A rapid compression facility study of OH time histories during iso-octane ignition

Combustion and Flame 145 (2006) 552–570 www.elsevier.com/locate/combustflame

A rapid compression facility study of OH time histories during iso-octane ignition X. He, B.T. Zigler, S.M. Walton, M.S. Wooldridge ∗ , A. Atreya Department of Mechanical Engineering, University of Michigan, 2350 Hayward Street, Ann Arbor, MI 48109-2125, USA Received 6 July 2005; received in revised form 17 November 2005; accepted 29 December 2005 Available online 31 March 2006

Abstract Iso-octane ignition delay times (τign ) and hydroxyl (OH) radical mole fraction (χOH ) time histories were measured under conditions relevant to homogeneous charge compression ignition engine operating regimes using the University of Michigan rapid compression facility. Absolute quantitative OH mole fraction time histories were obtained using differential narrow-line laser absorption of the R1 (5) line of the A2 Σ + ← X 2 Πi (0, 0) band of the OH spectrum (ν0 = 32606.56 cm−1 ). Ignition delay times were determined using pressure and OH data. Diluted iso-octane/argon/nitrogen/oxygen mixtures were used with fuel/oxygen equivalence ratios from φ = 0.25 to 0.6 for τign measurements and from φ = 0.25 to 0.35 for χOH measurements. The pressures and temperatures after compression ranged from 8.5 to 15 atm and from 945 to 1020 K, respectively, for the combined τign and χOH data. The maximum mole fraction of OH during ignition and the plateau value of OH after ignition are compared with model predictions using different iso-octane oxidation mechanisms. Sensitivity and rate of production analyses for OH identify reactions important in iso-octane ignition under these lean, intermediate-temperature conditions. The OH time histories show significant sensitivity to the OH + OH + M = H2 O2 + M, CH3 + HO2 = CH3 O + OH, and CH3 + HO2 = CH4 + O2 reactions, which have rate coefficients with relatively high uncertainties. Improved predictions of the OH time histories can be achieved by modifying the rate coefficient for these reactions. The enthalpy of formation used for OH also has a significant effect on the predicted ignition delay times. © 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Iso-octane; Hydroxyl radical; Ignition; Rapid compression facility

1. Introduction Branched alkanes are key components of real fuels, and although iso-octane is not a significant component of real fuels such as gasoline, iso-octane is an important primary reference fuel. Iso-octane with n* Corresponding author. Fax: +1 734 647 3170.

E-mail address: [email protected] (M.S. Wooldridge).

heptane is used to evaluate octane numbers and knock characteristics of gasoline fuels used under sparkignition operating conditions. Because the chemical kinetics of knock are considered similar to the chemical kinetics important in gasoline homogeneous charge compression ignition (HCCI) engines, ignition kinetics of iso-octane and mixtures of iso-octane with other fuels have been the focus of numerous experimental (e.g., [1–4]) and modeling (e.g., [5–8]) studies, including conditions relevant to HCCI applications.

0010-2180/$ – see front matter © 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2005.12.014

X. He et al. / Combustion and Flame 145 (2006) 552–570

Iso-octane oxidation can be divided into low-, intermediate-, and high-temperature regimes. The low-temperature regime (below approximately 900 K) includes slow combustion, cool flame, and negative temperature coefficient (NTC) regimes. According to Curran et al. [5], the boundary between the highand intermediate-temperature regimes occurs at about 1150 K. In the high-temperature regime iso-octane oxidation occurs mainly via fuel decomposition to produce alkyl radicals, followed by β-scission of the alkyl radicals. Smaller olefins and other species are formed rapidly, and chain branching is primarily due to the reaction: H + O2 = OH + O.

(R1)

A key feature of high-temperature iso-octane oxidation is that the ignition delay time (τign ) of an isooctane/air mixture decreases with decreasing equivalence ratio [9]. In the intermediate-temperature regime, chain branching occurs mainly due to reaction pathways leading through the hydrogen peroxide species. In the low-temperature regime, carbonylhydroperoxide species play a larger role in the chain branching process [5]. As noted by Curran et al. [5], ignition delay times in the low- and intermediate-temperature regime decrease with increasing equivalence ratio due to this change in the dominant chain branching reaction pathways. The characteristic of τign decreasing with increasing equivalence ratio has been observed experimentally for iso-octane air mixtures at low- to intermediate-temperatures (T ∼ = 940–1030 K) [1]. As the chemical kinetics of iso-octane oxidation in the temperature regimes are quite different, experimental data characterizing each regime are critical. Iso-octane combustion studies typically target measurements of ignition delay time [1,4,9–16], burning velocity [17], burn rate [14], heat release [18], and species concentration measurements [9,10,16,18–21] as means of characterizing and validating iso-octane combustion chemistry. The experimental studies cited cover a range of temperatures, pressures, equivalence ratios, and levels of dilution. Among the direct species measurements that have been made, researchers have generally focused on stable species (e.g., CO [16,18, 19,21], CO2 [18,21], CH4 [19,21]) and hydrocarbons present in moderately high concentrations for relatively long times (e.g., C2 H4 [19,21], C3 H6 [16,19, 21], and acetone [16,19,21]). There are comparatively few measurements of the important radical species H, O, and OH due to the challenges of measuring intermediate species which are typically short-lived and often present in small quantities. Davidson et al. [9] and Oehlschlaeger et al. [10] examined OH concentration time histories at high temperatures in shock tube studies of iso-octane air mixtures. Although iso-

553

octane ignition delay time data were determined in these studies for several fuels over a broad range of conditions, the OH data were obtained over a more limited set of conditions. Specifically, in the works by Davidson et al. [9] and Oehlschlaeger et al. [10], OH time histories were obtained at dilute conditions with temperatures ranging from T = 1299–1736 K and equivalence ratios ranging from φ = 0.5–2.0 with pressures near atmospheric (P = 1.3–1.6 atm). No OH radical concentration data are available for lean iso-octane mixtures at low- and intermediatetemperature regimes (T < 1150 K) and pressures higher than 2 atm, conditions which are vital for validating iso-octane combustion chemistry relevant to HCCI applications. The OH radical is particularly important in HCCI reaction kinetics. This is due primarily to the large role hydrogen peroxide formation from OH recombination, OH + OH (+M) = H2 O2 (+M),

(R2)

plays in controlling ignition in the intermediatetemperature regimes (850–1100 K) [22,23]. Understanding the effects of H2 O2 formation and decomposition and other key reactions on the radical pool via quantitative measurements of radical formation and removal is an important step for developing accurate fuel oxidation mechanisms at HCCI conditions and for improved understanding of the HCCI combustion processes. Based on the needs outlined above, the objective of the current work was to obtain quantitative experimental data on OH to improve our understanding of the behavior of this important radical at HCCI operating conditions. In order to achieve the objective, a rapid compression facility (RCF) was used to generate moderate pressure and temperature conditions for lean iso-octane air mixtures. Laser absorption of OH was used to obtain quantitative time histories of the hydroxyl radical. The results are compared with the predictions from several iso-octane reaction mechanisms available in the literature. Rate-of-production and sensitivity analyses are presented to provide insight into the reactions affecting ignition and the OH time histories.

2. Experimental approach All experiments were conducted using the rapid compression facility located at the University of Michigan (UM). Results of characterization studies of the UM-RCF performance can be found in Donovan et al. [24] and Donovan [25]. Previous application of the UM-RCF for iso-octane ignition delay time studies is provided in He et al. [1].

X. He et al. / Combustion and Flame 145 (2006) 552–570

Fig. 1. Schematic of the OH laser absorption diagnostic used in UM-RCF studies of iso-octane combustion.

554

The UM-RCF consists of five major components: the driver section, the driven section, the test manifold, the sabot (i.e., free-piston), and the hydraulic control valve assembly. For each experiment, the driven section was evacuated with a diffusion pump and the driver section was filled with high-pressure air. The driver and driven sections are separated by the hydraulic control valve assembly and a scored sheet of Mylar (0.002 inch thick). After filling the driven section with the prepared test gas mixture, the globe valve was opened (using the hydraulic control valve assembly), permitting the high-pressure driver gas to break the Mylar, enter the driven section, and rapidly accelerate the sabot. The test gas mixture in the driven section was compressed in front of the sabot and then sealed within the test manifold when the sabot nose cone seated forming an annular interference fit with the test manifold walls. All test gas mixtures were made using a dedicated mixing tank. Ultrahigh purity grade nitrogen (99.998%) and oxygen (99.98%), prepurified argon (99.998%), and iso-octane (>99.8%, 2,2,4-trimethylpentane, Aldrich) were used. The mixture composition was determined using the partial pressures of the mixture components. To minimize the potential for fuel condensation, the maximum partial pressure of the iso-octane in the mixing tank was limited to <50% of the room-temperature vapor pressure of iso-octane. As in our previous study of iso-octane ignition [1], argon was used as a balance gas to ensure that the heat capacities of the test-gas mixtures were approximately constant for all experiments. As a consequence, if the compression ratios for the experiments are the same, the test-gas mixtures will yield the same temperatures at the end of compression. A schematic of the laser absorption diagnostic used to obtain the OH profiles is shown in Fig. 1. The laser source was an intracavity frequency-doubled ring-dye laser (Coherent 899-05) operating on Rhodamine 6G dye that was pumped by an argon ion laser (Coherent Innova 420, 514 nm, ∼6.2 W). The ring-dye laser was intracavity doubled to the UV using a potassium-deuterated phosphorus (KDP) doubling crystal. This laser system was used for the experiments due to the exceptionally narrow laser linewidths that are achievable and the excellent tunability of the system. In this work, the laser was tuned to the resonant frequency of the R1 (5) transition in the A2 Σ + ← X 2 Πi (0, 0) band of the OH spectrum (ν0 = 32606.556 cm−1 ). The wavelength of the UV laser was confirmed using a wavemeter (Advantest, TQ8325) and by scanning the R1 (5) transition in a reference flame prior to the start of each experimental run. The UV beam was divided into transmitted and reference beams. The transmitted beam was cou-

X. He et al. / Combustion and Flame 145 (2006) 552–570

pled into a fiber optic cable (Multimode Fiber Optics, PCU100-10-SF) using a collimator (Multimode Fiber Optics, LC-4U-AR). On the output side of the optical fiber, a custom collimator (Multimode Fiber Optics) was mounted on the test section which focused the laser emission, yielding a converging laser beam with a diameter of approximately 3 mm at the center of the test manifold. The transmitted beam passed through the test section and was focused onto the active element of a photodiode detector. A spectral filter (ESCO UG11) was used with the detector to monitor the transmitted laser intensity in order to reduce interference effects from broadband emission during ignition. In addition, an identical filter and detector arrangement was placed at the same axial location as the transmitted signal detector in the test section (see Fig. 1) in order to monitor the emission from the test-gas mixture during ignition. The signal from the emission detector was used to correct for interference emission effects on the transmitted signal, which is discussed further below. Two sapphire windows (ESCO ZGC105197) provided the optical access to the test section for the UV absorption measurements. To prevent water condensation on the windows after combustion, the windows were heated (Kapton Flexible Heaters, Omega KHLV-0504/10). Power was applied to the

555

heaters for approximately 7 min before each experiment, maintaining the temperature of the windows above 373 K. Amplified photodiode detectors (Pacer HUV2000B) were used to monitor the reference, transmitted, and emission intensities. The detectors used identical amplifier circuits to ensure the same response time. A piezoelectric transducer (Kistler 6041AX4) and charge amplifier (Kistler 5010B) were used for the pressure measurements. All data were recorded using a high-resolution data acquisition system (National Instruments PXI, NI4472 data acquisition board) with a sampling rate of 100,000 Hz and 24 bit resolution. A quartz end-wall was used for optical access to the test section. A high-speed digital camera (Vision Research Phantom 7.1) operating at 26,000 frames/s and a spatial resolution of 256 × 256 pixels was used to monitor the ignition process and to confirm homogeneous conditions within the test volume. Additional details on the acquisition and analysis of the highspeed imaging can be found in Walton et al. [26,27].

3. Experimental results A summary of the experimental results and conditions studied are provided in Tables 1 and 2. In

Table 1 Summary of experimental conditions and results for iso-octane ignition delay times based on pressure and OH measurements φ

0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.35 0.35 0.4 0.4 0.4 0.6 0.6

N2 [%]

79.2 79.2 79.2 77.2 77.2 77.2 77.2 77.2 77.2 77.2 77.2 77.2 77.2 77.2 77.2 74.5 74.5 73.1 73.1 73.1 64.9 64.9

Ar [%]

3.9 3.9 3.9 5.9 5.9 5.9 5.9 5.9 5.9 5.9 5.9 5.9 5.9 5.9 5.9 7.9 7.9 9.8 9.8 9.8 17.8 17.8

Peff [atm]

8.60 13.80 15.13 8.54 8.86 8.96 9.23 9.43 9.90 9.97 10.47 10.84 11.41 11.42 14.77 14.14 14.27 8.88 9.72 13.73 8.64 8.83

Teff [K]

980 961 983 981 1015 1019 983 1003 1015 1016 954 964 975 980 983 969 971 982 969 945 982 987

Ignition delay time [ms] τP

τOH

τpred

Difference between τOH and τP [%]

24.4 20.6 12.4 22.0 10.9 10.3 19.0 12.7 10.0 9.9 31.2 23.7 17.6 16.6 11.3 13.8 13.2 17.2 19.7 20.5 13.0 11.6

25.5 22.0 14.0 22.6 11.2 10.6 19.5 12.7 10.3 10.1 32.1 24.7 18.5 17.2 12.0 14.1 13.4 17.5 20.0 20.8 13.3 11.9

25.4 21.6 13.1 21.6 11.5 10.7 19.4 13.2 10.2 10.1 28.8 23.2 17.7 16.2 11.7 14.0 13.4 16.2 18.7 20.5 12.3 10.9

4.3 6.4 11.4 2.7 2.7 2.8 2.6 0.0 2.9 2.0 2.8 4.0 4.9 3.5 5.8 2.1 1.5 1.7 1.5 1.4 2.3 2.5

Predictions are based on the correlation for τpred developed in He et al. [1].

Difference between τOH and τpred [%] 0.4 1.8 6.4 4.4 −2.7 −0.9 0.5 −3.9 1.0 0.0 10.3 6.1 4.3 5.8 2.5 0.7 0.0 7.4 6.5 1.4 7.5 8.4

556

X. He et al. / Combustion and Flame 145 (2006) 552–570

Table 2 Summary of experimental conditions and results for χOH and τign φ

Peff

Teff

Experimental results

Curran

τign based on OH

Maximum

OH Plateau

τign

OH Maximum

Plateau

Decrease reaction rate A by

0.25 0.25 0.3 0.35 0.35 0.25 0.3

φ 13.80 15.13 14.77 14.14 14.27 8.60 8.54

961 983 983 969 971 980 981

22 14 12 14.1 13.4 25.5 22.6

139 165 437 756 812 258 620

31 44 103 222 213 40 98

19.52 12.32 10.55 12.33 11.86 20.04 20.04

176 191 441 839 841 320 675

38 43 106 219 221 49 120

73.0% 74.0% 72.5% 75.6% 73.4% 81.1% 83.4%

0.3 0.3 0.3 0.3 0.3

Pressure 8.54 9.23 11.42 11.41 14.77

981 983 980 975 983

22.6 19.5 17.2 18.5 12

620 579 478 466 437

98 100 83 81 103

17.16 15.76 13.84 15.12 10.55

675 644 542 527 441

120 118 111 108 106

83.4% 79.7% 80.0% 78.8% 72.5%

0.3 0.3 0.3 0.3 0.3 0.3

Temperature 8.96 9.90 8.86 9.43 8.54 9.23

1019 1015 1015 1003 981 983

10.6 10.3 11.2 12.7 22.6 19.5

820 748 769 645 620 579

141 131 133 122 98 100

8.36 8.28 9.06 10.7 20.04 15.76

790 725 779 702 675 644

148 141 145 133 120 118

83.7% 82.0% 81.8% 77.5% 83.4% 79.7%

10.1 9.18 32.1 24.7

779 582 414 404

133 128 74 82

8.22 8.42 23.74 19.42

721 578 501 515

141 125 97 102

81.2% 70.0% 83.6% 80.8%

0.3 0.3 0.3 0.3

Other data 9.97 1016 12.50 1005 10.47 954 10.84 964

Predicted values for χOH data using the mechanism by Curran et al. [5] are provided. The last column specifies the best-fit values for the A coefficient for the (R2) reaction.

our previous investigation [1], the ignition delay time was defined based on the pressure profiles, τP . In this work, ignition delay time is also defined based on the OH mole fraction time histories, τOH , which are discussed further below. The effective pressure (Peff ) and temperature (Teff ) after compression were determined using the same method as the previous study [1]. Briefly, Peff is the time-averaged pressure at the end of compression which includes the effects of rapid heat loss that occurs immediately after the nose cone of the sabot lodges in the test manifold. Teff is determined by numerically integrating isentropic relations and using Peff , the initial pressure and temperature of the test-gas mixture and the ratio of the specific heats of the test-gas mixture (see Eq. (3)). For this study, Peff ranged from 8.5 to 15.1 atm and Teff ranged from 960 to 1020 K. A fixed oxygen mole fraction of 16.6% was used for all experiments and equivalence ratios ranged from φ = 0.25 to 0.6.

3.1. OH mole fraction time histories Data for χOH were obtained over the broadest range of conditions possible within the experimental constraints. The study of χOH time histories of isooctane combustion in the UM-RCF is limited by the following factors. First, the maximum χOH must be below the limit which saturates the UV beam, i.e., conditions leading to 100% absorption. Second, the ignition conditions must be homogeneous. Third, little soot should be generated. The presence of soot particles will lead to interference effects due to scattering and broadband emission. Based on these criteria, OH mole fraction time histories were studied for equivalence ratios 0.25  φ  0.35. The maximum UV absorption in these experiments was less than 85%. For equivalence ratios of φ  0.4, less than 5% of the UV signal was transmitted at the maximum OH levels observed. Thus, these data were used for ignition delay time measurements only. Additionally, copious amounts of soot were formed during

X. He et al. / Combustion and Flame 145 (2006) 552–570

557

Fig. 2. Typical experimental results for pressure, transmitted, reference, and spontaneous emission time histories for experimental conditions of Peff = 14.27 atm, Teff = 971 K, φ = 0.35, and χO2 = 16.6%. The fractional absorption shown in the lower panel was determined using the difference between the reference and the transmitted intensities.

ignition for all experiments with equivalence ratios φ  0.8. Typical experimental results for pressure and transmitted, reference, and emission intensities are presented in Fig. 2. Time “t = 0 s” is set to correspond to the first peak in the pressure time history. The effective pressure and temperature for this experiment are 14.3 atm and 971 K, respectively, with oxygen mole fraction of 16.6% and φ = 0.35. The pressure time history has been filtered using a lowpass filter (<2500 Hz). The first peak in the pressure trace occurs due to compression and the sealing of the gases in the test section. The peak is followed by a decrease in pressure due to heat losses to the test section walls, followed by an increase in pressure due to ignition, resulting in the maximum pressure observed in the experiment. The emission signal from the test-gas mixture also peaks during ignition. Fractional absorption data based on the difference between the reference and the transmitted laser intensities are presented in the lower panel of Fig. 2. Prior to 7 ms, there is no absorption of the UV laser emission. At approximately 9 ms, absorption starts to increase until 12 ms where a peak of 13% absorption is observed. This smaller peak in the absorption

profile is followed by a large and rapid increase in absorption which occurs simultaneous to ignition. The preignition absorption is observed in off-line absorption experiments (where the laser emission is set at a frequency that does not correspond to resonant transitions in the OH spectrum), whereas the large absorption feature is not observed in off-line experiments. Based on kinetic modeling, which is discussed further below, the preignition absorption is attributed to intermediate olefins. The preignition absorption is unlikely to have a large effect on the OH determination (described below); because the absorption is attributed to intermediate olefins, which peak in concentration before ignition, while the OH concentration peaks during ignition. Specifically, in the off-line experiments, the preignition absorption accounted for a maximum of 3% of the peak absorption measured during on-line ignition experiments. Consequently, the preignition absorption is not considered in the determination of the OH mole fraction, but it is included in the uncertainty analysis presented below. The absorption time histories can be converted to accurate quantitative OH mole fraction time histories only when the conditions within the test volume can

558

X. He et al. / Combustion and Flame 145 (2006) 552–570

Fig. 3. Typical end-view imaging sequence of iso-octane ignition in the RCF test section for experimental conditions of Peff = 9.9 atm, Teff = 1016 K, φ = 0.3, and χO2 = 16.6%.

be considered homogeneous. If ignition is not homogeneous, the absorption path length (required for the χOH determination) can be difficult to identify. In addition, the correction for emission from the test-gas mixture (discussed further below) assumes emission in the test volume to be isotropic and that the intensity can be measured using detector 3. An indication of homogeneity in the test volume was made using the results of the high-speed imaging system. For example, a typical imaging sequence of a RCF iso-octane ignition experiment is presented in Fig. 3. A significant imaging sequence spanning −50 to +100 ms (relative to the end of compression) of test time was acquired, and only the six sequential images corresponding to ignition are presented in Fig. 3. Each image in the sequence is separated by 38 µs. As seen in the images, ignition occurs homogeneously in the core region of the test volume within a period of 120 µs. No distinct, spatially resolved features were observed. For all experiments conducted in this study, the ignition events were similar to those shown in Fig. 3 and were therefore considered homogeneous. For further discussion and additional imaging of iso-octane ignition mixtures, please see Walton et al. [26]. The conversion of transmitted UV intensity to OH mole fraction is based on Beer’s law, where the at-

tenuation of incident radiation by a nonsaturating, linearly absorbing medium is described by the following relation,  L    I = exp − Sφv P χOH dx , (1) I0 v 0

where I0 is the intensity of the incident radiation intensity, I is the intensity observed after propagation through an absorbing medium of length L, S is the transition or line strength, φv is the line-shape function, P is pressure, and χOH is the OH mole fraction. If the environmental conditions along the probe lineof-sight are uniform, the OH mole fraction can be written as   1 I χOH = − (2) ln . Sφv P L I0 v The line shape is a function of the pressure, temperature, and composition of the test-gas mixture. In determining the line-shape function, Doppler and collisional broadening were considered and a Voigt convolution of the line shapes was assumed. Prior to ignition, the composition of the test-gas mixture (required for the determination of the collisional broadening) was assumed to consist of argon, nitrogen, and oxygen. Broadening by iso-octane was not considered because of small concentration. After ignition,

X. He et al. / Combustion and Flame 145 (2006) 552–570

the test-gas mixture is assumed to react to completion and broadening by water and carbon dioxide is included in the determination of φv . During ignition, the composition of the test-gas mixture is scaled from the reactants to the products based on the extent of reaction indicated by the pressure time history. Due to the limited data available for OH broadening by CO2 and O2 , the broadening parameters of H2 O and N2 (taken from Rea [28]) were used for CO2 and O2 , respectively. The path length L was estimated to be about 4.5 cm. This estimate is based on the images obtained from the high-speed camera and the heat transfer model used to predict the heat losses after compression. A detailed description of the heat transfer model can be found in Donovan et al. [29]. Uncertainties in the path length are considered in determining the overall uncertainty in the measured χOH described below. The temperature of the test-gas mixture is required for the determination of both the transition strength and the line-shape function. In this work, the temperature time history is calculated based on a modified pressure time history. The pressure in the test section is considered uniform throughout the compression and ignition processes. The temperature, however, is not homogeneous (due to the cold walls of the test volume). In order to calculate the temperature in the core region of the test section, where the temperature can be considered uniform, the pressure trace is divided into three time intervals. Fig. 2 indicates the three intervals of the pressure time history considered and the corresponding temperature profile calculated using the process described here. The first time interval is from the start of compression to the minimum pressure after compression, but prior to ignition. For this interval, we assume that the mixture composition does not change. The temperature is then calculated from the initial temperature (T0 , typically 297 K) and pressure (P0 , the charge pressure) by numerically integrating the isentropic relation, T T0

  γ P d ln T = ln , γ −1 P0

(3)

where γ is the specific heat ratio of the test-gas mixture. The second time interval is from the end of the first interval to the time when the transmitted UV intensity reaches the minimum value (or the peak absorption, see Fig. 2). The moment when the transmitted UV intensity reaches the minimum is defined as the end of ignition in the core region. During the second time interval, the mixture composition changes from the

559

unburned iso-octane mixture to combustion products and intermediates. The third time interval used for the temperature calculation uses only a portion of the experimental pressure data. Here, the later portion of the pressure trace after the peak pressure is observed (see Fig. 2) is fit to a polynomial. The polynomial fit to the pressure data is then extrapolated back in time until the end of the second time interval. This method results in a higher peak pressure at ignition compared to the experimentally observed value. In this manner, we are attempting to create a pressure time history consistent with a test volume where only the core region ignites. If the actual pressure data were used, the temperature of the core region of the test volume would be underestimated. The actual pressure is affected by cooling of the boundary layer gas. For the second and third time intervals, the temperature is determined using the pressure time histories, the ideal gas law, and the assumption of a constant volume. The change in the number of moles due to reaction is considered using the fractional rise in pressure to asses the extent of reaction. Fig. 4 presents results for the temperature determination for the pressure data presented in Fig. 2, based on the three-interval method. As an indication of the appropriateness of the approach, limiting extremes for the temperature of the test-gas mixture can be determined for comparison. For example, the upper limit of the mixture temperature after ignition is the constant volume (CV) adiabatic flame temperature, and a lower limit of the mixture temperature after ignition is the constant pressure (CP) adiabatic flame temperature. The corresponding values for TCV and TCP are presented in Fig. 4. As seen in the figure, within several milliseconds after ignition, the temperature calculated using the three-interval method lies between the two temperature limits. Specifically, the maximum temperature calculated using the three time interval method is 1730 K. The corresponding CV and CP temperatures are 1849 and 1630 K, respectively. Fig. 4 also presents the OH mole fraction time history determined using Beer’s law and the three time interval temperature profiles. The OH profiles based on the CP and CV temperature profiles are included for comparison. The maximum value for χOH for the three time interval method is 812 ppm. The maximum values for χOH calculated using the CV and CP temperature profiles are 870 and 765 ppm, respectively. Several features seen in the χOH profile shown in Fig. 4 are worth noting, as they are common to all the experimental data. Almost no OH is produced until homogeneous ignition occurs, and during ignition there is a sharp increase in the OH mole fraction. After the OH mole fraction reaches a maximum value, χOH rapidly decreases to a plateau level where the

560

X. He et al. / Combustion and Flame 145 (2006) 552–570

Fig. 4. OH mole fraction and supporting P and T time histories for the results presented in Fig. 2 (Peff = 14.27 atm, Teff = 971 K, φ = 0.35, and χO2 = 16.6%). The pressure time history used for the determination of the temperature time history is shown in the lower panel. Temperature profiles based on adiabatic assumptions are provided for comparison along with the resulting effects on the χOH time history. See text for details.

OH remains constant for a short period of time. At long times, the OH levels slowly decrease due to the decrease in temperature in the test volume caused by heat losses. The ignition delay time for each experiment was determined using the pressure time history and the methods described previously in the work by He et al. [1]. The process for determining τign from the pressure data is briefly reviewed here. The end of compression is designated as the first time the pressure reaches Peff due to compression. This point is designated t = 0 s and is used as the starting point for τign . The portion of the pressure trace which corresponds to the sharp initial pressure rise due to ignition is linearly extrapolated. The relatively constant portion of the pressure trace prior to ignition is also linearly extrapolated. The intersection of the two linear fits is designated the start of the ignition and is equal to τign . The ignition delay time can also be determined using the χOH time history. In this work, the end of the compression was defined as t = 0 ms in the same manner as used for the pressure data in He et al. [1], and the time when χOH reached the maximum value was designated as the start of ignition. The difference between these times was designated as the ignition

delay time τOH . The iso-octane ignition delay times at HCCI conditions (which include the τP data presented in Table 1) were well predicted using the correlation, −1.41 τpred = 1.3 × 10−4 P −1.05 φ −0.77 χO 2

× exp(33,700/R[cal/mol/K] T ),

(4)

where P is pressure [atm], T is temperature [K], φ is the equivalence ratio, χO2 is the oxygen mole percent [%], and τpred is the ignition delay time [ms]. Table 1 presents a summary of the results for ignition delay time based on the P (τP ) and OH (τOH ) data, and predicted ignition delay time using Eq. (4) (τpred ). Note that the τP data have been presented previously in He et al. [1] and are reproduced here to facilitate comparison with the OH data. As seen in the table, the agreement between the ignition delay time data based on χOH , based on pressure, and the predicted values is excellent (within 11% for the range of conditions studied). In this study, the ignition delay time, the maximum χOH , and the plateau χOH , are key features of each experiment. Hence, these characteristics are used for discussion of the effects of the experimental conditions on the OH radical time history and for benchmarking iso-octane reaction mechanisms. Table 2 summarizes the experimental results for χOH ,

X. He et al. / Combustion and Flame 145 (2006) 552–570 Table 3 Experimental uncertainties Uncertainty source

Direct uncertainty

Ui = uncertainty in χOH

Absorption due to olefin molecules Laser source departure from resonant laser frequency Peak temperature estimation Pressure oscillations, pressure transducer linearity, and amplifier drift Path length Spectroscopic parameters Combined uncertainty

3%

−8%

±0.05 cm−1

3%

+150/−100 K

+10/−7%

±4%

0.5%

±1.0 mm

±2.5% ±5% ±12%

where OH_max represents the maximum χOH during ignition and OH_plateau represents the plateau χOH after ignition. For discussion purposes, the table is sorted into four categories: temperature, pressure, equivalence ratio, and additional data. For the first three categories, only the named parameter is changed while all the other experimental conditions are approximately the same.

561

Table 4 Features of iso-octane chemical reaction mechanisms examined Source

Number of species

Curran et al. [5] 858 Golovichev/ 84 Chalmers [32] Tanaka et al. [31] 38 Glaude et al. [33] 353

Number of reactions

Mechanism type

3606 412

Detailed Skeletal

61 1481

Reduced Detailed

to the pressure oscillations. The combination of these two sources yields an overall pressure uncertainty of 4%, which results in a ±0.5% of uncertainty in χOH . Additional uncertainty comes from the estimate for the path length used in Eq. (3). In this study, we estimate a ±1.0 mm of uncertainty in path length, which yields additional uncertainty of ±2.5% in χOH . The last uncertainty comes from the spectroscopic parameters used to calculate line-shape function. For the conditions of the current work, this yields a total uncertainty in χOH of ±5%. Combining the sources of uncertainty using a square root of the sum-of-thesquares approach, all the uncertainties yield an overall uncertainty in χOH of ±12%.

4. Discussion 4.1. Trends in OH characteristic features

3.2. Uncertainty analysis Several uncertainties in experimental conditions contribute to uncertainty in the determination of χOH . A summary of the uncertainties and the effects on χOH are presented in Table 3. As noted previously, absorption due to the presence of olefin molecules may be as much as 3% of the incident laser intensity, which corresponds to a −8% uncertainty in the χOH measurements. The largest uncertainty comes from the estimate for temperature during ignition. Compared with the calculated peak temperature based on CP and CV adiabatic assumptions, the estimated peak core temperature has an uncertainty of approximately +150/−100 K. This translates into a maximum of +10/−7% error in χOH . The other main uncertainty comes from the laser source. Based on the accuracy of the wavemeter used to monitor the laser wavelength and the use of a reference flame to establish the laser wavelength at the resonant frequency, the uncertainty in the frequency of the UV laser is set at 0.05 cm−1 . This uncertainty in wavelength corresponds to a +3% uncertainty in the χOH measurements. Errors in the measurement of pressure arise from two sources: measurement error and error due

The characteristics of the χOH data presented in Table 2 exhibit clear trends with pressure, temperature, and equivalence ratio. As pressure increases, the maximum value for χOH decreases, whereas the mole fraction of OH increases with increasing temperature and with increasing equivalence ratio. These trends can be explained through understanding the reactions controlling the OH profiles under these experimental conditions. A detailed discussion of the reaction kinetics is presented in the following sections. 4.2. Comparison with kinetic modeling There are numerous iso-octane oxidation mechanisms available in the literature that have been developed and optimized for specific combustion applications. Several of these mechanisms were examined for the ability to reproduce the features of the OH data observed in the current work. Table 4 presents a summary of the mechanisms considered and the characteristics for each. For the modeling studies, the Closed Homogeneous Batch reactor/Chemkin 4.0.1 suite of programs [30] was used. A simplified model using Peff ,

562

X. He et al. / Combustion and Flame 145 (2006) 552–570

Fig. 5. Comparison between experimental and modeling results using different iso-octane reaction mechanisms for χOH time history. Experimental conditions are those of Fig. 4 (Peff = 14.27 atm, Teff = 971 K, φ = 0.35, and χO2 = 16.6%).

Teff , and the initial reactant composition as the initial conditions were used in the modeling study, in which constant internal energy and constant volume conditions were assumed. This simplified model yields very similar results for both ignition delay time and χOH time histories to more complex modeling approaches (e.g., a model which accounts for the rapid heat loss that occurs immediately after compression). For a detailed description and discussion of other modeling approaches for UM-RCF experiments, please see He et al. [1]. The modeling results for OH mole fraction time histories using the four iso-octane oxidation mechanisms are presented in Fig. 5. All the predicted results have good agreement with the general form of the experimental χOH profile. Note that because the model predictions are performed assuming adiabatic conditions, no change in χOH is observed after the plateau, with the exception of the reduced mechanism developed by Tanaka et al. [31]. The mechanism by Curran et al. [5] most closely reproduces the ignition delay time, the maximum χOH , and the plateau χOH . The mechanism by Golovichev [32] overpredicts the ignition delay time and underpredicts the maximum χOH . Both mechanisms by Tanaka et al. [31] and Glaude et al. [33] overpredict the maximum χOH . However, the mechanism by Tanaka and co-workers underpredicts the ignition delay time, while the mechanism by Glaude and co-workers overpredicts the ignition delay time.

4.3. OH rate of production and sensitivity analysis As seen in Table 3, the mechanism by Curran et al. [5] accurately predicts many of the quantitative features of the χOH time histories. Based on this good agreement, the mechanism by Curran et al. [5] was used to conduct a detailed kinetic analysis of the OH mole fraction profiles for representative experimental conditions. Results for rate of production (or contribution factor) and sensitivity analyses are presented in Figs. 6–8. The OH rate of production results show that OH is generated by H2 O2 decomposition at early times. The total OH rate of production peaks during ignition, where the OH production is primarily controlled by O + H2 O = OH + OH and H + O2 = O + OH. Two important OH scavenging reactions during ignition are CO + OH = CO2 + H and HO2 + OH = H2 O + O2 . These two reactions are the most important sources of heat release during iso-octane combustion. OH sensitivity analysis is presented for the Curran mechanism for two experimental conditions in Figs. 7 and 8, where the sensitivity coefficient is defined as S=

ki ∂χOH . ∂ki (χOH )local

(5)

Fig. 7 indicates that reaction (R2) (OH + OH (+M) = H2 O2 (+M)) is the dominant reaction affecting the OH profile during ignition. As the temperature and

X. He et al. / Combustion and Flame 145 (2006) 552–570

563

Fig. 6. OH rate of production analysis based on the iso-octane reaction mechanism developed by Curran et al. [5]. Experimental conditions are those of Fig. 5 (Peff = 14.27 atm, Teff = 971 K, φ = 0.35, and χO2 = 16.6%).

Fig. 7. OH sensitivity analysis based on the iso-octane reaction mechanism developed by Curran et al. [5]. Experimental conditions are those of Fig. 5 (Peff = 14.27 atm, Teff = 971 K, φ = 0.35, and χO2 = 16.6%).

pressure increase from the conditions of Fig. 7 to the conditions of Fig. 8, the influence of this reaction decreases, while the sensitivity to

and

H + O2 = OH + O

increases.

(R3)

CH3 + HO2 = CH3 O + OH

(R4)

564

X. He et al. / Combustion and Flame 145 (2006) 552–570

Fig. 8. OH sensitivity analysis based on the iso-octane reaction mechanism developed by Curran et al. [5]. Experimental conditions are Peff = 9.9 atm, Teff = 1016 K, φ = 0.3, and χO2 = 16.6%.

The results of the OH sensitivity analysis performed at the fuel lean, intermediate-temperature, and moderate pressure conditions have many reactions in common with the results for the brute force sensitivity analysis conducted by Curran et al. [5], for ignition delay time of iso-octane at a range of temperatures (725, 825, and 1000 K) and 40 bar pressure. Specifically, in the study by Curran et al. [5], β-scission reactions of alkyl species had the most affect on τ , as well as some hydrogen peroxide reactions, including (R2). However, Curran et al. [5] also found significant sensitivity to reactions involving carbonylhydroperoxide species which were not identified in the current work. The sensitivity to the hydrogen peroxide decomposition reaction can be used to interpret the ignition delay time trends reported previously [1]. In He et al. [1], the ability of several iso-octane reaction mechanisms to reproduce the experimentally observed trends for τ as a function of T , P , φ, and χO2 was examined. The mechanism by Curran et al. [5] yielded a pressure dependence of P −0.88 , compared to the experimental results of P −1.05 [1]. As seen in Fig. 9, for the experimental conditions studied in the current work, reaction (R2) is in the intermediate region between the high- and low-pressure limits. For the temperatures and pressures found at the end of compression to the start of ignition (i.e., T = 970–1600 K, P = 14 atm), the rate coefficient for (R2) is proportional to pressure in the range from

P 0.72 to P 0.86 , which is in excellent agreement with the functional relationship between τ and P observed for the mechanism by Curran et al. [5]. The results of the current work can be combined with data from previous studies to help clarify the pressure dependence of the ignition delay time for iso-octane and the significance of the negative temperature coefficient region. Specifically, the combined data from this work, He et al. [1], Fieweger et al. [11], and Davidson et al. [2] are grouped based on pressure and presented in Fig. 10. The data are in good agreement with respect to trends in pressure and temperature. Note that very limited NTC behavior is observed for iso-octane ignition, and the pressure dependence observed under the conditions examined in the current work is attributed to the H2 O2 + M reaction. 4.4. Effects of (Hf0 )298,OH and rate coefficient uncertainty on iso-octane ignition In the recent study of the OH enthalpy of formation ((Hf0 )298,OH ) by Herbon et al. [34], the authors conclude that values commonly used for (Hf0 )298,OH may be in error by as much as 2 kJ/mol. Many thermodynamic data bases (e.g., the Sandia data base [35]) set (Hf0 )298,OH at a value between 39.0 and 39.7 kJ/mol. The thermodynamic data included in the mechanism by Curran et al. [5]

X. He et al. / Combustion and Flame 145 (2006) 552–570

565

Fig. 9. Pressure dependence of reaction (R2) (OH + OH (+M) = H2 O2 (+M)) for 970 K. The rate coefficient data are taken from the mechanism by Curran et al. [5].

Fig. 10. Summary of the current work and previous studies of iso-octane ignition delay time as a function of temperature and pressure. All data have been normalized (as necessary) to ϕ = 1.0 and χO2 = 21% using Eq. (4).

use a value of (Hf0 )298,OH = 39.7 kJ/mol. Herbon et al. [34] recommend a value of (Hf0 )298,OH = 37.3 kJ/mol, which is in good agreement with other experimental and theoretical determinations by Ruscic et al. [36] and Joens [37]. When the (Hf0 )298,OH used in the mechanism by Curran et al. [5] is replaced by the value recommended by Herbon et al. [34],

there is a significant effect on the χOH time history as seen in Fig. 11. The peak of the χOH time history is relatively unchanged; however, the ignition delay time is decreased by ∼20% using the lower value for (Hf0 )298,OH . As seen by comparing the time histories, the change in (Hf0 )298,OH significantly reduced the agreement between the experimental data

566

X. He et al. / Combustion and Flame 145 (2006) 552–570

Fig. 11. Comparison of experimental and modeling results using the unmodified mechanism and thermochemical data by Curran et al. [5], the mechanism by Curran et al. [5] with revised (Hf0 )298,OH data, and the mechanism by Curran et al. [5] with revised (Hf0 )298,OH and rate coefficient data. Experimental conditions of those of Fig. 5 (Peff = 14.27 atm, Teff = 971 K, φ = 0.35, and χO2 = 16.6%). The residual (the difference between the experimental data and the modeling results) for the best fit of the revised mechanism is provided in the bottom panel.

and the prediction for ignition delay time using the mechanism by Curran et al. [5]. The large sensitivity of the ignition delay time to (Hf0 )298,OH is due to the change of concentration equilibrium constant (Kc ) which is calculated based on the thermodynamic data, and used to determine the reverse rate coefficient for some reactions. In the mechanism by Curran et al. [5], the majority of the reverse rate coefficients are explicitly provided, except for reactions involving three-body collisions. Among these reactions, (R2) is the dominant reaction that influences the OH mole fraction time histories. The decrease in (Hf0 )298,OH results in a decrease in Kc,R2 by about a factor of 2. By decreasing Kc,R2 , the reverse rate coefficient for (R2) is increased relative to the forward rate coefficient, leading to an increased rate of production of OH. (Note that reaction (R2) is running in the reverse direction under the experimental conditions studied, as seen in Fig. 6.) The faster OH production decreases the ignition delay time as seen in Fig. 11. Based on the results of the sensitivity analyses, the effects of the reactions with a combination of the

largest uncertainties and the highest OH sensitivities coefficients were investigated for their impact on the OH time histories. Specifically, changing the rate coefficients for reactions (R2), (R4), and (R5) (where (R5) is an alternative path for the CH3 + HO2 reaction) CH3 + HO2 = CH4 + O2

(R5)

within the respective uncertainties was investigated to determine if better agreement with the experimental χOH time histories could be obtained. Fig. 11 presents the modeling results where the revised value for (Hf0 )298,OH is used and the rate coefficient for (R2) (OH + OH (+M) = H2 O2 (+M)) has been reduced to obtain a best fit of the OH time history. The residual (the experimental time history minus the calculated time history) for the best-fit condition is shown in the lower panel of the figure. The A coefficient (or the preexponential coefficient) for the low-pressure rate coefficient was decreased by 74% (or multiplied by 0.26) for the best-fit case presented in Fig. 11. Modifying the rate coefficient to the best-fit value leads to excellent agreement with the experimentally observed ignition delay time, and

X. He et al. / Combustion and Flame 145 (2006) 552–570

567

Fig. 12. Comparison of recommendations for the low-pressure rate coefficient for reaction (R2) (OH + OH + M → H2 O2 + M).

good agreement with the maximum and plateau values for χOH . The A coefficient for the low-pressure limit for reaction (R2) was adjusted for each of the experiments and the optimum values are reported in Table 2. Because the mechanism by Curran et al. [5] consistently underpredicts the ignition delay time (see Table 2), the A coefficient for (R2) was reduced for each experiment. It is interesting to note that the bestfit values required modifying the A coefficient by approximately the same amount for each experiment. Although the decrease in the A coefficient required was large, the uncertainty in the rate coefficient for (R2) is also high, as seen in Fig. 12 which presents various recommendations for the low-pressure limit for OH + OH + M = H2 O2 + M. It is also important to note that there are very few experimental data available for (R2), and that the data presented in Fig. 12 are primarily from theoretical estimates (e.g., Brouwer et al. [38]), compilations of rate coefficient data (e.g., Baulch et al. [39], Warnatz [40], Tsang and Hampson [41]), and development of overall mechanisms which typically include fits to multiple recommendations (e.g., Curran et al. [5] and Petersen and Hanson [42]). Because reactions (R4) (CH3 + HO2 = CH3 O + OH) and (R5) (CH3 + HO2 = CH4 + O2 ) are different product channels of the CH3 + HO2 reaction, the effects of these reactions on the OH time

histories were investigated by modifying the rate coefficients simultaneously. A similar level of agreement to that shown in Fig. 11 can be achieved by increasing the rate coefficients of reactions (R4) and (R5) by a factor of 7. As with reaction (R2), the rate coefficients of (R4) and (R5) have not been well studied, and no direct measurements of the rate coefficient data are available at combustion conditions. Colket et al. [43] estimate kf,R4 = 1.99 × 1013 [cm3 mol−1 s−1 ] at 1100 K with an uncertainty factor of 3. Tsang and Hampson [41] estimated kf,R5 = 3.61 × 1012 [cm3 mol−1 s−1 ] with uncertainty factor of 5. In the mechanism by Curran et al. [5], the rates for (R4) and (R5) are taken from the expressions recommended by Amano and Dryer [44], where kf,R4 = 1.1 × 1013 [cm3 mol−1 s−1 ] and kf,R5 = 3.6 × 1012 [cm3 mol−1 s−1 ]. 4.5. Iso-octane oxidation at intermediate temperatures It is useful to consider how the reaction path sequence varies for the intermediate ignition temperatures considered in the current work compared to high- or low-temperature combustion of iso-octane. Figs. 13a and 13b present a simplified reaction path diagram for iso-octane combustion for conditions of Peff = 14.27 atm, Teff = 971 K, φ = 0.35, and

568

X. He et al. / Combustion and Flame 145 (2006) 552–570

(a) Fig. 13. Reaction path diagram for iso-octane combustion under fuel lean, intermediate-temperature, moderate pressure conditions of Peff = 14.27 atm, Teff = 971 K, φ = 0.35, and χO2 = 16.6%: (a) iso-octane reaction paths, (b) C3 H6 and C4 H8 reaction paths. The values next to the arrows indicate the relative significance of the reaction paths, with 0 being the least important (an inactive reaction path) and 100 being the most important (an exclusive reaction path).

χO2 = 16.6%. The values beside the arrows give the importance of each path on a scale of 0 to 100, where 100 is the most important and 0 is the least. These figures indicate that in this intermediate-temperature regime, unimolecular decomposition is not important to the direct removal of iso-octane, compared to hydrogen atom abstraction by OH and H. β-Scission is the major path for the C8 H17 alkyl radicals formed from the H-atom abstraction reactions, and subsequently C3 and C4 chemistry dominates the reaction sequence. Carbonylhydroperoxide species do not appear to have a large role under these conditions.

5. Summary and conclusions New data for absolute, quantitative OH mole fraction time histories have been obtained over a range of pressures (P = 8.54–15.13 atm), temperatures (T = 954–1019 K), and equivalence ratios (φ = 0.25–0.35). The OH data provide vital, rigorous benchmarks for an important intermediate species during iso-octane ignition under conditions where

OH has not been measured previously. The results are critical for more detailed understanding of isooctane autoignition kinetics under HCCI engine operation conditions and for refining iso-octane reaction mechanisms. The ignition delay time results for OH are in excellent agreement with τign data based on pressure [1], indicating that pressure and OH time histories can be used interchangeably for accurate determination of ignition delay time for iso-octane mixtures under these conditions. Of the several isooctane reaction mechanisms available in the literature and considered in this work, the mechanism by Curran et al. [5] exhibited the best ability to reproduce the quantitative features of the χOH time histories. The OH data were very sensitive to the enthalpy of formation for OH and reactions that have considerable uncertainties, specifically OH + OH + M = H2 O2 + M, CH3 + HO2 = CH3 O + OH, and CH3 + HO2 = CH4 + O2 . These reactions are in need of further investigation to reduce the uncertainties in rate coefficients that can have considerable impact on reliably predicting ignition delay times under HCCI operating conditions.

Fig. 13. (continued)

569

(b)

X. He et al. / Combustion and Flame 145 (2006) 552–570

570

X. He et al. / Combustion and Flame 145 (2006) 552–570

Acknowledgments The authors acknowledge the generous support of the Department of Energy via the HCCI University Consortium. We also thank Dr. William Pitz and Dr. Charlie Westbrook at Lawrence Livermore National Laboratory for their assistance with the sensitivity analysis.

References [1] X. He, M.T. Donovan, B.T. Zigler, T.R. Palmer, S.M. Walton, M.S. Wooldridge, A. Atreya, Combust. Flame 142 (2005) 266–275. [2] D.F. Davidson, B.M. Gauthier, R.K. Hanson, Proc. Combust. Inst. 30 (2005) 1175–1182. [3] S. Tanaka, F. Ayala, J.C. Keck, J.B. Heywood, Combust. Flame 132 (1–2) (2003) 219–239. [4] K. Fieweger, R. Blumenthal, G. Adomeit, Combust. Flame 109 (1997) 599–619. [5] H.J. Curran, P. Gaffuri, W.J. Pitz, C.K. Westbrook, Combust. Flame 129 (2002) 253–280. [6] S.-C. Kong, R.D. Reitz, Combust. Theory Model. 7 (2) (2003) 417–433. [7] P.L. Kelly-Zion, J.E. Dec, Proc. Combust. Inst. 28 (2000) 1187–1193. [8] D.L. Flowers, S.M. Aceves, J. Martinez-Frias, R.W. Dibble, Proc. Combust. Inst. 29 (2002) 687–693. [9] D.F. Davidson, M.A. Oehlschlaeger, J.T. Herbon, R.K. Hanson, Proc. Combust. Inst. 29 (2002) 1295–1301. [10] M.A. Oehlschlaeger, D.F. Davidson, J.T. Herbon, R.K. Hanson, Int. J. Chem. Kinet. 36 (2) (2004) 67–78. [11] K. Fieweger, R. Blumenthal, G. Admeit, Proc. Combust. Inst. 25 (1994) 1579–1585. [12] D.J. Vermeer, J.W. Meyer, A.K. Oppenheim, Combust. Flame 18 (1972) 327–336. [13] R. Minetti, M. Ribaucour, M. Carlier, L.R. Sochet, Combust. Sci. Technol. 113–114 (1996) 179–192. [14] S. Tanaka, F. Ayala, J.C. Keck, J.B. Heywood, Combust. Flame 132 (2003) 219–239. [15] P. Park, J.C. Keck, SAE Paper 900027, 1990. [16] R. Minetti, M. Carlier, M. Ribaucour, E. Therssen, L.R. Sochet, Proc. Combust. Inst. 26 (1996) 747–753. [17] M. Metghalchi, J.C. Keck, Combust. Flame 48 (1982) 191–210. [18] C.V. Callahan, T.J. Held, F.L. Dryer, R. Minetti, M. Ribaucour, L.R. Sochet, T. Faravelli, P. Gaffuri, E. Ranzi, Proc. Combust. Inst. 26 (1996) 739–746. [19] J.S. Chen, T.A. Litzinger, H.J. Curran, Combust. Sci. Technol. 156 (2000) 49–79. [20] H.J. Curran, W.J. Pitz, C.K. Westbrook, C.V. Callahan, F.L. Dryer, Proc. Combust. Inst. 27 (1998) 379–387. [21] P. Dagaut, M. Reuillon, M. Cathonnet, Combust. Sci. Technol. 95 (1994) 233–260. [22] S.M. Aceves, D.L. Flowers, C.K. Westbrook, J.R. Smith, W. Pitz, R. Dibble, M. Christensen, B. Johansson, SAE Paper 2000-01-0327, 2000. [23] J.F. Griffiths, K.J. Hughes, R. Porter, Proc. Combust. Inst. 30 (2005) 1083–1091.

[24] M.T. Donovan, X. He, B.T. Zigler, T.R. Palmer, M.S. Wooldridge, A. Atreya, Combust. Flame 137 (2004) 351–365. [25] M.T. Donovan, Ph.D. dissertation, Department of Mechanical Engineering, University of Michigan, 2003. [26] S.M. Walton, X. He, B.T. Zigler, M.S. Wooldridge, A. Atreya, in: Proceedings of the Fourth Joint Meeting of the U.S. Sections of The Combustion Institute, March 20–23, 2005. [27] S.M. Walton, X. He, B.T. Zigler, M.S. Wooldridge, A. Atreya, in preparation. [28] E.C. Rea Jr., Ph.D. dissertation, Mechanical Engineering Department, Stanford University, Standford, CA, 1991. [29] M.T. Donovan, T. Palmer, X. He, M.S. Wooldridge, A. Atreya, in: The Combustion Institute Canadian Section, 2002 Spring Technical Meeting, May 12–15, 2002, Paper No. 5, pp. 5.1–5.6. [30] R.J. Kee, F.M. Rupley, J.A. Miller, M.E. Coltrin, J.F. Grcar, E. Meeks, H.K. Moffat, A.E. Lutz, G. DixonLewis, M.D. Smooke, J. Warnatz, G.H. Evans, R.S. Larson, R.E. Mitchell, L.R. Petzold, W.C. Reynolds, M. Caracotsios, W.E. Stewart, P. Glarborg, C. Wang, O. Adigun, W.G. Houf, C.P. Chou, S.F. Miller, P. Ho, D.J. Young, CHEMKIN Release 4.0, Reaction Design, Inc., San Diego, CA, 2004. [31] S. Tanaka, F. Ayala, J.C. Keck, Combust. Flame 133 (2003) 467–481. [32] V. Golovichev, http://www.tfd.chalmers.se/~valeri, 2003. [33] P.A. Glaude, R. Fournet, V. Warth, F. Battin-Leclerc, G.M. Côme, G. Scacchi, http://www.ensic.u-nancy. fr/DCPR/Anglais/GCR/generatedmecanisms/isooctane, 2003. [34] J.T. Herbon, R.K. Hanson, D.M. Golden, C.T. Bowman, Proc. Combust. Inst. 29 (2002) 1201–1208. [35] R.J. Kee, F.M. Rupley, J.A. Miller, Sandia National Laboratories Report No. SAND87-8215B UC-4. [36] B. Ruscic, A.F. Wagner, L.B. Harding, R.L. Asher, D. Feller, D.A. Dixon, K.A. Peterson, Y. Song, X. Qian, C.-Y. Ng, J. Liu, W. Chen, D.W. Schwenke, J. Phys. Chem. A 106 (2002) 2727–2747. [37] J.A. Joens, J. Phys. Chem. A 105 (2001) 11041–11044. [38] L. Brouwer, C.J. Cobos, J. Troe, J. Chem. Phys. 86 (11) (1987) 6171–6182. [39] D.L. Baulch, C.J. Cobos, R.A. Cox, P. Frank, G. Hayman, Th. Just, J.A. Kerr, T. Murrells, M.J. Pilling, J. Troe, R.W. Walker, J. Warnatz, Combust. Flame 98 (1994) 59–79. [40] J. Warnatz, in: W.C. Gardiner (Ed.), Combustion Chemistry, Springer-Verlag, New York, 1985. [41] W. Tsang, R.F. Hampson, J. Phys. Chem. Ref. Data 15 (3) (1986) 1087–1279. [42] E.L. Petersen, R.K. Hanson, J. Prop. Power 15 (4) (1999) 591–600. [43] M.B. Colket, D.W. Naegeli, I. Glassman, Proc. Combust. Inst. 16 (1977) 1023–1039. [44] T. Amano, F.L. Dryer, Proc. Combust. Inst. 27 (1998) 397–404.