Research Article
Measurements of the laminar burning
velocity for propane: Air mixtures
Advances in Mechanical Engineering
2016, Vol. 8(6) 1–17
Ó The Author(s) 2016
DOI: 10.1177/1687814016648826
aime.sagepub.com
Munzer SY Ebaid and Kutiaba JM Al-Khishali
Abstract
In this research, an experimental setup was built based on using K-type thermocouples inserted in a cylindrical vessel
and coupled with a computer system to enable online reading of flame speed for propane-air mixtures. The work undertaken here has come up with data for laminar burning velocity of the propane-air mixtures based on three initial temperatures Tu = 300, 325 and 350 K, three initial pressures pu = 0.5, 1.0 and 1.5 bar over a range of equivalence ratios f
between 0.6 and 1.5. The results obtained gave a reasonable agreement with experimental data reported in the literature. Results showed that laminar burning velocity increases at low initial pressures and decreases at high pressures,
while the opposite occurs incase of temperatures. The maximum values of the laminar burning velocity occur at
T = 350 K, pu = 0.5 and f = 1.0, respectively, while the minimum values of the laminar burning velocity occur at T = 300 K,
pu = 1.5 and f = 1.2. Also, the influence of flame stretching on laminar burning velocity was investigated and it was found
that stretch effect is weak since Lewis number was below unity for all cases considered. Based on experimental results,
an empirical equation has been derived to calculate the laminar burning velocity. The values of the laminar burning velocity calculated from this equation show great compatibility with the published results. Therefore, the derived empirical
equation can be used to calculate the burning velocities of any gas of paraffin gas fuels in the range of mixture temperature and pressure considered.
Keywords
Propane-air mixture, burning velocity, equivalence ratio, initial pressure, initial temperature
Date received: 19 November 2015; accepted: 15 April 2016
Academic Editor: Jiin-Yuh Jang
Introduction
Boilers, heat engines and industrial plants are systems
that mainly involve rapid oxidation and generate heat.
This research is restricted to this part of combustion.
The study of laminar and turbulent flame propagation
is important to the analysis of the confined flame (i.e.
when the combustion process takes place in a limited
size) and unconfined flame which may occur when the
combustion process takes place in an open vessel or in
an unlimited size.1
Laminar burning velocities play an important role in
combustion applications such as in designing burners,
predicting explosions and the combustion in spark ignition engines. Properties such as heat release rates,
flammability limits, propagation rates, quenching and
emissions characteristics are associated entirely with
laminar premixed flames. Therefore, the production of
accurate measurements of laminar premixed flames
plays a key role in the process of understanding a large
range of flames.2 A laminar burning velocity is of
importance in validating chemical reaction mechanism
and in modelling of turbulent combustion and design
Philadelphia University, Amman, Jordan
Corresponding author:
Munzer SY Ebaid, Philadelphia University, P.O. Box 950674, Amman
11195, Jordan.
Email: [email protected]
Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License
(http://www.creativecommons.org/licenses/by/3.0/) which permits any use, reproduction and distribution of the work without
further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/
open-access-at-sage).
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Advances in Mechanical Engineering
of combustion devices. Also, in internal combustion
engines, initial combustion is laminar. Therefore, there
is a need for the laminar burning velocity. There are
several methods that have been used for measuring the
laminar burning velocity. These methods may be classified into two categories as follows:
1. Class 1: the stationary flame.
In this method, a stream of premixed gas flows into a
stationary flame with a velocity equal to burning velocity.3 Several methods that come under this classification were carried out by many researchers. Such as
Bunsen burner and flat flame burner methods,4,5 slot
burner method,6,7 and the nozzle burning method.8,9
2. Class 2: the non-stationary flame.
In this method, the flame moves through the initially
quiescent mixture.3 The methods classified under class
(2) are tube method,10,11 constant volume bomb
method which was applied by many researchers12–14
and finally soap-bubble method which was applied by
Lewis and Von Elbe.15
Previous studies
Burning velocity is a physical constant for a given combustible mixture. It is the velocity relative to the
unburned gas, with which a plane, one-dimensional
flame front travels along the normal to its surface as
reported by Andrews and Bradley.16 The reaction zone
is often called the flame zone, flame front or reaction
wave. Within the flame zone, rapid reactions take place
and light is usually (but not always) emitted from the
flame.17 The measurement of flame speed needs a special technique for detecting the flame front arrival along
a certain space. Therefore, many investigators worked
hard to find out different techniques for measuring
flame speed and burning velocity. These techniques for
flame speed are as follows: optical technique,1,2 thermocouple technique,10,11 visual technique18 and ionized
probe technique.19,20 For measuring burning velocity,
the techniques used are as follows: density ratio
method,21 pressure measurement,20 double kernel
method,14 hot wire technique22 and counter flow
method.23,24
Several parameters have an effect on burning velocity for combustible mixture. These parameters are as
follows: mixture ratio, adding additives, pressure, temperature, thermal diffusivity and specific heat, and
nitrogen dilution. Turns25 studied the effect of mixture
ratio on the burning velocity for hydrocarbon fuels and
found that the peak of the burning velocity occurs at
slightly rich mixture and fall off on either side. Also, he
concluded that very lean and very rich mixtures fail
to support a propagated flame because there is too little fuel or oxidant to maintain a steady deflagration
wave. Thus, there exist upper and lower flammability
limits. The effect of additives on combustible mixture
was investigated by Odger et al.10 whom their measurements have been made for propane-oxygen mixtures diluted with nitrogen, carbon dioxide, helium or
Argon. Metghalchi and Keck26 studied the effect of
adding simulated combustion products to stoichiometric iso-octane-air mixtures for diluent mass fraction. Yu et al.27 and Refael and Sher28 studied the
effect of adding a small amount of hydrogen to
methane and propane-air mixtures. They found that
adding a small amount of hydrogen supplement to a
hydrocarbon fuel might produce a very lean combustible mixture.
The effect of pressure on the burning velocity for
combustible mixture was investigated by many
researchers, among these, Lewis and Von Elbe.15 They
studied the effect of pressure on the burning velocity of
various hydrocarbon-air mixtures. They developed a
power law (Su } Pn ), where the exponent (n) is referred
to as the Lewis pressure index. He observed that when
Su \50 cm=s, the exponent (n) is usually negative,
implying that Su increases with decreasing pressure, for
50\Su \100 cm=s, and when Su .100 cm=s, Su
increases with increasing pressure. In addition,
Andrews and Bradley29 developed a relation
Su (cm=s) = 43 (Patm )0:5 for methane-air flames at
equivalence ratio equal to 1.0. Further work on the
pressure dependence of burning velocity was investigated by Iijima and Takeno20 and Egolfopoulos et al.23
and they showed the variation of burning velocity as a
function of equivalence ratio and pressure. They concluded that the burning velocity decreases with the
increase in pressure. Their work agreed well with the
work carried out by Saeed and Stone13 and Andrews
and Bradley.30
The initial temperature dependence on burning velocity was investigated by different researchers13,20,31,32
using tube method and constant volume vessel. They
showed that burning velocity of hydrocarbon-air mixtures increases with the initial mixture temperature and
is mainly due to the preheating effect which increases
the heat release rate as a result of increasing the initial
enthalpies of reacting materials. Over the temperature
ranges studied, it was shown that the burning velocity
could be linearly correlated to the initial fuel mixture.
Also, the maximum burning velocity is a function of the
final flame temperature (Tb ) and the dependency is very
strong for most mixtures.
K Kuo17 carried out a set of experiments to study
the effect of thermal diffusivity and reaction rates on
burning velocity. He measured the flame propagation
Ebaid and Al-Khishali
speed of methane in various oxygen-inert gas mixtures
where the volume rate of the oxygen to inert gas is
(0.21:0.79). The inert gases used were helium (He) and
argon (Ar). He suggested that the thermal diffusivity
and burning velocity of the mixture increase. However,
thermal diffusivity may have a negative effect in which
burning velocity decreases. Also, he found that the
lower the specific heat of the inert gases, the higher the
flame temperature and burning velocity of the mixture.
It has been well established for laminar flames that
their burning velocity is reduced by straining the velocity field. Tsuji and Yamaoka33 investigated the rich
and lean extinction of methane and propane-air mixtures in counter flow, twin flames. They attributed the
laminar flame stretch extinction to the outflow of heat
by conduction from the reaction zone towards the
unburnt mixture, outweighing the inflow of the deficient reactant by diffusion from the unburnt gas into
the reaction zone. This was a Lewis number effect.
Daneshyar and Mondes-Lopes34 showed that the laminar burning velocity decreased as the rate of flame
stretching increased. However, stretch may affect the
burning velocity in the other way as well. In a later
paper, Daneshyar et al.35 showed that the decrease in
laminar burning velocity was more pronounced with an
increased Lewis number. Research work by
Buckmaster and Mikolaitis36 and Durbin37 has
employed the mathematical technique of activation
energy asymptotic to examine theoretically the reduction of laminar burning velocity that occurs at high
straining rate of the gas. Results showed that the Lewis
number, associated with either fuel diffusion in a weak
mixture or oxygen diffusion in a rich mixture can be
considered a significant factor, as well as the activation
energy associated with the laminar burning velocity. In
his work, Tromans38 reported that if the Lewis number
for the limiting reactants is close to unity, the strain
field increases the temperature and concentration gradient; the heat source and reactant sink cannot support
these, and the burning velocity falls. It also falls if the
Lewis number is greater than unity, for then the relatively greater transport of energy from the flame
reduces its temperature.
Studies on flame thickness were carried out by
Andrews and Bradley.29 They measured the flame thickness using Schlieren photograph and obtained results
contain large differences relative to the total theoretical
results. Kanury39 assumed a relation between flame
thickness and burning velocity as d = l=(r Cp Su ),
whilesome researches 25,40 assumed a relation between
flame
thickness
and
burning
velocity
as
d = ((2l)=r Cp Su ) whereby Gulder41 used this relation in iso-octane mixture and alcohol with air. It is clear
from these relations that flame thickness is inversely
3
proportional to the burning velocity and depends basically on temperature distribution through flame front.
The effect of nitrogen dilution of propane-air mixtures on laminar burning characteristics has been studied by many researchers. Zhao et al.42 studied
experimentally the nitrogen addition and found linear
relationship between the laminar flame speed and the
dilution ratio. Similar work by Tang et al.43 showed
that laminar burning velocity decreases dramatically
with dilution ratio for equivalence ratios smaller than
1.4, indicating that nitrogen addition decreases preferential diffusion instability. Further work by Tang
et al.44 on nitrogen diluted propane-air premixed
flames at elevated pressures and temperatures has
shown that normalized laminar burning velocities have
linear correlation with nitrogen dilution. Also, hydrodynamic instability increases with the increase in initial
pressure and decreases with the increase in nitrogen
dilution ratio. Also, they found that laminar burning
velocities are increased with the increase in initial
temperature.
Akram et al.45 studied the effect of dilution using
CO2 and N2 gases (up to 40%) on C3H8-air burning
velocity. The peak burning velocity was observed for
slightly rich mixtures even at higher mixture temperatures and the minimum value of the temperature
exponent is observed for slightly rich mixtures. Also,
the burning velocity was observed to decrease with
the dilution of inert gases. The addition of CO2 shows
a pronounced decrease in the burning velocity, as
compared to N2. Akram and Kumar46 carried out an
experimental work to measure laminar burning velocity of liquefied petroleum gas (LPG)-air mixtures at
high temperatures. It was found that an increase in
mixture temperature significantly enhances the burning velocity. Maximum burning velocity is obtained
for slightly rich mixtures, unlike for the highly rich
mixtures reported in the literature. A minimum value
of the temperature exponent is observed for slightly
rich mixtures. Liao et al.47 studied the effects of dilute
gas on burning velocities at the equivalence ratios
from 0.7 to 1.2 for natural gas-air mixtures, and an
explicit formula of laminar burning velocities for
dilute mixtures was formulated. Further work on natural gas-air mixtures was carried out experimentally
by Kishore et al.48 over a range of equivalence ratios
at atmospheric pressure. Also, the effect of CO2 dilution up to 60%, N2 dilution up to 40% and 25%
enrichment of ethane on burning velocity of methaneair flames were studied. The experimental results were
in good agreement with the published data in the literature. Also, it was found that maximum burning
velocity for CH4/CO2-air mixtures occur near to
u = 1:0. Tuncer et al.49 studied the hydrogen-enriched
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Advances in Mechanical Engineering
confined methane combustion in a laboratory scale
premixed combustor. Results showed that the combustor can be operated under very lean conditions
with low flame temperature and thus favourably
impact thermal emissions under lower lean blowout.
Also, at higher hydrogen concentrations, flashback is
observed and appears to trigger a shift in the pressure
oscillation mode to lower frequencies. In addition, it
was seen that hydrogen enrichment shifts the flame
centre of mass more towards the dump plane as the
burning velocity is increased with hydrogen addition.
It is shown that there is a close link between the pressure cycle, the periodic flashback behaviour and the
NO emission.
Jomaas et al.’s50 experimental work on propane-air
mixture at one atmospheric pressure showed good
agreement with the work in the literature. Huzayin
et al.51 work on propane-air mixtures over wide ranges
of equivalence ratio (F = 0.7–2.2) and initial temperature (Ti = 295–400 K) and pressure (Pi = 50–400 kPa)
showed that the maximum laminar burning velocity
found for propane is nearly 455 mm/s at F = 1.1 and
the maximum explosion index, commonly called the
‘explosion severity parameter’, is calculated from the
determined laminar burning velocity and is found to be
93 bar m/s for propane.
Most burning velocity measurements for a closed
vessel have been found to be valid only in the initial
stages of combustion (generally taken as 1:1 pi ). In
this research, the laminar burning velocity has been
found for propane-air mixtures for which the laminar
burning velocity has been measured at a lower pressure
than the atmospheric pressure (vacuum pressure).
Three initial temperatures at Tu equal to 300, 325 and
350 K, three initial pressures at pu equal to 0.5, 1.0 and
1.5 bar and equivalence ratios f ranges from 0.8 to 1.2
were used in the experimental work. The burning velocities for these mixtures were calculated by measuring
the laminar flame speed in the pre-pressure period of
combustion, and employing the density ratio method
using thermocouple technique.
Fortran was written to carry out theoretical calculations.
In the programme, the equations of flame thickness correction factor (I), flame thickness (d) and the flame burning velocity (Su ) were solved.
The general equation for flame burning velocity
(Su) by Andrews and Bradley29 is given in equation
(1) whereby the flame speed Sf is related to burning
velocity during the pre-pressure period and can be
found experimentally. The other parameters of equation (1); i.e. mole ratio N and flame thickness correction factor I can be derived and calculated as follows.
Su = (Sf )(N )
Tu
(I)
Tb
ð1Þ
Flame thickness correction factor (I)
The flame thickness correction factor I27 can be written
as follows
2
14
I = 3 (rb d)3 + 3Tb
rb
r=
ð rb
r = rb r
3
2
r
dr5
Tr
ð2Þ
It should be noted here that I makes an allowance for
the temperature difference between temperature Tu to
Tb . To evaluate I, Tb must be known. It is reasonable to
consider that in the flame front zone, the temperature
profile is linear between Tu and Tad as reported by Daly
et al.3 and Andrews and Bradley,29 then the temperature at any radius r is given as follows
Tr =
r(Tu Tad ) + Tu (r rb ) + rb Tad
d
ð3Þ
We assume that Tb ’ Tad , then equation (3) becomes
r(Tu Tb ) + Tu (r rb ) + rb Tb
d
rTu
(r rb )(Tu Tb )
+
=
d
d
Tr =
ð4Þ
And the part integral of equation (2) can be evaluated as follows
ðrb
rb d
3 h
i2 T T T 2 h
i
r2
d
rb
d2
rb
b
u
b
(Tu Tb ) Tu + (Tu Tb ) ð5Þ
dr =
rb x Tb + (Tu Tb ) ln Tu Tb Tr
d
Tu
d
2
d
Equation (5) could be approximated and yields into
Theoretical analysis
29
Andrews and Bradley have derived a formula for burning velocity of propane-air mixtures from flame speed
measurements in explosions by density ratio method that
takes into account the temperature distribution through
the flame front. In this work, a computer program in
ðrb
rb d
T b r2
rb2 d
ln dr =
Tr
(Tu Tb ) Tu
ð6Þ
Substituting equation (6) into equation (2) resulted
into
Ebaid and Al-Khishali
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Tb 1
rb2 d
3
ln I = 3 (rb d) + 3
(Tb Tu ) Tu
rb
ð7Þ
For a stoichiometric mixture flame, equation (7)
gives a value for a correction factor I that is 4% below
the value obtained from the graphical integration of the
measured profile obtained by Andrews and Bradley.30
To take the discrepancy of 4% into account, the inclusion of a factor into equation (7) gives the value of I as
1:04
3Tb rb2 d Tb 3
ln
I = 3 (rb d) +
(Tb Tu ) Tu rb
ð8Þ
The burning velocities reported in this work are
based on rb = 2:5 cm, because the cut-off pressure rise
corresponding to this radius is very small and in most
cases of interest its effect on the burning velocity is negligible as reported by Gulder.41
Flame thickness (d)
A relation between flame thickness and burning velocity is reported by many researchers25,40 as follows
d=
2l
ru Cp Su
ð9Þ
where l is the thermal conductivity of the product which
is computed using equation (10a)–(10c) given by Perry52
X
l=
yi li
10:4
li = mi Cpi +
Mi
ð10aÞ
ð10bÞ
4:61Tr0:618 2:04e0:449:Tr + 1:94e4:058:Tr + 0:1
,
ei
Tad
ð10cÞ
Tr =
Tc
yi =
The values of molar mass of the product components
Mi and critical temperature Tc can be found from tables.
The other terms of equation (9), ru (the unburned gas
density) and Cp (the specific heat capacity at constant
pressure) can be computed as follows
ru = (yair )(rair ) + (yfuel )(rfuel )
X
yi Cpi
Cp =
ð10dÞ
Cpi = a + bT + cT 2 + dT 3
ð10fÞ
(9) based on the written computer program to find the
required burning velocity.
Experimental setup
The study of flame propagation subject needs technically modern systems because of the short period available for measurements, which is not longer than few
milliseconds, and this constitutes a big problem in
studying such a subject. In this research, a modern technique was used to measure flame front speed, which is
considered one of the advanced techniques that determine the flame front location using sets of K-type,
0.5 mm diameter thermocouples. The designed system
benefits from the high speed of the computer processer
that is connected to the cylinder through a hardware
and software interface (computer control system) to
enable online reading of flame speed. By doing so time
and effort to acquire the required data. The experimental setup facility consists mainly of the following units:
the combustion chamber, mixture preparing unit, control system with the ignition unit and finally the flame
speed measuring unit as shown in Figure 1. A brief
description of the main experimental facility components is given hereafter.
Combustion chamber unit
The combustion chamber unit is a cylindrical test vessel
of 300 mm external diameter, 305 mm external length
and 10 mm thickness. It is made of solid iron as shown
in Figure 2. The cylinder is provided with central ignition electrodes. The cylinder is designed and constructed in a way that makes it easy to study the
combustion of different types of gases at different initial conditions.
The ignition of the spark is performed by an electronic system away from the cylinder and behind the
room’s wall. The six thermocouples are placed radially
inside the cylinder, in which the angle between thermocouples T1 and T2 is 45°; thermocouples T3 and T4 is
90° and thermocouples T5 and T6 is 45°. However, their
positions with respect to the centre of the vessel are
shown in Figure 3.
Mixture preparation unit
ð10eÞ
where
where a, b, c and d are constants for each gas of combustion gases that can be found from tables. After computing the parameters l, ru , Cp using equation (10a)–
(10d), this leads to the solutions of equations (8) and
To prepare the mixture (fuel-air), a gas mixer has been
designed and constructed for hydrocarbon compounds
that have a low partial pressure such as methane, propane, LPG and butane. The main purpose of preparing
the fuel-air mixture in the mixing unit rather than in the
cylinder is to increase the total pressure of the mixture
and consequently to increase the partial pressure of
hydrocarbon fuel in order to increase the accuracy. The
mixer is made of iron-steel in a cylindrical shape
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Advances in Mechanical Engineering
Figure 1. Schematic diagram of the experimental facility setup.
without any skirt to improve the efficiency of mixing
operation. Mixer dimensions are 453 mm length,
270 mm diameter and 5 mm thickness as shown in
Figure 4. It undergoes a pressure of more than 60 bar
and withstands high temperatures.
Computer control system
Figure 2. Combustion chamber unit.
The computer control system is designed and used to
read flame speed propagation inside the cylinder by
means of six k-type thermocouples. Three of them represent start signals S1 , S2 , S3 and the other three represent stop end signals E1 , E2 , E3 as shown in Figure 5.
Their positions with respect to the ignition circuit (I:C)
as shown in Figure 5 are as follows: I:C S1 is 2 cm,
Figure 3. Schematic diagram of cylindrical vessel with six thermocouples.
Ebaid and Al-Khishali
7
Figure 6. Block diagram of interfacing circuit.
Figure 4. Schematic diagram of the mixture preparing unit.
relation to other parameters in the chamber. The circuit
consists of a DC power which is produced by a transformer and this transformer is connected to AC power
line (220 VAC). The transformer output is 24 V and the
peak DC voltage produced is around 30VDC. This
transformer charges a capacitor of 470 mF. Timing and
control circuit are designed to produce all signals controlling the timing periods and time delays between
events in the whole process from the start of ignition till
the transfer of data to the computer.
Experimental procedure
Preparation of the mixture
Figure 5. Schematic diagram of the internal structure of
cylindrical test vessel with the six thermocouples inserted in the
pre-pressure period.
I:C E1 is 7 cm, I:C S2 is 2:5 cm, I:C E2 is 7 cm,
I:C S3 is 1:5 cm and I:C E3 is 6:25 cm.
These thermocouples are connected to a computer in
order to collect, process and display the data obtained
from the thermocouples. Since the electrical voltage signals produced by the thermocouples are very low, and
because of very short time of heating due to high speed
computer interfacing port circuit. A non-inverting
amplifier circuit was designed and built around high
precision operational amplifier which has a gain equation. A computer program (control system software) is
used to process the data collected. A demonstration for
the hardware and software of the control system is
shown in Figure 6.
The process of mixture preparation is performed based
on partial pressure of mixture components (propaneair mixture). According to Gibbs-Dalton law, an accurate equivalence ratio can be obtained, which has an
effect on flame speed. The preparation of the mixture is
done inside the mixer unit. Since the partial pressure of
hydrocarbons propane is low, this method is used to
increase the partial pressure of the hydrocarbon
propane.
Sensors check
Since these sensors are very sensitive, it is very important to check the sensor function. The front end of these
sensors may be affected by the high temperature inside
the cylinder, so it is very important to check these sensors to see whether they are functioning correctly or
not, and to check whether a double flame grows spherically. A procedure is added to the interface software to
check whether these sensors function correctly and free
from any deficiency.
Ignition circuit
Calibration
In order to produce a spark between the two sparking
electrodes, an electronic circuit is used to furnish the
power needed by the sparking coil and to have the ability of precious timing of the spark start and end in
To ensure that all data read from the measuring devices
and sensors are correct, a calibration procedure is done
to all measuring devices and sensors. This includes the
interface circuit, thermocouples and pressure gauges.
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Advances in Mechanical Engineering
Flame speed measurements
The proposed technique simply involves the use of six
thermocouples. One of the effective factors of flame
speed is the initial temperature. The propane-air mixture initial temperature can be achieved and maintained
using a heating system and a digital thermometer. After
preparing and admitting the mixture to the cylinder at
a pre-pressure period that has been chosen according to
the value set by Andrews and Bradley,29 sensing thermocouples have been inserted in this area (an area
within the pre-pressure period). Such that when the
flame front moves across the first sensor, an electrical
signal is produced, and transferred to the interface electronic circuit where it is amplified and then it is sent to
the parallel port of the computer. This signal activates
the interface software saved in the computer memory
and takes it as a start signal, S1 . When the flame grows
and moves across the end signal, another signal is
transferred through the interface which identifies it as
an end signal, E1 . The programme will calculate the
time between start and end signal. This process is
repeated for the other start sensors, S2 , S3 and end sensors, E2 , E3 . The flame kernel is produced and the flame
front grows and moves through the unburned mixture
at a certain speed. This speed is referred to as the flame
speed.
Uncertainty analysis
In this study, experiments were conducted at least four
times for each condition, and the averaged values were
used in the analysis. This procedure was used to ensure
the repeatability of the results within the experimental
uncertainty (95% confidence level). The accuracy of
the thermocouple is 1 K, and the variation in initial
temperature is 300 6 2 K. Thus, the relative error in
initial temperature is 0.566%. Mixtures are prepared
according to the partial pressure of the constituents.
Uncertainties in the pressure measurements of the fuel
vapour and air are less than 0.1%. For each condition,
six tests were conducted to minimize random errors in
the experimentally determined flame speeds. The average value was reported along with 95% confidence
intervals from these experiments for each condition.
Experimental results and discussion
In this section, the experimental results for laminar
flame propagation are discussed. Experimentally, the
spark was fired centrally and the growth of the flame
kernel was measured using thermocouples with the aid
of a computer. Flame propagation is monitored during
the pre-pressure period, and experimental measurements were recorded for both laminar flame speed Sf
and flame temperature at different initial pressures and
temperatures for propane-air mixtures.
Figure 7. Comparison of the propane-air mixture burning
velocity Su at 300 K, and 1 bar with the reported work in
literature.
Validation of thermocouple technique
Figure 7 shows the comparison of the laminar burning
velocities for propane-air mixture at Tu = 300 K and
pu = 1 bar obtained from this work with the reported
mathematical models in the open literature. It shows a
very good agreement with the data of Hani53 and a very
small difference in the data obtained by Hamid.54
Discrepancy appears when the results are compared
with the work done by Yu et al.,27, Esam,55 Zhou and
Gamer56 and Arkan57 The maximum burning velocity
obtained from this study is (Su = 35:1 cm=s) at
(u = 1:0). It is observed from Figure 7, that the burning velocity increases as the mixtures shifts from the
lean limit towards the stoichiometric and then decreases
as it approaches the rich limits. This could be attributed
to the effect of the temperature behaviour at different
equivalence ratios. The quantity of fuel on the weak
side is increased with an increment that depends on
equivalence ratio together with the availability of oxygen quantity to burn the fuel as a complete combustion
process. Then the heat releases of combustion will
increase which gives rise to the flame temperature and
this will increase the burning velocity. The maximum
velocity occurs for slightly rich mixture (i.e. when
equivalence ratio is greater than 1.1). This means that
the quantity of the fuel in mixture is more than the
quantity of oxygen available to burn the fuel completely. This results in the introduction of the products
CO, CO2 and unburned hydrocarbons. Therefore, heat
releases from combustion tend to decrease. As a results
of that, flame temperature and burning velocity
decrease as well.
Ebaid and Al-Khishali
9
agreement with the different literatures; however, the
experimental values of this work give lower values than
those in the literature. This may be caused by the
slower flame propagation at fuel rich mixture conditions and the correspondingly larger downstream heat
loss. Furthermore, good agreement of the experimental
data with the work carried out by Jomaas et al.50 for
propane gas mixture at atmospheric pressure, and at
initial temperature of 350 K.
Effect of pressure (pu ) on burning velocity (Su ) at
fixed equivalence ratio (u) at different initial
temperatures (Tu ) for propane-air mixture
Figure 8. Comparison of the experimental data for propaneair mixture burning velocity Su at 300 K, 1 bar with work
reported by Dugger (367 K) and Tang et al. (370 K).
Figure 8(a) shows a comparison of the experimental
data for propane-air mixture burning velocity Su at 300
K, and 1 bar with previous work in the literature.26,42,58–61 Also, similar comparisons with the
reported literature27,44,51,59,62,63 are shown in Figure
8(b) and (c), respectively. All figures show good
Pressure is one of the most important parameter considered in this work, because it affects the laminar
burning velocity. Figure 9(a)–(c) shows the variation of
pressure (pu ) on burning velocity (Su ) at different values
of equivalent ratios 0.8, 1.0 and 1.2 (i.e. lean, stoichmetric and rich mixtures) and for different initial temperatures Tu = 300, 325 and 350 K. It can be seen
from Figure 9(a)–(c) that the trends of variation of
laminar burning velocity with pressure are similar at
different initial temperatures. Also, it appears that the
relationship between Su and pu is non-linear and inversely proportional. It could be concluded that the
increase in initial pressure has a significant effect inversely upon the laminar burning velocity of propane-air
mixture. Furthermore, for the highest fixed unburned
gas temperature of Tu = 350 K, it gives the highest
burning velocity values for all equivalence ratios and
pressures. Consequently, it can be deduced that the
maximum burning velocity occurs at the highest value
of Tu = 350 K, minimum value of pu and at stoichiometric mixture f = 1:0 as shown in Figure 9(b).
Meanwhile, the minimum burning velocity occurs at
minimum Tu = 300 K, maximum pu and at stoichiometric f = 1:2 as shown in Figure 9(c). This could be
explained as follows: when the pressure increases, the
intensity of the temperature sensitive, two-body,
branching reaction H + O2 ! OH + O is approximately fixed due to the insensitivity of adiabatic, while
the three-body, temperature insensitive, inhibiting reaction: H + O2 + M ! HO2 + M is enhanced, and a
retarding effect is therefore imposed on the overall
progress of the reaction with increasing temperature.44
Effect of initial temperature (Tu ) on burning velocity
(Su ) at fixed pressure (pu ) at different equivalence
ratios (f) for propane-air mixture
Figure 10(a)–(c) shows shows the variation of initial
temperatures (Tu ) on burning velocity (Su ) at different
values of equivalent ratios 0.8, 1.0 and 1.2 (i.e. lean,
10
Advances in Mechanical Engineering
Figure 9. (a) Effect of the pressure pu on burning velocity Su at f = 0:8 for different initial temperatures Tu = 300, 325 and 350 K;
(b) effect of pressure pu on burning velocity Su at f = 1:0 for different initial temperatures Tu = 300, 325 and 350 K and (c) effect of
pressure pu on burning velocity Su at f = 1:2 for different initial temperatures Tu = 300, 325 and 350 K.
stoichmetric and rich mixtures) and for different pressure
pu = 0.5, 1.0 and 1.5 bar. It can be seen from Figure
10(a)–(c) that the trends are all the same, and that burning
velocity increases with any increase in temperature for all
equivalence ratios under consideration at a given initial
pressure pu . Also, the relationship appears to be linear.
This can be attributed to the preheating effect which
increases the heat release rate as a result of increasing the
initial enthalpies of reacting materials. Furthermore,
Figure 8(c) shows that the highest burning velocity values
for all pressures of unburned gases and temperatures are
found at fixed equivalence ratio of stoichiometric f = 1:0.
It can be deduced that the maximum burning velocity
occurs at maximum Tu = 350 K, minimum pu and at stoichiometric f = 1:0, respectively, as shown in Figure
10(a), and the minimum burning velocity occurs at minimum Tu = 300 K, maximum pu and at f = 0:8, as shown
in Figure 10(c). The reason could be attributed to the fact
that the increase in the initial temperature of the unburned
gases increases the adiabatic temperature, which influences
the reaction rate, and the dependence becomes more sensitive at higher initial temperature because of the Arrhenius
factor.
Effect of the equivalence ratio (f) on burning
velocity (Su ) at fixed initial pressures (pu ) at different
initial temperatures (Tu ) for propane-air mixture
Figure 11(a)–(c) shows the effect of equivalent ratio on
burning velocity Su at different values of pressure pu =
0.5, 1.0 and 1.5 bar and for different initial propane-air
mixtures temperatures at Tu = 300, 325, 350 K.
Figure 11(a)–(c) shows similar trends regarding the
effect of equivalence ratio on burning velocity over the
range between 0.6 and 1.5. Also, they show that the
maximum burning velocity occurs for slightly rich mixtures (i.e. at stoichiometric mixture f = 1.1 on either
side), and it decreases at the lean and rich limits.
Furthermore, it can be observed that the highest burning velocity values ocuurs at temperature Tu = 350 K
for all values of equivalence ratios and pressures. It
should be noted here that the highest maximum burning velocity occurs at f = 1.1, Tu = 350 K and pu =
0.5, respectively, as shown in Figure 11(a) and the minimum burning velocity occurs at Tu = 300 K, pu = 1.5
and f = 1.5, as shown in Figure 11(c). Furthermore, it
can be seen from Figure 11(a)–(c) that the laminar
Ebaid and Al-Khishali
Figure 10. (a) Effect of the temperature Tu on burning velocity
Su at fixed pressure pu = 0:5 bar for different values of
equivalence ratios, f = 0:8, 1:0 and 1:2. (b) Effect of the
temperature Tu on burning velocity Su at fixed pressure
pu = 1:0 bar for different values of equivalence ratios,
f = 0:8, 1:0 and 1:2. (c) Effect of the temperature Tu on
burning velocity Su at fixed pressure pu = 1:5 bar for different
values of equivalence ratios, f = 0:8, 1:0 and 1:2.
burning velocity decreases with pressure and the effect
is most noticeable at pressure equal to 1.5 bar.
Effect of Lewis number (Le) on burning velocity (Su )
Non-uniform diffusion is caused by unequal thermal
and mass diffusivities of the deficient reactants. This
effect can be qualitatively represented by Lewis number. Lewis number is the ratio of the thermal to mass
diffusivity. It is an important parameter in any discussion on flame stretch. Lewis number combined with
preferential diffusion (ratio of mass diffusivity of the
deficient reactant to excess reactant) is used to represent
the non-equilibrium effects on flames.64 Lewis number,
Le, or ‘Lewis–Semenov’ number65 is given by
11
Figure 11. (a) Effect of the equivalence ratio f on burning
velocity Su at fixed pressure pu = 0.5 bar for different initial
temperatures Tu = 300, 325, 350 K. (b) Effect of the equivalence
ratio f on burning velocity Su at fixed pressure pu = 1.0 bar for
different initial temperatures Tu = 300, 325, 350 K. (c) Effect of
the equivalence ratio f on burning velocity Su at fixed pressure
pu = 0.5 bar for different initial temperatures Tu = 300, 325, 350 K.
Le =
a
k
and a =
D
rCp
ð11Þ
where a is the thermal diffusivity, k is the thermal conductivity of unburned mixture, r is the density of
unburned mixture, Cp is the specific heat capacity of
unburned mixture and D is the binary mass diffusion
coefficient of the deficient at reactant. Values of k and
D were found from Bird et al.,66 and values of r and Cp
were obtained from Baukal.67 Using the aforementioned values and equation (13), Lewis number can be
obtained and the results are listed in Table 1.
In this work, Lewis number calculated was less than
unity over the range of equivalence ratios, temperatures
and pressures which means that stretch effect on burning velocity is weak. This range of Le Number would
12
Advances in Mechanical Engineering
Table 1. Effect of equivalence ratio and temperature on Lewis number.
Lewis number (Le)
f
T = 300 K
T = 325 K
T = 350 K
p = 0.5 bar
p = 1.0 bar
p = 1.5 bar
0.8
1.0
1.2
0.715
0.741
0.634
0.755
0.736
0.744
0.760
0.734
0.676
0.685
0.741
0.640
0.702
0.736
0.672
0.721
0.734
0.642
not reduce the laminar burning velocity because
Marzouk68 reported that for a unity Lewis number, mass
and heat diffusion rates are equal, and the reactiondiffusion zone is essentially unaffected over a range of
weak to intermediate strains. Also, Bechtold and
Matalon69 reported that the enrichment of air will result
in the reduction of thermal diffusive coefficient leading to
the reduction of Lewis number and this suggests that the
flame front trends to more stable at lean mixtures. Also,
the experimental measurements were carried out during
the pre-pressure period, and the last thermocouple I.C –
S3 which was used in measuring the flame speed is 1.5 cm
away from the wall. This distance is considered too far
away from the wall and from the stagnation point where
the flame is supposed to be stretched.
Derivation of empirical equation
It was mentioned in the previous section that the laminar burning velocity is affected by many parameters
such as equivalence ratio, initial temperature and initial
pressure. These parameters u, p, Tu will be the independent variables and the laminar burning velocity Su will
be the dependent one. It was shown from the experimental results that the relationship between laminar
velocity and the equivalence ratio, initial temperature
and initial pressure is polynomial for equivalence ratio,
power relation for temperature and inverse power relation for pressure, respectively. The dependence of the
burning velocity on pressure and temperature of
unburnt flammable mixture is commonly given as a
power law equation, with a, the baric coefficient and b,
the thermal coefficient
a
Su = (b)(p) (Tu )
g
ð12aÞ
where Su is the dependent variable; p and Tu are the
independent variables; and b, a and g are constants.
The parameters are evaluated by a curve fitting
method using linear least square method and are
applied using Grapher Software from GoldenSoftware. Figures 12–14 show the flow charts to calculate b, a and g, and the results are given as follows
b = 20:20366 22:45810 f 17:52955 f2 + 20:14641 f3
ð12bÞ
Figure 12. Flow chart for the calculation of constant
parameter (a).
a = A1 + B1 f C1 f2 + D1 f3
A1 = 32:42 + 48:92 Tu 17:85 T22
ð12cÞ
ð12dÞ
B1 = 2:234 33:52 Tu 20:15 Tu2
ð12eÞ
C1 = 23:95 + 39:41 Tu 19:55 Tu2
ð12fÞ
D1 = 56:85 + 119:10 Tu 61:44 Tu2
g = A2 + B2 f + C2 f2
ð12gÞ
ð12hÞ
A2 = 1:00777 0:15397 pu + 1:07558 p2u
ð12iÞ
B2 = 1:51015 0:47336 pu 3:26617 p2u
ð12jÞ
C2 = 0:92645 + 0:19974 pu + 1:89562 p2u
ð12kÞ
The derived empirical equation can be used with an
error about 5.8% and can be calculated as follows:
Eabs = valueExp valueTheo ð13Þ
Ebaid and Al-Khishali
13
Figure 14. Flow chart for the calculation of constant
parameter (b).
Figure 13. Flow chart for the calculation of constant parameter (g).
Error =
abs
E
,
Rmax
"
#
N
1X
Eabs (i)
Eabs = Average absolute error
N i=1
ð14Þ
Rmax = Maximum burning velocity from experimental data
Comparison between the derived empirical equation
with other types of fuels
Figures 15 and 16 show the comparison between the
results of the derived empirical equation using a cylinder with the available published results found in Tseng
et al.,21 Andrews and Bradley,29,30 Hayder70 and Stone
and Khizer71 for methane, propane, LPG, and butaneair mixtures at constant Tu = 300 K and f = 1.0. It can
be observed that the agreement is acceptable and confirms the validity of the derived equation.
Also, Figures 17–20 show the comparison between
the results of the derived empirical equation with results
from the literature at constant values of Tu = 300 K
and pu = 1.0 bar. Again good agreement was found
with the work reported in the literature.
A comparison of the results of the derived equation
with the published work for ethane-air mixture is
shown in Figure 21. It can be observed that they are in
agreement with the reported literature. and confirms
that the derived empirical equation can be applied to
other types of fuel in paraffin family.
Figure 15. Comparison between present work (empirical
equation) for stoichiometric methane-air flames, with selected
values from the literature at different pressures.
Conclusion
A modern measuring system is used whereby thermocouples are inserted in a cylindrical vessel, and a high
speed computer has been employed for the measurement of laminar flame speed for propane-air mixture at
different initial pressures of 0.5, 1.0 and 1.5 bar, and at
different initial temperatures of 300, 325 and 350 K
over a range of equivalence ratio between 0.8 and 1.2 to
14
Advances in Mechanical Engineering
Figure 16. Comparison between present work (empirical
equation) for stoichiometric propane-air flames, with selected
values from the literature at different pressures.
Figure 19. Comparison of empirical equation results with the
published results for LPG-air mixtures.
Figure 17. Comparison of empirical equation results with the
published results for methane-air mixtures.
Figure 20. Comparison of empirical equation results with the
published results for butane-air mixtures.
Figure 18. Comparison of empirical equation results with the
published results for propane-air mixtures.
get the best results. The laminar burning velocity has
been measured at pressure lower than atmospheric pressure (vacuum pressure); while most published works
were measured at a pressure of 1 atm or higher (generally taken as 1.1 pu). The results obtained from the
present work give very good agreement with the work
reported data using other methods.
The laminar burning velocity for propane-air mixture increases linearly with the increase in initial temperature for lean, stoichmetric and rich propane-air
mixture; the trends are different as the laminar burning
velocity appears near stoichiometric mixture f = 1.0.
Also, the laminar burning velocity increases at low
Ebaid and Al-Khishali
Figure 21. Comparison of empirical equation results with the
published results for ethane-air mixtures.
initial pressure and decreases at high pressures, while
the opposite occurs for the temperatures. The maximum value of the laminar burning velocity occurs at
Tu = 350 K, pu = 0.5 and f = 1.0 and minimum value
of the laminar burning velocity occurs at Tu = 300 K,
pu = 1.5 and f = 1.2. The maximum laminar burning
velocity appears near stoichiometric mixture f = 1.1
on either side and decreases at the lean and rich limits
for all values of initial temperatures and pressures. It
was found that Lewis number Le was below unity for
all cases considered. This range of Le number would
not reduce the laminar burning velocity.
Empirical equation has been deduced from the
experimental results that take into consideration the
effects of equivalence ratio, initial pressure and initial
temperature upon the laminar burning velocity. The
values of laminar burning velocity calculated from this
equation show an acceptable agreement with the published work. So this empirical equation can be used to
calculate the burning velocities of any gas of paraffin
family with an estimated error of 6 5.8%.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship and/or publication of this
article.
Funding
The author(s) received no financial support for the research,
authorship and/or publication of this article.
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17
Appendix 1
Notation
Cpi
D
I
Le
Mi
ni
N
pu
r
rb
rb r
Sf
Su
Tad
Tb
Tc
Tr
Tu
yi
a
d
li , k
mi
ru
f
specific heat at constant pressure of
component (kJ/kmol K)
binary mass of the diffusion coefficient
(m2/s)
flame thickness correction factor
Lewis number
molar mass of component (kg/kmol)
number of moles of products
mole ratio
pressure of the unburned gases (bar)
thickness of flame front (mm)
exterior flame front radius (mm)
interior flame front radius (mm)
laminar flame speed (cm/s)
laminar burning velocity (cm/s)
adiabatic temperature (K)
flame temperature (K)
critical temperature (K)
temperature at radius (r)
unburned gas temperature (K)
mole fraction
thermal diffusivity (m2/s)
flame thickness (mm)
thermal conductivity of component (W/
cm K)
dynamic viscosity (N s/m2)
unburned gas density (kmol/m3)
equivalence ratio