flame structure and burning speed of jp-10 air mixtures

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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

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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

975

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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

976 F. PARSINEJAD ET AL.

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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.


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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.


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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.


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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


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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


�dr ð26Þ

is the displacement thickness of the preheat zone. Using the approxi-

mation

Z 10


�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


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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.


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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.


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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


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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.


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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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flame structure and burning speed of jp-10 air mixtures

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