GLOBAL COMBUSTION RESPONSES OF PRACTICAL HYDROCARBON FUELS:
n-HEPTANE, iso-OCTANE, n-DECANE, n-DODECANE AND ETHYLENE
by
KAMAL KUMAR
Submitted in partial fulfillment of the requirements
For the degree of Doctor of Philosophy
Dissertation Adviser: Prof. Chih-Jen Sung
Department of Mechanical and Aerospace Engineering
CASE WESTERN RESERVE UNIVERSITY
May, 2007
CASE WESTERN RESERVE UNIVERSITY
SCHOOL OF GRADUATE STUDIES
We hereby approve the dissertation of
Kamal Kumar
______________________________________________________
candidate for the Ph.D. degree *.
C.J. Sung
(signed)_______________________________________________
(chair of the committee)
J. Iwan D. Alexander
________________________________________________
J.S. T'ien
________________________________________________
T.A. Zawodzinski
________________________________________________
________________________________________________
________________________________________________
01/18/2007
(date) _______________________
*We also certify that written approval has been obtained for any
proprietary material contained therein.
Table of Contents
List of Tables ................................................................................................................... vii
List of Figures................................................................................................................. viii
Acknowledgment............................................................................................................ xiv
Abstract............................................................................................................................ xv
Chapter 1 ........................................................................................................................... 1
Introduction................................................................................................................... 1
1.1
Background......................................................................................................... 1
1.2
Global Combustion Responses.......................................................................... 2
1.3
Objectives............................................................................................................ 4
1.4
Structure of Dissertation ................................................................................... 5
Chapter 2 ........................................................................................................................... 9
Experimental Specifications......................................................................................... 9
2.1
Flame Speed Measurements.............................................................................. 9
2.1.1
Counterflow Burner Apparatus ................................................................ 9
2.1.2
Fuel Vaporization and Premixing ........................................................... 11
2.1.3
DPIV Specifications .................................................................................. 14
2.1.4
Laminar Flame Speed Determination..................................................... 17
2.2
Extinction Stretch Rate Measurements.......................................................... 21
2.3
Ignition Delay Measurements ......................................................................... 22
iii
Chapter 3 ......................................................................................................................... 34
Computational Specifications .................................................................................... 34
3.1
Laminar Flame Speed Computations............................................................. 34
3.2
Extinction Stretch Rate Computations .......................................................... 37
3.3 Ignition Delay Computations ............................................................................... 41
Chapter 4 ......................................................................................................................... 44
Laminar Flame Speeds of Preheated iso-Octane/O2/N2 and n-Heptane/O2/N2
Mixtures ....................................................................................................................... 44
4.1Scientific Background............................................................................................ 44
4.2
Experimental Results ....................................................................................... 47
4.2.1
Iso-Octane/O2/N2 ....................................................................................... 47
4.2.2
N-Heptane/O2/N2 ....................................................................................... 48
4.2.3
Comparison ............................................................................................... 49
4.2.4
Effect of Nitrogen Dilution....................................................................... 50
4.3
Sensitivity Analysis........................................................................................... 52
4.4
Concluding Remarks........................................................................................ 53
Chapter 5 ......................................................................................................................... 64
Laminar Flame Speeds and Extinction Limits of Preheated n-Decane/O2/N2 and
n-Dodecane/O2/N2 Mixtures....................................................................................... 64
5.1
Scientific Background ...................................................................................... 64
5.2
Experimental Results ....................................................................................... 67
5.2.1
Laminar Flame Speed Results ................................................................. 67
5.2.2
Overall Activation Energy Results .......................................................... 69
iv
5.2.3
Extinction Stretch Rate Results............................................................... 70
5.2.4
Flame Structure Response to Stretch Rate Variations.......................... 73
5.3
Sensitivity Analysis........................................................................................... 74
5.4
Concluding Remarks........................................................................................ 76
Chapter 6 ......................................................................................................................... 93
Laminar Flame Speeds and Ignition Delays for Ethylene/Oxidizer Mixtures ...... 93
6.1
Scientific Background ...................................................................................... 93
6.2
Experimental and computational specifications............................................ 95
6.2.1
Determination of Laminar Flame Speed ................................................ 95
6.2.2
Determination of Ignition Delays ............................................................ 96
6.2.3
Kinetic Models........................................................................................... 96
6.3
Results and Discussions ................................................................................... 97
6.3.1
Laminar Flame Speeds ............................................................................. 97
6.3.2
Ignition Delays......................................................................................... 101
6.4
Concluding Remarks...................................................................................... 106
Chapter 7 ....................................................................................................................... 121
Autoignition of n-Decane/Air Mixtures .................................................................. 121
7.1
Scientific Background .................................................................................... 121
7.2
Experimental and Computational Specifications........................................ 124
7.2.1
Determination of Ignition Delays .......................................................... 124
7.2.2
Kinetic Models......................................................................................... 125
7.3 Ignition Delay Results......................................................................................... 126
7.4
Concluding Remarks...................................................................................... 133
v
Chapter 8 ....................................................................................................................... 152
Autoignition of Binary Fuel Blends involving n-Decane: Influence of Fuel
Structure .................................................................................................................... 152
8.1
Scientific Background .................................................................................... 152
8.2
Experimental and Computational Specifications........................................ 154
8.2.1
Determination of Ignition Delays .......................................................... 154
8.3
Ignition Delay Results .................................................................................... 155
8.4
Practical Implications .................................................................................... 159
8.5 Concluding Remarks .......................................................................................... 161
Chapter 9 ....................................................................................................................... 167
Summary and Recommendations............................................................................ 167
References.................................................................................................................. 171
vi
List of Tables
Table 8.1 Composition of Mixtures Investigated
vii
List of Figures
Figure 2.1a) Twin counterflow nozzles b) Non-combusting stagnation flow c) Stagnation
Flow with twin flames d) DPIV image of the central region of twin flames.................... 24
Figure 2.2 Schematic of the experimental setup with the flow control/heating/mixing
elements. ........................................................................................................................... 25
Figure 2.3 Transient response for hydrocarbon buildup in the mixture - (a) n-dodecane (a
low vapor pressure / high boiling point liquid fuel) and (b) methane (a gaseous fuel). ... 26
Figure 2.4 Superposed chromatograms of ambient air and synthesized air used in the
experiments. ...................................................................................................................... 27
Figure 2.5 a) A single DPIV image and the corresponding vector map derived using
cross-correlation of two subsequent images; Sub-region size is indicated by the
rectangular annotation. b) An exploded view of the interrogation sub-region; image pair
captured at two different instants of time, t and t+Δt, showing the particle displacements
(enclosed in dotted circles) . ............................................................................................. 28
Figure 2.6 Measured particle size distribution for the silicone fluid seeding particles
generated. .......................................................................................................................... 29
Figure 2.7 (a) Axial velocity profile along the nozzle centerline. (b) Radial velocity
profile at the reference location identified in (a). ............................................................. 30
Figure 2.8 Histograms from 98 pairs of images demonstrating the equivalency of the
stretch rate values derived using (a) the radial velocity gradient at the reference location
(b) the maximum axial velocity gradient upstream of the flame, for a fixed nozzle exit
velocity.............................................................................................................................. 31
Figure 2.9 Reference stretch-affected flame speeds as a function of Karlovitz number for
various (a) n-heptane/air and (b) iso-octane/air flames, showing how the reference
stretch-affected flame speed is extrapolated to zero stretch to obtain the laminar flame
speed. The unburned mixture temperature Tu is 360 K. Solid lines represent linear
extrapolation, while dotted lines denote nonlinear extrapolation. .................................... 32
Figure 2.10 Schematic of RCM used for autoignition delay measurements; Figure
adapted from Mittal and Sung, (2006).............................................................................. 33
Figure 4.1 Laminar flame speeds of iso-octane/air mixtures - comparison with earlier
work. ................................................................................................................................. 55
Figure 4.2 Laminar flame speeds of iso-octane/air mixtures for various unburned mixture
temperatures. Experimental flame speed data are also compared with the computed
values using (a) the mechanism of Davis and Law (1998) and (b) the mechanism of
Hasse et al. (2000)............................................................................................................. 56
viii
Figure 4.3
work.
Laminar flame speeds of n-heptane/air mixtures - comparison with earlier
57
Figure 4.4 Laminar flame speeds of iso-octane/air mixtures for various unburned mixture
temperatures. Experimental flame speed data are also compared with the computed
values using (a) the mechanism of Davis and Law (1998) and (b) the mechanism of
Seiser et al. (2000). ........................................................................................................... 58
Figure 4.5 Comparison of measured laminar flame speeds for iso-octane/air (filled
symbols) and n-heptane/air (open symbols) mixtures at varying equivalence ratios and
preheat temperatures. ........................................................................................................ 59
Figure 4.6 Comparison of experimentally-determined mass burning fluxes for isooctane/air (filled symbols) and n-heptane/air (open symbols) mixtures of φ=0.8 and 1.0 at
varying preheat temperatures. The dotted lines represent the linear fits. ......................... 60
Figure 4.7 Laminar flame speed as a function of molar percentage of N2 in oxidizer,
[N2/(N2+O2)]×100, for (a) iso-octane/oxidizer and (b) n-heptane/oxidizer mixtures at
Tu=360 K........................................................................................................................... 61
Figure 4.8 Experimentally-deduced overall activation energies as a function of
equivalence ratio for iso-octane/air (filled symbols) and n-heptane/air (open symbols)
mixtures obtained by varying (a) N2 concentration and (b) preheat temperature............. 62
Figure 4.9 Comparison of the most sensitive reactions on mass burning flux at two
different unburned mixture temperatures using the iso-octane mechanism of Hasse et al.
(2000) and the n-heptane mechanism of Seiser et al. (2000). .......................................... 63
Figure 5.1 Experimental (symbols) and computed (lines) laminar flame speeds of ndecane/air mixtures with unburned mixture temperatures of 360, 400, and 470 K.......... 77
Figure 5.2 Comparison of the current n-decane/air laminar flame speed data with earlier
experimental studies.......................................................................................................... 78
Figure 5.3 Experimental (symbols) and computed (dashed lines) laminar flame speed
of n-dodecane/air mixtures with unburned mixture temperatures of 400 and 470 K. ...... 79
Figure 5.4 Comparison of experimental laminar flame speeds of n-decane/air (Tu=360,
400, and 470 K) and n-dodecane/air (Tu=400 and 470 K) mixtures................................. 80
Figure 5.5 Dependence of mass burning flux on unburned mixture temperature for ndecane/air and n-dodecane/air mixtures............................................................................ 81
Figure 5.6 (a) Arrhenius plot showing mass burning flux as a function of adiabatic flame
temperature for n-decane/air mixtures of varying equivalence ratios. Slope of the fitted
straight line is proportional to overall activation energy.(b) Plot of the overall activation
energy as a function of equivalence ratio for n- decane/air mixtures. .............................. 82
ix
Figure 5.7
Tu=400 K.
Direct images (negatives) of near extinction n-decane/O2/N2 flames with
83
Figure 5.8 Experimental (symbols) and computed (lines) extinction stretch rates of ndecane/O2/N2 mixtures...................................................................................................... 84
Figure 5.9 Computed flame response curves to stretch rate variations for n-decane
counterflow premixed flames using the kinetic mechanisms of (a) Bikas and Peters
(2001) and (b) Zhao et al. (2005)...................................................................................... 85
Figure 5.10
Experimental (symbols) and computed (lines) extinction stretch rates of
n-do-decane/O2/N2 mixtures. ............................................................................................ 86
Figure 5.11
Computed flame response curves to stretch rate variations for n-dodecane
counterflow premixed flames using the Utah Surrogate Mechanism (Zhang, 2005). ...... 87
Figure 5.12 Computed axial variations for (a) velocity and (b) temperature for varying
stretch rates obtained using numerical simulations for n-decane/O2/N2 counterflow
premixed flames. Half domain is plotted due to symmetry, with nozzle location at x =0.65
cm and stagnation surface at x =0.0 cm. Mechanism of Zhao et al. (2005) is employed. 88
Figure 5.13 Computed (a) flame thickness based on maximum temperature gradient and
(b) reaction zone thickness based on full width at half maximum of heat release profile,
as a function of stretch rate. Mechanism of Zhao et al. (2005) is used. ........................... 89
Figure 5.14 Ratio of the flame thickness and the reaction zone thickness as a function of
stretch rate......................................................................................................................... 90
Figure 5.15
Normalized sensitivity coefficients for mass burning flux based on the
mechanisms of Zhao et al. (2005), Bikas and Peters (2001), and Utah Surrogate
Mechanism (Zhang, 2005). ............................................................................................... 91
Figure 5.16
Normalized sensitivity coefficients for extinction stretch rate based on the
mechanisms of Zhao et al. (2005), Bikas and Peters (2001), and Utah Surrogate
Mechanism (Zhang, 2005). ............................................................................................... 92
Figure 6.1 Experimental (symbols) and computed (lines) laminar flame speeds of
atmospheric pressure ethylene/air mixtures as functions of equivalence ratio and
unburned mixture temperature. Computations shown for Tu=298, 400 and 470 K....... 107
Figure 6.2
Experimental (symbols) and computed (lines) laminar flame speed of
ethylene/air mixtures at atmospheric pressure and room temperature. The filled symbols
are data from this work. The open symbols indicate the results of previous works by
Egolfopoulous et al. (1990), Hirasawa et al. (2002), Jomaas et al.(2005), and Hassan et al.
(1998).
108
x
Figure 6.3 a) Experimentally obtained mass burning flux as a function of preheat
temperature with equivalence ratio as a parameter. b) Arrhenius plot showing mass
burning flux as a function of 1000/Tad for different equivalence ratios.......................... 109
Figure 6.4 Experimentally and numerically deduced overall activation energy for the
combustion process in a flame as a function of equivalence ratio.................................. 110
Figure 6.5
Sensitivity coefficients for mass burning flux (Tu=298 K, φ=1). ............. 111
Figure 6.6 Reaction flow analysis for (a) the mechanism of Wang and (b) the USCD
mechanism under flame conditions. .............................................................................. 112
Figure 6.7 Experimental and simulated pressure traces for ethylene autoignition. Molar
composition: C2H4/O2/N2/Ar = 1/3/6/27.84. Conditions at TDC: Tc = 904 K and Pc = 50
bar.................................................................................................................................... 113
Figure 6.8 Measured ignition delays for C2H4 autoignition at varying compressed
pressures and compressed temperatures. Molar composition: C2H4/O2/N2/Ar =
1/3/6/27.84. ..................................................................................................................... 114
Figure 6.9 Comparison of measured ignition delay times from the present RCM with the
literature data. ................................................................................................................. 115
Figure 6.10 Comparison of experimental ignition delay (filled symbols) with simulations
at Pc = 15 bar................................................................................................................... 116
Figure 6.11 Comparison of experimental ignition delay (filled symbols) with simulations
at Pc = 30 bar................................................................................................................... 117
Figure 6.12 Comparison of experimental ignition delay (filled symbols) with simulations
at Pc= 50 bar.................................................................................................................... 118
Figure 6.13 Reaction flow analysis for the mechanisms of a) Wang and b) UCSD for
autoignition. Conditions at TDC: Tc = 904 K and Pc = 50 bar....................................... 119
Figure 6.14 Comparison of percent sensitivity of ignition delay (Tc=904 K and Pc=50 bar)
obtained using the mechanism of Wang and the UCSD mechanism. ............................. 120
Figure 7.1 Typical experimental reproducibility............................................................. 135
Figure 7.2 a) Experimentally obtained pressure traces, Pc= 7 bar b) Simulated pressure
plots using mechanism of Bikas and Peters (2001), Pc= 7 bar....................................... 136
Figure 7.3 a) Experimentally obtained pressure traces, Pc= 14.3 bar .b) Simulated
pressure plots using mechanism of Bikas and Peters (2001), Pc= 14.3 bar .................... 137
Figure 7.4 a) Experimentally obtained pressure traces, Pc= 30 bar, b) Simulated
pressure plots using mechanism of Bikas and Peters (2001), Pc= 30 bar ....................... 138
xi
Figure 7.5 Definition of ignition delay τ1=first stage delay, τ1+ τ2=ignition delay a)
Second derivative of trace showing the inflection points b) First derivative of trace
showing the location of peaks corresponding to the inflection points in a).................... 139
Figure 7.6 Measured ignition delays (τ1+ τ2) as a function of compressed gas
temperature , Tc, at different post compression pressures, Pc for n-decane/air mixtures
corresponding to φ =0.8. ................................................................................................. 140
Figure 7.7 Comparison of ignition delay times obtained from the present RCM with
literature data .................................................................................................................. 141
Figure 7.8 a) Comparison of experimental ignition delays (symbols) with simulation
results (line) using the mechanism of Bikas and Peters (2001), Pc=7 bar b) Comparison of
experimental first stage delays (symbols) with simulation results (line) using the
mechanism of Bikas and Peters (2001), Pc=7 bar........................................................... 142
Figure 7.9 a) Comparison of experimental ignition delays (symbols) with simulation
results (line) using the mechanism of Bikas and Peters (2001), Pc=14.3 bar b)
Comparison of experimental first stage delays (symbols) with simulation results (line)
using the mechanism of Bikas and Peters (2001), Pc=14.3 bar ...................................... 143
Figure 7.10 a) Comparison of experimental ignition delays (symbols) with simulation
results (line) using the mechanism of Bikas and Peters (2001), Pc=30 bar b) Comparison
of experimental first stage delays (symbols) with simulation results (line) using the
mechanism of Bikas and Peters (2001), Pc=30 bar......................................................... 144
Figure 7.11
Correlation for the experimental ignition delay times. ......................... 145
Figure 7.12
Reaction Flow analysis for the mechanism of Bikas and Peters (2001).
Conditions at TDC : Tc = 658.8 K and Pc = 14.3 bar. ..................................................... 146
Figure 7.13 a) Comparison of percent sensitivity of second stage ignition delay (Tc=658.8
K and Pc=14.3 bar ) b) Comparison of percent sensitivity of first stage ignition delay.
(Tc=658.8 K and Pc=14.3 bar )........................................................................................ 147
Figure 7.14 a) Plot of Temperature profile and leading mode amplitude associated with
positive eigenvalues b) The corresponding eigenvalues for (a)...................................... 148
Figure 7.15 a) Plot showing the maximum and minimum eigenvalues. b) Temperature
profile showing the locations where the Participation Index of reactions to leading mode
with positive eigenvalues will be evaluated.................................................................... 149
Figure 7.16 a) Participation index of reactions to leading explosive mode; T= 701 K b)
Participation index of reactions to leading explosive mode; T= 804 K.......................... 150
Figure 7.17 a) Participation index of reactions to leading explosive mode; T= 852 K b)
Participation index of reactions to leading explosive mode; T= 1046 K........................ 151
xii
Figure 8.1a) Experimentally obtained pressure traces for n-decane/ethylene/air mixtures,
Pc= 7 bar b) Experimentally obtained pressure traces for n-decane/methane/air mixtures,
Pc= 7 bar ......................................................................................................................... 162
Figure 8.2 a) Experimental (symbols) and simulated ignition delays (lines) for fuel/air
mixtures, Pc= 7 bar for increasing amounts of second fuel component substituting ndecane. b) Experimental (symbols) and simulated first stage delays for fuel/air mixtures,
Pc= 7 bar for increasing amounts of second fuel component substituting n-decane. ..... 163
Figure 8.3 a) Experimental pressure traces for n-decane/ethylene/air mixtures, Pc= 7
bar b) Simulated pressure traces for n-decane/ethylene/air mixtures, Pc= 7 bar ............ 164
Figure 8.4 a) Experimental pressure traces for n-decane/dethane/air mixtures, Pc= 7
bar b) Simulated pressure traces for n-decane/methane/air mixtures, Pc= 7 bar ............ 165
Figure 8.5 Simulated ignition delay times for pure n-decane, ethylene, methane and
binary mixture of decane/ethylene or methane (1:5 molar ratios) computed using the
mechanism of Bikas and Peters (2001)........................................................................... 166
xiii
Acknowledgment
The author wishes to thank Professor Chih-Jen Sung for his guidance during the
course of this work.
Financial support for this work was provided by National Science Foundation
under Grant No. 0133161. A part of this research was also supported by the Army
Research Office under Grant No. W911NF-06-1-0155.
xiv
Global Combustion Responses of Practical Hydrocarbon Fuels:
n-Heptane, iso-Octane, n-Decane, n-Dodecane and Ethylene
Abstract
by
KAMAL KUMAR
The dissertation topic deals with experimental investigations into three distinct global
combustion responses for premixed hydrocarbon/oxidizer mixtures, namely laminar
flame speed, extinction stretch rate and ignition delay. The emphasis was on the alkane
components of practical liquid fuels namely n-heptane, iso-octane, n-decane and ndodecane. Additionally, ethylene, being one of the key intermediaries in the oxidation of
higher hydrocarbons, was also studied. The laminar flame speed and extinction stretch
rate are representative of high temperature oxidation, while the ignition delay represents
the low-to-intermediate temperature oxidation chemistry. A study to observe the
chemical kinetic interactions in binary fuel blends of n-decane/ethylene/air and ndecane/methane/air mixtures was also conducted. Additionally, a comparison of the
experimental data with results obtained using numerical simulations was also done. For
the purpose of numerical modeling, chemical kinetic models available in literature were
used. The results obtained in this work augment the relatively sparse experimental data
available for validation of chemical kinetic models intended to model liquid hydrocarbon
combustion, especially for the high boiling point fuels.
xv
The utility of the experimental results stems from the fact that all of the responses
investigated are of relevance to practical devices. The enhancement of mass burning rate
under ambient pressures due to mixture preheat has been obtained, which can be
associated to combustor power density. The high pressure and low temperature
autoignition results are of relevance to emerging internal combustion engine concepts,
some of which attempt to achieve a controlled autoignition. The kinetic features observed
in the autoignition characteristics of binary blends can also be put to good use.
xvi
Chapter 1
Introduction
1.1 Background
Commercially available liquid fuels consist of a wide array of hydrocarbons in terms of
carbon number, carbon to hydrogen ratio and chemical structure. These fuels are usually
modeled by means of surrogate mixtures consisting of pure hydrocarbon components.
These mixtures are able to reproduce the desired physical and/or chemical properties.
Blends of iso-octane and n-heptane are used as primary reference fuels for gasoline. Ndecane and n-dodecane have often been used as a surrogate component for jet fuel. In
general, the accuracy of the simulated results obtained from a chemical kinetic model for
a surrogate depends on the comprehensiveness of the sub-mechanisms of individual
components considered in the model. Therefore, the availability of benchmark
experimental data for the individual components is not only valuable by itself, but also
provides a database for testing and validating the chemical kinetic mechanisms
developed. Thus, there is a strong interest in acquiring experimental data on their
oxidation kinetics over extensive variations in the range of thermodynamic parameters.
The results from such experiments are either in the form of a global response,
characterizing the oxidation behavior, or detailed information in the form of time
evolution or spatial profile of temperature and species. Recognizing that efficient
utilization of liquid hydrocarbon fuels can be aided by a better understanding of the
oxidation kinetics of the fuel under different operating regimes encountered in practical
devices, this dissertation endeavors to provide experimental data of high fidelity on the
1
global responses such as laminar flame speeds, extinction stretch rates and ignition delay
times for selected pure hydrocarbon fuels.
In addition, a comparison between the
experimental data and numerical results obtained using existing chemical kinetic models
is also done. Through such a comparison the comprehensiveness of a specific reaction
mechanism can be assessed.
1.2 Global Combustion Responses
Understanding of flame propagation and autoignition characteristics of different fuels is
important for both existing and advanced combustion systems. Laminar flame speed and
extinction stretch rate are representative of global responses obtained for high
temperature oxidation processes in convective-diffusive systems. In particular, laminar
flame speed is a fundamental and practical parameter in premixed combustion. This
parameter contains key information relating to the physicochemical properties of the
fuel/oxidizer mixture. Here laminar flame speed refers to the stretch free flame
propagation speed. The earlier works have focused mainly on gaseous fuels or relatively
volatile liquid fuels with unburned mixture temperatures corresponding to the ambient
conditions. In contrast, a very limited amount of laminar flame speed data for highboiling point liquid fuels under conditions of mixture preheat and over a wide range of
equivalence ratios exists. This is partly attributable to the difficulties associated with fuel
atomization/vaporization and equipment preheating required for studying these high
boiling point, low vapor pressure fuels. There is also a similar paucity of information
regarding the influence of mixture preheating on the laminar flame speed and
consequently the mass burning flux. Considering the widespread use and the importance
2
of liquid fuels in practical combustion devices, it is desirable to have a fundamental
understanding of their laminar burning rates.
High stretch flame extinction data have also been found useful in kinetic model
validation purposes. Flame extinctions can be induced primarily by two mechanisms
depending on the stretch rate regime. The stretch rate (K) for a planar flame, is defined as
the time derivative of the logarithm of an area of the flame surface area (A), and is given
by K =
1 dA
(Williams, 1984). The existence of dual extinction limits, high stretch
A dt
blow-off limit and low stretch radiative extinction limit, has been demonstrated for nonpremixed combustion (T’ien, 1986) and premixed combustion (e.g. Sung and Law, 1996;
Maruta et al., 1996; Ju et al., 1997). The high stretch blow-off limit is a consequence of
either an incomplete reaction or the non-equidiffusion of heat and mass. In the low
stretch regime, the existence of an extinction limit is caused by excessive heat loss. In
general, it is difficult to measure the radiation induced low stretch extinction limit under
normal gravity conditions because of the complication of buoyancy-induced flows.
However the blow-off or the high stretch extinction limits have been widely investigated.
This is because the high stretch condition involves high convective flow, which is not
affected much by the buoyancy effect.
In addition, the high stretch extinction stretch
rate represents a kinetics-affected phenomenon and characterizes the interaction between
a characteristic flame/flow time to a chemical time.
Autoignition experiments in shock tubes and Rapid Compression Machines
(RCM’s) represent oxidation in a homogeneous system. Shock tubes have been widely
used to study the high-temperature chemistry of various fuels. On the other hand, RCM’s
provide access to the investigation of low-to-intermediate temperature chemistry. It is
3
noted that the behavior of most of the distillate fuels and their surrogate components are
not fully understood in the temperature range of less than 1000 K Furthermore,
hydrocarbons with longer carbon chains exhibit a distinct two-stage ignition phenomenon
in the low-to-intermediate temperature regime of 700-900 K. Low temperature
autoignition has been associated with engine knock in spark ignition engines as well as
combustion control in compression ignition engines, and continues to be the focus of
much research activity.
The above-mentioned global response parameters obtained from well-defined
laboratory configurations can also be employed to extract kinetic information related to
fuel oxidation. The fundamental data are very valuable for the development and
validation of chemical kinetic mechanisms. Furthermore, the availability of
comprehensive reaction mechanisms can be used as an aid in the design of practical
devices for efficient and clean combustion.
1.3 Objectives
The primary objective of this work is to study the global combustion responses of
premixed hydrocarbon oxidizer mixtures as manifested in the form of laminar flame
speeds, extinction stretch rates and ignition delays. The main emphasis is on the alkane
components of practical liquid fuels namely n-heptane, iso-octane, n-decane and ndodecane. Additionally, a related study on ethylene oxidation is also conducted, the
reasons for which are discussed in the following section.
4
Another objective of this work is to compare the experimental data with results
obtained using numerical simulations. For the purpose of numerical modeling of the
combustion processes, chemical kinetic models available in literature are used.
1.4 Structure of Dissertation
Laminar flame speed experiments on iso-octane and n-heptane are first discussed in this
work. This is followed by the flame propagation and high stretch flame extinction
investigations on n-decane and n-dodecane fuels. The importance of C2-C3 chemistry in
the laminar flame propagation speeds of these long chain hydrocarbon/air mixtures is
soon obvious through the sensitivity analysis of the numerical results. The laminar flame
speed is sensitive to the different amounts of ethylene formed on account of the βscission that governs the thermal decomposition of the long chain linear/branched radical.
Hence, a digression study was made to investigate flame propagation in ethylene/air
mixtures.
Having obtained the high-temperature oxidation responses such as the flame
propagation speeds and extinction stretch rates, the focus was shifted to the lowtemperature oxidation behavior. The low temperature oxidation response was studied
primarily by means of autoignition delay times of fuel/oxidizer mixtures. First the
ignition delay of ethylene/oxidizer mixture was investigated followed by autoignition
delay measurements on n-decane/air mixtures. The low temperature oxidation
investigations were concluded by a study that explored the effects of fuel interactions
(binary fuel blend), specifically the alkane–alkene (n-decane- ethylene) interaction. This
exploratory study provided an unambiguous evidence of extremely strong chemical
5
kinetic interactions, even for two fuel components on account of chemical structure
effects.
The dissertation is divided into chapters that are categorized broadly on the
basis of type of fuels and the oxidation regime investigated. Chapter 2 contains a brief
description of the experimental apparatus and procedures used for this work. A
description of the counterflow burner apparatus, flow and mixing components and
velocity measurement technique are provided. The data reduction techniques for
obtaining the laminar flame speed and extinction stretch rate results are also discussed.
The chapter concludes by providing a brief description of the Rapid Compression
Machine (RCM) used to obtain ignition delay times for fuel/oxidizer mixtures.
Chapter 3 provides an overview of the computational tools used in this work. The
laminar flame speed computations are discussed first, followed by the computation
procedure for extinction stretch rates. Finally, the procedure used for modeling
autoignition in the RCM is discussed. The purpose of this chapter is to outline the
governing equations that are solved along with the necessary boundary/initial conditions.
Chapter 4 contains experimental results on the laminar flame speed
measurements for preheated n-heptane/oxidizer and iso-octane/oxidizer mixtures. The
experimental results are compared to the numerically obtained results. Additionally, the
influence of mixture preheating and nitrogen dilution on flame speed is also presented.
Chapter 5 contains the experimental and computational results on laminar flame
speeds and extinction stretch rates for preheated n-decane/oxidizer and ndodecane/oxidizer mixtures.
6
Chapter 6 contains the experimental and computational results on laminar flame
speeds and ignition delays for ethylene/oxidizer mixtures.
Chapter 7 studies the autoigniton delay times of n-decane/air mixtures using a
rapid compression machine.
Chapter 8 explores the fuel blend interaction effects on the autoignition
characteristics of n-decane and ethylene.
Chapter 9 presents a summary of the results and suggests some future work.
Journal publications and conference papers of relevance to this dissertation either
published or under review are listed below.
Chapter 4: “Laminar Flame Speeds of Preheated iso-Octane/O2/N2 and n-Heptane/O2/N2
Mixtures,” by Kumar, K., Freeh, J.E., Sung, C.J., and Huang, Y., Journal of
Propulsion and Power, in press.
Chapter 5: “Laminar Flame Speeds and Extinction Limits of Preheated n-Decane/O2/N2
and n-Dodecane/O2/N2 Mixtures,” by Kumar, K., and Sung, C.J., submitted.
Chapter 6: “An Experimental Investigation on Ethylene/O2/Diluent Mixtures: Laminar
Flame Speeds with Preheat and Ignition Delays at High Pressures,” by
Kumar, K., Mittal, G., Sung, C.J., and Law, C.K., submitted.
Chapter 7: “Autoignition of n-Decane Under High Pressure Conditions” by Kumar, K.,
Mittal, G., and Sung, C.J., to be presented at the 5th US National
Combustion Meeting, San Diego, California, March-2007.
7
Chapter 8: “Autoignition of Binary Fuel Blends involving n-Decane Under High Pressure
Conditions” by Kumar, K., Mittal, G., and Sung, C.J., to be presented at the
43rd AIAA /ASME/SAE/ASEE Joint Propulsion Conference & Exhibit,
Cincinnati, OH, Jul 2007.
8
Chapter 2
Experimental Specifications
2.1 Flame Speed Measurements
The following sections describe the apparatus and procedures employed to determine the
laminar flame speeds of fuel/oxidizer mixtures investigated in this work. The components
of experimental hardware and the data reduction technique used to obtain the laminar
flame speed are discussed. The burner apparatus is described first, followed by a
description of the flow control, fuel vaporizing and mixing systems used to obtain a
homogeneous combustible mixture. The adequacy of the vaporization and mixing system
is demonstrated, especially for high boiling point liquid fuels. Next, the specifications for
another key hardware component, the Digital Particle Image Velocimetry (DPIV) system,
are discussed. Finally the procedure to systematically eliminate stretch effects to obtain
laminar flame speed for a given fuel/oxidizer mixture using the experimentally measured
velocities is presented.
2.1.1
Counterflow Burner Apparatus
The counterflow configuration with two opposed burners was used in the experiments for
the determination of laminar flame speed. High contraction ratio, contoured nozzles were
used to obtain a top hat velocity profile at the exit. The nozzle exit diameter was 13 mm
and the separation was kept close to one diameter. Two opposed flow gas streams
impinge to create a stagnation surface. Figure 2.1 shows the twin nozzles and also the
resulting flow field for both non-combusting and combusting cases. The flow has been
visualized using silicone fluid droplets. The flame images shown in Fig. 2.1 and the
DPIV determined flow field indicated that the core region of the flame was quasi one9
dimensional. The extent of this core region was approximately a quarter of the nozzle
radius over the entire flow rate range investigated, even close to abrupt blow-off. The
uniformity of the core was verified at two axial locations. The first was just upstream of
the flame and the other midway between the flame and the nozzle exit. Although the
same configuration had been used earlier in our laboratory for flame propagation studies
by Hirasawa et al. (2002), Huang (2003) and Freeh (2006), the current burner hardware is
different from the one used in the aforementioned studies. Specifically, the earlier watercooled brass burner was replaced by lighter aluminum burners. Since the flame speed
studies in this work involved reactant preheating, the lighter and more thermally
conductive aluminum burners enabled a faster warm up to the desired temperature. The
nozzle separation distance was sufficiently large, compared to the flame thickness, to
prevent significant upstream heat loss from the flame to the burner nozzles over the
stretch rate range of interest. The two burners were fed with identical premixed
fuel/O2/N2 mixture. The entire burner assembly was electrically heated to obtain the
desired unburned gas temperature at the nozzle exit. The unburned mixture temperature
was controlled using feedback from thermocouples placed along the nozzle axial
centerline at a location 4 cm upstream of the nozzle exit. In addition, the burner nozzles
were provided with an annular co-flow of heated nitrogen which served to stabilize the
flame and also limited the flame interaction with the surroundings. In order to achieve the
variation in stretch rate while keeping the mixture composition fixed, a bypass valve
located upstream of the burner, which controls the amount of premixed unburned mixture
flowing to an exhaust, was used.
10
2.1.2
Fuel Vaporization and Premixing
A premixed charge was prepared by adding the required amount of vaporized fuel to a
metered quantity of oxygen and nitrogen. The desired amount of liquid fuel was delivered
by means of a pre-calibrated syringe pump; while the flow rates of oxygen and nitrogen
were controlled using calibrated choked orifices. The liquid fuel was atomized into fine
droplets using an injector assisted by heated nitrogen, and converted to the vapor phase
inside a heated vaporization chamber. Specific design of the injector included the liquid
fuel being supplied through the inner thin tube and a co-annular flow of hot nitrogen
blowing out from the outer orifice with a higher speed. As such, the shear force
facilitated the atomization process. Typically, the hot nitrogen temperature was set to be
close to the boiling temperature of liquid hydrocarbon fuel. Additionally, the temperature
of the vaporization chamber was maintained in the range of 395−405 K. The fuel vapor
laden, hot nitrogen gas was then mixed with the required amounts of heated oxygen and
nitrogen. A schematic indicating the various components of the counterflow apparatus is
shown in Fig. 2.2. For experiments involving a gaseous fuel, the vaporization system was
not required and fuel was metered using a calibrated choked orifice.
A major difference between the layout of the current flow system and that used in
the earlier works is that a part of the oxidizer (~48%) without any fuel vapors was
diverted to a nebulizer for seeding particle generation. Two separate flow streams,
comprising of the seeded oxidizer, and the unseeded fuel/oxidizer mixture, were then
mixed together in a heated mixing chamber before proceeding to the twin burners. This
modification is crucial, as explained in the following. Since the nebulizer containing
silicone fluid was not heated, when flowing fuel/oxidizer mixture through, substantial
11
fuel vapor condensation would have otherwise occurred within the nebulizer, especially
for the high-boiling-point liquid fuels. Note that an only the oxidizer flows through the
nebulizer in the current setup as compared to the fuel/oxidizer mixture in the earlier
setup. The other difference in the current setup is that the bypass valve, used to achieve
stretch rate variations, is placed downstream of the nebulizer, while in the earlier setup it
was installed at an upstream location. This relocation of the bypass valve offers the
advantage of constant seeding density irrespective of the amount of mixture being
bypassed. To prevent condensation of fuel in the flow path, the temperature of the entire
flow system was maintained at an appropriate value. It was ensured that the partial
pressure of fuel vapor in the mixture was well below its saturation value corresponding to
the local gas temperature at any location in the flow system. Because the highest
temperatures set in the vaporization chamber and the heated flow system were less than
500 K, and the estimated flow residence time in the gas line was less than 2 seconds, the
extent of fuel pyrolysis prior to the pre-mixture being delivered to the burner is expected
to be negligible.
Since the current setup is a continuous flow system, special care had to be taken
to ensure the correct mixture composition. For this purpose, a series of characterization
experiments illustrating the system response for the fuel atomization/vaporization and
mixing were conducted. The characterization experiments using both gaseous and liquid
fuels will be discussed in due course. Specifically, a Heated Flame Ionization Detector
(HFID) and a Gas Chromatograph (GC) along with a Helium Ionization Detector (HID)
were used for measuring the hydrocarbon level and O2/N2 concentrations, respectively.
12
For characterizing the hydrocarbon buildup in the mixture to the final desired
composition, the HFID was first zeroed with nitrogen and then spanned with a known
concentration of methane in air. As the premixed charge had a hydrocarbon concentration
well in excess of the full scale detector range, sample dilution was used. A fixed
volumetric flow rate of the unburned mixture was continuously sampled and an extra 2.5
parts of heated air was added. This diluted mixture was continuously analyzed by means
of the HFID for total hydrocarbon concentration. Take the n-dodecane/air mixture of
equivalence ratio (φ) 1.4 as an example; the resulting molar composition of C12H26/O2/N2
in the diluted mixture works out to be in the ratio of 1.4/64.75/243.46. Ideally, the
response of the HFID should be linear on a per carbon atom basis. Hence the response for
n-dodecane is expected to be 12 times that of methane, which was the detector span gas,
for the same molar concentration. In practice, however, a correction factor needs to be
applied. This correction factor was obtained from a California Air Resources Board
document (1997) for detailed hydrocarbon analysis of gasolines by gas chromatography.
Figure 2.3 (a) shows the experimental responses for n-dodecane with equivalence ratios
of 0.8 and 1.4. The theoretically expected values are also indicated in the figure as a
comparison. It is seen that the time required for the present flow system to reach a steady
equivalence ratio at the nozzle outlet was approximately 200 s after the fuel pump was
switched on. It is noted that when using gaseous fuel, such as methane, the current system
exhibited an almost instantaneous buildup of the fuel to the expected value (transient time
< 5 s), as demonstrated in Fig 2.3. (b). Furthermore, during the steady-state operation
(beyond 200 s) the detector response values obtained were 98.7% and 98.2% of the
expected response for the equivalence ratios of 0.8 and 1.4, respectively. It may be noted
13
that methane and n-dodecane responses are chosen so as to represent the extreme
operating scenarios which respectively correspond to an easily mixed gaseous component
and the least volatile fuel studied in this work. The same test was also carried out on ndecane, and iso-octane, yielding similar results, but with a slightly shorter transient time
to steady state. These tests therefore demonstrated the adequacy of the current setup for
handling relatively less volatile liquid fuels such as n-decane and n-dodecane.
Recognizing that a finite buildup time to steady state was required, the combustible
mixture was vented for 200 seconds prior to igniting the flames. As such, any liquid flow
rate oscillations during experiments were avoided and experimental repeatability was
assured.
The “air” used in the experiments was a mixture of oxygen and nitrogen in the
molar ratio of 1:3.76. A gas chromatographic analysis of this synthesized air was
conducted and compared with that of ambient air. The separation was carried out using a
Hayesep® DB 100/120 packed GC column and a Helium Ionization Detector (HID) was
used. Figure 2.4 shows a sample chromatogram obtained for the synthesized air which is
superposed on the chromatogram of ambient air under identical test conditions. It can be
seen from Fig. 2.4 that argon is present in the ambient air, but not in the synthesized air.
The gas chromatographic results also confirmed the composition of the synthesized air
employed herein.
2.1.3
DPIV Specifications
The nozzle exit velocity profile of the unburned fuel/air mixture was obtained using a
planar Digital Particle Image Velocimetry (DPIV) system. The flow was seeded using
sub-micron size particles of silicone fluid. The uniformly dispersed particles in the flow
14
were illuminated by a dual laser head, pulsed Nd:YAG laser light sheet of 0.2 mm
thickness in the vertical plane. The laser system generated a 120 mJ/pulse light beam at
532 nm with 3–5 ns pulse width. The light scattered by the seeding particles in the flow
field was recorded by a 12-bit, 1280 × 1024 pixels Dantec HiSense CCD camera with a
pixel pitch of 6.7 μm × 6.7 μm. The double frame mode of image acquisition was used,
and image pairs were acquired at the rate of 4.5 Hz. An optical filter with a passband
centered around 532 nm was used to minimize the effects of luminous flame emission on
the image. The Dantec PIV 2100 system was used to control and synchronize the image
acquisition, firing of laser pulses, and subsequent analysis of image pairs using the crosscorrelation technique. The field of view was adjusted to include the entire nozzle
diameter and nozzle separation distance, the magnification M was ~0.745. Note that the
true magnification factor needed to be determined every time the optics were adjusted.
The interrogation sub-region size of 32 × 32 pixels with 50 percent overlap was used for
cross-correlation among the image pairs. Figure 2.5(a) shows an example of one
representative DPIV image (1280×1024 pixels) taken from an image pair and the
deduced vector map. The rectangular annotations in Fig. 2.5(a) indicate the size of an
interrogation sub-region. The exploded view of this interrogation sub-region (32×32
pixels) at two different instants of time as captured in one image pair is shown in Fig.
2.5(b). The timing between pulses (Δt) in these experiments was varied between 50 μs to
179 μs. This optimization was such that the maximum measurable velocity did not
exceed 1.4 times the average reference flame speed (to be defined later) for a given
equivalence ratio over the entire experimental stretch rate region. As such, the particle
displacement within an interrogation sub region near the reference location was close to
15
1/4 of the sub region size (i.e. 8 pixels) for the current experiments. The optimum timing
interval for a given magnification is inversely proportional to the average reference flame
speed. Keane and Adrian (1992) demonstrated that it needs 6 to 10 particles per subregion in order to obtain a high quality PIV correlation. The criteria related to particle
number density and displacements were clearly met, as seen in Fig. 2.5(b). The peakheight validation method was applied to validate the instantaneous velocity vector map
and remove the outliers (Hirasawa et al., 2002). A vector was rejected if the ratio of the
highest peak to the second highest peak in the correlation plane was less than 1.2.
A TSI Model 3310A Particle Sizer was used to experimentally quantify the size of
the silicone fluid seeding particles. Several representative flow rates and compositions
were analyzed with the Particle Sizer to obtain a complete set of data. A sample plot of
the number distribution is shown in Fig. 2.6, along with the cumulative percentile of the
particles counted. It can be seen that ⅔ of the particles were smaller than 1 micron in
diameter and over 90% were smaller than 2 µm. These relatively low density, micronsize silicone particles are expected to follow the strained flows studied here (Melling,
1997).
Since the seeding particles do not survive in the post flame zone, it is important to
determine how the measured flame speed is affected by the seeding concentration. For
the various flame conditions, in an earlier work by
a
Huang et al. (2004), the raw data
with three different particle loadings, corresponding to 6, 10, 17 particles per sub region
were compared. Their results showed that the effect of particle concentration on the
measured flame speed was insignificant for the range of mass loading investigated. In the
16
present study, ~10 particles per sub-region were used in the measurements (cf. Fig.
2.5(b)).
2.1.4
Laminar Flame Speed Determination
Laminar flame speed (Su0) is one of the fundamental parameters that characterize a
combustible premixed fuel/oxidizer mixture, and is defined as the propagation velocity of
planar, adiabatic, one dimensional flame front into an initially quiescent fuel air mixture.
However, in practice flame propagation can be severely affected by flame front curvature
and its interaction with the aerodynamics of the flow field. These effects can be
characterized by stretch rate. The stretch rate (K) for a planar flame, is defined as the time
derivative of the logarithm of an area of the flame surface area (A), and is given
by K =
1 dA
(Williams, 1984). Flame stretch can be caused by aerodynamic straining as
A dt
well as flame curvature (Law, 1988).The influence of flow non-uniformity and nonequidiffusion effects, through the Lewis number, on the structure and propagation of
premixed flames has been extensively studied. A recent review by Law and Sung (2000)
provides an update on the current state of knowledge about the influence of stretch on
premixed flames. Hence, the experimental determination of the laminar flame speed, Su0,
requires some care, as it can be effectively masked by the stretch effects. An
experimental technique based on a symmetric twin counterflow stagnation flames (Wu
and Law, 1985) provides a systematic method to compensate for the aerodynamic stretch
effects. In this technique a reference flame speed (Su,ref), identified as the minimum
velocity upstream of the flame is used to derive the laminar flame speed (Su0). This
technique is employed for the current laminar flame speed studies.
17
In the present conterflow configuration, the flow field on the unburned side along
the stagnation streamline was obtained for various flow rates (and hence stretch rates)
through the nozzles. The reference flame speed was taken to be the minimum axial
velocity upstream of the flame. This choice of the reference flame speed is convenient in
that it could be measured experimentally with good accuracy. The measured flow field
for a given nozzle flow rate was used to determine the corresponding maximum axial
velocity gradient, K, and a reference stretch affected flame speed Su,ref. In the limit of
vanishing K, the reference flame speed, Su,ref, approaches the laminar flame speed.
For the current experiments DPIV was used to obtain a two dimensional velocity
field in the vertical plane passing through the nozzle centerline as shown in Fig. 2.1. The
vector map obtained by DPIV was further analyzed to determine the reference stretchaffected flame speed and the associated stretch rate. By plotting the axial velocity along
the centerline, as shown in Fig. 2.7(a), the minimum axial velocity upstream of the flame
location is taken as the reference stretch-affected flame speed Su,ref. Figure 2.7(b) further
shows that the radial velocity profile at this reference location is linear. Hence, the radial
velocity gradient (a) can be used to unambiguously characterize the flame stretch rate.
The stretch rate (K) is conventionally defined using the axial velocity gradient and is
equal to twice the radial velocity gradient, i.e. K = 2a. The concordance between the
stretch rate values derived using the two definitions was also confirmed experimentally,
the results of which are shown in Fig. 2.8. The histograms for Fig. 2.8 were obtained
using a fixed nozzle exit velocity for a relatively weak iso-octane/air flame (φ=0.8,
Tu=400 K) for 98 successive image pairs. A relative deviation of ~ 3% of the mean
stretch rate ( K ) was observed, and provides a typical quantitative measure of the
18
precision in the experimental stretch rate determination. In fact, the scatter in
experimental results of Fig. 2.8 suggests that the radial velocity gradient yields a more
precise estimate of stretch rate. Based on the variation of Su,ref with K, the unstretched
laminar flame speed (Su0) can be determined by the methodology of either linear or
nonlinear extrapolation. The extrapolation procedure is demonstrated in Figure 2.9 which
plots Su,ref as a function of Karlovitz numbers (Ka) for various n-heptane/air and isooctane/air flames, with the unburned mixture temperature (Tu) of 360 K. The Karlovitz
o
number, defined as Ka = K α m /( S u )2, where α m is the thermal diffusivity of the
unburned mixture.
For each case, the linear extrapolation technique is compared to a nonlinear
extrapolation based on the theoretical analysis of Tien and Matalon (1991), obtained
using a potential flow field. In Fig. 2.9, the solid and dotted lines represent the linear and
nonlinear extrapolations, respectively. It may be noted that for the current experiments
the velocity profile at the nozzle exit closely resembles a plug flow.
The expression relating the reference flame speed and the Karlovitz number for the
non linear and linear extrapolations are given by equations 2.1 and 2.2, respectively:
⎡σ − 1⎤⎫
0 ⎧
S u , ref = S u ⎨ 1 − ( μ − 1 ) Ka + Ka ln ⎢
⎬
⎣ Ka ⎥⎦ ⎭
⎩
0
S u , ref = S u (1 + m × Ka )
(2.1)
(2.2)
In the above equations Su,ref and Ka are respectively treated as the dependent and
independent variable, with σ being the ratio of burned to unburned gas densities, a
quantity calculated from chemical equilibrium. The other quantities of interest, (Su0,μ ,m),
are the estimated parameters for Equations 2.1 and 2.2 based on the experimental data
19
obtained for Su,ref and Ka. Note that two non-dimensional parameters μ and m are
dependent on the physicochemical properties of the unburned mixture. It may be noted
that in the current work we wish to estimate Su0.
The necessity of the extrapolation procedure, to determine the laminar flame
speed, arises from the fact that it is impossible to approach the zero stretch condition by
means of reducing the nozzle exit velocity. There is a lower limit to the experimentally
achievable stretch rate (nozzle exit velocity), determined by the geometry and flow
characteristics, below which an abrupt and violent flame flashback into the burner nozzle
will occur. In the current experiments, based on operating experience, the lower bound
for the stretch rate is set to be slightly above this unsafe limit. As a consequence, the
experimental data needs to be extrapolated to zero stretch rate in order to determine the
laminar flame speed.
It is seen from Fig. 2.9 that for most of the experimental conditions, Ka is kept to
be less than 0.1. Vagelopoulos et al. (1994) and Chao et al. (1997) demonstrated that
when the Karlovitz numbers are kept to the order of O(0.1), the accuracy of linear
extrapolation is improved and the over-prediction by linear extrapolation can be reduced
to be within the experimental uncertainty. Figure 2.9 also shows that the linearlyextrapolated laminar flame speed is no more than 3 cm/s higher than the value obtained
by using a nonlinear extrapolation of Tien and Matalon (1991). Therefore, in the
subsequent sections all the laminar flame speeds presented refer to the linearlyextrapolated values.
20
2.2 Extinction Stretch Rate Measurements
The counterflow twin-flame configuration was also used to determine the stretch-induced
extinction limits. Extinction due to flame blowoff can be brought about with increasing
stretch rate. The stretch rate just prior to abrupt extinction was measured using DPIV and
identified as the extinction stretch rate. Since flame extinction is highly sensitive to
downstream heat loss, for a given fuel/oxidizer mixture this twin-flame configuration,
considered as adiabatic on account of flame symmetry, yields a higher extinction stretch
rate than other types of non-adiabatic counterflow/stagnation flames.
To determine the extinction stretch rate, counterflow twin flames were first
established close to the point of extinction with a part of unburned combustible mixture
being bled off through a bypass valve upstream of the burners. Continuous DPIV image
acquisition was triggered at the rate of 9 images per second. The stretch rate was slowly
increased by closing the bypass valve, i.e. increasing the overall flow rate through the
burner, till an abrupt extinction occurred. The rate of change of stretch rate was much
slower compared to the inverse of the characteristic flame time.
Furthermore, the sequence of 8 images captured just before the extinction were
processed to determine the stretch rate from the velocity maps. The extinction stretch rate
values reported herein are the averages deduced form 10 or more velocity maps obtained
from repeated runs. When presenting the experimental results, the associated standard
deviation are shown as an error bar in the figures. Again, the reported stretch rate are
based on twice the radial velocity gradient at the axial velocity minimum point ahead of
the flame. The linear variation of radial velocity in the radial direction provides an
unambiguous means in determining the flame stretch rate. As mentioned earlier, the
21
resulting stretch rate was found to be consistent with the magnitude of the maximum
axial velocity gradient along the nozzle centerline upstream of the flame. Some other
specifics of the extinction stretch rate experiments will be discussed in the results section.
2.3 Ignition Delay Measurements
The ignition delay measurements were conducted using a Rapid Compression Machine
(RCM). This device, as the name suggests, compresses a homogeneous fuel oxidizer
mixture in a very short interval of time, thereby rapidly raising its pressure and
temperature. It consists of a driver piston, a reaction chamber, a hydraulic motion control
cylinder, and a driving air tank. This particular RCM incorporates a creviced piston head
design which provides a homogeneous reaction environment (Mittal and Sung, 2006,
2007). Dynamic pressure during compression is measured using a Kistler 6125B
transducer with 5010B charge amplifier. A schematic of the RCM is presented in Fig.
2.10.The compressed gas temperature at the end of compression (top dead center, TDC)
was varied by altering the compression ratio or the initial charge temperature, whereas
the desired pressure at TDC was obtained by varying the initial pressure of the fed
mixture or the compression ratio. Further details of the rapid compression machine can be
found in the doctoral thesis of Mittal (2006) and the work of Mittal and Sung (2006,
2007).
For this specific work the RCM was used to conduct autignition investigations on
ethylene and n-decane fuels. For the investigation on the non-volatile liquid fuel, namely
n-decane, provisions for pre-heating had to be incorporated into the pre-existing setup.
The heating of the reaction chamber was achieved by means of heating tape wound on
22
the external cylindrical surface. The applied voltage to the heater was varied to adjust the
power output. The voltage was varied by means of a phase-angle fired triac. The firingangle was adjusted based on a 4-20 mA control signal obtained from a temperature
controller. The temperature controller in turn received a feedback from a K-type
thermocouple placed in the temperature measurement port of the reactor. All the other
components involved in the mixture preparation and delivery to the reactor volume were
also maintained at the required pre-set temperature by means of additional heaters and
controllers. Additionally, a magnetic stirrer was use to mix the fuel and oxidizer
components in a heated mixing tank. The homogeneity of the mixture was confirmed by
drawing several samples at various intervals and using a Flame Ionization Detector (FID)
to measure the hydrocarbon concentration.
23
Figure 2.1a) Twin counterflow nozzles b) Non-combusting stagnation flow c) Stagnation
Flow with twin flames d) DPIV image of the central region of twin flames.
24
Figure 2.2 Schematic of the experimental setup with the flow control/heating/mixing
elements.
25
Detector Response (ppm C 1 basis)
(a)Flow System Transient Response for n-Dodecane Buildup
φ = 1.4
5x104
Predicted
Steady State Values
4x104
3x104
φ = 0.8
2x104
1x104
0
Fuel injection
stopped
Fuel injection
started
0
50
100
150
Time (s)
200
250
300
Detector Response (ppm C1 basis)
(b)Flow System Transient Response for Gaseous Fuel (Methane)
5X104
φ = 1.4
4X104
3X104
Predicted
Steady State Values
φ = 0.8
2X104
Fuel injection
started
1X104
0
0
50
Fuel injection
stopped
100
Time (s)
150
200
Figure 2.3 Transient response for hydrocarbon buildup in the mixture - (a) n-dodecane (a
low vapor pressure / high boiling point liquid fuel) and (b) methane (a gaseous
fuel).
26
Detector Response (Arbitrary Units)
13
N2
12
Ambient air response
Baseline
Synthesized air response
11
10
O2
9
8
7
Ar
6
5
0
0.2
0.4
0.6
0.8
Retention Time (minutes)
1
1.2
Figure 2.4 Superposed chromatograms of ambient air and synthesized air used in the
experiments.
27
(a)
(b)
Figure 2.5 a) A single DPIV image and the corresponding vector map derived using
cross-correlation of two subsequent images; Sub-region size is indicated by the
rectangular annotation. b) An exploded view of the interrogation sub-region;
image pair captured at two different instants of time, t and t+Δt, showing the
particle displacements (enclosed in dotted circles) .
28
1.2
1
15
0.8
10
0.6
0.4
5
0.2
0
0.1
1
10
Particle Aerodynam ic Diam eter (μm )
Fraction of Total Particles
Particle Number Density (Number/cm3)
20
0
Figure 2.6 Measured particle size distribution for the silicone fluid seeding particles
generated.
29
(a) Axial Velocity Profile
Axial Velocity (cm/s)
160
140
120
100
80
Reference Flame Speed
60
40
Reference Location
0
0.5
1
1.5
2
2.5
Distance from Nozzle Exit (mm)
(b) Radial Velocity Profile at Reference Location
Radial Velocity (cm/s)
200
150
100
50
0
-50
-100
-150
-200
-6
-4
-2
0
2
4
6
Radial Distance from Centerline (mm)
Figure 2.7 (a) Axial velocity profile along the nozzle centerline. (b) Radial velocity
profile at the reference location identified in (a).
30
(a)
(b)
Figure 2.8 Histograms from 98 pairs of images demonstrating the equivalency of the
stretch rate values derived using (a) the radial velocity gradient at the reference
location (b) the maximum axial velocity gradient upstream of the flame, for a
fixed nozzle exit velocity.
31
Reference Flame Speed (cm/s)
(a) n-Heptane/air, Tu=360 K
70
60
φ = 1.0
50
φ = 1.4
40
30
φ = 0.7
20
10
0
0.02
0.04
0.06
0.08
0.1
Reference Flame Speed (cm/s)
Karlovitz Number
(b) iso-Octane/air, Tu=360 K
70
60
50
φ = 1.0
40
φ = 1.4
30
φ = 0.7
20
10
0
0.02
0.04
0.06
0.08
0.1
Karlovitz Number
Figure 2.9 Reference stretch-affected flame speeds as a function of Karlovitz number for
various (a) n-heptane/air and (b) iso-octane/air flames, showing how the reference
stretch-affected flame speed is extrapolated to zero stretch to obtain the laminar
flame speed. The unburned mixture temperature Tu is 360 K. Solid lines represent
linear extrapolation, while dotted lines denote nonlinear extrapolation.
32
Figure 2.10 Schematic of RCM used for autoignition delay measurements;
Figure adapted from Mittal and Sung, (2006).
33
Chapter 3
Computational Specifications
The computational tools used to model the various combustion phenomena studied in this
work are discussed in this chapter. It is noted at the outset that code development is not a
part of this dissertation. The specific solution algorithms corresponding to the problem
under consideration were either available in the public domain or have been developed by
our group. Available computational tools have been used to model the combustion
processes of interest in conjunction with CHEMKIN-II package (Kee et al., 1989) and
the Transport package (Kee et al., 1986).
3.1 Laminar Flame Speed Computations
The laminar flame speeds were computed using the PREMIX code (Kee et al.,1985), in
conjunction with the CHEMKIN (Kee et al.,1989), and TRANSPORT (Kee et al.1986)
packages, originally developed by the Sandia National Laboratories. The PREMIX code
solves for structure and propagation velocity of a planar, one-dimensional, freely
propagating flame by finite difference method using a damped, modified Newton
technique. The following section outlines the problem formulation and the solution
technique as discussed in the report by Kee et al. (1985). The formulation assumes that
viscous effects, radiation heat transfer, and thermal diffusion due to concentration
gradients are negligible (Smooke et al., 1983). Under these assumptions, the governing
equations for the steady one-dimensional isobaric flame in a flame fixed coordinate
system are given by:
34
Mass Conservation:
M& = ρuA = constant
(3.1)
Species Conservation:
dYk
d
M&
= − ( ρAYk Vk ) + Aω& k Wk
dx
dx
(3.2)
Energy Conservation:
1 d ⎛
dT
dT ⎞ A
M&
=
⎜ Aλ
⎟−
dx c p dx ⎝
dx ⎠ c p
∑
K
k =1
ρYk Vk c p ,k
dT A
−
dx c p
∑
K
k =1
ω& k hk Wk
(3.3)
Equation of State:
ρ=
pW
RT
(3.4)
In Equations (3.1)-(3.4), x is the spatial location, T is the temperature, Yk the mass
fraction of the kth specie,
M& the mass flow rate, ρ the mixture density, u the flow
velocity, A the area of the flame stream tube, Vk the diffusion velocity of the kth specie,
ω& k is the molar production rate for the kth specie, Wk the molecular weight of the kth
specie, W the average molecular weight of the mixture, cp the mixture specific heat at
constant pressure, cp,k the kth specie specific heat at constant pressure, hk is the specific
enthalpy for the kth specie, and R is the universal gas constant.
The problem for the freely propagating flame is theoretically posed over an
infinite spatial domain, [-∞ +∞], where the inlet boundary conditions (x=-∞) for
temperature and specie mass fractions variable are the unburned mixture temperature and
respective inlet mass fraction values. For the other set of boundary conditions (x=+∞),
the gradients for both the temperature and specie mass fractions must vanish. The above
35
boundary conditions over-specify the problem and can only be met for a unique value of
M& .
For the purpose of computer solution using the PREMIX code the problem is
posed on a finite domain, [0, L]. The boundary conditions on the unburned side are given
by
(3.5)
T =Tu
εk = Yk +
ρYk Vk
(3.6)
M&
Where Tu is the unburned mixture temperature and εk is the species inlet mass fraction.
For the hot boundary the condition of vanishing gradients on temperature and species
mass fraction is imposed.
dT
dx
dYk
dx
=0
(3.7)
x =L
=0
(3.8)
x=L
Additionally,
in
the
PREMIX
computations
the
mass
conservation
relation
M& = ρuA = constant is replaced by:
dM&
= 0.
dx
(3.9)
Since M& is now an eigenvalue of the problem, an additional internal condition is required
to complete the problem, that is
T(xfix) = Tfix.
(3.10)
This internal condition (3.10) fixes the temperature to a specified value at a fixed spatial
location, xfix. The choice of location xfix is recommended to be within the preheat zone
36
and the corresponding Tfix is about 100 K above the cold boundary value (Smooke et al.,
1983).
Mixture averaged transport property evaluation was carried out in the simulations.
Additionally, adaptive gridding already implemented in PREMIX was used to spatially
resolve the flame structure. The grid spacing in PREMIX is determined in such fashion
so as to satisfy the following inequalities:
φ n , j − φ n , j −1 < δ × (max(φ n ) − min(φ n ) )
(3.11)
d
d
d
d
⎛
⎞
(φ n , j ) − (φ n , j −1 ) < γ × ⎜ max( (φ n )) − min( (φ n )) ⎟ .
dx
dx
dx
dx
⎝
⎠
(3.12)
Here, φn,j represents the solution corresponding to the nth dependent variable at the jth grid
point. For all the current flame speed computations, the value of parameters δ and γ are
set lesser than or equal to 0.1, with a typical solution having at least 250 grid points in the
region of the adaptive gridding. Note that the parameter δ controls the insertion of grids
in the region of large gradients, while γ controls grid point addition in regions of high
curvature such as the wings of a typical intermediate species distribution. The adaptive
gridding is active only for species whose concentrations exceed a cutoff “floor” value.
Additional grid points were added manually, to further extend the domain both on the
cold inlet side and the burned product region, the purpose of which was to ensure that the
laminar flame speed is indeed independent of the grid points (Smooke et al., 1983).
3.2 Extinction Stretch Rate Computations
The governing equations and the mathematical model for the axisymmetric counterflow
twin flames follow the plug-flow formulation of Kee et al. (1988), while the flame
37
response curves were generated by using the one-point temperature controlling method of
Nishioka et al. (1996). The extinction turning point of the flame response curve defines
the extinction limit. At this turning point, the computed maximum axial velocity gradient
ahead of the flame was used to determine the extinction stretch rate. For completeness, a
summary of the governing equations and the boundary conditions as outlined in Kee et
al. (1988) are presented below.
In an axisymmetric stagnation flow, with x and r representing the axial and radial
coordinates, respectively, the continuity equation is given by:
∂ (rρu ) ∂ (rρv)
+
=0
∂x
∂r
(3.13)
For a stream function of the formψ ( x, r ) = r 2U ( x) , the continuity equation will be
automatically satisfied if :
∂ψ
dU
= −rρv = r 2
∂x
dx
(3.14)
∂ψ
= rρu = 2rU .
∂r
(3.15)
The axial and radial momentum equations reduce to:
Axial Momentum:
⎛ 1 dU ⎞ 4 d ⎧
∂p
d ⎛U ⎞
d ⎛U ⎞
dU ⎫
⎟⎟ +
= −4U ⎜⎜ ⎟⎟ − 2 μ ⎜⎜
⎨2 μ ⎜⎜ ⎟⎟ + ν
⎬
∂x
dx ⎝ ρ ⎠
dx ⎭
⎝ ρ dx ⎠ 3 dx ⎩ dx ⎝ ρ ⎠
(3.16)
Radial Momentum:
2
d ⎧ d ⎛ 1 dU ⎞⎫
1 ∂p d ⎛ 2U dU ⎞ 3 ⎛ dU ⎞
⎟⎟ − ⎜
⎟⎬
= ⎜⎜
⎟ − ⎨μ ⎜⎜
r ∂r dx ⎝ ρ dx ⎠ ρ ⎝ dx ⎠
dx ⎩ dx ⎝ ρ dx ⎟⎠⎭
(3.17)
Where p is the pressure, ρ the mixture density, μ the dynamic viscosity and ν the kinematic
viscosity.
38
The axial and radial momentum equations show that
∂p
1 ∂p
and
depend on x only. Also,
∂x
r ∂r
∂ ⎛ 1 ∂p ⎞ 1 ∂ ⎛ ∂p ⎞
1 ∂ ⎛ ∂p ⎞
⎛ 1 ∂p ⎞
⎜
⎟=
⎜ ⎟ = 0 and ⎜
⎟ = constant = H .
⎜ ⎟ which implies
∂x ⎝ r ∂r ⎠ r ∂r ⎝ ∂x ⎠
r ∂r ⎝ ∂x ⎠
⎝ r ∂r ⎠
Now defining G ( x) =
dU ( x)
⎛ 1 ∂p ⎞
, and using the relationship ⎜
⎟ = constant = H , the
dx
⎝ r ∂r ⎠
equations to be solved are:
G ( x) =
dU ( x)
dx
(3.18)
Radial Momentum
H=
d ⎛ 2UG ⎞ 3
d ⎧ d ⎛ 1 ⎞⎫
2
⎜⎜
⎟⎟ − (G ) − ⎨μ ⎜⎜ G ⎟⎟⎬
dx ⎝ ρ ⎠ ρ
dx ⎩ dx ⎝ ρ ⎠⎭
(3.19)
Species Conservation:
2U
dYk
d
= − ( ρYk Vk ) + ω& k Wk
dx
dx
(3.20)
Energy Conservation:
K
dT
d ⎛ dT ⎞
dT K
2Uc p
− ∑ ω& kWk hk
= ⎜λ
⎟ − ρ ∑ Yk Vk c p ,k
dx dx ⎝ dx ⎠
dx
k =1
k =1
(3.21)
Here T is the temperature, cp the mixture specific heat and λ the mixture thermal
conductivity. The quantities Yk, Vk, cp,k, ω& k ,Wk and hk are the mass fraction, diffusion
velocity, specific heat, molar production rate, molecular weight and specific enthalpy for
the specie k, respectively. Equations 3.18 -3.21 constitute a boundary value problem with
the following boundary conditions
At nozzle inlet:
U (− L) =
ρ Lu L
2
; G(-L)=0; T(-L)=TL ; Yk(-L)=Yk, L
39
At stagnation surface:
U (0) = 0 ;
dYk
dG
dT
= 0;
= 0;
=0
dx
dx
dx
The stagnation surface corresponds to x=0 and the nozzle exit is located at x=-L. In the
above formulation H is the eigenvalue to be determined as a part of the solution.
Additionally the inlet boundary condition G(-L)=0 specifies a plug flow boundary
condition, implying a zero spatial velocity gradient at the nozzle inlet.
The extinction turning points are generated using the one-point temperature
controlling method of Nishioka et al. (1996), and the numerical scheme employed is
similar to the one used in Nishioka et al. (1996) and Sung and Law (1996). Specifically,
the boundary condition of mass flux at the nozzle exit is replaced by an internal
condition: x=x0, T=T0, i.e. assigning a prescribed temperature T0 at a fixed location x0.
Having obtained a starting solution, the flame response curve is mapped out by advancing
the solution to the next point using T(x0)=T0+ΔT, where ΔT is the value of temperature
change. As noted in the work of Sung and Law (1996), the replaced boundary condition
of mass flux at the nozzle exit becomes an edge value to the solution.
Having obtained the solution for the velocity, temperature and species
distribution, the maximum flame temperature Tmax and the maximum axial velocity
gradient (K) upstream (unburned side) of the flame are obtained. The complete response
curve in terms of Tmax versus K is generated using a set of solutions obtained as
described. Again, the turning point of the flame response curve defines the extinction
limit.
40
3.3 Ignition Delay Computations
The ignition delay in a RCM is modeled in the form of an initial value problem that
governs the time evolution of a closed, homogeneous, adiabatic system whose volume is
a specified function of time. The Sandia SENKIN (Lutz et al., 1988) code, in conjunction
with the Sandia CHEMKIN package for gas phase kinetics is used to solve the problem.
For the current experimental configuration of the RCM, the system is closed and
homogeneous but not truly adiabatic. The non-adiabaticity (heat loss) in the RCM is
accounted for empirically, using an effective volume concept similar to that discussed in
the doctoral thesis of Mittal (2006).
In the current simulations, SENKIN solves the mass and energy conservation
equations for a closed adiabatic system, given a pre-determined time variation of the
system volume. Note that the heat loss effect is incorporated as an effective volume
change, to be discussed subsequently.
Following the development outlined in the
SENKIN report (Lutz et al., 1988), the governing equations that represent the specie and
temperature evolution for the aforementioned system are given by:
Species Conservation:
dYk
= vω& k Wk
dt
3.22
Energy Conservation:
cv
dT
dv
+p
+ v∑ ek ω& k Wk = 0 ,
dt
dt
3.23
where m is the total mass of the mixture, v the specific volume v = V(t)/m for a specified
system volume variation V (t), cv the mean specific heat of the mixture, ek is the internal
41
energy of the kth specie. Additionally, the ideal gas equation of state (Eq. 3.4) is used to
compute the pressure. The other symbols have their usual meaning described earlier.
As noted earlier, the experimental setup is not truly adiabatic, and the heat loss
effects need to be accounted for. An empirical heat loss model based on experimental
data is used. Two different approaches are used for the time durations corresponding to
the compression stroke and the post compression time, respectively. The model used
during the two time intervals is briefly discussed below.
As expected, the experimentally observed peak pressure at the end of compression
is lower than that computed using the RCM geometric parameters, because of heat loss to
the walls of the reaction chamber. In the simulations, this situation is remedied by adding
a constant extra volume, namely Vadd, to the geometric volume such that the peak
pressures at the end of the compression match, namely
Veffective(t)=Vgeometric(t)+Vadd
(start of compression<t< end of compression)
(with Vadd >0)
(3.24)
For the subsequent duration (post compression to pre-ignition), although the
physical volume of the system does not vary with time, the pressure drops on account of
heat loss. Thus a time dependent volume expansion term is used to model the heat loss.
Veffective(t)={Vgeometric(tc)+Vadd}×f(t) (end of compression <t< observed ignition) (3.25)
Where tc is the time corresponding to the end of compression. Also note that f(t)>1 and
f’(t) >0.
The parameters used in this time dependent function, f(t), are based on the
pressure decay profile for a non-reacting mixture having the same specific heat ratio. This
procedure for modeling the heat loss has been designated as the effective volume
42
approach in the work of Mittal (2006). In that work, f(t) was chosen to be a 10th order
polynomial. The simulated pressure is made to closely approximate the experimental
pressure decay profile of a non-reacting mixture under identical conditions. The present
model for heat loss is similar in spirit, differing only in the representation of the nondimensional function f(t). Specifically, f(t) is represented as
⎛ t − tc ⎞
⎟
⎜
a ⎠
⎝
f (t ) = 1 +
d
⎛ t − tc ⎞
b+⎜
⎟
⎝ c ⎠
(3.26)
where tc= time at the end of compression stroke and the fitting coefficients a,b,c,d are
positive. Note that this form forces the effective volume to be consistent in Eqs. 3.24 and
3.25 by setting f (tc) =1 at the end of compression. The fitting parameters (a,b,c,d) are
obtained using non-linear fitting techniques implemented in the MATLAB® software
package. Additionally, f (t) is strictly increasing for t>tc if d<1, and is increasing over the
1
⎛ b ⎞d
interval [tc , c × ⎜
⎟ ] otherwise. For the range of parameters obtained using this
⎝ d −1⎠
fitting procedure, the interval is long enough to always contain the ignition event.
43
Chapter 4
Laminar Flame Speeds of Preheated iso-Octane/O2/N2 and nHeptane/O2/N2 Mixtures
4.1Scientific Background
Iso-octane and n-heptane are the primary reference fuels for octane rating and are widely
used constituents of gasoline surrogates. Iso-octane has also been used as a significant
component (5 to 10 % by volume) to model surrogate blends for JP-8 (Mawid et al.,
2004; Cooke et al. 2005).These surrogate blends are used both experimentally and
computationally to simplify the complex, naturally-based mixtures while retaining the
essential properties of the fuel. Laminar flame speed is one of the fundamental properties
characterizing the global combustion of a fuel/oxidizer mixture. Therefore, at the global
level, laminar flame speed data have been widely used to validate a proposed chemical
reaction mechanism. Recognizing that it is important to have experimental data of high
fidelity for validating the comprehensiveness of a kinetic mechanism, the present
experimental work aims to determine the atmospheric pressure laminar flame speeds of
iso-octane/air and n-heptane/air mixtures over a wide range of equivalence ratios and
preheat temperatures. Preheating of air is one of the methods frequently employed in
practical combustion devices as a means of waste heat recovery and more stable
operation. Fuel preheating is also employed for heavier oils to enable better atomization.
Thus, in a majority of practical combustion devices the reactants are in a state of preheat
before entering the combustion chamber.
In the last decade, the laminar flame speed data for iso-octane and n-heptane are
available from mainly two different experimental techniques, namely the outwardly
44
propagating flame in a combustion bomb and the counterflow or opposed-jet
configuration. These two prototypical flames are configurationally simple, and hence
facilitate detailed experimentation as well as computational simulation. In addition, for
both flame configurations the corresponding methodology of determining laminar flame
speed through systematic extrapolation to zero stretch rate is well established. Bradley et
al. (1998) reported the experimental results on iso-octane/air flame speeds using an
optically accessible combustion bomb and high speed Schlieren ciné-photography. Their
experimental conditions extended over a pressure range of 1 to 10 bar and covered an
equivalence ratio range of 0.8 to 1.2 at an initial mixture temperature of 358 K. They also
provided flame speed data at preheat temperatures of 400 K and 450 K, for equivalence
ratios of 0.8, 1.0, and 1.2. Kwon et al. (2000) reported atmospheric flame speed data at a
mixture temperature of 298 K and an equivalence ratio range of 0.8 to 1.6 for both isooctane and n-heptane fuels by using the outwardly propagating spherical flame
configuration. Using the counterflow flame configuration, atmospheric flame speeds of
iso-octane/air and n-heptane/air mixtures have been recently reported by Davis and Law
(1998) and aHuang et al. (2004) at 298 K mixture temperature and over a range of
equivalence ratios. These stretch-corrected data for laminar flame speeds of iso-octane/air
and n-heptane/air flames will be compared with the current results.
Among the aforementioned stretch-corrected flame speed datasets, the work of
Bradley et al. (1998) is the only known source of iso-octane/air laminar flame speeds
under conditions of mixture preheating. Using a counterflow facility, this investigation
complements the previous endeavors by determining the atmospheric laminar flame
speeds of iso-octane/air and n-heptane/air mixtures over a wider range of preheat
45
temperatures, varying from 298 K to 470 K. In addition, the present study covers
equivalence ratios of φ = 0.7 to 1.4 under preheated conditions.
There are several detailed kinetic mechanisms available for n-heptane and isooctane. A detailed review of such kinetic models, along with many other hydrocarbons,
has been recently discussed by Simmie (2003). Specifically, this work will compare the
n-heptane experimental data with the numerical results obtained using the reaction
mechanisms of Davis and Law (1998) and Seiser et al. (2000). It is noted that the reaction
mechanism of Davis and Law (1998) is based on the earlier work of Held et al. (1997),
with the addition of the iso-octane oxidation steps taken from the more detailed model of
Curran et al. (2002). The n-heptane oxidation mechanism of Seiser et al. (2000) was
developed based on the extinction and ignition of n-heptane in strained laminar flows
under non-premixed conditions. For the comparison of iso-octane flame speeds,
calculations are conducted using the reaction mechanisms of Davis and Law (1998) and
Hasse et al. (2000). Furthermore, while the detailed n-heptane mechanism of Curran et
al. (1998) (550 species and 2450 reactions) and the detailed iso-octane mechanism of
Curran et al. (2002) (860 species and 3600 reactions) were validated for both high and
low temperature chemistry covering a broad set of equivalence ratios, temperatures,
pressures, and N2 dilution ratios, their large size imposes computational constraints and
prevents making a similar comparison using these two detailed mechanisms.
In the following sections, the experimental results will be discussed first.
Subsequently, these results will be compared with the computed results using different
kinetic mechanisms, followed by sensitivity analysis and discussion.
46
4.2 Experimental Results
4.2.1
Iso-Octane/O2/N2
The experimental results section begins by presenting a comparison of the current
datasets with some of the existing data in literature, where available. Figure 4.1 compares
the present experimental data with the literature data for the same or similar unburned
mixture temperature. Figure 4.1(a) compares the present laminar flame speed data under
room temperature condition with those of Davis and Law (1998) and Kwon et al. (2000).
In general, there is a good agreement between different datasets. In addition, except for
φ=1.4, the present counterflow-based data follow closely with those of Davis and Law
(1998).
A comparison with the preheated experimental data of Bradley et al. (1998) is
provided in Figs. 4.1(b) and 4.1(c). It is noted that the work of Bradley et al. (1998)
defines two burning velocities, one based on the rate of disappearance of cold unburned
gas and the second based on the rate of appearance of burned gas. Both sets of their data
are shown at each equivalence ratio. It is seen from Fig. 4.1 that the current work is
consistent with the available literature data.
Having demonstrated the concordance among the current and similar data
reported in literature, a comparison of the current data with simulated results is
conducted. The experimental flame speeds are compared with the computed results using
the PREMIX code (Kee et al. 1985) in conjunction with the CHEMKIN (Kee et al. 1989)
and TRANSPORT (Kee et al. 1986) packages, originally developed by the Sandia
National Laboratories. The computations used windward differencing on the convective
term and mixture averaged formulation, and included the thermal diffusion of H and H2.
47
The laminar flame speeds of iso-octane/air mixtures as a function of equivalence ratio for
various preheat temperatures are shown in Fig. 4.2. This figure summarizes all the flame
speeds of preheated iso-octane/air mixtures obtained in the present study. The error bars
presented in Fig. 4.2 indicate the 95% confidence interval estimate of the laminar flame
speed obtained by using linear extrapolation. Figures 4.2(a) and 4.2(b) show the
comparisons with the computed flame speeds using the reaction mechanisms of Davis
and Law (1998) and Hasse et al. (2000), respectively. It is seen from Fig. 4.2 that the
mechanism of Davis and Law (1998) significantly under-predicts the laminar flame
speeds under all conditions of equivalence ratios and unburned mixture temperatures
investigated. Such under-predictions worsen as the unburned mixture temperature is
increased. On the other hand, the mechanism of Hasse et al. (2000) shows a good
agreement with the current experimental dataset, especially for the near-stoichiometric
conditions at all unburned mixture temperatures investigated. Under lean equivalence
ratios, Fig. 4.2(b) shows that the mechanism of Hasse et al. (2000) under-predict the
experimental values. This under-prediction is seen to increase as Tu is increased.
4.2.2
N-Heptane/O2/N2
The laminar flame speeds of n-heptane/air mixtures as a function of equivalence ratio are
shown in Figs. 4.3 and 4.4. Figure 4.3 compares the present laminar flame speed data
under room temperature with those of Davis and Law (1998) and Kwon et al. (2000). In
contrast to the iso-octane/air cases, the comparison of n-heptane/air flame speeds among
the three datasets is not as good. Specifically, the mismatch is somewhat noticeable for
the near stoichiometric conditions. The measured and computed laminar flame speeds as
48
a function of equivalence ratio for different preheat temperatures are shown in Fig. 4.4. It
is seen that the mechanism of Davis and Law (1998) under-predicts the n-heptane/air
laminar flame speeds by a similar extent as that for the iso-octane/air flames. On the other
hand, the mechanism of Seiser et al. (2000) is found to over-predict the current
experimental data except for the conditions of φ=0.7 and φ=1.4.
4.2.3
Comparison
Figure 4.5 summarizes and compares the measured laminar flame speeds of iso-octane/air
and n-heptane/air mixtures obtained in the present investigation. It is seen that the flame
speeds of n-heptane/air mixtures can be 5-10 cm/sec higher than those of iso-octane/air
mixtures. As discussed by Davis and Law (1998) and aHuang et al. (2004), since the
differences in the flame temperature and transport properties for both fuel/air mixtures
are insignificant over the range of equivalence ratios investigated, the difference in
laminar flame speed is caused by differences in the chemical kinetics. In particular, the
oxidation of n-heptane produces a large quantity of ethylene, while the main
intermediates formed during the iso-octane oxidation are propene, iso-butene, and methyl
radicals. As a consequence, the flame speeds of n-heptane/air mixtures are higher.
It is further note that the mass burning flux, mo = ρ u Suo , is a fundamental
parameter in the laminar flame propagation, where ρ u is the unburned mixture density.
Figure 4.6 demonstrates the effect of mixture preheat on the mass burning flux for the
fuel lean and stoichiometric cases. Significant enhancement of mass burning flux is
observed with increase in the preheat temperature for both iso-octane/air and nheptane/air mixtures. Again, for given equivalence ratio and preheat temperature, the
49
mass burning flux of n-heptane/air mixture is higher than that of iso-octane/air mixture.
Figure 4.6 also shows that in the range of unburned mixture temperatures investigated the
mass burning flux increases linearly with Tu. As such, the increase in Suo with increasing
Tu is not only because of the reduction of ρ u .
4.2.4
Effect of Nitrogen Dilution
The effect of nitrogen concentration variation on laminar flame speed was also
experimentally studied at an unburned mixture temperature of 360 K. Molar percentage
of nitrogen in the oxidizer composed of nitrogen and oxygen is varied from 78.5% to
80.5% for three equivalence ratios: φ=0.8, 1.0, and 1.2. Figure 4.7 plots the measured
flame speeds for both iso-octane/oxidizer and n-heptane/oxidizer mixtures. As expected,
the laminar flame speed decreases with increasing level of nitrogen dilution.
Since this range of nitrogen contents, 78.5–80.5%, can be considered as
perturbations to that of normal air (79% N2), for a given equivalence ratio the flame
speed data at varying nitrogen dilution levels can be employed to deduce the overall
activation energy (Ea) of the corresponding fuel/air mixture, following the methodology
of Egolfopoulos and Law (1990). Namely, the overall activation energy can be
determined by
⎡ ∂ ln mo ⎤
Ea = −2 R ⎢
⎥ ,
(1/
T
)
∂
ad ⎦ p
⎣
(4.1)
where Tad is the adiabatic flame temperature and R is the universal gas constant. Because
the large scale computational fluid dynamics (CFD) simulations often invoke simplifying
kinetics as one-step overall reaction, the extraction of such bulk flame parameter as
50
overall activation energy is especially useful when the CFD calculation with detailed
chemistry is not feasible. Based on the experimental results of Fig. 4.7, the deduced
overall activation energies of the three equivalence ratios are shown in Fig. 4.8(a). It is
seen that the variation of Ea with φ is non-monotonic and peaks near the stoichiometric
condition. Recognizing that in Eq. (4.1) Tad can be perturbed by varying either nitrogen
dilution level or preheat temperature, it is of interest to compare the deduced values of Ea
using two different methods. Note that the former method perturbs the reactant
concentrations by keeping Tu constant, while the latter method perturbs the premixed
flame system without changing the reactant concentrations. Based on the experimentallydetermined mo of iso-octane/air and n-heptane/air mixtures and Eq. (1), Fig. 4.8(b)
shows the deduced Ea by varying Tu.
Comparison of Fig. 4.8(a) and Fig. 4.8(b) demonstrates that despite the
quantitative differences in the deduced values, both extraction methods yield a similar
trend in the range of equivalence ratios investigated. The overall activation energy is seen
to peak close to the stoichiometric condition and decrease on both the lean and rich sides.
In addition, the overall activation energy values for n-heptane/air mixtures are observed
to be lower compared to iso-octane/air mixtures for all equivalence ratios under
consideration. This similarity of trend and the differences in absolute values using two
different extraction methods are also observed in numerical computations with the
available detailed reaction mechanisms. Such a quantitative discrepancy possibly arises
out of chemical interactions that occur as a consequence of varying N2 concentration and
hence the concentrations of fuel and O2. Since the extraction method by varying Tu
51
without involving the changes in reactant composition, the values shown in Fig. 4.8(b)
are likely to be a better estimate of the overall activation energy.
4.3 Sensitivity Analysis
Sensitivity analysis on mass burning flux is further conducted using the iso-octane
mechanism of Hasse et al. (2000) and the n-heptane mechanism of Seiser et al. (2000),
because these two mechanisms appear to agree better with the present experimental
results. Figure 4.9 plots and compares the normalized sensitivity coefficients of important
reactions with respect to the mass burning flux for stoichiometric iso-octane/air and nheptane/air flames at two different preheat temperatures. The normalized sensitivity
o
k
coefficient of the ith reaction is defined as mio ∂∂mk , the sensitivity analysis of Fig. 4.9
i
shows that the mass burning flux is not sensitive to any of the reactions involving the
parent hydrocarbon fuel. As expected, H+O2→O+OH is the most sensitive reaction
enhancing burning rate, and the mass burning flux is also highly sensitive to the CO
oxidation reaction which has a major contribution to the overall heat release. However,
the chain initiation reactions involving the breakage of carbon-carbon bonds will always
occur and are responsible for the formation of smaller alkenes and hydrogen radicals
which subsequently lead to chain branching reactions (Glassman, 1987). The subsequent
hydrogen atom abstraction from the fuel hydrocarbon due to the attacks of radicals leads
to the formation of alkyl radicals, which further decompose according to the β-scission
rule into smaller alkenes. Although the products of this decomposition are greatly
influenced by the structure of the fuel molecule (Glassman, 1987), Fig. 4.9 indicates the
importance of the reactions involving C2-C4 species.
52
Experimentally-obtained profiles for stable species in the work of Bakali et
al.(1998) for rich atmospheric flames show that the concentrations of unsaturated stable
C3 species, namely propene, 1,2-propadiene (allene), and propyne, are significantly
higher in the iso-octane flames when compared to the n-heptane flames with propyne
being the major product. The same work also shows that the major stable C2 specie is
ethylene, while the relative amount of ethylene is much larger for n-heptane flames. It
can thus be concluded that the high temperature oxidation kinetics of these unsaturated
C2-C3 hydrocarbons along with their significantly different concentrations in the two
flames account for the differences in the measured laminar flame speed values.
Furthermore, the discrepancies in the prediction of laminar flame speeds using different
reaction mechanisms require a better understanding of the C2-C3 chemistry, as has
already been pointed out by the previous work of Davis and Law (1998).
4.4 Concluding Remarks
Atmospheric laminar flame speeds of iso-octane/air and n-heptane/air mixtures were
experimentally determined over a range of equivalence ratios and unburned mixture
temperatures. The present measured laminar flame speeds complement the existing
literature data on primary reference fuels and provide a benchmark database for
validating the detailed reaction mechanisms at the global level. Under the same
equivalence ratio, the flame speed of iso-octane/air mixture can be 5-10 cm/s lower than
that of n-heptane/air mixture depending on the preheat level. The predicted flame speed
data for iso-octane/air flames using the mechanism of Hasse et al.(2000) showed good
agreement with the measured values. However, the computed flame speeds for n-
53
heptane/air mixtures using the reaction mechanisms available in the literature did not
agree favorably with our experimental results. The effect of nitrogen dilution on laminar
flame speed was also experimentally investigated. In addition, the overall activation
energies at varying equivalence ratios were extracted from the experimental data because
their relevance to the CFD simulations using one-step reaction. As the previous findings,
the importance of C2-C3 chemistry in the flame propagation of iso-octane/air and nheptane/air mixtures was identified and emphasized through sensitivity analysis.
54
Laminar Flame Speed (cm/s)
(a) iso-Octane/Air Mixtures, Tu=298 K
40
30
20
Davis and Law (1998)
10
0
0.6
Current Work
Kwon et al. (2000)
0.8
1
1.2
1.4
Laminar Flame Speed (cm/s)
Laminar Flame Speed (cm/s)
Equivalence Ratio
60
(b) iso-Octane/Air Mixtures
50
40
30
20
Tu = 358 K, Bradley et al. (1998)
Tu = 360 K, Current Work
10
0
0.6
80
0.8
1
1.2
1.4
Equivalence Ratio
(c) iso-Octane/Air Mixtures
70
60
50
40
30
20
10
0
0.6
Tu = 400 K, Bradley et al. (1998)
Tu = 400 K, Current Work
0.8
1
1.2
1.4
Equivalence Ratio
Figure 4.1 Laminar flame speeds of iso-octane/air mixtures - comparison with earlier
work.
55
Laminar Flame Speed (cm/s)
Laminar Flame Speed (cm/s)
120
100
(a) iso-Octane/Air Mixtures
Experimental
Tu=298 K
Tu=360 K
Tu=400 K
Tu=470 K
Computational, Davis and Law (1998)
Tu=298 K
Tu=360 K
Tu=400 K
Tu=470 K
80
60
40
20
0.6
120
100
0.8
1
1.2
Equivalence Ratio
1.4
(b) iso-Octane/Air Mixtures
Experimental
Tu=298 K
Tu=360 K
Tu=400 K
Tu=470 K
Computational, Hasse et al. (2000)
Tu=298 K
Tu=360 K
Tu=400 K
Tu=470 K
80
60
40
20
0.6
0.8
1
1.2
Equivalence Ratio
1.4
Figure 4.2 Laminar flame speeds of iso-octane/air mixtures for various unburned mixture
temperatures. Experimental flame speed data are also compared with the
computed values using (a) the mechanism of Davis and Law (1998) and (b) the
mechanism of Hasse et al. (2000).
56
Laminar Flame Speed (cm/s)
60
n-Heptane/Air Mixtures, T u=298 K
50
40
30
20
Davis and Law (1998)
Current Work
Kwon et al. (2000)
10
0
0.6
0.8
1
1.2
Equivalence Ratio
1.4
Figure 4.3
Laminar flame speeds of n-heptane/air mixtures - comparison with earlier
work.
57
Laminar Flame Speed (cm/s)
Laminar Flame Speed (cm/s)
(a) n-Heptane /Air Mixtures
140
Experimental
Tu=298 K
Tu=360 K
Tu=400 K
Tu=470 K
120
100
Computational, Davis and Law (1998)
Tu=298 K
Tu=360 K
Tu=400 K
Tu=470 K
80
60
40
20
0.6
0.8
1
1.2
Equivalence Ratio
1.4
(b) n-Heptane/Air mixtures
140
Exprimental
Tu=298 K
Tu=360 K
Tu=400 K
Tu=470 K
120
Computational, Seiser et al. (2000)
Tu=298 K
Tu=360 K
Tu=400 K
Tu=470 K
100
80
60
40
20
0.6
0.8
1
1.2
Equivalence Ratio
1.4
Figure 4.4 Laminar flame speeds of iso-octane/air mixtures for various unburned mixture
temperatures. Experimental flame speed data are also compared with the
computed values using (a) the mechanism of Davis and Law (1998) and (b) the
mechanism of Seiser et al. (2000).
58
Laminar Flame Speed (cm/s)
Laminar Flame Speed (cm/s)
70
60
iso-Octane/Air
n-Heptane/Air
Tu = 298 K
Tu = 360 K
Tu=298 K
Tu=360 K
50
40
30
20
0.6
120
100
0.8
1
1.2
Equivalence Ratio
iso-Octane/Air
1.4
n-Heptane/Air
Tu=400 K
Tu=470 K
Tu=400 K
Tu=470 K
80
60
40
0.6
0.8
1
1.2
Equivalence Ratio
1.4
Figure 4.5 Comparison of measured laminar flame speeds for iso-octane/air (filled
symbols) and n-heptane/air (open symbols) mixtures at varying equivalence ratios
and preheat temperatures.
59
Mass Burning Flux (g/cm2-s)
0.07
0.06
0.05
}
φ=1.0
}
φ=0.8
0.04
iso-Octane/Air
n-Heptane/Air
0.03
0.02
300
350
400
450
500
Unburned Mixture Temperature (K)
550
Figure 4.6 Comparison of experimentally-determined mass burning fluxes for isooctane/air (filled symbols) and n-heptane/air (open symbols) mixtures of φ=0.8
and 1.0 at varying preheat temperatures. The dotted lines represent the linear fits.
60
Laminar Flame Speed (cm/s)
Laminar Flame Speed (cm/s)
(a) iso-Octane/O2/N2, Tu=360 K
55
φ
0.8
1.0
1.2
50
45
40
35
30
78
78.5
79
79.5
80
[N2/(N2+O2)]×100
80.5
81
(b) n-Heptane/O2/N2, Tu=360 K
60
φ
0.8
1.0
1.2
55
50
45
40
35
78
78.5
79
79.5
80
[N2/(N2+O2)]×100
80.5
81
Figure 4.7 Laminar flame speed as a function of molar percentage of N2 in oxidizer,
[N2/(N2+O2)]×100, for (a) iso-octane/oxidizer and (b) n-heptane/oxidizer mixtures
at Tu=360 K.
61
Overall Activation Energy,
Ea (kJ/mol)
250
(a) Deduced by Varying Nitrogen Dilution
200
150
100
Tu=360 K
iso-Octane/Air
n-Heptane/Air
50
0
0.7
0.8
0.9
1
1.1
Equivalence Ratio
1.2
1.3
Overall Activation Energy,
Ea (kJ/mol)
(b) Deduced by Varying Preheat Temperature
250
200
150
100
iso-Octane/Air
n-Heptane/Air
50
0
0.7
0.8
0.9
1
1.1
Equivalence Ratio
1.2
1.3
Figure 4.8 Experimentally-deduced overall activation energies as a function of
equivalence ratio for iso-octane/air (filled symbols) and n-heptane/air (open
symbols) mixtures obtained by varying (a) N2 concentration and (b) preheat
temperature.
62
I-C4H8+O=>I-C3H7+CHO
I-C4H8+O=>I-C4H7+OH
Tu=298 K
C3H5+OH<=>C3H4+H2O
Tu=470 K
C3H4+OH=>CHO+C2H4
p = 1 atm
iso-Octane/Air
Hasse et al. (2000)
φ = 1.0
C3H4+OH=>CH2O+C2H3
C3H5+H=>C3H4+H2
CHO+OH=>CO+H2O
H2+OH<=>H2O+H
H2+O<=>OH+H
CHO+H=>CO+H2
H+O2+M<=>HO2+M
CHO+M<=>CO+H+M
CO+OH<=>CO2+H
O2+H<=>OH+O
-0.1
0
0.1
0.2
0.3
0.4
Normalized Sensitivity Coefficient
C2H3+CH3=>C3H6
C3H5-A=>C3H4-A+H
Τu=298 Κ
C2H3+O2=>CH2CHO+O
Tu=470 K
C3H5-A+H=>C3H6
p = 1 atm
n-Heptane/Air
Seiser et al. (2000)
φ = 1.0
CH3+OH=>CH2(S)+H2O
CH2(S)+O2=>CO+OH+H
HCO+OH=>CO+H2O
OH+H2=>H+H2O
O+H2=>H+OH
HCO+H=>CO+H2
H+O2(+M)=>HO2(+M)
HCO+M=>H+CO+M
CO+OH=>CO2+H
H+O2=>O+OH
-0.1
0
0.1
0.2
0.3
0.4
0.5
Normalized Sensitivity Coefficient
Figure 4.9 Comparison of the most sensitive reactions on mass burning flux at two
different unburned mixture temperatures using the iso-octane mechanism of
Hasse et al. (2000) and the n-heptane mechanism of Seiser et al. (2000).
63
Chapter 5
Laminar Flame Speeds and Extinction Limits of Preheated nDecane/O2/N2 and n-Dodecane/O2/N2 Mixtures
5.1 Scientific Background
In view of the growing interest in combustion studies of higher hydrocarbons, the present
investigation aims to extend the previous flame studies on n-heptane and iso-octane to
include n-decane and n-dodecane. Note that n-decane and n-dodecane are among the
major straight chain paraffin components found in diesel and jet fuels and have
frequently been used as surrogate components in different studies (Violi et al., 2002;
Agosta et al., 2004; Dagaut et al., 2006). Experimental and modeling studies related to
the structure of n-decane flames have been conducted by Douté et al. (1995, 1997) while
ignition delay measurements have been carried out for n-decane in shock tubes (Pfahl et
al., 1996). Additionally, jet stirred reactor experiments for n-decane have provided
valuable kinetic data over a range of pressures and temperatures (Dagaut et al., 1995).
However, experimental data pertaining to laminar flame speeds are rather sparse for both
n-decane and n-dodecane. This is partly attributable to the difficulties associated with the
mixture preparation, including fuel atomization and vaporization, as well as the
subsequent equipment preheating required for studying these high boiling point, low
vapor pressure fuels. Recently, there have been some data reported for laminar flame
speed of n-decane/air mixtures. Specifically, n-decane/air flame speeds have been
measured by Zhao et al. (2005) and Skjøth-Rasmussen et al. (2003). Zhao et al. (2005)
conducted flame speed measurements using a single jet-wall stagnation configuration at
atmospheric pressure and at 500 K preheat temperature. Skjøth -Rasmussen et al. (2003)
64
reported flame speed data for n-decane/air mixtures at 473 K preheat temperature using a
Bunsen burner. It has to be noted that unlike the work of Zhao et al., the experimental
data of Skjøth-Rasmussen et al. were not corrected for the stretch effects. By contrast,
investigation of n-dodecane combustion is meager and the corresponding stretchcorrected flame speed data are not available in the literature, to the best of our
knowledge. Considering only one preheat temperature was studied by Zhao et al. for ndecane flame speeds and that there is a need for the laminar flame speed data of ndodecane, the first objective of this study was to experimentally determine the laminar
flame speeds of both n-decane/air and n-dodecane/air mixtures as a function of
equivalence ratio over a range of preheat temperatures.
In addition, the extinction stretch rates of n-decane/O2/N2 and n-dodecane/O2/N2
mixtures in a counterflow twin-flame configuration were measured over a range of
equivalence ratios. We note that while extinction stretch rates of premixed stagnationpoint flames have been extensively studied in the past for gaseous hydrocarbon fuels,
only a very limited number of experimental studies on liquid hydrocarbons can be found
in the literature. A recent study by Holley et al. (2006) reported experimental data for
extinction stretch rates as a function of equivalence ratio for premixed n-heptane and isooctane flames. In the work of Holley et al. (2006), the counterflow single-flame
configuration, with a fuel/air mixture flowing against an air or a nitrogen stream, was
adopted. Because of the presence of downstream heat loss in this configuration the
required flow velocity (and hence Reynolds number) leading to flame extinction is lower
as compared to the near-adiabatic twin-flame configuration. In order to maintain the
laminar flow condition in the present counterflow twin-flame extinction experiments,
65
nitrogen diluted flames were therefore investigated. A molar ratio of N2 in the (N2+O2)
oxidizer corresponding to 0.84 allows flame extinction to occur at relatively moderate
stretch rates even in the twin-flame configuration.
Furthermore, the experimentally-determined laminar flame speeds and extinction
stretch rates were compared with the computed values using the reaction mechanisms of
n-decane and n-dodecane available in the literature. Through such a comparison, the
comprehensiveness of the specific kinetic model, in terms of its predictability of the
global flame responses, can be assessed. Further sensitivity analysis was also conducted
to identify the key reaction steps controlling flame propagation and extinction.
Numerical modeling of laminar flame speed was performed using the PREMIX
code (Kee et al., 1985), in conjunction with the CHEMKIN (Kee et al., 1989) and
Transport (Kee et al., 1986) packages. The computations use the mixture average
transport equations and consider the thermal diffusion of H and H2.
The governing equations and the mathematical model for the axisymmetric
counterflow twin flames follow the plug-flow formulation of Kee et al. (1988), while the
flame response curves are generated by using the one-point temperature controlling
method of Nishioka et al. (1996). The extinction turning point of the flame response
curve defines the extinction limit. At this turning point, the computed maximum axial
velocity gradient ahead of the flame is used to determine the extinction stretch rate.
The chemical kinetic mechanisms of Bikas and Peters (67 species and 354
reactions) (2001) and Zhao et al. (86 species and 641 reactions) (2005) were used for
modeling the n-decane flames. The n-dodecane flames were simulated using the Utah
Surrogate Mechanism Version 3 Beta (208 species, 1087 reactions) (Zhang, 2005) with
66
very minor modifications. Specifically, two species, fulvene and fulvenyl, respectively
containing six carbons with 6 and 5 hydrogen atoms, and their seven associated reactions
were removed from the original mechanism. This removal was because of some
numerical difficulties in PREMIX calculations when extending the solution domain to the
cold boundary. Inspection of a converged PREMIX solution using the original
mechanism on a small domain (0.1 cm) revealed the existence of dual-peak in the species
profile for the removed species. One of the peaks was located in the preheat zone at ~9 K
temperature rise above the inlet value and the other was in the reaction zone.
Additionally, argon was also removed since it is entirely non-participating in the present
experimental conditions and does not occur in any reaction even as a third-body collision
partner. After the above-mentioned modifications, the resulting mechanism for
simulating n-dodecane flames reduces to 205 species and 1080 reactions.
In the following sections, the experimental results are provided first.
Subsequently, these results will be compared with the computed results using different
kinetic mechanisms, followed by sensitivity analysis and discussion.
5.2 Experimental Results
5.2.1
Laminar Flame Speed Results
The measured laminar flame speeds of n-decane/air mixtures as a function of equivalence
ratio for three different mixture preheat temperatures, Tu=360, 400, and 470 K, are shown
in Fig. 5.1. Here, ‘air’ is synthesized by mixing O2 and N2 in the molar ratio of 1:3.76. A
comparison with two previous experimental results is also shown in Fig. 5.2. Note that
the work of Zhao et al. (2005) used a stagnation jet-wall flame configuration and their
67
experimental data were stretch corrected, while Skjøth-Rasmussen et al. (2003) used a
Bunsen flame and their reported results were affected by the stretch effects. Some
quantitative differences between the measured flame speeds seen in Fig. 5.2 are due to
the slight difference in preheat temperature (as compared to Zhao et al. (2005)) and the
effect of flame stretch (as compared to Skjøth-Rasmussen et al. (2003)).
Figure 5.1 also compares the present flame speed data with the computed values
using two published reaction mechanisms. Both mechanisms are seen to predict the flame
speed closely near the stoichiometric conditions. Although the mechanism of Zhao et al.
(2005) predicts well the experimental trend on the lean side, an under-prediction is seen
for the fuel rich mixtures. On the other hand, the mechanism of Bikas and Peters (2001)
tends to slightly under- and over-predict the experimental data for the fuel lean and fuel
rich mixtures, respectively.
The experimental data for n-dodecane/air mixtures along with the computed
values using the Utah Surrogate Mechanism (Zhang, 2005) with minor modifications are
shown and compared in Fig. 5.3. Two different unburned mixture temperatures, Tu=400
and 470 K, are studied here. It is seen in Fig. 5.3 that this mechanism over-predicts the
laminar flame speeds for n-dodecane/air mixtures over the range of equivalence ratios
investigated. It may be noted that this discrepancy is not attributable to the removal of
three species (fulvene, fulvenyl, and argon) because the computed flame speed using the
original mechanism on a small domain is close to that obtained using the modified
mechanism on an extended domain.
Figure 5.4 summarizes the measured laminar flame speeds of n-decane/air and ndodecane/air mixtures at varying equivalence ratios and preheat temperatures. This
68
comparison also shows that n-decane flames have slightly higher flame speed values
(~2−3 cm/s) than n-dodecane flames, under the same equivalence ratio and preheat
temperature.
Furthermore, Fig. 5.5 demonstrates the effect of preheat temperature on the mass
burning flux, mo = ρ u Suo , for three representative equivalence ratios, where ρ u is the
unburned mixture density. It is seen that mass burning flux increases with increasing
preheat temperature for both n-decane/air and n-dodecane/air mixtures. As such, the
increase in Suo with increasing Tu dominates over the reduction of ρ u with increasing Tu.
Also, for given equivalence ratio and preheat temperature, the mass burning flux of ndecane/air mixture is higher than that of n-dodecane/air mixture.
5.2.2
Overall Activation Energy Results
The measured mass burning flux variation with preheat temperature for a given fuel/air
mixture can also be used to deduce the corresponding overall activation energy, Ea. As
shown in the work of Egolfopoulos and Law (1990), the overall activation energy can be
determined by
⎡ ∂ ln mo ⎤
Ea = −2 R ⎢
⎥
⎣ ∂ (1/ Tad ) ⎦ p
(5.1)
It is further noted that in the work of Egolfopoulos and Law overall activation energy was
extracted by varying m o and Tad through different levels of nitrogen dilution. In this
nitrogen dilution method, however, the reactant concentrations are also perturbed.
Alternatively, Ea can be deduced from Eq. (5.1) through the changes in mixture preheat.
As such, mo and Tad are varied without changing the reactant concentrations. Figure
69
5.6(a) plots natural logarithm of the measured mass burning flux as a function of (1/Tad)
for n-decane/air mixtures of different equivalence ratios. The linear variation of ( ln mo )
with (1/Tad) seen in Fig. 5.6(a) demonstrates the validity of the extraction method through
the changes in mixture preheat. Figure 5.6(b) shows the experimentally-determined
overall activation energies of n-decane/air mixtures at varying equivalence ratios. It is of
interest to note that the variation of Ea with φ is non-monotonic and peaks near the
stoichiometric condition.
5.2.3
Extinction Stretch Rate Results
Experimentally, two modes of extinction, based on the separation between the twin
flames, were observed. Specifically, the extinction of lean counterflow flames of ndecane/O2/N2 and n-dodecane/O2/N2 mixtures occurred with a finite separation distance,
while that of rich flames exhibited a merging of two luminous flamelets. The two distinct
extinction modes can be clearly seen in Fig. 5.7. It is well-established in the stretched
flame theory that the reactivity of a positively stretched flame with Lewis number smaller
(greater) than unity increases (decreases) with increasing stretch rate [cf. Law ,1988; Law
and Sung, 2000]. Therefore, the experimental observation is in agreement with the
anticipated behavior in that the sub-unity Lewis number (Le<1) counterflow flames, such
as rich n-decane/O2/N2 and rich n-dodecane/O2/N2 mixtures, extinguish in the merged
flame mode because of incomplete reaction, while the Le>1 counterflow flames, such as
lean n-decane/O2/N2 and lean n-dodecane/O2/N2 mixtures, extinguish being located at a
finite distance away from the stagnation surface due to the non-equidiffusion effect.
70
The measured extinction stretch rates for n-decane/O2/N2 mixtures at 400 K
preheat temperature as a function of equivalence ratio are shown in Fig. 5.8. Here, the
molar ratio of N2/(N2+O2) is 0.84. The flame response curves, in terms of maximum
flame temperature variation with stretch rate, at varying equivalence ratios were also
computed using the kinetic mechanisms of Bikas and Peters (2001) and Zhao et al.
(2005), which are shown in Fig. 5.9. As expected, the maximum flame temperature in the
upper, stable branch decreases with increasing stretch rate when approaching extinction.
Again, the stretch rate at the turning point of a given response curve represents the
corresponding extinction limit. It is of interest to note that the maximum flame
temperatures at the extinction turning point predicted by both mechanisms lie in a
relatively narrow range of 1600−1700 K.
Based on the turning points shown in Fig. 5.9, the computed extinction stretch
rates were determined and compared with the experimental values in Fig. 5.8. It is seen
that the computed extinction stretch rates obtained by using the two n-decane reaction
mechanisms are fairly close to each other. Although the agreement between experimental
and computed results was satisfactory at φ=0.8, the experimental values were generally
lower at other equivalence ratios investigated.
The measured extinction stretch rates of n-dodecane/O2/N2 mixtures are shown in
Fig. 5.10. As with the n-decane cases, the molar ratio of N2/(N2+O2) was 0.84 and the
preheat temperature, 400 K. Consistent with the measured laminar flame speed
comparison, the experimental extinction stretch rates for n-dodecane/O2/N2 flames were
found to be slightly lower than those for n-decane/O2/N2 flames. The computed
extinction stretch rates based on the Utah Surrogate Mechanism are also plotted and
71
compared in Fig. 5.10. Similar to the n-decane cases, Fig. 5.10 shows that the computed
extinction stretch rates are higher than the experimental values. Figure 5.11 further plots
the simulated flame response curves, in terms of the maximum flame temperature versus
stretch rate, at varying equivalence ratios. Again, the turning point of each response curve
defines the predicted extinction limit. It is also of interest to note that the predicted
extinction temperatures of n-dodecane counterflow flames are slightly lower, by
comparing Fig. 5.10 with Fig. 5.9.
Despite the over-prediction by the reaction mechanisms employed, it is seen from
Figs. 5.8 and 5.10 that both the experimental and predicted extinction stretch rates for the
n-decane counterflow flames show a similar trend as those for the n-dodecane flames,
with the extinction stretch rate peaking at φ~1.4. This rich-shift is cause by the combined
effects of positive stretch and sub-unity Lewis number for rich mixtures, as discussed
earlier. We further note that the over-prediction of extinction stretch rate could be due to
the deficiencies of the combustion chemistry of n-decane and n-dodecane as well as the
quasi-one-dimensional nature of the counterflow flame modeling. The former is reflected
from the fact that the existing reaction mechanisms still cannot well-predict the
experimental laminar flame speed data. For the latter, a detailed computational study
would be needed to compare the extinction stretch rates predicted by quasi-onedimensional and two-dimensional modeling. At the global level, both the flame images
(cf. Fig. 5.7) and the DPIV-determined flow fields indicate that the core region of the
flame remains fairly one-dimensional even prior to the abrupt blow-off. However,
experimental mapping of major and key minor species contours are needed to confirm the
one-dimensionality of the near-extinction flame structure.
72
It also needs to be mentioned that the φ, Kextinction plots shown in figure 5.8 and
5.10 can also be used for the determination of the flammability limit for the given inlet
temperature and diluent ratio. Specifically, an extrapolation of the curve to zero stretch
must be done, the x-intercept/φ(Κ =0), provides the flammability limit. A mapping of these
flammability limits for various diluent levels, inlet temperatures, and pressure conditions
can be a valuable guide in the design for certain combustion devices (cf. Sung et al.
(2007)).
5.2.4
Flame Structure Response to Stretch Rate Variations
In this section the numerically obtained response of flame structure to the imposed stretch
rate is presented. The current discussion is limited to the simulation results obtained for
n-decane fuel using the mechanism of Zhao et al. (2005).
To begin, with we first examine the computed axial velocity profiles with varying
stretch rates in Fig 5.12(a). It may be noted that in the computations the maximum
velocity gradient upstream of the flame is the stretch rate, while the minimum velocity
upstream is the reference flame speed. The inset in this plot also includes direct images of
the flame for different stretch rates as an illustration. The mixture composition for the
simulations corresponds to φ =1.4, where the peak extinction stretch rate was observed in
the experiments. The corresponding temperature profiles are shown in Fig. 5.12(b). As
expected, when approaching extinction the maximum flame temperature decreases with
increasing stretch.
The variations of the flame thickness and the reaction zone thickness with stretch
rate are shown in figure 5.13(a) and 5.13(b) respectively. The definition of flame
73
thickness is based on the maximum velocity gradient in the preheat zone, while the
reaction zone thickness is defined as and the full width at half maximum (FWHM) of the
heat release zone. Figure 5.13 indicates a decrease in both thicknesses. Moreover, it is
seen that the off-stoichiometric flames are more sensitive to the stretch rate variation
because of the Lewis number effect. The ratio of the two flame thicknesses is shown in
Fig. 5.14. It can be seen that this ratio ranges from 2.3 to 3.1 for all the cases studied. The
thickness ratio shows a rather weak dependence on stretch. Additionally, the thickness
ratio was seen to decrease with increasing equivalence ratio.
5.3 Sensitivity Analysis
A sensitivity analysis of the mass burning flux with respect to the rate constants for the
individual reactions was carried out for stoichiometric fuel/air mixtures of Tu=400 K
based on the three kinetic schemes used in the numerical simulations. Figure 5.15 shows
the normalized sensitive coefficients, ∂ln( m o )/∂ln(ki), of the important reactions
identified, where ki is the reaction rate of the ith reaction. The laminar flame speed is seen
to be most sensitive to the reactions which involve either chain branching or termination
reactions. Additionally, the CO oxidation reaction which is responsible for the majority
of the heat release also shows a positive sensitivity.
To conduct a similar sensitivity analysis for the extinction stretch rate, the
eigenvalue in the plug-flow formulation was used, namely the radial pressure gradient
Ħ=(∂p/∂r)/r. Note that the magnitude of Ħ scales with the square of the stretch rate in the
corresponding fully-developed potential flow (Kee et al., 1988). Hence, the normalized
sensitivity of the radial pressure gradient with respect to the ith reaction is defined as
74
SĦ,i=(ki/Ħ)(∂Ħ/∂ki). When evaluating SĦ,i at the extinction turning point, the positive
(negative) value of SĦ,i indicates an increase (a decrease) in the extinction stretch rate
with increasing ki. Figure 5.16 shows such results for stoichiometric fuel/O2/N2
counterflow flames with Tu=400 K, based on the three reaction mechanisms considered in
this study. The controlling reactions identified for flame extinction are generally
consistent with the sensitivity analysis of the mass burning flux.
Additional kinetic analysis was conducted using the Kinalc program (Turányi,
1997) at the location of peak HO2 mole fraction, where most of the intermediate species
reach their maximum. The analysis shows that the reactions responsible for the
decomposition of parent fuel are dominated by the H atom abstraction reactions via the
attacks of H, OH, and O radicals. It is further noted that the fuel consumption due to
thermal decomposition for the low stretch, high temperature case is ~15%, which reduces
to ~7% in the case of the near extinction, lower temperature flame. Although all the three
reaction mechanisms considered here predict similar trends mostly, there are also some
differences between the mechanisms. Most noticeable is the presence of the reactions that
involve the addition of molecular oxygen to the alkyl radicals formed by the removal of
one hydrogen atom from the parent fuel. These reactions are included in the mechanism
of Bikas and Peters (20001), but missing from the two other mechanisms of Zhao et
al.(2005) and the Utah surrogate mechanism (Zhang, 2005). Moreover, these particular
reactions along with the subsequent reactions are found to introduce some peculiarities in
the computed profiles of molar production rates and heat release rate using the
mechanism of Bikas and Peters (2001). Specifically, at around 800 K these reactions are
responsible for small initial peaks in the profiles of heat release rate and molar production
75
rate of molecular oxygen. It is noted that the formation reaction of alkyl peroxy radical
has been identified as a key reaction in the low temperature mechanism of alkane
oxidation (Curran et al., 2002). Though it does not appear to be of relevance in high
temperature flame chemistry, its inclusion/exclusion is expected to impact the predictive
capabilities of a reaction mechanism for application targets, such as ignition delays, in the
low temperature regime (700–900 K).
5.4 Concluding Remarks
A flow control system was specially designed and developed for handling low vapor
pressure, high boiling point, liquid fuels. Characterization experiments were first
conducted to demonstrate the capability and adequacy of the present system. Using the
counterflow twin-flame configuration, this experimental study documents the laminar
flame speeds and extinction stretch rates of premixed n-decane and n-dodecane flames.
These experimental global flame parameters provide a test-bed for the validation and
optimization of the existing reaction mechanisms. While the kinetic mechanisms for ndecane are seen to predict the laminar flame speeds satisfactorily at the lean equivalence
ratios, they over-predict at the rich conditions. Comparison of the experimental and
computed laminar flame speeds of n-dodecane/air mixtures at varying preheat
temperatures shows significant over-prediction by the mechanism. Furthermore, the
measured extinction stretch rate data for both fuels are lower than the predicted values for
all the kinetic mechanisms used, although the trend is well predicted. Therefore, further
kinetic studies are needed to improve the predictability of the existing reaction
mechanisms of n-decane and n-dodecane, at least for the global flame response.
76
n-Decane/Air Mixtures
Laminar Flame Speed (cm/s)
110
Tu=360 K
100
Tu=400 K
90
Tu=470 K
80
70
60
50
40
----- Computational, Zhao et al. (2005)
____
30
0.7
0.8
Computational, Bikas and Peters (2001)
0.9
1
1.1
1.2
1.3
1.4
Equivalence Ratio, φ
Figure 5.1
Experimental (symbols) and computed (lines) laminar flame speeds of ndecane/air mixtures with unburned mixture temperatures of 360, 400, and 470 K.
77
n-Decane/Air Mixtures
Laminar Flame Speed (cm/s)
100
90
80
70
60
Current - T u=470 K
Skjoth-Rasmussen et al. (2003) - T u=473 K
50
40
Zhao et al. (2005) - T u=500 K
0.6
0.8
1
1.2
1.4
Equivalence Ratio, φ
Figure 5.2 Comparison of the current n-decane/air laminar flame speed data with earlier
experimental studies.
78
n-Dodecane/Air Mixtures
Laminar Flame Speed (cm/s)
120
Tu=400 K
Tu=470 K
100
80
60
40
----- Computational, Utah Surrogate Mechanism (2005)
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Equivalence Ratio, φ
Figure 5.3
Experimental (symbols) and computed (dashed lines) laminar flame speed
of n-dodecane/air mixtures with unburned mixture temperatures of 400 and 470
K.
79
Laminar Flame Speed (cm/s)
110
100
90
n-Decane/Air and n-Dodecane/Air Mixtures
Filled Symbols: n-C12H26
Empty Symbols: n-C10H22
470 K
80
400 K
70
60
50
Tu=360 K
40
30
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Equivalence Ratio, φ
Figure 5.4
Comparison of experimental laminar flame speeds of n-decane/air
(Tu=360, 400, and 470 K) and n-dodecane/air (Tu=400 and 470 K) mixtures.
80
Mass Burning Flux (g/cm2-s)
0.08
φ =1.1
0.07
φ =0.9
0.06
0.05
φ =0.7
0.04
Filled Symbols: n-C12H26
Empty Symbols: n-C10H22
0.03
0.02
350
400
450
500
Unburned Mixture Temperature (K)
Figure 5.5
Dependence of mass burning flux on unburned mixture temperature for ndecane/air and n-dodecane/air mixtures.
81
n-Decane/Air Mixtures
-2.6
(a)
ln (mo)
-2.8
φ=1.2
φ=0.8
φ=0.9
-3
-3.2
φ=0.7
-3.4
-3.6
0.42
0.44
0.46
0.48
0.5
0.52
Overall Activation Energy (kJ/mol)
1000/Tad (1/K)
250
(b)
200
150
100
50
0
0.7
0.8
0.9
1
1.1
1.2
1.3
Equivalence Ratio, φ
Figure 5.6 (a) Arrhenius plot showing mass burning flux as a function of adiabatic flame
temperature for n-decane/air mixtures of varying equivalence ratios. Slope of the
fitted straight line is proportional to overall activation energy.(b) Plot of the
overall activation energy as a function of equivalence ratio for n- decane/air
mixtures.
82
Figure 5.7
Direct images (negatives) of near extinction n-decane/O2/N2 flames with
Tu=400 K.
83
n-Decane/O2/N2 Mixtures
Extinction Stretch Rate (s-1)
1200
1000
N2/(N2+O2) = 0.84
Tu=400 K
800
600
400
Experimental
200
0
Computational, Bikas and Peters (2001)
Computational, Zhao et al. (2005)
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Equivalence Ratio, φ
Figure 5.8 Experimental (symbols) and computed (lines) extinction stretch rates of ndecane/O2/N2 mixtures.
84
Maximum Flame Temperature (K)
2000
Maximum Flame Temperature (K)
2000
n-Decane/O2/N2 Mixtures
(a) Computational, Bikas and Peters (2001)
N2/(N2+O2)=0.84
Tu=400 K
1900
1800
1.4
1700
1.5
1600
φ=0.8
0.9
1.1
1.2
800
1000
1.3
1.0
1500
0
200
400
600
1200
(b) Computational, Zhao et al. (2005)
1900
φ = 1.3
φ = 1.4
φ = 1.5
1800
1700
φ=0.8
1600
1500
1.2
1.0
0.9
0
200
400
600
1.1
800
1000
1200
Stretch Rate (s-1)
Figure 5.9 Computed flame response curves to stretch rate variations for n-decane
counterflow premixed flames using the kinetic mechanisms of (a) Bikas and
Peters (2001) and (b) Zhao et al. (2005).
85
n-Dodecane/O2/N2 Mixtures
Extinction Stretch Rate (s-1)
1500
1200
N2/(N2+O2)=0.84
Tu=400 K
Computational,
Utah Surrogate Mechanism (2005)
900
Experimental
600
300
0
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Equivalence Ratio, φ
Figure 5.10 Experimental (symbols) and computed (lines) extinction stretch rates of ndo-decane/O2/N2 mixtures.
86
Maximum Flame Temperature (K)
n-Dodecane/O2/N2 Mixtures
2000
Computational, Utah Surrogate Mechanism (2005)
1900
N2/(N2+O2)=0.84
Tu=400 K
1800
φ = 1.3
φ = 1.4
φ = 1.5
1700
1600
1.1
1500
1400
φ=0.8
0
1.2
1.0
0.9
500
1000
1500
Stretch Rate (s-1)
Figure 5.11 Computed flame response curves to stretch rate variations for n-dodecane
counterflow premixed flames using the Utah Surrogate Mechanism (Zhang,
2005).
87
(a) n-Decane/O /N , φ=1.4
2
2
Axial Velocity (cm/s)
400
300
200
100
increasing stretch rate
0
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
Distance From Stagnation Plane (cm)
(b) n-Decane/O /N , φ=1.4
2
2000
2
Temperature (K)
1800
1600
1400
1200
1000
800
increasing stretch rate
600
400
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
Distance From Stagnation Plane (cm)
Figure 5.12 Computed axial variations for (a) velocity and (b) temperature for varying
stretch rates obtained using numerical simulations for n-decane/O2/N2
counterflow premixed flames. Half domain is plotted due to symmetry, with
nozzle location at x =0.65 cm and stagnation surface at x =0.0 cm. Mechanism of
Zhao et al. (2005) is employed.
88
(a) n-Decane/O /N
2
0.06
(T
Flame Thickness (cm)
max
2
φ
-T )/(dT/dx)
u
max
1.0
1.1
1.2
1.3
1.5
0.055
0.05
0.045
N /(N +O )=0.84
2
2
2
T =400 K
u
0.04
200
400
600
800
1000
1200
-1
Stretch Rate (s )
(b) n-Decane/O /N
2
Reaction Zone Thickness (cm)
0.028
2
φ
FWHM of heat release zone
1.0
1.1
1.2
1.3
1.5
0.026
0.024
0.022
N /(N +O )=0.84
2
2
2
T =400 K
u
0.02
0.018
0.016
200
400
600
800
1000
1200
-1
Stretch Rate (s )
Figure 5.13 Computed (a) flame thickness based on maximum temperature gradient and
(b) reaction zone thickness based on full width at half maximum of heat release
profile, as a function of stretch rate. Mechanism of Zhao et al. (2005) is used.
89
n-Decane/O /N
2
Thickness Ratio
4
2
φ
1.0
1.1
1.2
1.3
1.5
3.5
3
2.5
2
N /(N +O )=0.84
2
2
2
T =400 K
1.5
200
u
400
600
800
1000
1200
-1
Stretch Rate (s )
Figure 5.14 Ratio of the flame thickness and the reaction zone thickness as a function of
stretch rate.
90
Sensitivity for Mass Burning Flux ( φ=1.0, Tu=400 K )
HCO+O2=CO+HO2
Bikas and Peters (2001)
H+O2(+M)=HO2(+M)
Zhao et al. (2005)
H+HCO=H2+CO
Zhang (2005)
H+OH+M=H2O+M
C2H3+O2=CH2CHO+O
CH2+O2=>CO+OH+H
O+H2=OH+H
HCO+M=H+CO+M
CO+OH=CO2+H
H+O2=OH+O
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Normalized Sensitivity Coefficient
Figure 5.15 Normalized sensitivity coefficients for mass burning flux based on the
mechanisms of Zhao et al. (2005), Bikas and Peters (2001), and Utah Surrogate
Mechanism (Zhang, 2005).
91
Sensitivity for Extinction Stretch Rate (φ=1.0, Tu=400 K )
HCO+O2=CO+HO2
Bikas and Peters (2001)
Zhao et al. (2005)
H+O2(+M)=HO2(+M)
H+HCO=H2+CO
Zhang (2005)
H+OH+M=H2O+M
C2H3+O2=CH2CHO+O
CH2+O2=>CO+OH+H
O+H2=OH+H
HCO+M=H+CO+M
CO+OH=CO2+H
H+O2=OH+O
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Normalized Sensitivity Coefficient
Figure 5.16 Normalized sensitivity coefficients for extinction stretch rate based on the
mechanisms of Zhao et al. (2005), Bikas and Peters (2001), and Utah Surrogate
Mechanism (Zhang, 2005).
92
Chapter 6
Laminar Flame Speeds
Ethylene/Oxidizer Mixtures
and
Ignition
Delays
for
6.1 Scientific Background
Recent advances in the development of chemical kinetic mechanisms for hydrocarbon
fuels have been considerably aided by the availability of experimental data of high
fidelity. Since ethylene is one of the key intermediates in the oxidation of higher
hydrocarbons (e.g. Douté et al., 1997; Zeppieri et al., 2000), there exists strong interest in
acquiring experimental data on its oxidation kinetics over extensive variations in the
range of thermodynamic parameters. As shown, the importance of C2 chemistry
(including ethylene) is evident from the sensitivity analysis for the laminar flame speeds
in the earlier part of this work. In addition, the need for reduced pollutant formation in
combustion systems necessitates the study of ethylene chemistry since it is identified as
one of the soot precursors. Furthermore, ethylene is one of the preferred products of
thermal cracking of higher hydrocarbons under certain conditions. This feature, in
particular, has potentially significant implications on the utilization of liquid hydrocarbon
fuels for hypersonic propulsion (Curran, E.T., and Murthy, S.N.B. (eds.), Scramjet
Propulsion). In addition to providing the propulsive power, liquid hydrocarbon fuels have
been proposed to serve as thermal heat sinks in such propulsion systems. Ethylene, being
a cracked product and highly reactive, has in fact been used to simulate the cracked
hydrocarbon fuels in the testing of combustors for these propulsion systems (Kay et al.,
1992). Consequently, preheating of fuel mixtures including that of ethylene is recognized
as an important parameter in the study of fuel chemistry, from both fundamental and
93
practical considerations.
Global kinetic parameters, such as ignition delay and laminar flame speed, are
important targets for the validation and optimization of chemical kinetic mechanisms.
Previous shock tube measurements of ignition delay of ethylene (Gay et al., 1967; Baker
and Skinner, 1972; Hidaka et al., 1974; Jachimowski, 1977; Brown and Thomas, 1999;
Hidaka et al., 1999) have focused mostly on high temperature (>1100 K) and low
pressure (<5 atm) conditions. More recently, ignition delays of ethylene/O2/inert mixtures
in shock tubes were obtained at a maximum pressure of 8 atm at temperatures greater
than 1100 K (Colket and Spadaccini, 2001). A summary of shock tube experiments on
ethylene/O2 ignition can be found in the study of Varatharajan and Williams (2002).
Laminar flame speeds for ethylene/air mixtures have also been studied at room
temperature under both atmospheric (Hirasawa et al., 2002) and elevated pressure
conditions (Egolfopoulos et al., 1990; Jomaas et al., 2005).
This work contributes to the development of comprehensive reaction mechanism
of ethylene by providing experimental data for two situations that have not been
previously investigated. First, atmospheric-pressure laminar flame speeds are determined
for preheated ethylene/O2/N2 mixtures over a mixture temperature range of 298–470 K,
thereby yielding useful information on the influence of preheat on flame propagating.
Second, ignition delay measurements are conducted in a rapid compression machine
(RCM) at high compressed pressures (up to 50 bar) in the low-to-intermediate
temperature range (<1100 K), hence providing access to the low temperature chemistry.
Investigations with other lower hydrocarbons, such as methane, have shown that the
ignition delay data at high temperature cannot be extrapolated to low temperature, due to
94
a change in controlling chemistry under conditions of high pressure and intermediate
temperature (bHuang et al., 2004; Petersen et al., 1999).
In the following sections, the experimental conditions for the laminar flame speed
and ignition delay measurements are described, followed by the experimental and
modeling results. Possible improvements to the existing ethylene mechanism are then
discussed based on the experimental data and kinetic analysis.
This chapter concludes the flame experiments and introduces the low-tointermediate temperature autoignition experiments (less than 1100 K) that were
conducted as a part of this work. The autoignition experiments are introduced in the
second part of this chapter and continue to be topic of the next two chapters.
6.2 Experimental and computational specifications
6.2.1
Determination of Laminar Flame Speed
The laminar flame speeds of ethylene/O2/N2 mixtures were measured as a function of
equivalence ratio in the range of φ=0.5–1.4, with the unburned mixture temperature
variations of Tu=298, 360, 400, and 470 K. Measurements were made in a nozzlegenerated twin-flame counterflow configuration. The nozzle exit diameter is 13 mm and
the separation between the two nozzles is kept close to one diameter. Details of the
experimental setup have been described earlier.
The experimentally obtained laminar flame speeds are then compared with the
computed results using the using the PREMIX code (Kee et al., 1985) in conjunction
with the CHEMKIN (Kee et al., 1989) and TRANSPORT (Kee et al., 1986). The
computations used windward differencing on the convective term and mixture-averaged
95
transport equations. The thermal diffusion of H and H2 was also considered.
Determination of Ignition Delays
6.2.2
Ignition delay measurements for stoichiometric ethylene mixtures with the composition
C2H4/O2/N2/Ar=1/3/6/27.84 were conducted over the temperature range of 850–1050 K
and the pressure range of 15–50 bar, using a RCM. Since the reactants are at room
temperature, the compressed gas temperature at the end of compression (top dead center,
TDC) is varied by altering the compression ratio, whereas the desired pressure at TDC is
obtained by varying the initial pressure of the reacting mixture. The temperature at TDC,
Tc,
is
determined
relation ∫
Tc
T0
by
the
adiabatic
core
hypothesis
according
to
the
γ
dT
= ln[ Pc / P0 ] , where P0 is the initial pressure, T0 the initial
γ −1 T
temperature, γ is the specific heat ratio, and Pc the measured pressure at TDC. Further
details of the rapid compression machine can be found in the works of Mittal and Sung
(2006).
Numerical modeling of ignition delay is performed using the Sandia SENKIN
code (Lutz et al., 1998) in conjunction with CHEMKIN (Kee et al., 1989). The modeling
begins from the start of compression stroke, and includes the effect of heat loss during
compression and after the end of compression. The present heat transfer modeling
approach has been described in Chapter 3.
6.2.3
Kinetic Models
The experimental data were modeled using chemical kinetic mechanisms taken from
Wang (2006) and UCSD (Center for Energy Research- Combustion Division, UCSD,
96
Website; electronic download April-2006). In the subsequent sections they are referred to
as the mechanism of Wang and the UCSD mechanism. The ethylene mechanism of Wang
has been validated extensively against experimental measurements of ignition delays in
shock tubes, laminar flame speeds, and specie profiles in flames. This mechanism has 111
species and 781 reactions. The UCSD mechanism consists of 46 species and 235
reactions. It has also been validated against laminar flame speed and ignition delay data.
It is noted that when evaluating transport properties the model of Wang uses updated
diffusion coefficients for several key pairs (Middha et al., 2002). Within the framework
of the PREMIX code (Kee et al.,1985), a compatible transport database and modified
transport property evaluation subroutines, which were provided by Wang, were used to
account for these diffusion coefficient updates.
6.3
Results and Discussions
6.3.1
Laminar Flame Speeds
The measured laminar flame speeds of C2H4/O2/N2 mixtures as a function of equivalence
ratio for various preheat temperatures are shown as symbols in Fig. 6.1. The error bars
indicate the 95% confidence interval estimate of the laminar flame speed obtained by
linear extrapolation of the experimental Su,ref versus stretch rate data. A comparison of the
present experimental data with some recent stretch-corrected flame speed data in the
literature is shown in Fig. 6.2. The comparison is limited to atmospheric pressure and
room temperature cases. These datasets have been obtained using either the counterflow
configuration (Hirasawa et al., 2002; Egolfopoulos et al., 1990) or the outwardly
propagating spherical flames in constant pressure chambers (Jomaas et al., 2005; Hassan
97
et al., 1998). It is seen that despite some noticeable small differences among different
counterflow-based flame speed data, they are generally consistent with each other. It is
also noted that one possible reason for the current data being slightly higher is due to the
use of synthetic air with 21% oxygen, as compared to ambient air which has slightly less
oxygen. This difference, nevertheless, is expected to be well within the error bars
associated with the data points. On the other hand, using synthetic air permits us to
exactly specify the mixture composition in the simulations without concern for trace
gases such as argon (~0.9%) that are present in ambient air, thereby allowing a more
direct comparison between experiment and simulation.
Computed laminar flame speeds based on the two reaction mechanisms are also
shown and compared in Fig. 6.1. Note that in Fig. 6.1 the computed laminar flame speeds
for the 360 K case have been omitted for clarity. It is seen from Fig. 6.1 that calculations
using the mechanism of Wang yield flame speed results that are consistently lower
compared to the experimentally obtained values. Additionally, such an under-prediction
becomes more severe as the preheat temperature is increased. Figure 6.1 also shows that
although calculations using the UCSD mechanism compare well with the experimental
data for the cases of Tu=298−400 K, significant under-prediction is observed for the
Tu=470 K case. The largest discrepancy for both mechanisms is observed at 470 K
preheat, with differences of ~8 cm/s using the UCSD mechanism and ~18 cm/s using the
Wang mechanism. Since flame temperature increases with increasing preheat
temperature, such discrepancies could be caused by the uncertainty of high-temperature
chemistry.
Figure 6.3(a) shows the effect of preheat on the mass burning flux, mo=ρu Suo ,
98
since mo is a fundamental parameter in laminar flame propagation, where ρu is the
unburned mixture density and Suo is the laminar flame speed. It is seen that the mass
burning flux increases with increasing unburned mixture temperature, thereby indicating
that the increase in Suo with Tu overcomes the reduction in ρu. This mass burning flux
increase is of interest, because it is related to the power density of a combustion device.
Furthermore, the variations of the mass burning flux and adiabatic flame
temperature (Tad) with Tu can be utilized to determine the overall activation energy (Ea),
using the relation Ea=-2R×[∂ln(mo)/∂(1/Tad)]p, where R is the universal gas constant.
Figure 6.3(b) plots the relationship of ln(mo) versus (1/Tad) at different equivalence ratios,
showing a trend of linear variation. Figure 6.4 shows and compares the experimentallydeduced and computed values of the overall activation energy as a function of
equivalence ratio. The experimental results show a non-monotonic dependence of the
overall activation energy on equivalence ratio, with a peak close to the stoichiometric
condition. Similar trend with slightly smaller values are seen for the numerical results
using the two kinetic mechanisms.
Sensitivity analysis of the mass burning flux with respect to the rate constants for
the individual reactions was further conducted for the two reaction mechanisms. Since
the sensitivity results are found not to be significantly affected by the preheat
temperature, Fig. 6.5 only shows the normalized sensitivity coefficients for a
stoichiometric flame with Tu=298 K. It is seen that the major reactions impacting the
flame speed for the two mechanisms
are the chain branching/termination reactions
involving H and OH radicals, formation of CO from HCO, and the subsequent oxidation
of CO to CO2. The sensitivity results also show that the reactions of ethylene, vinyl
99
radical, and formyl radical with H radical assume greater importance under fuel rich
conditions. Additionally, the H abstraction reactions from ethylene exhibit a positive
sensitivity for the mass burning flux.
To better understand the differences between the two mechanisms, a reaction
pathway analysis was conducted for both mechanisms. The major pathways were
identified by integrating the contribution of a particular reaction to consumption of a
given species over the width of the heat release zone (≥1% of the maximum heat release
rate). The results for the major pathways are respectively shown in Figs. 6.6(a) and 6.6(b)
for the mechanisms of Wang and UCSD, where the value within the parentheses is the
percentage of the species indicated in the box consumed by a particular path.
Figure 6.6 shows that the H abstraction reactions are the dominant fuel consuming
paths for both mechanisms, accounting for ~54 % of fuel consumption. The two
mechanisms, however, lead to a varying selectivity for the abstraction reaction by H
radical, with the UCSD mechanism showing three times greater consumption via this
route as compared to the model of Wang. It is noted that the H abstraction reaction of
C2H4+O→C2H3+OH is only considered in the mechanism of Wang, which accounts for
11% of ethylene consumption. Although the vinyl radicals are consumed mainly through
the reactions with molecular oxygen and with H radical, the proportion of vinyl
consumed by each of the paths, leading to C1/C2 oxygenated products and acetylene,
differs significantly between the two mechanisms. The resulting differences in the
intermediate species concentrations, in part, explain the variations in laminar flame speed
predictions using the two mechanisms. It is further noted that while the hydrogen
abstraction reaction of C2H4+H→C2H3+H2 is important for the high-temperature flame
100
chemistry, it does not appear to be of similar importance for the low-temperature
autoignition phenomena discussed in the following section.
6.3.2
Ignition Delays
Figure 6.7 shows a typical pressure trace from the RCM for autoignition, with 50 bar and
904 K at TDC. Ignition delay is defined as the time from the end of compression to the
subsequent instant of rapid rise in pressure due to autoignition. The measured pressure
trace for the corresponding nonreactive mixture with the same specific heat ratio as well
as the simulated results using the mechanism of Wang are also shown in Fig. 6.7. It is
seen that the experimental and simulated pressure traces for the nonreactive case match
very well, indicating the adequacy of the present model. On the other hand, the simulated
pressure trace for the reactive mixture shown in Fig. 6.7 differs significantly from the
experimental data. This disagreement indicates that a mechanism validated for shock tube
ignition delay measurements at relatively high temperatures may not be inadequate for
the present range of experimental conditions.
Figure 6.8 shows the Arrhenius plot (ignition delay versus 1/Tc) of the measured
ignition delays at compressed pressures of 15, 30, and 50 bar. As mentioned earlier, the
pressure range of the previous shock tube studies was less than 12 bar, which is lower
than the pressure range studied in the current work. Additionally, the temperature range
investigated herein was 850–1050 K, while the earlier shock tube studies mostly
investigated the temperature range exceeding 1070 K. Figure 6.9 compares the present
RCM data with the previous shock tube results for stoichiometric mixtures, by plotting
the ignition delay scaled to the first order of oxygen concentration versus the inverse of
101
temperature. Note that various definitions of ignition delay have been used by the
previous researchers, and the specific definition can be found in the cited references.
Moreover, for the data of Hidaka et al. (1999), an average pressure value corresponding
to their reported pressure range of 0.2–0.35 atmospheres was used. The data for the work
of Baker and Skinner (1972) was obtained from a fit to the parameters reported in Table 1
of their work. It is seen from Fig. 6.9 that the present study fills the void in the highpressure, low-to-intermediate temperature conditions in a consistent manner.
The experimental and computed ignition delays for compressed pressures of 15,
30 and 50 bar are compared in Figs. 6.10-6.12, respectively. It is seen that, for the
conditions investigated, although the Wang mechanism consistently predicts ignition
delays shorter than the experimental values, the computations using the UCSD
mechanism generally show good agreement. To further study the differences in the
ignition predictability of the two mechanisms, sensitivity analysis and integral reaction
flow analysis techniques (Warnatz, 1981) were employed. The analyses were carried out
for the case corresponding to Pc=50 bar and Tc=904 K. Here, the focus is on the preignition event. Since the two mechanisms yield different ignition delays, for the purpose
of quantitative comparison the time with 1% fuel consumption was used in the analysis.
It was then observed that for the majority of the simulated cases, the location of 1%
ethylene consumption is either beyond or close to the location of dT/dt=0 prior to ignition
(abrupt pressure rise), i.e. the time at which the effect of heat loss starts to be fully
compensated by the pre-ignition heat release. Also, at this instant the simulated post
compression temperature drops are within 10 K for both mechanisms. Thus, the choice of
this instant is well suited for conducting a comparison of reaction mechanism
102
performance since both the local concentrations and temperature are at comparable levels
for the two mechanisms.
The consumption pathways for the Wang and UCSD mechanisms are shown in
Figs. 6.13(a) and 6.13(b), respectively. For this integrated reaction flow diagram, only the
consumption pathways for ethylene and the major products of the associated reactions
were considered. Note that the contribution to the consumption of a specific species from
the individual reaction was integrated over the duration starting from the end of
compression to the time of 1% fuel consumption. Again, the number within the
parentheses is the percent consumption of the species indicated in the box through a
particular reaction. In addition, the species whose concentration is significantly
increasing are shown with gray background, while the species indicated without gray
background, except ethylene, are approximately in steady state during this pre-ignition
event.
Figure 6.13 shows that ethylene primarily reacts with OH to produce vinyl. In
addition, a small amount of ethylene reacts with the H atom to form C2H5, which also
coverts back to ethylene and produces HO2 via its reaction with O2. In both mechanisms,
while a significant amount of ethylene is consumed by the reaction with O atom yielding
CH3 and HCO, the overall product distribution for the C2H4+O reactions is different. In
the Wang mechanism, C2H4+O=C2H3+OH is present; whereas in the UCSD mechanism
C2H4+O=CH2CHO+H is included. Vinyl radicals further react with O2 through the
following two major channels: C2H3+O2=CH2CHO+O (R1) and C2H3+O2=CH2O+HCO
(R2). It is noted that under the high temperature conditions in flames, R1 is significantly
more important than R2, as shown in Fig. 6.6. In the sensitivity analysis of Fig. 6.5, R1
103
also shows high sensitivity for the mass burning flux, whereas R2 does not. In contrast,
under conditions of elevated pressure and low temperature, Fig. 6.13 demonstrates that
the magnitude of the reaction flux of R2 is comparable to that of R1.
For the sensitivity analysis on the ignition delay (τ), the rate constant of each
reaction, ki, is individually doubled. The resulting percentage change in the ignition delay,
namely 100×[τ(2ki)−τ(ki)]/τ(ki), is then taken as the percent sensitivity of that particular
reaction. Figure 6.14 demonstrates such a sensitivity analysis. A positive sensitivity
implies that ignition delay increases by increasing the rate constant of a particular
reaction.
Figure 6.14 shows that while both R1 and R2 exhibit very high sensitivity, they
have opposite effect on the ignition delay prediction. Both reactions compete for the vinyl
radical, but increasing the rate constants of R1 and R2 leads to a reduction and an
increase in the ignition delay, respectively. This is because the fate of vinyl radicals
through these two reactions determines the chain branching of the overall reactivity. In
particular, more than 95% of the formyl radicals produced via R2 are consumed through
HCO+O2=HO2+CO. On the other hand, R1 leads to the production of branching radicals
as shown in Fig. 6.13. Hence, when the reaction rate of R2 is increased, the reaction flux
of the vinyl radicals through R1 decreases, resulting in less chain branching and longer
ignition delay. Additionally, the difference in the reaction flux of vinoxy radicals between
the two mechanisms can be seen in Fig. 6.13. Specifically, the UCSD mechanism does
not include the reaction CH2CHO+O2=CH2CO+HO2, and consequently almost the entire
vinoxy flux is through CH2CHO+O2=CH2O+CO+OH. However, in the Wang mechanism
the major consumption of vinoxy is via CH2CHO+O2=CH2CO+HO2.
104
Another important feature that characterizes the oxidation of ethylene in the lowto-intermediate temperature range is its reaction with the HO2 radical that leads to the
formation of ethylene oxide and OH radical. The significance of this reaction is well
recognized under these temperature conditions (Wilk et al., 1990; Hunter et al., 1996;
Carriere et al., 2002). The reaction sequence involved in the production of ethylene oxide
is important in that this sequence consumes the relatively un-reactive HO2 radical and
produces a reactive OH, thereby enhancing the overall reaction (Wilk et al., 1990). Both
the kinetic models include the reaction between ethylene and HO2. Analysis of both the
consumption pathway and the OH sensitivity illustrates that the reaction of C2H4+HO2 is
important under the current experimental conditions. Figure 6.13 shows that the two
mechanisms consume at least 15% of the fuel via this reaction. It is also noted that under
the conditions of high temperature, this reaction is unimportant, as shown in Fig. 6.6.
Furthermore, a common feature exhibited in the present RCM simulation is the
rapid buildup of HO2 prior to ignition, whose concentration becomes several orders of
magnitude greater than those of O, H, CH3, and OH. The resulting oxidation sequence
converts a major portion of the fuel to formyl radicals. The subsequent reaction of the
formyl radical with molecular oxygen is the major contributor to the production of HO2,
most of which leads to H2O2. Although the concentration of H2O2 is less than that of HO2
in the pre-ignition phase, it is larger than those of all other radical species present just
prior to ignition event by several orders of magnitude. Hence, the ignition event for the
conditions investigated is characterized by a sharp reduction in fuel and H2O2
concentrations and a corresponding increase in the concentrations of OH, H, and O.
105
6.4
Concluding Remarks
Laminar flame speed data and ignition delay data for various ethylene O2/N2/diluent
mixtures were obtained. While laminar flame speed experiments are representative of the
high temperature, atmospheric pressure oxidation kinetics, the ignition delays provide
valuable data in the high pressure and intermediate temperature regime. The controlling
chemistry related to the oxidation of ethylene under two distinct combustion phenomena
was also investigated. The differences in the oxidation under these two conditions are
related to the low temperature chemistry involving the fuel and HO2 radical. Fuel-HO2
reactions, while critical to predicting the ignition behavior for the current RCM
experiments, are not particularly important for the flame conditions. Additionally, at low
temperatures hydrogen abstraction reaction from the fuel is mainly by means of the
hydroxyl radical, with the attack of hydrogen radical becoming important under flame
conditions. The current measurements, though for global quantities, provide additional
benchmark data of high fidelity for the validation of the oxidation kinetics of ethylene.
Existing chemical kinetic mechanism for C1-C2 oxidation tested against the acquired
datasets showed mixed results. Specifically, the flame speed data and ignition delay were
reasonably modeled by the UCSD mechanism. Significant improvements may be
possible by re-optimizing the models to better predict the ignition delay times at low
temperature/ high pressure conditions and the laminar flame speeds for high
temperatures.
106
Laminar Flame Speed (cm/s)
150
125
Tu=298 K
Tu=360 K
Tu=400 K
Tu=470 K
Computed
} Tu=470 K
100
Computed
Tu=400 K
75
Computed
Tu=298 K
50
Computation (Wang)
Computation (UCSD)
Experiment
Symbols
25
0.4
0.6
0.8
1
1.2
1.4
1.6
Equivalence Ratio, φ
Figure 6.1 Experimental (symbols) and computed (lines) laminar flame speeds of
atmospheric pressure ethylene/air mixtures as functions of equivalence ratio and
unburned mixture temperature. Computations shown for Tu=298, 400 and 470 K.
107
Laminar Flame Speed (cm/s)
80
70
60
50
40
Current
Hirasawa et al. (2002)
Egolfopoulous et al. (1990)
Jomaas et al. (2005)
Hassan et al. (1998)
30
20
10
0
0.4
0.6
0.8
1.0
1.2
1.4
Equivalence Ratio, φ
Figure 6.2
Experimental (symbols) and computed (lines) laminar flame speed of
ethylene/air mixtures at atmospheric pressure and room temperature. The filled
symbols are data from this work. The open symbols indicate the results of
previous works by Egolfopoulous et al. (1990), Hirasawa et al. (2002), Jomaas et
al.(2005), and Hassan et al. (1998).
108
Mass Burning Flux (g/cm2-s)
0.12
(a)
φ=1.0
0.1
φ=1.4
0.08
0.06
0.04
φ=0.7
300
350
400
450
Unburned Mixture Temperature (K)
(b)
-2.4
φ=1.0
φ=1.4
ln(mo)
-2.8
φ=0.7
-3.2
φ=0.6
-3.6
-4
φ=0.5
0.4
0.45
0.5
0.55
0.6
0.65
1000/Tad (K-1)
Figure 6.3
a) Experimentally obtained mass burning flux as a function of preheat
temperature with equivalence ratio as a parameter. b) Arrhenius plot showing
mass burning flux as a function of 1000/Tad for different equivalence ratios.
109
Overall Activation Energy (kJ/mol)
450
400
Experimental
Computational, Wang
Computational, UCSD
350
300
250
200
150
0.4
0.6
0.8
1
1.2
1.4
1.6
Equivalence Ratio, φ
Figure 6.4
Experimentally and numerically deduced overall activation energy for the
combustion process in a flame as a function of equivalence ratio.
110
C2H3+H=C2H2+H2
HCO+H=CO+H2
H+OH+M=H2O+M
HO2+OH=O2+H2O
C2H4+O=CH3+HCO
C2H4+H=C2H3+H2
C2H2+O=HCCO+H
CH3+OH=CH2*+H2O
HO2+H=OH+OH
C2H4+OH=C2H3+H2O
HO2+H=OH+OH
HCO+M=CO+H+M
C2H3+O2=CH2CHO+O
CO+OH=CO2+H
H+O2=O+OH
UCSD
Wang
-0.2
-0.1
0
0.1
0.2
0.3
Normalized Sensitivity Coefficient for Mass Burning Flux
Figure 6.5
Sensitivity coefficients for mass burning flux (Tu=298 K, φ=1).
111
Integrated Species Consumption within Heat Release Zone of Stoichiometric C2H4/Air Flame,
Tu=400 K
(a) Mechanism of Wang
+O2 / -HO2 (17)
C2H4
+H
(14)
+H / -H2
+OH / -H2O
(9)
(34)
C2H3
C2H5
+O2
+O
(26)
(13)
+M / -H
(27)
+O / -H
(70)
(15)
C2H2
CH2CHO
+O2 / -O
(22)
+O2 / -HO2
(18)
HCCO
CH2CO
+OH / -H
(0.8)
C
C C
+H
(24)
+H / -H2
+O / -OH
(11)
+O / -H
(31)
+H
+H
(80) (27) (39)
CH2O
CC
C CC
CH3
+M (24)
+H2O (25)
+O2(30)
HCO
C
+H (48)
+O (18)
+O2(12)
C
CO
CO2
(b) UCSD Mechanism
+O2 / -HO2 (17)
C2H4
+H
(13)
+O2 / -O
C2H3
+O
(21)
+O2
+H / -H2
(10)
(33)
HCCO
+OH / -H
(27)
CH2O
+O2 / -HO2; +H / -H2; +OH / -H2O
(95)
+O / -OH
(5)
CH2CHO
-H
(90)
CH2CO
+OH
(22)
CH2OH
+H
(65)
C
C
CH3
(37)
+O / -H
(47)
C2H2
C
C C
(29)
(24)
C2H5
+H
(24)
+O / -H
(11)
+OH / -H2O
+H / -H2
HCO
+M (50)
+O2(34)
+H(7)
+H (43)
+O (12)
+O2(43)
CO
CO2
Figure 6.6 Reaction flow analysis for (a) the mechanism of Wang and (b) the USCD
mechanism under flame conditions.
112
Simulated
(Wang)
Pressure (bar)
80
Measured
Ignition Delay
Pc=50 bar
Tc=904 K
60
Experimental
40
Nonreactive
experimental and simulated
20
End of Compression
0
0
10
20
30
40
50
60
70
Time (ms)
Figure 6.7 Experimental and simulated pressure traces for ethylene autoignition. Molar
composition: C2H4/O2/N2/Ar = 1/3/6/27.84. Conditions at TDC: Tc = 904 K and
Pc = 50 bar.
113
103
Ignition Delay (ms)
Pc=15 bar
30 bar
50 bar
102
101
100
10-1
0.95
1
1.05
1.1
1.15
1000/Tc (K-1)
Figure 6.8 Measured ignition delays for C2H4 autoignition at varying compressed
pressures and compressed temperatures. Molar composition: C2H4/O2/N2/Ar =
1/3/6/27.84.
114
Ignition Delay x [O2] (ms-mol/cm3)
10-2
10-4
Current (15-50 bar)
Brown & Thomas (1.3-3.0 atm)
Colket & Spadaccini (6.16-7.64 atm)
Hidaka et al. (0.20-0.35 atm)
Jachimowski (1.2-1.7 atm)
Baker & Skinner (3.0 atm)
10-6
10-8
10-10
0.4
φ=1.0
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1000/T (K-1)
Figure 6.9 Comparison of measured ignition delay times from the present RCM with the
literature data.
115
Pc=15 bar
Ignition Delay (ms)
102
Wang
UCSD
Experimental
101
100
0.95
1
1.05
1.1
1000/Tc (K-1)
Figure 6.10 Comparison of experimental ignition delay (filled symbols) with simulations
at Pc = 15 bar.
116
Pc=30 bar
Ignition Delay (ms)
102
101
100
10-1
0.98
Wang
UCSD
Experimental
1
1.02
1.04
1.06
1.08
1.1
1.12
1000/Tc (K-1)
Figure 6.11 Comparison of experimental ignition delay (filled symbols) with simulations
at Pc = 30 bar.
117
Ignition Delay (ms)
103
Pc=50 bar
102
101
Wang
100
UCSD
Experimental
10-1
1
1.05
1.1
1.15
1.2
1000/Tc (K-1)
Figure 6.12 Comparison of experimental ignition delay (filled symbols) with simulations
at Pc= 50 bar.
118
Pre-ignition Species Consumption Pathways, Pc=50 bar, Tc=904 K
(a) Mechanism of Wang
+O (19)
+O2 +H
-HO2 (5)
(78)
+HO2 / -OH
(20)
CH2OCH2
+OH
(81)
(41)
C
CH3
+O
(6)
+O2 / -O
(2)
(47)
CH2CHO
(50)
+O2 / -HO2
+O2 / -HO2
+O2
+O2 / -OH
(88)
+O / -H
(19)
C2H2
C
C C
(15)
C2H3
+M/
+M -CH CO
2
(53)
(46)
CH2O
HCCO
+OH / -H2O
(95)
(11)
CH2CO
C
+HO2
+O / -OH
(3.5)
+OH / -H2O
CH2OCH
C2H5
CH3 + HCO
C2H4
+OH / -H2O +HO2 / -H2O2
(41)
(54)
+O2 / -OH
(99)
HCO
+O2 / -HO2
(95)
CO
Accumulating
in system
CO2
(b) UCSD Mechanism
C2H4
+H
(6)
+HO2 / -OH
C2H4O
C2H5
+HO2
-H2O2
(100)
CH3
+O2 / -O
C2H3
+O2
+O2/ -H2O2
(55)
(9)
C2H2
C
+O
(12)
(16)
+O / -H
(7)
+OH / -H2O
(54)
CH2CHO
(35)
-H
(6)
+O2 / -OH
(93)
+OH / -H
(88)
CH2O
CH2OH
CH2CO
+OH
(85)
C
+O2
-HO2
(95)
+OH / -H2O +HO2 / -H2O2
(74)
(24)
HCO
+O2 / -HO2
(97)
CO
CO2
Accumulating
in system
Figure 6.13 Reaction flow analysis for the mechanisms of a) Wang and b) UCSD for
autoignition. Conditions at TDC: Tc = 904 K and Pc = 50 bar.
119
C2H3+O2=CH2O+HCO
C2H3+O2=C2H2+HO2
2HO2=H2O2+O2
CH2O+OH=HCO+H2O
UCSD
C2H4+O=CH3+HCO
C2H4+O=C2H3+OH
Wang
CH3+HO2=CH3O+OH
C2H4+OH=C2H3+H2O
2OH(+M)=H2O2(+M)
C2H4+HO2=C2H4O+OH
C2H3+O2=CH2CHO+O
-100
-50
0
50
Percent Sensitivity of Ignition Delay
100
Figure 6.14 Comparison of percent sensitivity of ignition delay (Tc=904 K and Pc=50 bar)
obtained using the mechanism of Wang and the UCSD mechanism.
120
Chapter 7
Autoignition of n-Decane/Air Mixtures
7.1 Scientific Background
Many practical combustion devices use liquid hydrocarbon fuel as the primary energy
source. Constituents of practical liquid fuels consist of a wide spectrum of hydrocarbons
in terms of carbon number, carbon to hydrogen ratio and chemical structure. Each of
these properties can have a significant influence on the oxidation kinetics. For simplicity,
while trying to model real fuels one often resorts to using surrogate mixtures consisting
of representative pure hydrocarbon components. Linear alkanes such as n-decane and ndodecane are one such representative class of hydrocarbons present in surrogate jet and
diesel fuels. Furthermore, synthetic fuels derived from gas to liquids conversion
processes also have a significant proportion of n-alkanes which results in a higher cetane
rating (Dry, 2002). The synthetic diesel fuels are considered to be environment friendly
on account of low aromatics and sulfur content (Knottenbelt, 2002). They have proven to
be technically and commercially viable fuel options, and are currently marketed in certain
parts of the world (Vosloo, 2001; Steynberg et al., 1999). Alongside the cost benefits, the
future prospect of substitution of petroleum based fuels with synthetic diesel fuel is a
strong motivator for developing high efficiency, less polluting engine technologies based
on diesel fuel.
Diesel engines based on the Premixed Charge Compression Ignition (PCCI)
concept have the potential to mitigate some of the emission problems associated with the
conventional diesel engine (Hardy and Reitz, 2006). The idea is to have a premixed
fuel/air mixture before combustion, thereby eliminating the fuel rich zones that occur in a
121
conventional diesel engine and are responsible for increased emissions. The problems
which confront this engine concept are to a great extent similar to that occur in its S.I
counterpart, namely the Homogeneous Charge Compression Ignition (HCCI) engine.
They mainly relate to combustion phasing, narrow operating limits and combustion
stability. The underlying phenomenon for both the PCCI and HCCI is essentially an
autoignition event, governed mainly by the chemical-kinetic processes. Significant
insight into these problems can be gained by a proper understanding of the oxidation
behavior of the fuel under the different operating regimes encountered in these devices.
One of the fundamental global oxidation responses of relevance to these devices is the
autoignition delay time.
Under similar conditions, the high cetane number (CN) diesel fuel components
such as n-decane and n-dodecane are prone to ignite much faster in comparison to typical
gasoline surrogate component such as iso-octane. While this is advantageous for the
conventional diesel cycle, it poses a problem in the premixed combustion mode. There
are ongoing efforts to control the combustion characteristics of diesel fuels for the
premixed mode by employing methods such as use of Exhaust Gas Recirculation (EGR),
inlet temperature variations and chemical additives. While recognizing that experimental
data obtained in a real engine environment provide invaluable information related to
design improvements, often such data are invariably influenced by a host of secondary
physical and chemical processes acting in tandem. Typical examples of such processes
are the degree of fuel vaporization and premixing, intake pressure and temperature
variations, in-cylinder aerodynamics, cycle to cycle variations in the EGR level and
possibly even the equivalence ratio/fuel composition, among other things. It is therefore a
122
formidable task to extract device independent information/conclusion related to the
combustion process, more so if it relates purely to the oxidation kinetics.
The situation is not necessarily unique to reciprocating engines but applies to
other devices as well, such as a premixed-gas turbine combustor, which must take into
careful consideration the fuel autoignition propensity (Lee et al., 2003; Spadaccini and
TEVelde, 1982). It is precisely in these circumstances that a well characterized,
configurationally simple laboratory apparatus which operates at conditions relevant to the
real process, and is amenable to mathematical modeling can make a useful contribution.
One such device, which can represent the engine like operating conditions, while to a
great extent avoiding its real life complexities, is the Rapid Compression Machine
(RCM). The subsequent sections relate to experimental investigations on the autoignition
characteristics of n-decane in the low to intermediate temperature regime and under high
pressure conditions using a rapid compression machine.
Considering the practical importance of n-decane and similar long straight chain
alkanes, it is somewhat surprising that not much experimental data on their autoignition is
available, especially for conditions that are relevant to engine combustion. Even from the
perspective of fundamental kinetic studies, they deserve greater attention, given the rich
variety of kinetic features they exhibit in the low-to-intermediate temperature oxidation
process.
Previous measurements on n-decane autoignition have been reported by Pfahl
et al. (1996), and more recently by Olchanski and Burcat (2006) and Zhukov et al.
(2006). All the aforementioned works have used a heated shock tube to determine the
autoignition delay times.
Pfahl et al. (1996) have conducted autoignition studies on n-decane/air mixtures at
123
13 and 50 bar, for the temperature range of 650-1300 K and for the equivalence ratio
range of 0.5-2.0. The work of Olchanski and Burcat (2006) investigated n-decane/oxygen
autoignition in argon diluted mixtures in the pressure range of 1.8-10 atmospheres and for
a temperature range of 1239-1616 K. Zhukov et al. (2006) have studied decane/air
autoignition at 13 and 80 atmospheres, in the temperature range of ~770-1325 K, and for
equivalence ratios of 0.5 and 1.0.
7.2 Experimental and Computational Specifications
7.2.1
Determination of Ignition Delays
Ignition delay measurements for n-decane air mixtures, corresponding to an equivalence
ratio of 0.8 were conducted over the temperature range of 635–706 K and the pressure
range of 7–30 bar, using a RCM. The current experiments span a temperature range not
investigated in earlier works on n-decane. As noted from the literature survey, the
autoignition data for this important surrogate component at low temperatures and high
pressures is meager. This is primarily because of the low vapor pressure of high-boilingpoint liquid hydrocarbons, which poses significant challenges in preparation of a
homogeneous reactive mixture for experimentation. The mixture preparation in the
current setup used mechanical stirring which provides for a homogeneous pre-mixture.
Additionally, no oxidation of the fuel was observed in the heated charge preparation tank.
This was confirmed using a GC column in conjunction with a flame ionization detector,
where only a single hydrocarbon peak was seen for three samples drawn at 2 hour
intervals. A final confirmation was provided by the repeatability of the data obtained from
3 runs conducted at similar intervals as shown in Fig. 7.1.
124
Numerical modeling of ignition delay was performed using the Sandia SENKIN
code (Lutz et al., 1998) in conjunction with CHEMKIN (Kee et al., 1989). The details of
the experimental equipment and the modeling procedure have already been described in
Chapter 6.
7.2.2
Kinetic Models
The experimental data are modeled using the chemical kinetic mechanism of Bikas and
Peters (2001). The mechanism of Bikas and Peters has been validated against
experimental species profile obtained using an atmospheric pressure, premixed flat flame.
Additionally it has also been checked against ignition experiments in jet stirred reactors
and shock tube reactors. In particular, the autoignition sub-model in this mechanism is
stated to include reactions relevant to ignition under both high and low temperature
conditions. This model has also successfully reproduced the negative temperature
coefficient (NTC) behavior displayed in an earlier shock tube ignition experiment of
Pfahl et al. (1996). The chemical kinetic mechanism of Bikas and Peters (2001) consists
of 67 species and 354 reactions. It is noted that the two other mechanisms used for flame
speed simulations studies in Chapter 5, namely the mechanism of Zhao et al. (2005) and
the Utah surrogate Mechanism (Zhang, 2005), are not compared to the current data on
account of their inability to lead to ignition under the current experimental conditions.
Also, they do not predict a two-stage ignition under the temperature conditions where
they eventually lead to an ignition. This is simply because the low-temperature chemistry
was not included in the mechanism of Zhao et al. (2005) and the Utah Surrogate
Mechanism (Zhang, 2005).
125
7.3 Ignition Delay Results
Figures 7.2(a) and 7.2(b) show the experimental and simulated pressure traces
respectively, for a compressed gas pressure of 7 bar with varying compressed gas
temperature. The variation in the compressed gas temperature is achieved by changing
the initial temperature of the mixture fed to the reaction chamber. Similar plots for the
two other pressure conditions of 14.3 bar and 30 bar are shown in Figs. 7.3 and 7.4. From
the experimental traces it can be seen that n-decane exhibits a distinct two-stage ignition
event under the current temperature and pressure conditions. Also, the discrepancy in the
ignition delay times as seen in the experimental and simulated traces is substantial. The
corresponding experimental pressure traces of the nonreactive counterparts are also
shown in Figs. 7.2-7.4. By referring to the nonreactive pressure trace, it can be inferred
that the extent of reaction during compression stroke is minimal. This facilitates the
reporting of ignition delay data in terms of the post compression pressures and
temperatures, since no reaction has occurred till the end of the compression stroke. The
pressure rise due to autoignition in the current experiments is rather slow, and occurs over
a time span of a few milliseconds. This is in contrast to the ethylene experiments where
the pressure rise was comparatively rapid and the ignition time could be discerned
visually, with sufficient accuracy. Hence the ignition delay time needs to be defined in a
consistent fashion across the range of the current experiments and also the simulations.
Therefore, the definition of ignition delay is chosen to be the time difference between the
end of compression and the occurrence of the inflection points in the pressure traces,
corresponding to the first and second stages of ignition. The plot in Fig. 7.5 clearly
illustrates the definition of ignition delay used. In this definition τ1 is the time interval
126
between the end of compression and the onset of the first stage ignition. The time interval
τ2 is the duration between the first stage ignition delay and the second stage ignition
delay. The ignition delay is the sum of the two intervals (τignition=τ1+ τ2).
Figure 7.6 shows the Arrhenius plot of measured ignition delays at compressed
pressures of 7, 14.3, and 30 bar. The current experimental data are compared alongside
the earlier work of Pfahl et al. (1996) and a recent work in progress poster (Zhukov et al.,
2006) under similar pressure conditions in Fig. 7.7, although different equivalence ratios
are different definitions for ignition delays were used. This plot serves to demonstrate the
fact that the current experiments have been conducted in a temperature range not
investigated earlier, and that the current data are consistent with the few known source for
n-decane autoignition.
The experimental and computed ignition delays for pressures of 7, 14.3 and 30
bar are compared in Figs. 7.8-7.10. The computations using the mechanism of Bikas and
Peters consistently predict delays that are higher compared to experimentally obtained
values. The ignition delay predictions at 7 bar are higher by a factor of ~2.2. The
predictions deteriorate with increasing pressure and the over prediction by a factor of 4-5
is observed at 14.3 and 30 bar. Similar over-prediction is seen for the first stage delays as
well. However, it must be emphasized again that this mechanism is the only one amongst
the 3 considered that is capable of ignition under the current conditions, albeit with a
higher ignition delay time. Also note-worthy is its ability to predict the two-stage
behavior. The mechanism of Zhao et al. (2005) and the Utah Surrogate Mechanism
(Zhang, 2005) exhibit a single stage ignition when the compressed gas temperature is
artificially increased to induce an autoignition. A kinetic pathway analysis of the
127
mechanism of Bikas and Peters will be performed in due course.
Continuing with the experimental data, it can be seen from Fig. 7.7 that the
current data have not yet approached the region of the negative temperature coefficient
(NTC) where the ignition delay increases with increasing temperature, and a nonmonotonic trend is seen. For the current dataset the ignition delay is a monotonic function
of temperature and pressure, which decreases with increasing values of pressure and
temperature. It is thus reasonable to attempt to reduce all the experimental data points to a
single correlation, which describes the ignition delay time in terms of the pressure and
temperature variables, for this particular mixture composition. It is an established practice
to use the form τ ignition = A × Pcn × exp( E / RTc )
(Heywood, 1988), for such a
representation, where A, n and E are fitting parameters representing the pre-exponential
factor, the pressure exponent and the activation energy, respectively. Here τignition is in
milliseconds, Pc in bar and Tc in Kelvin. The result of such data correlation is shown in
Fig. 7.11, showing that for the indicated pressure dependence the experimental data
points are fairly well represented by a single parameter, i.e. the compressed gas
temperature.
The mechanism of Bikas and Peters (2001) includes the low temperature submechanism and is therefore capable of predicting the two stage phenomena. Their work
has also demonstrated the capability of capturing the NTC type dependence of ignition
delay on temperature. The work of Bikas and Peters (2001) further notes that they used
some simplifying assumptions while representing the low temperature chemistry.
Noticeable among them are the inclusion of only two n-decyl radicals in place of the
possible five; additionally they have also not considered the formation of cyclic ether
128
from the alkylhydroperoxy radicals by OH elimination. A schematic illustrating the low
temperature reaction pathway implemented in their mechanism is shown in Fig. 7.12. For
this integrated reaction flow diagram (Warnatz, 1981), only the consumption pathways
for n-decane and the major products of the associated reactions are considered. Note that
the contribution to the consumption of a specific species from the individual reaction is
integrated over the duration starting from the end of compression to the time of the first
stage ignition. The number within the parentheses is the percent consumption of the
species indicated in the box through a particular reaction. In addition, the species whose
concentration is significantly increasing are shown with gray background, while the
species indicated without gray background, except the parent fuel, are approximately in
steady state during this pre-first stage ignition event.
The kinetic processes that lead to a two-stage ignition event are well understood
and a description can be found in a topical review article by Westbrook (2000). The fate
of the decyl radicals, depending on the temperature regime, determines the branching
characteristics of the overall reaction. For completeness a brief description of the key
reactions (500-1000 K) as outlined in the volume on low temperature combustion and
autoignition (Pilling, 1997) is provided in the following.
The primary initiation reaction is:
RH + O2 → R& + HO& 2
(r1)
The alkyl radicals that are formed in (r1) or as a result of subsequent abstraction reaction
involving the fuel and OH undergo an addition reaction with molecular oxygen to from
alkylperoxy in the temperature range of 500-600 K.
R& + O2 ⇔ R& O2
(r2)
129
The subsequent steps involve an isomerization reaction, followed by oxygen addition and
several other pathways which are overall branching in nature (cf. Fig 7.12). As the
temperature increases to 570-630 K, the R& O2 formed in (r2) disassociates back to the
reactants, i.e. a decrease in the rate of reaction with temperature is observed. The
concentration of R& builds up and with increasing temperature the following reaction
becomes important
R& + O2 → HO& 2 + alkene
(r3)
Above 750 K the C-C bond for the R& radical can be broken, resulting in smaller alkenes.
All along this duration the concentration of H2O2 steadily builds up by the reaction:
HO& 2 + HO& 2 → H 2 O2
(r4)
A secondary initiation is provided by the decomposition of H2O2 at ~1000 K (Westbrook,
2000) as a consequence of the reaction:
H 2 O2 + M → O& H + O& H + M
(r5)
The reaction (r5) is the trigger for the more violent second stage ignition.
Keeping in mind the basic kinetic pathways that lead to a two-stage ignition, a
sensitivity analysis of ignition delay to change in rate coefficients is conducted for the
mechanism of Bikas and Peters (2001). For the sensitivity analysis on the ignition delay
(τ), the rate constant of each reaction, ki, is individually doubled. The resulting percentage
change in the ignition delay, namely 100×[τ(2ki)−τ(ki)]/τ(ki), is then taken as the percent
sensitivity for that particular reaction. Figure 7.13 demonstrates such a sensitivity
analysis. A positive sensitivity implies that ignition delay increases by increasing the rate
constant of a particular reaction. Also, only the reactions which contribute to more than
2% change are considered in the sensitivity plots.
130
Another method often employed to study a chemical reaction mechanism is the
eigenvalue analysis. In this section such an analysis using the mechanism of Bikas and
Peters (2001) is conducted. It is noted that there exist far more sophisticated techniques
such as the Computational Singular Perturbation (CSP) method (Lam, 1993), the Intrinsic
Low-Dimensional Manifold (ILDM technique) (Maas and Pope, 1992) and the Directed
Relations Graph (Lu and Law, 2006) which are extremely useful to understanding and
simplifying the chemical kinetics. Here the attempt is limited to a local eigenvalue type
analysis. First the underlying concept provided followed by the results for the mechanism
under consideration. The next section follows the ideas as outlined in Warnatz (1998).
The system of differential equations that govern the time evolution of species in a
homogeneous chemical system can be represented by
r
r
dY
= G (Y )
dt
(7.1)
Here Y = [Y1 , Y2 ,......, YK ] consists of the dependent variables (species mass fractions) and
G (Y ) is the reaction rate, a function of the stoichiometric coefficients, species
concentrations and the reaction rate parameters. In the neighborhood of Y = Y 0
G (Y0 + d Y ) = G (Y0 ) + Jd Y .
(7.2)
Here J is the Jacobian , consisting of k by k matrix of
dGi
with the indices i and j run
dY j
over K, the total number of variables. Around Y = Y 0 the problem is linear in Y and the
eigenvalues of J are related to the characteristic time scales of the problem
dY
= G (Y0 ) + J (Y − Y 0 ) .
dt
(7.3)
131
A decomposition of the form J=QUQ-1 is carried out where Q is a unitary matrix and U is
an upper triangular matrix whose diagonal elements contain the eigenvalues of J. Note
that the columns of Q form an orthonormal basis. We first look for positive eigenvalues
associated with J as they will lead to a blow up of the system, exactly the phenomena we
Pir =
are interested in. A participation index is defined as
((Q −1 ) i • S r ) × F r
(Lam,
∑ ((Q −1 ) i • S r ) × F r
R
1993). Here r denotes the rth reaction, R the total number of recations and i the mode
corresponding to the ith eigenvalue. Also G (Y ) = ∑ S r F r , where Sr and Fr are the
R
stoichiometric coefficient vector and the reaction rate vector, respectively, for the rth
reaction. We look for the unstable (positive eigenvalue) mode that has the highest
amplitude. The amplitude of the mode is given by f i = ∑ ((Q −1 ) i • S r ) × F r .It is noted
R
that in recent work Kazakov et al. (2006) have conducted a kinetic analysis of n-heptane
mechanisms using CSP. The terminology and concepts used in this and the above section
has followed the works of Lam (1993), Turányi (1997) and Kazakov et al. (2006).
Figure 7.14(a) shows a plot of the simulated temperature results along with the value
for the amplitude for the leading explosive mode associated with a positive eigenvalue.
As expected the peak of the leading explosive mode amplitudes coincide with the
occurrence of the first and second stage ignition. The plot in Fig.7.14(b) shows the
corresponding eigenvalues. Note that an arbitrary upper cut-off of 10,000 has been set for
the eigenvalues (λ), which corresponds to a lower cutoff for time of (1/λ) 0.1
milliseconds. The largest magnitude eigenvalues, positive as well as negative, that occur
during the calculations are shown in Fig. 7.15 (a) are shown for reference. The next step
132
is to evaluate the participation index of reactions in the leading explosive modes, as
defined in the earlier section. For clarity, the locations where these evaluations are done
have been marked by circles in Fig 7.15 (b).The locations roughly correspond to the
beginning and the approximate end of the first and second stage ignition events.
The
constituent reactions of the leading explosive modes at the selected times (temperatures)
during the system evolution are shown in Figs. 7.16 and 7.17. The conclusions that can
be drawn from the makeup of the leading explosive modes are pretty much expected and
self evident, based on the brief discussion on the low-intermediate temperature kinetics
presented in the earlier section. For the first stage ignition, the ketohydroperoxide
decomposition reaction, the formation of alkyl-peroxy, and other reactions of the parent
fuel are important. The second stage is driven by the hydrogen peroxide decomposition
reaction and the C1-C2 reactions also assume importance.
A noteworthy fact that emerges from all of the above kinetic analyses is the
importance of C1-C2 oxidation kinetics at relatively higher temperature (> 1100 K). Not
surprisingly, ethylene being one of the main stable intermediates assumes an important
role. The seemingly incongruous interjection by ethylene, in this study on higher
hydrocarbons, now requires no further justification.
7.4
Concluding Remarks
The autoignition delay times for n-decane-air mixtures have been obtained for a
temperature range not investigated previously. Two stage ignition is observed for the
entire range of temperatures and pressures studied, with a rather strong first stage
activity. The experimental results have been compared to numerical simulations using a
133
kinetic mechanism that included the low temperature oxidation sub-mechanism. The
mechanism performed very well in capturing the essential feature related to the two-stage
ignition. However, a discrepancy was observed between the experimentally and
numerically observed ignition delay times, with the mechanism predicting a considerably
longer ignition delay time. The sets of experiments also serve to demonstrate the utility of
a Rapid Compression Machine in studying the low temperature oxidation for high boiling
point, low vapor pressure liquid fuels. The current experimental measurements, though
for global quantities, provide additional benchmark data of high fidelity for the validation
of the oxidation kinetics of n-decane, in the low temperature (635-706 K) regime and
under high pressure conditions (7-30 bar). This is particularly relevant to emerging
technologies involving premixed combustion of diesel like fuels.
134
n- Decane/Air, φ =0.8, Pc = 7 bar
20
Typical Experimental Reproducibility
(3 runs under similar conditions)
Pressure (bar)
15
10
Tc = 668 K
5
End of Compression
Nonreactive trace
0
28
32
36
Time (ms)
Figure 7.1 Typical experimental reproducibility.
135
40
44
(a) n- Decane/Air, φ =0.8, Pc = 7 bar
20
Tc (K) = 692
Pressure (bar)
15
681
Experimental
10
5
656
Nonreactive trace
End of Compression
0
24
28
32
36
40
Time (ms)
44
48
(b) n- Decane/Air, φ =0.8, Pc = 7 bar
20
Tc (K) = 692
681
15
Pressure (bar)
662
662
Simulated
Bikas and Peters (2001)
656
10
5
End of Compression
Nonreactive trace
0
30
40
50
Time (ms)
60
70
Figure 7.2 a) Experimentally obtained pressure traces, Pc= 7 bar b) Simulated pressure
plots using mechanism of Bikas and Peters (2001), Pc= 7 bar
136
(a) n- Decane/Air, φ =0.8, Pc = 14.3 bar
35
Tc (K)=
Pressure (bar)
30
697
682
25
659
Experimental
647
20
635
15
10
Nonreactive trace
5
End of Compression
0
28
32
Pressure (bar)
25
40
Time (ms)
44
48
(b) n- Decane/Air, φ =0.8, Pc = 14.3 bar
35
30
36
Tc (K)
697
Simulated
Bikas and Peters (2001)
682
659
635
647
20
15
End of Compression
10
Nonreactive trace
5
0
30
50
70
Time (ms)
90
110
Figure 7.3
a) Experimentally obtained pressure traces, Pc= 14.3 bar .b) Simulated
pressure plots using mechanism of Bikas and Peters (2001), Pc= 14.3 bar
137
(a) n- Decane/Air, φ =0.8, Pc = 30 bar
50
Tc (K) = 683
Pressure (bar)
40
672
662
650
Experimental
30
Nonreactive trace
20
10
End of Compression
0
20
25
Time (ms)
30
35
(b) n- Decane/Air, φ =0.8, Pc = 30 bar
Pressure (bar)
50
Tc (K) =
683
672
662
650
40
30
End of Compression
20
Nonreactive trace
10
Simulated
Bikas and Peters (2001)
0
20
30
40
Time (ms)
50
60
Figure 7.4
a) Experimentally obtained pressure traces, Pc= 30 bar, b) Simulated
pressure plots using mechanism of Bikas and Peters (2001), Pc= 30 bar
138
(a) Pc = 7 bar
P(t)
Pressure (bar) and its
Second Time Derivative
15
10
5
0
-5
End of
Compression
τ2
τ1
-10
τignition
-15
24
28
32
36
Time (ms)
P"(t)
40
44
(b) Pc = 7 bar
Pressure (bar) and its
First Time Derivative
16
P(t)
12
End of Compression
8
P'(t)
τ2
τ1
4
τignition
0
24
28
32
36
Time (ms)
40
44
Figure 7.5 Definition of ignition delay τ1=first stage delay, τ1+ τ2=ignition delay a)
Second derivative of trace showing the inflection points b) First derivative of
trace showing the location of peaks corresponding to the inflection points in a)
139
Ignition Delay (ms)
Pc= 7 bar
14.3 bar
101
30 bar
100
1.42 1.44
1.46 1.48
1.5
1000/Tc
1.52 1.54 1.56
1.58
(K-1)
Figure 7.6
Measured ignition delays (τ1+ τ2) as a function of compressed gas
temperature , Tc, at different post compression pressures, Pc for n-decane/air
mixtures corresponding to φ =0.8.
140
Comparison of Current results with Literature data for 13-14 bar range
102
n-Decane/Air
100
p
y
101
10-1
τ1+τ2-Current
τ1-Current
} φ = 0.8
10-2
τ1+τ2-Pfahl et al. (1996)
10-3
τ1+τ2-Zhukov et al. (2006)
0.6
τ1-Pfahl et al.(1996)
0.8
1
1000/Tc
1.2
} φ = 1.0
} φ = 1.0
1.4
1.6
(K-1)
Figure 7.7
Comparison of ignition delay times obtained from the present RCM with
literature data
141
Ignition Delay (ms)
50
(a) n- Decane/Air, φ =0.8, Pc = 7 bar
Ignition Delay = τ1 +τ2
40
30
Experiment
Simulation
20
10
0
1.42
1.44
1.46
1.48
1.5
1.52
1.54
1000/Tc (K-1)
First Stage Delay (ms)
25
20
15
(b) n- Decane/Air, φ =0.8, Pc = 7 bar
First Stage Delay = τ1
Experiment
Simulation
10
5
0
1.42
1.44
1.46
1.48
1000/Tc (K-1)
1.5
1.52
1.54
Figure 7.8 a) Comparison of experimental ignition delays (symbols) with simulation
results (line) using the mechanism of Bikas and Peters (2001), Pc=7 bar b)
Comparison of experimental first stage delays (symbols) with simulation results
(line) using the mechanism of Bikas and Peters (2001), Pc=7 bar
142
Ignition Delay (ms)
100
(a) n- Decane/Air, φ =0.8, Pc = 14.3 bar
Ignition Delay = τ1 +τ2
80
Experiment
Simulation
60
40
20
0
1.42
1.44
1.46
1.48
1.5
1.52
1.54
1.56
1.58
1000/Tc (K-1)
First Stage Delay (ms)
60
50
40
30
(b) n- Decane/Air, φ =0.8, Pc = 14.3 bar
First Stage Delay = τ1
Experiment
Simulation
20
10
0
1.46
1.48
1.5
1.52
1000/Tc (K-1)
1.54
1.56
1.58
Figure 7.9 a) Comparison of experimental ignition delays (symbols) with simulation
results (line) using the mechanism of Bikas and Peters (2001), Pc=14.3 bar b)
Comparison of experimental first stage delays (symbols) with simulation results
(line) using the mechanism of Bikas and Peters (2001), Pc=14.3 bar
143
(a) n- Decane/Air, φ =0.8, Pc = 30 bar
80
Ignition Delay = τ1 +τ2
Ignition Delay (ms)
70
60
Experiment
Simulation
50
40
30
20
10
0
1.46
1.47
1.48
1.49
1.5
1.51
1.52
1.53
1.54
1000/Tc (K-1)
First Stage Delay (ms)
60
50
40
30
(b) n- Decane/Air, φ =0.8, Pc = 30 bar
First Stage Delay = τ1
Experiment
Simulation
20
10
0
1.46
1.47
1.48
1.49
1.5
1.51
1000/Tc (K-1)
1.52
1.53
1.54
Figure 7.10 a) Comparison of experimental ignition delays (symbols) with simulation
results (line) using the mechanism of Bikas and Peters (2001), Pc=30 bar b)
Comparison of experimental first stage delays (symbols) with simulation results
(line) using the mechanism of Bikas and Peters (2001), Pc=30 bar
144
n- Decane/Air, φ =0.8
τignition x Pc-n
200
150
τignition= A x Pcn x exp( E/RTc )
100
A = 4.55823x10-8
n = -0.83104
E/R = 13992
50
0
1.42
1.44
1.46
1.48
1.5
1000/Tc
Figure 7.11
1.52
1.54
(K-1)
Correlation for the experimental ignition delay times.
145
1.56
1.58
Pre- first stage ignition Species Consumption Pathways, Pc=14.3 Bar, Tc=658.8K
(Bikas and Peters, 2001)
CH
decane
CH
C10H22
+OH / -H2O
(49.7)
dec-3-yl
C10H21-3
O2 (99.9)
-O2
(28.9)
O
+OH / -H2O
(49.7)
O2 (99.9)
RO
RO22-2
-2
O
-O2
(28.9)
O
decylperoxy
RO2H-32
CH
2-hydroperoxydec-3-yl
C10H21-2
(42.25)
(41.8)
OH
dec-2-yl
(57.5)
O
OH
O2RO2H-32
-OH (100)
O
HO
O decyl ketohydroperoxide
C2H4
O
O hydroperoxydecylperoxy
ORO2H-32
-OH (100)
+O2 / -HO2
(97.3)
CH2O
C2H5
Accumulating
in system
CO
+O2/ -HO2
(98.6)
HCO
+OH / -H 2O
(99.9)
Figure 7.12 Reaction Flow analysis for the mechanism of Bikas and Peters (2001).
Conditions at TDC : Tc = 658.8 K and Pc = 14.3 bar.
146
(a) Sensitivity of Ignition Delay at the time of Second Stage Ignition
H2O2(+M)<=>2OH(+M)
O2RO2H-32<=>ORO2H-32+OH
C2H4+OH<=>C2H3+H2O
ORO2H-32=>CH2O+CO+3C2H4+C2H5+OH
CH2O+OH=>HCO+H2O
C2H3+O2<=>CH2CHO+O
2HO2<=>H2O2+O2
CO+HO2<=>CO2+OH
Bikas and Peters
(2001)
N-C10H22+HO2=>C10H21-2+H2O2
N-C10H22+HO2=>C10H21-3+H2O2
2HO2<=>H2O2+O2
C2H3+O2<=>C2H2+HO2
RO2H-32<=>C10H20-1+HO2
H2O2+OH<=>H2O+HO2
HO2+OH<=>H2O+O2
-40
-20
0
20
Percent Sensitivity of Ignition Delay
40
(b) Sensitivity of Ignition Delay at the time of First Stage Ignition
O2RO2H-32<=>ORO2H-32+OH
ORO2H-32=>CH2O+CO+3C2H4+C2H5+OH
N-C10H22+HO2=>C10H21-2+H2O2
Bikas and Peters
(2001)
N-C10H22+HO2=>C10H21-3+H2O2
N-C10H22+O2=>C10H21-2+HO2
N-C10H22+O2=>C10H21-3+HO2
-60
-40
-20
0
20
Percent Sensitivity of First Stage Ignition Delay
Figure 7.13 a) Comparison of percent sensitivity of second stage ignition delay (Tc=658.8
K and Pc=14.3 bar ) b) Comparison of percent sensitivity of first stage ignition
delay. (Tc=658.8 K and Pc=14.3 bar )
147
Temperature (K)
1500
0.3
1000
0.2
500
0.1
0
Magnitude of Leading Mode Eigenvalue
Temperature
Leading Mode Amplitude
0
10
20
30
40
50
Time (ms)
60
70
Leading Mode Amplitude
Simulated Results using the Mechanism of Bikas and Peter (2001)
(a)
0.6
Pc=14.3 bar
2500
0.5
Tc= 658.8 K
2000
0.4
0
(b)
10000
Pc=14.3 bar
8000
T = 658.8 K
c
6000
4000
2000
0 32
36
40
44
48
52
56
60
64
Time (ms)
Figure 7.14 a) Plot of Temperature profile and leading mode amplitude associated with
positive eigenvalues b) The corresponding eigenvalues for (a).
148
(a)
9
Magnitude of Eigenvalue
3 10
9
2 10
Maximum (λ)
9
1 10
Pc=14.3 bar
Minimum (λ)
0
Tc= 658.8 K
9
-1 10
9
-2 10
9
-3 10
32
36
40
44
48
52
56
60
64
Time (ms)
(b) Plot Indicating Locations where Participation Indices are Calculated
1400
P =14.3 bar
Temperature (K)
c
T = 658.8 K
1200
c
T=1046 K
1000
800
T=804 K
T=853 K
T=701 K
600
400
25
30
35
40
45
50
55
60
65
Time (ms)
Figure 7.15 a) Plot showing the maximum and minimum eigenvalues. b) Temperature
profile showing the locations where the Participation Index of reactions to leading
mode with positive eigenvalues will be evaluated.
149
(a) Participation Index of Reactions in Leading Explosive Mode (T= 701K)
N-C10H22+OH=>C10H21-2+H2O
N-C10H22+OH=>C10H21-3+H2O
RO2-2=>C10H21-3+O2
RO2-2=>C10H21-2+O2
O2RO2H-32<=>ORO2H-32+OH
C2H5+O2<=>C2H4+HO2
Bikas and Peters
(2001)
ORO2H-32=>CH2O+CO+3C2H4+C2H5+OH
C10H21-2+O2=>RO2-2
C10H21-3+O2=>RO2-2
RO2H-32+O2<=>O2RO2H-32
-1
-0.5
0
Participation Index
0.5
1
(b) Participation Index of Reactions in Leading Explosive Mode (T= 804K)
HCO+O2<=>CO+HO2
C2H5+O2<=>C2H4+HO2
C10H21-3+O2=>RO2-2
C10H21-2+O2=>RO2-2
C2H3+O2<=>CH2O+HCO
RO2-2=>C10H21-3+O2
Bikas and Peters
(2001)
RO2-2=>C10H21-2+O2
2HO2<=>H2O2+O2
2HO2<=>H2O2+O2
O2RO2H-32<=>ORO2H-32+OH
-1
-0.5
0
Participation Index
0.5
1
Figure 7.16 a) Participation index of reactions to leading explosive mode; T= 701 K b)
Participation index of reactions to leading explosive mode; T= 804 K
150
(a) Participation Index of Reactions in Leading Explosive Mode (T= 852K)
C2H5+O2<=>C2H4+HO2
O2RO2H-32<=>ORO2H-32+OH
2HO2<=>H2O2+O2
2HO2<=>H2O2+O2
HCO+O2<=>CO+HO2
C2H4+O<=>CH3+HCO
Bikas and Peters
(2001)
C2H4+H(+M)=>C2H5(+M)
H2O2+OH<=>H2O+HO2
CH2O+OH=>HCO+H2O
C2H4+OH<=>C2H3+H2O
-1
-0.5
0
Participation Index
0.5
1
(b) Participation Index of Reactions in Leading Explosive Mode (T= 1046K)
C2H4+OH<=>C2H3+H2O
2HO2<=>H2O2+O2
CH2O+OH=>HCO+H2O
C2H4+H(+M)=>C2H5(+M)
2HO2<=>H2O2+O2
C2H5+O2<=>C2H4+HO2
Bikas and Peters
(2001)
HCO+O2<=>CO+HO2
CH3+HO2<=>CH3O+OH
CO+HO2<=>CO2+OH
H2O2(+M)<=>2OH(+M)
-1
-0.5
0
0.5
Participation Index
1
Figure 7.17 a) Participation index of reactions to leading explosive mode; T= 852 K b)
Participation index of reactions to leading explosive mode; T= 1046 K
151
Chapter 8
Autoignition of Binary Fuel Blends involving n-Decane:
Influence of Fuel Structure
8.1 Scientific Background
This dissertation has so far made an attempt to characterize the global combustion
responses of pure components, pertinent to high and low-to-intermediate temperature
chemistry. The rationale being to help improve the “comprehensiveness” of the submechanisms for pure components, so that they could accurately predict the combustion
characteristics of surrogate blend, and ultimately the real world fuels. While serving as a
logical starting point, it by no means is sufficient in itself. The ultimate goal is not only to
be able to observe and predict combustion properties, but also to modify them to suit the
objectives at hand. The importance of such modifications is very well recognized, with
anti-knock additives providing a classic example. Over the years fuel additives have been
tailor made to enhance/inhibit some physical or chemical trait unique to the particular
class of fuels. Some of the properties of particular relevance to combustion are flame
propagation velocities, autoignition times and pollutant formation/ removal rates. It is
well known that these properties can be influenced either by varying the thermodynamic
conditions under which a reaction occurs, given a composition, or the chemistry could be
altered by varying the reactant composition and/or using some other chemical means.
One of the chemical methods often resorted to is the use of fuel blends. This method has
found much favor, as is evident from the various refining processes such as catalytic
cracking/reforming, hydrocracking, alkylation and other means that have been developed
for making the right blend for gasoline (Kalghatgi, 2005). The objective is to make the
152
fuel compatible to its intended end use as gasoline, diesel or jet-fuel. These processes are
technology and cost intensive, and both the refiners and the automakers are adapting to
the demands of future trends ((Kalghatgi, 2005). The obvious practical significance of
fuel blend combustion makes it extremely important that the intricacies of fuel blend
combustion also are understood at a fundamental level. While it is a sine qua non that a
comprehensive mechanism predicts the fundamental global combustion responses for
pure components, it should also, among other things, be capable of predicting the kinetic
interactions that may potentially arise due to multiple fuel components.
In this study, autoignition delay times of fuel oxidizer mixtures, containing two
fuel components were investigated. The fuels chosen were n-decane and ethylene. Ndecane exhibits a two-stage ignition in the 600-750 K range (7-30 bar for current study),
with a strong first stage activity. Ethylene on the other hand displays a single stage
ignition for the 850-1050 K temperature range (15-50 bar for current study). Note that
ethylene will not ignite in the 600-750 K range for the current experiments using a Rapid
Compression Machine (RCM). Clearly we have a conflicting situation at 600-750 K and
7-30 bar conditions, as far as ignition behavior in the current RCM is concerned. One
component (n-decane) is prone to easily ignite while the other (ethylene) is resistant. The
first fuel (n-decane) shows a significant first stage activity, while the second fuel
(ethylene), when it ignites, does not. Another key difference lies in the structure of the
two fuel components. N-decane is a linear, saturated hydrocarbon, while ethylene is the
simplest alkene. Note however, that ethylene is one of the major stable intermediaries in
the oxidation of n-decane and similar straight chain saturated hydrocarbons. Taking note
of these disparities, while also recognizing the natural hierarchical dependence between
153
these two hydrocarbons, we find this to be one of the most natural pair whose chemical
interactions require investigation. Consequently, experiments were conducted in an
attempt to address the following specific questions:
a) What is the effect of the presence of a second fuel component on ignition
delay times, while maintaining a fixed overall equivalence ratio?
b) Is the effect chemical in origin, or can it be attributed to fuel loading
effects?
1. What role does the presence of a double bond in one of the fuel
components play?
2. How are the first and second stages of ignition affected?
c) Can the interactions, if any observed, be exploited in practical devices?
An experimental attempt is made to provide clues to the questions posed above.
Answers to questions a) and b) will be sought through a series of systematic experiments,
while implications of the results for practical use will be suggested after a survey of some
of the recent literature. To specifically highlight the importance of the fuel structure
(saturated vs. unsaturated), a set of control experiments were conducted, where ethylene
was substituted by methane. This helped maintain approximately similar fuel loading for
n-decane while holding a constant overall equivalence ratio.
8.2 Experimental and Computational Specifications
8.2.1
Determination of Ignition Delays
Ignition delay measurements for n-decane/ethylene/air and n-decane/methane/air
mixtures, corresponding to an overall equivalence ratio of 0.8, were conducted for a fixed
154
compression ratio and for a post compression pressure of 7 bar, using an RCM. A
parametric study was conducted by changing the relative amounts of n-decane:ethylene
and n-decane:methane in the fuel, to observe the influence on ignition delays. Table 1
provides the composition of the mixtures studied in these experiments
Test #
1
2
3
4
5
6
7
8
9
10
n-Decane Ethylene Methane Oxygen Nitrogen
Molar Proportion in Mixture
1.00
0.00
0.00
19.38
72.85
1.00
1.00
0.00
23.13
86.95
1.00
2.00
0.00
26.88
101.05
1.00
3.00
0.00
30.63
115.15
1.00
5.00
0.00
38.13
143.35
1.00
7.00
0.00
45.63
171.55
1.00
0.00
2.00
24.38
91.65
1.00
0.00
3.00
26.88
101.05
1.00
0.00
5.00
31.88
119.85
1.00
0.00
7.00
36.88
138.65
Table 8.1 Composition of Mixtures Investigated
Numerical modeling of ignition delay was performed using the Sandia SENKIN
code (Lutz et al., 1998) in conjunction with CHEMKIN (Kee et al., 1989). The details of
the experimental equipment and the modeling procedure have already been described
earlier. The chemical kinetic model chosen for the simulations is that of Bikas and Peters
(2001), for reasons that have been discussed in Chapter 7.
8.3
Ignition Delay Results
Figures 8.1(a) and 8.1(b) show the experimental results for n-decane/ethylene/air and ndecane/methane/air mixtures. The two plots are shown on a similar time scale to enable a
fair and easy visual comparison of the effects observed. The following facts can be
inferred from the plots shown in Fig. 8.1. The total ignition delay times undergo a
155
dramatic increase due to the presence of ethylene while methane exerts a limited
influence. The first stage activity of n-decane is influenced in a very different manner due
to the presence of the second component. While ethylene is seen to significantly increase
the first stage ignition delay, methane appears to have no influence at all. Additionally the
intensity of the first stage, as measured by the rise in pressure after the first stage ignition,
is lowered/suppressed progressively with increasing substitution of n-decane by ethylene.
A similar suppression of the first stage intensity is not seen for the methane experiments
until much higher methane to n-decane ratio. The possibility of such an influence due to
temperature effects can be safely ruled out, since the temperatures are within 1 K for both
the ethylene and methane experiments with the same amount of substitution. Also, for the
various mixtures, in Fig.8.1, the ignition delay is seen to increase with increasing
substitution of n-decane, in spite of the compressed charge temperatures increasing due to
a change in the mixture specific heats.
Figures 8.2 (a) and (b) respectively show the total and the first stage ignition
delay times as a function of the amount of the second fuel components substituting ndecane. Note the lines shown in figures 8.2 are fits to the simulated data. The simulations
have been conducted using the mechanism of Bikas and Peters (2001). The simulation
results are very interesting and require to be interpreted with caution. The simulated
results are seen to predict the total ignition delays fairly well, for both ethylene and
methane substitution experiments, over the entire range. The first stage ignition delay
predictions however are in conflict with the experiments. While the experiments show an
increasing first stage delay with increased amounts of n-decane substitution by the second
component, the simulated results do not. In fact, contrary to the experimental findings,
156
the simulated results predict a decrease in the first stage ignition delay time, as greater
amounts of methane replaces n-decane. The corresponding simulation results for ethylene
predict a near constant first stage ignition delay, while the experimental results show a
very substantial increases as the amount of ethylene is increased. Comparative plots of
the experimental and simulated traces are shown in Figs. 8.3-8.4, for n-decane/ethylene
and n-decane/methane mixtures, respectively.
The results therefore hint at the possibility that the observed differences are
chemical in origin. The chemical nature of the interaction is very different at the first and
second stage of ignition. To gain further insight into the observed trends for the ignition
delay time (second stage), ignition delay times are computed for the pure fuel
components as well as a representative binary mixture (n-Decane : Ethylene = 1:5; nDecane : Methane = 1:5), under similar pressure and equivalence ratios. These results, for
a constant volume, adiabatic simulation are shown in Fig. 8.5. The time of ignition
corresponds to the mixture attaining a temperature of 1700 K. The computations show
that under the temperature range investigated in the current work, pure ethylene is slower
to ignite when compared to pure methane. Also, as expected, n-decane has the shortest
ignition delay time. Note the anomalous temperature dependence of the ignition delay
time for n-decane in the temperature range of 700-900 K, better known as the Negative
Temperature Coefficient (NTC) dependence. It can also be seen that the slopes of the
Arrhenius plots for pure ethylene and pure methane are different, and there exists a
crossover temperature ~ 1050 K where the ignition delay times of ethylene are shorter
than methane, i.e. ethylene ignites faster than methane. A similar cross-over temperature
is seen for the binary mixtures, with n-decane/ ethylene mixtures igniting slower than n-
157
decane/ methane mixtures ~below 885 K. The crossover trend for the blends is consistent
with that seen for the pure components substituting n-decane. Also, very interesting is the
prediction that the given blend of n-decane and ethylene should ignite faster than either of
its pure fuel constituents above ~990 K. The trend of significantly longer ignition delay
times for n-decane/ethylene/air mixtures as compared to n-decane/methane/air mixture
for the current experiments is correctly predicted. Note however that the simulations
show the second stage ignition delay, which represents the main heat release event.
The sensitivity of the ignition delay times, both for the first and second stages of
ignition, was conducted by doubling the rate constants of each reactions individually. The
calculations were conducted for both n-decane/ethylene/air mixtures and ndecane/methane/air mixtures, for the molar ratio of n-decane to the second fuel
component of 1:5. The results differ from the pure n-decane ignition case only with
respect to the reaction involving the second component, methane or ethylene, with the
OH radical. Specifically, the reaction of ethylene/methane with the hydroxyl radical show
a positive sensitivity (longer ignition delay) for the first stage ignition. Viewed in the light
of the above sensitivity results, the near constant first stage ignition delay and a
decreasing first stage ignition delay observed in the ethylene and methane simulations,
respectively, become even more perplexing (cf. Figs. 8.3(b) and 8.4(b)). A possible
explanation could lie in the increasing post compression temperatures as the fraction of
the second gaseous fuel component increases. It is likely that even the limited
temperature rise of ~ 8 K is sufficient to cause a decrease in the first stage ignition delay
of n-decane, counterbalancing or exceeding the competing opposite influence that the
reaction of the second gaseous component with OH.
158
8.4
Practical Implications
The experimental results discussed above can potentially be of use in premixed controlled
autoigniton devices using fuels with high cetane number and linear long chain alkanes. A
typical application, discussed earlier is the Premixed Charge Compression Ignition
(PCCI) engine (Hardy and Reitz, 2006), using Fisher-Tropsch (F-T) diesel. Recognizing
that ethylene is a major product that results from thermal/catalytic cracking of linear
alkanes, and the wide range of control on ignition timing that it can exert for such fuels, it
would be useful to consider the possibility of using an onboard cracking unit. It would
require a small proportion of the fuel to be thus processed, to obtain the desired ignition
delay/ combustion timing. Ignition delay times could be changed by adjusting the relative
amounts of the liquid fuel and its own cracked products. Ethylene, by virtue of its
chemical structure seems to have a disproportionately strong influence on the ignition
delay times. A computational study on the effects of fuel structure on ignition time in
HCCI by Kelly Zion and Dec (2000) highlights the advantages and disadvantages of the
fuel type for HCCI combustion. They compare iso-octane and n-heptane in their work,
and note that iso-octane can sustain higher compression ratios compared to n-heptane.
One of their important observations is that for initial temperature in the range of 800 K
iso-octane needs a time interval five times longer compared to n-heptane to display the
first stage activity. Hence, they opine that for HCCI engine computations, the first stage
ignition of iso-octane plays a minor role when compared to n-heptane. Iso-octane ignition
can be regarded effectively as single stage process, with the second stage ignition being
the controlling factor for ignition timing. The key point here, so far as HCCI engine
combustion goes, is the ability to delay the onset of the first stage activity, which is the
159
precursor to the main ignition event. This is precisely what the current set of experiments
has demonstrated. It was clearly shown that the onset of first stage ignition can be
delayed by as much as a factor of 8 by substituting a fraction of for n-decane by ethylene.
The gain factor accrued for the second stage ignition is even greater. One of their other
important observations is that above 1100 K, the low temperature chemistry no longer
controls the ignition. For these conditions the reaction H+O2→H+OH assumes the main
chain branching role and is apparently not influenced by the fuel structure.
While the practicality of the approach suggested above is open to question, the
results are unambiguous and may offer a better solution than other dual fuel firing
options. This method is self sufficient, in that it does not require a second fuel or any
other additive. Also note this scheme does not sacrifice power output, since the
equivalence ratio is maintained and no dilution is required. The idea of dual fuel firing
and the use of additives have been extensively studied earlier. The work of Stanglmaier et
al. (2001) used the ratio of F-T naptha and natural gas (95% methane) to control
combustion phasing. They also note that this method was first put forward by Furutani et
al. (1998). In a particularly interesting observation on the work of Stanglmaier et al.
(2001), Eng (2003) notes that the use of natural gas in a dual fuel engine can be viewed
from the perspective of ignition inhibitor for Fisher-Tropsch diesel fuels, akin to the
dimethy ether and natural gas pair. Indeed, this is valid conclusion, but there are
fundamental differences in the nature of the inhibition observed, as shown by the current
experiments. The extent of control that can be exercised can vastly differ, depending on
the fuel type.
160
8.5 Concluding Remarks
Experiments to study ignition characteristics of binary fuel blends with n-decane as one
of the components have been conducted. The experimental results show very different
trends for the response of the first and second stage ignition times, depending on the
nature of the second fuel component. The difference is seen not only for the ignition
delay times but also the intensity of the first stage activity. Specifically, the presence of
ethylene is found to severely inhibit the first and second stage ignition delay times and
suppress the first stage pressure rise when compared to methane under the conditions
investigated. Numerical results, while successfully predicted the enhancement of the
second stage ignition delay, were in conflict with the trends observed for the first stage
ignition.
161
Pressure (bar)
8.5
(Molar Ratio)
1:7
1:3
1:5
9
n-C10H22 : C2H4
1:1
1:2
9.5
Pure n-Decane
(a) (n- Decane+Ethylene)/Air, overall φ =0.8, Pc = 7 bar
10
1: 1 (Tc=685 K)
1: 2 (Tc=687 K)
1: 3 (Tc=688 K)
1: 5 (Tc=691 K)
8
1: 7 (Tc=693 K)
Pure n-C10H22 (Tc=681 K)
7.5
7
Inert
6.5
End of Compression
6
40
80
120
Time (ms)
160
200
8.5
1:7
1:5
(Molar Ratio)
1:3
Pressure (bar)
9
n-C10H22 : CH4
1:2
9.5
Pure n-Decane
(b) (n- Decane+Methane)/Air, overall φ =0.8, Pc = 7 bar
10
1: 2 (Tc=686K)
1: 3 (Tc=687 K)
1: 5 (Tc=691 K)
8
1: 7 (Tc=693K)
7.5
Pure n-C10H22 (Tc=681 K)
7
Inert
6.5
6
End of Compression
40
80
120
Time (ms)
160
200
Figure 8.1a) Experimentally obtained pressure traces for n-decane/ethylene/air mixtures,
Pc= 7 bar b) Experimentally obtained pressure traces for n-decane/methane/air
mixtures, Pc= 7 bar
162
Ignition Delay (ms)
Ignition Delay of Binary Fuel Blends For a Fixed Compression Ratio
200
n-Decane+Ethylene (Experimental)
Pc =7 bar
n-Decane+Methane (Experimental)
T0 =386 K
n-Decane+Ethylene (Simulation)
150
φ =0.8
n-Decane+Methane (Simulation)
100
50
0
0
1
2
3
4
5
6
7
8
Molar Ratio of Ethylene or Methane to n-Decane in Binary Blend
Ignition Delay (ms)
First Stage Delay of Binary Fuel Blends For a Fixed Compression Ratio
30
n-Decane+Ethylene (Experimental)
Pc =7 bar
n-Decane+Methane (Experimental)
25 T =386 K
0
n-Decane+Ethylene (Simulated)
φ =0.8
n-Decane+Methane (Simulated)
20
15
10
5
0
0
1
2
3
4
5
6
7
8
Molar Ratio of Ethylene or Methane to n-Decane in Binary Fuel Blend
Figure 8.2
a) Experimental (symbols) and simulated ignition delays (lines) for
fuel/air mixtures, Pc= 7 bar for increasing amounts of second fuel component
substituting n-decane. b) Experimental (symbols) and simulated first stage delays
for fuel/air mixtures, Pc= 7 bar for increasing amounts of second fuel component
substituting n-decane.
163
8.5
1:7
1:5
1:3
1: 2 (Tc=687 K)
1: 3 (Tc=688 K)
Experimental
1: 5 (Tc=691 K)
8
1: 7 (Tc=693 K)
Pure n-C10H22 (Tc=681 K)
7.5
7
Inert
6.5
n-C10H22 : C2H4
(Molar Ratio)
1:7
120
160
200
Time (ms)
(b) (n- Decane+Ethylene)/Air, overall φ =0.8, Pc = 7 bar
1:5
9
80
1:3
9.5
40
1:2
10
End of Compression
Pure
n-Decane
6
Pressure (bar)
(Molar Ratio)
1: 1 (Tc=685 K)
1:1
Pressure (bar)
9
n-C10H22 : C2H4
1:1
1:2
9.5
Pure n-Decane
(a) (n- Decane+Ethylene)/Air, overall φ =0.8, Pc = 7 bar
10
8.5
8
Bikas and Peter (2001)
7.5
7
6.5
6
1: 1 (Tc=685 K)
1: 5 (Tc=691 K)
1: 2 (Tc=687 K)
1: 7 (Tc=693 K)
1: 3 (Tc=688 K)
Pure n-C10H22 (Tc=681 K)
End of Compression
40
80
120
Time (ms)
160
200
Figure 8.3
a) Experimental pressure traces for n-decane/ethylene/air mixtures, Pc= 7
bar b) Simulated pressure traces for n-decane/ethylene/air mixtures, Pc= 7 bar
164
1:7
1:5
(Molar Ratio)
8.5
8
7.5
1: 2 (Tc=686K)
Experimental
1: 3 (Tc=687 K)
7
1: 5 (Tc=691 K)
1: 7 (Tc=693K)
6.5
9
40
Pure n-C10H22 (Tc=681 K)
50
60
Time (ms)
70
80
n-C10H22 : CH4
(Molar Ratio)
1:7
(a) (n- Decane+Methane)/Air, overall φ =0.8, Pc = 7 bar
1:5
9.5
30
1:3
10
End of Compression
1:2
6
Pressure (bar)
n-C10H22 : CH4
Pure
n-Decane
Pressure (bar)
9
1:3
9.5
1:2
Pure
n-Decane
10
(a) (n- Decane+Methane)/Air, overall φ =0.8, Pc = 7 bar
8.5
8
Bikas and Peters (2001)
7.5
1: 2 (Tc=686K)
1: 3 (Tc=687 K)
7
1: 5 (Tc=691 K)
1: 7 (Tc=693K)
6.5
6
End of Compression
30
40
Pure n-C10H22 (Tc=681 K)
50
60
Time (ms)
70
80
Figure 8.4
a) Experimental pressure traces for n-decane/dethane/air mixtures, Pc= 7
bar b) Simulated pressure traces for n-decane/methane/air mixtures, Pc= 7 bar
165
Computed Ignition Delay Times
( Adiabatic Constant Volume Simulations,φ=0.8)
Mechanism of Bikas and Peters (2001)
3
Ignition Delay (ms)
10
2
10
1
10
0
10
Pure Decane
Pure Ethylene
Pure Methane
X
:X
(1:5)
-1
10
Decane
-2
10
Ethylene
XDecane :XMethane (1:5)
0.8
1
1.2
-1
1.4
1.6
1000/T (K )
Figure 8.5
Simulated ignition delay times for pure n-decane, ethylene, methane and
binary mixture of decane/ethylene or methane (1:5 molar ratios) computed using
the mechanism of Bikas and Peters (2001).
166
Chapter 9
Summary and Recommendations
The importance of reliable and comprehensive data on the oxidation kinetics of pure
hydrocarbon components has already been highlighted earlier. The need for such
experimental data is even more acute for liquid hydrocarbons. As such, the current work
endeavors to address this problem. The oxidation characteristics of such fuel have been
studied for both the high-temperature and the low-to-intermediate temperature regime in
the current investigations; insofar the global responses are concerned. Alongside the
experiments, an effort has been also made to conduct a comparison with computations
using available chemical kinetic models.
The work started out with the principal constituents of gasoline surrogates,
namely iso-octane and n-heptane. The specific contribution has been to study the
influence of mixture preheating on laminar flame speeds. An increase in mass burning
flux with increasing temperature was observed. Also, the experimentally determined
laminar flame speeds for the two fuels were found to differ 5-10 cm/sec under similar
conditions.
The differences in the laminar flame speeds for the two fuels could be
reconciled on the basis of structural differences which led to a significantly different
product distribution during the fuel breakdown. On the basis of the sensitivity results for
the computations, the results were found to be influenced by the C2-C3 species, including
ethylene. Out of the three kinetic mechanisms used for the computations, only the
mechanism of Hasse et al. (2000) was able to provide a reasonably good prediction for
the laminar flame speed values of iso-octane/oxidizer mixtures when compared to the
experimental results.
167
The study was advanced to the next higher hydrocarbons often employed as surrogate
components for diesel and jet-fuel, n-decane and n-dodecane. These fuels presented a
significant challenge in the preparation of a homogeneous mixture, given the relatively
low vapor pressure for these higher order hydrocarbons. To ensure the reliability of the
data, a series of characterization experiments had to be done to confirm mixture
homogeneity. The laminar flame speeds of both fuels were obtained for a range of
equivalence ratios and mixture preheat temperatures. At the time of conducting these
experiments there was only one set of reported data for the stretch-free laminar flame
speed of n-decane, limited to a single preheat temperature. No reported data for ndodecane could be found. In this work, we therefore studied the influence of preheat on
laminar flame speeds for n-decane and additionally obtained similar data for n-dodecane.
The high stretch extinction stretch rates for nitrogen diluted fuel/oxidizer mixtures were
also obtained for n-decane and n-dodecane over a wide range of equivalence ratios.
Among the three mechanisms used for the simulations, only the mechanism of Bikas and
Peters (2001) was found to predict the laminar flame speeds for n-decane air mixtures
reasonably well. The extinction stretch rates were over-predicted by the numerical
simulations. Interestingly however, the trend of the extinction stretch rate versus
equivalence ratio was reproduced quite well. The simulated results showed a peak flame
temperature of 1600-1700 K for the near extinction flames, and incomplete CO oxidation
seems to be the primary reason for extinction for fuel rich flames.
The recurrent theme of sensitivity of the measured laminar flame speed for the higher
hydrocarbons to the subsequent reactions of ethylene was taken note of, and hence the
laminar flame speeds of ethylene/air mixtures were also investigated. The measured
168
laminar flame speeds of ethylene/air mixtures were found to be nearly one and a half time
greater compared to the liquid fuels investigated, for stoichiometric mixtures and at 470
K. Even for this relatively simple hydrocarbon, the mechanisms were unable to predict
the trends for laminar flame speed with increasing preheat. The ambient temperature
flame speeds were however well reproduced. This highlighted the need for mechanism
validations over a broad range of preheat temperatures for laminar flame speeds.
An investigation into the low-to-intermediate temperature oxidation response was also
conducted for ethylene. Single stage ignition was observed for the range of conditions
investigated. The key differences in the oxidation pathways at low-to-intermediate
temperatures were highlighted by comparing the fuel consumption pathways with that
under flame conditions. The ethylene+HO2 and the vinyl+O2 reactions were found to be
among the main controlling reactions under high pressures and low-to-intermediate
temperatures for ethylene autoignition.
Autoignition experiments on n-decane/air mixtures were conducted in a heated RCM.
Two-stage ignition was seen over the range of experiments conducted. The importance of
the low-temperature sub-mechanism for predicting the two-stage behavior for n-decane is
highlighted. The observed experimental features were simulated only by a mechanism
that included the low-temperature oxidation sub-mechanism. The basic feature of twostage ignition provides an example of one of the metrics to gauge the comprehensiveness
of a kinetic mechanism for large n-alkanes. Another possible measure is the interaction
between fuel components. This was studied next, in the context of kinetic interactions
observed between n-decane and ethylene in binary fuel blend autoignition experiments. It
was demonstrated that such an interaction cannot be merely interpreted as simple
169
inhibiting or enhancing effects, either due to specific heat or fuel loading variations.
There is a kinetic influence at play which influences the ignition response in an
unexpected, almost a counterintuitive fashion, and depends strongly on the fuel structure.
Additionally, the nature of modification is different in the low-to-intermediate and the
high-temperature conditions. The implication of these kinetic interactions viewed from
the perspective of a combustion phasing tool for premixed controlled-autoignition
devices has also been discussed.
The experiments results obtained during this research represent global quantities. It is
expected that the current experimental results will prove useful in real applications. There
exists a very wide scope for further research that can be conducted on neat fuel
components as well as their blends. Future work could consider including the following
options:
1. Extension of the study to other neat components, with special focus on
different classes of hydrocarbons such as cyclic/branched alkanes/alkenes and
aromatics.
2. Detailed Species and temperature profile measurements for neat
component oxidation, both for flame and autoignition experiments.
3. Influence of pressure on flame propagation
4. Wider parametric variations in terms of both thermodynamic variables and
mixture composition for autoignition experiments.
5. Basic study on the kinetic interactions for various binary/tertiary fuel
blends including the development of detailed and reduced kinetic mechanisms.
170
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