame, 157
(2010) 277–287.
[12] Curtiss C. F., & Hirschfelder J. O. The Journal of Chemical Physics, 17 (1949) 550.
[13] Coffee T., & Heimerl J. Combustion and Flame, 43 (1981) 273–289.
[14] Dixon-Lewis G. Proceedings of the Royal Society of London A: Mathematical, Physical and
Engineering Sciences, 307 (1968) 111–135.
[15] Glarborg P., Miller J. A., & Kee R. J. Combustion and Flame, 65 (1986) 177–202.
[16] Einstein A. Annalen der Physik 17 (1905) 549-560.
[17] Rosner D., Israel R., & La Mantia B. Combustion and Flame, 123 (2000) 547–560.
[18] Holley A. T., You X. Q., Dames E., Wang H., & Egolfopoulos F. N. Proc. Comb. Inst, 32
(2009) 1157–1163.
[19] Kee, R. J., Coltrin, M. E., & Glarborg, P. (2005). Chemically reacting flow: theory and practice.
John Wiley & Sons.
35
[20] Peric, M. (1996). Computational methods for fluid dynamics. Heidelberg: Springer —Verlag.
[21] A. Cuoci, A. Frassoldati, T. Faravelli, E. Ranzi, Combust. Flame 160 (2013) 870-886
[22] OpenFOAM, www.openfoam.org, 2014
[23] A. Cuoci et al., OpenSMOKE: numerical modeling of reacting systems with detailed kinetic
mechanisms, in: XXXIV Meeting of the Italian Section of the Combustion Institute, Rome, Italy,
2011.
[24] G. Strang, SIAM Journal on Numerical Analysis 5 (1968), 506-517
[25] P. N Brown, G. D. Byrne, A. C. Hindmarsh, SIAM journal on scientific and statistical
computing 10(5) (1989), 1038-1051
[26] R.I Issa, Journal of Computational Physics, 62 (1986) 40-65
[27] Wang H., You X., Joshi A.V., Davis S.G., Laskin A., Egolfopoulos F.N., and Law C.K.(2007)
(http://ignis.usc.edu/USC_Mech_II.htm)
[28] Wang H., Dames E., Sirjean B., Sheen D.A., Tangko R., Violi A., Lai J.Y.W., Egolfopoulos
F.N., Davidson D.F., Hanson R.K., Bowman C.T., Law C.K., Tsang W., Cernansky N.P., Miller
D.L., and Lindstedt R.P. (2010) (http://melchior.usc.edu/JetSurF/JetSurF2.0)
[29] Smith G. P., Golden D. M., Frenklach M., Moriarty, N. W., Eiteneer, B., Goldenberg M.,
Gardiner Jr, W. C. (1999). GRI-Mech 3.0.
36
[30] Westbrook, C. K., Pitz, W. J., Herbinet, O., Curran, H. J., & Silke, E. J. Combustion and Flame,
156 (2009) 181–199.
[31] Mehl M., Pitz W. J., Westbrook C. K., & Curran H. J. Proc. Comb. Inst, 33 (2011) 193–200.
[32] Dooley S., Won S. H., Chaos M., Heyne, J., Ju Y., Dryer F. L., Oehlschlaeger M. A.
Combustion and Flame, 157 (2010) 2333–2339.
[33] Lu T., & Law C. K. Combustion and Flame, 144 (2006) 24–36.
[34] Jayachandran J., Lefebvre A., Zhao R., Halter F., Varea E., Renou B., & Egolfopoulos F. N.
Proc. Comb. Inst, 35 (2015) 695–702.
37
4 Chapter 4: Determination of Laminar Flame Speeds: Molecular
Transport Effects
4.1 Introduction
As discussed in Chapter 1,
o
S
u
is a fundamental property of any combustible mixture
and it serves to constrain and validate kinetic models [1,2].Furthermore,
o
S
u
along with
the Markstein length, L, which characterizes the response of laminar flame propagation to
stretch, are inputs in turbulent flame models under conditions that the flamelet concept is
applicable [3-5].
Measurement of
o
S
u
began as early as in the 1920’s when Stevens [6,7] studied
flame propagation at constant pressure by tracking spherically expanding flames, SEF, in
a soap bubble filled with a flammable mixture. Since then, significant progress has been
made both in the experimental and numerical determination of
o
S
u
. However, notable
scatter by as much as 25 cm/s was persistent in published
o
S
u
’s of methane flames [8] until
the 1980’s when the effect of flame stretch [9] on flame propagation was accounted for
and subtracted from the measurements reducing thus the experimental uncertainty
notably [10-13]. Despite this progress, due to the relatively low sensitivity of
o
S
u
to
chemical kinetics [14], there is need for experimental data with even lower uncertainty
compared to what is reported currently so that they can be used for kinetic model
validation.
38
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0.35 0.4 0.45 0.5 0.55 0.6 0.65
Flame Speed, Deviation from a reference
Normalized Equivalence Ratio, Φ = ϕ/(1+ ϕ)
Kumar
Kelly
Smallbone
Ji et al. Baseline
Figure 4.1. Deviation of experimental
o
S
u
’s of n-heptane/air mixtures at p = 1 atm from
that of Ji et al. [16] (T
u
= 353 K) represented by the solid line. Data represented by
symbols include: ( ●) Kelley et al. [17] (T
u
= 353 K), ( ♦ ) Smallbone et al. [18]
(T
u
= 350 K) and (x) Kumar et al. [19] (T
u
= 360 K).
Despite the fact that considerable effort has been devoted to understanding the
intricacies and physics behind the measurements, significant discrepancies persist in
reported data, even when using the same method. Figure 4.1 depicts the relative
deviation of experimental
o
S
u
with a normalized equivalence ratio ϕ/(1+ ϕ) [15],
where ϕ is the equivalence ratio, of n-heptane/air mixtures reported in different studies
from the data of Ji et al. [16] that are used as the reference value. One can observe the
39
increasing discrepancy between data obtained using the SEF [17] and counter flow
flames, CFF, [18,19] configurations for off-stoichiometric ϕ > 1 mixtures; corrections of
the data reported in Refs. 18 and 19 to account for the different unburned mixture
temperatures, T
u
, were made using the recommendation of Wu et al. [20]. It is evident
that the disparity between the
o
S
u
data sets increases with ϕ and this trend persists for
flames of several high molecular weight, MW, fuels [16]. For ϕ > 1 hydrocarbon/air
mixtures, air is abundant on both mass and molar basis compared to the fuel. Thus, the
thermal diffusivity of the mixture is nearly that of nitrogen, and hence a Lewis number,
Le, calculated based on oxygen, being the deficient reactant for ϕ > 1 mixtures, will be
close to unity as shown in Fig. 4.2a regardless of the fuel MW.
40
(a) (b)
Figure 4.2. (a) Variation of Le with carbon number for n-alkane/air mixtures at p = 1 atm
and T
u
= 298 K, for ϕ = 0.7 (dashed line) and ϕ = 1.4 (solid line). (b) Variation of the
ratio of oxygen diffusivity to fuel diffusivity with carbon number for ϕ = 1.4 n-alkane/air
mixtures at p = 1 atm and T
u
= 298 K.
These inconsistencies point to possible uncertainties in the experimental
determination of
o
S
u
, and could be associated with the reactant flow rates, i.e. ϕ, diagnostic
equipment, the flow velocity measuring approach, data analysis, and finally data
interpretation. In order to tackle uncertainties associated with each experimental
approach, detailed understanding of the physics controlling the flame behavior and
response to fluid mechanics and loss mechanisms is required.
At pressures less than 10 atm,
o
S
u
can be measured using the CFF approach in which
steady, laminar, and planar flames (e.g. [5,13]) are established. Under such conditions,
41
the only parameter that can be varied for a given set of thermodynamic conditions is the
flame stretch, and this effect can be characterized readily using available quasi-one
dimensional codes (e.g. [22]).
Law and co-workers introduced the CFF approach to determine
o
S
u
[5,13,23]. The
method involves the determination of the axial velocity profile along the system
centerline and subsequently the identification of two distinct observables. A reference
flame speed, Su,ref, which is the minimum velocity just upstream of the flame, and a
characteristic stretch, K, which is the maximum absolute value of the axial velocity
gradient in the hydrodynamic zone. Thus, by varying Su,ref with K in the experiments,
it was proposed [5,13,23] that
o
S
u
can be determined by performing a linear
extrapolation of the experimental data to zero stretch given that as K 0, Su,ref should
degenerate to
o
S
u
. This approach was used in several studies (e.g., [24-26]) for H2 and
C1-C2 hydrocarbon flames.
Subsequently, Tien and Matalon [27] demonstrated through asymptotic analysis that
the S
u,ref
vs. K response is non-linear as K 0, and that linear extrapolation of S
u,ref
to
K = 0 results in the over-estimation of
o
S
u
; it should be noted that S
u,ref
is not the stretched
flame speed, Su, as it is affected by thermal dilatation and flow divergence effect
[13,27,28]. Tien and Matalon [27] produced also a non-linear expression describing the
variation S
u,ref
with K, which subsequently was expressed by Davis and Law [29] in a
more compact way as:
42
S
u,ref
=
o
S
u
{1 – ( -1) Ka + Ka ln[( - 1)/Ka]}. (1)
In Eq. 1, is the Markstein number, Ka K / (
o
S
u
)
2
the Karlovitz number, 𝛼 the
thermal diffusivity of the mixture, and 𝜎 (
u
/
b
) with
u
and
b
being the densities of
the unburned and burned states at equilibrium respectively.
Chao et al. [30] used asymptotic analysis to show that the error introduced by linear
extrapolations can be reduced for small Ka and large burner separation distance relative
to the flame thickness. Vagelopoulos et al. [31] further showed computationally and
experimentally that in order for the linear extrapolation to be accurate, Ka must be of the
order of 0.1 for CH
4
/air, C
3
H
8
/air, and lean H
2
/air flames.
Recently, Egolfopoulos and co-workers [16,32,33] introduced a computationally
assisted approach in quantifying the non-linear variation of S
u,ref
with K. Specifically,
direct numerical simulations (DNS) of the experiments are carried out with detailed
description of molecular transport and chemical kinetics to avoid simplifying
assumptions used in asymptotic analysis. Thus, the variation of S
u,ref
with K is
computed and can be used to perform the non-linear extrapolations of the experimental
data; indeed the DNS approach reproduces the non-linear behavior of S
u,ref
with K as
predicted by Tien and Matalon [27]. Given that the computed S
u,ref
vs. K curve may lie
over or below the data due to transport and kinetic model uncertainties, it was shown that
as long as the discrepancies between data and predictions are not large, say within
30-40%, the shape of the S
u,ref
vs. K curve is minimally affected and could be translated
43
to best fit the data and derive
o
S
u
at K = 0. This was confirmed through DNS in which
the rates of main H+O2 OH+O branching or CO+OH CO2+H oxidation reactions
as well as the diffusion coefficients of the reactants were modified intentionally by as
much as 30-40%. It was shown that even under such notable but not excessive
modifications of the overall reaction rate, the shape of the computed S
u,ref
vs. K curves are
nearly indistinguishable [32].
Ji et al. [16] showed that for the same sets of experimental data of C5-C12 n-alkanes,
linear extrapolation yield higher
o
S
u
’s for fuel rich mixtures, as compared to nonlinear
extrapolation using the computationally assisted approach. Considering also the results
shown in Fig. 4.1, it is reasonable to assume that the discrepancies between reported
o
S
u
’s
for ϕ > 1 mixtures could be attributed partially to the extrapolations.
4.2 Numerical Approach
In order to assess the validity of current practices in determining
o
S
u
, detail numerical
simulation were performed using a variety of codes and detailed description of chemical
kinetics and molecular transport. The DNS results were treated as “data” for the range
of K’s that are typically used in both types of experiments, and subsequently Eqs. 1 was
used to perform extrapolations. The advantage of this approach is that both the response
of flame propagation to K from high to near-zero values and
o
S
u
are known so that the
merits and shortcomings of Eqs. 1 can be assessed.
44
Furthermore, the DNS approach allows for the rigorous assessment of reactant
differential diffusion effects. A parametric study was performed on the effect of the fuel
diffusivity on the response of CH
4
/air flames to K given the relatively small size of the
kinetic model and the fact that diffusivities of CH
4
and O
2
do not differ substantially.
The variation of the CH
4
diffusivity was implemented through modification of its
Lennard-Jones (L-J) parameters. The unperturbed case is referred to as OD (original
diffusivity). ID (increased diffusivity) and DD (decreased diffusivity) refer to the cases
in which the L-J parameters of CH
4
were replaced with those of H
2
and n-C
12
H
26
respectively. This approach ensures that the chemistry is consistent in all computations,
and also circumvents the complexities associated with fuel cracking which high MW
fuels are susceptible to. The values of Le and ratio of fuel to oxygen diffusivities in the
mixture are shown in Table 4.1 for ϕ = 0.7, 1.0, and 1.4. DNS were performed also for
steady n-C
12
H
26
/air flames in order to verify the results obtained from CH
4
/air flames.
45
Table 4.1. Lewis number, Le and ratio of fuel to O
2
diffusivities for the mixtures used in
the present study.
ϕ Le D
fuel
/D
O2
Original L-J Parameters (OD)
0.7 1.0 1.14
1.0 N/A 1.16
1.4 1.1 1.17
n-C
12
H
26
L-J Parameters (DD)
0.7 2.3 0.45
1.0 N/A 0.48
1.4 1.0 0.51
H
2
L-J Parameters (ID)
0.7 0.7 1.67
1.0 N/A 1.67
1.4 1.2 1.68
o
S
u
’s and variation of S
u,ref
with K were computed respectively, using the PREMIX
code [55,56] and an opposed-jet flow code [57] that was originally developed by Kee and
co-workers [22]. Both codes were integrated with the CHEMKIN [58] and the Sandia
transport [59,60] subroutine libraries. The H and H
2
diffusion coefficients of several
46
key pairs are based on the recently updated set [61]. Both codes have been modified to
account for thermal radiation (OTL) of CH
4
, CO, CO
2
, and H
2
O [57,62].
o
S
u
’s and the variation of S
u,ref
with K were computed using the USC-Mech II [63] and
JetSurF 1.0 [64] kinetic models for CH
4
/air and n-C
12
H
26
/air flames respectively. The
simulations were performed for the twin flame configuration and for a large burner
separation distance (10 cm) to avoid conductive heat loss to the burner at very low K’s.
4.3 Results and Discussion
Figure 4.3 depicts the variation of
o
S
u
with ϕ for CH
4
/air mixtures for various CH
4
diffusivities, D
CH4
, while in Fig. 4.4 the logarithmic sensitivity coefficients of
o
S
u
to the
CH
4
-N
2
and O
2
-N
2
binary diffusion coefficients are shown. Results indicate that the
modification of D
CH4
has an opposite effect on
o
S
u
for ϕ < 1.0 and ϕ ≥ 1.0.
47
5
10
15
20
25
30
35
40
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Laminar Flame Speed, (cm/s)
Equivalence Ratio,
Figure 4.3. Computed
o
S
u
’s of CH
4
/air flames at p = 1 atm and T
u
= 298 K using
USC-Mech II. ( ─) OD; (---) DD; (-
.
-) ID.
48
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
ϕ=1.4
ϕ=1.0
ϕ=0.7
Figure 4.4. Logarithmic sensitivity coefficients of
o
S
u
to the CH
4
-N
2
(red) and O
2
-N
2
(blue) binary diffusion coefficients for CH
4
/air flames at p = 1 atm, T
u
= 298 K, and
various ϕ’s.
49
(a) (b)
Figure 4.5. (a) Normalized mass fraction profiles of CH
4
( ┄) and O
2
( ─), and CH
4
consumption rate profile ( ─ ) for a = 1.4 freely propagating CH
4
/air flame at
T
u
= 298 K and p = 1 atm, computed using USC-Mech II and OD. (b) Normalized mass
fraction profiles of CH
4
( ┄) and O
2
( ─), and CH
4
consumption rate profile ( ─) for a
freely propagating flame at T
u
= 298 K, p = 1 atm, and = 1.4, computed using
USC-Mech II and DD.
Details of the flame structure are shown in Fig. 4.5, and it can be seen that a change
in D
CH4
results in a corresponding change in its diffusion length relative to O
2
. The
diffusion length of CH
4
for a ϕ = 1.4 CH
4
/air flame computed with DD (Fig. 4.5b) is
reduced compared to the OD case (Fig. 4.5a). Thus, Y
CH
4
and the local equivalence ratio,
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2
CH
4
Consumption Rate (mole/cm
3
· s)
Normalized Mass Fraction
Spatial Location (cm)
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2
Spatial Location (cm)
CH
4
Consumption Rate (mole/cm
3
· s)
Normalized Mass Fraction
50
ϕ
local
, increase at the location at which the CH
4
consumption initiates as shown in Fig. 4.6,
which results in the reduction of reactivity, shown also in Fig. 4.6.
Figure 4.6. Variation of ϕ
local
with temperature in a ϕ = 1.4 freely propagating CH
4
/air
flame at p = 1 atm, and T
u
= 298 K computed using USC-Mech II with OD ( ●) and DD
( ■), and variation of CH
4
consumption rate with temperature with OD ( ─) and DD
(-
.
-).
Similar analysis can be used to explain the dependence of
o
S
u
on D
CH4
for all
mixtures shown in Table 4.1. Furthermore, it is of interest to note that the dependence
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
0.6
0.8
1
1.2
1.4
1.6
1.8
2
300 500 700 900 1100 1300 1500 1700 1900
CH
4
Consumption Rate (mole/cm
3
· s)
Local Equivalence Ratio,
local
Temperature (K)
51
of
o
S
u
on D
CH4
is not captured by the following equation that is based on Le
considerations [76]:
o
S
u
(Le ≠ 1) =
o
S
u
(Le = 1) Le (3)
The effect of reactant differential diffusion on the propagation of stretched flames
was assessed in the CFF configuration. Figures 4.7-4.9 depict the variation of S
u,ref
/
o
S
u
with Ka for ϕ = 0.7, 1.0, and 1.4 mixtures respectively. These figures include also the
extrapolation curves using Eq. 1 that fit the DNS results for a range of Ka that are
representative of those used in experiments (e.g. [27, 29]). Using OD, Eq. 1 predicts
closely the DNS results. As D
CH4
starts deviating from the oxygen diffusivity, D
O2
, for
the ID and DD cases, a discrepancy is observed between the extrapolated
o
S
u
from its
known value by as much as 5% for ϕ = 0.7 with ID and 30% for ϕ = 1.4 with DD.
52
Figure 4.7. Variation of S
u,ref
/
o
S
u
with Ka of a ϕ = 0.7 CH
4
/air CFF at p = 1 atm and
T
u
= 298 K computed using USC-Mech II with ID ( ■), OD ( ●), and DD ( ▲). ID (-
.
-),
OD ( ─), and DD (---) correspond to fitting using Eq. 1. The full range DNS results are
shown in hollow symbols, while the DNS results used for fitting Eq. 1 are shown in solid
symbols.
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
0 0.05 0.1 0.15 0.2 0.25
S
u,ref
/S
u
o
Karlovitz number , Ka
53
Figure 4.8. Variation of S
u,ref
/
o
S
u
with Ka of a ϕ = 1.0 CH
4
/air CFF at p = 1 atm and
T
u
= 298 K computed using USC-Mech II with ID ( ■), OD ( ●), and DD ( ▲). ID (-
.
-),
OD ( ─), and DD (---) correspond to fitting using Eq. 1. The full range DNS results are
shown in hollow symbols, while the DNS results used for fitting Eq. 1 are shown in solid
symbols.
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
0 0.02 0.04 0.06 0.08 0.1
S
u,ref
/S
u
o
Karlovitz number , Ka
54
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
S
u,ref
/S
u
o
Karlovitz number , Ka
Figure 4.9. Variation of S
u,ref
/
o
S
u
with Ka of a ϕ = 1.4 CH
4
/air CFF at p = 1 atm and
T
u
= 298 K computed using USC-Mech II with ID ( ■), OD ( ●), and DD ( ▲). ID (-
.
-),
OD ( ─), and DD (---) correspond to fitting using Eq. 1. The full range DNS results are
shown in hollow symbols, while the DNS results used for fitting Eq. 1 are shown in solid
symbols.
From Figs. 4.7-4.9 it is apparent also that there is a significant change in slope of the
S
u,ref
/
o
S
u
vs. Ka curve when D
CH4
is modified for the ϕ = 0.7 and 1.4 mixtures. In CFF’s,
it is not possible to monitor the modification of the burning intensity with K by simply
tracking the variation of S
u,ref
with K, as S
u,ref
is affected also by thermal dilatation and
55
flow divergence [13,28,29]. On the other hand, the burning intensity is best described
by the total heat release rate per unit area, HRR
tot
, obtained by integrating the heat release
rate over the entire flame. Figures 4.10-4.12 depict the variation of HRR
tot
with Ka for
ϕ = 0.7, 1.0, and 1.4 mixtures respectively. The results for the ϕ = 0.7 mixture shown in
Fig. 10 can be explained based on Le ≠ 1.0 effects caused by the imbalance of energy
loss from and energy gain by the reaction zone [76]. For the ϕ = 1.4 mixture however,
even though Le 1.0 for all hydrocarbons, a substantial increase in HRR
tot
with Ka is
seen for the DD case for which there is a notable difference between D
CH4
and D
O2
.
Thus, the diffusion rate of O
2
towards the reaction zone increases compared to CH
4
with
increasing K, making thus the mixture more stoichiometric and increasing the overall
reactivity [76]. For the ϕ = 1.0 mixture the slope of HRR
tot
with Ka does not change for
the different D
CH4
values. This is due to the fact that for near-stoichiometric mixtures
there is a minor sensitivity of the overall reactivity to modifications in ϕ as it reaches a
maximum value.
56
Figure 4.10. Variation of HRR
tot
with Ka of a ϕ = 0.7 CH
4
/air CFF at p = 1 atm and
T
u
= 298 K computed using USC-Mech II with ID (-
.
-), OD ( ─), and DD (---).
0
10
20
30
40
50
60
0 0.05 0.1 0.15 0.2 0.25
Total Heat Release Rate (J/cm
2
· s)
Karlovitz number , Ka
57
Figure 4.11. Variation of HRR
tot
with Ka of a ϕ = 1.0 CH
4
/air CFF at p = 1 atm and
T
u
= 298 K computed using USC-Mech II with ID (-
.
-), OD ( ─), and DD (---).
0
20
40
60
80
100
120
140
160
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Total Heat Release Rate (J/cm
2
· s)
Karlovitz number , Ka
58
Figure 4.12. Variation of HRR
tot
with Ka of a ϕ = 1.4 CH
4
/air CFF at p = 1 atm and
T
u
= 298 K computed using USC-Mech II with ID (-
.
-), OD ( ─), and DD (---).
Figures 4.13 and 4.14 depict the variations of ϕ
local
and the consumption rate of CH
4
for a ϕ = 1.4 flame at K = 30 and 200 s
-1
respectively and computed with OD and DD.
The results confirm that as K increases, ϕ
local
decreases at the locations at which the CH
4
consumption begins. As a result, there is a notable increase of the CH
4
consumption
rate as K increases for the DD case compared to OD. More specifically, the maximum
CH
4
consumption rate is about 40% higher for the DD case for K = 30 s,
-1
and by a factor
0
10
20
30
40
50
60
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Total Heat Release Rate (J/cm
2
· s)
Karlovitz number , Ka
59
of 3.5 for K = 200 s.
-1
These results reveal the basis physics that control the dependence
of the overall flame reactivity with stretch for rich mixtures of high MW fuels and which
need to be accounted for when raw experimental data are interpreted to determine
non-directly measured properties such as
o
S
u
.
Figure 4.13. Variation of ϕ
local
with temperature in a ϕ = 1.4 CH
4
/air CFF at p = 1 atm,
T
u
= 298 K, and K = 30 s
-1
computed using USC-Mech II with OD ( ●) and DD ( ■), and variation
of CH
4
consumption rate with temperature with OD ( ─) and DD (-
.
-).
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
0.6
0.8
1
1.2
1.4
1.6
1.8
2
300 500 700 900 1100 1300 1500 1700 1900
CH
4
Consumption Rate (mole/cm
3
· s)
Local Equivalence Ratio,
local
Temperature (K)
60
Figure 4.14. Variation of ϕ
local
with temperature in a ϕ = 1.4 CH
4
/air CFF at p = 1 atm,
T
u
= 298 K, and K = 200 s
-1
computed using USC-Mech II with OD ( ●) and DD ( ■), and
variation of CH
4
consumption rate with temperature with OD ( ─) and DD (-
.
-).
n-C
12
H
26
/air CFF’s were computed also in order to verify the findings for CH
4
/air
flames. The diffusivity of n-C
12
H
26
/air was modified also by using the L-J parameters
of CH
4
and this case is referred to as ID given that n-C
12
H
26
becomes more diffusive.
Figures 4.15 and 4.16 depict the variation of S
u,ref
/
o
S
u
with Ka for ϕ = 0.7 and 1.4
respectively and the behavior is consistent with that observed for CH
4
/air flames. The
ϕ = 0.7 flame computed with OD mixture exhibits lower S
u,ref
values and the flame
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
3.5E-03
4.0E-03
0.6
0.8
1
1.2
1.4
1.6
1.8
2
300 500 700 900 1100 1300 1500 1700 1900
CH
4
Consumption Rate (mole/cm
3
· s)
Local Equivalence Ratio,
local
Temperature (K)
61
extinguishes at lower K compared to the ID case as shown in Fig. 4.15. Furthermore,
the use of Eq. 1 in both OD and ID cases results in
o
S
u
’s that are close to its known value.
On the other hand, for the ϕ = 1.4 flame, using Eq. 1 results in the over-prediction of the
known
o
S
u
value by 9% and 4% for the OD and ID cases respectively. The variations
of the peak local equivalence ratio, of ( ϕ
local
)
peak
and HRR
tot
are shown in Fig. 4.17 for a
ϕ = 1.4 n-C
12
H
26
/air flame computed with OD. Similarly to CH
4
/air flames computed
with DD, ( ϕ
local
)
peak
decreases and HRR
tot
increases as Ka increases given that the flame
becomes more stoichiometric.
62
Figure 4.15. Variation of S
u,ref
/
o
S
u
with Ka of a ϕ = 0.7 n-C
12
H
26
/air CFF at p = 1 atm
and T
u
= 443 K computed using JetSurF 1.0 with ID ( ■) and OD ( ●). ID (-
.
-) and OD
( ─) correspond to fitting using Eq. 1. The full range DNS results are shown in hollow
symbols, while the DNS results used for fitting Eq. 1 are shown in solid symbols.
0.9
1
1.1
1.2
1.3
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
S
u,ref
/S
u
o
Karlovitz number , Ka
63
Figure 4.16. Variation of S
u,ref
/
o
S
u
with Ka of a ϕ = 1.4 n-C
12
H
26
/air CFF at p = 1 atm
and T
u
= 443 K computed using JetSurF 1.0 with ID ( ■) and OD ( ●). ID (-
.
-) and
OD ( ─) correspond to fitting using Eq. 1. The full range DNS results are shown in
hollow symbols, while the DNS results used for fitting Eq. 1 are shown in solid symbols.
0.9
1
1.1
1.2
1.3
1.4
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
S
u,ref
/S
u
o
Karlovitz number , Ka
64
Figure 4.17. Variation of ( ϕ
local
)
peak
( ─) and HRR
tot
(--) with Ka of a ϕ = 1.4 n-C
12
H
26
/air
CFF at p = 1 atm and T
u
= 443 K computed using JetSurF 1.0 with OD.
Clearly, in steady state experiments like those of CFF’s the directly measured S
u,ref
’s
can be optimized so that the uncertainties are minimized. In carefully performed CFF
experiments, the uncertainty based on 2σ, where σ is the standard deviation, can be as
low as 5% [16]. However, the uncertainty of CFF experiments can be 10% or higher if
issues related to the quality of the flow, reactant concentrations especially for ϕ > 1.0
flames of liquid fuels, flow tracer seeding density, the implementation of particle image
velocimetry (PIV) or laser Doppler velocimetry (LDV) to measure flow velocities, and
102
103
104
105
1.58
1.59
1.6
1.61
0 0.02 0.04 0.06 0.08 0.1
Total Heat Release Rate (J/cm
2
· s)
Peak Local Equivalence Ratio, (
local
)
peak
Karlovitz number , Ka
65
interpretation of the raw data are not addressed carefully and rigorously. It should be
noted that uncertainties in the reported
o
S
u
of the order of 10% or higher are not
desirable as such data cannot be used effectively for the validation of kinetic models
given the relatively low sensitivity of
o
S
u
to kinetics. An alternative viable approach in
validating kinetic models is to compare the raw experimental data from experiments
against corresponding DNS results, so that the uncertainties associated with
extrapolations are removed.
4.4 Concluding Remarks
Direct numerical simulations of counterflow flames were carried out in order to
assess uncertainties stemming from current practices that are used to interpret
experimental data and derive the laminar flame speed. The results of the simulations were
treated as data in the range of stretch rates that are encountered in experiments, and were
used to perform extrapolations to zero stretch using formulas that have been derived from
asymptotic analyses. The validity of these practices was tested upon comparing the
results against the known answers of the direct numerical simulations.
The effect of molecular transport was studied by varying the fuel diffusivity. It was
concluded that for fuel lean hydrocarbon/air mixtures, the preferential diffusion of heat or
mass as manifested by the Lewis number dominates the flame response to stretch. For
fuel rich mixtures, the controlling factor was determined to be the differential diffusion of
the reactants into the reaction zone for heavy hydrocarbons. It was found also that using
66
extrapolation equations derived based on asymptotics analysis and simplifying
assumptions to obtain the laminar flame speeds, could result in significant errors for rich
flames of heavy hydrocarbons.
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Wang, S. S. Vasu, D. F. Davidson, R. K. Hanson, H. Pitsch, C. T. Bowman, A. Kelley, C. K.
Law, W. Tsang, N. P. Cernansky, D. L. Miller, A. Violi, R. P. Lindstedt, “A
High-Temperature Chemical Kinetic Model of n-Alkane Oxidation, JetSurF Version 1.0,”
http://melchior.usc.edu/JetSurF/JetSurF1.0/ Index.html.
[65] T. Lu, C.K. Law, Proc. Combust. Inst. 30 (2005) 1333–1341.
[66] C.K. Law, Combustion Physics, Cambridge University Press, 2008.
71
5 Chapter 5: An Experimental and Modeling Study of the Propagation
and Extinction of Neat Hydrocarbons, Practical Fuels and Jet Fuels
5.1 Introduction
Conventional and practical fuels and their surrogates are complex mixtures of
hundreds or even thousands of chemical components, and as a result it is not possible to
model and understand their combustion characteristics. On the other hand, the
formulation of reliable fuel surrogates is a viable solution towards providing the
much-needed fundamental understanding, as they can be modeled from first principle.
Along with studies in homogeneous systems, flame studies are essential towards the
formulation of fuel surrogates given that the kinetics can be evaluated over wide ranges
of temperature and species concentrations.
For neat liquid hydrocarbons, flame studies have focused on C
5
-C
12
hydrocarbons (e.g.,
[1-11]). For example, the experimental and computational studies of Ji et al. [3,8] for
n-C
10
H
22
and n-C
12
H
26
premixed and non-premixed flames showed that the n-C
10
H
22
flames exhibit lower extinction propensity than n-C
12
H
26
flames. Kumar et al. [5]
investigated the extinction limits of premixed n-C
10
H
22
/O
2
/N
2
and n-C
12
H
26
/O
2
/N
2
flames,
and computed results obtained using two kinetic models were found to over-predict the
data.
Flame studies for fuels with carbon numbers higher than 12, e.g. n-C
14
H
30
and
n-C
16
H
34
, are scarce or non-existing. At the same time it should be realized that such
72
heavier compounds dominate the composition of a range of practical fuels including
those used in naval aviation and diesel engines. The reason behind the lack of
systematically derived flame data for those heavy fuels is that in order to be sustained in
the gaseous phase in concentrations that are sufficiently large to support a flame, they
must be heated to temperatures that are high enough to cause cracking. In the recent
review, of Pitz and Mueller [12] emphasized that for the development of surrogates of
diesel fuels there is a profound need for experimental data for hydrocarbon oxidation in
the C
15
-C
20
carbon range.
Recently, detailed kinetic models for n-alkanes up to C
16
have been developed [13-15].
Shen et al. [16] studied the ignition of n-C
14
H
30
in a shock tube at elevated pressures.
Holley et al. [17] investigated the extinction of non-premixed C
5
-C
14
n-alkane flames and
it was found that the single-component hydrocarbon fuels with lower carbon number
exhibit greater resistance to extinction. Jet stirred reactor studies of the oxidation of
n-C
16
H
34
[14] and n-C
16
H
34
/n-C
10
H
22
blends [15] have been carried out at atmospheric
pressure. Ristori et al. [14] found that n-C
16
H
34
follows the general oxidation paths
already delineated for lighter alkanes. Biet et al. [18] found that C
16
compounds exhibit
a slightly larger reactivity than n-C
10
H
22
, but the formation of the lighter intermediates
are similar for n-C
10
H
22
and n-C
16
H
34
. Seshadri and coworkers [19,20] have studied the
extinction and autoignition of n-C
16
H
34
in non-premixed flames. It was found that the
critical conditions of autoignition for the straight-chain hydrocarbons depend on the
73
relative importance of low- and high-temperature kinetic pathways as well as of
molecular transport. It was shown also, that the n-C
16
H
34
flames exhibit a higher
extinction propensity compared to lighter hydrocarbons due to the lower fuel diffusivity.
Haylett et al. [21] measured ignition delay times of n-C
16
H
34
in a shock tube and the
experimental results were compared against predictions using different kinetic models.
As for practical fuels, there are notably fewer flame studies compared to neat heavy
liquid fuels. The oxidation of diesel fuels has been studied in jet-stirred reactors [22,23].
The ignition of Jet-A and JP-8 has been studied in shock tubes [24] and counterflow
flames [25]. Laminar flame speeds, S
u
o
, and extinction limits of conventional and
alternative fuels have been studied at different preheat temperatures [26] also in the
counterflow configuration. The jet-wall stagnation flame configuration was used for
measuring S
u
o
’s of jet and diesel fuels [27]. Ji et al. [8] investigated the extinction of
premixed and non-premixed flames of conventional and alternative jet fuels, and the
results revealed that flames of conventional jet fuels exhibit greater extinction propensity
compared to n-C
10
H
22
and n-C
12
H
26
.
Studies of surrogate fuels have appeared recently also (e.g., [28-30]). In terms of
flames studies, Ji and Egolfopoulos [28] measured S
u
o
’s of mixtures of air with
[80% n-C
12
H
26
+ 20% methylcyclohexane] and [80% n-C
12
H
26
+ 20% toluene] in the
counterflow configuration, and a mixing rule was established to estimate S
u
o
’s for fuel
blends. Furthermore, Honnet et al. [29] investigated the ignition and extinction
74
characteristics [80% n-C
10
H
22
+ 20% 1,2,4-trimethyl-benzene] non-premixed flames.
Finally, Holley et al. [31] determined numerically that flame extinction is, in addition
to kinetics, very sensitive to the fuel diffusivity especially for large molecular weight
fuels under non-premixed conditions, and this finding was confirmed also by the
subsequent studies of Ji et al. [8] and Wang et al. [32].
Based on the aforementioned literature search, it is apparent that studies of n-C
14
H
30
and n-C
16
H
34
have been carried out largely in homogeneous reactors, while flame studies
are scarce and thus no extensive database is available that could be used towards the
validation of kinetic models.
Thus, the first part of this study focuses on providing archival data of laminar flame
speed and extinction strain rate for gasoline ethanol blends. The second half of this study
was to validate a recently developed lump kinetic model for aviation fuels, and to gain
further insight into the controlling physical and chemical mechanisms that control flame
propagation.
5.2 Experimental Approach
The experiments were carried out under atmospheric pressure in the counterflow
configuration [e.g., (3,4,6-9,32-38)] as schematically shown in Fig 2.2. The
vaporization system included a high precision syringe pump and a glass nebulizer that
injected fuel as fine droplets into a cross-flow of heated air and heated nitrogen for
75
premixed flames and non-premixed flames respectively. It was determined that the
cross-flow injection configuration minimizes the fluctuations stemming from
vaporization, and allows very efficient mixing of the fuel with the heated gaseous stream.
All tubes along the heating path were wrapped with heating elements and insulation to
eliminate cold spots. To prevent fuel cracking, six K-type thermocouples were arranged
along the heating path to ensure that the temperature of fuel/air mixture was maintained
below 490 K, which ensured also that the partial pressure of the fuel was lower than its
vapor pressure. The temperature of the unburned mixture, T
u
, was measured in the
center of the burner exit. All the measurements were taken at T
u
= 443 K in this study.
The single-flame configuration was chosen for the premixed flame experiments as
compared to twin-flames, it results in lower extinction strain rates, K
ext
, and thus in lower
Reynolds numbers to minimize the intrinsic flow instabilities [37,38] and establish stable
flames. Single premixed flames were established by counterflowing an ambient
temperature N
2
jet against a preheated fuel/air jet. The extinction measurements for
premixed flames were similar to previous studies (e.g., [3,8,37]). A near-extinction
flame was established first, the prevailing strain rate K, defined as the maximum absolute
value of the axial velocity gradient in the hydrodynamic zone, was measured then by
using particle image velocimetry (PIV), and finally extinction was achieved by slightly
varying the fuel flow rate. The modification to K due to the small variations in the fuel
flow rate has been determined to be insignificant, and thus the measured K for the
76
near-extinction flame is reported as K
ext
. Burner nozzle diameters of D = 14 mm and
burner separation distance of L = 14 mm were used for all measurements
For premixed flames, measurements were performed for the equivalence ratio range
0.8 < < 1.5 for all mixtures. A RD387 gasoline (LLNL surogate) was used as the target
gasoline candidate for the gasoline-ethanol blends study. Total of five cases were studied
where gasoline volume fraction varied from 0 to 100 %. Case 1 (E100) represents 100%
pure ethanol with less than 0.1% water content; Case 2 (E85) represents 15% gasoline
and 85% ethanol in volume basis; Case 3 (E50) represents 50% of both gasoline and
ethanol; Case 4 (E15) represents 85% gasoline and 15% ethanol in volume basis and
Case 5 (E0) represents gasoline and no ethanol. The Air Force Research Laboratory
(AFRL) has provided three jet fuels with attendant “POSF” identification numbers, and
their compositions are summarized in Table 5.1. Jet-A, JP8 and JP5 were selected as the
representative aviation fuel.
77
Table 5.1. Fuel specific properties.
Jet A
a
(POSF 10325)
JP- 8
b
(POSF 10264)
JP-5
c
(POSF 10289)
RD387
d
iso-paraffin
29.45% 39.69% 18.14%
73%
n-paraffins 20.03% 26.82% 13.89%
Aromatics 18.66% 13.41% 20.59% >23%
Cycle-paraffin
24.87% 17.01% 31.33% 4.2%
Dicyclo-paraffin 6.78% 2.95% 15.97%
Trycyclo-paraffin 0.21% 0.12% 0.08%
a
Average carbon number ~ C
11.37
b
Average carbon number ~ C
10.83
c
Average carbon number ~ C
11.98
d
Average carbon number ~ C
14.8
5.3 Numerical Approach
o
S
u
’s and K
ext
’s were computed with PREMIX and opposed-jet flow code [39], which
was developed originally by Kee and coworkers [40]. This code has been modified to
allow for any type of boundary conditions and to account for thermal radiation of CH
4
,
H
2
O, CO and CO
2
at the optically thin limit [41]. Additionally, the code was integrated
with the CHEMKIN [42] and Sandia Transport [43] subroutine libraries. The H and H
2
diffusion coefficients of several key pairs are based on an updated set of Lennard-Jones
(L-J) parameters [44].
78
For the K
ext
computations, a two-point continuation approach was used to solve for K
at the state of extinction [45,46]. In the simulations, a vigorously burning flame was
established first, and then K was increased to achieve extinction. At the extinction state,
the opposed-jet code solves around the turning-point behavior by introducing a two-point
continuation approach [45,46]. The experimental values of the axial velocity gradients
at the burners exits, (du/dx)
exit
, L, and T
u
were accounted for in the simulations; in all
experiments it was determined that (du/dx)
exit
≈ 0.
The effects of chemical kinetics and molecular diffusion on K
ext
were evaluated by
performing rigorous sensitivity analysis with respect to rate constants and binary
diffusion coefficients [31]. Molecular transport was treated using mixture-averaged
formulation for premixed flames, while for the non-premixed extinction simulations the
Rosner formulation was chosen as shown in Chapter 5, the computed K
ext
can differ
significantly from the mixture-average formulation without considering soret effect [8].
As mentioned in Chapter 3, a detailed C
8
-C
16
n-alkane high-temperature kinetic
model is used in the simulation. A skeletal mechanism based on a detailed C
8
-C
16
n-alkane high-temperature kinetic model for n-alkanes up to n-C
16
H
34
is used,
consisting of 157 species and 1161 reactions. For gasoline and its surrogates simulation, a
reduced 679 species and 3479 reaction mechanism is used and followed by a reduced 323
species version mechanism. A gasoline surrogate compositions suggested is used to
represent the RD387 fuel in the simulation; the compositions are listed in Table 5.2. A
79
recent developed lump model built based on USC-Mech II for jet fuel simulation is used,
consisting 115 species and 805 reactions.
Table 5.2. RD 387 Surrogate Molar Compositions.
RD387
C
5
H
10
-2
0.053
C
6
H
5
CH
3
0.306
i-C
6
H
18
0.488
n-C
7
H
16
0.153
5.4 Results and Discussion
5.4.1 Propagation and extinction of n-C
14
H
30
/air and n-C
16
H
34
/air flames
Figure 5.1 illustrates the results for experimental and computed
o
S
u
’s for flames of
n-C
14
H
30
/air mixture and n-C
16
H
34
/air mixtures at p = 1 atm with T
u
= 443 K. The dashed
line represents a skeletal version of the recent developed high temperature kinetic model
by Westbrook et al. [44] for n-alkanes up to n-C
16
H
34
, consisting of 157 species and 1161
reactions, here referred as Model I. The n-C
14
H
30
and n-C
16
H
34
sub-models of Model I
were superimposed on to JetSurF 2.0 that describes the hydrocarbon kinetics up to C12,
and which has been tested successfully against flame propagation data for n- and
80
cyclo-alkanes. This combined model, hereafter referred to as Model II, consists of 241
species and 1841 reactions.
(a) (b)
Figure 5.1. (a) Experimental and computed laminar flame speeds of (a) n-C
14
H
30
/air
mixture, (b) n-C
16
H
34
/air mixtures at p = 1 atm and T
u
= 443 K.
For n-C
14
H
30
/air mixture, the experimental peak value, (
o
S
u
)
peak
, is 75 cm/s at ϕ = 1.05.
The computed
o
S
u
’s using Model I are slightly higher than the data for ϕ > 1.0 and
notably lower for ϕ < 1.0, with a maximum discrepancy of 6.0 cm/s at ϕ = 0.9.
Furthermore, using Model I ( ϕ)
peak
= 1.1. The predicted
o
S
u
’s using Model II are in better
agreement with data, with a maximum discrepancy of 3.8 cm/s around ϕ = 1.0, and ( ϕ)
peak
= 1.05 in agreement with the experimental ( ϕ)
peak
.
81
For n-C
16
H
34
/air mixture, the experimental peak value, (
o
S
u
)
peak
, is 74 cm/s at ϕ = 1.05.
Similarly to n-C
14
H
30
/air flames, the predicted
o
S
u
’s using Model I under-predict the data
for ϕ > 1.0, with a maximum discrepancy of 2.5 cm/s around ϕ = 1.0. On the other hand,
the predicted
o
S
u
’s using Model II are more consistent with the data and result in ( ϕ)
peak
=
1.05. Note that both the experimental and computed
o
S
u
’s for n-C
14
H
30
/air mixture and
n-C
16
H
34
/air flames are very close to each other for the same T
u
. This is reasonable, as
flame propagation is sensitive to small hydrocarbon kinetics [15].
Figure 5.2. Ranked logarithmic sensitivity coefficients of laminar flame speed with
respect to kinetics computed using (a) Model I and (b) Model II, for ϕ = 0.7, 1.0, and 1.4
n-C
14
H
30
/air mixture at T
u
= 443 K.
In order to obtain further insight into the effects of kinetics and molecular transport,
sensitivity analyses are performed using Models I and II. Figure 5.2 depicts the
82
logarithmic sensitivity respect to
o
S
u
for n-C
14
H
30
/air flames at ϕ = 0.7, 1.0 and 1.4,
respectively. Results show that the high-temperature oxidation of n-C
14
H
30
is dominated
by H
2
, CO, and small hydrocarbon kinetics only. This is as expected as fuel rapidly
decomposes into intermediates through 𝛽 -session.
Extinction phenomenon is more sensitive to chemical kinetics and molecular
transport than flame speed measurements. Thus it is worthwhile to conduct extinction
measurement to validate against kinetic models. Figure 5.3 depicts the experimental and
computed extinction strain rates of n-C
14
H
30
/air mixture and n-C
16
H
34
/air mixtures at
p = 1 atm with T
u
= 443 K.
(a) (b)
Figure 5.3. (a) Experimental and computed extinction strain rate of (a) n-C
14
H
30
/air
mixture, (b) n-C
16
H
34
/air mixtures at p = 1 atm and T
u
= 443 K.
Figure 5.3.a depicts the experimental and computed K
ext
of n-C
14
H
30
/air mixture at
p = 1 atm with T
u
= 443 K. Experimental peak value (K
ext
)
peak
≈ 1220 s
-1
at ( ϕ)
peak
= 1.2,
83
which is higher compared with that of
o
S
u
. This can be attributed to stretch and
preferential diffusion effects. For ϕ > 1.0, the Le is less than unity, and thus positive
stretch increases the flame temperature for conditions far from extinction, increasing the
extinction resistance. The computed K
ext
using Model I are in satisfactory agreement
with the data for ϕ < 1.0, whereas for ϕ > 1.0, Model I overpredicted the data notably,
with the maximum discrepancy being 240 s
-1
. Model II provides in general closer
agreements with the data, with the maximum discrepancy being 59 s
-1
at ϕ = 1.13.
Considering both the experimental and numerical uncertainties, the agreements obtained
using Model II are considered as satisfactory. Figure 5.3.b depicts the experimental and
computed K
ext
of n-C
16
H
34
/air mixtures at T
u
= 443 K. Experimentally, (K
ext
)
peak
≈ 1250
s
-1
and ( ϕ)
peak
= 1.2. The simulation results are similar to n-C
14
H
30
/air flames, with Model
II providing closer agreement with the data compared with Model I. Additionally, it is
determined that the experimental and computed K
ext
for n-C
14
H
30
/air and n-C
16
H
34
/air
flames are close to each other as expected.
5.4.2 Propagation and extinction of Gasoline Ethanol Blends
Figure 5.4 depicts the experimentally determined
o
S
u
’s of E100/air, E85/air, E50/air,
E15/air and E0/air flames at T
u
= 393 K for 0.7 ≤ 𝜙 ≤1.5 in the present study. ϕ is
calculated based on the surrogate molar compositions listed in Table 5.2.
o
S
u
’s of
E100/air flames are the highest among all fuels while E0/air flames exhibits the lowest.
The experimental peak value, (
o
S
u
)
peak
, is at ϕ ≈ 1.1. E100/air and E85/air flames exhibit
84
similar
o
S
u
’s across all ϕ’s. E15 and E0 flames also show similar
o
S
u
at stoichiometric
and rich condition, while deviated from each other at lean condition. The computed
o
S
u
’s
are slightly lower than the data at ϕ < 1.0 for ethanol and ethanol/gasoline blends while
notably higher at ϕ > 1.0 for all three cases, as shown in Fig. 5.5. The general trend is
consistent with the combustion theory as ethanol has higher flame speed then normal
alkanes due to the replacement of C-H bond in the n-alkane molecule by an OH
functional group and thus has a large effect in enhancing the rate of flame propagation.
For gasoline/air flames, the
o
S
u
’s are lower than normal alkanes due to the presence of
branched alkanes and aromatics in the mixture.
85
Figure 5.4. Experimentally determined
o
S
u
’s at T
u
= 393 K of E100/air ( ●), E85/air
( ■), E50/air (♦), E15/air ( ▲), and E0/air ( ○). The error bars shown in the present
experimental data are based on the 2-𝜎 standard deviations.
10
20
30
40
50
60
70
80
0.6 0.8 1 1.2 1.4 1.6
Laminar Flame Speed, cm/s
Equivalence Ratio, φ
86
Figure 5.5. Experimental and computed laminar flame speeds of ( ○) E100/air mixture,
( □) E50/air mixtures, and ( ◇) E0/air mixtures at p = 1 atm and T
u
= 393 K.
20
30
40
50
60
70
80
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
Laminar Flame Speed ,S
u
o
, cm/s
Equivalence Ratio, ϕ
87
Figure 5.6. Experimentally determined K
ext
’s at T
u
= 393 K of E100/air ( ●), E85/air
( ■), E50/air (♦), E15/air ( ▲), and E0/air ( ○). The error bars shown in the present
experimental data are based on the 2-𝜎 standard deviations.
Figure 5.6 depicts the experimentally determined K
ext
’s of E100/air, E85/air, E50/air,
E15/air and E0/air flames at T
u
= 393 K for 0.8 ≤ 𝜙 ≤1.5. Similar to
o
S
u
, E100/air
flames flames exhibits stronger resistance to extinction than E0/air flames. The maximum
extinction strain rate happens at close to ϕ = 1.2 for all mixtures. The K
ext
’s of E100/air
and E85/air flames showed similar extinction propensity, similar phenomenon can be
observed for E0/air and E15/air flames as well. Interestingly, as the equivalence ratio
moves towards 𝜙 > 1.4 condition, the K
ext
’s for all five cases merge.
0
200
400
600
800
1000
1200
1400
0.6 0.8 1 1.2 1.4 1.6
Extinction Strain Rate, 1/s
Equivalence Ratio, φ
88
5.4.3 Propagation and extinction of jet fuel flames
Figure 5.7 depicts the experimental and computed
o
S
u
’s of Jet-A/air, JP8/air and
JP5/air flames at T
u
= 403 K for 0.7 ≤ 𝜙 ≤1.4.
o
S
u
’s of JP8/air flames are the highest
among all three fuels. The maximum values of
o
S
u
’s are 57.9 cm/s, 59.4 cm/s and 55.65
cm/s for Jet-A/air, JP8/air and JP5/air flames respectively and all occur at 𝜙 = 1.05
condition. While
o
S
u
’s of JP5/air flame at 𝜙 = 1.4 is highest among all three fuels, raw
data of reference flame speed of JP5/air flames exhibits steeper dependence to stretch rate
which is not captured by simulation indicating this may be an artifact due to improper
transport parameter assigned in the chemical model.
89
Figure 5.7. Experimental and computed
o
S
u
’s at T
u
= 403 K of Jet A/air ( ▲), JP-8/air
( ●), and JP-5/air (♦). The error bars shown in the present experimental data are based on
the 2-𝜎 standard deviations.
20
30
40
50
60
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Laminar Flame Speed, cm/s
Equivalence Ratio, φ
90
Figure 5.8. Experimental and computed K
ext
’s at T
u
= 473 K of Jet A/air ( ▲), JP-8/air
( ●), and JP-5/air (♦). The error bars shown in the present experimental data are based on
the 2-𝜎 standard deviations.
Figure 5.8 depicts the experimental and computed K
ext
’s as function of fuel/N
2
mass
ratio, (F/N
2
)
mass
, for non-premixed flames of Jet-A, JP8 and JP5; in all experiments the
oxidizer was O
2
. The simulation is conducted with updated thermal diffusion ratio by
Rosner formula as mentioned earlier. It should be noted that the L-J parameters for all
aviation fuels considered here are considered as n-alkanes’ with similar molecular weight
i.e. Jet-A and JP8 are treated as n-decane and JP-5 is treated as n-dodecane, respectively.
The JP-8 exhibits strongest resistance to extinction for a given fuel/N
2
mass ratio and
JP-5 shows the weakest resistance. The numerical results show a similar trend as the data,
0
100
200
300
400
500
0.06 0.065 0.07 0.075 0.08
Extinction Strain Rate, 1/s
Fuel/N2 Mass Ratio
91
and reaches good agreement at low fuel/N
2
mass ratio. Compared to the data, the
simulation is over-predicted by roughly 10% at high fuel/N
2
mass ratio which could be
attributed to the use of transport parameter from normal alkanes.
5.5 Concluding Remarks
Laminar flame speeds of mixtures of air with n-C
14
H
30
, n-C
16
H
34
, Jet-A, JP8 and JP5
were determined in the counterflow configuration at atmospheric pressure and elevated
reactant temperatures. Measurements for such heavy fuels became possible after
upgrading the liquid fuel injection and heating path so that vaporization unsteadiness as
well as fuel decomposition and condensation are eliminated. The flow velocities were
measured using digital particle image velocimetry. The experiments were modeled
using several recently developed kinetic models that describe the pyrolysis and oxidation
kinetics of H
2
, CO, C
1
-C
16
hydrocarbons and practical fuel surrogates. Insight into the
controlling mechanisms was obtained through sensitivity analysis on both the kinetics
and molecular transport.
The results showed that the laminar flame speeds of n-C
14
H
30
/air and n-C
16
H
34
/air
mixtures are indistinguishable, stemming from the fact that for both flames fuel-related
kinetics are not rate-controlling and that flame propagation is sensitive largely to H
2
, CO,
and small hydrocarbon chemistry. The simulations reproduced the experimental data
for both n-C
14
H
30
/air and n-C
16
H
34
/air mixtures satisfactorily. Compared to n-C
14
H
30
/air
and n-C
16
H
34
/air mixtures, the laminar flame speeds for the petroleum-derived fuels are
92
lower due to the presence of aromatic compounds. On the other hand, the compositions
of the bio-derived fuels are dominated by n- and iso-alkanes and as a result they exhibit
laminar speeds that are higher that the petroleum-derived fuels but lower compared to
n-alkanes.
The close assembly of laminar flame speed and extinction strain rate for
gasoline-ethanol blends E0 and E15 suggests that ethanol could be a good additive
candidate to gasoline. Laminar flame speed and non-premixed extinction strain rate of
JP8 shows greatest performance, while JP5 shows the worst.
It is emphasized in closing, that the measured laminar flame speeds for those higher
molecular weight fuels in this study are the first ones to be reported, and are expected to
be of notable importance towards the fundamental understanding of the combustion of
low vapor pressure practical fuels.
5.6 References
[1] Holley A.T., Dong Y., Andac M.G., Egolfopoulos F.N., Combust. Flame 144 (2006) 448–460.
[2] Huang Y., Sung C.J., Eng J.A., Combust. Flame 139 (2004) 239–251.
[3] Ji C., Dames E., Wang Y .L., Wang H., Egolfopoulos F.N., Combust. Flame 157 (2010) 277–
287.
[4] Liu N., Ji C., Egolfopoulos F.N., Combust. Flame 159 (2012) 465–475.
[5] Kumar K., Sung C.J., Combust. Flame 151 (2007) 209–224.
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[7] Ji C., Sarathy S.M., Veloo P.S., Westbrook C.K., Egolfopoulos F.N., Combust. Flame 159
(2012) 1426-1436.
[8] Ji C., Wang Y.L., Egolfopoulos F.N., J. Propul. Power 27 (2011) 856–863.
[9] Kumar K., Mittal G., Sung C.J., Combust. Flame 156 (2009) 1278-1288.
[10] Dagaut P., Reuillon M., Cathonnet M., Combust. Sci. Technol. 103 (1994) 349-359.
[11] Won S.H., Sun W., Ju Y., Combust. Flame 157 (2010) 411-420.
[12] Pitz W.J., Mueller C.J., Prog. Energy Combust. Sci. 37 (2011) 330-350.
[13] Westbrook C.K., Pitz W.J., Herbinet O., Curran H.J., Sillke E.J., Combust. Flame 156 (2009)
181–199.
[14] Ristori A., Dagaut P., Cathonnet M., Combust. Flame 125 (2001) 1128-1137.
[15] Ranzi E., Frassoldati A., Granata S., Faravelli T., Ind. Eng, Chem, Res, 44(2005) 5170-5183.
[16] H.S. Shen, J. Steinberg, J. Vanderover, Oehlschlaeger M.A., Energy Fuels, 23(2009)
2482-2489.
[17] Holley A.T., Dong Y., Andac M.G., Egolfopoulos F.N., Edwards T., Proc. Combust. Inst. 31
(2007) 1205–1213
[18] Biet J., Hakka M.H., Warth V., Glaude P., Battin-Leclerc F., Energy Fuels, 22(2008),
2258-2269
[19] Grana R., Seshadri K., Cuoci A., Niemann U., Faravelli T., Ranzi E., Combust. Flame 159
(2012) 130–141.
[20] Seshadri K., Humer S., Seiser R., Combust. Theory Model. 12(2008) 831-855.
[21] Haylett D.R., Davidson D.F., Hanson R.K., Combust. Flame 159 (2012) 552–561.
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[22] Mati K., Ristori A., Gail S., Pengloan G., Dagaut P., Proc. Combust. Inst. 31 (2007) 2939–
2946
[23] Ramirez L H.P.R., Hadj-Ali K., Dievart P., Moreac G., Dagaut P., Energy Fuels, 24(2010),
1668-1676
[24] Vasu S.S., Davidson D. F., Hanson R.K., Combust. Flame 152 (2008) 125–143
[25] Humer S., Frassoldati A., Granata S., Faravelli T., Ranzi E., Seiser R., Seshadri K., Proc.
Combust. Inst. 31 (2007) 393–400.
[26] Kumar K., Sung C.J., Combust. Flame 151 (2007) 209–224.
[27] Chong C.T., Hochgreb S., Proc. Combust. Inst. 33 (2011) 979–986.
[28] Ji C., Egolfopoulos F.N., Proc. Combust. Inst. 33 (2011) 955-961.
[29] Honnet S., Seshadri K., Niemann U., Peters N., Proc. Combust. Inst. 32 (2009) 485-492.
[30] Natelson R.H., Kurman M.S, Cernansky N.P., Miller D.L., Fuel, 87(2008) 2339-2342.
[31] Holley A.T., You X.Q., Dames E., Wang H., Egolfopoulos F.N., Proc. Combust. Inst. 32 (2009)
1157-1163.
[32] Wang Y.L., Veloo P.S., Egolfopoulos F.N., Tsotsis T.T., Proc. Combust. Inst. 33 (2011)
1003-1010.
[33] Zhang H., Egolfopoulos F.N., Proc. Combust. Inst. 28 (2000) 1875-1882.
[34] Wu C.K., Law C.K., Proc. Combust. Inst. 20 (1984) 1941–1949.
[35] Law C.K., Zhu D.L., Yu G., Proc. Combust. Inst. 21 (1986) 1419–1426.
[36] Zhu D.L., Egolfopoulos F.N., Law C.K., Proc. Combust. Inst. 22 (1988) 1537–1545.
[37] Wang Y.L., Feng Q.Y., Egolfopoulos F.N., Tsotsis T.T., Combust. Flame 158 (2011) 1507–
95
1519.
[38] Wang Y .L., Holley A.T.,Ji C., Egolfopoulos F.N., Proc. Combust. Inst. 32 (2009) 1035–1042.
[39] Egolfopoulos F.N., Campbell C.S., J. Fluid Mech. 318 (1996) 1-29.
[40] Kee R.J., Miller J.A., Evans G.H., Lewis G.D., Proc. Combust. Inst. 22 (1988) 1479–1494.
[41] Egolfopoulos F.N., Proc. Combust. Inst. 25 (1994) 1375-1381.
[42] Kee R.J., Rupley F.M., Miller J.A., Sandia Report SAND 89-8009, Sandia National
Laboratories, 1989.
[43] Kee R.J., Warnatz J., Miller J.A., Sandia Report SAND83-8209, Sandia National Laboratories,
1983.
[44] Dong Y., Holley A.T., Andac M.G., Egolfopoulos F.N., Davis S.G., Middha P., Wang H.,
Combust. Flame 142 (2005) 374-387.
[45] Egolfopoulos F.N., Dimotakis P.E., Proc. Combust. Inst. 27 (1998) 641-648.
[46] Nishioka M., Law C.K., Takeno T., Combust. Flame 104 (1996) 328-342.
[47] Westbrook C.K., Pitz W.J., Herbinet O., Curran H.J., Sillke E.J., Combust. Flame 156 (2009)
181–199.
[48] Wang H., Dames E., Sirjean B., Sheen D.A., Tangko R., Violi A., Lai J.Y.W., Egolfopoulos
F.N., Davidson D.F., Hanson R.K., Bowman C.T., Law C.K., Tsang W., Cernansky N.P.,
Miller D.L., Lindstedt R.P., A high-temperature chemical kinetic model of n-alkane (up to
n-dodecane), cyclohexane, and methyl-, ethyl-, n-propyl and n-butyl-cyclohexane oxidation at
high temperatures, JetSurF version 2.0, September 19, 2010
(http://melchior.usc.edu/JetSurF/JetSurF2.0).
96
[49] Law C.K., Proc. Combust. Inst. 22 (1988) 1381-1402.
[50] Law C.K., Sung C.J., Prog, Energy Combust. Sci. 26 (2000) 459-505.
[51] Li B., Liu N., Zhao R., Zhang H., Egolfopoulos F.N., “Flame propagation of mixtures of air
with high molecular weight neat hydrocarbons and practical jet and diesel fuels”, Proc.
Combust. Inst. 34, doi:10.1016/j.proci.2012.05.063.
[52] Won S.H., Dooley S., Dryer F.L., Ju Y., Proc. Combust. Inst. 33 (2011) 1163-1170.
[53] Won S.H., Ju Y., Combust. Flame 157 (2010) 411-420.
97
6 Chapter 6: An Experimental and Modeling Study of the Propagation
and Extinction of Cyclopentadiene
6.1 Introduction
Aromatics are present in significant quantities in all petroleum-derived practical fuels
(e.g., [1,2]), and the understanding of their fundamental combustion properties is
essential to the development of reliable combustion models. In past studies (e.g., [3-7]),
it has been shown that the cyclopentadienyl (CPDyl, C
5
H
5
) radical is an important
transition species between cyclic and acyclic combustion. For example, in the oxidation
of benzene (C
6
H
6
), CPDyl forms via
C
6
H
5
+ O
2
C
6
H
5
O + O (R1)
C
6
H
5
O +M C
5
H
5
+ CO + M (R2)
in which C
6
H
5
corresponds to the phenyl radical and C
6
H
5
O to phenoxy. Thus, in order
to describe the aromatics oxidation accurately, the details of CPDyl combustion need to
be well characterized.
Few experimental studies of cyclopentadiene (CPD, C
5
H
6
) have been performed in
order to understand the CPDyl combustion, compared to other compounds such as, for
example, benzene and toluene. Previous studies on the pyrolysis of CPD in a flow
reactor [8] and a shock tube [9-11], showed that the CPDyl radical decomposes mainly to
propargyl (C
3
H
3
) and acetylene (C
2
H
2
) via
98
C
5
H
5
C
3
H
3
+ C
2
H
2
. (R3)
Oxidation studies of CPD have attracted more interest recently due to its importance
in aromatics combustion. Burcat et al. [12] proposed a kinetic model of CPD using
shock tube data, and the importance of cyclopentadienone (CPDone, C
5
H
4
O) during the
oxidation of CPDyl was emphasized based on the study of the thermal decomposition of
CPDone by Wang and Brezinsky [13]. However, another shock tube study performed
by Murakami et al. [14] suggested that cyclopentadienoxy (CPDoxy, C
5
H
5
O) should be
the major intermediate from the oxidation of CPDyl via
C
5
H
5
+ O
2
C
5
H
5
O + O, (R4)
but no further discussion about the decomposition of CPDoxy was provided due to
limited information. Recently, Butler and Glassman [15] studied the CPD oxidation in a
plug flow reactor, and reported the lack of observable quantities of CPDone and indicated
that the CPDoxy radical should be the main intermediate. In the same study [15], the
CPDoxy radicals were determined to form either n-butadienyl (n-C
4
H
5
) and CO via
C
5
H
5
O n-C
4
H
5
+ CO, (R5)
or 2,4-pentadienal-5-yl via the -scission reaction
C
5
H
5
O CH=CH-CH=CH-CHO (R6)
to transfer from cyclic to acyclic molecular structures. The most recent kinetics study of
CPD oxidation was done by Robinson and Lindstedt [16], in which it was shown that in
99
Butler and Glassman’s experiments [15], the dominant CPDyl removal paths are
oxidative via HO
2
attack, i.e.,
C
5
H
5
+ HO
2
C
5
H
5
O + OH. (R7)
Although many efforts have focused on the development of reliable kinetic models
for CPD/CPDyl, challenging problems are still remaining due to the inherent complexity
of the kinetics and the lack of a sufficient experimental database, especially in flames.
The present study thus aims to provide archival experimental data for the propagation and
extinction of CPD flames for the first time, as to the authors’ knowledge such data do not
exist in the literature. Laminar flame speeds,
o
u
S , and extinction strain rates, K
ext
, were
determined in the counterflow configuration for a wide range of equivalence ratios, .
The experiments were carried out at atmospheric pressure and elevated unburned mixture
temperatures. Further insight was provided into the physical and chemical processes
that control the burning characteristics of CPD/air mixtures through detailed numerical
simulations.
6.2 Experimental Approach
Similarly to previous studies (e.g., [17-19]), the experiments were performed in the
counterflow configuration, under ambient pressure, and 0.7 ≤ ≤ 1.5 for both flame
propagation and extinction. The burners include several internal and external heating
capabilities as well as aerodynamically designed nozzles and N
2
co-flow channels
surrounding the main nozzles. The shape of the nozzle results in top-hat exit velocity
100
profile, while the shape of the co-flow channel assures isolation of the main jet from the
ambient. The single-flame configuration was used to determine both
o
u
S ’s and
extinction resulting from counterflowing an ambient temperature N
2
jet against an
opposing fuel/air jet (e.g., [20]). Burner nozzle diameters, D = 14 mm, and nozzle
separation distances, L = 14 mm, were used.
A major challenge with CPD experiments is that it is not a stable species, and
dimerizes easily to dicyclopentadiene (DCPD, (C
5
H
6
)
2
) at room temperature. As a
result, in the present study DCPD (TCI America, 97%) was chosen as the fuel source.
DCPD can quickly decompose into CPD at temperatures above 150 ℃. DCPD is a
white crystalline solid at room temperature with a melting point 32.5 ℃ and boiling
point 170 ℃. In order to perform the experiments with DCPD, modifications of the
experimental configuration had to be made and are shown schematically in Fig. 2.2.
DCPD was first melted within a heated oil bath and then injected into a nebulizer by a
high-precision syringe pump. The high-precision syringe pump was heated at
temperatures about 35 ℃ to keep DCPD in the liquid phase. Uniform size fuel droplets,
ranging from 0.5 μm to 5 μm, were produced by a nebulizer that were mixed and
vaporized instantly with portion of the test air instantly in a glass vaporization chamber
heated at 200 ℃. The gaseous mixture was sent then through a heated coil with wall
temperature at 250 ℃, which allows for a total residence time around 5-6 seconds
ensuring thus full monomerization of DCPD. Such conditions allow for the conversion
101
of more than 97% DCPD to CPD, with isoprene being the main impurity. The balance
of the test air was added after the heated coil in order to cool down the mixture and
achieve the desired . All measurements were made at an unburned mixture
temperature T
u
= 353 K.
The axial flow velocities were measured along the stagnation streamline using digital
particle image velocimetry (DPIV). The flow was seeded with submicron size droplets
of silicon oil that was previously mixed with the fuel at small concentrations, i.e.
0.2~0.5%. A dual laser head, Solo Nd:YAG laser system (New Wave Research, type
Solo-III-15) and a PIV imager intense system (LaVision) were used in this work. To
determine
o
u
S , the minimum point of the velocity profile upstream of the flame was
measured and defined as a reference flame speed, Su,ref. The absolute value of the
maximum velocity gradient in the hydrodynamic zone is defined as the imposed strain
rate, K. Monitoring the variation of Su,ref with K,
o
u
S could be determined by
performing a non-linear extrapolation of S
u,ref
to K = 0, using a recently developed
computationally-assisted technique [20-22]. Similar to
o
u
S , K
ext
cannot be measured
directly. Its determination requires a near-extinction flame being established first,
followed by measurement of the prevailing K just upstream of the flame. Subsequently,
the fuel flow rate in the fuel/air jet is varied slightly to achieve extinction [20]. For
fuel-lean mixtures this is done by reducing the fuel flow rate, while for fuel-rich mixtures,
102
extinction is achieved by increasing the fuel flow rate. The modification to K due to the
slight change in the fuel flow rate has been determined to be insignificant.
6.3 Numerical Approach
’s and K
ext
’s were computed using the PREMIX code [23,24] and an opposed-jet
code [25,26] respectively. Both are modified to account for thermal radiation of CH
4
,
CO, CO
2
, and H
2
O in the optically thin limit and are coupled with the Sandia CHEMKIN
[27] and Transport [28] subroutine libraries. The H and H
2
diffusion coefficients of
several key pairs are based on the recently updated set of Lennard–Jones parameters
[29,30],
The experimental results were mainly simulated using two kinetic models. USC
Mech II [31], hereafter referred to as Model I, was developed by Wang and co-workers to
describe the high-temperature oxidation of hydrogen, carbon monoxide, and C
1
-C
4
hydrocarbons, but it contains also benzene and toluene kinetics, which however require
further validation. Dooley et al. [32] developed a detailed kinetic model for jet fuel
surrogates that include oxidation kinetics of toluene, hereafter referred to as Model II.
Both models include oxidation kinetics of CPD as a sub-model for aromatics flame.
The consumption of CPD and CPDyl radicals via O
2
, HO
2
, O, OH, and H are similar in
both models, as determined in the study by Zhong and Bozzelli [33]. Regarding the
oxidation kinetics of CPDone and CPDoxy, Model I includes reaction rates that are
mostly estimated, while in Model II the rates recommended by Alzueta et al. [34] have
S
u
o
103
been adopted. The laminar flame speeds of CPD/air mixtures computed by Lindstedt
and Park [35] using their recent developed kinetic model [16] were also plotted in order
to compare with Models I and II.
6.4 Results and Discussion
Figure 6.1 depicts the experimental and computed
o
u
S ’s of CPD/air mixture along
with the predictions using Models I and II. The experimentally determined peak
o
u
S
value is 50 cm/s at = 1.05. Using Model I, the experimental
o
u
S ’s are predicted
closely for all ’s. The largest discrepancy is about 2 cm/s, but still within the
experimental uncertainty. Model II results in good agreements with the data for < 1.0,
however the data are over-predicted for > 1.0. Simulation results using kinetic model
from Ref. 16 under-predict the data for < 1.0, but show a general good agreement for
> 1.0. Lindstedt and coworkers [16, 35] argued that the reaction pathways of CPD
flames under fuel rich conditions result in substantial formation of propargyl and
acetylene with the C
3
H
3
+ OH and HCCO + O
2
reactions exerting a strong influence on
computed burning velocities. The determination by Klippenstein et al. [36] was used
for the latter reaction with the estimated rates and product channels of Hansen et al. [37]
applied for the C
3
H
3
+ OH reaction [16]. The latter channel is absent in JetSurf 2.0 and
related work [38] suggests that the earlier estimate [37] provides an upper limit.
Though Lindstedt and coworkers [16, 35] suggested new reaction pathways in CPD
flames, due to the wide verification of C
0
-C
4
sub-models of Models I and II in predicting
104
high-temperature global flame phenomena such as laminar flame speeds and extinction
limits, Models I and II were used to perform the analysis in the following discussion.
Figure 6.1. Experimental and computed laminar flame speeds of cyclopentadiene/air
flames at T
u
= 353 K and p = 1 atm. Symbols: present experimental data. Solid lines:
simulations using Model I. Dashed Lines: simulations using Model II. Dashed-dot
Lines: simulations provided by Lindstedt and Park [35] using kinetic model in Ref. 16.
The error bars shown in the present experimental data are based on the 2-𝜎 standard
deviations.
Figure 6.2 depicts the logarithmic sensitivity coefficients of
o
u
S with respect to
kinetics for a = 0.7 CPD/air flame. Unlike n-alkane [20] and cycloalkane [39] flames
whose propagation is sensitive only to the small hydrocarbon chemistry,
o
u
S ’s of
CPD/air flames are sensitive also on the kinetics of the fuel and the subsequent
intermediates such as CPDyl and CPDoxy. The recombination of CPDyl with the H
105
radical to form CPD retards
o
u
S . The H-abstraction reaction of CPD to form CPDyl is
shown to be slow and retards propagation. The production of CPDoxy via R7, favors
o
u
S by consuming HO
2
and producing OH.
Figure 6.2. Ranked logarithmic sensitivity coefficients of laminar flame speeds with
respect to kinetics, computed using Models I and II for a = 0.7 cyclopentadiene/air
flame at T
u
= 353 K and p = 1 atm.
-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25
Logarithmic Sensitivity Coefficient
Model I
Model II
= 0.7
H+O
2
O+OH
CO+OH CO
2
+H
HCO+M CO+H+M
C
5
H
5
+HO
2
C
5
H
5
O+OH
C
4
H
6
+H C
2
H
4
+C
2
H
3
H+O
2
+M HO
2
+M
C
5
H
5
+H+M C
5
H
6
+M
H+OH+M H
2
O+M
HCO+O
2
CO+HO
2
aC
3
H
5
+H+M C
3
H
6
+M
C
5
H
6
+H C
5
H
5
+H
2
C
5
H
6
+OH C
5
H
5
+H
2
O
106
(a) (b)
Figure 6.3. Reaction path analysis of a = 0.7 cyclopentadiene/air flame at T
u
= 353 K,
and p = 1 atm using (a) Model I, and (b) Model II. The numbers indicate the conversion
percentages.
Figures 6.3 depict the reaction path analysis of a = 0.7 CPD/air flame performed
using Model I and Model II. As both models adopt the H-abstraction reactions of CPD
from Zhong and Bozzelli [33], they exhibit a similar initial CPD consumption which
approximately 85% of CPD producing CPDyl radicals. The rest of CPD produces either
acetylene and allyl or CPDoxy. In both models, 30% of CPDyl recombines with H to
form CPD. In Model I, 13% of CPDyl radicals decompose to acetylene and propargyl
(C
3
H
3
) via reaction R3. In Model II, however, nearly half of the CPDyl radicals form
1,3-butadiene (C
4
H
6
) via reaction [33]
C
5
H
5
+ OH C
4
H
6
+ CO. (R8)
C
5
H
6
C
5
H
5
84
34
C
5
H
5
O
7
7
C
2
H
2
+aC
3
H
5
c-C
4
H
5
47
C
2
H
2
+C
3
H
3
13
C
5
H
4
O
24
47
C
5
H
5
OH
18
63
7
11
CO+HCO+C
3
H
3
26
36
C
5
H
4
OH
64 100
CH
2
CHO+C
2
H
2
54
C
4
H
6
24
C
4
H
4
10
10
C
2
H
4
+C
2
H
2
C
5
H
6
C
5
H
5
86
27
C
5
H
5
O
7
4
C
2
H
2
+aC
3
H
5
n-C
4
H
5
57
C
5
H
4
O
11
31
C
5
H
5
OH
6
52
6
14
58
C
5
H
4
OH
42 100
aC
3
H
5
+CO
26
C
4
H
4
42
C
4
H
6
28
C
2
H
3
CHO+HCO
47
C
5
H
3
O
34
C
2
H
2
+CO+C
2
H
65
31
107
In both Model I and Model II, the rest of the CPDyl radicals react to yield CPDoxy,
CPDone, and cyclopentadienol (CPDol, C
5
H
5
OH). The ring opening process takes
place via CPDone and CPDoxy. The CPDol radical either result in CPDoxy or CPDone
via cyclopentadienol-yl (C
5
H
4
OH). Both CPDoxy and CPDone react to yield either
cyclobutenyl (c-C
4
H
5
) in Model I or n-butadienyl in Model II. Cyclobutenyl is not a
stable radical and thus is not considered as rate limiting in Model I. Figure 6.4 depicts
the spatial mole fraction profiles of computed C
2
H
2
and C
4
H
6
concentration profiles for a
= 0.7 CPD/air flame using Models I and II. As expected, Model I results in about 2
times more C
2
H
2
but about 10 times less C
4
H
6
compared to Model II due to the different
reaction pathways of CPDyl radicals. As reported in a previous study on cyclo-alkane
flames [39], the reaction involving C
4
H
6
can have a notable positive influence on flame
propagation via reaction
C
4
H
6
+ H C
2
H
4
+ C
2
H
3
. (R9)
Thus, the higher computed
o
u
S values using Model II could be attributed to the excess
production of C
4
H
6
in Model II compared to Model I.
o
u
S exhibits a finite positive
sensitivity on R9 as shown also in Fig. 6.2.
108
Figure 6.4. Computed intermediate species profiles for a = 0.7 cyclopentadiene/air
flame at T
u
= 353 K and p = 1 atm, using Model I (solid lines) and Model II (dashed
lines).
Given that flame propagation and extinction are both high temperature phenomena,
extinction strain rates provide additional constraints for the flame kinetics of the fuels
studied, especially considering the fact that K
ext
is more sensitive to the reaction kinetics
compared to
o
u
S (e.g., [40, 41]). Thus, predicting flame extinction limits is an
additional important validation test for a kinetic model.
Figure 6.5 depicts the experimental and computed K
ext
’s of CPD/air mixtures along
with the predictions using Model I and Model II. The experimentally determined peak
K
ext
value is around 900 s
-1
at = 1.15. Unlike the predictions obtained for flame
propagation, using Model II better agreements are obtained with the K
ext
data for all ’s.
On the other hand, using Model I the K
ext
data are under-predicted for all ’s.
0.0
2.0
4.0
6.0
8.0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Mole Fraction x 10
4
Distance (cm)
C
4
H
6
C
2
H
2
(/5)
109
Figure 6.5. Experimental and computed extinction strain rates of cyclopentadiene/air
flames at T
u
= 353 K and p = 1 atm. Symbols: present experimental data. Solid lines:
simulations using Model I. Dashed Lines: simulations using Model II. The error bars
shown in the present experimental data are based on the 2- standard deviations.
The ranked logarithmic sensitivity coefficients of K
ext
on kinetics are shown in Fig.
6.6 for a = 1.05 CPD/air flame. Similar to the results shown in Fig. 6.2, K
ext
’s of
CPD/air flames are sensitive not only to small hydrocarbon reactions but also to the fuel
and related intermediates’ chemistry. In addition, due to the different reaction pathways
of CPDyl decomposition between Model I and Model II, the distribution of the resulting
small intermediates could affect the prediction of K
ext
.
0
200
400
600
800
1000
0.6 0.8 1 1.2 1.4 1.6
Extinction Strain Rate, K
ext
, s
-1
Equivalence Ratio,
110
Figure 6.6. Ranked logarithmic sensitivity coefficients of extinction strain rates with
respect to kinetics, computed using Models I and II for a = 1.05 cyclopentadiene/air
flame at T
u
= 353 K and p = 1 atm.
Figure 6.7 depicts the computed species concentration profiles of C
3
H
3
and C
4
H
6
for a
near-extinction = 1.05 flame, using Models I and II. It is apparent that Model I
results in notably higher production of C
3
H
3
, and notably less C
4
H
6
compared to Model II
similarly to the results shown in Fig. 6.4. C
3
H
3
radicals are produced largely by R3, and
can react with H to yield propyne (C
3
H
4
) via
C
3
H
3
+ H C
3
H
4
, (R10)
a reaction that based on Model I, has a negative effect on extinction as shown in Fig. 6.6.
On the other hand there is no measurable sensitivity of K
ext
on R10 based on Model II
-0.2 0 0.2 0.4 0.6 0.8
Logarithmic Sensitivity Coefficient
Model I
Model II
= 1.05
H+O
2
O+OH
CO+OH CO
2
+H
HCO+M CO+H+M
C
4
H
6
+H C
2
H
4
+C
2
H
3
C
5
H
5
+H+M C
5
H
6
+M
H+OH+M H
2
O+M
C
3
H
3
+H C
3
H
4
HCO+H CO+H
2
H+O
2
+M HO
2
+M
HCO+O
2
CO+HO
2
C
5
H
6
+H C
5
H
5
+H
2
111
given that it results in significantly lower C
3
H
3
concentrations. For similar reasons
while K
ext
is sensitive to R9 based on Model II, this is not the case for Model I.
Figure 6.7. Computed intermediate species profiles for a near-extinction = 1.05
cyclopentadiene/air flame at T
u
= 353 K and p = 1 atm, using Model I (solid lines) and
Model II (dashed lines).
Selected concentration profiles from the CPD oxidation in a plug flow reactor
reported by Butler and Glassman [15] were modeled also in order to provide further
insight into the oxidation of CPDyl radicals and the results are shown in Fig. 6.8. The
experiments were conducted at initial temperature of 1198 K, initial fuel concentration of
2243 ppm, and 𝜙 = 1.03. The computed results of Models I and II were time-shifted by
-20 ms and -28 ms respectively to best fit the data. In general, both Models I and II
exhibit good agreement with the experimental data for CPD consumption and CO
production. Model I predicts closely the C
2
H
2
profile but underpredicts the C
4
H
6
0.0
0.5
1.0
1.5
2.0
2.5
0.58 0.6 0.62 0.64 0.66
Mole Fraction x 10
3
Distance (cm)
C
4
H
6
C
3
H
3
112
concentrations by a factor of about 12. Model II predicts closely the C
4
H
6
data, but it
underpredicts the C
2
H
2
data by a factor of 2.
Figure 6.8. Concentration profiles during CPD oxidation in a plug flow reactor with
initial temperature of 1198 K, initial fuel concentration of 2243 ppm, and = 1.03.
Symbols: experimental data from Butler and Glassman [15]; ( ○) C
5
H
6
, ( ●) CO, ( ■)
C
2
H
2
, and ( ▲) C
4
H
6
; Lines: simulation with (a) Model I (solid lines) time-shifted by
-20 ms and (b) Model II (dashed lines) time-shifted by -28 ms.
Based the results obtained from flame propagation, flame extinction, and the flow
reactor, it is apparent that the production pathways of C
3
H
3
via R3 and C
4
H
6
via R8
constitute a source of uncertainty between Model I and Model II. To illustrate the
attendant effects, Model I was modified by adding the rate constant of R8 by those of
Model II. Figure 6.9 depicts the computed
o
u
S ’s and K
ext
’s using both the original and
modified Model I. It can be seen that the modified Model I results in much improved
predictions of the data for both flame propagation and extinction of CPD/air mixtures.
0
1000
2000
3000
4000
5000
6000
0 50 100 150
Mole Fraction, ppm
Time, ms
CO
C
5
H
6
0
100
200
300
400
500
600
700
0 50 100 150
Time, ms
C
2
H
2
C
4
H
6
113
Figure 6.9. Experimental and computed laminar flame speeds and extinction strain
rates of cyclopentadiene/air flames at T
u
= 353 K and p = 1 atm. Symbols: present
experimental data. Solid lines: simulations using Model I. Dotted lines: simulations
using modified Model I by adding R8 from Model II. The error bars shown in the
present experimental data are based on the 2- standard deviations.
6.5 Concluding Remarks
Laminar flame speeds and extinction strain rates of cyclopentadiene/air flames were
determined experimentally over an extended range of equivalence ratios in the
counterflow configuration under atmospheric pressure and at an elevated unburned
mixture temperature. The experimental data are the first ones to be reported and were
modeled using several detailed kinetic models. Overall satisfactory agreements were
found. Sensitivity analyses revealed that the oxidation of cyclopentadiene/air mixtures
depends notably on the chemistry of fuel itself and subsequent intermediates such as
cyclopentadienone and cyclopentadienoxy radicals. The analysis further revealed that
0
200
400
600
800
1000
0.6 0.8 1 1.2 1.4 1.6
Extinction Strain Rate, K
ext
, s
-1
Equivalence Ratio,
114
reactions of small hydrocarbon intermediates resulting from the consumption of
cyclopentadienyl have a significant effect on both flame propagation and extinction.
Comparing the simulation results, it was concluded that among others, there are
uncertainties associated with the consumption pathways of cyclopentadienyl, including
C
5
H
5
C
3
H
3
+ C
2
H
2
and C
5
H
5
+ OH C
4
H
6
+ CO that can have a rather
significant effect on the prediction of various combustion properties both in
homogeneous reactors and flames.
6.6 References
[1] A. Roubaud, R. Minetti, L.R. Sochet, Combust. Flame 121 (2000) 535–541.
[2] N. Grumman, Northrop Grumman Petroleum Product Survey Reports,
Updated Annually, http://pps.ms.northropgrumman.com/.
[3] T. Edwards, L.Q. Maurice, J. Propul. Power 17 (2001) 461–466.
[4] A.S. Violi, S. Yan, E.G. Eddings, A.F. Sarofim, S. Granata, T. Faravelli, E. Ranzi, Combust.
Sci. Technol. 174 (2002) 399-417.
[5] E.G. Eddings, S. Yan, W. Ciro, A.F. Sarofim, Combust. Sci. Technol. 117 (2005) 715-739.
[6] J.A. Cooke, M. Bellucci, M.D. Smooke, A. Gomez, A. Violi, T. Favarelli, E. Ranzi, Proc.
Combust. Inst. 30 (2005) 439-446.
[7] S. Humer, A. Frassoldati, S. Granata, T. Faravelli, E. Ranzi, R. Seiser, K. Seshadri, Proc.
Combust. Inst. 31 (2007) 393–400.
115
[8] O.S.L. Bruinsma, P.J.J. Tromp, H.J.J. de Sauvage Nolting, J. A. Moulijn, Fuel 67 (3) (1988)
334-340.
[9] A. Burcat, M. Dvinyaninov, Int. J. Chem. Kinet. 29 (7) (1997) 505-514.
[10] K. Roy, C. Horn, P. Frank, V.G. Slutsky, T. Just, Proc. Combust. Inst. 27 (1) (1998)
329-336.
[11] R.D. Kern, Q. Zhang, J. Yao, B.S. Jursic, R.S. Tranter, M.A. Greybill, J.H. Kiefer,
Proceedings of Combustion Institute 27 (1) (1998) 143-150.
[12] A. Burcat, M. Dvinyaninov, E. Olchanski, Int. J. Chem. Kinet. 33 (9) (2001) 491-508.
[13] H. Wang, K. Brezinsky, J. Phys. Chem. A 102 (1998) 1530-1541.
[14] Y. Murakami, K. Mitsui, K. Naito, T. Itoh, T. Kobayashim, N. Fuji, Shock Waves 13 (2003)
149-154.
[15] R.G. Butler, I. Glassman, Proc. Combust. Inst. 32 (2009) 395-402.
[16] R.K. Robinson, R.P. Lindstedt, Combust. Flame 158 (4) (2011) 666-686.
[17] C. K. Wu, C.K. Law, Proc. Combust. Inst. 20 (1984) 1941-1949.
[18] G. Yu, C.K. Law, C.K. Wu, Combust. Flame 63 (1986) 339-347.
[19] D. L. Zhu, F.N. Egolfopoulos, C.K. Law, Proc. Combust. Inst. 22 (1988) 1537-1545.
[20] C. Ji, E. Dames, Y.L. Wang, H. Wang, F.N. Egolfopoulos, Combust. Flame 157 (2) (2010)
277-287.
[21] Y.L. Wang, A.T. Holley, C. Ji, F.N. Egolfopoulos, T.T. Tsotsis, H.J. Curran, Proc. Combust.
Inst. 32 (2009) 1035-1042.
116
[22] P.S. Veloo, Y.L. Wang, F.N. Egolfopoulos, C.K. Westbrook, Combust. Flame 157 (10) (2010)
1989-2004.
[23] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, A FORTRAN Program for Modeling Steady
Laminar One-Dimensional Premixed Flames, Sandia Report.SAND85-8240, Sandia National
Laboratories, 1985.
[24] J.F. Grcar, R.J. Kee, M.D. Smooke, J.A. Miller, Proc. Combust. Inst. 21 (1986) 1773-1782.
[25] R.J. Kee, J.A. Miller, G.H. Evans, G. Dixon-Lewis, Proc. Combust. Inst. 22 (1988) 1479 –
1494.
[26] F.N. Egolfopoulos, C.S. Campbell, J. Fluid Mech. 318 (1996) 1-29.
[27] R.J. Kee, F.M. Rupley, J.A. Miller, Chemkin-II: A FORTRAN Chemical Kinetics Package for
the Analysis of Gas-Phase Chemical Kinetics, Sandia Report SAND89-8009, Sandia National
Laboratories, 1989.
[28] R.J. Kee, J. Warnatz, J.A. Miller, A FORTRAN Computer Code Package for the Evaluation
of Gas-Phase Viscosities, Conductivities, and Diffusion Coefficients, Sandia Report
SAND83-8209, Sandia National Laboratories, 1983.
[29] Y. Dong, A.T. Holley, M.G. Andac, F.N. Egolfopoulos, S.G. Davis, P. Middha, H. Wang,
Combust. Flame 142 (2005) 374-387.
[30] P. Middha, H. Wang, Combust. Theor. Model. 9 (2005) 353-363.
[31] H. Wang, X. You, A.V. Joshi, S.G. Davis, A. Laskin, F.N. Egolfopoulos, C.K. Law, USC
Mech Version II. High-Temperature Combustion Reaction Model of H
2
/CO/C
1
-C
4
Compounds. http://ignis.usc.edu/USC_Mech_II.htm, May 2007.
117
[32] S. Dooley, S.H. Won, M. Chaos, J. Heyne, Y. Ju, F.L. Dryer, K. Kumar, C-J. Sung, H Wang,
M. Oehlschlaeger, R.J. Santoro, T.A. Litzinger, Combust. Flame 157 (12) (2010) 2333-2339.
[33] X. Zhong, J.W. Bozzelli, J. Phys. Chem. A 102 (1998) 3537-3555.
[34] M.U. Alzueta, P. Glarborg, K. Dam-Johansen, Int. J. Chem. Kinet. 32 (8) (2000) 498-522
[35] R.P. Lindstedt, S.W. Park, personal communication (2012).
[36] S.J. Klippenstein, J.A. Miller, L.B. Harding, Proc. Combust. Inst. 29 (2002) 1209-1217.
[37] N. Hansen, J.A. Miller, T. Kasper, K. Kohse-Hö inghaus, P.R. Westmoreland, J. Wang, T.A.
Cool, Proc. Combust. Inst. 32 (2009) 623–630.
[38] E. Meeks, C.V. Naik, K.V. Puduppakkam, A. Modak, C.K. Westbrook, F. Egolfopoulos, T.
Tsotsis, Experimental and Modeling Studies of Combustion Characteristics of Conventional
and Alternative Jet Fuels, NASA/CR NNC07CB45C-Final Report 1 (2009).
[39] C. Ji, E. Dames, B. Sirjean, H. Wang, F.N. Egolfopoulos, Proc. Combust. Inst. 33 (2011)
971-978.
[40] C.K. Law, Combustion Physics, first ed., Cambridge University Press, New York, USA, 2006,
p. 410 (Chapter 10).
[41] C. Ji, E. Dames, H. Wang, F.N. Egolfopoulos, Combust. Flame (2011)
doi:10.1016/j.combustflame.2011.10.01.
118
7 Chapter 7: Determination of Extinction Strain Rate: Molecular
Transport Effects
7.1 Introduction
Flame properties involving diffusion-kinetic coupling are critical to a basic
understanding of combustion properties of hydrocarbon fuels [1]. The extinction state of
laminar, non-premixed counterflow flames represents one such key property. A large
number of studies have been conducted to date especially in light of the recent interest in
the combustion kinetics of real fuels and their single or multi-component surrogates (see,
e.g., [2-11]). Holley et al. [8] carried out a detailed sensitivity analysis of non-premixed
extinction strain rate with respect to kinetic and transport model parameters. It was
found that the flame extinction responses could be particularly sensitive to the mass
diffusivity of the fuel, especially for heavy fuel molecules. The cause is quite clear, as
in these flames fuel diffusion is typically slow due to the fuel size and weight but
diffusion is critical to supplying the fuel to the thermal mixing layer, allowing it react
with the oxidizer flowing from the opposite direction. Won et al. [3] developed a
radical index method for determining the chemical kinetic contribution to non-premixed
flame extinction of large hydrocarbons. It was shown that the mass diffusivity of the
fuel plays a role critical to the flame extinction; and it becomes possible to isolate the fuel
kinetic effects only when the transport effects are properly accounted for.
119
A class of compounds of particular interest to a range of real liquid fuels is normal
paraffin. Previously, Ji et al. [10] made measurements for the extinction strain rates,
K
ext
, of counterflow, non-premixed n-decane (n-C
10
H
22
) and n-dodecane (n-C
12
H
26
)
flames. They found that JetSurF 1.0 [12] overpredicts the K
ext
data notably.
Interestingly, the model predicts the laminar flame speeds and shock tube ignition delay
time rather well. Sensitivity analyses suggest that the uncertainty in the kinetic
parameters alone could not explain the observed discrepancies between the experimental
and computed K
ext
or the kinetic uncertainty alone is not enough to reconcile K
ext
with
flame propagation and shock tube ignition data. Rather, the sensitivity tests suggest that
the uncertainties of the transport properties could be the cause for the discrepancy.
In the JetSurF effort [12], the diffusion coefficients of long-chain n-alkanes were
calculated via the Lennard-Jones 12-6 potential parameters for the self-interaction of the
hydrocarbon molecules. These potential parameters were only rough estimates as they
are based on the equations of the law of corresponding states [13] using more basic
phase-change properties including the critical pressure and temperature and boiling points.
The method was used earlier for estimating the Lennard-Jones 12-6 parameters of
polycyclic aromatic hydrocarbons [14]. Since the equations used to estimate the LJ
parameters are empirical and their use for large n-alkanes represents an extrapolation of
data from which these equations were developed, the accuracy of the potential parameters
are obviously highly uncertain. Aside from this concern, there is very little theoretical
120
evidence that the mixing rule for the potential parameters is valid or the spherical,
isotropic potential interactions are adequate to describe chain-like n-alkane molecules.
Jasper and coworkers [15, 16] carried out classical trajectory studies of several
n-alkanes in some typical diluent gases to determine diffusion collision cross sections.
They showed that diffusion coefficients of n-alkanes estimated from the use of the law of
corresponding states deviate quite notably from the classical trajectory results.
Unfortunately, their work had included n-alkane molecules only up to n-heptane, which is
somewhat short of allowing us to test the plausible cause for the experiment and model
discrepancy observed for non-premixed flame extinction of n-C
10
H
22
and n-C
12
H
26
of Ji
et al. [10] just discussed.
The main objectives of current study is to extend a recently developed transport
theory of cylindrical molecular structure in dilute gases [17] to model the binary diffusion
coefficients of long-chain n-alkanes up to n-dodecane in N
2
and He. Next, we show that
the non-premixed flame K
ext
of n-C
10
H
22
and n-C
12
H
26
of Ji et al. [10] can be predicted
accurately with the updated binary diffusion coefficients of n-C
10
H
22
and n-C
12
H
26
in N
2
with either the multicomponent or mixture averaged transport formulation, provided that
the Soret effect on the transport of large fuel molecules is accounted for.
7.2 Experimental Approach
To supplement the data from a previous study [10], additional measurements were
made for non-premixed flame extinction of n-dodecane. The experiments were carried
121
out at atmospheric pressure in the counterflow configuration (see, [9, 29-31]). Details of
the measurement have been discussed in Chapter 2 [10]. Briefly, non-premixed flames
were established by impinging a fuel/N
2
stream on to an opposing ambient temperature
O
2
stream. The burner nozzle diameter and the burner separation distance were 1.4 cm.
Screens were placed in the burner to assure top-hat burner velocity profile at the nozzle
exit. The gaseous flow rates were metered using sonic nozzles, which were calibrated
using a dry-test meter with a reported accuracy of ± 0.21%. The upstream pressure of each
sonic nozzle was monitored by a pressure gauge with ± 0.25% precision. The vaporization
system included a precision syringe pump of ± 0.35% accuracy and a glass nebulizer
(Meinhard TR-50-A1), through which the liquid fuel was injected as fine droplets into a
crossflow of heated nitrogen. All gas lines were heated to prevent fuel vapor
condensation. The temperature of the gas lines was measured with K-type inline
thermocouples. The temperature of the unburned fuel/N
2
stream, T
u
, was measured at the
center of the burner exit. The variation of this temperature is within ± 5 K. Flow
composition uncertainty has been determined to be less than 0.5% [10]. Flow velocity
measurements were made by seeding the flow with submicron size silicon oil droplets
and by using particle image velocimetry (PIV). The uncertainty associated with the PIV
measurements is within 0.8 to 1.0% [10]. The maximum absolute axial velocity gradient
on the fuel side of the hydrodynamic zone was defined as the strain rate, K, and K
ext
was
determined for a near extinction flame. The uncertainty of K
ext
to be quoted here is the
±2σ standard deviation of repeated measurements.
122
7.3 Numerical Approach
K
ext
was computed using an opposed-jet flow code [32] developed originally by Kee
et al. [33]. This code was modified to allow the use of a wider range of boundary
conditions than the initial version and to account for thermal radiation of CH
4
, H
2
O, CO
and CO
2
at the optically thin limit [34]. The JetSurF 1.0 kinetic model [12] was used to
describe the high-temperature pyrolysis and oxidation of n-C
10
H
22
and n-C
12
H
26
.
For K
ext
computations, a two-point continuation approach solves for K at the state of
extinction [35, 36]. The experimental values of the axial velocity gradients at the burner
exits were considered as the respective boundary conditions in the simulation [31]. The
code was integrated with the Sandia Transport subroutine libraries [37] with the diffusion
coefficients of H and H
2
in several key diluent gases updated from Ref [38] and those of
n-C
10
H
22
and n-C
12
H
26
in N
2
from the current diffusion coefficient model. Molecular
transport was treated comparing both mixture-averaged formulation and multicomponent
formulation.
We note that the mixture-averaged transport formulation of the original Sandia
PREMIX and OPPDIF codes does not consider the Soret effect of large/heavy molecules
even if the thermal diffusion (TDIF) keyword is turned on. To account for thermal
diffusion of heavy fuel molecules, the approximation of Rosner et al. [39] for the thermal
diffusion factor α
T
was implemented into the mixture-averaged formulation. The
thermal diffusion factor of species B in A takes the form of
123
𝛼 𝑇 = [0.454 ∙ 𝑑 (Λ + 0.261) + 0.116(Λ − 1)][1 − 𝐶 𝑇 ⁄ ], (6)
where Λ is related to molecular size disparity, which may be evaluated by Λ ≅
1.31 Sc (1 + d)
−1/2
, Sc is the Schmidt number, d = (M
B
-M
A
)/(M
B
+M
A
) is the normalized
molecular mass disparity, and
𝐶 = 1.45[𝘀 𝐵𝐴
𝑘 𝐵 ⁄ − 85], (7)
For the cases considered here, C/T ≪ 1 and thus the temperature correction is
unimportant. Four computational cases were used to examine the impact of updated
binary diffusion coefficients on non-premixed flame extinction of n-C
10
H
22
and n-C
12
H
26
.
They are summarized in Table 7.1. While Cases I and II test the predictions of K
ext
using the old diffusion coefficient estimates [12] from the law of corresponding state with
the purpose of comparing the impact of the Soret effect, Cases III and IV test the updated
diffusion coefficients.
124
Table 7.1. Summary of computational cases.
Case
Source of
parameters
Formulation Soret effect
I JetSurF [12]
a
Multicomponent Yes
II JetSurF [12]
a
Multicomponent No
III This work Mixture averaged Yes
b
IV This work Multicomponent Yes
a
Estimated using the law of corresponding state [13, 14].
b
Using the thermal diffusion ratio of Rosner et al. (eq. 6) [39].
7.4 Results and Discussion
Figure 7.1 shows the computed K
ext
compared to the experimental data collected in
the current work from counterflow non-premixed flames of n-C
12
H
26
in N
2
at 473 K
against O
2
at 300 K over a range of fuel to N
2
mass ratio. The effective potential
parameters are summarized in Table 7.2. Cases I and II both use the diffusion coefficient
estimates from the law of corresponding state. These estimates are shown to grossly
overpredict K
ext
. Comparing the Cases I and II, we see that K
ext
becomes lower with the
Soret effect considered. As the fuel is transported to the mixing zone by molecular
diffusion, it encounters an upward temperature, which by thermal diffusion pushes it back
towards the colder fuel/N
2
jet. Thus, the Soret effect reduces the rate at which the fuel
125
can be transported into the mixing zone and makes the flame more readily to undergo
extinction.
Table 7.2. Effective LJ-12-6 potential parameters of n-alkane-N2 interactions for
calculating the binary diffusion coefficients of n-alkane in N2.
Species σ ( Å) ε/k
B
(K)
a
n-butane 4.749 101.6
n-pentane 5.086 107.2
n-hexane 5.437 106.8
n-heptane 5.744 111.7
n-octane 6.106 104.2
n-nonane 6.415 103.6
n-decane 6.683 107.8
n-undecane 6.994 103.4
n-dodecane 7.222 109.8
a
An average value of 106 K may be used for all species considered.
The updated diffusion coefficients of n-C
12
H
26
in N
2
lead to significantly better
predictions for K
ext
(Cases III and IV), as seen in Fig. 7.1. As Table 7.1 shows, there are
126
two differences between the two cases. Case III uses the mixture-averaged transport
formula with Rosner’s approximate thermal diffusion ratio; Case IV employs
multicomponent transport formulation with a more exact thermal diffusion ratio [20].
Interestingly, the computed K
ext
values do not differ significantly, suggesting that the
mixture-averaged formation is adequate at least for the conditions of the present study.
Similar comparisons may be made using the K
ext
data of Ji et al. [10] for both n-C
12
H
26
and n-C
10
H
22
. As Fig. 7.2 shows the updated diffusion coefficients yield predicted K
ext
values much closer to the experimental data, whether one uses the mixture-averaged or
multicomponent transport. These results indicate that accurate diffusion coefficients of
large fuel molecules and the Soret effect are both important elements towards a
satisfactory prediction of flame properties that are governed by diffusion-kinetic
coupling.
127
Figure 7.1. Extinction strain rate of non-premixed n-C
12
H
26
/N
2
-O
2
flames (T
u
= 473 K
for the fuel jet and 300 K for the oxygen jet) with p = 1 atm. Symbols: experimental data
(this work); lines are simulations (see Table 7.1).
100
200
300
400
500
600
0.060 0.065 0.070 0.075
K
ext
(s
–1
)
Fuel/N
2
Mass Ratio
n-dodecane/N
2
versus O
2
Case IV
Case III
Case I
Case II
128
Figure 7.2. Extinction strain rate of non-premixed n-C
12
H
26
/N
2
-O
2
flames and
n-C
10
H
22
/N
2
-O
2
flames all at T
u
= 403 K for the fuel jet and 300 K for the oxygen jet,
with p = 1 atm. Experimental data (symbols) were taken from Ref. [10]; lines are
simulations (see Table 7.1).
100
200
300
400
500
K
ext
(s
–1
)
n-dodecane/N
2
versus O
2
Case IV
Case III
Case I
0.06 0.07 0.08
100
200
300
400
500
n-decane/N
2
versus O
2
Case IV
Case III
Case I
Fuel/N
2
Mass Ratio
K
ext
(s
–1
)
129
To amplify the above point, we plot in Fig. 7.3 the structures of the near extinction
flames of n-dodecane/N
2
(473 K) versus O
2
(300 K), computed for Case III and IV.
Except for the shift in the stagnation surface marked by the vertical dashed-dotted-dashed
lines, the two structures are nearly the same. The fuel is transported to the mixing layer
by diffusion and is decomposed to a small number of key intermediates, including
ethylene, methane, propene, 1,3-butadiene, and hydrogen. The concentrations of these
intermediates reach their respective peaks when the concentration of n-C
12
H
26
drops to a
negligible level. The oxidation of the intermediates follows and the concentrations of
the intermediates drop rapidly as they enter into the region where the H atom peaks in its
concentration. The molecular diffusion process of the fuel enables the delivery of the
fuel into the thermal mixing layer, allowing it to undergo pyrolytic reactions, replacing
the fuel by the key intermediates just discussed.
130
Figure 7.3. Structures of n-dodecane/N
2
(473 K) versus O
2
(300 K) near extinction
flames computed for (a) Case IV (full multicomponent and thermal diffusion transport
with updated diffusion coefficients) and (b) Case III (mixture averaged transport with the
thermal diffusion ratio of Rosner et al. [39]). The vertical dashed-dotted-dashed line
indicates the position of the stagnation surface.
7.5 Concluding Remarks
The gas-phase binary diffusion coefficient of n-alkane in nitrogen is studied using
gas-kinetic theory analysis. Effective Lennard-Jones 12-6 potential parameters are
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
0
500
1000
1500
0.0 0.7 0.8 0.9 1.0 1.1 1.2
Mole Fraction
Temperature, T (K)
T
O
2
n-C
12
H
26
CO
2
CO
H
2 H
C
2
H
4
C
3
H
6
1,3-C
4
H
6
CH
4
(a)
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
0
500
1000
1500
0.0 0.7 0.8 0.9 1.0 1.1 1.2
Mole Fraction
Temperature, T (K)
Distance, x (cm)
T O
2
n-C
12
H
26
CO
2
CO
H
2 H
C
2
H
4
C
3
H
6
1,3-C
4
H
6
CH
4
(b)
131
proposed for n-butane through n-dodecane in nitrogen. It is shown that the updated
diffusion coefficients resolve the earlier difficulty of predicting the extinction strain rate
of non-premixed counterflow flames of n-dodecane/N
2
and n-decane/N
2
against O
2
.
The ability of the generalized transport theory for cylindrical structures in dilute gases to
reconcile a wide range of binary diffusion coefficient data and to predict the flame
extinction data suggests that the theory is valid for the diffusion coefficients of
long-chain molecules. It is also shown that the mixture-average transport formulation is
adequate for predictions of the extinction strain rate, provided that the Soret effect is
taken into consideration.
7.6 References
1. C. K. Law, Combustion physics, Cambridge university press, 2006.
2. M. Colket, T. Edwards, S. Williams, N. P. Cernansky, D. L. Miller, F. Egolfopoulos, P.
Lindstedt, K. Seshadri, F. L. Dryer, C. K. Law, Development of an experimental database and
kinetic models for surrogate jet fuels, 45th AIAA Aerospace Sciences Meeting and Exhibit,
2007; Reno, Nevada, 2007; paper no. AIAA-2007-0770.
3. S. H. Won, S. Dooley, F. L. Dryer, Y. Ju, Combust. Flame 159 (2012) 541-551.
4. S. Dooley, S. H. Won, M. Chaos, J. Heyne, Y. Ju, F. L. Dryer, K. Kumar, C.-J. Sung, H. Wang,
M. A. Oehlschlaeger, Combust. Flame 157 (2010) 2333-2339.
5. S. H. Won, W. Sun, Y. Ju, Combust. Flame 157 (2010) 411-420.
132
6. K. Seshadri, T. Lu, O. Herbinet, S. Humer, U. Niemann, W. J. Pitz, R. Seiser, C. K. Law, Proc.
Combust. Inst. 32 (2009) 1067-1074.
7. S. Honnet, K. Seshadri, U. Niemann, N. Peters, Proc. Combust. Inst. 32 (2009) 485-492.
8. A. Holley, X. You, E. Dames, H. Wang, F. Egolfopoulos, Proc. Combust. Inst. 32 (2009)
1157-1163.
9. A. Holley, Y. Dong, M. Andac, F. Egolfopoulos, T. Edwards, Proc. Combust. Inst. 31 (2007)
1205-1213.
10. C. Ji, Y. L. Wang, F. N. Egolfopoulos, J. Propul. Power 27 (2011) 856-863.
11. B. Li, Y. Zhang, H. Zhang, F. N. Egolfopoulos, Proc. Combust. Inst. 35 (2015) 965-972.
12. B. Sirjean, E. Dames, D. Sheen, X. You, C. Sung, A. Holley, F. Egolfopoulos, H. Wang, S. Vasu,
D. Davidson A high-temperature chemical kinetic model of n-alkane oxidation. 2009,
http://web.stanford.edu/group/haiwanglab/JetSurF/JetSurF1.0/index.html
13. L. S. Tee, S. Gotoh, W. E. Stewart, Ind. Eng. Chem. Fundmen. 5 (1966) 356-363.
14. H. Wang, M. Frenklach, Combust. Flame 96 (1994) 163-170.
15. A. W. Jasper, E. Kamarchik, J. A. Miller, S. J. Klippenstein, J. Chem. Phys. 141 (2014) 124313.
16. A. W. Jasper, J. A. Miller, Combust. Flame 161 (2014) 101-110.
17. C. Liu, Z. G. Li, H. Wang, Phys. Rev. E submitted (2015).
18. W. S. McGivern, J. A. Manion, Combust. Flame 159 (2012) 3021-3026.
19. J. A. Manion, W. S. McGivern, Direct measurements of binary gas phase diffusion coefficients
for Combustion Applications, Argonne National Laboratory, Darien, IL, 2011,
133
20. J. O. Hirschfelder, C. F. Curtiss, R. B. Bird, M. G. Mayer, Molecular theory of gases and liquids,
Wiley, New York, 1954.
21. R. C. Reid, J. M. Prausnitz, B. E. Poling, The properties of gases and liquids, McGraw-Hill, New
York, 1987.
22. R. Trengove, H. Robjohns, P. J. Dunlop, Ber. Bunsen. Phys. Chem. 86 (1982) 951-955.
23. K. Chae, P. Elvati, A. Violi, J. Phys. Chem. B 115 (2010) 500-506.
24. A. Einstein, Ann. Phys. 17 (1905) 549.
25. Z. Li, H. Wang, Phys. Rev. E 68 (2003) 061206.
26. Z. Li, H. Wang, Phys. Rev. E 68 (2003) 061207.
27. C. Liu, H. Wang, J. Chem. Phys. Manuscript in preparation (2015).
28. A. Boushehri, J. Bzowski, J. Kestin, E. Mason, J. Phys. Chem. Ref. Data 16 (1987) 445-466.
29. C. Wu, C. Law, Symp. Int. Combust. 20 (1985) 1941-1949.
30. D. Zhu, F. Egolfopoulos, C. Law, Symp. Int. Combust. 22 (1989) 1537-1545.
31. C. Ji, E. Dames, Y. L. Wang, H. Wang, F. N. Egolfopoulos, Combust. Flame 157 (2010)
277-287.
32. F. N. Egolfopoulos, C. S. Campbell, J. Fluid Mech. 318 (1996) 1-29.
33. R. J. Kee, J. A. Miller, G. H. Evans, G. Dixon-Lewis, Symp. Int. Combust. 22 (1989) 1479-1494.
34. F. Egolfopoulos, Symp. Int. Combust. 25 (1994) 1375-1381.
35. M. Nishioka, C. Law, T. Takeno, Combust. Flame 104 (1996) 328-342.
36. F. N. Egolfopoulos, P. E. Dimotakis, Symp. Int. Combust. 27 (1998) 641-648.
134
37. R. J. Kee, G. Dixon-Lewis, J. Warnatz, M. E. Coltrin, J. A. Miller, A Fortran computer code
package for the evaluation of gas-phase, multicomponent transport properties, Livermore, CA,
1986.
38. Y. Dong, A. T. Holley, M. G. Andac, F. N. Egolfopoulos, S. G. Davis, P. Middha, H. Wang,
Combust. Flame 142 (2005) 374-387.
39. D. Rosner, R. Israel, B. La Mantia, Combust. Flame 123 (2000) 547-560.
135
8 Chapter 8: Determination of Laminar Flame Speeds Using
Axisymmetric Bunsen Flames: Intricacies and Accuracy
8.1 Introduction
Combustion of fossil fuels has been a significant driver in accelerating industrial and
economic development for more than a century [1,2]. This was accompanied by an
attendant increase in fundamental understanding of the combustion processes through
identification of parameters controlling the combustion phenomena and formulating a
basic combustion theory [3-8]. From the early treatment of combustion problems [9-11],
laminar flames were recognized as an important ingredient in developing combustion
theories and models for a wide range of practical applications.
The significance of determining the laminar flame combustion parameters for the
design and optimization of energy production systems has lead to the development of a
series of experimental flame configurations such as the Bunsen flame [12-16], the
counter-flow flames [17-19], the stagnation flame [20-22], and the spherically expanding
flame [19,23-26]. The exploitation of these experimental tools primarily offers a viable
means of estimating fundamental combustion properties such as ignition characteristics,
laminar flame speeds, strain sensitivity and extinction strain rates [26,27].
The laminar flame speed ( ) is the one of the most important, observable, traditional
target parameter. Data acquired for laminar flame speed plays a significant role in
developing kinetic models and is used in the prediction of critical combustor design
parameters such as flashback and blow-off [26-29]. It also serves as a scaling parameter
in turbulent combustion [2,30,31].
S
u
o
136
Amongst the various laminar flame configurations, the Bunsen flame is historically
the oldest [12,32-34], the simplest, and the most popular one, exploited from the very
early days of combustion analyses. Since then this configuration has been widely
accepted as a suitable test bed for the investigation and testing of a range of combustion
theories and characteristics [2,3,11,13,32,33,35-61]. Since its initial introduction, the
Bunsen flame technique has significantly evolved to current day maturity benefitting
from continuous developments in flame measuring techniques
[14,16,25,27,44,47,49,56,61-67], burner operation control and regulation methodologies
[6,22,26,27,43,49,51,62,63,65,66,68] and impressive advances in laminar flame
simulation techniques [29,64,69,70-72]. Nevertheless, uncertainties still remain
regarding the control of its operating parameters, the optimum experimental
methodologies and the interpretation of the experimental results
[22,27,38,40,41,46,48,53,59]. The difficulty in interpretation of the experimental results
stems primarily from the uncertainties involved in estimation of flame speed using the
flame surface area or the flame angle methods.
Recently, renewed interest has emerged in the technique due to its amenability and
suitability in quantifying, in a straightforward manner, ’s of a multiplicity of fuel
blends, over a wide range of conditions [16,27,55-58,60,61], as mandated by the urgent
need for advanced low emission new combustor concepts. As a consequence, the
exploitation of a simplified experimental methodology, whereby the reliability of the
results could be verified or systematically adjusted by accompanying direct numerical
simulations (DNS), would be an attractive and cost effective procedure under conditions
of routine evaluations in laboratory and industrial level. This particular approach of
S
u
o
S
u
o
137
utilizing DNS to correct for non-idealities in combustion measurements has found
success in cases such as improving the quality of extrapolation techniques to obtain flame
speed using counter-flow flames [73], and elucidating probe effects in sampling
low-pressure flames [74].
In the present work, a parametric study was carried out on the effect of a series of
parameters on the acquisition uncertainty for methane (CH
4
) and propane (C
3
H
8
)
flames. With the advent of DNS the experimental results from the Bunsen cone
technique can now be more systematically verified/validated by concomitant
computational results. The aim here is to measure the Bunsen cone laminar flame
characteristics with a low cost/minimal involvement methodology and then correlate their
departure from the “target” values with the help of the DNS results. This could allow
the deduction of suitable correction factors, which would systematically incorporate the
uncertainties involved in the described routine experimental campaign. This procedure
could lead to an easy-to-validate method for measuring using the Bunsen flame
method.
8.2 Experimental Approach
Experiments were completed by collaborators from University of Patras, Laoratory of
Applied Thermodynamics, the detail description of the experimental setup can be found
elsewhere [76]. In short, flames with low and high Re were measured to allow for an
evaluation of the effect of Re on the flame speed measurement methods. To vary Re, the
inlet mixture velocity of the measured Bunsen flames was a set as a multiple of the
expected unburned laminar flame speed at each equivalence ratio. For CH
4
, reactant
S
u
o
S
u
o
138
velocities investigated at different equivalence ratios were 3.5*S
u
o
, 4*S
u
o
, 4.5*S
u
o
.
Bunsen flames were also stabilized and measurable at inlet mixture reactant velocities as
low as 3*S
u
o
. The investigated ’s for CH
4
ranged from about Φ=0.8 (the blow off limit
for all air inlet conditions) up to 1.5. Stable and measurable flames were stabilized
between Φ=0.85 and 1.2 which had well defined and symmetric cone characteristics. Tip
flickering was observed but not as significant as that observed in propane flames. At
lower reactant velocities (e.g. below 3*S
u
o
) intense curvature and low cone height were
the main characteristics of the flames especially due to the nozzle exit boundary layer.
Above Φ=1 a diffusion flame envelope was seen to develop. Above 1.2 intense flickering
and curvature of the flame tip but no tip opening was identified up to Φ=1.5, as also
observed in [75]. A lean CH
4
/air flame is also expected to exhibit tip opening, but this
phenomenon could not be observed in the present experimental configuration,
presumably because the range of equivalence ratios were limited to 0.85 for successful
flame stabilization (e.g. [76]).
For C
3
H
8
, reactant velocities investigated at different ’s were 3*S
u
o
, 3.5*S
u
o
, 4*S
u
o
.
Bunsen flames were also stabilized and measurable at 2.5*S
u
o
. The investigated ’s range
from about Φ=0.82 (the blow off limit for all air inlet conditions) up to 1.5. Stable and
measurable flames were stabilized between Φ=0.85 and 1.2. The selected flames had well
defined and symmetric cone characteristics, although an imperceptible tip flickering was
also observed more than that for the CH
4
flames. At lower reactant velocities (below
139
2.5*S
u
o
) intense curvature and low flame cone heights were the main characteristics of
the flames mainly due to the thickness of the boundary layer at the nozzle exit. Also
above Φ=1 the diffusion envelope was formed and its intensity increased in proportion to
the equivalence ratio. Above Φ=1.2 intense flickering and curvature of the flame tip were
observed and at Φ between 1.4 and 1.45 the flame tip opened and was rather insensitive
to any further variation of the velocity of the reactants, as also reported in literature (e.g.
[75], [77]), rendering these flames rather inappropriate for laminar flame speed
estimation.
Two well-established techniques were employed to determine the flame speed (S
u
)
from the images; the term is reserved for the true laminar flame speed. The first
one is using the angle of the flame image and the velocity of the reactants and the second
involves the flame front area and the volumetric flow rate of the reactants. Once the
targeted flame is stabilized on the nozzle rim, digital camera images (Shutter speed: 1/25,
Aperture: F5.6 ISO 800) were taken to determine the flame front angle and cone surface
area. The velocity of the reactants was determined from the mass flow rate of the used
mixture and the nozzle diameter. Flame speeds were then calculated from direct flame
photographs using the cone angle method. S
u
is then determined from the knowledge of
the fuel-air mixture nozzle exit velocity (U
e
) and the angle (α) of the flame front with
respect to the vertical axis (Both the bulk value, U
b
, i.e. mass-weighted average velocity
and the value corresponding to the flat portion of the exit profile, U
p
, were used in place
of U
e
). The flame speed is then given as:
S
u
=U
e
*sin(α) (1)
S
u
o
140
Flames with low and high Re were evaluated using the cone surface area and the
flame front angle techniques to establish accuracy of each method as a function of Re.
As Cadwell et al. [78] have shown, the uniform velocity across the nozzle tends to revert
to a parabolic velocity distribution over a comparatively short distance downstream of the
exit plane. Also Johnston [79] found that the measured burning velocity decreased as the
flow rate increased introducing yet another uncertainty in the cone angle method for tall
Bunsen flames. Thus it was concluded that the use of high flow rates with their associated
taller cones should better be avoided when the cone angle method is employed. At higher
reactant velocities (High Re) the cone area method is considered suitable in achieving a
more sharply defined surface area at the rim and the apex and therefore is conducive to a
more accurate estimation of the cone area. However in this technique the round vertex of
the cone and the curvature near the burner rim are two effects with strongly changing
curvature that introduce an additional source of inaccuracy as mentioned by Andrews and
Bradley [80]. The inner edge was used in the cone area method and as Fristrom [81] has
shown this inner region of the luminous zone represents the best location to measure gas
velocities and areas for these curved flames. Taking into account the merits and
drawbacks of each method both techniques were exploited to illustrate the limitations of
each methodology.
The volumetric flow rates (Q) of the C
3
H
8
/air and CH
4
/air mixtures were acquired by
using calibrated sonic nozzles with Omega® pressure regulators with an accuracy of
141
± 0.5%. S
u
was then deduced from the division of the volumetric flow rate of the
reactants by the area of the flame cone.
S
u
=Q/A
b
(2)
8.3 Numerical Approach
Complementing the experiments, direct numerical simulations (DNS) are carried out
which involve the solution of the full set of conservation equations of mass, momentum,
species, and energy along with reaction chemistry as specified by a chemical mechanism
for the fuel-air mixture [82]. Radiation heat loss is incorporated using an optically thin
radiation model with the significant radiating species considered being H
2
O, CO, CO
2
,
and CH
4
.
Two kinetic models were used in this work, one for CH
4
/air and another for C
3
H
8
/air
mixtures. They are both derived from the USC Mech II kinetic model [83], which
consists of 111 species and 784 elementary reactions. The full model is reduced using
DRG [84] to a 35 species, 226 reaction model for CH
4
/air mixtures and a 44 species, 342
reaction model for C
3
H
8
/air mixtures. Both models incorporate chemistry for excited
species: CH
*
[85], OH
*
[85], and CO
2
*
[86]. The excited state species were used to
track the flame surface consistent with experiments that use total luminescence to track
the flame surface. Figure 8.1 shows comparisons between S
u
o
’s computed from the
reduced models along with those predicted by the full USC Mech II model using the
PREMIX code [87]. The results are in good agreement over the range of ’s studied in
this work.
142
Figure 8.1. S
u
o
’s as a function of as obtained from the full USC Mech II kinetic
model and the reduced models derived for CH
4
and C
3
H
8
.
The numerical simulations are carried out using laminarSMOKE [82], which is an
open-source computational framework for modeling steady and unsteady reacting flow
configurations. laminarSMOKE is built on the framework of OpenFOAM [88] which is
an open-source finite-volume CFD code. A time-splitting technique is used in
laminarSMOKE to handle the stiffly-coupled energy and species transport equations [82].
The continuity and momentum equations are handled in a segregated manner using a
PISO algorithm [89]. The code is highly parallelized with inter-processor
communication being handled by MPI protocols.
0
10
20
30
40
50
0.5 0.7 0.9 1.1 1.3
S
u
0
[cm/s]
CH4 - USC Mech II
CH4 - 35 species
C3H8 - USC Mech II
C3H8 - 44 species
143
Figure 8.2. Computational grid used in the numerical simulations overlaid with
boundary conditions applied for pressure, temperature, velocity, and chemical species.
An axisymmetric grid as shown in Fig. 8.2, with a radius of 6 cm and height of 20 cm
is used in the numerical simulations. The approximate flame height and thickness are
estimated using the 1-D calculations. The initial grid is constructed to be uniform in the
area where the flame is expected to reside. The grid spacing in this region is set to be
about 3 cells per flame thickness. A stretched non-uniform grid is utilized outside of this
refined area. An initial non-reacting flow-field is established following which the mixture
is ignited and the simulation is carried on until a steady-state solution for the flame is
reached. Steady-state is established by ensuring that residuals for pressure, temperature,
and velocity have reached a constant value. Further, the flame position and height are
144
observed to be constant. At this point, an adaptive mesh refinement is performed at the
flame front to increase the grid resolution in that location. The location of the flame front
is determined by computing the gradient and curvature of the temperature field. The
simulation results from steady state are mapped on to the refined grid and computations
are performed till a new steady state is achieved. This sequence of steps is carried out
repeatedly till a highly refined flame region is established with an average of 70-80 cells
through the flame thickness for each condition investigated. This level of refinement is
considered adequate for the laminar conditions investigated in this work. Figure 8.3
shows a plot of temperature as a function of distance along a 1-D cut through the flame
for a CH
4
-air mixture with =0.80 at the high Re condition. The data points in Fig. 8.3
correspond to individual grid points illustrating the refinement achieved in the solution
through the flame thickness.
Figure 8.3. Temperature as a function of distance along a 1-D cut through the flame
front for a CH
4
/air mixture with =0.80 at the high Re condition.
145
Figure 8.2 also shows the boundary conditions used in the numerical simulations. The
inlet velocity profile is specified according to the one measured in the experiments. A
fixed temperature of 298 K is also specified at the inlet along with species mass fractions
corresponding to the fuel-air equivalence ratio. The nozzle wall temperature is also set to
298 K following experimental observations. No species diffusion is allowed into the
walls which are also assigned no-slip boundary conditions. Far-field boundary conditions
are implemented at the outflow boundaries using the waveTransmissive and InletOutlet
boundary conditions for pressure and velocity respectively.
Similarly to the experiments, numerical simulations were carried out to obtain highly
resolved flame fronts for CH
4
/air and C
3
H
8
/air mixtures at five different ’s (0.8, 0.9, 1.0,
1.1, and 1.2) for two different inlet Re. In estimating S
u
, both the angle and area methods
are utilized as in the experiments. For the angle method, the cone angle is estimated using
the healthy region of the flame surface away from the tip and burner rim. For the area
method, an iso-surface of total luminescence (CH
*
+OH
*
+CO
2
*
) is estimated.
Similar to the experiments, the inner edge of the cone is utilized in the area method. A
curve is fit to the iso-surface and utilized to extrude a 3-D conical surface using CAD
software (SolidWorks). The area of the surface is estimated using the same software.
Equations 1 and 2 were then utilized to obtain S
u
.
8.4 Results and Discussion
Experimental and numerical results were obtained for CH
4
/air and C
3
H
8
/air mixtures
at 1 atm and 298 K for a variety of ’s at the medium and high Re inlet conditions. To
eliminate any confusion, the different inlet Re cases will be referred to as low and high
146
Re inlet conditions. We analyze the results in three parts. First, non-idealities
introduced into the measurement technique due to effects such as the inlet boundary layer,
extinction at the burner rim, strain and curvature effects, etc. are studied using numerical
simulations which allow for systematically isolating these effects. The effect of these
non-idealities as they pertain to errors introduced in the interpretation methods, viz. the
angle and area methods to estimate S
u
are studied using experimental and simulation
results. Next, the complete set of results from the parametric analysis for CH
4
/air and
C
3
H
8
/air mixtures from experiments and simulations with varying and inlet Re are
presented. Finally, we try to estimate correction factors for the experimental and
computed S
u
based on known values of .
8.4.1 Non-ideal effects in Bunsen flames
i) Effect of boundary layer
In the experiments, a contoured nozzle is used to minimize the effect of boundary
layers and produce an almost top-hat velocity profile. However, a finite boundary layer
always develops whose thickness decreases with increasing inlet velocity. The presence
of a boundary layer has been known to affect measurements that utilize an angle method
to estimate S
u
[16]. Using the numerical simulations we attempt to understand the effect
of the boundary layer.
S
u
o
147
Figure 8.4. Iso-contours of velocity (left) and density (right) for a CH
4
/air flame at
=1.0 with a high Re at the inlet for a) case with an inlet boundary layer and b) case
without an inlet boundary layer. The black iso-surface represents the location of the flame
front.
Numerical simulations were carried out for CH
4
/air and C
3
H
8
/air mixtures at =1 for
the medium and high Re condition. In each case, the simulation is carried out using the
experimentally measured velocity profile with the boundary layer and with a top-hat
uniform velocity profile. The velocity used for the top-hat profile is equal to the
velocity in the flat region for the profile with a boundary layer causing it to have a higher
net flow rate. Figure 8.4 shows results for the CH4/air cases at =1.0 using the high Re
inlet condition with and without an inlet boundary layer. Velocity iso-contours are plotted
on the left and density iso-contours on the right. The flame location is indicated by a
black line corresponding to an iso-surface of the total luminescence. One of the effects of
removing the inlet boundary layer appears to be that the flame is lifted higher away from
the burner rim. The flame is still stabilized by heat loss to the burner rim but is lifted up
due to the finite velocity at the burner rim. A benefit of this is that the curvature in the
flame surface near the rim as observed for the case with the boundary layer is absent for
148
the case without the boundary layer. The edges of the cone formed by the flame surface
are hence almost exactly straight.
The simulations are carried out till steady state and the flame surface is identified.
Next, S
u
is estimated using the angle method and the flame surface in the “healthy”
region, i.e., far from the tip and the extinguished region close to the burner rim. Table
8.1 shows the results of this analysis. In each case, S
u
can be estimated using the
velocity corresponding to the flat section (U
p
) or the bulk velocity (U
b
) as mentioned in
Section 2. For the cases with no boundary layer, U
p
and U
b
are essentially the same.
The percentages in brackets give the corresponding differences from . At low and
high Re, the cases without boundary layer have less difference from as compared to
the cases with boundary layer. However, at high Re, the differences are comparable to
each other due to decrease in the thickness of the boundary layer. Using U
b
to compute
S
u
under predicts the known values of for the cases with a boundary layer. Overall,
with or without boundary layers, the error in S
u
computed using U
p
or U
b
seems to be
significant (4-20%), with the error being generally higher in the presence of a boundary
layer at the inlet. The lowest error is obtained for the case with high Re and no boundary
layer at the inlet.
S
u
o
S
u
o
S
u
o
149
Table 8.1. S
u
calculations using simulation results with and without the presence of
boundary layer in the inlet velocity profile for a CH
4
/air flame at =1.0. The values in the
brackets indicate the percentage difference for each S
u
from S
u
0
.
U
p
(m/s)
U
b
(m/s)
α (deg) S
u
(m/s) S
u
0
(m/s)
Using U
p
Using U
b
Low Re With BL 1.125 0.884 21.51 0.412 (+15%) 0.324 (-10%) 0.359
No BL 1.125 1.125 21.75 0.416 (+16%) 0.416 (+16%) 0.359
High Re With BL 1.58 1.27 14.79 0.403 (+12%) 0.324 (-10%) 0.359
No BL 1.58 1.58 15.78 0.430 (+20%) 0.430 (+20%) 0.359
ii) Pressure induced velocity changes
Figure 8.5 shows simulation results for a CH4/air flame at =1.0 for the high and
low Re cases. Iso-contours of pressure are plotted on the left while those for radial
velocity are plotted on the right. The radial velocity is expressed as a percentage value of
the inlet velocity. The black line corresponds to an iso-surface of the total luminescence
and denotes the flame surface. The figure shows that a small but finite pressure jump
exists across the flame. The radial velocity iso-contours shows a small region near the
bottom of the flame close to the burner rim where its magnitude rises to about 10-20% of
the inlet velocity. This is driven by the pressure jump across the flame and the region of
local extinction near the burner rim which causes some flow of unburned gas from the
core to flow out without passing through the flame surface.
150
Figure 8.5. Iso-contours of pressure (up) and radial velocity (down) for a CH
4
/air flame
at =1.0 for a) high Re case and b) low Re case. Radial velocity is expressed as a
percentage of the inlet velocity.
This has an implication on the region of the flame surface used in the angle method.
Care must be taken to ensure that the “healthy” flame surface used to estimate the angle
should not include any region where this pressure induced radial velocity exists. This
further implies that while using the flame angle method, it is preferable to have a taller
flame using a higher inlet Re so as to increase the length of the “healthy” surface that can
be used to determine the flame angle.
151
iii) Tip curvature effects
The curved tip of the Bunsen flame has been the subject of research in several
previous works [84, 90]. In utilizing the flame angle method for estimating S
u
, the
curvature at the tip can affect the “healthy” region of the flame used to determine the
flame angle. In this respect, it is desired to avoid the flame tip region altogether in
determining the flame angle. Figure 8.6 shows iso-surfaces of velocity overlaid on
iso-contours of temperature a CH
4
/air and a C
3
H
8
/air flame at =1.0 for the high inlet Re
case. As long as the flame surface utilized for the angle calculation lies outside of the
region where the velocity iso-surfaces start to bend towards each other and stop being
parallel to one another, the angle method should remain unaffected by the flame tip.
Figure 8.6. Iso-surfaces of velocity overlaid on iso-contours of temperature for a)
CH
4
/air flame at =1.0 for high Re case and b) C
3
H
8
/air flame at =1.0 for high Re case.
Velocity values for iso-surfaces are in units of m/s.
iv) Flame surface identification
It is worthy to consider the location of the flame surface as determined from the
luminescence with respect to temperature iso-surfaces as determined from the simulation.
1.6
1.9
2.3
2.6
2.9
2.6
2.3
1.9
2.0
2.4
2.8
3.1
2.8
2.4
2.0
152
This information is provided in Fig. 8.7 where iso-surfaces of temperature are overlaid on
iso-contours of density for a CH
4
/air flame at =1.0 for high Re case. The flame surface
as determined by an iso-surface of total luminescence is shown by a black line. It can be
noted from the figure that the flame surface determined by total luminescence
corresponds to a temperature iso-surface of about 1800 K. The value of luminescence
used to locate the flame surface is half the maximum value in the domain. Following the
discussion presented by Bradley [80] and Santoro [16], the appropriate flame area to be
deduced for use in Eq. 2 is that corresponding to the unburned gases just before reactant
pre-heating. This area is unavailable in the experimental measurements but can be
obtained using the numerical simulations. Estimates for S
u
were obtained using different
temperature iso-surfaces and compared to the one obtained using the total luminescence.
These results are presented in Fig.8.8. for this case is estimated as 35.97 cm/s using
PREMIX calculations. As seen from Fig. 8.8, the temperature iso-surfaces tend to
overestimate .
S
u
o
S
u
o
153
Figure 8.7. Iso-surfaces of temperature overlaid on iso-contours of density for a
CH
4
/air flame at =1.0 for high Re case.
Figure 8.8. S
u
estimates using different temperature iso-surfaces for a CH
4
/air flame at
=1.0 for high Re case. S
u
estimated using the luminescence iso-surface is also presented
for the same case.
786
445
300
591
882
1027
1900
Flame surface from
luminescence
1755
154
v) Extinction at the burner rim
Figure 8.9 shows simulation results obtained for a CH
4
/air flame at =1.0 for a high
Re case. Fluid flow paths are highlighted by streamlines colored by velocity magnitude.
The plot shows iso-contours of heat release rate. As can be seen from Fig. 8.9(a), the
flame is extinguished near the burner rim due to heat loss to the constant temperature
wall. A similar effect is observed in the experimental result for a CH
4
/air flame presented
in Fig. 8.9 (b). This poses a problem in utilizing the flame surface area method to
determine flame speed.
Figure 8.9. (a) Fluid flow path highlighted by streamlines overlaid on iso-contours of
heat release rate for a CH
4
/air flame at =1.0 for a high Re case. (b) Snapshot of
experimental observation of a CH
4
/air flame at =0.9 for a high Re case.
155
Figure 8.10. Iso-contours of total luminescence for a CH
4
/air flame at =1.0 for high
Re case overlaid with iso-surfaces of total luminescence having three different values;
a)1e-9; b)1e-8; c)1.5e-8.
Figure 8.11. S
u
estimates using different temperature iso-surfaces for a CH
4
/air flame at
=1.0 for high Re case. S
u
estimated using the luminescence iso-surface is also presented
for the same case.
156
Figure 8.10 shows iso-contours of total luminescence for a CH
4
/air flame at =1.0
for high Re case overlaid with iso-surfaces of total luminescence corresponding to three
different values: 1e-9, 1e-8, and 1.5e-8. The maximum value of total luminescence in the
domain corresponds to 1.80e-8. Figure 8.11 shows S
u
values estimated using different
total luminescence iso-surfaces. Using the iso-surface corresponding to half the
maximum value of total luminescence gives an S
u
value of 35.43 cm/s which compares
well to an of 35.97 cm/s obtained using PREMIX calculations. As will also be seen
in the results presented below for other ’s for CH4/air and C3H8/air flames, good
agreement between S
u
and is obtained by using a total luminescence iso-surface
corresponding to half the maximum value.
vi) Stretch effects
Figure 8.12. Ratio of consumption speed to computed locally along the flame
surface plotted as a function of local stretch rate for three different ’s for a) CH
4
/air
flames and b) C
3
H
8
/air flames.
S
u
o
S
u
o
S
u
o
157
The Bunsen flame method inherently incorporates stretch effects into the flame
speed determination. However, the effect of local stretch on the flame surface can be
evaluated by computing a local consumption speed and comparing it to . The
consumption speed (S
c
) is computed using the following equation:
(3)
Figure 8.12 shows results obtained for three different ’s for CH
4
/air and C
3
H
8
/air
flames. As can be seen from the results, for CH
4
flames whose Lewis number (Le) is
close to unity, the ratio of S
c
to is close to 1. On the other hand, for C
3
H
8
flames,
whose Le is greater than unity, the ratio of S
c
to increases with increasing negative
stretch values. Flame stretch increases towards the apex of the flame as seen in Fig. 8.12.
8.4.2 Results of the parametric analysis
Figure 8.13 depicts results obtained from experiments for CH
4
/air and C
3
H
8
/air
mixtures. S
u
’s computed using the angle and area techniques for different inlet Re and
are compared with accurate literature values [91]. Figure 8.14 shows similar
results obtained from numerical simulations. In this case, the S
u
’s are compared with
computed ’s.
S
u
o
S
u
o
S
u
o
S
u
o
S
u
o
158
Figure 8.13. Experimental results for measured flame speeds using area and angle
methods at different inlet Re for CH
4
/air and C
3
H
8
/air mixtures.
Considering the results for CH
4
/air mixtures in Fig. 8.13(a), it can be seen that all
methods give results close to the reference value at stoichiometry and the spread away
from the reference value increases as the mixture is made lean or rich. This is consistent
with the flame being strongest near stoichiometry and extinction near the burner rim
0.25
0.3
0.35
0.4
0.45
0.5
0.8 0.9 1 1.1 1.2 1.3
S
u
[m/s]
Park et al, [73]
Angle method, medium Re
Angle method, high Re
Area method, medium Re
Area method, high Re
CH
4
-air
0.25
0.3
0.35
0.4
0.45
0.5
0.8 0.9 1 1.1 1.2 1.3
S
u
[m/s]
Park et al, [73]
Angle method, medium Re
Angle method, high Re
Area method, medium Re
Area method, high Re
C
3
H
8
-air
159
which occurs more readily for weakly burning flames. It is also seen that all measured
results overestimate the reference values of . Next it is seen that the angle method
performs better than the area method at both Re especially at lean and stoichiometric
conditions. Further the area method at high Re appears to perform better than the area
method at low Re at lean and stoichiometric conditions. This is consistent with the
higher surface area produced at high Re resulting in a lower sensitivity to computed S
u
.
Considering the results for C
3
H
8
/air mixtures presented in Fig. 8.13(b), the agreement is
not as good as that observed for CH
4
especially at stoichiometry and = 1.1. The area
methods and angle method at medium Re show results close to each other but the angle
method at high Re shows considerable difference from the other methods. It is to be
noted that the bulk velocity, U
b
is used in the angle method for all cases presented in Fig.
8.13 and Fig. 8.14.
Figure 8.14(a) shows simulation results for the CH
4
/air mixtures. The area method is
seen to clearly perform better than the angle method at both Re. The angle method
produces results consistently lower than the values predicted by the area method. It is to
be noted that if U
p
is used to estimate S
u
using the angle method instead of U
b
, the values
are consistently higher than the reference values. Figure 8.14(b) shows simulation
results for the C
3
H
8
/air mixtures. Similar to the results for CH
4
/air flames, simulation
results for C
3
H
8
/air flames show better agreement with using the area method as
compared to the angle method.
S
u
o
S
u
o
160
Figure 8.14. Simulation results for flame speeds estimated using area and angle
methods at different inlet Re for CH
4
/air and C
3
H
8
/air mixtures.
161
8.4.3 Correction factors
We now estimate simple correction factors for S
u
based on experiments and
simulations that can be multiplied to the estimated value of S
u
using the angle or area
methods to obtain the reference values. The assumption is that the correction factor
for experiments and simulations are almost the same, since they are processed in a similar
manner. The correction factor is given by,
CF =
𝑆 𝑢 𝑛𝑢𝑚
𝑆 𝑢 𝑛𝑢𝑚
0
≅
𝑆 𝑢 𝑒𝑥𝑝 𝑆 𝑢 𝑒𝑥𝑝 0
(4)
where the value of
num
are obtained from freely propagating flame speeds using
PREMIX. The values of
exp
thus can be derived using the equation (4) and be
compared with those values from literature [91]. The objective is to see the percentage
difference of the obtained from Bunsen flame experiments as compared to those
obtained from literature. Figure 8.15(a) shows the ratio of for CH
4
/air mixtures and
Fig. 8.15(b) shows the same for C
3
H
8
/air mixtures. It can be observed that the for
CH
4
/air mixtures are consistently over predicted (close to 1.1) over the range of unlike
for the C
3
H
8
-air mixtures that tend to be less than 1 for lean mixtures and increases close
to stoichiometry. It is to be noted that these trend lines being estimated using all data
points (angle and area methods, different Re) encapsulate a range of factors within them.
The results seem to indicate that it may be possible to use simple algebraic scaling factors
using such analyses to correct S
u
measured using the Bunsen flame technique and
evaluate .
S
u
o
S
u
o
S
u
o
S
u
o
S
u
o
S
u
o
S
u
o
162
Figure 8.15. Ratio of for CH
4
/air and C
3
H
8
/air mixtures from experiments and
literature.
S
u
o
163
8.5 Concluding Remarks
A parametric study of Bunsen flame techniques for measuring flame speeds of
methane/air and propane/air mixtures was carried out using experiments and numerical
simulations. Two common techniques, the angle method and the area method are
utilized to extract the flame speed. The simulation results show a large effect of the
boundary layer in the inlet to flame speed estimated using the angle method. In case of
the area method, underestimation of flame surface area near the burner rim due to local
extinction of the flame is seen to be one of the primary sources of measurement error.
From the experimental data, the flame speed for methane/air mixtures is overestimated in
general, and on average is within 6 % of the reference value. Trends are qualitatively
similar to each other using different estimation techniques and inlet velocities. For
propane-air mixtures, the average deviation from the reference value is also about 6 %.
However, the trends are considerably different especially at rich mixture conditions.
Simulation results for methane/air mixtures show the area method, which uses half the
maximum intensity of OH
*
to generate the flame surface gives good agreement with
reference flame speeds. The angle method however under predicts the flame speed.
For propane-air mixtures, the simulation results show more deviation from the reference
value closer to stoichiometry than at lean conditions as in the experiments. Trends
generated for simple correction factors from experiment and simulation results show
similar behavior for both fuels. These correction factors in essence reflect the effect of
measurement method (angle or area) and inlet velocity for different equivalence ratios
and fuels. Future work will focus on extension of such correction factors to take into
account inlet temperature and pressure variations.
164
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170
9 Chapter 9: Zimont Scale Vortex Interactions with Premixed Flames
9.1 Introduction
The vortex-flame interaction is a complicated yet fundamental problem in combustion
theory [1-3]. Such topic requires extensive computation resources and experimental
capabilities, and often provides only limited information. A study of the interaction of a
vortex with a laminar flame can provide valuable insights into the dynamics of the
coupling of fluid mechanics and chemistry with reasonable cost.
Previous work of vortex-laminar flame interaction has been conducted mostly on the
scale vortex size, l
v
, greater than the flame thickness, δ
f
[4-8]. Under such condition,
flame is stretched and wrinkled by the vortex. Three phenomenons have been observed in
these vortex flame interaction, namely the dilatation and expansion of the vortex by the
heat release in the flame; convection and stretching of the flame by the vortex and
production of vorticity by flame curvature. While these studies are important towards the
understanding of global flame vortex interaction, they provide little information about the
fine scale flame dynamics response to vortex when large vortex cascades into size
comparable to l
v
, a scenario typically happened in turbulent environment.
Oran and co-workers [9,10] showed that the flame thickness increases by turbulent
motions, which affects the flame structure in the preheat zone and their effect becomes
less pronounced with increasing temperature toward the reaction zone. Their results
shows that such flame broadening is determined by scales large or equal to the flame
171
thickness rather than small-scale motions, i.e. kolmogorov scale. The turbulent energy
cascade fails to penetrate the internal structure of the flame, i.e. reaction zone, δ
r
, a
scale much smaller than δ
f
.
Bilger and co-workers [11] showed similar results via experiments that considerable
broadening of the flame front can occur at Re number conditions relevant to high-speed
propulsion while there is no evidence of flame reaction zone thickening at Karlovitz
numbers, Ka = 100, which suggests that flamelet model may be extend well beyond the
regime as traditional classification of combustion regimes.
Recently, Bobbitt and Blanquart [12] studied the interaction of a single vortex with a
premixed flame through sets of vortex size and strength. Their simulation results
identified the existence of four regimes in the vortex laminar flame interaction and
showed the final characteristics of the initial vortex. Their results also suggest that strong
vortex of size much smaller than δ
f
persist after passing through the flame.
In the current study, Zimont scale, l
v
≈ δ
f
, [13,14] vortex-laminar flame interaction
is investigated with simplified chemistry model to establish a foundation for the
following investigation using realistic fuels i.e. JP-10 with detailed chemistry model,
because very little work has been done on this topic utilizing aviation fuels. The
implications of previous work [9-11] suggest that such flame front broadening can cause
significant differences in the interaction between turbulent flow structures and flame
fronts while considering small MW fuels vs. large MW fuels.
172
The objective of this study is to validate if the flame front broadening phenomenon
occurs with Zimont scale vortex-flame interaction; the impact of flow field distortion on
light and heavy hydrocarbon fuel decomposition. The results will be presented in the
same manner following the objective steps.
9.2 Numerical Approach
Detail description of the 3D code can be found in Chapter 3. In short, a finite
volume based CFD code package called laminarSMOKE is used [16-19]. A time-splitting
technique is used in laminarSMOKE to handle the stiffy-coupled energy and species
transport equation [20, 21], the continuity and momentum equations are handled using
PISO algorithm [22].
A steady state acceleration field was introduced by introducing a source term
explicitly in the momentum equation. A two-dimensional, Cartesian, 2.5 cm × 2.5 cm
computation domain was used to represent a typical stagnation flow configuration, with
impinging flow velocity 0.8 m/s, of a CH4/air mixture from the left boundary. A no-slip,
no-penetration, adiabatic wall boundary condition was set at the right end of the domain
and outlet boundary conditions were used in the vertical direction. The field can be
visualized in Fig. 9.1, where vortex is imposed in the location adjacent to the flame front,
with a vortex size l
v
/ δ
f
=0.2 and vortex strength u
v
/s
u
o
= 4, where u
v
is the
characteristic velocity of the vortex and s
u
o
is the laminar flame speed. All cases were
performed on a uniform mesh of 40,000 cells until a steady state solution was reached.
173
Figure 9.1. Schematic view of the computation domain.
All 2-D simulations were performed using a three-step kinetic model, hereafter
referred as TSM. Lagrangian temperature histories, using particles injected at specific
locations in the presence/absence of vortex, were imported to the SENKIN code [23],
upon which a detailed chemistry model, JetSurF 1.0 [24], was used to investigate the fuel
decomposition process.
174
9.3 Results and Discussion
9.3.1 Vortex-Flame Interaction
Figure 9.2 depicts the centerline velocity and temperature profile for a
stoichiometric , 0.1 atm CH
4
/Air flame using the TSM. The case without the presence of
a vortex is referred to as the unperturbed case (UPC) and the one with the vortex is
referred as the perturbed case (PC). The UPC shows the classic velocity distribution
with a single peak due to thermal dilatation. In the PC, however, because of the presence
of the vortex due to the acceleration field near the flame, the velocity profile consists of
two peaks. The first velocity peak is caused by the fluid particle passing through the
acceleration field and the second velocity peak is due to the combined effect of vortex
and thermal expansion, causing a much higher peak than the unperturbed case. The result
shows that a strong vortex, u
v
/s
u
o
= 4 in this case, affects the velocity distribution and
readjusts the flame location due to the local velocity field distortion.
175
Figure 9.2. Velocity component in x-direction and Temperature as a function of spatial
location. (---) V
upc
; (−) V
pc
; (∙∙∙) T
upc
; (-∙-) T
pc
Figure 9.3 shows the temperature contour plot and streamline trajectory for the UPC
((a) and (b)) and the PC ((c) and (d)), respectively. The temperature and velocity fields
in the UPC are symmetric about the center line. However, due to the presence of a
clockwise rotational acceleration field near the flame front, the velocity below the
centerline is lower than the corresponding location in the UPC, and the velocity above the
centerline is likewise higher. This non-uniform distribution of velocities causes the flame
to readjust to a new location. More interestingly, the vortex carries the relatively “cold”
reactant mixture into the region above the centerline and circulates a “hot”
reactant-product mixture, the overall effect amounts to a redistribution of the species and
a broadening of the preheat zone near the vortex region, causing a milder temperature
gradient near centerline as shown in Fig 9.3 (c).
300
600
900
1200
1500
1800
2100
2400
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0E+00 5.0E-03 1.0E-02 1.5E-02 2.0E-02 2.5E-02
Temperature, K
Velocity, m/s
Spaital Location, m
176
Figure 9.3. (a) Temperature contours for the UPC; (b) Streamlines for the UPC; (c)
Temperature contours for the PC; (d) Streamlines for the PC.
Figure 9.4 (a) depicts the streamlines near the vortex region. As can be deduced from
the density of streamlines, the velocities far from the vortex are high compared to those
close to the vortex. The path lines far above the vortex cover a longer distance with high
U
U
T
T
177
velocity, while those far below the vortex experience a shorter path but at lower
velocities. The velocities close to the vortex center however are much smaller in
comparison, meaning the mixture inside the vortex is subject to a longer residence time.
This phenomenon is illustrated in Fig. 9.4 (b), where particles are injected at a constant
rate from the left boundary, thus the time histories for each particle can be traced in
material/Lagrangian coordinates. The difference in path lengths for equal times is
immediately apparent.
178
Figure 9.4. (a) Streamlines ; (b) Path lines carrying particles depicted at different times
179
9.3.2 Fuel Decomposition
The thermal structure of a flame is more or less determined by the local
hydrodynamic conditions. It is thus reasonable to assume that the thermal structure
brought about by the vortex-flame interaction described above is a good representation
for any fuel subjected to the same velocity field. But while two flames corresponding to
two different fuels may have the same thermal structures, they can vary remarkably in
their chemical structures. It is of natural interest to study this difference and we can
exploit the information in Fig. 9.4 (b), i.e. Temperature histories of fluid packets in the
vicinity of the vortex.
If we further simplify the problem by ignoring differences in the flame thickness
caused by different mass diffusivities, and idealize each fluid packet as a
zero-dimensional batch reactor subject to a varying temperature field, we can model its
chemical composition over time. This simplified approach allows us to use detailed
chemistry at very little computational cost.
180
(a)
(b)
Figure 9.5. (a) The UPC Fuel Fraction and Temperature as functions of time; (b) The
PC Fuel Fraction and Temperature as functions of time (-
.
-) CH
4
/Air mixure at 𝜙 = 1.0,
T
u
= 300 K and P = 0.1 atm; ( ─) n-C
12
H
26
/Air mixure at 𝜙 = 1.0, T
u
= 300 K and P =
0.1 atm; (---) Temperature.
0
500
1000
1500
2000
2500
0
0.2
0.4
0.6
0.8
1
12 14 16 18 20 22 24
Temperature, K
Scaled Fuel Fraction
Time, ms
0
500
1000
1500
2000
2500
0
0.2
0.4
0.6
0.8
1
6 8 10 12 14 16 18
Temperature, K
Scaled Fuel Fraction
Time, ms
181
Figure 9.5 depicts the temperature of a fluid packet originating from the center-line as it
moves in space, i.e. in material/Lagrangian coordinates. Fig 9.5 (a) shows the UPC where
n-C
12
H
26
starts to decompose around 1050 K and is consumed almost entirely at 1500 K.
CH
4
is not consumed until the temperature reaches about 1800 K. It confirms our long held
understanding that long chain can be easily decomposed through 𝛽 -session at moderately
high temperatures. Fig 9.5 (b) is the corresponding plot for the PC. The temperature field is
distorted due to the presence of vortex, as described in the previous section. While CH4 is
not affected by the non-monotonic temperature profile, n-C
12
H
26
exhibits some interesting
behavior. When the temperature reaches its first peak around 1000 K, n-C
12
H
26
starts to
decompose. But right after the temperature exceeds 1200 K, it falls back to about 700 K in
less than 2 ms. The residence time is not long enough to complete the decomposition
process; 40% of the fuel is decomposed in this case. The fuel stops decomposition due to
the temperature dip caused by the vortex and proceeds in a mixture containing C
1
-C
4
hydrocarbon fragments from 𝛽 -session. The fuel is entirely consumed once the
temperature climbs back to 1000 K again.
The residence time for n-C
12
H
26
is significantly different in these two cases. In the
unperturbed case, the fuel is completely consumed in less than half a microsecond, while in
the perturbed case, it lasts more than 3 ms. Such differences in fuel residence times also
imply that the distribution of C
1
-C
4
hydrocarbon fragments in both time and space is no
182
longer the same and the chemical structure inside the flame differs. The results presented
here only represent one path line of the temperature-time history. Our preliminary results
suggest that for each path line, the temperature-time history is different, meaning each
profile could lead to different decomposition distribution in time and space.
These findings underline the importance of chemistry when heavy hydrocarbons are
burnt in the turbulent conditions, an aspect that is usually overlooked in favor of modeling
all complexities using simple fuels like methane and hydrogen. Figure 9.5 (b) shows that
the strong bond energy in simple fuels may not be applicable to heavy hydrocarbons and
could be misleading.
9.4 Concluding Remarks
Laminar vortex-flame interactions were studied numerically using a stagnation flow
configuration in a two-dimensional Cartesian domain. The Lagrangian temperature
histories were extracted from the simulation result and implemented in SENKIN, where
detailed chemistry was employed. Results from the vortex-flame interaction were found to
thicken the preheat zone by mixing the cold reactant with heated mixtures. The flame was
seen to readjust its location based on local velocity changes. In the SENKIN simulations,
the results for n-dodecane were found to be significantly different from methane. The
difference in the consumption pathways between methane and n-dodecane emphasizes the
importance of heavy hydrocarbon chemistry when dealing with turbulent combustion.
183
9.5 References
[1] P.-H. Renard, D. Thevenin, J.C. Rolon, and S.M. Candel, Prog. Energy Combust Sci. 26(2000)
225-282.
[2] J. F. Driscoll, Prog. Energy Combust. Sci. 34 (2008) 91-134.
[3] N. Peter, Proc. Combust. Inst. 32 (2009) 1-25.
[4] W.-H. Jou, and J.J. Riley, AIAA J. 27 (1989) 1543-1557.
[5] A. M. Laverdant, and S. M. Candel, Prop. Power. 5 (1989) 134-143.
[6] C. J. Rutland, and J.H. Ferziger, Combust. Flame. 84 (1991) 343-360.
[7] T. Poinsot, D. Veynante, and S. M. Candel, J. Fluid Mech. 228 (1991) 561-606.
[8] J. B. Bell, N.J. Brown, M. S. Day, M.Frenklach, J. F. Grcar, and S. R. Tonse, Proc. Comb.
Inst, 28 (2000) 1933-1939.
[9] A. Y. Poludnenko, and E.S. Oran, Combust. Flame. 157 (2010) 995-1011.
[10] P. E. Hamlington, A.Y. Poludnenko, and E. S. Oran, Phys. Fluids. 23(2011) 125111.
[11] M. J. Dunn, A. R. Masri, and R. W. Bilger, Combust. Flame. 151 (2007) 46-60.
[12] B. Bobbit, and G. Blanquart, 8
th
US National Combustion Meeting
[13] V. L. Zimont, Combust. Expl Shock Waves. 15 (1979) 305-311.
[14] N. Peters, J. Fluid Mech. 384 (1999) 107-132.
[15] R.J. Kee, M.E. Coltrin, P. Glarborg, Chemically reacting flow: theory and practice, Wiley
Interscience. (2005)
[16] J. H. Ferziger, M. Perić, Computational methods for fluid dynamics, Chapter 5, Berlin:
Springer, 1996
184
[17] A. Cuoci, A. Frassoldati, T. Faravelli, E. Ranzi, Combust. Flame 160 (2013) 870-886
[18] OpenFOAM, www.openfoam.org, 2014
[19] A. Cuoci et al., OpenSMOKE: numerical modeling of reacting systems with detailed kinetic
mechanisms, in: XXXIV Meeting of the Italian Section of the Combustion Institute, Rome,
Italy, 2011.
[20] G. Strang, SIAM Journal on Numerical Analysis 5 (1968), 506-517
[21] P. N Brown, G. D. Byrne, A. C. Hindmarsh, SIAM journal on scientific and statistical
computing 10(5) (1989), 1038-1051
[22] R.I Issa, Journal of Computational Physics, 62 (1986) 40-65
[23] A.E. Lutz, R.J. Kee, J.A. Miller, Report SAND-87-8248; Sandia National Laboratories:
Albuquerque, NM, 1988.
[24] Sirjean, B., Dames, E., Sheen, D. A., You, X.-Q., Sung, C., Holley, A. T., Egolfopoulos, F.
N.,Wang, H.,Vasu, S. S., Davidson, D. F., Hanson, R. K., Pitsch, H., Bowman, C. T., Kelley,
A., Law, C. K., Tsang, W., Cernansky, N. P., Miller, D. L., Violi, A., and Lindstedt, R. P., “A
High-Temperature Chemical Kinetic Model of n-Alkane Oxidation, JetSurF Version 1.0,”
http://melchior.usc.edu/JetSurF/JetSurF1.0/ Index.html [retrieved 15 Sept. 2009].
185
10 Chapter 10: Conclusions and Recommendations
10.1 Concluding Remarks
In this dissertation, a detailed experimental and numerical investigation into the
fundamental flame properties of heavy hydrocarbons was conducted, with the main goal
being the accurate determination of laminar flame speeds and extinction strain rates of a
wide range of fuel surrogate candidates and realistic fuels in the counterflow
configuration. The experimental data were modeled using a variety of chemical kinetic
models. Rigorous sensitivity analyses on both chemical kinetics and molecular transport
as well as reaction path analyses were performed to illustrate the chemical and physical
mechanisms that control the combustion of these fuels.
To assess the uncertainties stemming from the current practices that are used to
interpret experimental data and derive the laminar flame speed, direct numerical
simulations of counterflow flames were carried out for n-dodecane/air flames. The effect
of molecular transport was studied by varying the fuel diffusivity. The results showed
that for fuel lean hydrocarbon/air mixtures, the preferential diffusion of heat or mass as
manifested by the Lewis number dominates the flame response to stretch. For fuel rich
mixtures, the controlling factor was determined to be the differential diffusion of the
reactants into the reaction zone for heavy hydrocarbons. The conclusion is that using
extrapolation equations derived based on asymptotics analysis and simplifying
186
assumptions to obtain the laminar flame speeds, could result in significant errors for rich
flames of heavy hydrocarbons.
Compare to flame propagation, flame extinction is more sensitive on molecular
transport, especially under non-premixed condition. It is shown that the updated diffusion
coefficients resolve the earlier difficulty of predicting the extinction strain rate of
non-premixed counterflow flames of n-dodecane/N
2
and n-decane/N
2
against O
2
. It is
also shown that the mixture-average transport formulation is adequate for predictions of
the extinction strain rate, provided that the Soret effect is taken into consideration.
A parametric study of Bunsen flame techniques for measuring flame speeds of
methane/air and propane/air mixtures was carried out using experiments and numerical
simulations. Two common techniques, the angle method and the area method are utilized
to extract the flame speed. The simulation results show a large effect of the boundary
layer in the inlet to flame speed estimated using the angle method. In case of the area
method, underestimation of flame surface area near the burner rim due to local extinction
of the flame is seen to be one of the primary sources of measurement error. Simulation
results for methane/air mixtures show the area method gives good agreement with
reference flame speeds. The angle method however under predicts the flame speed.
For propane-air mixtures, the simulation results show more deviation from the reference
value closer to stoichiometry than at lean conditions as in the experiments. Thus, using
187
the Bunsen flame technique to measure propagation speeds of flames of heavy
hydrocarbons can result in notable errors.
Laminar vortex-flame interactions were studied numerically using a stagnation flow
configuration in a two-dimensional Cartesian domain. The Lagrangian temperature
histories were extracted from the simulation result and implemented in SENKIN, where
detailed chemistry was employed. Results from the vortex-flame interaction were found to
thicken the preheat zone by mixing the cold reactant with heated mixtures. The flame was
seen to readjust its location based on local velocity changes. In the SENKIN simulations,
the results for n-dodecane were found to be significantly different from methane. The
difference in the consumption pathways between methane and n-dodecane emphasizes the
importance of heavy hydrocarbon chemistry when dealing with turbulent combustion.
10.2 Recommendations for Future Work
The direct numerical simulations of a variety of combustion phenomena constitute the
core of the present study to investigate rigorously the fundamental combustion and
emission characteristics of practical fuels and reexamine the conventional methods in
determining such characteristics based on combustion theory. Simple configuration such
as counterflow flames and Bunsen flames may nevertheless result in complex flow field
phenomenon and complication which can only be solved via direct numerical simulation.
Many problems of interest should be addressed further and recommendations for future
work are listed below:
188
The experiments should be extended to higher pressures using novel approaches such
as spherical expanding flames in order to validate the kinetic models at condition relevant
to engines (~40 atm). The experiments should also be extended to sub-atmospheric
pressure to validate the kinetics relevant to the condition from low-pressure flame
sampling experiments (~0.1 atm) and would allow for the validation of pressure dependent
rate constants.
Clear coupling phenomenon was already found for flame-vortex interaction at scale
close to flame thickness, which is relevant in high intensity turbulent flame. Such
phenomenon should be further investigated via both experiments and simulation especially
for practical fuels towards a better understanding of flame behavior at condition relevant to
engines.
With the advancements in direct numerical simulations, such powerful tool should
not be limited to just mimic the experiments but to help in designing the experiments.
The iteration time usually took several generations for perfecting the experimental design
could be dramatically shortened via the assistance from full scale simulation.
189
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Abstract (if available)
Abstract
The main focus of this dissertation was the experimental and numerical investigations of laminar flames of heavy liquid and solid hydrocarbons under simple (one-dimensional, steady state flow field using canonical configuration) and complex (two/three-dimensional, transient flow at high Karlovitz number) flow conditions. ❧ A number of theories that have developed based on simplified assumptions and asymptotic analysis and more important for light fuels such as methane, were examined both experimentally and numerically in two steady state and canonical configuration, namely counter-flow configuration and Bunsen flame configuration. The counter-flow configuration was used to determine laminar flame speeds and extinction strain rates over a wide range of heavy hydrocarbons including normal alkanes (up to carbon number 16), practical gasolines and jet fuels and aromatics (cyclopentadiene). The analytical solution derived from asymptotic analysis provides good agreement for laminar flame speeds for fuel lean conditions. However notable discrepancies have been identified for fuel rich conditions due to lack of consideration of fuel-oxygen differential diffusion especially for heavy fuels for which the molecular weight disparity between oxygen and fuel is large. ❧ For the Bunsen flame configuration, the area and angle methods were examined to measure laminar flame speeds of methane/air flames (representative of light fuel) and propane/air flames given that propane is the lightest hydrocarbon with distinctly higher molecular weight than oxygen. The results indicated that apart from issues raised from inlet boundary condition, flame extinction induced complex flow distribution at burner edge and flame tip effect, such configuration can’t produce quantitative results for fuels heavier than methane due to lack of consideration of flame speed variation to stretch for fuel/air mixtures with non-unity Lewis number. ❧ Based on the understanding of the propagation of flames of heavy fuels, accurate measurements of laminar flame speeds were carried out using the counter-flow configuration at atmospheric pressure for a variety of complex fuel molecules for which data are non-existing and which are of direct relevance to practical fuels. ❧ The interaction between a flame and turbulence is a fundamental aspect of combustion. To further illustrate the difference of flame behaviors between light and heavy fuels, the vortex laminar flame interaction was studied numerically in a canonical two-dimensional configuration for methane and n-dodecane flames. The n-dodecane exhibits early decomposition prior entering the flame due to the local temperature rise caused by the vortex, and such phenomenon is not observed in methane/air flames. ❧ In summary, the main conclusion of this dissertation is that the fuel complexity that has been frequently ignored in flame research needs to be accounted for in simple and complex flows. It was shown that the fuel effects are both of physical and chemical nature.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Zhao, Runhua
(author)
Core Title
Studies of combustion characteristics of heavy hydrocarbons in simple and complex flows
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Mechanical Engineering
Publication Date
02/23/2016
Defense Date
01/15/2016
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
counterflow,laminar flame speed,nonpremixed extinction,OAI-PMH Harvest,premixed extinction
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application/pdf
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Language
English
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Electronically uploaded by the author
(provenance)
Advisor
Egolfopoulos, Fokion (
committee chair
), Eliasson, Veronica (
committee member
), Ronney, Paul (
committee member
), Tsotsis, Theodore (
committee member
)
Creator Email
runhuacalifornia@gmail.com,rzhao@usc.edu
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https://doi.org/10.25549/usctheses-c40-214775
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UC11278911
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214775
Document Type
Dissertation
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Zhao, Runhua
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(contributing entity),
University of Southern California Dissertations and Theses
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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...
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Tags
counterflow
laminar flame speed
nonpremixed extinction
premixed extinction