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 Copyright © 2007 by ASME Transactions of the ASME Downloaded 16 Aug 2007 to 130.207.50.192. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm 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 UrefBlowoff 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 Downloaded 16 Aug 2007 to 130.207.50.192. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm 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 Transactions of the ASME Downloaded 16 Aug 2007 to 130.207.50.192. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm 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 Downloaded 16 Aug 2007 to 130.207.50.192. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm 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 Downloaded 16 Aug 2007 to 130.207.50.192. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm 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 UbBlowoff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 Downloaded 16 Aug 2007 to 130.207.50.192. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm 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. 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