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FLAME STRUCTURE ANDBURNING SPEED OF JP-10 AIRMIXTURESFARZAN PARSINEJAD a , CHRISTIAN ARCARI a &HAMEED METGHALCHI* aa Mechanical and Industrial EngineeringDepartment , Northeastern University , Boston,Massachusetts, USAPublished online: 25 Jan 2007.
To cite this article: FARZAN PARSINEJAD , CHRISTIAN ARCARI & HAMEED METGHALCHI*(2006) FLAME STRUCTURE AND BURNING SPEED OF JP-10 AIR MIXTURES, CombustionScience and Technology, 178:5, 975-1000, DOI: 10.1080/00102200500270080
To link to this article: http://dx.doi.org/10.1080/00102200500270080
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FLAME STRUCTURE AND BURNING SPEED
OF JP-10 AIR MIXTURES
FARZAN PARSINEJADCHRISTIAN ARCARIHAMEED METGHALCHI*
Mechanical and Industrial Engineering Department,Northeastern University, Boston, Massachusetts, USA
The burning speed and flame structure of Jet Propellant (JP)-10 fuel-
air mixtures have been studied using two similar constant volumes: a
cylindrical vessel with end windows and a spherical chamber. Both
vessels are equipped with a central ignition, pressure transducer
for measuring pressure rise during combustion process and ioniza-
tion probes for monitoring flame arrival time. Both spherical and
cylindrical chambers can be heated up to 500 K. The spherical vessel
can withstand 425 atm pressures while the maximum allowable
pressure for cylindrical chamber is 50 atm due to the two windows
at end caps. A thermodynamic model has been developed to calcu-
late burning speed using dynamic pressure rise in the spherical ves-
sel. The model considers a central burned gas core of variable
temperature surrounded by a preheat zone, an unburned gas shell
with uniform temperature and a thermal boundary layer at the wall.
The model also includes losses associated with thermal radiation
from burned gas to the wall and heat losses to the electrodes and
the wall. Measurements in the spherical chamber start when the flame
radius is almost half of the chamber radius (about 3.8 cm), where ratio
of flame radius to flame thickness is larger than 25, hence curvature
and flame thickness effects can be neglected. Shadowgraph photo-
graphic observations were made through the end windows in the
Received 10 August 2004; accepted 16 June 2005.
This work was supported by the Naval Research Office, Grant number N00014-03-1-
0640 under technical monitoring of Dr. Gabriel Roy.�Address correspondence to [email protected]
Combust. Sci. and Tech., 178: 975–1000, 2006
Copyright Q Taylor & Francis Group, LLC
ISSN: 0010-2202 print/1563-521X online
DOI: 10.1080/00102200500270080
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cylindrical chamber using a high-speed Charged Coupled Device
(CCD) camera with variable speed of up to 8000 frames=second.
Burning speeds of JP-10 air mixtures have been measured in a press-
ure range of 1–55 atm, temperature range of 450–700 K and equiva-
lence ratios of 0.7–1. A correlation for burning speed as a function
of temperature, pressure and equivalence ratio has been developed.
Keywords: burning speed, JP-10, flame structure
INTRODUCTION
Missile fuels usually consist of pure synthesized hydrocarbons or mix-
tures of a few pure synthesized hydrocarbons for use in air breathing
missile engines. These hydrocarbons are compounds of high energy con-
tent per unit volume tailored to meet the operational requirements of
their assigned system. These include Ram Jet (RJ)-4, RJ-5, RJ-6, JP-9
and JP-10. JP-9 is an Air Force fuel that was specified for use in the
Air Launched Cruise Missile. JP-10 is a fuel meeting the�54�C. Air
Force operational requirements and has replaced JP-9 as the operational
fuel for the Air Launched Cruise Missile. JP-10 is a high density syn-
thetic fuel which is a single molecule C10H16. It is prepared by hydroge-
nating commercially available di(cyclopentadiene), which yields the solid
material endo-tetrahydrodi(cyclopentadiene). The intermediate structure
is then isomerized in the presence of catalyst to produce pure JP-10
(Coordinating Research Council, 1983). This fuel is used in volume-lim-
ited combustion chambers such as those of supersonic combustion ram-
jets and is of interest to the U.S. Navy for its propulsion systems. To
model the effects of JP-10 on both the emissions and performance of
combustors, knowledge of its fundamental combustion properties,
especially its burning speed, autoignition characteristics and the com-
bustion chemistry is needed.
Williams et al. (Li et al., 2001; Varatharajan and Williams, 2003)
have studied the chemistry of JP-10 ignition and has come up with a sim-
ple kinetic model as well as a developed chemistry for JP-10 detonation.
Shepherd and his co-workers (Cooper and Shepherd, 2002; Austin and
Shepherd, 2003) have studied the detonation characteristics of JP-10
and similar fuel blends and have measured and reported the vapor press-
ure of JP-10 as a function of temperature <http:==www.galcit.caltech.
edu=EDL=projects=pde=JP10web.xls>. His study shows that the vapor
pressure of JP-10 is low at room temperature. They have studied the
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decomposition of JP-10 through thermal and catalytic cracking mechan-
isms at elevated temperature. They also reported the feasibility of burn-
ing premixed JP-10 air mixtures at high equivalence ratios (Cooper and
Shepherd, 2002) and have estimated the laminar burning speed of stoi-
chiometric JP-10 air mixture at 100 kpa and 398 K to be almost
64 cm=sec (Cooper and Shepherd, 2002).
The laminar burning speed is a fundamental property of homogen-
ous fuel=oxygen=diluent gas mixtures. It is of basic importance both
for developing and testing chemical kinetic models of hydrocarbon oxi-
dation for a wide range of practical applications including engines, bur-
ners, explosions, and chemical processors. Currently there is no data on
burning speed of JP-10 for the range of pressure and temperature
encountered in practical combustors.
A number of different methods have been used to experimentally
determine the laminar burning speed. They can be characterized as being
either constant pressure (Iijima and Takeno, 1986; Egolfopoulos and
Law, 1990; Vosen, 1990) or constant volume methods (Metghalchi and
Keck, 1980, 1982; Shebeko et al., 1995; Daly et al., 2001). The constant
pressure experiments, such as those made using flat flame burners, are
limited to a relatively narrow range of temperatures and are most useful
for obtaining data at atmospheric pressure. The disadvantages of the
constant pressure experiments are that they provide data at only a single
condition in each experiment and they require significant corrections for
conductive heat loss to the burner. Recently there have been efforts to
measure the heat loss to the burner (Bosschaart and de Goey, 2003)
and calculate the adiabatic burning speed, but the measurements could
only be done at low pressures and room temperature. The constant vol-
ume methods, such as combustion in a spherical chamber, cover a much
wider range of temperatures and pressures, provide a range of data along
an isentrope in a single experimental run, and require very little correc-
tion for heat loss or other effects. Metghalchi and co-workers (Elia
et al., 2001; Rahim et al., 2002; Kahraman et al., 2003; Parsinejad and
Metghalchi, 2003) have used the spherical combustion chamber method
for the determination of laminar burning speeds for a relatively wide
range of fuels, equivalence ratios, diluent concentrations, pressures and
temperatures.
Over the past several years a number of experimental (Hunter et al.,
1994; Davis et al., 1998) and theoretical (Warnatz, 1984; Habik et al.,
1999) studies have been done on the measurement of laminar burning
JP-10-AIR MIXTURE CHARACTERISTICS 977
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speed for various fuel=oxidizer=diluent mixtures over a range of equival-
ence ratios. However, these measurements and theoretical studies have
been performed only at low pressure and high temperature (Hunter
et al., 1994; Davis et al., 1998) or at low temperature and high pressure
(Warnatz, 1984; Habik et al., 1999). There are many practical applica-
tions that run at high pressures and temperatures; hence there is a need
to measure burning speed experimentally over a range of temperatures
and pressures.
This paper reports measurements of the burning speed of JP-10 air
mixtures over wide range of equivalence ratios (0.7–1), temperatures
(450–700 K) and pressures (1–55 atm). The measured burning speed data
have been fitted to a power law relation.
EXPERIMENTAL SETUP
Burning speed measurements were made in the existing spherical com-
bustion chamber. The spherical chamber consists of two hemispheric
heads bolted together to make a 15.24 cm inner diameter sphere. The
chamber was designed to withstand pressures up to 425 atm and is fitted
with ports for spark electrodes, diagnostic probes, and ports for filling
and evacuating it. A thermocouple inserted through one of the chamber
ports was used to measure the initial temperature of the gas inside the
chamber. A Kistler 603B1 piezo-electric pressure transducer with a
Kistler 5010B charge amplifier was used to obtain dynamic pressure
vs. time records from which the burning speed was determined. Ioniza-
tion probes mounted flush with the wall located at the top and bottom of
the chambers were used to measure the arrival time of the flame at the
wall and to check for spherical symmetry and buoyant rise.
The spherical vessel is housed in an oven which can be heated up to
500 K. Liquid fuel is stored in a 115 cc heated pressure vessel and is
transferred through a heated line inside the oven to the spherical cham-
ber. Several thermocouples are located on the line from the fuel reservoir
to the vessel to monitor temperature of the fuel passageway. A heated
strain gauge (Kulite XTE-190) in the oven is used to measure partial
pressure of fuel in the vessel. Figure 1 is a drawing of the spherical vessel
and the locations of three ionization probes, pressure transducer and
thermocouple are shown in this figure.
The companion cylindrical chamber is made of SAE4140 steel with
an inner diameter and length of 133.35 mm. The two end windows are
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34.93 mm thick Pyrex with a high durability against pressure and tem-
perature shocks as well as having very good optical properties. This
chamber was designed to operate over the same temperature range as
the spherical chamber. However, since there is one window at each
end cap of the chamber, the maximum allowable pressure in the vessel
cannot exceed 50 atm. This vessel is equipped with access ports similar
to those in the spherical vessel. The primary purpose of this facility is
to permit optical observation of the flame shape and structure under
conditions as close as possible to those in the spherical chamber and
to insure the initial development of the flame and pressure rise are ident-
ical in both chambers.
Two band heaters and a rope heater wrapped around the cylindrical
vessel are used to heat up the vessel to 500 K. This chamber is equipped
with a heated liquid fuel line system, a pressure strain gauge and thermo-
couples similar to the spherical vessel. Figure 2 is a drawing of the
Figure 1. Spherical combustion vessel.
JP-10-AIR MIXTURE CHARACTERISTICS 979
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cylindrical chamber with heating system. Figure 3 shows the liquid fuel
heating and injecting system.
A Z-type Schlieren=Shadowgraph (Kahraman et al., 2003; Parsinejad
and Metghalchi, 2003) ensemble has been set up to visualize the flame
propagation. A high speed CCD camera (1108-0014, Redlake Inc.)
with a capture rate of up to 8000 frames per second is placed very
close to the focal point of the second mirror. The capture rate and
shutter speed of the camera were optimized depending on the burning
speed of the mixture and the brightness of the flame.
The light source for the optical system is a 10-Watt Halogen lamp
with a condensing lens and a small pinhole of 0.3 mm in diameter, which
provides a sharp and intense illumination throughout the whole system.
Two aluminized spherical mirrors with 1=8 wavelength surface accuracy,
over-coated with silicon monoxide and mounted in metal-stands with a
diameter of 152.4 mm and focal length of 1524 mm, are placed on two
sides of the chamber.
Figure 2. Cylindrical combustion vessel and heating system.
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The gas handling system used with these facilities consists of a vac-
uum pump for evacuating the system and a valve manifold connected to
gas cylinders for preparation of the fuel=oxidizer=diluent mixtures.
Partial pressures of the fuel mixtures were measured using Kulite strain
gauge pressure transducers in the 0–15 atm range. Two spark plugs with
extended electrodes were used to ignite the mixture at the desired
location in the chambers. An electronic ignition system controlled by
the data acquisition program provides a spark with the necessary energy.
The data acquisition program synchronizes the ignition with the dynamic
pressure recording and Shadowgraph photography.
The data acquisition system consists of a Data Translations 16 bit
data acquisition card, which records the pressure change of the combus-
tion event at a rate of 250 kHz. The analog to digital converter card
receives the pressure signal from the charge amplifier and the signals
from the ionization probes. All signals are recorded by a personal com-
puter and an output data file is automatically generated. The output data
files include the dynamic pressure and its corresponding time. The initial
data file contains information about the partial pressures and initial
Figure 3. Liquid fuel evaporation system.
JP-10-AIR MIXTURE CHARACTERISTICS 981
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temperature of all the fuel, oxygen and diluent. An oscilloscope is used to
monitor the ignition signal and the outputs of the ionization probes and
the pressure transducer to insure that the various sensors are working
and that the system has fired properly.
The test procedure begins by evacuating the vessel and gas handling
system using the vacuum pump. The chamber then is filled with JP-10
vapor to the desired pressure and air is added. The vessel and the fuel
tank are at the same temperature during the filling. After the chamber
is filled with the proper mixture, several minutes are allowed for the
system to become quiescent before it is ignited. This will prevent any
turbulence inside the vessel. Six thermocouples on the liquid line are
used to make sure that temperature along the filling line is never below
the condensation temperature for JP-10. At least three runs at each
initial condition are made to provide a good statistical sample. Based
on statistical analysis, it was found that three runs are sufficient to
achieve a 95% confidence level (Rahim, 2002).
THEORETICAL MODEL
The theoretical model used to calculate the burning speed from the press-
ure rise is based on one previously developed by Metghalchi and co-work-
ers (Metghalchi and Keck, 1982; Rahim et al., 2002) and has been
modified to include corrections for heat losses to electrodes and radiation
from the burned gas to the wall as well as including the temperature gradi-
ent in the preheat zone. It is assumed that gases in the combustion cham-
ber can be divided into burned and unburned regions separated by a
reaction layer of zero thickness as shown schematically in Figure 4. The
burned gas in the center of chamber is divided into n number of shells
where the number of shells used is proportional to the combustion dur-
ation. Burned gases temperatures in shells are different from each other
and they are in chemical equilibrium in each shell at their corresponding
temperatures. The burned gas is surrounded by the unburned gas in pre-
heat zone (dph) with variable temperature. Core unburned gas with uni-
form temperature surrounds the preheat zone gases. A boundary layer
(dbl) separates core unburned gas from vessel wall. It is further assumed
that: the burned and unburned gases are ideal, the unburned gas compo-
sition is frozen, the pressure throughout the chamber is uniform, com-
pression of both burned and unburned gases is isentropic, and the heat
flux due to the temperature gradient in the burned gas is negligible. For
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the conditions of interest in the present work, all these assumptions have
been validated by numerous experiments in constant volume chambers
and internal combustion engines carried out over the past several decades.
Burned Gas Mass Fraction and Temperature
For spherical flames, the temperature distribution of the gases in
the combustion chamber and the burned gas mass fraction can be
Figure 4. Three different regions of gases in the combustion chamber.
JP-10-AIR MIXTURE CHARACTERISTICS 983
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determined from the measured pressure using the equations for conser-
vation of volume and energy together with the ideal gas equation of state
pv ¼ RT ð1Þ
where p is the pressure, v is the specific volume, R is the specific gas con-
stant and T is the temperature.
The mass conservation equation is
m ¼ mb þmu ¼ qbVb þ quVu ¼piðVc � VeÞ
RTi
ð2Þ
where m is the mass of gas in the combustion chamber, mb is the burned
gas mass, mu is the unburned gas mass, Vc is the volume of the combustion
chamber, Ve is the electrode volume, and the subscript i denotes initial
conditions. Subscripts b and u represent burned and unburned conditions
respectively. q is average density and V is the volume of the gas.
The total volume of the gas in the combustion chamber is
Vi ¼ Vc � Ve ¼ Vb þ Vu ð3Þ
where
Vb ¼Z mb
0
v0ðT 0; pÞdm0 ¼Z mb
0
v0bsðT 0; pÞdm0 � Veb ð4Þ
is the volume of the burned gas, vbs is the specific volume of isentropically
compressed burned gas,
Veb ¼Z
eb
ðv0bs � v0Þdm0 ð5Þ
is the displacement volume of the electrode boundary layers,
Vu ¼Z m
mb
v0ðT 0; pÞdm0 ¼ mð1� xbÞvus � Vwb � Vph ð6Þ
is the volume of the unburned gas, xb ¼ mb=m is the burned gas mass frac-
tion, vub is the specific volume of isentropically compressed unburned gas,
Vwb ¼Z
wb
ðvus � v0Þdm0 ð7Þ
is the displacement volume of the wall boundary layer,
Vph ¼Z
ph
ðvus � v0Þdm0 ð8Þ
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is the displacement volume of the preheat zone ahead of the reaction
layer.
The energy conservation equation is
Ei � Qe � Qw � Qr ¼ Eb þ Eu ð9Þ
where Ei is the initial energy of the unburned gas, Qw is the conduction
heat loss to the wall, Qe is the conduction heat loss to the electrodes, Qr is
the heat loss due to radiation from the burned gas,
Eb ¼Z mb
0
e0ðT 0; pÞdm0 ¼Z mb
0
e0bsðT 0; pÞdm0 � Eeb ð10Þ
is the energy of the burned gas, ebs is the specific energy of isentropically
compressed burned gas,
Eeb ¼Z
eb
ðe0bs � e0Þdm0 ð11Þ
is the energy defect of the electrode boundary layer,
Eu ¼Z m
mb
e0ðT 0; pÞdm0 ¼ mð1� xbÞeus � ðEwb þ EphÞ ð12Þ
is the energy of the unburned gas, eus is the specific energy of isentropi-
cally compressed unburned gas,
Ewb ¼Z
wb
ðeus � e0Þdm0 ð13Þ
is the energy defect of the wall boundary,
Eph ¼Z
ph
ðeus � e0Þdm0 ð14Þ
is the energy defect of the preheat layer.
Using the perfect gas relation
e � hf ¼pv
c� 1ð15Þ
where hf is the enthalpy of formation of the gas at 0 Kelvin and c ¼ cp=cv
is the specific heat ratio, and assuming constant specific heats for the
gases in the boundary layers and the preheat zone, the integrals in
JP-10-AIR MIXTURE CHARACTERISTICS 985
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Eqs. (11), (13), and (14) may be evaluated approximately to give
Eeb ¼ p
Zeb
ðvbs � v0Þdm0
cb � 1¼ pVeb
cb � 1ð16Þ
Ewb ¼ p
Zwb
ðvus � v0Þdm0
cu � 1¼ pVwb
cu � 1ð17Þ
Eph ¼ p
Zph
ðvus � v0Þdm0
cu � 1¼ pVph
cu � 1ð18Þ
A relationship between the wall heat transfer and the displacement
volume for a gas subject to a time dependent pressure has been derived
by Keck (1981). In the case of rapidly increasing pressure such as that
occurring during constant volume combustion, the terms representing
compression work on the boundary layer may be neglected and resulting
equations are
Qe ¼pVeb
cb � 1¼ Eeb ð19Þ
Qw ¼pVwb
cu � 1¼ Ewb ð20Þ
in which we have used Eqs. (16) and (17). Note that, to this approxi-
mation, the heat loss to the wall exactly equals the energy defect in the
boundary layer.
Substituting the relation dm ¼ qdV into Eqs. (5), (7), and (8) we
obtain
Veb ¼ 2prerb deb ð21Þ
Vwb ¼ 4pr2c dwb ð22Þ
Vph ¼ 4pr2b dph ð23Þ
where re is the radius of the electrodes, rb is the radius of the burned gas,
rc is the radius of the combustion chamber,
deb ¼Z rb
0
Z 10
�qðr; gÞqbs � 1
�dg dr
rb
ð24Þ
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is the displacement thickness of the electrode boundary layer in which gis the radial distance from the electrode,
dwb ¼Z
wb
�qðr; gÞqus � 1
�dr ð25Þ
is the displacement thickness of the wall boundary layer, and
dph ¼Z
ph
�qðr; gÞqus � 1
�dr ð26Þ
is the displacement thickness of the preheat zone. Using the approxi-
mation
Z 10
�qðr; gÞqus � 1
�dg ¼
�Tb
Tw � 1
��abðrb � rÞ
_rrb
�1=2
ð27Þ
Equation (24) can be integrated over r to give
deb �2
3
�abrb
_rrb
�1=2�Tb
Tw � 1
�ð28Þ
where ab is the thermal diffusivity of the burned gas, Tw is the wall
temperature, and Tb is the burned gas temperature.
The wall boundary layer displacement thickness can be calculated
using the expression derived by Keck (1981)
dwb ¼ausp
� �1=2
z�1c
Z z
0
ðz0 � z01c Þ�Z z
z0z00dz00
��12
dy0 ð29Þ
where au is the thermal diffusivity of the unburned gas, s is a character-
istic burning time, y ¼ t=s is the dimensionless time, and z ¼ p=pi is the
dimensionless pressure.
The displacement thickness of the preheat zone has been evaluated
assuming an exponential temperature profile
qus
qðrÞ � 1þ�
Tb
Tu
� 1
�e�auðr�rbÞ= _rrb ð30Þ
Substituting Eq. (30) into Eq. (26) we obtain
dph ¼ �Z
Tb
Tu
� 1
� ��1
eauðr�rbÞ= _rrb þ 1
!�1r
rb
� �2
dr ð31Þ
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r >> au= _rrb, Eq. (31) can be integrated approximately to give
dph � �au
_rrb
� �Tb
Tu
� 1
� �ln
Tb
Tu
� �ð32Þ
Note that the displacement thickness of the preheat zone is negative
while those of the thermal boundary layers are positive.
The radiation heat loss from the burned gas was calculated using
Qr ¼Z t
0
_QQrðt0Þdt0 ¼ 4apVbrT 4b ð33Þ
where ap is the Planck mean absorption coefficient and r is the Stefan—
Boltzmann constant (Tien, 1968; Egolfopoulos, 1994; Samaniego et al.,
1995; Siegel and Howell, 2002).
Finally combining Eqs. (3), (4), and (6) gives
Z xb
0
ðvbsðT 0; pÞ � vusÞdx0 ¼ vi � vus þðVeb þ Vwb þ VphÞ
mð34Þ
and combining Eqs. (9), (10), (12) and (18)–(20) gives
Z xb
0
ðebsðT 0; pÞ � eusÞdx0 ¼ ei � eus þðpVph=ðcu � 1Þ � QrÞ
mð35Þ
where vi ¼ (Vc�Ve)=m and ei ¼ Ei=m are the initial specific volume and
energy of the unburned gas in the chamber. Eqs. (34) and (35) contain
the three unknowns p(t), xb(t), and Tb(t). Given pressure, p(t), as a func-
tion of time, they can be solved numerically using the method of shells to
obtain the burned mass fraction, xb(t), as a function of time and the
radial temperature distribution T(r,t). The mass burning rate, _mmb ¼ m _xxb
can be obtained by numerical differentiation of xb(t) (Rahim et al.,
2002). The thermodynamic properties of the burned and unburned
used in the calculations were obtained from the JANAF Tables and
STANAJAN code (JANAF, 1986; Reynolds, 1986).
Burning Speed, Flame Speed and Gas Speed
Burning speed may be defined
Sb ¼_mmb
quAb
¼ m _xx
quAb
ð36Þ
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where Ab is the area of a sphere having a volume equal to that of the
burned gas. This expression is valid for smooth, cracked, or wrinkled
flames of any shape. For smooth spherical flames
_mmb ¼d
dtðqbVbÞ¼ qbAb _rr þ Vb _qqb ð37Þ
where qb is the average value of the burned gas density. Differentiating
the mass balance equation
mb ¼ m� quVu ¼�
qu
qb
�qbðVc � Ve � VbÞ ð38Þ
with respect to time and neglecting the small contribution from the
derivative of qu=qb, we obtain
_mmb ¼�
qu
qb
�ððVc � Ve � VbÞ _qqb � qbAb _rrbÞ ð39Þ
where
Ab ¼ 4pr2b � 2pr2
e ð40Þ
is area of the reaction zone, re is the electrode radius and rb is given by the
equation
Vb ¼�
4
3
�pr3
b � 2pr2e rb ð41Þ
Using Eq. (37) to eliminate _qqb in Eq. (39), gives
Sf ¼ _rrb ¼ Sb qu=qb � yb
qu
qb � 1
� �� �ð42Þ
where Sf is the flame speed and yb ¼ Vb=ðVc � VeÞ is the burned gas vol-
ume fraction and, note that for yb ¼ 0;Sf ¼ ðqu=qbÞSb and for yb ¼ 1,
Sf ¼ Sb.
The gas speed is defined by
ug ¼ Sf � Sb ð43Þ
Substituting Eq. (42) into Eq. (43) we obtain
ug ¼ Sb
�qu
qb � 1
�ð1� ybÞ ð44Þ
Another consideration in burning speed measurement is the effect of
flame curvature and stretch rate. Corrections for stretch rate should be
JP-10-AIR MIXTURE CHARACTERISTICS 989
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applied to the burning speed calculation as has been suggested by many
investigators (Sivashinski et al., 1982; Law et al., 1986; Kwon et al., 1992;
Bradley et al., 1998; Kwon et al., 2002). However the curvature and
stretch corrections are most important when flame radius is small and
flame thickness is of a similar order to the flame radius. The effect of
flame thickness is negligible for a flame radius greater than three centi-
meters. This condition will be achieved by the time that pressure begins
to rise, which is the starting point for our calculations. Hence this correc-
tion diminishes as the flame grows and gets thinner. Flame front thick-
ness can be calculated using the Rallis and Garforth (1980) relation
df ¼4:6k
qucpSb
ð45Þ
where k is the average thermal conductivity of the species, qu is the
density of unburned gas, and cp is the average specific heat of the species.
To calculate the average thermal conductivity, k the thermal conduc-
tivity of each species is required. Thermal conductivity of each species is
calculated using the Lennard-Jones parameters a and e=k, and using rela-
tions by Hirschefelder et al. (1967). It is important to note that having
the ratio of 25 and higher for the ratio of flame radius to flame thickness
minimizes stretch effects on burning speed. Figure 5 shows the normal-
ized flame radius with respect to flame thickness as a function of normal-
ized flame radius with respect to chamber radius for a stoichiometric
mixture of JP-10 with air and at initial temperature and pressure of
450 K and 1 atm. It can be observed that for normalized radii larger than
0.5 (flame radius of 3.8 cm) when the pressure rise starts, this ratio is lar-
ger than 25 and it increases as the flame radius increases; consequently
the stretch corrections are small and negligible. All of our measurements
have been made for normalized flame radii larger than 0.5.
Minimum ignition energy of 52 mJ was introduced to the premixed
mixture from the centered spark plugs. The effect of ignition energy
through spark discharge has been studied by Bradley and Harper
(1994). They pointed out that the influence of spark energy on burning
speed rapidly decreases with increasing of the flame radius and fully
diminishes at radii larger than 5–6 mm. Spherical vessel and pressure
method were our sole means of burning speed measurements in this
study. Since all measurements in spherical vessel start after the pressure
rise in the vessel which happens at radii larger than 3.8 cm and minimum
ignition energy was applied, the effect of spark ignition energy does not
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have any contribution in burning speed measurements using pressure
method.
EXPERIMENTAL RESULTS
Mixtures of JP-10 and air of equivalence ratios between 0.7–1 have been
burned at initial temperature of 450 K and initial pressures of 1–10 atm.
Final temperature and pressure can reach 700 K and 55 atm respectively
depending on the initial conditions and mixture equivalence ratio. Press-
ure time data, the primary output from the experiments, for the case of
stoichiometric JP-10=air at Pi ¼ 1 atm and Ti ¼ 450 K measured in
spherical vessel is shown in Figure 6. Ionization probe signals are also
shown in the figure, which help us to learn the arrival time of the flame
to vessel wall. As can be seen, ionization probes signals are very close to
peak pressure and there is no sign of buoyancy effect. Figure 7 shows
flame pictures of stoichiometric JP-10 air mixture at initial temperature
of 450 K. The frame rate of the CCD camera has been set on 1000 frames
per second. The camera can capture images of the entire chamber. These
Figure 5. Ratio of flame radius to flame thickness vs. normalized flame radius for stoichio-
metric JP-10=air mixture at initial pressure and temperature of 1 atm and 450 K.
JP-10-AIR MIXTURE CHARACTERISTICS 991
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pictures are shown here to report our observation of flame propagation
in a constant volume vessel. Discussion about instabilities on the flame
and auto-turbulization is beyond the scope of this study. Law and
co-workers (Kwon et al., 2002; Jomaas et al., 2005) and Bradley and
co-workers (1996) have investigated the parameters that are important
in instability analysis.
One of the important parameters for the outwardly expanding flames
is the Karlovitz number, which is the non-dimensional stretch rate and is
defined as Ka ¼ ð2=RÞðdR=dtÞ=ðSb=df Þ, where t is time and R is the flame
radius. Bechtold and Matalon (1987) demonstrated the effect of stretch
on the instability of the outwardly expanding flames and concluded that
positive stretch tends to stabilize flames. Flame thickness also has strong
influence on the hydrodynamic stability. The thinner the flame, the
weaker is the influence of curvature and consequently the stronger is
the destabilizing propensity (Kwon et al., 2002). The time, normalized
pressure (with respect to initial pressure) and Karlovitz number are given
for each snapshot. Note that except for the early stages (t < 5–6 ms)
Figure 6. Pressure time history for stoichiometric JP-10=air at initial pressure and tempera-
ture of 1 atm and 450 K in spherical vessel.
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Figure 7. Shadowgraph pictures of stoichiometric JP-10=air at 1, 2 and 5 atm initial
pressures.
JP-10-AIR MIXTURE CHARACTERISTICS 993
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pressure and temperature increase as flame expands and consequently
flame thickness and flame front speed are not constant through the whole
process. Pressure is measured using the Kistler 603B1 piezo-electric
pressure transducer and corresponding temperature can be calculated
using the ideal gas law relation ðTu=T0Þ ¼ ðP=P0Þ1�1=c.
Figure 7a (Left column) shows the snapshots of JP-10 air flame with
initial pressure of 1 atm. It can be observed that the flame is smooth from
the beginning of ignition till it hits the wall after 30 ms with no evidence
of wrinkles or cracks on the surface. The final pressure in the last snap-
shot is 5 atm and the corresponding unburned gas temperature is 650 K.
Flame thickness at this time is about 0.04 mm. Figure 7b shows flame
propagation for initial pressure of 2 atm. Few small cracks form on the
flames surface probably as a consequence of disturbance caused by spark
plug discharge and their sizes grow but no evidence of cell emerging on
the flame surface exist till the end of the process (t ¼ 35 ms). This com-
bustion process produced a final pressure and temperature of 11 atm and
675 K, respectively. At this point flame thickness is about 0.015 mm. The
initial pressure is 5 atm in Figure 7c. A few large cracks form at early
stages (t ¼ 6 ms) where pressure is almost constant. These cracks grow
as flame expands and around the Ka ¼ 0.037 and pressure ratio of
2.13 small cells emerge on the flame surface. Flame thickness is about
0.0015 mm at this point.
The measured burning speed data from spherical vessel (pressure
method) have been fitted to the following power law relation
Sb ¼ Sb0ð1þ a1ð1� /Þ þ a2ð1� /Þ2Þ Tu
Tu0
� �aP
P0
� �b
ð47Þ
where Sb0 is the burning speed at reference point (P0 ¼ 1 atm,
Tu0 ¼ 450 K and / ¼ 1) in cm=s, / is the mixture equivalence ratio, Tu
is the unburned gas temperature in K, Tu0 is the reference temperature
and is equal to 450 K, P is the mixture pressure in atm and P0 is the ref-
erence pressure and is equal to 1 atm. a1, a2, a and b are constant. Using
a least squares method, the values for these constants and their RMS
fluctuations have been calculated as following
S0b � DS0
b a1 � Da1 a2 � Da2 a� Da b� Db
62� 1:52 �1:51� 0:05 �0:89� 0:02 2:02� 0:13 �0:16� 0:01
994 F. PARSINEJAD ET AL.
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The above correlation is valid for the range of 0:7 < / < 1; 450 K <
T < 700 K and 1atm < P < 55atm. The correlation and the constants for
power of pressure ratio and temperature ratio clearly show that the burn-
ing speed of JP-10 is directly proportion to temperature and inversely
proportion to pressure.
The power law fit results have been plotted in Figures 8, 9 and 10. In
these figures the symbols are experimental data and the continuous curve
is the fitted curve. Figure 8 illustrates laminar burning speed measure-
ment of stoichiometric JP-10 air at initial pressure of 1 atm and initial
temperature of 450 K for equivalence ratios of 0.8–1. There was no
ignition at / ¼ 0:7. Note that the burning speed has been plotted along
the isentrope, i.e., pressure is increasing based on the relation on the
upper left corner of the figure.
In Figure 9, the burning speed of JP-10 air mixtures for equivalence
ratios of 0.7–1 with initial pressure and temperature of 5 atm and 450 K
respectively have been plotted along the isentropes. The effect of initial
pressure on burning speed is shown in Figure 10. It can be seen that the
Figure 8. Laminar burning speed for JP-10=air at 1 atm and 450 K initial pressure and
temperature.
JP-10-AIR MIXTURE CHARACTERISTICS 995
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Figure 9. Burning speed for JP-10=air at initial pressure and temperature of 5 atm
and 450 K.
Figure 10. Burning speed of stoichiometric JP-10=air at initial temperature of 450 K.
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burning speed has an inverse relation to the initial pressure of the
unburned mixture.
As mentioned earlier the effects of heat loss through radiation and
losses to electrodes have been added to the previous burning model. It
was noticed that the effect of radiation for the whole range of equival-
ence ratio on the measured burning speed is not significant (less than
1%). The contribution of spark effect and losses to electrodes are also
negligible at the window of our measurements which spans from the time
flame radius is more than 3 cm.
SUMMARY AND CONCLUSION
Using two constant volume chambers, measurements of the burning
speed of JP10-air mixtures have been made over a range of conditions.
These conditions include higher temperatures and pressures than have
ever been previously used in such experiments. Flame structure has also
been observed, using the cylindrical vessel which can be useful to learn
about the onset of instabilities on flame. A comprehensive thermodyn-
amic model has been developed that incorporates correction for heat
losses to electrodes and radiation loss to previous models and is incor-
porated with the pressure measurements in spherical vessel. The effects
of radiative heat transfer on the burning speed of JP-10 for the range of
the equivalence ratio of 0.7–1 was shown to be negligible.
A power law correlation for the burning speed of JP-10 air mixtures
in the range of 0:7 < / < 1; 450 K < T < 700 K and 1atm < P < 55 atm
was developed using a least square method. This correlation shows that
burning speed of JP-10 has an inverse relation with pressure but is
directly proportional to temperature.
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