ABSTRACT 
 
 
 
 
Title of Thesis: MEASUREMENT OF INVERSE 
DIFFUSION FLAME QUENCHING LIMITS 
  
 Yi Zhang, Master of Science, 2013 
  
Directed By: Associate Professor Peter B. Sunderland 
Department of Fire Protection Engineering 
 
 
Quenching limits of inverse diffusion flames were measured for different conditions. 
The flames were laminar and axisymmetric and were obtained by injecting various 
oxidizers into fuels. Burner inside diameters were 0.75, 1.53, 3.02, 4.56, and 10.1 mm. 
Oxygen mole fractions were 0.21, 0.3, 0.4, and 1, and the balance was nitrogen. Fuels 
were methane, ethylene, and propane. The flames were observed in a weak co-flow of 
fuel inside a glass chimney. The flames were ignited at relatively high oxidizer flow 
rates, after which the oxidizer flow was reduced until extinction. The typical heat 
release rate of quenching inverse flame ranged from 1 ? 2 W, compared to a typical heat 
release rate of quenching normal hydrocarbon flames of 3 W. The quenching limits of 
inverse flames were generally independent of burner diameter, were proportional to the 
fuel quenching distance in premixed flames, and scaled with XO2
 -1.5. The results may 
help assess the hazards of firefighter respirator leaks in underventilated fires. 
  
 
 
 
 
 
 
 
 
 
 
 
MEASUREMENT OF INVERSE DIFFUSION FLAME QUENCHING LIMITS 
 
 
 
By 
 
 
Yi Zhang 
 
 
 
 
 
Thesis submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Master of Science 
2013 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Associate Professor Peter B. Sunderland, Chair 
Professor Emeritus James G. Quintiere 
Assistant Professor Stanislav I. Stoliarov 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
? Copyright by 
Yi Zhang 
2013 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
ii 
Acknowledgements 
 
This work is supported by NIOSH. Without the funding, the work might not be 
possible on the first place and I would not have the chance to get involved in this 
meaningful work that might provide some useful information in the firefighter safety 
applications. 
I would like to thank all the people in the fire protection department. It is their 
warming kindness and helpfulness that make this comfortable environment for the 
daily learning and working. The friendship I found here help me relief the loneliness 
of being away from my family and hometown. The teachers lectured me with great 
patience and encouragement. Most of all, I would like to recognize my advisors, Dr. 
Sunderland and Dr. Quintiere. Dr. Sunderland gave me great help and faith without 
any hesitation when I, as a new foreign student, talked to him at his office for the first 
time. In the progress of this project, he kindly offered invaluable suggestions and 
guidance. Although Dr. Quintiere didn?t get involved directly in this project, I learned 
a lot and gained inspiration from his passion and attitude toward his work and life. I 
am very fortunate to have the chance working with these knowledgeable and nice 
people.  
Last but not least, I would like to thank my parents. They are very supportive to 
my study overseas even though they miss me so hard. No matter how difficult the 
situation I am facing, I know they are always on my back. There is just not enough 
gratitude to them I could express.  
iii 
Contents 
Acknowledgements ............................................................................................................................ ii 
List of Figures ....................................................................................................................................iv 
List of Tables ......................................................................................................................................vi 
List of Symbols ................................................................................................................................ vii 
1. Introduction ................................................................................................................................ 1 
1.1 Background ............................................................................................................................... 1 
1.2 Correlations ............................................................................................................................... 4 
1.3 Objectives.................................................................................................................................. 5 
2. Literature Review ....................................................................................................................... 6 
2.1 Oxygen leak from the firefighter mask..................................................................................... 6 
2.2 Inverse flame ............................................................................................................................. 8 
2.3 Quenching limit ...................................................................................................................... 18 
3. Experimental ............................................................................................................................. 28 
4. Results....................................................................................................................................... 33 
5. Conclusions .............................................................................................................................. 40 
References ......................................................................................................................................... 41 
 
iv 
List of Figures  
Figure 1.1 A demonstration of a methane inverse flame [3] .......................................... 4 
Figure 2.1 Time sequence of velocity vectors [2] .......................................................... 7 
Figure 2.2 Top view of the oxygen leakage from the respirator [2] .............................. 7 
Figure 2.3 Flammability diagram of Propane [2] .......................................................... 8 
Figure 2.4 Comparison of inverse Jet flame with increased oxygen concentration in 1g 
and microgravity [4] ...................................................................................................... 9 
Figure 2.5 Schematic of a co-flow burner [5] .............................................................. 10 
Figure 2.6 Experimental and predicted flame height results depending on the air flow 
rate [5] .......................................................................................................................... 11 
Figure 2.7 Peak PAH, OH and soot PLII contours in the ethylene (top) and methane 
(bottom) inverse flame. [13] ........................................................................................ 12 
Figure 2.8 Schematic of the natural gas inverse flame burner [6] ............................... 14 
Figure 2.9 The sequence of the natural gas inverse flames with increased air flow. [6]
 ...................................................................................................................................... 14 
Figure 2.10 Shaddix?s experimental set up for the inverse flame [15] ........................ 16 
Figure 2.11 Color images of microgravity flames from the burner. (a) Ethylene issuing 
into air (b) diluted ethylene issuing into oxygen (c) air issuing into ethylene (d) 
oxygen issuing into diluted ethylene. [16] ................................................................... 17 
Figure 2.12 Methane flames close to the quenching limits. [8] ................................... 19 
Figure 2.13 Methane quenching velocity as a function of tube diameter [8] .............. 20 
Figure 2.14 Computed OH mass fraction contour near the extinction limit [8] .......... 21 
Figure 2.15 Mass flow rates at quenching and blow off limits with respect to tube 
diameter [10] ................................................................................................................ 22 
Figure 2.16 Different configurations of the round-hole burner [10]............................ 23 
Figure 2.17 The quenching mass flow rates of different burner configurations [10] .. 23 
Figure 2.18 The quenching mass flow rates of different burner orientations [10] ...... 24 
Figure 2.19 Propane flames close to the quenching limits [7] ..................................... 25 
Figure 2.20 Quenching limit as a function of ambient temperature [7]....................... 25 
v 
Figure 2.21 Equivalence ratio near quenching and blow-off with respect to radius [7]
 ...................................................................................................................................... 26 
Figure 2.22 Numerical simulation of the flame close to the quenching limit [8] ........ 27 
Figure 3.1 Schematic for the burner ............................................................................ 28 
Figure 3.2 Pressure vessel ............................................................................................ 29 
Figure 3.3 Flow system ................................................................................................ 30 
Figure 3.4 Colored photo of the experimental set up with the inverse flame at the 
center ............................................................................................................................ 31 
Figure 3.5 Calibration of the rotameter measurements ................................................ 31 
Figure 4.1 Color images of inverse flames close to their quenching limits. ................ 33 
Figure 4.2 Color photos of the flame near quenching limits for all the tests ............... 34 
Figure 4.3 Quenching mass flow rate of oxidizers injecting into CH4, C2H4 and C3H8 
with respect to XO2. ...................................................................................................... 35 
Figure 4.4 Quenching mass flow rate of oxidizers with respect to burner diameters .. 36 
Figure 4.5 Quenching mass flow rate of oxidizers with respect to quenching distances
 ...................................................................................................................................... 37 
Figure 4.6 Heat release rate at the quenching limit with respect to burner diameter. .. 38 
 
vi 
List of Tables 
Table 1 Differences in sooting characteristics between normal and inverse diffusion 
flames [18] ................................................................................................................... 18 
Table 2 Selected properties of methane, ethylene and propane ................................... 38 
Table 3 Quenching limit measurements for all tests .................................................... 39 
 
 
 
vii 
List of Symbols 
a fuel specific constant 
d  burner inner diameter 
c normalized half-width of the 
inner wall 
D0 diffusion coefficient 
HRR heat release rate 
Lf laminar diffusion flame 
length 
Lq premixed flame quenching 
distance 
LFL lower flammability limit 
mfuel fuel mass flow rate 
Pe Peclet number 
Q volumetric flow rate 
r fuel-to-oxygen 
stoichiometric mass fraction 
Re Reynolds number 
S fuel-to-air stoichiometric 
volume ration 
SL laminar burning velocity  
T0 fuel stream temperature 
Tf mean flame temperature 
 
UFL upper flammability limit 
X mole fraction 
Y mass fraction 
Zf
 * normalized flame height 
?n (Pe
 2+4?2n2)1/2 
?hc heat of combustion 
? dynamic viscosity  
Subscripts 
f flame 
F fuel 
O oxidizer 
O2 oxygen 
q at quenching limit 
 
1 
1. Introduction 
 
1.1 Background 
A self-contained breathing apparatus, or SCBA, that recycle exhaled air must 
remove carbon dioxide, but save oxygen and inert gases (nitrogen). Augmenting the 
portion of oxygen in the compressed gas cylinder would allow either extended service 
times with the same size cylinder or lighter weight with a smaller cylinder. It has been 
found that by breathing oxygen-enriched air (e.g., 40% oxygen by volume in nitrogen), 
firefighters can improve their physical performance and increase the operational time 
available from an SCBA [1]. However, many SCBA are used in firefighting or other 
combustible atmospheres. Oxygen-rich air mixtures leaking from the positive-pressure 
facepiece could pose a burn hazard for the wearer during these situations. Thus, oxygen 
enrichment is presently prohibited.  
NIOSH has imposed a long-standing advisement against the use of oxygen-based 
closed-circuit respirators in the presence of high radiant heat or open flames based upon 
concerns of user burn injury from the potential oxygen enriched atmospheres in the 
vicinity of face piece leaks. Flame engulfment testing has been conducted with mixed 
results on closed-circuit respirators at the ETL Laboratories in Cortland, New York 
according to NFPA 1981 standard for open-circuit respirators. It has been revealed in 
these tests that the face piece fit represents the biggest problem for a closed-circuit 
respirator to provide adequate protection against oxygen leaks. 
2 
 A typical closed-circuit respirator provides the user with three stages of oxygen 
supply into the breathing loop. There is: 1) a constant flow rate of air designed to 
accommodate a moderate rate of consumption, 2) a pressure demand flow designed to 
supplement oxygen supplies to users consuming oxygen above the constant rate, and 3) 
an emergency flow rate, designed to compensate for pressure regulator failure. The 
constant oxygen flow rate is usually within a range 1.5 to 2.0 Lpm while pressure 
demand and emergency flows are in the range of 80 to 100 Lpm. Typical steady-state 
maximum oxygen consumptions for people are about 3.5 Lpm or 5.5 Lpm for 
highly-trained individuals. 
 There are only two situations that cause actuation of the pressure demand oxygen 
flow. When a user consumes oxygen at a rate higher than the constant add, the pressure 
demand supplements the oxygen feed with short duration 80-100 Lpm additions. Or, 
should a closed-circuit respirator develop a leak in any portion of the breathing loop, 
escaping oxygen decreases the amount of the constant add available to the user, and 
will initiate pressure demand additions. 
 A computational fluid dynamics (CFD) simulation of oxygen leaks from the face 
piece of an SCBA [2] has shown that, no matter how small the leak, there is for each 
leak a region in which the ratio of oxygen to combustible gas is able to support 
combustion. It would seem, then, that any leak at all could be dangerous. However, it is 
not practically possible to detect oxygen leaks of the smallest magnitude. Realistic 
sensitivity specifications for an oxygen leak detector should be derived from 
information about the threat of combustion from different sized leaks. 
3 
 If the seal between the respirator and face is imperfect, supplied oxygen can leak. 
An oxidizer leak into a hot, rich environment can result in an inverse flame, in this case 
one that could burn the firefighter?s face and damage his or her respirator. It is not 
known how large of a leak would be required to present this type of hazard. 
 Unlike normal flames, where the fuel is surrounded by oxidizer, inverse flames are 
those where oxidizer is surrounded by fuel. Alan [3] presented a demonstration of air in 
methane inverse flame. The apparatus in their experiment, as shown in Figure 1.1, is 
similar to what we have in this study. A glass vessel was filled with methane and the 
flame was ignited on top of the vessel. Then the inner tube flowed with air was lifted 
from the bottom of the vessel and the inverse flame was ignited by the normal flame at 
the top.  
Past work revealed some of the characteristics for inverse diffusion flames [4-6]. 
Quenching limits of normal flames have been reported by many studies [7-9]. However 
no investigation to date has measured the quenching limits of inverse flames.  
4 
 
1.2 Correlations 
A scaling analysis for quenching limit in Butler?s paper [10] is presented here. 
Although the prediction may not work the same way for the inverse flame, it provides 
some guidelines to understand the result of this study. For the round-hole burners, the 
stoichiometric length of the laminar gas jet diffusion flames could be expressed as: 
 / Re 4 / ( )f fuelL d a m a d??= =  (1.1) 
where d is the burner inner diameter, Re is the Reynolds number, a is a fuel specific 
coefficient, fuelm is the fuel mass flow rate and ? is the dynamic viscosity. The standoff 
distance of a diffusion flame could be approximated as 50 % of the quenching distance 
of a premixed flame. The flame would be quenched if its stoichiometric length is less 
than the premixed quenching distance, / 2f qL L< . Inserting this criterion back to 
equation (1.1) yields the following correlation 
 
Figure 1.1 A demonstration of a methane inverse flame [3] 
 
5 
 / (8 )fuel qm L a? ?=  (1.2) 
Based on this correlation, the mass fuel flow rate at the quenching point is independent 
of the fuel port diameter. 
 
1.3 Objectives 
It is proposed here to experimentally characterize the quenching limits of inverse 
flames with application to firefighter safety. Quartz chimneys will surround the 
co-flowing fuel to prevent the formation of secondary flames. Flames will be ignited at 
relatively high oxidizer flow rates and then the oxidizer flow will be reduced to the 
point of extinction. 
 The fuels to be considered will be methane, propane, and ethylene. The oxidizers 
will be O2/N2 mixtures with oxygen mole fractions of 0.21, 0.3, 0.4, and 1. Co-flow 
burners will be used. These burners are brass with ceramic honeycomb and have central 
(oxidizer) ports of 1, 3, and 14 mm and concentric (fuel) ports of 100 mm.  
  
6 
2. Literature Review 
2.1 Oxygen leak from the firefighter mask 
Butler [2] used CFD to model the oxygen leak from a fire fighter masker under 
different scenarios and examined how it would influence the gas flammability around 
the wearer. The cases that were studied in this report consisted of three different 
surrounding fuel concentration, two different oxygen concentrations and two different 
breathing patterns. 
Figure 2.1 shows the sequence of simulated velocity vector in the case of pure 
oxygen leak into pure propane. The exhalation during 1-2 s and 5-6 s induced a flow at 
the rate of about 1 m/s. However the flow region is very narrow and in a short distance 
away from that region, the flow rate reduced to about 0.2 m/s.  
Figure 2.2 depicts the propane concentration near the leak. The red contour is the 
UFL and the LFL is very close to the leak. So anywhere between the contour and the 
leak is the flammable region. 
Figure 2.3 is the flammability diagram of propane. For the pure oxygen, all the 
possible mixtures lie on the side marked by the yellow line, where the lower left corner 
indicates the pure oxygen and top indicates pure propane. As shown in the diagram, the 
LFL for the propane oxygen mixture is 2.1% and UFL is 58%. 
 
7 
 
 
 
Figure 2.1 Time sequence of velocity vectors [2] 
 
 
 
 
Figure 2.2 Top view of the oxygen leakage from the respirator [2] 
 
 
 
8 
In summary, the worst situation is the leakage into a fuel-rich environment. In that case, 
a low flow rate leakage may lead to flammability. An enhanced breathing rate under 
stress would enlarge the flammable region. In the scenario of pure oxygen leaking into 
pure fuel, the flammable region is very small and a non-flammable region is created 
near the leak.  
2.2 Inverse flame 
In 1997, there was a fire accident on Mir space station [11]. The oxygen leaked 
from lithium-perchlorate oxygen generator and induced an inverse flame that 
threatened the lives of six crew members. When a crew member initiated the oxygen 
generator in a canister to increase the oxygen concentration, the canister ruptured and 
 
Figure 2.3 Flammability diagram of Propane [2] 
 
 
 
9 
emitted a 0.5 m flame torch. The reactants were the oxygen jet and the fiber glass and 
iron in the canister case.  
Motivated by the fire safety concerns in microgravity, Sunderland et al. [4] 
investigated the inverse flame in ethane with enhanced oxygen concentration. The 
oxygen concentrations were 21%, 30%, 50% and 100%. The tests were conducted in 
normal gravity and microgravity environment. The burner was a 5.5 mm stainless tube. 
The ambient gas was sealed in a 27 L cylindrical pressure vessel. 
 
Figure 2.4 shows the results for both normal and microgravity inverse flames. They 
found that by enhancing the oxygen concentration, the soot production, soot emission 
and luminosity have been increased. The soot was formed in the fuel side of the flame. 
 
Figure 2.4 Comparison of inverse Jet flame with increased oxygen concentration in 1g and 
microgravity [4] 
 
 
 
10 
Gravity variation had little effect on the flame shape because the convection was much 
more significant.  
Mikofski et al. [5] measured the flame height of air-methane and air-ethylene 
inverse flame for different air velocities. The apparatus they used to generate an inverse 
flame was a co-flow burner with three concentric tubes, as shown in Figure 2.5. The air 
flowed through the central tube. The fuel flowed through an annulus surrounding the 
central tube. Nitrogen was flowed through the second annulus to prevent the secondary 
flame formed between the fuel and air in the ambient.  
  
 
The Roper?s equation [12] for the normal diffusion flame height of the circular port 
burner is expressed as 
 
Figure 2.5 Schematic of a co-flow burner [5] 
 
 
11 
 1 0.670 0/ [4 ln(1 1 / )] ( / )fH Q D S T T?
 ?= +  (2.1) 
In order to apply it for the inverse flame, the following parameters were modified: 
Q is the oxidizer volumetric flow rate rather than the fuel. 
S is the stoichiometric fuel-to-air volume ratio rather than air-to-fuel. 
Using the modified equation, the author predicted the inverse flame height of various 
air flow rate and thus verified the similarity between the flame structure of normal 
diffusion flame and inverse diffusion flame. Figure 2.6 shows the prediction results 
with different flame height coefficients as well as the experimental measurements.  
 
The same co-annular burner was used to study the sooting structure in the 
air-ethylene inverse flame and air-methane inverse flame [13]. Planar laser-induced 
fluorescence of hydroxyl radicals (OH PLIF) and polycyclic aromatic hydrocarbons 
 
Figure 2.6 Experimental and predicted flame height results depending on the air flow rate [5] 
 
12 
(PAH PLIF), planar laser-induced incandescence of soot (soot PLII), and thermocouple 
determined gas temperatures were the diagnosis applied in the study. PAH is the soot 
precursor and OH radicals is the indication of the reaction zone.  
 
Figure 2.7 depicts the contours of the peak PAH, OH and soot PLII in the ethylene 
and methane inverse flame. A series of flow rates were tested to examine its effect on 
the flame sooting structure. The OH layer initiated at the burner is about 2mm in 
thickness which was similar to that for a normal diffusion flame. The PAH originated at 
the fuel side of the top of the burner. The radial distance of PAH and soot contour from 
the central axis increased at the flame region while decreased about the flame. As the 
air flow rate increased, the PAH signals moved further away from the central axis.  
 
Figure 2.7 Peak PAH, OH and soot PLII contours in the ethylene (top) and methane (bottom) inverse 
flame. [13] 
13 
Although the soot PLII signal was not detect in the methane flame, a luminous smoke 
layer could be seen from the color photo.  
Sobiesiak et al. [6] studied the characteristics of natural gas inverse flames using a 
similar co-flow burner. The schematic of this burner is depicted in Figure 2.8. The 
burner had three annular tubes, which delivered air, natural gas and nitrogen. A 
honeycomb section was placed in the nitrogen tube to ensure a uniform flux. They 
changed the fuel to air tube diameter ratio and measured the temperature and flame 
length. Figure 2.9 shows the sequence of increasing the air flow at the central tube. 
Initially a normal diffusion flame was established without the air flow in Figure 2.9A. 
Then the air flow was gradually increased through the sequence form B to D. A light 
blue flame structure was created inside the normal flame. Then the normal diffusion 
flame was opened at the tip and leaded to a flame blow-out. In Figure 2.9D, only the 
inner inverse flame remained. 
14 
 
 
 
Figure 2.8 Schematic of the natural gas inverse flame burner [6]  
 
 
Figure 2.9 The sequence of the natural gas inverse flames with increased air flow. [6] 
 
15 
Shaddix et al.[14] studied steady and pulsed inverse flames set up on a slot burner 
as shown in Figure 2.10. OH and PAH laser induced fluorescence (LIF), soot 
laser-induced incandescence (LII), and soot thermal emission have been measured in 
the lower flame region to study the flame structure and soot formation.  
Soot is formed in the fuel side of a diffusion flame. In the case of an inverse 
diffusion flame, soot is formed outside of the flame sheet at the downstream of the 
convection. Thus it does not experience the high temperature flame sheet and leaves the 
flame unoxidized. Soot collected from the inverse flame is tarlike and has high 
hydrogen content. As far as the chemical composition, they are close to those collected 
from the underventilated normal diffusion flames.  
Blevins et al. [15] found that inverse flames facilitated the collection of soot 
precursors and early soot. They propose the hypothesis that the early soot precursors 
could be collected in the exhausts of the inverse diffusion flame and validate it by post 
analysis of the soot. Their experimental set up is shown in Figure 2.10. 
 
16 
 
Sunderland et al. [16] used inverse spherical flames to distinguish the effects of 
convection direction and stoichiometry on soot formation. Figure 2.11 shows four 
different configuration of the test using a spherical porous burner in 2.2 s drop facility. 
The burner was placed in a pressured vessel with supported fuel delivery system. 
Figure a and b are normal flames. Figure c and d are inverse flames. For the 
stoichiometric mixture fraction Zst=0.064, the flame is yellow and when Zst=0.78 the 
flame is soot free regardless of the convection direction.  
Soot particles were formed in the flame. In flame (a) the convection direction is 
toward the oxidizer where the soot growth is eliminated. In flame (c), which is an 
inverse flame, the convection direction is toward fuels side which enhanced the soot 
growth.  
 
Figure 2.10 Shaddix?s experimental set up for the inverse flame [15]  
 
17 
 
Bhatia et al [17] presented a global chemistry calculation for inverse flames with 
oxygen enhancement [4] using an axisymmetric CFD code. The temperature contour 
they computed qualitatively matched the shape and location of the color changes 
observed in the photographs. They also showed the axial plot for gas velocity and 
temperature. The finding was that the inverse flame is less sensitive with respect to the 
oxygen and gravity variation compare to the normal diffusion flame. 
Kaplan and Kailasanath [18] examined the effects of flow-field configuration on 
soot formation in inverse diffusion flames using direct numerical simulation. The result 
was comparable to the experimental results conducted by others. Table 1 summarized 
the main differences of soot formation in normal and inverse diffusion flames with 
 
Figure 2.11 Color images of microgravity flames from the burner. (a) Ethylene issuing into air (b) 
diluted ethylene issuing into oxygen (c) air issuing into ethylene (d) oxygen issuing into diluted 
ethylene. [16] 
18 
same fuel and air velocities. It shows that the inverse flames produce much less soot 
than the normal diffusion flames. The surface growth rate for inverse flames is also 
smaller because of the unfavorable temperature and stoichiometric conditions along the 
soot path. Inverse flame emits soot due to the fact that surface growth continues after 
oxidation ceases.  
 
2.3 Quenching limit 
Cheng et al. [8] investigated the quenching flow velocity of methane microjet flames. 
The tube diameters range from 186 to 778 ?m. Figure 2.12 shows the flames just above 
the quenching limit.  
 
Table 1 Differences in sooting characteristics between normal and inverse diffusion flames [18]  
 
 
19 
 
The flame shapes and the standoff distances are similar regardless of the tube 
diameter. When the flame is near the quenching limit, the spherical flame is dominated 
by diffusion and the buoyancy is less important at the moment. In addition, the flame 
length is hypothesized to be equal to the quenching distance. The author reviewed a 
series of correlations for jet diffusion lengths. 
The model of Turns [19] that does not include the buoyancy: 
 
,
 3
 8
 f
 f
 F stoic
 Q
 L
 DY?
 =  (2.2) 
where fL  is the flame length, fQ is the volumetric flow rate, D is the mass diffusivity 
and ,F stoicY  is the stoichiometric fuel mass fraction. 
Roper?s equation can be applied whether or not buoyancy is important: 
 
0.67
 4 ln(1 1 / )
 f O
 f
 O f
 Q T
 L
 D S T?
 ? ?
 = ? ?? ?+ ? ?
  (2.3) 
where S is the molar stoichiometric oxidizer-fuel ratio, OD is the mean diffusion 
coefficient, OT is the oxidizer stream temperature where OD is evaluated and fT is the 
flame temperature.  
 
Figure 2.12 Methane flames close to the quenching limits. [8] 
20 
Chung and Law [20] derived an equation that includes both axial streamwise effects 
and preferential diffusion: 
 *0 0 0
 1
 [ (1 ) ] 2(1 ) sin( )exp[( ) / 2] / ( ) 0O O O n fc T Y Y n c Pe Z n? ? ?+ ? + + ? =?  (2.4) 
where c is the normalized half-width of the inner wall, 0OY is the mass fraction of the 
oxidizer in the oxidizer stream, 2 2 2 1/2( 4 )n Pe n? ?= +  and 
*
 fZ  is the normalized flame 
height. 
They analyzed the experimental results based on Roper?s equation [12]. Roper?s 
prediction agrees well with the experimental measurements as shown in Figure 2.13. It 
was also found that the result align with the straight line of Re d? =  const.  
 
The nozzle configuration effect was also studied by conducting the numerical 
simulation for d=186, 324, 529 ?m. A full set of governing equation and skeletal 
 
Figure 2.13 Methane quenching velocity as a function of tube diameter [8] 
21 
chemical mechanisms were calculated. The comparison of these burner diameters with 
different wall thermal conductivities are shown in Figure 2.14.  
 
The variation in quenching distance is within 5 % for the same diameter with 
different materials. However the gap between the bottom of the flame and the tube tip 
decreases for lower conductivity materials.  
Butler et al [10] tested the hydrogen quenching limit on round-hole tube burners with 
different diameter, varying from 0.051 mm to 2.21 mm. Figure 2.15 shows their result 
 
Figure 2.14 Computed OH mass fraction contour near the extinction limit [8] 
     
22 
as well as results from other researchers. The quenching limit does not vary much with 
the diameter of the tube. 
 
They also investigated the effect of burner configuration on the quenching limit of 
hydrogen. The difference occurred for smaller burner diameters due to the different 
heat loss effect. Figure 2.16 illustrates the three different burner configurations: 
pinhole, curved-wall and tube. The quenching mass flow rates for these three burners 
are shown in Figure 2.17. The pin-hole burner loses much of its heat to the ambient so 
it requires higher flow rates to maintain the flame. For the tube burner, the heat obtained 
by the tube largely goes back the fuel flow so the total energy in the system is not 
affected greatly. As for the curved-wall burner, the larger the curvature, the more the 
 
Figure 2.15 Mass flow rates at quenching and blow off limits with respect to tube diameter [10] 
23 
heat is lost from the system. So the 6.4 mm curved-wall burner behaves like the pinhole 
burner while the 1.6 mm curved-wall burner behaves like the tube burner. 
 
 
 
Apart from the measurements of the quenching limits in the horizontal 
configuration, the tests were also conducted in vertical and inverted configurations. The 
result in the Figure 2.18 shows little effect of the orientations on the quenching limit. 
 
Figure 2.16 Different configurations of the round-hole burner [10]  
 
Figure 2.17 The quenching mass flow rates of different burner configurations [10]  
24 
This observation could also be proved by examining the Froude number, which in this 
case is about 0.17-0.39. It indicates that the flame is in the nonbuoyant region where the 
orientation has little effect on the burning behaviors. 
 
Matta et al. [7] showed some results of quenching limits of propane on stainless 
steel hypodermic tubes with diameter ranging from 101 ?m to 838 ?m. The flame shape 
and the quenching distances were also found to be similar as presented in Figure 2.19. 
 
Figure 2.18 The quenching mass flow rates of different burner orientations [10] 
25 
 
The quenching limit?s dependency on the ambient air temperature was also studied. 
As shown in the Figure 2.20, the quenching flow rate of propane at three different sizes 
of tube diameter, 100, 178 and 254 ?m, decreases as the ambient temperature increase 
to 500 ?C. The reasoning for that could be the heat loss is eliminated by preheating the 
ambient. Similar effect goes with the premixed flame. The flammability of premixed 
gas decreases as its temperature increases.  
 
 
          
 
Figure 2.20 Quenching limit as a function of ambient temperature [7]  
26 
A region of premixed flame exists at the base part of a diffusion flame where the 
mixture of air and fuel happens as the fuel passes through the standoff distance. Figure 
2.21 predicts the equivalence ratio along the radial axis at the quenching flow rate. It is 
generated by calculating the laminar flame equations. Compared to the blow-off limit, 
the combustible zone is much wider near the quenching limit leading to the hypothesis 
that it burns as premixed flame near the quenching limit. 
 
However, in Cheng?s paper [8], they presented the result of a careful numerical 
calculation, which generated the contour plot of velocities, temperature and species 
concentrations. The results are depicted in Figure 2.22. It strongly suggested that the 
flame burns as a diffusion flame near the quenching limit. 
 
 
Figure 2.21 Equivalence ratio near quenching and blow-off with respect to radius [7]  
27 
 
 
 
  
 
Figure 2.22 Numerical simulation of the flame close to the quenching limit [8] 
28 
3. Experimental 
Brass co-flow burners were used in the experiment with central oxidizer ports of 
0.75, 1.53, 3.02, 4.56 and 10.1 mm diameter and concentric fuel ports of 100 mm 
diameter. The fuel passage contains screens and 3.0 mm glass beads to provide a 
uniform fuel flow. A ceramic honeycomb section with 1.5 mm cell size is used as the 
final section of the fuel passage. A glass chimney was placed on top of the burner, 
covered with aluminum foil with a 13 mm diameter opening at the center (See Figure 
3.1). The connections of these parts were sealed by O-rings. 
 
 
The oxidizers used in the experiment were O2 mixtures of 21%, 30%, 40% and 
100% mole fraction in nitrogen mixed by partial pressure technique in a pressure vessel 
shown in Figure 3.2. The vessel was first filled with nitrogen and the resulting pressure 
 
Figure 3.1 Schematic for the burner 
Oxidizer
 Inverse 
Flame
 Secondary
 Flame
 Fuel
 Glass 
Chimney
 Al Foil
29 
is recorded. Then the oxygen was filled until the pressure reaches a certain value that 
satisfies the required gas proportion based on the fact that partial pressure is 
proportional to the volume fraction under ideal gas law assumption.  
 
The fuels were methane, ethylene and propane. Both fuel and oxidizer were 
delivered through a pressure regulator and an OMEGA? FL 5000 series rotameter as 
shown in Figure 3.3. 
 
 
Figure 3.2 Pressure vessel 
30 
 
All tests were conducted at normal lab pressure and temperature. The fuel flow rate 
was about 4 mg/s. Its ratio with the oxidizer flow rate was about 5- 10 times greater than 
the stoichiometric ratio. When the chimney was fully filled with fuel, the secondary 
flame was ignited. The inverse flame was then ignited at a relative high oxidizer flow 
rate by a platinum wire of 0.3 mm diameter placed close to the oxidizer port. The 
oxidizer flow rate was gradually decreased until the flame was quenched. The flow rate 
of oxidizer at quenching was recorded. Figure 3.4 shows the flame near the quenching 
limit. The ignition wire was moved to the side. Later these flow rates are calibrated by 
the glass soap bubble meter. The calibration result is shown in Figure 3.5.  
 
Figure 3.3 Flow system 
31 
 
 
 
 
 
Figure 3.4 Colored photo of the experimental set up with the inverse flame at the center 
 
Figure 3.5 Calibration of the rotameter measurements 
0
 0.1
 0.2
 0.3
 0.4
 0.5
 0.6
 0.7
 0.8
 0 50 100 150
 Fl
 ow
  r
 at
 e 
cc
 /s
 Rotameter scale
 100%  Oxygen
 40% Oxygen
 30% Oxygen
 21% Oxygen
32 
Butler [10] reported to use a K type thermocouple positioned above the port to 
detect the hydrogen flame quenching. In our case, the flames were sufficiently 
luminous that quenching could be observed visually. For large diameters, the flame was 
burning in the tube when it reached the quenching limit. In these cases, the flow rate of 
oxidizer was tuned up after the extinction to ensure the flame was indeed quenched.  
The product of the combustion could be condensed on the glass chimney if the 
inverse flame burned long enough. Once this happened, the chimney was opened and 
cleaned to ensure a clear observation of the inverse flame. 
Four to five tests were conducted for each condition to assure the repeatability. The 
estimated uncertainty in the reported quenching flow rates is ?10%.  
 
  
33 
4. Results 
 
Figure 4.1 shows images of three series of flames burning just above the quenching 
limits. The flame height, referring to the distance between the flame tip and the burner, 
varies with diameters, oxygen concentration and the fuel type. In the top series, the 
flame height decreases as the diameter of the port increases. For normal flame, 
however, the flame height is essentially independent of the burner tube diameter. As 
indicated in Figure 4.4, the series with different tube diameters have almost the same 
 
Figure 4.1 Color images of inverse flames close to their quenching limits. 
Methane Propane Ethylene
 3 mm
 1 mm
 10.4XO2=0.3
 3 mm
 1.53 3.02D=0.75 mm
 C3H8
 XO2=0.4
 C2H4
 D=0.75 mm
 XO2=0.21
 D=3.02 mm
34 
flow rate of oxidizer. Given the same mass flow rate, the larger the diameter of the port, 
the smaller the velocity would be. The same reasoning would also explain the two other 
 
Figure 4.2 Color photos of the flame near quenching limits for all the tests 
 
 
D=0.75 mm
 C2H4 XO2=30% C2H4 XO2=40% C2H4 XO2=100% C3H8 XO2=40% C3H8 XO2=100% CH4 XO2=100%
 D=1.5 mm
 C2H4 XO2=21% C2H4 XO2=30% C2H4 XO2=40% C3H8 XO2=30% C3H8 XO2=40% C3H8 XO2=100%
 CH4 XO2=30% CH4 XO2=40% CH4 XO2=100%
 D=3.02 mm
 C2H4 XO2=21% C2H4 XO2=30% C3H8 XO2=21% C3H8 XO2=30% C3H8 XO2=40% CH4 XO2=21%
 CH4 XO2=30% CH4 XO2=40%
 D=4.56 mm
 C3H8 XO2=21% C3H8 XO2=30% CH4 XO2=21% CH4 XO2=30%
 D=10.1 mm
 CH4 XO2=21%
35 
series (center and bottom in Figure 4.1). Since the diameters are the same, flow 
velocities correspond to mass flow rates and the flame height is reflected by the mass 
flow rate. A complete set of the test photos is shown in Figure 4.2.  
Figure 4.3 shows the quenching limits for inverse flames burning in methane, 
ethylene and propane on different burners with respect to XO2. The quenching limits 
generally decrease as XO2 increases. They fitted in a power function with an exponent 
of -1.4 to -1.6. The quenching limits for different fuels show a clear distinction among 
each other.  
 
Figure 4.4 depicts the quenching mass flow rate with respect to the burner diameter. 
The methane/air and propane/air inverse flame quenching limits by Yoshimoto et al 
 
Figure 4.3 Quenching mass flow rate of oxidizers injecting into CH4, C2H4 and C3H8 with respect to 
XO2. The error bars include the results for different burner diameters. 
0.04
 0.4
 0.1 1
 ?
 q
 (m
 g/
 s)
 XO2
 CH4
 C2H4
 C3H8
 Fuel R2Slope
 -1.608
 -1.394
 -1.438
 0.91
 0.96
 0.95
 Methane
 Propane
 Ethylene
36 
[21]. are also plotted. It shows that the mass flow rates at quenching of inverse flames 
do not vary largely with the burner diameter. That is consistent with the quenching 
limits? dependency on burner diameters for the normal flames reported in Butler [10] 
for methane and propane. The line fits represent the mean values for each fuel. The 
mass flow rates were multiplied by XO2
 -1.5 to reduce the oxidizer effect. 
 
Figure 4.5 shows that the quenching limits are proportional to the quenching 
distances of the corresponding fuels (see Table 2). The mass flow rates are again 
multiplied by XO2
 -1.5. In average, the quenching limits for methane are greater than that 
for propane and the quenching limits for propane are greater than that for ethylene.  
 
Figure 4.4 Quenching mass flow rate of oxidizers with respect to burner diameters. The error bars 
include the results for different oxygen concentrations.  
0
 0.05
 0.1
 0.15
 0.2
 0.25
 0.3
 0 2 4 6 8 10 12
 ?
 qX
 O
 21.
 5
 (m
 g/
 s)
 d (mm)
 C2H4
 CH4
 C3H8
 CH4/Air (Yoshimoto)
 C3H8/Air (Yoshimoto)
 Methane
 y = 0.13
 Propane
 y = 0.086
 Ethylene
 y = 0.058
37 
 
 
Matta [7] and Cheng [8] reported the quenching heat release rates for methane and 
propane were about 3 and 2.78 W. In our study, the heat release rates for inverse flames 
at quenching were in the range from 1- 2 W. The result is shown in Figure 4.6.  
The heat release rates presented here are calculated by  
 2q q O cHRR m X r h??= ??  (4.1) 
where r is the stoichiometric fuel to oxygen mass fraction. Since the combustion occurs 
at its quenching limit is close to ideal complete combustion, ?hc used here is taken as 
the thermodynamic value shown in Table 2.  
 
 
 
Figure 4.5 Quenching mass flow rate of oxidizers with respect to quenching distances. The error 
bars include the results for different burner diameters. 
0
 0.02
 0.04
 0.06
 0.08
 0.1
 0.12
 0.14
 0.16
 0.18
 0.2
 1 1.5 2 2.5
 ?
 qX
 O
 21.
 5
 (m
 g/
 s)
 Lq (mm)
 XO2 = 0.21  0.3  0.4  1
 y=0.0558x
 CH4
 C3H8
 C2H4
38 
 
 
 
Table 2 Selected properties of methane, ethylene and propane 
Fuel Lq (mm) SL (cm/s) ? (g/m-s) ?hc(kJ/g) 
CH4 2.03 37.3 1.09E-2 50.1 
C2H4 1.13 58.2 1.00E-2 47.1 
C3H8 1.78 42.9 7.95E-3 46 
Values Lq and SL for methane and propane are from [22], Lq for 
ethylene is from [23], SL for ethylene is from [24], ? is from [25] 
and ?hc is from [26]. 
 
 
 
Figure 4.6 Heat release rate at the quenching limit with respect to burner diameter. The error bars 
include the results for different oxygen concentrations. 
0
 1
 2
 3
 4
 5
 6
 7
 0 5 10 15
 H
 R
 R
  (
 W
 )
 d (mm)
 C2H4
 CH4
 C3H8
 CH4/Air (Yoshimoto)
 C3H8/Air (Yoshimoto)
39 
Ignition is difficult for smaller nozzle diameters. For ethylene in the air, the inverse 
flame could not be ignited for 0.75 mm diameter nozzle. For methane, the inverse flame 
never got ignited on 0.75 mm oxidizer port except for 100% oxygen. For propane, no 
results were gained for 0.75 mm diameter for 21% and 30% oxygen. The detailed 
quenching limit results are listed in Table 3. 
 
Table 3 Quenching limit measurements for all tests 
Quenching limit (mg/s) of oxidizers in ethylene 
D (mm)\XO2 0.21 0.3 0.4 1 
0.75  0.46 0.24 0.068 
1.5 0.58 0.28 0.19  
3.02 0.53 0.33   
4.56 0.61    
 
Quenching limit (mg/s) of oxidizers in methane 
D (mm)\XO2 0.21 0.3 0.4 1 
0.75    0.13 
1.5  0.63 0.30 0.14 
3.02 1.87 0.63 0.31  
4.56 1.58 0.75   
10.1 1.87    
 
Quenching limit (mg/s) of oxidizers in propane 
D (mm)\XO2 0.21 0.3 0.4 1 
0.75   0.28 0.09 
1.5  0.40 0.26 0.11 
3.02 1.13 0.48 0.33  
4.56 0.90 0.54   
40 
5. Conclusions 
The quenching limits of inverse diffusion flames have been measured for different 
fuel-oxidizer combustion on different sizes of burners. The fuels considered were 
methane, ethylene and propane. The O2 mole fractions were 0.21, 0.3, 0.4 and 1. The 
diameters of the oxidizer port were 0.75, 1.53, 3.02, 4.56 and 10.1 mm. The key 
findings are: 
1. The quenching limits of inverse flames decreases as the oxygen concentration 
increases. Based on our analysis, it scales with XO2
 -1.5. 
2. The quenching limits of inverse flames do not depend largely on the diameter of the 
oxidizer port. This conclusion is the same for the normal diffusion flame as for its 
quenching limits? dependency on the burner diameter.  
3. The quenching limits of inverse flames are proportional to the fuel quenching 
distance. 
4. The heat release rates of the quenching inverse flames vary from 1 ? 2 W. They are 
lower than the heat release rates of normal diffusion flames with the same 
configurations.  
 
41 
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