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Measurements and calculations of formaldehyde concentrations in a methane/N 2/air, non-premixed ﬂame: Implications for h

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Proceedings of the

Combustion Institute

Proceedings of the Combustion Institute 32 (2009) 1311–1318

www.elsevier.com/locate/proci

Measurements and calculations of formaldehyde concentrations in a methane/N2/air, non-premixed ﬂame: Implications for heat release rate S.B. Dworkin a, A.M. Schaﬀer a, B.C. Connelly a, M.B. Long a, M.D. Smooke a, M.A. Puccio b, B. McAndrew b, J.H. Miller b,* b

a Department of Mechanical Engineering, Yale University, New Haven, CT 06520-8284, USA Department of Chemistry, The George Washington University, 725 21st St., NW, Room 107, WA 20052, USA

Abstract A non-sooting, lifted, methane/air, coﬂowing, non-premixed ﬂame has been studied experimentally and computationally. The ﬂame structure was computed by solving the fully elliptic governing equations, utilizing a 35 species chemical kinetic mechanism, detailed transport coeﬃcients and an optically thin radiation submodel. Gas temperature, major species mole fractions, and non-fuel hydrocarbon concentrations were experimentally mapped in two dimensions with both probe techniques (coupled to infrared absorption spectroscopy and on-line mass spectrometry) and in situ optical diagnostics (laser-induced ﬂuorescence, Rayleigh and Raman scattering). Contour plots of measured and computed formaldehyde concentrations and ﬂuorescence signals agree well and both revealed a region of intense formaldehyde production near the lifted ﬂame base. High formaldehyde production rates correlated well with regions of high heat release. Further, regions of the dominant formaldehyde formation reaction, CH3 + O = HCHO + H, also correlated with areas of maximum heat release rate. Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Formaldehyde concentrations; Methane/air diﬀusion ﬂame; Heat release rates

1. Introduction As reviewed by Najm et al.[1], there has been considerable research aimed at characterizing the heat release region of both premixed and nonpremixed ﬂames [2]. Most of these measurements have utilized optical diagnostics and they include both chemiluminescence of nascent species (CH* and OH*) as well as laser-induced ﬂuorescence measurements of radicals such as CH and *

Corresponding author. Fax: +1 202 994 5873. E-mail address: [email protected] (J.H. Miller).

OH. Najm et al. [1] found that LIF concentrations of the HCO radical spatially and temporally correlate with local heat release. Unfortunately, these signals are suﬃciently weak that planar imaging measurements of the ﬂuorescence may not provide adequate signal-to-noise ratios. Several years ago, we used tunable diode laser absorption spectroscopy coupled with microprobe sampling to determine quantitatively formaldehyde concentrations in a neat methane/air nonpremixed ﬂame [3]. The resulting concentrations were combined with other data from this ﬂame in an analysis of formaldehyde formation and

1540-7489/$ - see front matter Ó 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2008.05.083

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destruction paths to determine HCHO’s dependence on speciﬁc reaction steps. Formaldehyde formation is dominated by the reaction between methyl radical and oxygen atom and its destruction is dominated by hydrogen abstraction. Both processes occur near the stoichiometric surface. The analysis also veriﬁed several points made by other researchers about the heat release rates in methane ﬂames. First, the heat release rate correlates well with the destruction rate of methane, the rate of the reaction between methyl radicals and oxygen atoms, and HCO concentrations. A condition of chemical steady-state was found for HCO and the steady-state estimate of HCO concentration could also be used to estimate local heat release rate. The present study is part of a coordinated program, the goal of which is an improved understanding of the complex interaction between ﬂame chemistry and ﬂuid motion. A variety of diagnostics are being applied to both forced and unforced, axially symmetric ﬂames burning methane or ethylene diluted with nitrogen. These ﬂame systems are also being modeled using the full set of steady, elliptic, partial diﬀerential governing equations for mass, momentum, species and energy conservation. In this paper we demonstrate this approach by returning to the problem of heat release in lifted methane/nitrogen ﬂames. Major, minor, and trace species concentrations have been determined through a combination of in situ optical, extractive optical, and extractive mass spectrometric diagnostics. Measured species concentrations are compared with those computed. Finally, contour maps for the net formaldehyde formation and destruction rate are compared with the heat release rate. 2. Experimental and numerical procedure 2.1. Description of the burner and ﬂame A fuel mixture of 65% methane and 35% nitrogen (mole fraction) ﬂows through a 0.4 cm inner diameter vertical tube, and air issues from the annular region between this tube and a 7.4 cm inner diameter concentric tube (Fig. 1). The fuel was N2-diluted to reduce soot concentrations in the ﬂame and associated diﬃculties with optical measurement interference and with uncertainties in the numerical model due to soot radiation and scrubbing of hydrocarbons. The fuel velocity at the burner surface was a parabolic proﬁle with an average velocity of 35 cm/s and air velocity proﬁles at the burner surface were plug ﬂow of 35 cm/s; physically this was realized by having a honeycomb cover the region of coﬂowing air. The ﬂame was unconﬁned, and the ﬂow was laminar. The combination of N2 fuel dilution, a narrow fuel tube, and a high ﬂow rate of air caused

Fig. 1. Schematic of the burner system.

the ﬂame to be lifted approximately 6 mm above the burner surface. This prevented heat conduction from the ﬂame to the burner and consequent preheating of the reactants. Thus, the thermal boundary condition used in the numerical model at the burner surface was well deﬁned (the reactant temperature equaled room temperature at each radial position), which is crucial to obtaining good agreement between the model and experiments [4,5]. 2.2. Extractive measurements Samples were withdrawn from the ﬂame using a quartz probe similar to the one originally described by Fristrom and Westenberg [6]. Resolution of ﬂame structure in the axial and radial directions is accomplished via movement of the burner assembly on a stepper motor. In this study, argon was added to the fuel ﬂow in the same mole fraction level as it is present in the laboratory’s air. This ensures that the argon mole fraction is constant at all locations sampled within the ﬂame (diﬀusion eﬀects are neglected) and can be used to correct for probe clogging and temperature ﬂuctuations within the ﬂame. This method of calibration was originally described by McEnally et al. [7] for analysis of PAH using microprobe extraction followed by SPIMS. For mass spectrometry measurements, extracted gas passed into a diﬀerentially-pumped region held between 1 and 3 torr by a rotary pump. Samples were withdrawn from here with a second probe and passed into a Stanford Research Systems Residual Gas Analyzer 300 quadrupole mass spectrometer for analysis. For TDLAS measurements, gases from the probe were continuously drawn into a Herriot cell with an 18 m optical path length. Previous TDLAS measurements of formaldehyde line strengths [8] and broadening parameters [9] have been reported [10–12]. We have used TDLAS cou-

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pled with microprobe sampling to determine quantitative formaldehyde concentrations in a neat methane/air non-premixed ﬂame [3]. Cell pressure was maintained at 5 torr during the measurements in order to minimize pressure broadening and isolate neighboring transitions while still maintaining a high signal-to-noise ratio for direct absorption measurements. A type II interband cascade laser [13] was used to generate light near 2807.3 cm1. This light was collimated, passed through a monochromator to select a single longitudinal mode, and then focused into the multipass cell. Transmitted light from the cell was collected with a parabolic mirror and focused onto a cryogenically cooled InSb detector, whose signal was ampliﬁed by a low noise transimpedance preampliﬁer and then recorded on a digital storage oscilloscope. Spectra were obtained over a 0.2 cm1 region chosen to cover a strong formaldehyde transition at 2807.36 cm1 and a relatively weak methane transition at 2807.29 cm1. The much higher concentration of methane encountered throughout most of the ﬂame results in the total absorption from these two transitions being of the same order, allowing for the determination of both species’ concentration from a single spectrum. Spectral ﬁtting of both transitions was performed using the HITRAN database and a Delphi (PASCAL) program to obtain concentrations. 2.3. Laser-induced ﬂuorescence of formaldehyde The third harmonic of a Nd:YAG laser (355 nm) is used to excite a weak rotational trane 1 A2 X e 1 A1 41 vibronic manifold of sition in the A 0 formaldehyde [14,15]. A 30 cm focal length quartz lens is used to focus the UV beam across the diffusion ﬂame. To ensure that the ﬂuorescence is in the linear regime, with no partial saturation, the measurements are made 5 cm before the focus of the UV beam, resulting in a beam diameter of roughly 0.5 mm in the measurement region. The laser energy is monitored using a pyroelectric energy meter (Scientech PHD25) connected to a digital oscilloscope. The linear ﬂuorescence is imaged onto an intensiﬁed CCD camera (Princeton Instruments ICCD-576TG/RB) by a camera lens (Nikon 50 mm, f/1.8). The intensiﬁer is gated so that it is fully on upon arrival of the laser pulse. A gate time of 70 ns was chosen to guarantee collection of the full formaldehyde ﬂuorescence signal (maximum lifetime of 18 ± 8 ns [16]) and to minimize interferences from signals with longer lifetimes. An interference ﬁlter centered at 412.5 nm (10 nm bandwidth) is placed in front of the camera lens to image the 201 412 vibrational ﬂuorescence band and to ﬁlter out interferences and ﬂame luminosity [14]. Some interference from the broadband PAH ﬂuorescence is still transmitted

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by the ﬁlter. Eﬀorts to subtract out the background PAH ﬂuorescence using an oﬀ-resonance signal above the formaldehyde bandhead (after 550 nm) were unsuccessful, as this background signal possesses a temperature-dependent bias with respect to the on-resonance signal. The ﬂuorescence signal is integrated on the detector for 64 laser pulses, chosen to correspond to event sampling on the oscilloscope. The experiment is controlled through a computer, which records synchronized data from both the CCD camera and the digital oscilloscope. A two-dimensional image of the formaldehyde ﬂuorescence distribution is created by tiling together a series of images recorded at 0.1-mm intervals from 2 to 35 mm above the burner. Each image is normalized by the recorded laser energy, and corrected for detector background and for nonuniform detector gain and optical throughput. For linear ﬂuorescence, the scattered intensity has the form Sf / Ng fB/Q21, where Ng is the total number density in the ground electronic state, fB is the Boltzmann population fraction, and Q21 represents the total collisional quenching rate. The Boltzmann correction for formaldehyde is well accounted for using the analysis of Clouthier and Ramsay [15,17]. A model that accounts for the species dependent quenching rate is not available, however. Instead, the quenching rate is determined by assuming a temperature dependence of the quenching cross section [18]. The result provides an upper and lower bound on the temperature dependence of the overall correction [15,18], where the quenching rate is found to vary between Q21 T 0:5 and Q21 T 1 . To make a direct comparison with computational results, the Boltzmann and quenching corrections must be accounted for. Instead of using the experimental data from Rayleigh and Raman experiments to determine an experimental mole fraction, a reverse quenching correction is applied to the calculated ﬂame to determine an expected ﬂuorescence signal for comparison with the experimental results. This approach has the advantage of comparing quantities with less uncertainty than the traditional approach of determining an experimental mole fraction, where the noise level increases as multiple measurements are combined. 2.4. Rayleigh/Raman measurements Two-dimensional images of temperature and major species mole fractions were measured using vibrational Stokes-shifted Raman scattering and Rayleigh scattering [19–21]. The scattering was excited with the second harmonic of a Qswitched Nd:YAG laser which was focused into a 300-lm beam over the center of the burner (Fig. 2). To prevent air breakdown over the burner, the laser was double-pulsed, with pulse sep-

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dence of Raman cross sections was modeled for all species [23,24], and the depolarization of the Raman signals was taken into account. An iterative technique, which usually converged in three iterations, was used to determine species mole fractions and temperature. 2.5. Numerical method

Fig. 2. Schematic of the Rayleigh/Raman/IV system.

arations of 100 ls and an average energy of 150 mJ per pulse. Measurements were performed from z = 0.2–5.4 cm, in 0.05 cm steps close to the burner surface and 0.1 cm steps further downstream. These line measurements were then tiled together to form images. Each measurement was integrated over 1000 double laser pulses to obtain adequate signal/noise. The scattered light was collected with a f/1.8 camera lens, rotated 90° by a pair of mirrors placed behind the lens, and focused onto the 700 lm vertical entrance slit of a 0.27 m, f/4 imaging spectrograph. The spectrograph dispersed the Rayleigh line and Stokes-shifted Raman lines and focused them onto a gated, image-intensiﬁed, cooled charge coupled device (CCD) camera (1 ls gate time). The spatial resolution was 200 lm in the radial direction, and the spectral resolution was 3 nm. The Raman lines for each species and the Rayleigh line were integrated spectrally over a window large enough to account for the spectral broadening due to temperature increases, but small enough to minimize cross talk with neighboring species. Fluorescence from C2 and polycyclic hydrocarbons interfere with Raman signals measured on the fuel-rich side of ﬂame fronts [22]. These interferences were reduced to shot noise levels by taking the diﬀerence of the detected light intensities under two orthogonal linear polarizations that were parallel and perpendicular to the linearly polarized laser source. A modiﬁed liquid crystal shutter was used as a programmable polarizer, which enabled independent measurement of the two polarization components. The images were corrected for throughput and spectral eﬃciency using room temperature air and CH4 calibrations, for laser energy variation, and for cross talk between species. Calibrations of relative Raman cross sections were obtained at room temperature and in a premixed ﬂat ﬂame. The temperature depen-

The computational model solves the full set of steady, elliptic, partial diﬀerential governing equations for mass, momentum, species and energy conservation [25]. The modiﬁed vorticityvelocity formulation in [26] is used to compute the velocity ﬁeld as it is more eﬀective at conserving mass than the original formulation [27]. As the problem is cylindrically symmetric, the governing equations are solved over a two-dimensional mesh, bounded by an inﬂow plane, an axis of symmetry, an outﬂow plane at z = 25 cm, and a far ﬁeld boundary condition at r = 7.5 cm. The inﬂow boundary condition speciﬁes axial velocity, ambient temperature and species concentrations of either fuel or air. The radial velocity is set to zero and the vorticity is deﬁned as the curl of velocity. They symmetry boundary condition speciﬁes zero radial velocity, zero vorticity and zero radial derivatives of all other variables. The outﬂow boundary condition assumes fully developed ﬂow and sets all axial derivatives to zero. The far ﬁeld boundary condition is speciﬁed using the continuity equation, the deﬁnition of vorticity, and the condition that radial derivatives of axial velocity, temperature and species vanish. All other boundary conditions are discretized according to the framework for mass conservation presented in [26]. The gas is assumed Newtonian and diﬀusion is Fickian: the nth species diﬀusion velocity is calculated using a detailed mixture averaging. The Soret and Dufour eﬀects are neglected; viscous dissipation terms, however, are maintained. The ﬂow’s small Mach number implies that the pressure ﬁeld can be obtained via the ideal gas law. The chemical mechanism employed is GRI 3.0 [28] which considers C2 chemistry but nitrogen chemistry has been removed [29]. The reaction set involves 35 species and 217 reversible reactions. All thermodynamic, chemical, and transport properties are evaluated using vectorized and highly eﬃcient libraries [30]. The divergence of the net radiative ﬂux, is calculated using an optically thin radiation submodel with three radiating species (H2O, CO, and CO2), the details of which are found in [31,32]. The resulting set of strongly-coupled, highlynonlinear, partial diﬀerential equations are discretized using ﬁnite diﬀerences and solved using a damped, modiﬁed Newton’s method [33,34]. Pseudo-transient continuation with adaptive step size selection is used to help bring the starting

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estimate [35,36] into the convergence domain of Newton’s method. The linear Newton equations are solved using Bi-CGSTAB [37] with a block Gauss–Seidel preconditioner. Newton’s method is converged when the norm of the Newton correction vector is below a speciﬁed tolerance. Once a solution is obtained, the computational mesh is reﬁned according to the regions of highest gradient and curvature. A new solution is computed on the reﬁned mesh and this process is repeated until further mesh reﬁnement does not change the solution. This process ensures a well-resolved, mesh-independent solution. Calculations were performed on a 2.0 GHz AMD Opteron processor with 8 GB RAM.

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3. Results and discussion 3.1. Experimental and computed concentrations Contour plots of some of the computed and measured concentrations for major species and temperature as determined by Rayleigh/Raman scattering are shown in Fig. 3. Here, the vertical centerline of each panel corresponds to the centerline of the ﬂame, the bottom edge of each panel corresponds to the burner surface, and the mole fractions at each ﬂame location are represented by a color, as indicated by the color scale to the far right in each ﬁgure. Not shown here are contour plots of data collected for methane using

Fig. 3. Computational and experimental isopleths of (a) temperature, (b) molecular oxygen, (c) carbon dioxide and (d) carbon monoxide in the lifted methane-air diﬀusion ﬂame.

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IC laser absorption and several major species collected using the mass spectrometric technique. In each case, these contours showed good agreement with both the Raman measurements and the computed proﬁles. Of particular interest in these plots is the triple ﬂame structure at the base of the lifted diﬀusion ﬂame, most evident in proﬁles of carbon monoxide. Figure 4 compares computed contour plots of formaldehyde with those determined experimentally. The computed mole fraction is compared with the measured mole fraction from the gas sampled with the quartz microprobe. Also, an expected ﬂuorescence signal is determined from the computational results, for the upper and lower bounds of the quenching correction, and compared with the measured formaldehyde ﬂuorescence signal. Both computed and measured ﬂuorescence signals have been normalized to unity since there is not a calibration of the ﬂuorescence data currently available. The formaldehyde proﬁles reveal several interesting features. First, formaldehyde, like CO, shows an unusual proﬁle at the ﬂame base with wispy ‘‘wings” appearing on the lean (outer) side of the ﬂame. Second, the concentration of formaldehyde has very steep gradients in both the radial and axial directions at the ﬂame base, much larger than those observed for most stable molecules in ﬂames. Further, the volume of gas sampled with the quartz microprobe is generally thought to be 5–7 times the oriﬁce diameter, which was 200 lm in these measurements. Thus, the TDLAS measurements of formaldehyde do not fully capture the ﬁne structure predicted for the ﬂame base, but they do show that the highest formaldehyde concentrations occur at the ﬂame base and the general shape of the contour plots throughout the ﬂame is in good agreement with the calculations. Further, the calculations and ﬂuorescence measurements of formaldehyde showed excellent agreement capturing not only the steep gradients of HCHO concentration at the ﬂame base but also all of the structural nuances of the 2D proﬁle. The region of greatest ﬂuorescence intensity at the base of the ﬂame is more widely distributed in the measured ﬂuorescence. This discrepancy is most likely due to the steep temperature gradient across that zone, which aﬀects the Boltzmann and quenching corrections used to calculate a signal. It should be noted that there is some interference in the measured ﬂuorescence from PAH ﬂuorescence in the upper-middle region of the ﬂame. 3.2. Heat release rate correlations The local heat release rate can be determined by summing the products of the net chemical formation rates, x_ i , speciﬁc enthalpies, hi, and molecular weights Wi for all species, i:

Q_ ¼

X

x_ i hi W i

ð1Þ

i

Figure 5 shows the heat release rate proﬁle calculated for this ﬂame. Although there is some exothermicity throughout the ﬂame, the region of maximum heat release follows a thin curve that begins near the ﬂame base and extends upwards. Also shown in Fig. 5 is the net formaldehyde production rate proﬁle. These data show broad regions of formaldehyde formation dominated by a thin formation region that appears coincident with the region of highest heat release. Also evident in the formaldehyde rate proﬁle is a small spatial region of intense formaldehyde consumption located at the ﬂame base and on the rich side of the production feature. In this mechanism, formaldehyde is consumed by hydrogen loss forming the formyl radical. Our analysis shows that the intense destruction region observed at the ﬂame base is dominated by reaction of formaldehyde with atomic hydrogen, one of three competing pathways (HCHO + H, HCHO + O and HCHO + OH). In our paper in the 27th Symposium [3], we concluded that the reaction of CH3 and atomic oxygen dominates formaldehyde in neat methane/air nonpremixed ﬂames. To test that conclusion in the present case, the ﬁnal panel in Fig. 5 shows the forward rate for that reaction. The data in this contour plot show clearly that this single reaction is responsible for the most intense formaldehyde production and is also spatially correlated with regions of high heat release rate. To conﬁrm that point, Fig. 6 shows a scatter plot of heat release rate vs. the forward rate of CH3 + O for the entire ﬂame. This correlation shows a similar ‘‘petal” shape to that reported previously. 4. Conclusions We have studied a lifted, methane–air coﬂow diﬀusion ﬂame using a detailed transport/ﬁnite rate chemistry computational model with a variety of diagnostic methods. The gas temperature, major species mole fractions, and non-fuel hydrocarbon concentrations were experimentally mapped in two dimensions with both probe techniques (coupled to infrared absorption spectroscopy and on-line mass spectrometry) and in situ optical diagnostics (Rayleigh and Raman scattering and laser-induced ﬂuorescence). We compared measured and computed formaldehyde concentrations and ﬂuorescence signals, and the results indicated the existence of an intense region of formaldehyde production near the lifted ﬂame base. Computationally, high formaldehyde production rates correlated well with regions of high heat release. Further, regions where the dominant formaldehyde formation reaction, CH3 + O =

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Fig. 4. Comparison of computed contour plots of formaldehyde experimental measurements. From left to right: the computed mole fraction, the measured mole fraction, the computed ﬂuorescence signal for Q21 T0.5, the computed ﬂuorescence signal for Q21 T1, and the measured ﬂuorescence signal. Both computed and measured ﬂuorescence signals have been normalized to unity.

Acknowledgments The authors thank the NSF (Grants NSF-CTS 0330230 and CTS-0328296), DoE (Grant DEFG02-88ER13966) and NASA (Grants NAG901480 and NNC04AA03A) for their generous ﬁnancial support. The authors also thank Dr. Rui Yang who led the IC laser development team at the Jet Propulsion Laboratory. Appendix A. Supplementary data Fig. 5. Computational isopleths of the heat release rate (ergs/cm3/s), the formaldehyde production rate (moles/ cm3/s) and the forward rate (moles/cm3/s) of the primary formaldehyde production reaction CH3 + O = HCHO + H.

Fig. 6. Scatter plot showing correlation between local heat release and HCHO production from CH3 + O at each of the computational grid points.

HCHO + H peaked also correlated with the areas of maximum heat release rate.

Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.proci.2008.05.083. References [1] H.N. Najm, P.H. Paul, C.J. Mueller, P.S. Wyckoﬀ, Combust. Flame 113 (3) (1998) 312–332. [2] N.T. Clemens, P.H. Paul, Combust. Flame 102 (3) (1995) 271–284. [3] M.P. Tolocka, J.H. Miller, Proc. Combust. Inst. 27 (1998) 633–640. [4] M.D. Smooke, M.B. Colket, R.J. Hall, Chem. Phys. Process. Combust. (1999) 344–347. [5] C.S. McEnally, A.M. Schaﬀer, M.B. Long, et al., Proc. Combust. Inst. 27 (1998) 1497–1505. [6] R.M. Fristrom, A.A. Westenberg, Flame Structure, McGraw Hill, New York, USA, 1965. [7] C.S. McEnally, L.D. Pfeﬀerle, Combust. Flame 121 (4) (2000) 575–592. [8] S. Nadler, S.J. Daunt, D.C. Reuter, Appl. Optics 26 (1987) 1641–1646. [9] D.S. Cline, P.L. Varghese, Appl. Optics 27 (1988) 3219–3224. [10] G.I. Mackay, D.R. Karecki, H.I. Schiﬀ, J. Geophys. Res. 101 (D9) (1996) 14721–14728. [11] A. Fried, S. Sewell, B. Henry, B.P. Wert, T. Gilpin, J.R. Drummond, J. Geophys. Res. 102 (D5) (1997) 6253–6266. [12] D. Trapp, C. De Serves, Atmos. Environ. 29 (22) (1995) 3239–3243.

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[13] R.Q. Yang, Microelectr. J. 30 (1999) 1043–1056. [14] J.E. Harrington, K.C. Smyth, Chem. Phys. Lett. 202 (3-4) (1993) 196–202. [15] D.C. Kyritsis, V.S. Santoro, A. Gomez, Exp. Fluids 37 (5) (2004) 769–772. [16] D.I. Shin, T. Dreier, J. Wolfrum, Appl. Phys. BLasers O. 72 (2) (2001) 257–261. [17] D. Clouthier, D. Ramsay, Annu. Rev. Phys. Chem. 34 (1983) 31–58. [18] P. Paul, H. Najm, Proc. Combust. Inst. 27 (1998) 43–50. [19] M.D. Smooke, P. Lin, J.K. Lam, M.B. Long, Proc. Combust. Inst. 23 (1990) 575–582. [20] W. Reckers, L. Huwel, G. Grunefeld, P. Anderson, Appl. Optics 32 (1993) 907–918. [21] D.F. Maran, Quantitative Two-dimensional Laser Diagnostics in Idealized and Practical Combustion Systems, Ph.D, thesis, Yale University, Mechanical Engineering Department. [22] F. Beretta, V. Cincotti, A. D’Alessio, P. MEnna, Combust. Flame 61 (1985) 211–218. [23] P. Miles, Carbon Dioxide Spectral Synthesis Code, Sandia National Laboratories Report, 1996. [24] E.P. Hassel, RAMSES Spectral Synthesis Code, University of Darmstadt Report, 1996. [25] B.A.V. Bennett, J. Fielding, R.J. Mauro, M.B. Long, M.D. Smooke, Combust. Theor. Model. 3 (1999) 657–687.

[26] S.B. Dworkin, B.A.V. Bennett, M.D. Smooke, J. Comput. Phys. 215 (2005) 430–447. [27] A. Ern, M.D. Smooke, J. Comput. Phys. 105 (1993) 58–71. [28] G.P. Smith, D.M. Golden, M. Frenklach, et al., GRI-Mech 3.0, http://www.me.berkeley.edu/gri_mech/. [29] B.A.V. Bennett, M.D. Smooke, Combust. Theor. Model. 2 (1998) 221–258. [30] V. Giovangigli, N. Darabiha, Vector Computers and Complex Chemistry Combustion, Mathematical Modeling in Combustion and Related Topics, in: C. Brauner, C. Schmidt-Laine (Eds.), NATO ASI Series, M. Nijhoﬀ Pub., 1988, pp. 491-503 140. [31] R.J. Hall, J. Quant. Spectrosc. Radiat. Transfer 49 (1993) 517–523. [32] R.J. Hall, J. Quant. Spectrosc. Radiat. Transfer 51 (1995) 635–644. [33] P. Deuﬂhard, Numer. Math. 22 (1974) 289–315. [34] M.D. Smooke, J. Opt. Theory Appl. 39 (1983) 489– 511. [35] M.D. Smooke, R.E. Mitchell, D.E. Keyes, Combust. Sci. Technol. 67 (1989) 85–122. [36] D.E. Keyes, M.D. Smooke, J. Comput. Phys. 73 (1987) 267–288. [37] H.A.V.D. Vorst, SIAM J. Stat. Comput. 13 (1992) 631–644.