摘要：本文构建并优化了高温 H₂-CO 燃烧详细动力学模型，整合最新热力学、反应速率与输运参数，包含 14 种组分、30 步基元反应。以激波管点火延迟、层流火焰速度、流动反应器组分浓度及火焰结构等 36 组实验为优化目标，对 28 个关键反应指前因子与三体效率进行系统优化。重点修正 H+O₂+M、CO+OH 等核心反应速率，显著提升模型预测精度。优化模型可准确复现宽工况（880–2625 K、0.3–33 atm）下的燃烧特性，为氢 - 一氧化碳混合燃料的数值模拟提供可靠动力学基础。An optimized kinetic model of H2/CO combustionScott G. Davisa,*, Ameya V. Joshia, Hai Wanga, Fokion Egolfopoulos ba Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USAb Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USAAbstractWe propose a H2–CO kinetic model which incorporates the recent thermodynamic, kinetic, and species transport updates relevant to high-temperature H2 and CO oxidation. Attention has been placed on obtaining a comprehensive and kinetically accurate model able to predict a wide variety of H2–CO com- bustion data. The model was subject to systematic optimization and validation tests against reliable H2– CO combustion data, from global combustion properties (shock-tube ignition delays, laminar flame speeds, and extinction strain rates) to detailed species profiles during H2 and CO oxidation in flow reactor and in laminar premixed flames.◎ 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.Keywords: Kinetics; Detailed reaction model; Hydrogen; Carbon monoxide1. IntroductionThe most successful model of H2–CO combus- tion has been that of Mueller et al. [1], developed on the basis of a careful evaluation of relevant ki- netic parameters and flow reactor experiments. The model is also able to predict a wide range of flame experiments. Over the last few years, however, the rate parameters of the key reaction H + O2 + M = HO2 + M and its third-body effi- ciencies have been revised [2,3], giving an urgent reason for a re-examination of the H2–CO com- bustion model. The downward revision of the en- thalpy of formation of OH [4] may also exert an influence on the overall reaction kinetics of H2 combustion.Several new studies [5–7] have been reported in recent years. Two of these studies a nalyzed the hydrogen submodel [5,6], both being an extension of the model of Mueller et al. The third an alysis [7] considered both H2 and CO chemistry and is the predecessor to the present study. The objec- tives of the present study are (1) to provide an up- date for the H2–CO combustion reaction model on the basis of recent kinetic data, and (2) to opti- mize the H2–CO model against available H2–CO combustion data.2. Reaction modelThe unoptimized (trial) reaction model consists of 14 species and 30 reactions as shown in Fig. 1. The model and its thermochemistry and transport property files can be found at the URL: http:// ignis.me.udel.edu/h2co. The trial model was based on a careful review of recent kinetics literature, considering both direct data and compilations. A large number of GRI 3.0 rate parameters [8] were found to be appropriate and are used. The discus- sion below highlights the choice of key rate parameters.Fig. 1. Trial reaction model of H2–CO oxidation, active parameters, and their spans employed in model optimization (see Refs. [9,14,16–18]).The rate expression of H + O2 = O + OH was taken from GRI 3.0 [8]. The rate coeffi- cient of H + O2(+M) = HO2(+M) was based on Troe [2], who employed a high-pressure rate krec,∞ (cm3 mol__1 s__1) = 4.65 × 1012 T0.44 and developed the low-pressure and fall-off expres- sions for Ar and N2 as the bath gases. The broad- ening factor Fc was found to be 0.5 for both third bodies. Troe’s fall-off rate parameterization, how- ever, could not be directly used in CHEMKIN [19], because the low-pressure limit rate coefficient k0 does not share the same temperature depen- dence for different third bodies. We had to devel- op parameterized rate expressions (see Fig. 1) based on the k0 expression of Ar and using the fall-off formula of Troe [20]. A collision efficiency factor β = 0.53 was used for Ar relative to N2. The collision efficiency of He was assumed to be equal to that of Ar. The study of Michael et al.[3] supports a collision efficiency of O2 s maller than that of N2. We found that for O2, β = 0.75 gives a good agreement with experiment [3] and theory [2]. For H2O, Troe [2] suggested that the broadening factor is close to the strong-collision limit. We chose a β value of 12 (relative to N2) with the resulting rate in good agreement with those of Troe and others [2,3,21].The k0 expression of H + OH + M = H2O + M was taken from [8] with the β values equal to 0.38 and 6.3 for Ar and H2O, respectively [12]. The rate expression of Michael et al. [10] was employed for H2 + O2 = H + HO2. For OH + OH(+M) = H2O2(+M), the k0 expression, given in the reverse direction by Baulch et al.[12], was refitted based on the new heat of forma- tion of the OH radical along with the low temper- ature data of Zellner et al. [11]. The krec,∞ expression and the β value of H2O (6) were taken from [11] while the Troe fall-off parameters [22] were the same as those in GRI 3.0. The rate expressions for H2O2 + OH = HO2 + H2O were taken directly from [15], though the high-temper- ature expression was refitted using a modified Arrhenius expression to avoid the rate constant values exceeding the collision limit when extrapo- lated to high temperatures.For CO + O(+M) = CO2(+M), the k∞ expres- sion was taken from [13], and following Allen et al. [23], k0 was taken from the QRRK ana lysis of Westmoreland et al. [24] and fall-off was that of Lindemann. The collision efficiency of H2O was assumed to be 12. The rate constant for CO + OH = CO2 + H was re-an alyzed in the present study, and the experimental data were refitted by the sum of two modified Arrhenius expressions. The new expression resolves more accurately the high temperature data of Woold- ridge et al. [25] as well as the data found in [26]. Without this revision, it was not possible to recon- cile the high-temperature H2 ignition data with the H2–CO laminar flame speeds. The known pressure dependence of this reaction was not con- sidered as this dependence is quite unimportant for the CO oxidation experiments considered herein. 3. Computational and optimization methodA comprehensive review was conducted for a large number of H2–CO combustion data. Thir- ty-six experiments were chosen as optimization targets as shown in Table 1. They can be classified into four categories: (1) laminar flame speeds of H2–air, H2–O2–He, and H2–CO–air mixtures, (2) the peak mole fractions of H and O in a low-pres- sure burner-stabilized H2–O2–Ar flame, (3) the consumption rates of H2 and CO during the reac- tion of H2–O2–N2 and CO–O2–H2O–N2 mixtures in a turbulent flow reactor, and (4) ignition delay times of H2–O2–Ar and H2–CO–O2–Ar mixtures behind reflected shock waves.Ignition delay and flow reactor calculations were conducted using a kinetic integrator inter- faced with CHEMKIN [19] by assuming adiabatic condition. Ignition delays were modeled using the constant-density model, whereas flow reactor modeling used the constant-pressure assumption. The numerical ignition delays were determined following the same ignition criteria as in the respective experiments. Laminar flame speeds and structure were calculated using Premix [40], employing thermal diffusion, and multicomponent transport. Diffusion coefficients of several key pairs were updated [41].Sensitivity an alyses were conducted for igni- tion delay and consumption rates of the fuel in flow reactor with a brute force method. For lam- inar flame speeds and H and O peak mole frac- tions in burner-stabilized flames, the local sensitivity methods were utilized. Based on the sensitivity information, active rate parameters (to be optimized) were chosen for each target. The entire set of active parameters consists of 28 A-factors and third-body efficiency factors as shown in Figs. 1 and 2.The optimization approach is similar to earlier studies [8,43]. Briefly, the solution mapping tech- nique was employed to express a response by a sec--ijp, a’sl n(2d) ’0a1iii1,x’s are factorial active variables given by x = ln (a/atrial)/ln (f), where a is the active A factor or third-body efficiency factor, and f is its span or uncertainty factor. The uncertainty factor was esti- mated on the basis of kinetic uncertainty and is pro- vided in Fig. 1 for each active parameter. Though an optimization of the temperature dependence of rate coefficients is possible, we chose not to vary the T-dependence because of the insufficient num- ber of systematic experimental targets [43].For flow reactor targets, the response was found to be highly non-linear with respect to x’s. These responses are expressed by adding a hyper- bolic tangent term to account for the S-shaped dependence of response with respect to x’s,η = η(2) + ctanh(a +Σ= 1 axi +Σ1 Σ≥ibxixj). The coefficients for the flow reactor and igni- tion delay targets were calculated by a factorial design test [43]. The coefficients for flame targets were obtained using the sensitivity an alysis based method [44].Minimization was carried out on the objective function L2 = Σi[(ηi,expt __ ηi,calc)/σi]2 subject to the constraint __1 < {x} < +1, where the subscript i denotes the ith target. Each target was individually weighted by their uncertainty σi . The target values and their uncertainties are presented in Table 1.4. Results and discussionThe trial kinetic model was tested against a wide range of experimental data. The predictions of the trial model for the 36 target values are shown in Table 1 (the ‘‘trial’’ column). Overall the model performed well against these experi- mental data. The exceptions are: it overpredicts H2–O2–He flame speeds, the H and O mole frac- tions in the burner-stabilized flame, and the consumption rate of H2 for the 1.0% H2–1.5 O2%–N2 flow reactor mixture at 943 K and 2.5 atm.To reconcile these discrepancies, optimization was then carried out for 28 active parameters with respect to 36 targets. All active parameters were allowed to vary freely within their uncertainty spans. The optimal parameter set was obtained as the minimum of L2, first from a random sample of the multidimensional parameter space, fol- lowed by a Newton search of the L2 minimum in the parameter space. The values of optimized active parameters are shown in the last column of Fig. 2 (expressed as the optimized-to-trial parameter ratio). To obtain the optimized model, the active parameters (A-factors and third-body efficiency factors) shown in Fig. 1 should be mul- tiplied by their corresponding ratios.Validation of the optimized model will be dis- cussed below. Figure 3 presents experimental [27–31,45] and computed laminar flame speeds of H2–air and air-equivalent mixtures where N2 was replaced by Ar or He. With trial model predictions already close to the experimental values, the opti- mization served only to fine-tune the model, result- ing in excellent agreement with the experiment as can be seen in Fig. 3 and Table 1. The trial model tends to overpredict the H2–O2–He flame speeds at elevated pressures (Table 1). The discrepancies are clearly caused by kinetics as a previous study showed that the uncertainty in the transport coeffi- cients cannot account for the observed differences [41]. Now the optimized model can successfully pre- dict these H2–O2–He flame speeds [27] as seen in Fig. 4. This agreement was brought by lowering the rate of OH + H2 = H + H2O, H + HO2 = OH + OH, and a s mall increase in the rate of H + O2 + H2O = HO2 + H2O.The dominant sensitivity of the laminar flame speeds of H2–CO–air mixtures, especially the 95% CO + 5% H2 mixtures, to CO + OH = CO2 + H has been observed elsewhere [32] and necessitated a re-evaluation this reaction. It was determined that the sum of two modified Arrhe- nius expressions was necessary to predict the lam-the optimized model reproduces experimental H2–CO–air laminar flame speeds [32,33].Figure 7 depicts species profiles for four se- lected H2 oxidation experiments in a turbulent flow reactor [13]. Time shift was necessary to match the computed profiles with the experimen- tal counterparts. The amounts of time shift were found to be similar with those used by Mueller et al. [13]. It is seen that the optimized model pre- dicts the experimental species profile accurately, and it also improved the prediction of the experi- ment as compared to the trial model (cf. Fig. 7B). Similarly, the results of Fig. 8 show that for CO oxidation [35] the optimized model accurately pre- dicts the CO consumption rate over an extended pressure range.Fig. 2. Target-active parameter matrix.Fig. 3. Experimental (symbols) and computed (lines: the optimized model) H2–air and air equivalent (N2 is replaced by Ar or He) flame speed at a pressure of 1 atm.Fig. 4. Experimental (symbols [27]) and computed (lines: the optimized model) H2–O2–He flame speeds.The trial model could accurately reconcile most of the ignition delay data for H2–O2–diluent mixtures, and optimization served only to im- prove these predictions as can be seen in Table 1. In addition, Fig. 9 shows a plot of experimental and computed ignition delay times for H2–O2–Ar mixtures [36–38,46] behind reflected shock waves. Here, the experimental shock-tube ignition delay data were fitted into τ (μs) = [H2]__0.154[O2]__0.693 [Ar]0.04 [6.77 × 10__8 T0.252 e9234/T] for non-‘‘run-Fig. 5. Experimental (symbols [32]) and computed (lines: the optimized model) H2–CO–air flame speeds at a pressure of 1 atm.Fig. 6. Experimental (symbols [33]) and computed (lines: the optimized model) H2–CO–air flame speeds at a pressure of 1 atm.Fig. 7. Experimental (symbols [13]) and computed (lines) species mole fraction profiles during hydrogen oxidation in a flow reactor. Solid lines: optimized model; dashed lines: trial model.Fig. 8. Experimental (symbols [35]) and computed (lines) [CO]/[CO]0 profiles during moist CO oxidation in a flow reactor. Cases (a): 1.014% CO + 0.517% O2 + 0.65% H2O in N2, p = 1 atm, T0 = 1038 K, (b) 1.01% CO + 0.496% O2 + 0.65% H2O in N2, p = 2.44 atm, T0 = 1038 K, (c) 0.988% CO + 0.494% O2 + 0.65% H2O in N2, p = 3.46 atm, T0 = 1038 K, (d) 0.984% CO + 0.497% O2 + 0.65% H2O in N2, p = 6.5 atm, T0 = 1040 K, and (e) 0.994% CO + 1.47% O2 + 0.65% H2O in N2, p = 9.6 atm, T0 = 1039 K.Fig. 9. Experimental (symbols) and computed (lines) ignition delay times of H2–O2–Ar mixtures behind reflected shock waves. Symbols: (a) 6.67% H2 + 3.33% O2, p5 = 1.35–2.90 atm; (b) 5% H2 + 5% O2, p5 = 1.35– 2.90 atm (onset of pressure rise [36]), (c) 0.5% H2 + 0.25% O2, p5 = 33 atm, (d) 2% H2 + 1% O2, p5 = 33 atm, (e) 0.5% H2 + 0.25% O2, p5 = 57 atm, (f) 0.33% H2 + 0.17% O2, p5 = 64 atm, (g) 0.1% H2 + 0.05% O2, p5 = 64 atm, (h) 0.5% H2 + 0.25% O2, p5 = 87 atm (maximum OH absorption rate [38]), (i) 8% H2 + 2% O2, p5 = 5 atm (maximum OH emission) [46], and (j) four H2 + O2 mixtures [37]. Lines: (1) 0.5% H2 + 0.25% O2, p5 = 87 atm (maximum [OH] rate), (2) 2% H2 + 1% O2, p5 = 33 atm (maximum [OH] rate), (3) 8% H2 + 2% O2, p5 = 5 atm (maximum [OH]), and (4) 5% H2 + 5% O2, p5 = 2 atm (maximum pressure gradient).Fig. 10. Experimental (symbols) and computed (lines) ignition delay times behind reflected shock waves for H2–O2–N2 mixtures. Experimental data were determined from onset of pressure rise [47] and maximum rate of OH emission [48].详细内容请见附件免责声明：本页面/内容部分素材来源于互联网公 开 信 息，旨在传递更多信息，不代表本平台立场。版权归原作者或机构所有，如涉及侵权，请通过平台联系我们，我们将在核实后第一时间处理。本平台对转载内容的真实性、准确性不作任何保证，用户需自行判断并承担使用风险。
