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Reduction of a detailed reaction mechanism for hydrogen combustion under gas turbine conditions
Combustion and Flame 144 (2006) 545–557 www.elsevier.com/locate/combustflame
Reduction of a detailed reaction mechanism for hydrogen combustion under gas turbine conditions Jochen Ströhle ∗ , Tore Myhrvold SINTEF Energy Research, 7465 Trondheim, Norway Received 23 March 2005; received in revised form 14 July 2005; accepted 11 August 2005 Available online 27 September 2005
Abstract The aim of this study is to find a reduced mechanism that accurately represents chemical kinetics for lean hydrogen combustion at elevated pressures, as present in a typical gas turbine combustor. Calculations of autoignition, extinction, and laminar premixed flames are used to identify the most relevant species and reactions and to compare the results of several reduced mechanisms with those of a detailed reaction mechanism. The investigations show that the species OH and H are generally the radicals with the highest concentrations, followed by the O radical. However, the accumulation of the radical pool in autoignition is dominated by HO2 for temperatures above, and by H2 O2 below the crossover temperature. The influence of H2 O2 reactions is negligible for laminar flames and extinction, but becomes significant for autoignition. At least 11 elementary reactions are necessary for a satisfactory prediction of the processes of ignition, extinction, and laminar flame propagation under gas turbine conditions. A 4-step reduced mechanism using steady-state approximations for HO2 and H2 O2 yields good results for laminar flame speed and extinction limits, but fails to predict ignition delay at low temperatures. A further reduction to three steps using a steady-state approximation for O leads to significant errors in the prediction of the laminar flame speed and extinction limit. 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Hydrogen combustion; Modeling; Reduced mechanism; Gas turbine
1. Introduction In the context of reducing CO2 emissions from power production, hydrogen has recently drawn increased attention as a clean fuel. However, the use of hydrogen in gas turbine combustors is not straightforward since hydrogen has some characteristics that strongly deviate from those of the main components of conventional fuels, such as methane. Hydrogen is strongly exposed to molecular diffusion processes * Corresponding author. Fax: +47 7359 2889.
E-mail address: [email protected] (J. Ströhle).
and has a wide flammability range, short ignition times, and a high laminar flame speed. The relatively high adiabatic temperatures of H2 /air mixtures might cause large amounts of thermal NOx in the flame. The flame temperature, and therefore NOx emissions, can be reduced by lean premixing of fuel and air. However, the high reactivity and flame speed of premixed H2 /air mixtures enhance the danger of autoignition and flashback, respectively. Computational fluid dynamics (CFD) have evolved to serve as a design tool for combustors. The flow in gas turbine combustors is strongly turbulent, and turbulent combustion is strongly influenced by the
0010-2180/$ – see front matter 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2005.08.011
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Table 1 Hydrogen mechanism of Li et al. [2] in the form k = AT n exp(−E/RT ) for N2 as the main bath gas (units are cm, moles, s, cal, K) No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Reaction
A
n
E
H + O2 = O + OH O + H2 = H + OH H2 + OH = H2 O + H O + H2 O = OH + OH H 2 + M = H + H + Ma O + O + M = O2 + M a O + H + M = OH + Ma H + OH + M = H2 O + Ma H + O2 + M = HO2 + Mb
3.547 × 1015 0.508 × 1005 0.216 × 1009 2.970 × 1006 4.577 × 1019 6.165 × 1015 4.714 × 1018 3.800 × 1022 1.475 × 1012 6.366 × 1020 1.660 × 1013 7.079 × 1013 0.325 × 1014 2.890 × 1013 4.200 × 1014 1.300 × 1011 2.951 × 1014 1.202 × 1017 0.241 × 1014 0.482 × 1014 9.550 × 1006 1.000 × 1012 5.800 × 1014
−0.406 2.67 1.51 2.02 −1.40 −0.50 −1.00 −2.00 0.60 −1.72 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.0
16,599 6290 3430 13,400 104,380 0 0 0 0 524.8 823 295 0 −497 11,982 −1629.3 48,430 45,500 3970 7950 3970 0 9557
HO2 + H = H2 + O2 HO2 + H = OH + OH HO2 + O = O2 + OH HO2 + OH = H2 O + O2 HO2 + HO2 = H2 O2 + O2 HO2 + HO2 = H2 O2 + O2 H2 O2 + M = OH + OH + Mc H 2 O2 H 2 O2 H 2 O2 H 2 O2 H 2 O2
+ H = H2 O + OH + H = HO2 + H2 + O = OH + HO2 + OH = HO2 + H2 O + OH = HO2 + H2 O
k∞ k0
k∞ k0
a Third body enhancement factors: H = 2.5, H O = 12. 2 2 b Third body enhancement factors: H = 2, H O = 11, O = 0.78; Troe parameter: 0.8. 2 2 2 c Third body enhancement factors: H = 2.5, H O = 11; Troe parameter: 0.5. 2 2
processes of ignition, extinction, and flame propagation. Detailed kinetic mechanisms are necessary to predict these processes. However, the use of detailed reaction mechanisms for turbulent combustion in CFD is computationally very expensive. Although a detailed mechanism for H2 /air combustion typically consists of only 8 species and 19 reactions, the elimination of some species or reactions might lead to a significant reduction in computational effort. The aim of this study is to find a reduced mechanism that accurately represents chemical kinetics for lean hydrogen combustion at elevated pressures as present in a typical gas turbine combustor. Detailed mechanisms for H2 /O2 combustion have been developed by several researchers, e.g., [1–6]. Recently, Li et al. [2] updated the H2 /O2 mechanism of Mueller et al. [1] and validated it against a wide range of experimental conditions (298–3000 K, 0.3– 87 atm, φ = 0.25–5.0) found in laminar premixed flames, shock tubes, and flow reactors. This mechanism is chosen for the present investigations because it was found to accurately represent H2 /O2 kinetics under gas turbine conditions [7,8]. The reaction mechanism is shown in Table 1. In the following, a re-
action of this mechanism is referred to by prefixing the letter R. A detailed reaction mechanism can be reduced by several means. The most straightforward way is to eliminate reactions that only negligibly influence the overall combustion process constituting a skeletal mechanism. Kreutz and Law [9] identified the most relevant reactions for inhomogeneous ignition. Reactions R1 and R2 are the most important chain branching steps, R3 is responsible for fast chain propagation, and R9 is the most important chain termination step. In the low-pressure regime, the reaction progress is determined by the balance of reactions R1 and R9. The corresponding increase of ignition temperature with pressure is called the second ignition limit. The temperature where both reaction rates are equal is also called the crossover temperature. In the high-pressure regime, H2 O2 formation and decomposition through reactions R14, R15, and R17 becomes relevant. The corresponding decrease of ignition temperatures with pressure constitutes the third ignition limit. Although these ignition limits have been derived by investigating nonpremixed flames, Zheng et al. [10] found the same ignition characteristics to be valid for the premixed case. Furthermore, Zheng and Law [11] ob-
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served two more ignition limits at even higher pressures for a lean premixed flame. Brown et al. [12] identified reactions R1, R2, R3, R5, R9, R10, and R11 to show significant sensitivity on the laminar flame speed of atmospheric H2 /air flames. Briones et al. [13,14] showed that the consumption of reactants in counterflow H2 /air partially premixed flames primarily occurs through reactions R1, R2, R3, and R9. Helenbrook et al. [15] found a skeletal mechanism with seven elementary single steps adequate to determine the ignition of counterflowing H2 /O2 at temperatures above crossover. Kreutz and Law [16] applied several skeletal mechanisms to ignition in nonpremixed counterflowing H2 /air. Using partial equilibrium or quasi-steady-state assumptions, the elementary reactions can be transformed to a small number of global reactions constituting a reduced mechanism [17,18]. Gutheil and Williams [19] and Balakrishnan et al. [20] investigated a hydrogen–air counterflow diffusion flame using one overall step and a 2-step mechanism, respectively. Balakrishnan et al. [21] studied extinction and ignition limits in laminar nonpremixed counterflowing hydrogen–air streams for several reduced mechanisms. They obtained a 4-step mechanism using steady-state approximations for HO2 and H2 O2 , two 3-step mechanisms using an additional steady-state approximation for either OH or O, and a 2-step mechanism assuming steady state for both OH and O. A third alternative 3-step mechanism applied steady-state approximations for all radicals except H and HO2 . Treviño and Liñán [22] analyzed high-temperature ignition in a mixing layer between hydrogen and air using two different 2-step mechanisms. Sohn and Chung [23] investigated extinction in diluted hydrogen–air counterflow diffusion flames using a 4-step mechanism applying steady-state approximations to O and OH, a 3-step mechanism assuming steady state for H2 O2 , and a 4-step mechanism assuming steady states for HO2 and H2 O2 . All mechanisms predicted the extinction strain rate reasonably accurately. Kreutz and Law [16] derived several reduced mechanisms from skeletal mechanisms to study ignition in nonpremixed counterflowing hydrogen versus heated air. Chen and Kollmann [24] used several reduced hydrogen mechanisms to derive reaction progress variables for a Monte Carlo scalar pdf combustion model. Various advanced mathematical methods have been developed for a systematic reduction of large reaction mechanisms, such as eigenvalue analysis [18], the intrinsic low-dimensional manifolds (ILDM) method [25], the computational singular perturbation (CSP) method [26], and genetic algorithms [27]. Eggels and de Goey [28] reduced several hydrogen/air reaction systems to 1-step schemes using the ILDM
547
method. Lu et al. [26] employed the complex CSP method to generate a 4-step reduced mechanism for high-temperature H2 /air oxidation. The method automatically eliminated the two species HO2 and H2 O2 . Most of the previous work mentioned above has been focused on the investigation of individual phenomena, e.g., ignition, in laminar flames. However, a reduced mechanism for the application to gas turbine combustors has to account for all phenomena relevant in turbulent combustion. Hence, calculations of autoignition, extinction, and laminar premixed flames under gas turbine conditions are used in the present study to investigate a detailed reaction mechanism and to derive reduced mechanisms.
2. Numerical methods The processes of ignition and extinction are computed with an in-house code using a perfectly stirred reactor (PSR) model at constant pressure and enthalpy. The temporal change of species mass fraction, Yi , is calculated from dYi = ωi + νr Yim − Yi , dt
(1)
where ωi is the production of species i due to all reactions, νr is the mixing rate, and Yim is the species mass fraction of the initial mixture. The actual temperature is calculated from the enthalpy and species concentrations of the mixture using the CHEMKIN library [29]. Autoignition is reproduced by a homogeneous closed reactor with νr = 0. For the determination of the ignition delay time, the maximum OH mass fraction is used to define the moment of ignition. The process of extinction is reproduced by an open PSR with νr 0. Starting with a gas mixture in equilibrium state, i.e., with νr = 0, the mixing rate is increased linearly with time so that the hot burnt gases are mixed with cold unburnt reactants, leading to a decrease in temperature. When the temperature falls below a certain value, the reactions terminate and the temperature drops to the temperature of the unburnt gases; i.e., extinction occurs. The lowest value of the mixing rate for which extinction occurs is called the extinction limit, νr,ext . The predicted extinction behavior is to some degree dependent on the gradient dνr /dt. However, its influence becomes negligible for dνr /dt < 105 s−2 . A gradient of dνr /dt = 104 s−2 is used in the present calculations. Calculations of freely propagating one-dimensional laminar premixed flames have been performed using the PREMIX code [30]. This code is used to calculate laminar flame speed, species profiles, reaction flow rates, and sensitivity coefficients of the preexponential factors, Aj , of the individual reactions, j , to
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the laminar flame speed, SL : sj =
Aj ∂SL . SL ∂Aj
(2)
The effects of thermal diffusion (Soret effect) and multicomponent diffusion are included, since they are important in hydrogen combustion. The numerical method in the PREMIX code is based on a hybrid time-integration/Newton-iteration technique to solve the equations for energy and mass fractions. The largest source of errors in relation to the numerical method is the spatial discretization. The present simulations have been performed with a grid resolution of about 700–800 points, which is sufficient to produce grid-independent solutions.
3. Analysis of the detailed mechanism Typical conditions for lean premixed gas turbine combustors are a pressure of 17 bar, an equivalence ratio of 0.5, an air inlet temperature of 400 ◦ C, and a fuel inlet temperature of 15 ◦ C, resulting in a fuel/air mixture temperature of 336 ◦ C or 609 K. In the following, the processes of ignition, extinction, and laminar flame propagation under these conditions are investigated using species profiles, sensitivity analysis, and reaction flow analysis. Furthermore, several skeletal mechanisms are derived from the detailed mechanism of Li et al. [2], and the results of these mechanisms are compared with those of the full mechanism. 3.1. Laminar flames A freely propagating laminar flame in a lean H2 /air mixture at 17 bar and an initial temperature of 609 K has been computed using the PREMIX code. The calculated mole fraction profiles of the individual species are illustrated in Fig. 1. The computational domain ranges from x = 0–0.3 cm, but only the most important region around the flame front is shown. As expected, the H2 and O2 concentrations decrease, and the H2 O concentration increases within the flame front. All hydrogen is consumed at x > 0.055 cm, whereas half of the oxygen remains. The effect of differential diffusion can be clearly observed in Fig. 1a. The light hydrogen molecules strongly diffuse toward the reacted side, leading to a decrease of the hydrogen concentration at x < 0.048 cm where no reactions have occurred yet. The drop of hydrogen results in a rise of all other concentrations leading to oxygen concentrations higher than that of the initial mixture. The OH molecule is the radical with the highest concentrations, reaching far into the reacted side; see Fig. 1b. The maximum concentrations of O and H are
Fig. 1. Mole fraction, Xi , of the (a) main species and (b) radicals as a function of position, x, in a laminar H2 /air flame at φ = 0.5, 17 bar, and 609 K.
located close to that of OH, but the absolute values are much smaller. The amounts of HO2 and particularly of H2 O2 are generally very small, but their maxima are located closer to the unreacted side so that these two species are the radicals with the highest concentrations at x < 0.052 cm. This effect can be explained by an accumulation of these two species prior to ignition, which will be discussed in more detail in Section 3.2. Computations of freely propagating laminar flames have also been performed for a stoichiometric mixture at 17 bar and for atmospheric mixtures at various equivalence ratios (not shown here). The amount of H radicals strongly increases with equivalence ratio, while O and OH have their highest concentrations under stoichiometric conditions. Under atmospheric conditions, the H concentrations are much higher than at 17 bar, so that the dominance of OH for fuel-lean conditions vanishes, and the amounts of HO2 and H2 O2 are even smaller than at 17 bar. Briones et al. [13,14] also found H, O, and OH to be the major intermediate species in counterflow H2 /air partially premixed flames. The PREMIX code was further used to calculate the contribution of each reaction in Table 1 to the
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Fig. 2. Contribution of each reaction to the molar conversion, dni /dt , of several species for a lean laminar H2 /air flame at φ = 0.5, 17 bar, and 609 K.
molar conversion rate, dni /dt, of species i integrated over the whole domain. The results for the H2 /air flame at 17 bar and φ = 0.5 are presented in Fig. 2. Positive and negative values of the conversion rate mean that the species is formed and consumed by the reaction, respectively. The conversion rates of the main species are most important, since these are the initial reactants and the main product of the overall reaction, respectively, and they are associated with the highest concentrations. The consumption of H2 in Fig. 2a is governed by reaction R3, and to a lesser degree by R2. The O2 molecule is equally consumed by reactions R1 and R9 (see Fig. 2b), indicating that
flame propagation is at least partly determined by the balance of these two reactions corresponding to the second ignition limit. Some O2 is also formed through reaction R13 and to a small amount through R12. The formation of H2 O is dominated by reaction R3, and to a lesser degree by R13 and R8 (see Fig. 2c). Small amounts of H2 O are also consumed through R4. As shown in the species profiles in Fig. 1b, the OH molecule is the most important radical in the considered flame, followed by the species H and O. The OH radical is mainly consumed by reaction R3 and formed by R1 (see Fig. 2d). However, the reactions R2, R4, R11, and R13 also contribute to the con-
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Fig. 3. Sensitivity coefficients, sj , of the reactions in Table 1 to the laminar flame speed, SL , of a lean H2 /air mixture at φ = 0.5, 17 bar, and 609 K.
Fig. 4. Laminar flame speed, SL , as a function of equivalence ratio, φ, for lean H2 /air mixtures at 17 bar and 609 K; computed with the full and three skeletal mechanisms.
version of OH. The H radical in Fig. 2e is equally consumed by reactions R1 and R9 and mainly formed by R3, whereas reactions R2, R8, and R11 have some minor influence. The O radical is solely formed by reaction R1 and mainly consumed by R2, and in small amounts by R4 and R12; see Fig. 2f. On the whole, reactions R1, R3, and R9 dominate the overall reaction flow, but reactions R2, R4, R8, R11, and R13 are also relevant. Briones et al. [13,14] achieved similar results in counterflow H2 /air partially premixed flames where the consumption of reactants occurred primarily through reactions R1, R2, R3, and R9. However, in contrast to the lean premixed flame investigated in the present study, they found reaction R5 to be of some relevance for H2 formation because the main reaction zone of the partially premixed flames was located in the fuel-rich regime. The PREMIX code was used to calculate the sensitivity of the preexponential factor, Aj , of each reaction, j , in Table 1 to the laminar flame speed, SL . The sensitivity coefficients, sj , for the lean H2 /air mixture at 17 bar and 609 K are shown in Fig. 3. The reactions R1 and R9 have the largest impact on the laminar flame speed. An increase of the reaction rate of R1 will enhance flame speed to the same degree as an increase of the reaction rate of R9 will lower the flame speed. Hence, the propagation of the flame is to a large degree controlled by the competition of these two reactions corresponding to the second ignition limit, as stated previously. In addition to R1, reaction R3 also strongly enhances the flame speed. Furthermore, reactions R2, R8, R11, and R13 have significant sensitivity on flame speed. Except for a small negative contribution of R19, the sensitivity of all reactions, including H2 O2 , is very small. Hence, H2 O2 seems to play a negligible role under these conditions. The calculated sensitivity coefficients for a stoichiometric H2 /air mixture at 17 bar (not shown here)
are very similar. However, the importance of reaction R9 is much lower, while that of R8 becomes higher. The same reactions are also relevant for atmospheric mixtures, however, with varying effect. In fuel-rich conditions, the flame speed is dominated by reaction R1, whereas reaction R3 has the greatest impact for fuel-lean conditions. The sensitivities of reactions R2, R11, and R13 decrease with increasing equivalence ratio. The strongest dependency on φ can be observed for R9. This reaction has the largest negative impact for φ = 0.5 and shifts to a positive contribution for stoichiometric and fuel-rich mixtures. Reaction R5 is only significant under fuel-rich conditions. Compared to the flames at 17 bar, the sensitivities to reactions R2, R3, R11, and R13 are higher, while those to R1 and R9 are lower. Hence, the second ignition limit seems to play a more pronounced role at elevated pressures. Brown et al. [12] identified almost the same reactions to show significant sensitivity on the laminar flame speed of atmospheric H2 /air flames. In the fuel-lean regime (φ ≈ 0.7), the flame speed was enhanced by reactions R3, R2, R11, and R1 (ordered by decreasing sensitivity) and decelerated by R10. They also found reaction R5 only significant in the fuelrich regime. The sensitivity of R9 was almost zero at φ = 0.7, but strongly decreased with decreasing φ. Hence, R9 could be expected to reach large negative values for φ < 0.7. Based on the previous results, several skeletal mechanisms are tested for an accurate prediction of the laminar flame speed. Reactions R1, R2, R3, R9, and R11 show the highest sensitivity to flame speed. Also including R10 as an initiation step, the resulting 6-step mechanism is taken as a basis for further inclusions of other reactions. The computed laminar flame speed for lean H2 /air mixtures at 17 bar and 609 K in the range φ = 0.3–0.7 using the full and several skeletal mechanisms is shown in Fig. 4. The basic 6-step mechanism strongly overpredicts the laminar
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flame speed, which can be explained by the absence of reactions R8 and R13, both of which have negative sensitivities to flame speed, as shown in Fig. 3. Including reaction R8, the resulting 7-step mechanism significantly improves the results, but still performs badly particularly for very lean mixtures. Adding reaction R13, the resulting 8-step mechanism yields satisfactory results for the whole equivalence ratio range investigated. The inclusion of all reactions including H2 O2 (R14–R19) has a negligible influence on the results (not shown in Fig. 4), confirming that H2 O2 has only a minor effect on the laminar flame speed. Computations of the laminar flame speed have also been performed for atmospheric H2 /air mixtures at 298 K in the range φ = 0.3–2.0 (not shown here). The trends for the different skeletal mechanisms are the same as for 17 bar. The differences between the results of the full and the 8-step mechanism are very small for lean mixtures, but increase slightly on the fuel-rich side, most probably because reaction R5 becomes significant. 3.2. Ignition Furthermore, autoignition of H2 /air mixtures at 17 bar and φ = 0.5 is considered. At an initial temperature of 609 K, the calculated ignition delay time is greater than 100 s and therefore too large to be relevant for gas turbine combustors. However, in real applications, the reactants are heated by recirculated hot flue gas, so that ignition will take place at temperatures higher than that of the initial fuel/air mixture. The ignition process strongly depends on whether the mixture temperature lies above or below the crossover temperature. Hence, autoignition calculations using a homogeneous reactor model have been performed for both cases. The computed mole fraction profiles of the radicals for a lean H2 /air mixture at 17 bar and 1300 K, which lies above the crossover temperature, are illustrated in Fig. 5. Looking at the absolute values in Fig. 5a, the ignition process seems to be dominated by the H, OH, and O radicals, whereas the HO2 and H2 O2 concentrations seem to be negligibly small. Fig. 5b shows exactly the same results as Fig. 5a. However, a different scale is used for the y-axis to highlight the very low radical concentrations prior to ignition (i.e., at t < 0.003 ms). The HO2 radical is accumulated first, followed by a rapid increase of H radicals. Above the crossover temperature, the H radicals react with O2 primarily through the chain-branching reaction R1, so that ignition occurs almost immediately, and HO2 is quickly consumed by H through R10 and R11. Hence, only small amounts of H2 O2 are formed at this high temperature. Autoignition results for an atmospheric H2 /air mixture at 1000 K
Fig. 5. Mole fraction, Xi , of the radicals as a function of time, t , for the ignition of a lean H2 /air mixture at φ = 0.5, 17 bar, and 1300 K.
(not shown here) exhibit the same qualitative behavior, since the temperature also lies above crossover. However, the importance of the H radical is much higher. The computed mole fraction profiles of the radicals for a lean H2 /air mixture at 17 bar and 900 K are illustrated in Fig. 6. At this temperature below crossover, the H radicals react with O2 primarily through the chain termination reaction R9, so that HO2 is formed and further reacts to H2 O2 . Hence, the H, OH, and O radicals remain at very low concentrations for more than 100 ms, whereas the accumulation of the radical pool is dominated by H2 O2 , and to a lesser degree by HO2 (see Fig. 6b). Once the radical pool is large enough to start ignition, the concentrations of H, OH, and O reach the highest absolute values, and the conversion of H2 lasts only 0.01 ms, as shown in Fig. 6a. Similar results have also been obtained for an atmospheric H2 /air mixture at 900 K (not shown here). In addition to an increased importance of the H radical, the fraction of HO2 in the radical pool prior to ignition is much higher than at 17 bar. The ignition delay times of H2 /air mixtures at 17 bar with φ = 0.5 have been computed using the full and three different skeletal mechanisms. The cal-
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nism strongly overpredicts the ignition delay time. The errors stay the same when all reactions without H2 O2 (R1–R13) are applied, supporting the observations in Fig. 6b that H2 O2 has a significant influence on ignition in this temperature range. Including reactions R15 and R17 in the 6-step mechanism, the resulting 8-step∗ mechanism slightly underpredicts the ignition delay times below the crossover temperature (note that this 8-step∗ mechanism differs from the 8-step mechanism in the previous section). If reaction R14 is used additionally, the resulting 9-step mechanism yields excellent agreement with the full mechanism over the whole temperature range investigated. The present results for autoignition are in good agreement with previous work on inhomogeneous ignition in counterflow diffusion flames. Helenbrook et al. [15] and Kreutz and Law [16] found skeletal mechanisms including the same reactions as in the basic 6-step mechanism adequate to determine ignition at temperatures above the crossover temperature. Exactly the same reactions as in the present 9-step mechanism were used by Kreutz and Law [16], yielding excellent results for ignition of H2 /air flames at all three ignition limits. 3.3. Extinction Fig. 6. Mole fraction, Xi , of the radicals as a function of time, t , for the ignition of a lean H2 /air mixture at φ = 0.5, 17 bar, and 900 K.
Fig. 7. Ignition delay time, τign , as a function of the inverse of the temperature, 1000/T , for lean H2 /air mixtures at φ = 0.5 and 17 bar; computed with the full and three different skeletal mechanisms.
culated ignition delay time as a function of the inverse of the temperature, 1000/T , is shown in Fig. 7. The basic 6-step mechanism including reactions R1, R2, R3, R9, R10, and R11 yields very good agreement with the full mechanism above the crossover temperature, ∼1250 K (1000/T ≈ 0.8 K−1 ). However, below the crossover temperature, the basic 6-step mecha-
The process of extinction for a lean H2 /air mixture at 17 bar and 609 K has been studied using a PSR model. The calculated mole fractions, Xi , in the PSR as a function of mixing rate are illustrated in Fig. 8. At νr = 0 the mixture is in equilibrium, so that XH2 ≈ 0. With increasing mixing rate, the concentration of the reactants H2 and O2 increases while the product H2 O decreases until only reactants are left after extinction for νr > νr,ext . The OH molecule is the most important radical at very low mixing rates, whereas the H radical dominates the radical pool for νr > 104 s−1 up to extinction. The O concentrations generally lie somewhere in between. The concentrations of HO2 and H2 O2 are generally very small. The computed temperature in the PSR as a function of mixing rate for the full and various skeletal mechanisms is shown in Fig. 9. The basic 6-step mechanism strongly underpredicts the PSR temperature and overpredicts the extinction limit by 3.8%. Hence, the reactions having the largest impact on the PSR results have been sequentially added to the 6-step mechanism. Including reaction R8, the resulting 7step mechanism significantly improves the calculated temperature distributions and reduces the error for the predicted extinction limit to 2.8%. An accurate PSR temperature is achieved by adding the two reactions R7 and R13 constituting a 9-step∗ mechanism (note that this 9-step∗ mechanism differs from the 9-step mechanism in the previous section). However, the de-
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Table 2 Maximum percent weighted mole fractions of the radicals in a laminar H2 /air flame at 17 bar, 609 K, and φ = 0.5 H
O
OH
HO2
H2 O2
0.42
0.19
0.51
0.07
0.03
Similar results have been obtained for a stoichiometric H2 /air mixture at atmospheric pressure (not shown here), where the extinction limit is accurately predicted even by the 9-step∗ mechanism. Sohn et al. [31] identified almost the same reactions to show high sensitivity on the extinction strain rate in H2 /O2 diffusion flames at 50 atm. However, their reaction mechanism included an additional reaction, while reaction R7 was not accounted for. In contrast to the lean premixed flame of the present study, they found no effect of reaction R4, whereas R5 showed a slightly positive sensitivity to the extinction strain rate, since part of the reaction zone was located on the fuel-rich side.
4. Reduction of the mechanism
Fig. 8. Mole fractions, Xi , in a PSR as a function of mixing rate, νr , for a lean H2 /air mixture at φ = 0.5, 17 bar, and 609 K.
The investigations of the detailed mechanism show that the reactions R1, R2, R3, R8, R9, R10, R11, R13, R14, R15, and R17 have to be included in a skeletal mechanism that will satisfactorily represent the processes of ignition, extinction, and laminar flame propagation. However, the resulting 11-step mechanism will probably not yield the envisaged reduction of computational effort within CFD calculations, compared to the full 19-step mechanism. Hence, a further reduction of the skeletal mechanism using steady-state approximations is performed below. 4.1. Steady-state approximations
Fig. 9. Temperature, T , in a PSR as a function of mixing rate, νr , for a lean H2 /air mixture at φ = 0.5, 17 bar, and 609 K; computed with the full and three skeletal mechanisms.
viation for the extinction limit from the full mechanism is still as high as 2.1%. The inclusion of at least two more reactions, R4 and R12, is necessary to yield an exact prediction of the extinction limit (not shown in Fig. 9). The inclusion of all reactions with H2 O2 (R14–R19) does not change the results, indicating that H2 O2 has no effect on extinction.
A species can be assumed to be in steady state when the reactions consuming the species are much faster than the transport processes within the flame. An indicator for this criterion is the maximum concentration of the species. Peters [32] considered all species with a weighted mole fraction, Xw , less than 1% to be in steady state. The laminar H2 /air flame investigated in Section 3.1 is used as a basis for the reduction of the mechanisms. The maximum weighted mole fractions of the radicals have been derived from the maximum mole fractions in Fig. 1 and are listed in Table 2. All radicals have values less than 1%, so that a lower limit has to be defined for the present flame. The OH molecule has the largest values, and the highest OH concentrations in Fig. 1b reach far into the burnt mixture. Hence, the OH radical should not be assumed to be in steady state. The weighted
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H mole fraction is close to that of OH, so that a steady-state assumption for H is not acceptable either. The weighted O mole fraction is significantly lower than that of OH and H. However, a steady-state assumption for O cannot necessarily be made and has to be further investigated. The HO2 and H2 O2 radicals may be assumed to be in steady state in this flame, since their mole fractions are below 0.1%. The steady-state assumption implies that the overall reaction rate of a species is zero. For each steadystate species, one reaction rate can then be expressed as a function of other reaction rates. Usually, the rate of the fastest reaction consuming the steady-state species is eliminated [32]. For an estimated temperature of 1500 K in the main reaction zone, these reactions are R13 for HO2 , R17 for H2 O2 , and R2 for O. Following the procedure described by Peters [32], a 4-step reduced mechanism similar to that of Balakrishnan et al. [21] can be derived from the 11-step skeletal mechanism using the steady-state assumption for HO2 and H2 O2 , H + O2 OH + O, ωI = r1 + r11 + r15 , O + H2 H + OH, ωII = r2 + r11 + r15 , OH + H2 H + H2 O, ωIII = r3 + r8 + r9 − r10 − r11 − r14 − r15 , H + H H2 , ωIV = r8 + r9 − r15 , where rj is the rate of the elementary reaction Rj , and ωk is the overall rate of the global reaction. Applying an additional steady-state assumption for the O radical, a 3-step reduced mechanism similar to that of Balakrishnan et al. [21] can be derived: H2 + O2 OH + OH, ωI = r1 + r11 + r15 , OH + H2 H + H2 O, ωII = r3 + r8 + r9 − r10 − r11 − r14 − r15 , H + H H2 , ωIII = r8 + r9 − r15 . It has to be noted that the number of steps in the reduced mechanisms indicates the number of independent conservation equations to be solved, whereas the number of steps in the skeletal mechanisms corresponds to the number of elementary reactions. In the following, the reduced 3-step and 4-step mechanisms are compared with the skeletal 11-step and the full
Fig. 10. Laminar flame speed, SL , as a function of equivalence ratio, φ, for lean H2 /air mixtures at 17 bar and 609 K; computed with the full, the 11-step skeletal, and two reduced mechanisms.
mechanism using laminar flame, ignition, and extinction calculations. 4.2. Laminar flame speed The reduced mechanisms have been applied to laminar flame-speed calculations using the PREMIX code. The computed laminar flame speed for a lean H2 /air mixture at 17 bar and 609 K is shown in Fig. 10. The 11-step skeletal mechanism is almost identical to the behavior of the 8-step mechanism in Fig. 4. The results of the 4-step mechanism are in excellent agreement with those of the 11-step skeletal mechanism for equivalence ratios higher than 0.5. The deviation increases for leaner mixtures up to a relative error of 79% for φ = 0.3 at a very low absolute value of the flame speed. However, for the most relevant equivalence ratio at φ = 0.5, the deviation is as low as 1.6%, showing that the steady-state assumption for HO2 and H2 O2 is justified for laminar flamespeed calculations under gas turbine conditions. The results of the 3-step mechanism are almost identical to those of the 4-step mechanism for very lean mixtures. However, the deviation from the 4-step mechanism increases with increasing equivalence ratio up to 6.6% at φ = 0.7. The deviation from the 11-step skeletal mechanism at φ = 0.5 is 4.9%. Hence, the steady-state assumption for O is acceptable under the restriction of approximately 5% uncertainty for laminar flame propagation. The effect of pressure on laminar flame speed for H2 /air mixtures at φ = 0.5 is illustrated in Fig. 11. An exponential decrease of flame speed with increasing pressure is observed for all mechanisms. The absolute deviation of the results of the 11-step mechanism from those of the full mechanism is approximately constant. The results of the 4-step mechanism are in excellent agreement with those of the full mechanism
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Fig. 11. Laminar flame speed, SL , as a function of pressure, p, for H2 /air mixtures at φ = 0.5 and 609 K; computed with the full, the 11-step skeletal, and two reduced mechanisms.
Fig. 12. Laminar flame speed, SL , as a function of temperature, T , for H2 /air mixtures at φ = 0.5 and 17 bar; computed with the full, the 11-step skeletal, and two reduced mechanisms.
up to 12 bar. Above this value, the deviation between these two mechanisms slightly increases due to the increasing importance of HO2 and H2 O2 at high pressures. In contrast, the error of the 3-step mechanism is greatest at low pressures. The effect of temperature on laminar flame speed for H2 /air mixtures at φ = 0.5 is illustrated in Fig. 12. An exponential increase of flame speed with increasing temperature is observed for all mechanisms. The agreement between the results of the different mechanisms is generally good at low temperatures, and the deviations slightly increase above 700 K. 4.3. Ignition delay Autoignition of lean H2 /air mixtures with φ = 0.5 at 17 bar has been investigated using a homogeneous reactor model. The computed ignition delay times as a function of the inverse of the temperature, 1000/T , for the full and reduced mechanisms are shown in Fig. 13. The results of the 11-step skele-
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Fig. 13. Ignition delay time, τign , as a function of the inverse of the temperature, 1000/T , for H2 /air mixtures at 17 bar and φ = 0.5; computed with the full, the 11-step skeletal, and two reduced mechanisms.
tal mechanism are in excellent agreement with those obtained from the full mechanism. The 4-step mechanism generally underpredicts ignition delay, particularly below the crossover temperature, where the error is several orders of magnitude. This result reflects the observations in Section 3.2 that the accumulation of the radical pool is mainly dominated by HO2 and H2 O2 . Hence, a steady-state assumption for HO2 and H2 O2 is not justified for low-temperature ignition. The 3-step mechanism follows the trend of the 4-step mechanism with some larger deviations at high temperatures. Thus, a steady-state assumption for O seems to be acceptable for ignition at low temperatures, but leads to significant errors above 1100 K. Other researchers used different reduced mechanisms for ignition in H2 /air counterflow diffusion flames. Sohn and Chung [23] suggested a 4-step mechanism applying steady-state approximations to O and OH for diluted flames. Kreutz and Law [16] found a 4-step reduced mechanism assuming steady state for O and OH to underpredict ignition temperatures. By removing the steady-state approximation for O, the corresponding 5-step reduced mechanism yielded much better results for first-limit ignition temperatures. However, the results in Section 3.1 show that steady-state assumptions for O and particularly for OH are not favorable when other processes such as extinction or flame propagation become relevant. Since ignition under gas turbine combustors is expected to take place in the high-temperature regime, the steady-state assumption for HO2 and H2 O2 might probably yield reasonable results within corresponding CFD calculations. 4.4. Extinction limit The process of extinction for a lean H2 –air mixture at 17 bar and 609 K is investigated using per-
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conditions of a typical lean premixed gas turbine combustor, i.e., H2 /air mixtures at φ = 0.5, 17 bar, and 609 K. The main results are summarized as follows:
Fig. 14. Temperature, T , in a PSR as a function of mixing rate, νr , for a lean H2 /air mixture at φ = 0.5, 17 bar, and 609 K; computed with the full, the 11-step skeletal, and two reduced mechanisms.
fectly stirred reactor (PSR) calculations. The computed PSR temperature as a function of mixing rate using the mechanisms under consideration is shown in Fig. 14. The 11-step skeletal mechanism satisfactorily reflects the trend of the full mechanism. The 4-step mechanism is in excellent agreement with the 11-step mechanism (the lines in Fig. 14 are not distinguishable). Hence, a steady-state assumption is to HO2 and H2 O2 is justified for the prediction of extinction. This can be explained by the very small amounts of HO2 and H2 O2 in the PSR calculations in Fig. 8. The 3-step mechanism generally overpredicts the temperature in the PSR and therefore also the extinction limit. Hence, a steady-state assumption for the O radical leads to significant errors for extinction calculations. The reason for these errors is probably the relatively high O molar concentration of approximately 1% shown in Fig. 8. Other researchers obtained corresponding results for extinction in laminar nonpremixed counterflowing H2 /air flames. Balakrishnan et al. [21] obtained a similar 4-step mechanism using steady-state approximations for HO2 and H2 O2 that accurately reproduced the dependence of the maximum flame temperature on the strain rate. Furthermore, they found the OH and O steady states to be inaccurate. Sohn and Chung [23] obtained good results on the extinction strain rate for the 4-step mechanism assuming steady state for HO2 and H2 O2 , but they also achieved good results for a 2-step mechanism assuming steady state for O and OH.
5. Conclusions The detailed reaction mechanism of Li et al. [2] for hydrogen combustion has been analyzed, and several reduced mechanisms have been tested under the
• In a freely propagating laminar flame, OH is the radical with the highest concentrations, whereas H and O are also important. The amounts of HO2 and particularly of H2 O2 are relatively small. Flame propagation is to a large degree controlled by the competition of reactions R1 and R9 corresponding to the second ignition limit. In addition, reaction R2 and R3, and to a less degree reactions R4, R8, R11, and R13 are also important. An 8step skeletal mechanism including reactions R1, R2, R3, R8, R9, R10, R11, and R13 yields satisfactory results for the laminar flame speed in the range φ = 0.3–0.7. • For the process of extinction in a perfectly stirred reactor (PSR), the H radical is the dominating radical, followed by OH and O. The HO2 and H2 O2 concentrations are very small, and the effect of the H2 O2 reactions is negligible. A 7-step skeletal mechanism including reactions R1, R2, R3, R8, R9, R10, and R11 yields a satisfactory prediction of the PSR temperature for varying mixing rate and of the extinction limit. However, the inclusion of four additional reactions is necessary for an exact prediction of the extinction limit. • In autoignition calculations, H, O, and OH are also the radicals with the highest concentrations. However, the accumulation of the radical pool is dominated by HO2 for temperatures above, and by H2 O2 below the crossover temperature. A 9step mechanism including reactions R1, R2, R3, R9, R10, R11, R14, R15, and R17 yields excellent agreement with the full mechanism for the calculation of the ignition delay time over a large temperature range. • The present investigations show that at least 11 elementary reactions are necessary for satisfactory prediction of the processes of ignition, extinction, and laminar flame propagation under gas turbine conditions. A reduced 4-step mechanism assuming steady state for HO2 and H2 O2 yields accurate results for a laminar flame and extinction, but is not able to predict low-temperature ignition. Nevertheless, the 4-step mechanism might yield reasonable results for gas turbine combustor simulations since ignition is expected to take place in the high temperature regime. A reduced 3-step mechanism assuming steady state for the O radical introduces additional errors for all of these processes. The application of these mechanisms to CFD calculations of turbu-
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lent flames and gas turbine combustors will be examined in further work.
Acknowledgments This study was funded within the ENCAP project in the European 6th Framework Program and within the Climit programme operated by the Norwegian Research Council and Gassnova. The authors thank Professor F.L. Dryer at Princeton University for providing his chemical data.
References [1] M.A. Mueller, T.J. Kim, R. Yetter, F. Dryer, Int. J. Chem. Kinet. 31 (1999) 113–125. [2] J. Li, Z. Zhao, A. Kazakov, F. Dryer, Int. J. Chem. Kinet. 36 (2004) 566–575. [3] M. O’Conaire, H.J. Curran, J.M. Simmie, W.J. Pitz, C.K. Westbrook, Int. J. Chem. Kinet. 36 (2004) 603– 622. [4] G. Del Álamo, F.A. Williams, A.L. Sánchez, Combust. Sci. Technol. 176 (2004) 1599–1626. [5] A.A. Konnov, Khim. Fiz. 23 (2004) 5–18. [6] S. Davis, A. Joshi, H. Wang, F. Egolfopoulos, Proc. Combust. Inst. 30 (2005) 1283–1292. [7] T. Myhrvold, J. Ströhle, Ø. Langørgen, in: Proc. 26th Task Leader Meeting, IEA Implementing Agreement on Energy Conservation and Emission Reduction in Combustion, Helsinki, Finland, 2004. [8] J. Ströhle, T. Myhrvold, in: Proc. European Combustion Meeting, Louvain-la-Neuve, Belgium, 2005. [9] T.G. Kreutz, C.K. Law, Combust. Flame 104 (1996) 157–175. [10] X.L. Zheng, J.D. Blouch, D.I. Zhu, T.G. Kreutz, C.K. Law, Proc. Combust. Inst. 29 (2002) 1637–1643. [11] X.L. Zheng, C.K. Law, Combust. Flame 136 (2004) 168–179. [12] M.J. Brown, D.B. Smith, S.C. Taylor, Combust. Flame 117 (1999) 652–656. [13] A. Briones, I.K. Puri, S.K. Aggarwal, Combust. Flame 140 (2005) 46–59.
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[14] A.M. Briones, S.K. Aggarwal, Int. J. Hydrogen Energy 30 (2005) 327–339. [15] B.T. Helenbrook, H.G. Im, C.K. Law, Combust. Flame 112 (1998) 242–252. [16] T.G. Kreutz, C.K. Law, Combust. Flame 114 (1998) 436–456. [17] N. Peters, R.J. Kee, Combust. Flame 68 (1987) 17–29. [18] J. Warnatz, U. Maas, R.W. Dibble, Combustion, Springer-Verlag, Berlin, 2003. [19] E. Gutheil, F.A. Williams, Proc. Combust. Inst. 23 (1990) 513–521. [20] G. Balakrishnan, C. Treviño, F. Mauss, Combust. Flame 91 (1991) 246–256. [21] G. Balakrishnan, M.D. Smooke, F.A. Williams, Combust. Flame 102 (1995) 329–340. [22] C. Treviño, A. Liñán, Combust. Flame 103 (1995) 129– 141. [23] C.H. Sohn, S.H. Chung, Combust. Flame 121 (2000) 288–300. [24] J.-Y. Chen, W. Kollmann, Combust. Flame 79 (1990) 75–99. [25] U. Maas, J. Warnatz, Proc. Combust. Inst. 22 (1988) 1695–1704. [26] T. Lu, Y. Ju, C.K. Law, Combust. Flame 126 (2001) 1445–1455. [27] L. Elliott, D.B. Ingham, A.G. Kyne, N.S. Mera, M. Pourkashanian, C.W. Wilson, Prog. Energy Combust. Sci. 30 (2004) 297–328. [28] R.L.G.M. Eggels, L.P.H. de Goey, Combust. Flame 100 (1995) 559–570. [29] R.J. Kee, F.M. Rupley, E. Meeks, J.A. Miller, CHEMKIN-III: A Fortran chemical kinetics package for the analysis of gas-phase chemical and plasma kinetics, Report SAND96-8218, Sandia National Laboratories, Livermore, 1996. [30] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, A Fortran program for modeling steady laminar onedimensional premixed flames, Report SAND85-8240, Sandia National Laboratories, Livermore, 1985. [31] C.H. Sohn, S.H. Chung, S.R. Lee, J.S. Kim, Combust. Flame 115 (1998) 299–312. [32] N. Peters, in: A.L. Kuhl, J. Bowen, J. Leyer, A. Borisov (Eds.), Dynamics of Reactive Systems, Part I, Prog. Astronautics and Aeronautics, AIAA, Washington, DC, 1988, pp. 67–86.
Reduction of a detailed reaction mechanism for hydrogen combustion under gas turbine conditions Jochen Ströhle ∗ , Tore Myhrvold SINTEF Energy Research, 7465 Trondheim, Norway Received 23 March 2005; received in revised form 14 July 2005; accepted 11 August 2005 Available online 27 September 2005
Abstract The aim of this study is to find a reduced mechanism that accurately represents chemical kinetics for lean hydrogen combustion at elevated pressures, as present in a typical gas turbine combustor. Calculations of autoignition, extinction, and laminar premixed flames are used to identify the most relevant species and reactions and to compare the results of several reduced mechanisms with those of a detailed reaction mechanism. The investigations show that the species OH and H are generally the radicals with the highest concentrations, followed by the O radical. However, the accumulation of the radical pool in autoignition is dominated by HO2 for temperatures above, and by H2 O2 below the crossover temperature. The influence of H2 O2 reactions is negligible for laminar flames and extinction, but becomes significant for autoignition. At least 11 elementary reactions are necessary for a satisfactory prediction of the processes of ignition, extinction, and laminar flame propagation under gas turbine conditions. A 4-step reduced mechanism using steady-state approximations for HO2 and H2 O2 yields good results for laminar flame speed and extinction limits, but fails to predict ignition delay at low temperatures. A further reduction to three steps using a steady-state approximation for O leads to significant errors in the prediction of the laminar flame speed and extinction limit. 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Hydrogen combustion; Modeling; Reduced mechanism; Gas turbine
1. Introduction In the context of reducing CO2 emissions from power production, hydrogen has recently drawn increased attention as a clean fuel. However, the use of hydrogen in gas turbine combustors is not straightforward since hydrogen has some characteristics that strongly deviate from those of the main components of conventional fuels, such as methane. Hydrogen is strongly exposed to molecular diffusion processes * Corresponding author. Fax: +47 7359 2889.
E-mail address: [email protected] (J. Ströhle).
and has a wide flammability range, short ignition times, and a high laminar flame speed. The relatively high adiabatic temperatures of H2 /air mixtures might cause large amounts of thermal NOx in the flame. The flame temperature, and therefore NOx emissions, can be reduced by lean premixing of fuel and air. However, the high reactivity and flame speed of premixed H2 /air mixtures enhance the danger of autoignition and flashback, respectively. Computational fluid dynamics (CFD) have evolved to serve as a design tool for combustors. The flow in gas turbine combustors is strongly turbulent, and turbulent combustion is strongly influenced by the
0010-2180/$ – see front matter 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2005.08.011
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Table 1 Hydrogen mechanism of Li et al. [2] in the form k = AT n exp(−E/RT ) for N2 as the main bath gas (units are cm, moles, s, cal, K) No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Reaction
A
n
E
H + O2 = O + OH O + H2 = H + OH H2 + OH = H2 O + H O + H2 O = OH + OH H 2 + M = H + H + Ma O + O + M = O2 + M a O + H + M = OH + Ma H + OH + M = H2 O + Ma H + O2 + M = HO2 + Mb
3.547 × 1015 0.508 × 1005 0.216 × 1009 2.970 × 1006 4.577 × 1019 6.165 × 1015 4.714 × 1018 3.800 × 1022 1.475 × 1012 6.366 × 1020 1.660 × 1013 7.079 × 1013 0.325 × 1014 2.890 × 1013 4.200 × 1014 1.300 × 1011 2.951 × 1014 1.202 × 1017 0.241 × 1014 0.482 × 1014 9.550 × 1006 1.000 × 1012 5.800 × 1014
−0.406 2.67 1.51 2.02 −1.40 −0.50 −1.00 −2.00 0.60 −1.72 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.0
16,599 6290 3430 13,400 104,380 0 0 0 0 524.8 823 295 0 −497 11,982 −1629.3 48,430 45,500 3970 7950 3970 0 9557
HO2 + H = H2 + O2 HO2 + H = OH + OH HO2 + O = O2 + OH HO2 + OH = H2 O + O2 HO2 + HO2 = H2 O2 + O2 HO2 + HO2 = H2 O2 + O2 H2 O2 + M = OH + OH + Mc H 2 O2 H 2 O2 H 2 O2 H 2 O2 H 2 O2
+ H = H2 O + OH + H = HO2 + H2 + O = OH + HO2 + OH = HO2 + H2 O + OH = HO2 + H2 O
k∞ k0
k∞ k0
a Third body enhancement factors: H = 2.5, H O = 12. 2 2 b Third body enhancement factors: H = 2, H O = 11, O = 0.78; Troe parameter: 0.8. 2 2 2 c Third body enhancement factors: H = 2.5, H O = 11; Troe parameter: 0.5. 2 2
processes of ignition, extinction, and flame propagation. Detailed kinetic mechanisms are necessary to predict these processes. However, the use of detailed reaction mechanisms for turbulent combustion in CFD is computationally very expensive. Although a detailed mechanism for H2 /air combustion typically consists of only 8 species and 19 reactions, the elimination of some species or reactions might lead to a significant reduction in computational effort. The aim of this study is to find a reduced mechanism that accurately represents chemical kinetics for lean hydrogen combustion at elevated pressures as present in a typical gas turbine combustor. Detailed mechanisms for H2 /O2 combustion have been developed by several researchers, e.g., [1–6]. Recently, Li et al. [2] updated the H2 /O2 mechanism of Mueller et al. [1] and validated it against a wide range of experimental conditions (298–3000 K, 0.3– 87 atm, φ = 0.25–5.0) found in laminar premixed flames, shock tubes, and flow reactors. This mechanism is chosen for the present investigations because it was found to accurately represent H2 /O2 kinetics under gas turbine conditions [7,8]. The reaction mechanism is shown in Table 1. In the following, a re-
action of this mechanism is referred to by prefixing the letter R. A detailed reaction mechanism can be reduced by several means. The most straightforward way is to eliminate reactions that only negligibly influence the overall combustion process constituting a skeletal mechanism. Kreutz and Law [9] identified the most relevant reactions for inhomogeneous ignition. Reactions R1 and R2 are the most important chain branching steps, R3 is responsible for fast chain propagation, and R9 is the most important chain termination step. In the low-pressure regime, the reaction progress is determined by the balance of reactions R1 and R9. The corresponding increase of ignition temperature with pressure is called the second ignition limit. The temperature where both reaction rates are equal is also called the crossover temperature. In the high-pressure regime, H2 O2 formation and decomposition through reactions R14, R15, and R17 becomes relevant. The corresponding decrease of ignition temperatures with pressure constitutes the third ignition limit. Although these ignition limits have been derived by investigating nonpremixed flames, Zheng et al. [10] found the same ignition characteristics to be valid for the premixed case. Furthermore, Zheng and Law [11] ob-
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served two more ignition limits at even higher pressures for a lean premixed flame. Brown et al. [12] identified reactions R1, R2, R3, R5, R9, R10, and R11 to show significant sensitivity on the laminar flame speed of atmospheric H2 /air flames. Briones et al. [13,14] showed that the consumption of reactants in counterflow H2 /air partially premixed flames primarily occurs through reactions R1, R2, R3, and R9. Helenbrook et al. [15] found a skeletal mechanism with seven elementary single steps adequate to determine the ignition of counterflowing H2 /O2 at temperatures above crossover. Kreutz and Law [16] applied several skeletal mechanisms to ignition in nonpremixed counterflowing H2 /air. Using partial equilibrium or quasi-steady-state assumptions, the elementary reactions can be transformed to a small number of global reactions constituting a reduced mechanism [17,18]. Gutheil and Williams [19] and Balakrishnan et al. [20] investigated a hydrogen–air counterflow diffusion flame using one overall step and a 2-step mechanism, respectively. Balakrishnan et al. [21] studied extinction and ignition limits in laminar nonpremixed counterflowing hydrogen–air streams for several reduced mechanisms. They obtained a 4-step mechanism using steady-state approximations for HO2 and H2 O2 , two 3-step mechanisms using an additional steady-state approximation for either OH or O, and a 2-step mechanism assuming steady state for both OH and O. A third alternative 3-step mechanism applied steady-state approximations for all radicals except H and HO2 . Treviño and Liñán [22] analyzed high-temperature ignition in a mixing layer between hydrogen and air using two different 2-step mechanisms. Sohn and Chung [23] investigated extinction in diluted hydrogen–air counterflow diffusion flames using a 4-step mechanism applying steady-state approximations to O and OH, a 3-step mechanism assuming steady state for H2 O2 , and a 4-step mechanism assuming steady states for HO2 and H2 O2 . All mechanisms predicted the extinction strain rate reasonably accurately. Kreutz and Law [16] derived several reduced mechanisms from skeletal mechanisms to study ignition in nonpremixed counterflowing hydrogen versus heated air. Chen and Kollmann [24] used several reduced hydrogen mechanisms to derive reaction progress variables for a Monte Carlo scalar pdf combustion model. Various advanced mathematical methods have been developed for a systematic reduction of large reaction mechanisms, such as eigenvalue analysis [18], the intrinsic low-dimensional manifolds (ILDM) method [25], the computational singular perturbation (CSP) method [26], and genetic algorithms [27]. Eggels and de Goey [28] reduced several hydrogen/air reaction systems to 1-step schemes using the ILDM
547
method. Lu et al. [26] employed the complex CSP method to generate a 4-step reduced mechanism for high-temperature H2 /air oxidation. The method automatically eliminated the two species HO2 and H2 O2 . Most of the previous work mentioned above has been focused on the investigation of individual phenomena, e.g., ignition, in laminar flames. However, a reduced mechanism for the application to gas turbine combustors has to account for all phenomena relevant in turbulent combustion. Hence, calculations of autoignition, extinction, and laminar premixed flames under gas turbine conditions are used in the present study to investigate a detailed reaction mechanism and to derive reduced mechanisms.
2. Numerical methods The processes of ignition and extinction are computed with an in-house code using a perfectly stirred reactor (PSR) model at constant pressure and enthalpy. The temporal change of species mass fraction, Yi , is calculated from dYi = ωi + νr Yim − Yi , dt
(1)
where ωi is the production of species i due to all reactions, νr is the mixing rate, and Yim is the species mass fraction of the initial mixture. The actual temperature is calculated from the enthalpy and species concentrations of the mixture using the CHEMKIN library [29]. Autoignition is reproduced by a homogeneous closed reactor with νr = 0. For the determination of the ignition delay time, the maximum OH mass fraction is used to define the moment of ignition. The process of extinction is reproduced by an open PSR with νr 0. Starting with a gas mixture in equilibrium state, i.e., with νr = 0, the mixing rate is increased linearly with time so that the hot burnt gases are mixed with cold unburnt reactants, leading to a decrease in temperature. When the temperature falls below a certain value, the reactions terminate and the temperature drops to the temperature of the unburnt gases; i.e., extinction occurs. The lowest value of the mixing rate for which extinction occurs is called the extinction limit, νr,ext . The predicted extinction behavior is to some degree dependent on the gradient dνr /dt. However, its influence becomes negligible for dνr /dt < 105 s−2 . A gradient of dνr /dt = 104 s−2 is used in the present calculations. Calculations of freely propagating one-dimensional laminar premixed flames have been performed using the PREMIX code [30]. This code is used to calculate laminar flame speed, species profiles, reaction flow rates, and sensitivity coefficients of the preexponential factors, Aj , of the individual reactions, j , to
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the laminar flame speed, SL : sj =
Aj ∂SL . SL ∂Aj
(2)
The effects of thermal diffusion (Soret effect) and multicomponent diffusion are included, since they are important in hydrogen combustion. The numerical method in the PREMIX code is based on a hybrid time-integration/Newton-iteration technique to solve the equations for energy and mass fractions. The largest source of errors in relation to the numerical method is the spatial discretization. The present simulations have been performed with a grid resolution of about 700–800 points, which is sufficient to produce grid-independent solutions.
3. Analysis of the detailed mechanism Typical conditions for lean premixed gas turbine combustors are a pressure of 17 bar, an equivalence ratio of 0.5, an air inlet temperature of 400 ◦ C, and a fuel inlet temperature of 15 ◦ C, resulting in a fuel/air mixture temperature of 336 ◦ C or 609 K. In the following, the processes of ignition, extinction, and laminar flame propagation under these conditions are investigated using species profiles, sensitivity analysis, and reaction flow analysis. Furthermore, several skeletal mechanisms are derived from the detailed mechanism of Li et al. [2], and the results of these mechanisms are compared with those of the full mechanism. 3.1. Laminar flames A freely propagating laminar flame in a lean H2 /air mixture at 17 bar and an initial temperature of 609 K has been computed using the PREMIX code. The calculated mole fraction profiles of the individual species are illustrated in Fig. 1. The computational domain ranges from x = 0–0.3 cm, but only the most important region around the flame front is shown. As expected, the H2 and O2 concentrations decrease, and the H2 O concentration increases within the flame front. All hydrogen is consumed at x > 0.055 cm, whereas half of the oxygen remains. The effect of differential diffusion can be clearly observed in Fig. 1a. The light hydrogen molecules strongly diffuse toward the reacted side, leading to a decrease of the hydrogen concentration at x < 0.048 cm where no reactions have occurred yet. The drop of hydrogen results in a rise of all other concentrations leading to oxygen concentrations higher than that of the initial mixture. The OH molecule is the radical with the highest concentrations, reaching far into the reacted side; see Fig. 1b. The maximum concentrations of O and H are
Fig. 1. Mole fraction, Xi , of the (a) main species and (b) radicals as a function of position, x, in a laminar H2 /air flame at φ = 0.5, 17 bar, and 609 K.
located close to that of OH, but the absolute values are much smaller. The amounts of HO2 and particularly of H2 O2 are generally very small, but their maxima are located closer to the unreacted side so that these two species are the radicals with the highest concentrations at x < 0.052 cm. This effect can be explained by an accumulation of these two species prior to ignition, which will be discussed in more detail in Section 3.2. Computations of freely propagating laminar flames have also been performed for a stoichiometric mixture at 17 bar and for atmospheric mixtures at various equivalence ratios (not shown here). The amount of H radicals strongly increases with equivalence ratio, while O and OH have their highest concentrations under stoichiometric conditions. Under atmospheric conditions, the H concentrations are much higher than at 17 bar, so that the dominance of OH for fuel-lean conditions vanishes, and the amounts of HO2 and H2 O2 are even smaller than at 17 bar. Briones et al. [13,14] also found H, O, and OH to be the major intermediate species in counterflow H2 /air partially premixed flames. The PREMIX code was further used to calculate the contribution of each reaction in Table 1 to the
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Fig. 2. Contribution of each reaction to the molar conversion, dni /dt , of several species for a lean laminar H2 /air flame at φ = 0.5, 17 bar, and 609 K.
molar conversion rate, dni /dt, of species i integrated over the whole domain. The results for the H2 /air flame at 17 bar and φ = 0.5 are presented in Fig. 2. Positive and negative values of the conversion rate mean that the species is formed and consumed by the reaction, respectively. The conversion rates of the main species are most important, since these are the initial reactants and the main product of the overall reaction, respectively, and they are associated with the highest concentrations. The consumption of H2 in Fig. 2a is governed by reaction R3, and to a lesser degree by R2. The O2 molecule is equally consumed by reactions R1 and R9 (see Fig. 2b), indicating that
flame propagation is at least partly determined by the balance of these two reactions corresponding to the second ignition limit. Some O2 is also formed through reaction R13 and to a small amount through R12. The formation of H2 O is dominated by reaction R3, and to a lesser degree by R13 and R8 (see Fig. 2c). Small amounts of H2 O are also consumed through R4. As shown in the species profiles in Fig. 1b, the OH molecule is the most important radical in the considered flame, followed by the species H and O. The OH radical is mainly consumed by reaction R3 and formed by R1 (see Fig. 2d). However, the reactions R2, R4, R11, and R13 also contribute to the con-
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Fig. 3. Sensitivity coefficients, sj , of the reactions in Table 1 to the laminar flame speed, SL , of a lean H2 /air mixture at φ = 0.5, 17 bar, and 609 K.
Fig. 4. Laminar flame speed, SL , as a function of equivalence ratio, φ, for lean H2 /air mixtures at 17 bar and 609 K; computed with the full and three skeletal mechanisms.
version of OH. The H radical in Fig. 2e is equally consumed by reactions R1 and R9 and mainly formed by R3, whereas reactions R2, R8, and R11 have some minor influence. The O radical is solely formed by reaction R1 and mainly consumed by R2, and in small amounts by R4 and R12; see Fig. 2f. On the whole, reactions R1, R3, and R9 dominate the overall reaction flow, but reactions R2, R4, R8, R11, and R13 are also relevant. Briones et al. [13,14] achieved similar results in counterflow H2 /air partially premixed flames where the consumption of reactants occurred primarily through reactions R1, R2, R3, and R9. However, in contrast to the lean premixed flame investigated in the present study, they found reaction R5 to be of some relevance for H2 formation because the main reaction zone of the partially premixed flames was located in the fuel-rich regime. The PREMIX code was used to calculate the sensitivity of the preexponential factor, Aj , of each reaction, j , in Table 1 to the laminar flame speed, SL . The sensitivity coefficients, sj , for the lean H2 /air mixture at 17 bar and 609 K are shown in Fig. 3. The reactions R1 and R9 have the largest impact on the laminar flame speed. An increase of the reaction rate of R1 will enhance flame speed to the same degree as an increase of the reaction rate of R9 will lower the flame speed. Hence, the propagation of the flame is to a large degree controlled by the competition of these two reactions corresponding to the second ignition limit, as stated previously. In addition to R1, reaction R3 also strongly enhances the flame speed. Furthermore, reactions R2, R8, R11, and R13 have significant sensitivity on flame speed. Except for a small negative contribution of R19, the sensitivity of all reactions, including H2 O2 , is very small. Hence, H2 O2 seems to play a negligible role under these conditions. The calculated sensitivity coefficients for a stoichiometric H2 /air mixture at 17 bar (not shown here)
are very similar. However, the importance of reaction R9 is much lower, while that of R8 becomes higher. The same reactions are also relevant for atmospheric mixtures, however, with varying effect. In fuel-rich conditions, the flame speed is dominated by reaction R1, whereas reaction R3 has the greatest impact for fuel-lean conditions. The sensitivities of reactions R2, R11, and R13 decrease with increasing equivalence ratio. The strongest dependency on φ can be observed for R9. This reaction has the largest negative impact for φ = 0.5 and shifts to a positive contribution for stoichiometric and fuel-rich mixtures. Reaction R5 is only significant under fuel-rich conditions. Compared to the flames at 17 bar, the sensitivities to reactions R2, R3, R11, and R13 are higher, while those to R1 and R9 are lower. Hence, the second ignition limit seems to play a more pronounced role at elevated pressures. Brown et al. [12] identified almost the same reactions to show significant sensitivity on the laminar flame speed of atmospheric H2 /air flames. In the fuel-lean regime (φ ≈ 0.7), the flame speed was enhanced by reactions R3, R2, R11, and R1 (ordered by decreasing sensitivity) and decelerated by R10. They also found reaction R5 only significant in the fuelrich regime. The sensitivity of R9 was almost zero at φ = 0.7, but strongly decreased with decreasing φ. Hence, R9 could be expected to reach large negative values for φ < 0.7. Based on the previous results, several skeletal mechanisms are tested for an accurate prediction of the laminar flame speed. Reactions R1, R2, R3, R9, and R11 show the highest sensitivity to flame speed. Also including R10 as an initiation step, the resulting 6-step mechanism is taken as a basis for further inclusions of other reactions. The computed laminar flame speed for lean H2 /air mixtures at 17 bar and 609 K in the range φ = 0.3–0.7 using the full and several skeletal mechanisms is shown in Fig. 4. The basic 6-step mechanism strongly overpredicts the laminar
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flame speed, which can be explained by the absence of reactions R8 and R13, both of which have negative sensitivities to flame speed, as shown in Fig. 3. Including reaction R8, the resulting 7-step mechanism significantly improves the results, but still performs badly particularly for very lean mixtures. Adding reaction R13, the resulting 8-step mechanism yields satisfactory results for the whole equivalence ratio range investigated. The inclusion of all reactions including H2 O2 (R14–R19) has a negligible influence on the results (not shown in Fig. 4), confirming that H2 O2 has only a minor effect on the laminar flame speed. Computations of the laminar flame speed have also been performed for atmospheric H2 /air mixtures at 298 K in the range φ = 0.3–2.0 (not shown here). The trends for the different skeletal mechanisms are the same as for 17 bar. The differences between the results of the full and the 8-step mechanism are very small for lean mixtures, but increase slightly on the fuel-rich side, most probably because reaction R5 becomes significant. 3.2. Ignition Furthermore, autoignition of H2 /air mixtures at 17 bar and φ = 0.5 is considered. At an initial temperature of 609 K, the calculated ignition delay time is greater than 100 s and therefore too large to be relevant for gas turbine combustors. However, in real applications, the reactants are heated by recirculated hot flue gas, so that ignition will take place at temperatures higher than that of the initial fuel/air mixture. The ignition process strongly depends on whether the mixture temperature lies above or below the crossover temperature. Hence, autoignition calculations using a homogeneous reactor model have been performed for both cases. The computed mole fraction profiles of the radicals for a lean H2 /air mixture at 17 bar and 1300 K, which lies above the crossover temperature, are illustrated in Fig. 5. Looking at the absolute values in Fig. 5a, the ignition process seems to be dominated by the H, OH, and O radicals, whereas the HO2 and H2 O2 concentrations seem to be negligibly small. Fig. 5b shows exactly the same results as Fig. 5a. However, a different scale is used for the y-axis to highlight the very low radical concentrations prior to ignition (i.e., at t < 0.003 ms). The HO2 radical is accumulated first, followed by a rapid increase of H radicals. Above the crossover temperature, the H radicals react with O2 primarily through the chain-branching reaction R1, so that ignition occurs almost immediately, and HO2 is quickly consumed by H through R10 and R11. Hence, only small amounts of H2 O2 are formed at this high temperature. Autoignition results for an atmospheric H2 /air mixture at 1000 K
Fig. 5. Mole fraction, Xi , of the radicals as a function of time, t , for the ignition of a lean H2 /air mixture at φ = 0.5, 17 bar, and 1300 K.
(not shown here) exhibit the same qualitative behavior, since the temperature also lies above crossover. However, the importance of the H radical is much higher. The computed mole fraction profiles of the radicals for a lean H2 /air mixture at 17 bar and 900 K are illustrated in Fig. 6. At this temperature below crossover, the H radicals react with O2 primarily through the chain termination reaction R9, so that HO2 is formed and further reacts to H2 O2 . Hence, the H, OH, and O radicals remain at very low concentrations for more than 100 ms, whereas the accumulation of the radical pool is dominated by H2 O2 , and to a lesser degree by HO2 (see Fig. 6b). Once the radical pool is large enough to start ignition, the concentrations of H, OH, and O reach the highest absolute values, and the conversion of H2 lasts only 0.01 ms, as shown in Fig. 6a. Similar results have also been obtained for an atmospheric H2 /air mixture at 900 K (not shown here). In addition to an increased importance of the H radical, the fraction of HO2 in the radical pool prior to ignition is much higher than at 17 bar. The ignition delay times of H2 /air mixtures at 17 bar with φ = 0.5 have been computed using the full and three different skeletal mechanisms. The cal-
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nism strongly overpredicts the ignition delay time. The errors stay the same when all reactions without H2 O2 (R1–R13) are applied, supporting the observations in Fig. 6b that H2 O2 has a significant influence on ignition in this temperature range. Including reactions R15 and R17 in the 6-step mechanism, the resulting 8-step∗ mechanism slightly underpredicts the ignition delay times below the crossover temperature (note that this 8-step∗ mechanism differs from the 8-step mechanism in the previous section). If reaction R14 is used additionally, the resulting 9-step mechanism yields excellent agreement with the full mechanism over the whole temperature range investigated. The present results for autoignition are in good agreement with previous work on inhomogeneous ignition in counterflow diffusion flames. Helenbrook et al. [15] and Kreutz and Law [16] found skeletal mechanisms including the same reactions as in the basic 6-step mechanism adequate to determine ignition at temperatures above the crossover temperature. Exactly the same reactions as in the present 9-step mechanism were used by Kreutz and Law [16], yielding excellent results for ignition of H2 /air flames at all three ignition limits. 3.3. Extinction Fig. 6. Mole fraction, Xi , of the radicals as a function of time, t , for the ignition of a lean H2 /air mixture at φ = 0.5, 17 bar, and 900 K.
Fig. 7. Ignition delay time, τign , as a function of the inverse of the temperature, 1000/T , for lean H2 /air mixtures at φ = 0.5 and 17 bar; computed with the full and three different skeletal mechanisms.
culated ignition delay time as a function of the inverse of the temperature, 1000/T , is shown in Fig. 7. The basic 6-step mechanism including reactions R1, R2, R3, R9, R10, and R11 yields very good agreement with the full mechanism above the crossover temperature, ∼1250 K (1000/T ≈ 0.8 K−1 ). However, below the crossover temperature, the basic 6-step mecha-
The process of extinction for a lean H2 /air mixture at 17 bar and 609 K has been studied using a PSR model. The calculated mole fractions, Xi , in the PSR as a function of mixing rate are illustrated in Fig. 8. At νr = 0 the mixture is in equilibrium, so that XH2 ≈ 0. With increasing mixing rate, the concentration of the reactants H2 and O2 increases while the product H2 O decreases until only reactants are left after extinction for νr > νr,ext . The OH molecule is the most important radical at very low mixing rates, whereas the H radical dominates the radical pool for νr > 104 s−1 up to extinction. The O concentrations generally lie somewhere in between. The concentrations of HO2 and H2 O2 are generally very small. The computed temperature in the PSR as a function of mixing rate for the full and various skeletal mechanisms is shown in Fig. 9. The basic 6-step mechanism strongly underpredicts the PSR temperature and overpredicts the extinction limit by 3.8%. Hence, the reactions having the largest impact on the PSR results have been sequentially added to the 6-step mechanism. Including reaction R8, the resulting 7step mechanism significantly improves the calculated temperature distributions and reduces the error for the predicted extinction limit to 2.8%. An accurate PSR temperature is achieved by adding the two reactions R7 and R13 constituting a 9-step∗ mechanism (note that this 9-step∗ mechanism differs from the 9-step mechanism in the previous section). However, the de-
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Table 2 Maximum percent weighted mole fractions of the radicals in a laminar H2 /air flame at 17 bar, 609 K, and φ = 0.5 H
O
OH
HO2
H2 O2
0.42
0.19
0.51
0.07
0.03
Similar results have been obtained for a stoichiometric H2 /air mixture at atmospheric pressure (not shown here), where the extinction limit is accurately predicted even by the 9-step∗ mechanism. Sohn et al. [31] identified almost the same reactions to show high sensitivity on the extinction strain rate in H2 /O2 diffusion flames at 50 atm. However, their reaction mechanism included an additional reaction, while reaction R7 was not accounted for. In contrast to the lean premixed flame of the present study, they found no effect of reaction R4, whereas R5 showed a slightly positive sensitivity to the extinction strain rate, since part of the reaction zone was located on the fuel-rich side.
4. Reduction of the mechanism
Fig. 8. Mole fractions, Xi , in a PSR as a function of mixing rate, νr , for a lean H2 /air mixture at φ = 0.5, 17 bar, and 609 K.
The investigations of the detailed mechanism show that the reactions R1, R2, R3, R8, R9, R10, R11, R13, R14, R15, and R17 have to be included in a skeletal mechanism that will satisfactorily represent the processes of ignition, extinction, and laminar flame propagation. However, the resulting 11-step mechanism will probably not yield the envisaged reduction of computational effort within CFD calculations, compared to the full 19-step mechanism. Hence, a further reduction of the skeletal mechanism using steady-state approximations is performed below. 4.1. Steady-state approximations
Fig. 9. Temperature, T , in a PSR as a function of mixing rate, νr , for a lean H2 /air mixture at φ = 0.5, 17 bar, and 609 K; computed with the full and three skeletal mechanisms.
viation for the extinction limit from the full mechanism is still as high as 2.1%. The inclusion of at least two more reactions, R4 and R12, is necessary to yield an exact prediction of the extinction limit (not shown in Fig. 9). The inclusion of all reactions with H2 O2 (R14–R19) does not change the results, indicating that H2 O2 has no effect on extinction.
A species can be assumed to be in steady state when the reactions consuming the species are much faster than the transport processes within the flame. An indicator for this criterion is the maximum concentration of the species. Peters [32] considered all species with a weighted mole fraction, Xw , less than 1% to be in steady state. The laminar H2 /air flame investigated in Section 3.1 is used as a basis for the reduction of the mechanisms. The maximum weighted mole fractions of the radicals have been derived from the maximum mole fractions in Fig. 1 and are listed in Table 2. All radicals have values less than 1%, so that a lower limit has to be defined for the present flame. The OH molecule has the largest values, and the highest OH concentrations in Fig. 1b reach far into the burnt mixture. Hence, the OH radical should not be assumed to be in steady state. The weighted
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H mole fraction is close to that of OH, so that a steady-state assumption for H is not acceptable either. The weighted O mole fraction is significantly lower than that of OH and H. However, a steady-state assumption for O cannot necessarily be made and has to be further investigated. The HO2 and H2 O2 radicals may be assumed to be in steady state in this flame, since their mole fractions are below 0.1%. The steady-state assumption implies that the overall reaction rate of a species is zero. For each steadystate species, one reaction rate can then be expressed as a function of other reaction rates. Usually, the rate of the fastest reaction consuming the steady-state species is eliminated [32]. For an estimated temperature of 1500 K in the main reaction zone, these reactions are R13 for HO2 , R17 for H2 O2 , and R2 for O. Following the procedure described by Peters [32], a 4-step reduced mechanism similar to that of Balakrishnan et al. [21] can be derived from the 11-step skeletal mechanism using the steady-state assumption for HO2 and H2 O2 , H + O2 OH + O, ωI = r1 + r11 + r15 , O + H2 H + OH, ωII = r2 + r11 + r15 , OH + H2 H + H2 O, ωIII = r3 + r8 + r9 − r10 − r11 − r14 − r15 , H + H H2 , ωIV = r8 + r9 − r15 , where rj is the rate of the elementary reaction Rj , and ωk is the overall rate of the global reaction. Applying an additional steady-state assumption for the O radical, a 3-step reduced mechanism similar to that of Balakrishnan et al. [21] can be derived: H2 + O2 OH + OH, ωI = r1 + r11 + r15 , OH + H2 H + H2 O, ωII = r3 + r8 + r9 − r10 − r11 − r14 − r15 , H + H H2 , ωIII = r8 + r9 − r15 . It has to be noted that the number of steps in the reduced mechanisms indicates the number of independent conservation equations to be solved, whereas the number of steps in the skeletal mechanisms corresponds to the number of elementary reactions. In the following, the reduced 3-step and 4-step mechanisms are compared with the skeletal 11-step and the full
Fig. 10. Laminar flame speed, SL , as a function of equivalence ratio, φ, for lean H2 /air mixtures at 17 bar and 609 K; computed with the full, the 11-step skeletal, and two reduced mechanisms.
mechanism using laminar flame, ignition, and extinction calculations. 4.2. Laminar flame speed The reduced mechanisms have been applied to laminar flame-speed calculations using the PREMIX code. The computed laminar flame speed for a lean H2 /air mixture at 17 bar and 609 K is shown in Fig. 10. The 11-step skeletal mechanism is almost identical to the behavior of the 8-step mechanism in Fig. 4. The results of the 4-step mechanism are in excellent agreement with those of the 11-step skeletal mechanism for equivalence ratios higher than 0.5. The deviation increases for leaner mixtures up to a relative error of 79% for φ = 0.3 at a very low absolute value of the flame speed. However, for the most relevant equivalence ratio at φ = 0.5, the deviation is as low as 1.6%, showing that the steady-state assumption for HO2 and H2 O2 is justified for laminar flamespeed calculations under gas turbine conditions. The results of the 3-step mechanism are almost identical to those of the 4-step mechanism for very lean mixtures. However, the deviation from the 4-step mechanism increases with increasing equivalence ratio up to 6.6% at φ = 0.7. The deviation from the 11-step skeletal mechanism at φ = 0.5 is 4.9%. Hence, the steady-state assumption for O is acceptable under the restriction of approximately 5% uncertainty for laminar flame propagation. The effect of pressure on laminar flame speed for H2 /air mixtures at φ = 0.5 is illustrated in Fig. 11. An exponential decrease of flame speed with increasing pressure is observed for all mechanisms. The absolute deviation of the results of the 11-step mechanism from those of the full mechanism is approximately constant. The results of the 4-step mechanism are in excellent agreement with those of the full mechanism
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Fig. 11. Laminar flame speed, SL , as a function of pressure, p, for H2 /air mixtures at φ = 0.5 and 609 K; computed with the full, the 11-step skeletal, and two reduced mechanisms.
Fig. 12. Laminar flame speed, SL , as a function of temperature, T , for H2 /air mixtures at φ = 0.5 and 17 bar; computed with the full, the 11-step skeletal, and two reduced mechanisms.
up to 12 bar. Above this value, the deviation between these two mechanisms slightly increases due to the increasing importance of HO2 and H2 O2 at high pressures. In contrast, the error of the 3-step mechanism is greatest at low pressures. The effect of temperature on laminar flame speed for H2 /air mixtures at φ = 0.5 is illustrated in Fig. 12. An exponential increase of flame speed with increasing temperature is observed for all mechanisms. The agreement between the results of the different mechanisms is generally good at low temperatures, and the deviations slightly increase above 700 K. 4.3. Ignition delay Autoignition of lean H2 /air mixtures with φ = 0.5 at 17 bar has been investigated using a homogeneous reactor model. The computed ignition delay times as a function of the inverse of the temperature, 1000/T , for the full and reduced mechanisms are shown in Fig. 13. The results of the 11-step skele-
555
Fig. 13. Ignition delay time, τign , as a function of the inverse of the temperature, 1000/T , for H2 /air mixtures at 17 bar and φ = 0.5; computed with the full, the 11-step skeletal, and two reduced mechanisms.
tal mechanism are in excellent agreement with those obtained from the full mechanism. The 4-step mechanism generally underpredicts ignition delay, particularly below the crossover temperature, where the error is several orders of magnitude. This result reflects the observations in Section 3.2 that the accumulation of the radical pool is mainly dominated by HO2 and H2 O2 . Hence, a steady-state assumption for HO2 and H2 O2 is not justified for low-temperature ignition. The 3-step mechanism follows the trend of the 4-step mechanism with some larger deviations at high temperatures. Thus, a steady-state assumption for O seems to be acceptable for ignition at low temperatures, but leads to significant errors above 1100 K. Other researchers used different reduced mechanisms for ignition in H2 /air counterflow diffusion flames. Sohn and Chung [23] suggested a 4-step mechanism applying steady-state approximations to O and OH for diluted flames. Kreutz and Law [16] found a 4-step reduced mechanism assuming steady state for O and OH to underpredict ignition temperatures. By removing the steady-state approximation for O, the corresponding 5-step reduced mechanism yielded much better results for first-limit ignition temperatures. However, the results in Section 3.1 show that steady-state assumptions for O and particularly for OH are not favorable when other processes such as extinction or flame propagation become relevant. Since ignition under gas turbine combustors is expected to take place in the high-temperature regime, the steady-state assumption for HO2 and H2 O2 might probably yield reasonable results within corresponding CFD calculations. 4.4. Extinction limit The process of extinction for a lean H2 –air mixture at 17 bar and 609 K is investigated using per-
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conditions of a typical lean premixed gas turbine combustor, i.e., H2 /air mixtures at φ = 0.5, 17 bar, and 609 K. The main results are summarized as follows:
Fig. 14. Temperature, T , in a PSR as a function of mixing rate, νr , for a lean H2 /air mixture at φ = 0.5, 17 bar, and 609 K; computed with the full, the 11-step skeletal, and two reduced mechanisms.
fectly stirred reactor (PSR) calculations. The computed PSR temperature as a function of mixing rate using the mechanisms under consideration is shown in Fig. 14. The 11-step skeletal mechanism satisfactorily reflects the trend of the full mechanism. The 4-step mechanism is in excellent agreement with the 11-step mechanism (the lines in Fig. 14 are not distinguishable). Hence, a steady-state assumption is to HO2 and H2 O2 is justified for the prediction of extinction. This can be explained by the very small amounts of HO2 and H2 O2 in the PSR calculations in Fig. 8. The 3-step mechanism generally overpredicts the temperature in the PSR and therefore also the extinction limit. Hence, a steady-state assumption for the O radical leads to significant errors for extinction calculations. The reason for these errors is probably the relatively high O molar concentration of approximately 1% shown in Fig. 8. Other researchers obtained corresponding results for extinction in laminar nonpremixed counterflowing H2 /air flames. Balakrishnan et al. [21] obtained a similar 4-step mechanism using steady-state approximations for HO2 and H2 O2 that accurately reproduced the dependence of the maximum flame temperature on the strain rate. Furthermore, they found the OH and O steady states to be inaccurate. Sohn and Chung [23] obtained good results on the extinction strain rate for the 4-step mechanism assuming steady state for HO2 and H2 O2 , but they also achieved good results for a 2-step mechanism assuming steady state for O and OH.
5. Conclusions The detailed reaction mechanism of Li et al. [2] for hydrogen combustion has been analyzed, and several reduced mechanisms have been tested under the
• In a freely propagating laminar flame, OH is the radical with the highest concentrations, whereas H and O are also important. The amounts of HO2 and particularly of H2 O2 are relatively small. Flame propagation is to a large degree controlled by the competition of reactions R1 and R9 corresponding to the second ignition limit. In addition, reaction R2 and R3, and to a less degree reactions R4, R8, R11, and R13 are also important. An 8step skeletal mechanism including reactions R1, R2, R3, R8, R9, R10, R11, and R13 yields satisfactory results for the laminar flame speed in the range φ = 0.3–0.7. • For the process of extinction in a perfectly stirred reactor (PSR), the H radical is the dominating radical, followed by OH and O. The HO2 and H2 O2 concentrations are very small, and the effect of the H2 O2 reactions is negligible. A 7-step skeletal mechanism including reactions R1, R2, R3, R8, R9, R10, and R11 yields a satisfactory prediction of the PSR temperature for varying mixing rate and of the extinction limit. However, the inclusion of four additional reactions is necessary for an exact prediction of the extinction limit. • In autoignition calculations, H, O, and OH are also the radicals with the highest concentrations. However, the accumulation of the radical pool is dominated by HO2 for temperatures above, and by H2 O2 below the crossover temperature. A 9step mechanism including reactions R1, R2, R3, R9, R10, R11, R14, R15, and R17 yields excellent agreement with the full mechanism for the calculation of the ignition delay time over a large temperature range. • The present investigations show that at least 11 elementary reactions are necessary for satisfactory prediction of the processes of ignition, extinction, and laminar flame propagation under gas turbine conditions. A reduced 4-step mechanism assuming steady state for HO2 and H2 O2 yields accurate results for a laminar flame and extinction, but is not able to predict low-temperature ignition. Nevertheless, the 4-step mechanism might yield reasonable results for gas turbine combustor simulations since ignition is expected to take place in the high temperature regime. A reduced 3-step mechanism assuming steady state for the O radical introduces additional errors for all of these processes. The application of these mechanisms to CFD calculations of turbu-
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lent flames and gas turbine combustors will be examined in further work.
Acknowledgments This study was funded within the ENCAP project in the European 6th Framework Program and within the Climit programme operated by the Norwegian Research Council and Gassnova. The authors thank Professor F.L. Dryer at Princeton University for providing his chemical data.
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