高温 H₂-CO 氧化动力学模型优化分析(h2-co）

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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 combustion

Scott G. Davisa,*, Ameya V. Joshia, Hai Wanga, Fokion Egolfopoulos b

a Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA

b Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA

Abstract

We 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.

Keywords: Kinetics; Detailed reaction model; Hydrogen; Carbon monoxide

1. Introduction

The 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 model

The 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 method

A 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≥ibxi

xj). 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 discussion

The 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].

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