Qingguo Zhang
David R. Noble
Tim Lieuwen
School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0150
Characterization of Fuel
Composition Effects in
H2 / CO / CH4 Mixtures Upon Lean
Blowout
This paper describes measurements of the dependence of lean blowout limits upon fuel
composition for H2 / CO / CH4 mixtures. Blowout limits were obtained at fixed approach
flow velocity, reactant temperature, and combustor pressure at several conditions. Consistent with prior studies, these results indicate that the percentage of H2 in the fuel
dominates the mixture blowout characteristics. That is, flames can be stabilized at lower
equivalence ratios, adiabatic flame temperatures, and laminar flame speeds with increasing H2 percentage. In addition, the blowoff phenomenology qualitatively changes with
hydrogen levels in the fuel, being very different for mixtures with H2 levels above and
below about 50%. It is shown that standard well stirred reactor based correlations, based
upon a Damköhler number with a diffusivity ratio correction, can capture the effects of
fuel composition variability on blowoff limits. 关DOI: 10.1115/1.2718566兴
Keywords: syngas, lean blowout, hydrogen
Introduction
This paper describes measurements of the dependence of lean
blowout limits upon fuel composition. This work is motivated by
interest in developing fuel-flexible combustors capable of operating with highly variable and potentially low quality fuels, while
producing minimal air pollutants. Such plants would be useful in
a range of settings and geographic locations by having capabilities
for efficiently and cleanly operating with a range of fuels, such as
liquids or synthetic gases derived from other organic sources, e.g.,
coal, sewage gas, biomass, or landfill gas 关1兴.
Current dry low emissions technology primarily focuses on
burning natural gas, a fuel that is mainly composed of methane. It
seems clear, however, that natural gas cannot be relied upon as the
exclusive source for fueling the clean power plants of the future.
Rapidly increasing demand due to new installations has caused
substantial price volatility and concerns about future supplies. In
addition, interest in utilizing other energy resources, as well as
concern about energy security have motivated interest in utilizing
coal-derived syngas or fuels from other sources, such as biomass,
landfill gas, or process gas. Technologies such as integrated gasification combined cycle 共IGCC兲 plants enable the combustion of
coal and other solid or liquid fuels, while still maintaining aggressive emissions targets and high efficiency.
The inherent variability in composition and heating value of
these fuels provides one of the largest barriers towards their usage,
however. Syngas fuels are typically composed primarily of H2,
CO, and N2, and may also contain smaller amounts of CH4, O2,
CO2, and other higher order hydrocarbons 关2兴. Depending upon
the source and particular processing technique, these fuels can
have significant ranges in relative composition of these constituents. To illustrate, Moliere 关3兴 presents a comparison of compositions for 12 different syngas fuels, showing that the volumetric
H2 / CO ratio varies from a low of 0.33 to a high of 40, the perContributed by the International Gas Turbine Institute 共IGTI兲 of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript
received August 15, 2006; final manuscript received December 26, 2006. Review
conducted by Dilip R. Ballal. Paper presented at the ASME Turbo Expo 2005: Land,
Sea and Air 共GT2005兲, June 6–9, 2005, Reno, NV, Paper No. GT2005-68907.
688 / Vol. 129, JULY 2007
centage of diluents gases 共e.g., N2, CO2, Ar兲 from 4 to 51%, and
the percentage of water from 0 to 40%. The primary constituents
of landfill or sewage gas are typically CH4 and CO2 关4兴.
This variability is a significant problem because low emission
combustion systems are optimized for operation within a tight fuel
specification. Expensive test programs and hardware modifications are generally required if there are significant changes to gas
fuel properties. This variability in fuel content, and resultant combustion kinetics, will likely introduce substantial modifications in
steady state and dynamic combustor behavior from one syngas to
the next.
This paper describes results from an experimental program that
is investigating an issue that will be of acute significance toward
realization of low emissions, fuel-flexible combustors: lean blowout. Blowout can be expected to be a serious issue, given the
substantial variability in chemical kinetic properties of the various
fuels encountered in fuel flexible combustors, particularly because
achieving low emissions often requires operating very near the
blowout limits of the system.
Background
Flame stabilization involves competition between the rates of
the chemical reactions and the rates of turbulent diffusion of species and energy. While a significant amount of fundamental understanding of flame propagation and stability characteristics of
lean, premixed systems has been gained in conventionally fueled,
natural gas-air systems 关5兴, little is known about these issues for
alternate gaseous fuels, such as syngas or low BTU fuel mixtures.
Furthermore, the majority of the fundamental investigations of the
combustion characteristics of these synthetic gases are for nonpremixed flame configurations 关6–10兴.
Consider syngas fuels which are composed primarily of H2,
CO, and N2. Both H2 and CO act as fuels when oxidized. Individually, they produce higher adiabatic flame temperatures 共at stoichiometric conditions in air兲 than CH4, 2383 and 2385 K, as
compared to 2220 K. H2 and CO also have lower flammability
limits 共␾ = 0.14 and 0.34, respectively兲 than CH4 共␾ = 0.46兲, and
higher maximum adiabatic laminar flame speeds 共320 and
55 cm/ s versus 40 cm/ s for methane兲 关11兴. This would suggest
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that these fuels could have better flame holding characteristics
than natural gas. The picture for the pure fuels becomes slightly
more complicated at lean mixtures, however, because the flame
speed of CO drops below that of CH4. This comparison of pure
fuels does not, however, paint a complete picture. The turbulent
propagation and stability properties of premixed H2 / CO mixtures
are not well documented, and performance characteristics of these
mixtures cannot be simply inferred from knowledge of the global
performance of the constituents. To begin, CO and H2 have significantly different transport properties and flame speeds. Next,
CO chemistry, which releases slightly more heat than the same
amount of H2 by mass, is highly coupled to H2 oxidation through
the reaction CO + OH → CO2 + H, which dominates CO ignition
共at least兲 at atmospheric pressure.
The coupling is also important in that, together, CO and H2
oxidation can cover a wide range of time scales that may bridge
the relevant fluid dynamic, turbulent time scales. As shown below,
chemical time scales of CO / H2 mixtures are quite different, and
given the large spectrum of turbulent time scales in practical combustors, the combustion processes can cover several orders of
magnitude of the Damköhler number. For example, interactions
between turbulent mixing processes and, say, H2 oxidation may
occur in the “flamelet” regime, those associated with CO oxidation in a “torn flamelets” regime, and OH recombination 共whose
chemistry plays a key role in CO oxidation兲 in the distributed
reaction regimes. Furthermore, the oxidation and, hence, rates of
heat release of CO and H2 display different or opposite sensitivities to mean pressure or flame strain/stretch imposed by the turbulent flow field.
In addition, syngas fueled plants sometimes co-fire with a certain fraction of natural gas, so the additional interactions associated with H2 / CH4 and CO / CH4 flames also need to be considered. Several recent studies have focused on H2 / CH4 flames
关12,13兴 and have shown that addition of H2 enhances the mixture’s resistance to extinction or blowoff. For example, fundamental studies in opposed flow burner geometries show that the extinction strain rate of methane flames is doubled with the addition
of 10% H2 关14,15兴. The acceleration of the CH4 reaction rate by
the radical pool created by the early breakdown of H2 has been
suggested as a key mechanism for this behavior.
CO / CH4 flames also have interesting dynamics because of
their coupled chemistry. The CO burning rate is highly dependent
on the reaction CO + OH → CO2 + H. The addition of CH4 increases the radicals for this reaction. In addition, CO is also believed to be a significant intermediate during the low temperature
reaction path of CH4 关16兴.
The above discussion clearly indicates the need for more extensive systematic studies of the blowout characteristics of premixed
flames using the fuels that will be encountered in fuel-flexible
combustors. Several studies have been initiated relatively recently
to investigate the characteristics of premixed, hydrogen-enriched
methane fuels 关12,13,17兴. Additional studies are needed, however,
to broaden the scope of fuels of interest.
Having briefly considered the kinetic characteristics of these
fuels, we turn our attention next to issues associated with blowoff.
Developing physics-based correlations of blowout behavior is
complicated by the lack of understanding of the flame characteristics at the stabilization point. Currently, there is disagreement on
whether premixed flames in high turbulent intensity gas turbine
environments have flamelet, “thickened” flamelet, or well stirred
reactor 共WSR兲-like properties.
Methods for developing blowout correlations in the latter case
共i.e., using WSR scaling ideas兲 have been studied extensively.
Several different theories or physical considerations have been
used in past blowout correlation studies, such as those of Zukoski
and Marble 关18兴, Spalding 关19兴, or Longwell 关20兴. As noted by
Glassman 关11兴, however, they lead to essentially the same form of
correlation. These correlations generally involve relating the
blowoff limits to a ratio of a chemical kinetic time and residence
Journal of Engineering for Gas Turbines and Power
Fig. 1 Relationship between chemical time calculated using
Eq. „1… and blowout residence time for ␾ = 0.6H2 / CO / CH4 mixtures. Results obtained using CHEMKIN with the GRI 3.0
mechanism.
time, ␶chem / ␶res. In well stirred reactor theory, this ratio is often
referred to as a combustor loading parameter. It is possible that the
recirculation regions that stabilize many high intensity flames,
which may have flamelet properties at most other points along the
flame, have distributed reactor-like properties; hence, the success
in WSR models in correlating blowout behavior.
When applied to blowoff limits of premixed flames, this chemical time can be estimated as
␶chem = ␣/SL2
共1兲
where SL and ␣ denote the laminar flame speed and thermal diffusivity, respectively 关21,22兴. Alternative methods of estimating a
global chemical time are also possible, but generally lead to results qualitatively similar to Eq. 共1兲. For example, Fig. 1 compares
the blowoff residence time, ␶blowoff, of a well stirred reactor model
to the chemical time from Eq. 共1兲 for several H2 / CO / CH4 mixtures. The two time scales are closely related, with a best fit given
by ␶chem = 3.4*␶blowoff 共denoted by the solid line兲 except for cases
with greater than 95% CO 共not shown兲. In this paper, we will use
␶blowoff in estimating chemical times, for the pragmatic reason that
they are much simpler and easier to calculate for lean flames.
Determination of ␶chem is hampered by problems with obtaining
converged solutions for SL at the very low equivalence ratios at
which the high hydrogen mixtures blow off.
Returning to WSR based methods for scaling blowoff limits,
the residence time scales as d / Uref, where d and Uref denote a
characteristic length scale 共e.g., a recirculation zone length兲 and
velocity scale, respectively. If this reactor based theory is correct,
then blowoff limits should scale with the loading parameter or
Damköhler number,
Da =
d
␶res
=
␶Blowoff Uref␶Blowoff
共2兲
This Damköhler number correlation is equivalent to Peclet number correlations 关23兴 if ␶blowoff is replaced by ␶chem. Defining the
Peclet numbers based upon flame and flow velocity, Peu
= Urefd / ␣ and PeSL = SLd / ␣ note that
Da =
2
PeSL
Peu
共3兲
These purely combustion considerations are incomplete without
consideration of the corresponding fluid mechanics, however. For
example, note that Uref does not need to directly scale with the
approach flow velocity, U0, due to the acceleration of the burned
gas 关21兴. Since the burned gas velocity scale is given by Ub
= 共Tb / T0兲U0, then Uref = f共U0 , Tb / T0兲. Similar considerations apply
for the recirculation zone scale, d. For this reason, prior workers
have often had to measure the recirculation zone length in bluff
body flames in order to use Eq. 共2兲, e.g., see Ref. 关18兴.
JULY 2007, Vol. 129 / 689
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Fig. 2 Cross section of premixer assembly
The work of Hoffman et al. 关24兴 is of special interest, as it
found good success with the Peclet number correlation of Eq. 共3兲
to capture the dependence of blowoff limits in swirling, premixed
flames upon combustor diameter, flow velocity, and swirl number.
They used the azimuthal velocity component, U␪, as the reference
velocity, Uref = U␪, and combustor diameter, D, as the characteristic length, D = d.
Significantly less attention has been given to correlating premixed flame blowout limits assuming flamelet-like combustion
properties, where the stabilization mechanism is related to front
propagation, rather than reactor extinction. In this case, a flame
would blow off when the turbulent flame speed is everywhere less
than the flow velocity, ST ⬍ Uref, where ST denotes the turbulent
flame speed. If this propagation mechanism is controlling, then
blowoff limits should scale with the parameter,
L2 =
ST
Uref
共4兲
Evaluating the turbulent flame speed introduces additional complications for mixtures with widely varying compositions. Correlations of the turbulent flame speed of the form, ST
= SL · f共u⬘ , geometry兲, where u⬘ denotes turbulent intensity, have
been used successfully in many prior studies across limited fuel
ranges. However, recent studies across broader ranges of fuels
clearly indicate the limitations of the above correlation; other fuel
properties are also very important. For example, Kido et al. 关25兴
measured the dependence of the turbulent flame speed for a variety of H2, CH4, and C3H8 mixtures. These mixtures were carefully chosen to have identical laminar flame speeds, as indicated
by the ST curves converging at u⬘ = 0. Interestingly, however, the
curves widely diverge as u⬘ increases from zero, e.g., the lean
hydrogen mixture has a turbulent flame speed almost ten times
higher than the lean propane mixture. We have not pursued correlations of this form due to lack of data on ST for the fuel blends
of interest.
Instrumentation, Experimental Facility, and Experimental Procedures
Measurements were obtained in a lean, premixed gas turbine
combustor simulator, which has also been previously described in
Ref. 关26兴. The facility consists of inlet/premixer, combustor, and
exhaust sections. High-pressure natural gas and air are supplied
from building facilities. The air can be preheated up to 700 K. The
hydrogen and carbon monoxide are supplied from bottles. The air
and fuel flow rates are measured with a critical orifice and mass
flow controllers 共MFCs兲, respectively. Both the orifice and MFCs
were calibrated using the specific gas with which they were to
690 / Vol. 129, JULY 2007
meter. This is necessary for H2 in particular, as the manufacturer
supplied corrections that relate the flow of some other gas to the
H2 flow rate were found to be very inaccurate. The resultant uncertainty in the flow rate measurements is 2% of full scale and in
blowoff equivalence ratios is 0.01–0.02 for most of the cases. The
largest uncertainty in ␾ of 0.03 occurs in the 39 m / s case, with
pure CH4. In order to ensure that acoustic oscillations did not
affect the fuel/air mixing processes, the fuel and air are mixed
upstream of a second choke point. Thus, the equivalence ratio of
the reactive mixture entering the flame is constant. The temperature of the reactants was measured with a thermocouple located
just upstream of the swirler.
The fuel-air mixture entered the circular 4.75 cm diameter,
60 cm long inlet section and passed through a nozzle and swirler
section prior to entering the combustor, see Fig. 2. The nozzle
outer body slightly constricts along the axial flow direction. However, the overall flow area remains constant at 10.8 cm2, as the
center body diameter also decreases in the axial flow direction.
This nozzle is fully modular as the center body and swirler can be
easily removed and replaced; these tests were performed with a
single 12 vane, 35 deg swirler. A thermocouple is imbedded in the
center body for flashback detection.
The nozzle terminates into the 5 ⫻ 5 cm square combustor. The
square part of the combustor is 51 cm long and optically accessible. It then transitions into a circular 7.6 cm diameter, 195 cm
long exhaust section. The exhaust sections are water cooled. The
flow leaves the setup through an exhaust nozzle with an adjustable
bypass valve. This adjustable bypass valve is controlled in order
to maintain the combustor pressure at some prescribed value.
The basic test sequence is to operate at uniformly spaced fuel
compositions in H2 / CO / CH4 space, such as is depicted in Fig. 3.
At each fuel composition, the mixture equivalence ratio is adjusted 共at constant premixer velocity兲 until the mixture blows off.
The flame was viewed with a standard and UV sensitive 共down
to 270 nm兲 video camera, each connected to a monitor in the
control room. The second UV sensitive camera was needed at the
high pressure condition, where the high H2 flames, even when
well stabilized, were often not visible.
Obtaining these data was complicated by the need to keep the
approach flow velocity, combustor pressure, and mixture temperature constant across the range of fuel compositions. As such, approaching blow off limits with a certain fuel composition required
simultaneously adjusting the air and three fuel flow rates in order
to keep constant approach flow velocity. In addition, due to variations in mixture burned gas temperature, maintaining a constant
combustor pressure required simultaneous adjustment of the back
pressure valve. Finally, variations in molar volume of the fuel
necessitated adjusting the air temperature in order to maintain a
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Fig. 4 Dependence of flame speed „cm/s… upon fuel composition at fixed 1500 K „left… and 2000 K „right… adiabatic flame
temperatures with 300 K reactant temperature
Fig. 3 Composition map describing regions where sharply defined blowoff event occurs „gray… and blowoff preceded by significant flame liftoff „white…
constant reactant temperature. For the data shown in the Results,
the approach flow velocity, pressure, and temperature remains
constant to within 2%, 5%, and 15 K of their quoted values.
Applying a uniform definition of blowoff is complicated by the
fact that the manner in which the flame blew off varied with
composition. In many cases, the blowoff event occurred abruptly
with a small change in fuel composition, although sometimes preceded by slight liftoff of the flame from the burner. Defining the
blowoff point was unambiguous in these instances; moreover, the
point of blowoff and flame liftoff was nearly identical. This was
the case for mixtures with less than approximately 50% H2 by
volume. However, for high H2 mixtures, the blowoff and liftoff
events were quite distinct, see Fig. 3. Usually, the flame became
visibly weaker, lifted off from the holder, and moved progressively downstream with decreases in equivalence ratio before
blowing off for good. As such, blowoff is defined here as the point
where the flame is no longer visible in the 10.2 cm long optically
accessible section of the combustor. Undoubtedly, this variation of
liftoff/blowoff characteristics with fuel composition is responsible
for some of the scatter in the experimental data. This point should
be kept in mind when comparing 0–50% H2 and 50–100% H2
containing fuels.
DF =
兺 AD
k
km
共7兲
k=fuel
where Ak is the fraction of heat release due to fuel k relative to
that of the entire mixture.
In order for the reader to obtain some familiarity with the properties of H2 / CO / CH4 mixtures, a number of results are included
below. Consider first the flame speed, SL. Figure 4 illustrates the
dependence of the flame speed upon fuel composition at two fixed
adiabatic flame temperatures, 1500 and 2000 K. The fuel composition by volume is given by the location within the triangle,
where the three vertices denote pure CO, H2, or CH4. At each
point, the mixture equivalence ratio is adjusted such that the mixture has the given flame temperature. As expected, the high H2
mixtures have the highest flame speeds. Note also the slightly
higher flame speeds of the high CH4 mixtures relative to those of
CO mixtures.
An alternative way to view these results is to plot adiabatic
flame temperature at a fixed flame speed. This is done in Fig. 5 for
SL = 10 and 20 cm/ s. Note the progression in flame temperatures
from CO and H2 mixtures being the highest and lowest, respectively.
Figure 6 plots the dependence of the chemical time, ␶chem
= ␣ / SL2 , upon fuel composition at a fixed flame temperature of
1500 K. Note the order of magnitude variation in chemical time
from the fast H2 mixtures to the slow CO mixtures.
Results and Discussion
Analysis Approach
This section describes the methods used to postprocess the data
and correlate blowout limits. Adiabatic flame temperatures were
calculated for a given mixture using standard methods. Laminar
flame speeds were calculated with the PREMIX application in
CHEMKIN, using the GRI3.0 mechanism. While this mechanism
was primarily optimized for methane/air mixtures, good comparisons between its results and measurements have been obtained for
a range of H2 / CO mixtures as well 关27兴. Chemical times, determined with Eq. 共1兲, require the thermal conductivity of the reactive mixture, determined using transport properties from TRAN in
CHEMKIN and the equation 关28兴
␭=
1
2
冉兺
K
k=1
X k␭ k +
1
K
兺k=1
Xk/␭k
冊
This section presents blowout results at two constant nozzle
exit velocities: 59 and 39 m / s. This corresponds to combustor
velocities 共cold flow兲 of 6.0 and 4.0 m / s. Tests were performed at
two pressure/temperature conditions: combustor pressure of
1.7 atm and 300 K reactants, and combustor pressure of 4.4 atm
and 460 K reactants. The mean equivalence ratios ranged from
roughly 0.15 to 0.60.
In order to facilitate presentation of results, we represent the
mixture composition of H2 / CO / CH4 by its color. Primary colors
共5兲
Diffusivity coefficients of a given species in the mixture were
determined from
Dkm =
兺Kj⫽kX jW j
W̄兺Kj⫽kX j/D jk
共6兲
where W and X denotes the molecule weight and mole fraction,
respecitvely. The “effective” diffusivity of the fuel mixture was
defined as
Journal of Engineering for Gas Turbines and Power
Fig. 5 Dependence of adiabatic flame temperature „K… upon
fuel composition at fixed laminar flame speed 10 cm/ s „left…
and 20 cm/ s „right… with 300 K reactant temperature
JULY 2007, Vol. 129 / 691
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Fig. 6 Dependence of chemical time „ms… upon fuel composition at fixed adiabatic flame temperature, 1500 K
at the three vertices are used to represent each fuel constituent,
where red, yellow, and blue denote H2, CO, and CH4, respectively. This is illustrated in Fig. 7.
These blowout limits were correlated with a variety of parameters. As noted in previous studies 关13兴, the presence of H2 has a
strong impact on blowout limits of either H2 / CH4 or H2 / CO
flames. Figure 8, which plots the dependence of the blowoff
equivalence ratio upon the mole fraction of H2 in the fuel, shows
that H2 strongly affects the lean blowout limits of syngas mixtures
共H2 / CO / CH4兲, in spite of the complicated coupling chemical
mechanisms among these species. It shows the well known result
that, in general, mixtures can be stabilized with lower equivalence
ratios as the H2 concentration increases. However, note that the
Fig. 7 Primary color mixing scheme used to denote fuel blend
composition
Fig. 8 Dependence of LBO equivalence ratio upon H2 mole
fraction at premixer flow velocities of 59 m / s at 300 K reactants
temperature and 1.7 atm combustor pressure „circle… and
458 K and 4.4 atm „diamond…
692 / Vol. 129, JULY 2007
Fig. 9 Damköhler numbers of mixtures at constant premixer
flow speed of 59 m / s at 300 K reactants temperature and
1.7 atm combustor pressure
addition of small amounts of H2 has a small impact upon blowoff
limits and that the sensitivity of the blowoff equivalence ratio to
H2 level variations remains essentially constant across the entire
range of H2 levels. In other words, no discontinuous or steep drop
in blowoff equivalence ratio was observed with small amounts of
H2 addition.
At a specific H2 mole fraction there is scatter in the data within
a relatively narrow band due to variations in the CO / CH4 ratio—a
higher ratio of CO / CH4 resulting in blowout at lower equivalence
ratios.
The adiabatic flame temperature of the mixture at blowout correspondingly decreases as the percentage of H2 increases. Although not shown, there is a nearly linear relationship between the
percentage of H2 and adiabatic flame temperature at lean blowout.
For example, the adiabatic flame temperature linearly decreased
from 1400 K to 1000 K for the high reactant temperature case
shown in Fig. 8. This may be partly explained by the chemical
kinetics. The chain-branching reaction H + O2 ⇔ O + OH, which is
very sensitive to flame temperature, plays an important role in
flames with H2 addition 关15兴. For a given fuel composition, when
the equivalence ratio decreases to some level where either the
flame zone temperature or the concentration of radicals is too low
to maintain this chain-branching reaction, local extinction occurs.
However, higher H2 fuels may provide more radicals for this
chain-branching reaction, so that flames which have a higher percentage of H2 could stabilize at a lower adiabatic flame temperature.
Similarly good correlations between the laminar flame speed,
Lewis number, and a number of other combustion parameters at
blowoff upon H2 level were observed. This brings us to an important point that must be recognized in extracting an understanding
of the blowoff physics from these correlations. First, blowoff limits are clearly a strong function of H2 levels. Second, many other
parameters, such as diffusivities, flame temperature, etc. are also
strong functions of H2 level. As such, it is important to not draw
conclusions about blowoff physics only because one can correlate
results with parameters that are simply functions of the H2 percentage. For example, a very nice correlation between Tad versus
Le at blowout exists, because both of them are functions of percentage of H2. In other words, regardless of whether the mixture
Le is a physically meaningful parameter, a good correlation will
still be observed. In some sense, this is analogous to correlating
Tad versus 2*Tad at blowoff—obviously, a perfect correlation is
observed, regardless of whether this is a physically significant
parameter.
Damköhler 共Da兲 number correlations were found to correlate
the data over all flow velocities, pressures and temperatures for all
mixtures with H2 levels below 50%, as shown in Fig. 9. In the
plot, the reference length scale, D, was the combustor width,
5.1 cm. Damköhler numbers were evaluated using both the unTransactions of the ASME
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Table 1 Summary of optimum model constants for correlating
blowoff data and resulting scatter in fitted data
Best fit C value
Fig. 10 Damköhler numbers of mixtures based on adjusted
equivalence ratio at premixer flow velocities of 59 m / s at 458 K
reactants temperature and 4.4 atm combustor pressure
burned, DaU, and burned flow speed, DaB, as reference velocity
scales. Utilizing the burned gas speed resulted in slightly better
ability to correlate the data, as reflected in slightly lower errors
共about 10%兲 in predicted blowoff equivalence ratio, ␦␾rms 共described below兲, and so is used for these results. Figure 9 shows
that blowout occurs at a nearly constant Da for these composition
values 共although Fig. 9 was plotted in the logarithm scale, ␶Blowoff
is an exponential function of equivalence ratio兲. At the same time,
Fig. 9 also shows that a constant Da correlation is inadequate for
describing blowout limits of higher H2 level mixtures. It is possible that this is simply a reflection of the fact that the blowout
process changes with H2 levels and that our “blowoff definition”
is not the most physically meaningful, see discussion of Fig. 3.
For example, perhaps identifying the point where the flame first
lifted off the flame holder would have been more useful.
A second possibility for this change in blowoff Da value shown
in Fig. 9 may be due to preferential diffusion effects, a consideration that has also been used to scale changes in turbulent flame
speed of mixtures whose constituents have significant variations
in diffusivity. One approach for incorporating these effects is to
note that the local equivalence ratio changes along the wrinkled
flame, being both higher and lower than the average at different
spatial locations. Kido and co-workers关29兴 suggested correlating
mixture turbulent flame speeds by utilizing mixture properties at
an adjusted equivalence ratio, ␾adj, i.e., not at the average equivalence ratio, ␾ave, but the average value plus some ⌬␾. As such,
mixture properties are correlated at ␾adj = ␾ave + ⌬␾. They suggest
the following relation for ⌬␾, based upon empirical fits of their
data:
⌬␾ = C ln共DF/DOX兲
共8兲
where DF and DOX denote the mass diffusivity of fuel 共see Eq.
共7兲兲 and oxygen, respectively, and C is an empirical constant
whose value they suggest as 0.3.
We found that utilizing a value of C close to 0.1 gives a nearly
constant blowoff Damköhler number for all of our data sets, Fig.
10. This plot shows that blowoff occurs at a nearly constant value
of local Damköhler number, where the ␶Blowoff is estimated at the
equivalence ratio ␾adj = ␾ave + ⌬␾. In this case, the best value for
C = 0.07 and the average value over all the test points of DaB at
blowoff is 0.2. Table 1 summarizes the results from the other two
tests by presenting the best fit value for C for each individual data
set and the corresponding DaB value. It can be seen that DaB does
vary with each data set, but is always an O共1兲 quantity.
In order to quantify the scatter in the correlations shown in the
table and the capability for actually inverting the above procedure
to be used as a blowoff prediction methodology, we employed the
following procedure. Assume that the equivalence ratio at blowoff
is now the unknown and must be predicted, ␾LBO,pred. Assume
also that the Damköhler number at blowoff is known and equal to
Journal of Engineering for Gas Turbines and Power
Test group
C
DaB at ␾adj
␦␾rms
T = 300 K, P = 1.7
atm, U0 = 59 m / s
T = 300 K, P = 1.7
atm, U0 = 39 m / s
T = 458 K, P = 4.4
atm, U0 = 59 m / s
0.1
2.1
0.04
0.08
1.1
0.03
0.07
0.2
0.02
the value DaB compiled in the table. We then solve the following
implicit equation for ␾LBO,pred for each fuel composition:
DaB =
d
Ub␶Blowoff关␾LBO,pred + C ln共DF/Dox兲兴
共9兲
This procedure is repeated for each fuel composition. In general, ␾LBO,meas and ␾LBO,pred are not identical, and so the root
mean square 共rms兲 of their difference over all the data points is
referred to as ␦␾rms. The table also compiles the values of ␦␾rms.
As can be seen, assuming a constant Damköhler number at blowoff results in a capability for predicting the equivalence ratio value
to within about 0.02–0.04.
Moreover, due to the exponential dependence of ␶Blowoff upon
equivalence ratio, varying the precise value of DaB or C does not
substantially impact the errors in ␾LBO,pred. For example, in the
first case above, assuming blowoff occurs at constant values of
Da= 1.0 or 3, instead of the best fit value of 2.1, results in
␦␾rms = 0.045 and 0.043, respectively.
Moreover, both Tin = 300 K, P = 1.7 atm data sets can be reasonably collapsed with a single ⌬␾ equation or C value. To illustrate,
Fig. 11 compares the predicted and actual blowoff equivalence
ratios for all low temperature data taken in this study, assuming
C = 0.1 and DaB = 1.7. It can be seen that the error in ␾LBO,pred is
generally less than 0.05, and ␦␾rms = 0.045. Moreover, the highest
errors are encountered with the very high CO mixtures, which
may simply be a manifestation of the sensitivity of high CO mixtures to ambient humidity levels and other factors influencing H
levels. If the P = 4.4 atm, T = 460 K data set were also plotted, they
would also cluster along a line, but with a systematic difference
from the grouping in this graph., In other words, the optimum
model constants 共particularly the C value兲 vary with operating
conditions.
There are a variety of reasons that the remaining scatter could
be present, such as inherent noise in the blowoff equivalence ratio.
Fig. 11 Comparison of predicted and measured blowoff
equivalence ratio for all T = 300 K, p = 1.7 atm data. circle: U0
= 59 m / s, square: U0 = 39 m / s
JULY 2007, Vol. 129 / 693
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In addition, other more subtle factors, such as reference length and
reference flow velocity could easily change somewhat with approach flow velocity.
We should emphasize that the C value in the ⌬␾ calculation
was chosen empirically to give the best fit. Although the Da
mechanism, considering preferential diffusion effects, could correlate and predict the lean blowout limits very well, the real physical meaning behind these correlations are still uncertain and require further study.
Concluding Remarks
Although a variety of correlations of varying complexity were
assessed, many of which were not reported here, the percentage of
H2 in the fuel was found 共for a given set of operating conditions兲
to be a very powerful parameter for correlating blowoff data over
a wide range of fuel compositions. A Damköhler number correlation was found to also correlate the data, even across the range of
fuel compositions. The near unity value of this Damköhler number 共at least for low H2 levels兲, as well as the ability to capture a
range of fuel compositions 共for ⬍50% H2兲, flow velocities, and
ambient conditions suggests that classical well stirred reactor approaches can capture the key blowoff physics. Moreover, the ability of the ⌬␾ correction, motivated by prior studies for correlating
turbulent flame speeds, to capture the entire range of H2 levels is
also suggestive of the need to account for differential diffusive
corrections when scaling data across broad ranges of H2 levels.
However, we should emphasize that the latter ⌬␾ correction may
not necessarily reflect the underlying physics, but simply be another manifestation of the fact that the blowoff limits are a strong
function of H2 levels 共note that ⌬␾ is closely correlated with the
percentage of H2兲. Moreover, comparison of these data at low and
high H2 levels should be done with some caution, given the necessary, but somewhat arbitrary nature of our definition of the
blowoff equivalence ratio. In particular, the definition of the blowoff equivalence ratio at the very high H2 levels, while repeatably
given our methodology, could certainly also be done differently,
with consequently different values for ␾LBO at high hydrogen levels.
Acknowledgment
This publication was prepared with the support of the U.S. Department of Energy, Office of Fossil Energy, National Energy
Technology Laboratory, under Contract No. 03-01-SR111 共Dr. Richard Wenglarz, contract monitor兲. Any opinions, findings, conclusions, or recommendations included herein are those of the
authors and do not necessarily reflect the views of the DOE.
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