Combined experimental and computational study of laminar, axisymmetric hydrogen–air diffusion flames

Combined experimental and computational study of laminar, axisymmetric hydrogen–air diffusion flames

Proceedings of the Proceedings of the Combustion Institute 30 (2005) 485–492 Combustion Institute Combined experiment...

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Proceedings of the

Proceedings of the Combustion Institute 30 (2005) 485–492

Combustion Institute

Combined experimental and computational study of laminar, axisymmetric hydrogen–air diffusion flames V.V. Toroa, A.V. Mokhova, H.B. Levinskya,b,*, M.D. Smookec a

Stratingh Institute of Chemistry and Chemical Engineering, Rijksuniversiteit Groningen, Groningen, The Netherlands b Gasunie Research, Groningen, The Netherlands c Department of Mechanical Engineering, Yale Center for Combustion Studies, Yale University, New Haven, CT 06520-8286, USA

Abstract We investigate the structure of two-dimensional, axisymmetric, laminar hydrogen–air flames in which a cylindrical fuel stream is surrounded by coflowing air, using laser-diagnostic and computational methods. Spontaneous Raman scattering and coherent anti-Stokes Raman scattering (CARS) are used to measure the distributions of major species and temperature. Computationally, we solve the governing conservation equations for mass, momentum, energy, and species, using detailed chemistry and transport. The fuel is diluted with nitrogen (1:1) to reduce heat transfer to the burner, to match the zero temperature gradient at the fuel exit. Three average fuel exit velocities are studied: 18, 27, and 50 cm/s. Comparisons of the measured and computed results are performed for radial profiles at a number of axial positions, and along the axial centerline. Peak major species mole fractions and temperatures are quantitatively predicted by the computations, and the axial species profiles are predicted to within the experimental uncertainty. In the radial profiles studied, base-case computations excluding thermal diffusion of light species were in excellent agreement with the measurements. While the addition of thermal diffusion led to some discrepancy with the measured results, the magnitude of the differences was no more than 25%. The computations predicted the axial centerline profiles from the burner exit to the maximum temperature well, though the experimental temperatures in the downstream mixing region decreased somewhat faster than the computed profiles. Radiative losses are seen to be negligible in these flames, and changes in transport properties and variations in initial flow velocities generally led to only modest changes in the axial profiles. The results also show that the detailed axial profiles of major species and temperature at different fuel jet velocities scale quantitatively with the jet velocity.  2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Laminar flames; Diffusion flames; Laser diagnostics; Numerical modeling; Flame structure

1. Introduction The axisymmetric laminar diffusion flame has attracted much attention as a model system with


Corresponding author. Fax: +1 31 50 5211946. E-mail address: [email protected] (H.B. Levinsky).

a relatively simple geometry and sharing many properties with flames in practical devices. Combined experimental and computational effort has been devoted to the study of the detailed structure of these flames, largely using methane as a fuel [1– 3]. Less attention has been paid to the structure of hydrogen diffusion flames, despite the interesting combination of comparatively simple chemistry with significant differences in transport properties

1540-7489/$ - see front matter  2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2004.08.221


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between fuel and oxidizer. Hydrogen as a fuel is also courant due to the role that it can play as a future sustainable energy carrier. In this regard, the utilization of hydrogen in the wide range of hydrocarbon-fired combustion systems in use today will require understanding the microscopic processes governing flame stability and pollutant formation under practical conditions. We expect computational studies of flame structure to play an important role in achieving this goal. Laminar axisymmetric coflow hydrogen–air flames have been used for the experimental study of Lewis number effects, such as the opening of flame tips [4], and for developing laser-diagnostic methods for species and temperature determination in flame studies [5–7]. The emphasis in the diagnostic studies was on the adequacy of the diagnostic method, rather than on insight into flame structure, although one report [7] discussed possible premixing of fuel and oxidizer based on oxygen and nitrogen mole fractions measured in the stabilizing region of a hydrogen–nitrogen jet flame. To our knowledge, only a small number of studies have presented combined experimental and detailed computational results for the steady structure of these flames [8–10,12]. Measurements of OH concentration and rotational temperature, obtained by direct UV absorption [8], in axisymmetric H2–air flames were compared with simulations of flame structure using detailed chemistry, neglecting radiation and thermal diffusion, to assess the one-step-chemistry approximation, and to examine the stabilizing region. Another study [9] compared maximum radial temperatures obtained by solving the governing equations, using complex chemistry and transport, with coherent anti-Stokes Raman scattering (CARS) measurements to assess the effects of thermal diffusion. Temperature profiles in H2–N2–air flames obtained using Rayleigh scattering were compared with numerical simulations neglecting axial diffusion [10] to examine differential transport in inverse diffusion flames (see also [11]). A recent report [12] compared species data obtained by laser-induced plasma spectroscopy with those using a simplified transport model; although, here too the objective was to quantify the measurement technique. The comparison and analysis of the species fields in conjunction with the temperature field are essential to provide checks on the internal consistency of the experimental results, to yield insight into the structure of these flames, and to appraise the adequacy of the computational results, as shown in studies on methane flames [1–3,13]. In this paper, we report the quantitative comparison of measured and computed major species and temperatures distributions in laminar axisymmetric hydrogen–air diffusion flames. Towards this end, the major species concentrations are measured using spontaneous Raman scattering, and the temperature both derived from the

Raman data and measured independently using CARS. The governing equations are solved with detailed chemistry and transport; the sensitivity of the solutions to selected changes in transport properties, chemical reaction mechanism, and flow conditions are considered. The experimental conditions were chosen to match the boundary conditions used in the computations. In particular, heat transfer to the fuel tube was minimized by diluting the hydrogen fuel with nitrogen; this moved the reaction zone downstream so that the gradients in temperature and concentration at the exit of the burner are small.

2. Experimental method In the present burner arrangement, an upright stainless tube (45.5 cm length, i.d. 0.9 cm) carrying the H2/N2 fuel (in 1:1 mole ratio) is surrounded by an air-coflow annulus (i.d. 9.5 cm). The velocity profile in the coflow is homogenized by a settling chamber 10 cm high filled with glass beads, and by using a perforated plate as the exit plane to increase the pressure drop. The exit plane of the fuel tube extends 0.8 cm above the exit of the coflow, so that the small jets generated by the perforated plate can relax to plug flow. Three average fuel exit velocities (18, 27, and 50 cm/s) were chosen for the experiments. A parabolic velocity profile at the exit of the fuel tube was verified by hot-wire anemometry. In all experiments, the velocity of the coflow air was set to the average velocity of the fuel jet. The flows of all gases were measured using calibrated mass flow meters (Bronkhorst); the flow ranges of the meters were selected to provide an accuracy of better than 5%. Concentration and temperature profiles were obtained by moving the burner vertically and horizontally by a precision positioner (Parker, positioning uncertainty less than 0.1 mm). Raman scattering data were obtained by the following method. The second harmonic of a pulsed Nd:YAG laser (50 mJ pulse energy and 25 Hz output frequency) was focused by a quartz lens with focal length of 800 mm into the test location. The pulse energy was sufficiently low to avoid optical breakdown. An electromechanical shutter installed in front of the burner was used to block the laser beam for taking measurements of the background (see below). The scattered radiation along the line of the laser beam was collected at right angles by a camera lens (f/2.8, 300 mm) and projected onto the entrance slit of a spectrometer (Acton Spectra Pro, f/4, 150 mm, 5 nm/mm dispersion) with a magnification factor of 0.5. The spectrometer was oriented such that the slit was parallel to the image of the laser beam. The slit width of the spectrometer was set at 120 lm. At the exit plane of the spectrometer, an intensified 1024 · 256 pixel CCD camera

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(Princeton Instruments, 25 lm pixel size) was mounted. To increase the signal-to-noise ratio (SNR), the pixels were binned in 2 · 4 groups; this resulted in covering a distance of 13 mm along the laser beam, and yielded a net spatial resolution of 0.2 mm. To span the radial cross section of the flame (25 mm), the Raman spectra were measured around radial positions of 0, +6, and 6 mm and then pasted together. The spectral resolution was approximately 0.5 nm, which was sufficient to resolve the vibrational Raman lines for all major flame components. At every point, 50 accumulations with 10 s exposure times were measured with the laser shutter open (Raman signal + background) and closed (background only), and subsequently subtracted. This yielded acceptable SNR even at high flame temperatures. The reproducibility of the Raman measurements is of the same order as the scatter in the data in the figures presented. The species concentrations and temperature were determined from the measured spectra by a fitting procedure that will be described in detail separately [14]. In this procedure, the theoretical Raman spectra for all major species were synthesized from known literature data; this limited the calibration measurements to using only dry air. This substantially simplified the daily procedure, and more importantly increased the measurement accuracy. Comparison of the major species mole fractions derived experimentally in near-adiabatic flat flames with the equilibrium mole fractions demonstrated an absolute accuracy of better than 0.03 mol fraction. Although local temperatures can be derived from the Raman measurements themselves, we performed independent CARS measurements using broadband planar BOXCARS nitrogen thermometry. The details of the CARS setup is reported elsewhere [15]; the accuracy of the CARS measurements is estimated at better than 40 K [15]. The agreement between Raman and CARS temperatures was usually good (generally within 100 K), although the CARS temperatures showed substantially less scatter.

3. Problem formulation and method of solution Our model of an axisymmetric laminar diffusion flame considers an unconfined laminar flame in which a cylindrical fuel stream is surrounded by a coflowing oxidizer jet. Computationally, we utilize a velocity–vorticity approximation in which the elliptic two-dimensional governing equations are discretized on a two-dimensional mesh. The resulting nonlinear equations are then solved by a combination of time integration and NewtonÕs method. The Newton equations are solved by a preconditioned Bi-CGSTAB iteration. We determine the grid points of the two-dimensional mesh by equidistributing positive weight functions over


mesh intervals in both the r and z directions. The size of the time steps is chosen by monitoring the local truncation error of the time discretization process (see also [1]). Due to the cost of forming the Jacobian matrices with detailed transport and finite rate chemical kinetics, a modified NewtonÕs method is implemented along with several theoretical estimates that determine when a new Jacobian should be reformed. These theoretical results help increase the overall efficiency of the algorithm. The binary diffusion coefficients, the viscosity, the thermal conductivity of the mixture, the chemical production rates as well as the thermodynamic quantities are evaluated using vectorized and highly optimized transport and chemistry libraries [16]. Thermal diffusion is modeled in the trace light component limit (more comprehensive treatments are given in [17]). Radiative losses are included in an optically thin model. For the flames we consider, we assume that the only significant radiating species is H2O [18,19]. Computations were made on adaptively determined grids containing approximately 15,000 nodes, where the size of the domain was 9.5 cm radially and 20 cm axially. To obtain this level of resolution on an equispaced grid, approximately 108 grid points would be required. We mention in passing that increasing the number of nodes in the flame front by a factor of four or extending the domain further downstream did not significantly change the solution. The computations were performed on a 13GB-RAM IBM RS6000 Model 44P-270 workstation. Each flame typically took several minutes of CPU time. The hydrogen–oxygen submechanism (nine species) contained in GRI 2.11 [20] was used in the computations. As will be seen below, additional calculations utilizing the hydrogen–oxygen submechanism in [1] produced small variations in the results.

4. Results and discussion To illustrate the overall flame structure, we present two-dimensional false-color plots of the computed distribution of temperature at the three exit velocities in Fig. 1. Here, we see the characteristic high-temperature ‘‘wishbone’’ of the jet flame [1]. Similar to the methane/nitrogen flame in [2], the temperature rise in the diluted hydrogen flames occurs very close to the burner outlet. Further, the unreacted core of the jet is seen clearly, whose length also increases with velocity. It is interesting to note that the computed maximum temperature just above the exit plane occurs at a radial distance of nearly 6 mm, 1.5 mm outside the fuel tube; this indicates the extent to which the radial diffusion of hydrogen causes the flame to spread. We also observe that the maximum temperature increases substantially with exit velocity, and that the temperature never


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Fig. 1. Two-dimensional false-color plots of computed temperature distributions at the three exit velocities.

approaches the adiabatic stoichiometric temperature of 2023 K calculated for this mixture. To follow the development of the flame, we present the radial profiles (r) of temperature and major species in the 50 cm/s flame, at axial positions (z) of 3, 10, 20, and 30 mm in Figs. 2–5, respectively. Both the experimental profiles and the computed profiles using GRI-Mech 2.11 are presented; since the addition or neglect of thermal diffusion had the largest effects on the computed results, both results are given. In these figures, the full experimental axial profile, measured between 13 and 13 mm, is shown, while the computed profiles are shown per half plane: the results obtained neglecting thermal diffusion are plotted for r 6 0, while the results including thermal diffusion for r P 0. In the data shown, the symmetry of the experimental profiles around the centerline is sufficient for comparison with the computations. At 3 mm above the exit of the fuel tube (the lowest axial position achievable for the Raman measurements), shown in Fig. 2, the peak in the temperature, 1800 K is at r = 6 mm, 1.5 mm

Fig. 3. Radial temperature and species profiles for 50 cm/s flame at z = 10 mm; same use of symbols as in Fig. 2.

Fig. 4. Radial temperature and species profiles for 50 cm/s flame at z = 20 mm; same use of symbols as in Fig. 2.

Fig. 5. Radial temperature and species profiles for 50 cm/s flame at z = 30 mm; use of symbols same as in Fig. 2.

Fig. 2. Radial temperature and species profiles for 50 cm/s flame at z = 3 mm; points are measurements, lines in same color as points are computed results. Results excluding thermal diffusion plotted for r 6 0, with thermal diffusion for r P 0.

outside the radius of the fuel tube, as mentioned above. The high temperature zone is thin: the width at half maximum is 3 mm. Here, the core of the jet, where the temperature and composition are essentially those of the original mixture,

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extends for more than 1.5 mm from the centerline. As expected, the maxima in the temperature and water profiles coincide. The computed results reproduce the experimental profiles well; the results excluding thermal diffusion are nearly quantitative, while those with thermal diffusion are shifted to slightly larger radial distances. Results obtained in a high-velocity laminar jet [9] show the experimental data lying closer to calculations including thermal diffusion. In both cases in Fig. 2, the fuel-rich inner side of the jet is predicted quantitatively, while the results suggest that mixing on the fuel-lean side of the jet is underpredicted. This is evident in the water and oxygen profiles, for which both models overpredict the water mole fractions and underpredict the oxygen on the lean side of the flame, although the data including thermal diffusion are more displaced into the coflow. Particularly interesting in Fig. 2 is the non-monotonic change in the nitrogen mole fraction. While simple mixing would suggest a monotonic change in the mole fraction from 0.5 in the jet to 0.79 in the coflow air, differential transport and the change in the number of moles within the flame combine to yield a complex profile. Both transport models capture this behavior well. At z = 10 mm, shown in Fig. 3, the width of the high temperature zone has increased to 4.5 mm. Although the temperature at the centerline is still room temperature, diffusion has reduced the H2 mole fraction at this position to 0.43 and increased the N2 mole fraction to 0.57. Anticipating the discussion below, the enrichment of the nitrogen mole fraction by transport will have significant consequences for the attainable flame temperature when the fuel burns: the adiabatic stoichiometric temperature for this H2:N2 ratio is 1921 K, 100 K lower than the original fuel. As was the case at z = 3 mm, the fuel-rich side of the flame is predicted nearly quantitatively, but the profiles without thermal diffusion are now 0.6 mm wider than the measurements, while the predictions with thermal diffusion are 1.2 mm wider than the measurements. Although both differences are outside the measurement uncertainty, the maximum discrepancy in profile width is only 25%. At this axial position, differences in the predicted mole fractions at the centerline are also visible, though slight. Here too, the models capture the essential features of the nitrogen profile. Parenthetically, we also present the CARS data together with the Raman temperatures, showing the excellent agreement in the profiles, both in form and magnitude. This agreement also places stringent limits on possible errors in the physical scale of the line-Raman measurements. At z = 20 mm, in Fig. 4, the centerline temperature has risen to 620 K, while the H2 mole fraction has dropped to below 0.2, and water has


diffused to the centerline from the reaction zone. Whereas the centerline major species and temperature were well predicted at z = 3 and 10 mm, both models begin to show differences with the experimental data and with each other at this axial position. Interesting is that the centerline temperature excluding thermal diffusion is closer to the experimental data, but that the results for H2 and N2 are better predicted using thermal diffusion. As at the other axial locations, mixing on the fuel-lean side of the flame appears to be underpredicted by both models, more strongly by incorporation of thermal diffusion. These trends are continued at z = 30 mm, shown in Fig. 5. Now the centerline temperature has reached 1100 K, and the H2 mole fraction has decreased to nearly 0.05. Both transport models predict the centerline mole fraction of water well, and the neglect of thermal diffusion still yields better temperature predictions than its inclusion. An intriguing result is shown, again, by the nitrogen profile: the clear dip in the mole fraction in the high temperature region is reproduced very well by the computations. The combustion of hydrogen decreases the number of moles, so that the nitrogen concentration should actually increase in the reaction zone. Further, the peak temperature at this position, 1800 K, is too low for a significant radical pool to increase the total number of moles. We also note that the peak temperature is 100 K lower than that at z = 20 mm; the fuel is nearly exhausted, and dilution with coflow air is beginning to dominate the further development of the flame structure. The overall consequences of the mixing field are illustrated in the axial centerline profiles for the 27 cm/s flame in Fig. 6. Here, we see that the fuel is completely consumed by z  25 mm, coinciding with the maximum in the water concentration. The temperature continues to rise slightly after this point, reaching a maximum of 1550 K at z  30 mm. The agreement between measured and computed species profiles is within the limits of the experimental uncertainty, where the experimental data do not allow for discrimination between the two transport models. (We are currently improving the Raman system to be able to do so.) The calculated temperature profiles are also in excellent agreement with the measurements until just past the maximum temperature; the difference between calculations and measurements increases progressively downstream, up to 120 K at z = 100 mm, as the hot gases are further diluted by the coflow air. Since the measured temperatures are more accurate than the species, the discrepancy is more apparent. Comparing the two transport models, we observe that thermal diffusion leads to a consistently higher temperature, and that this difference is consistent with the higher water and lower oxygen mole fractions, as seen in the radial profiles above. Interestingly, the

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temperature (K)



expt H2

expt. H2O x2

O2 expt.

N2 expt.




















mole fraction


0 0


40 60 80 axial distance (mm)


Fig. 6. Axial centerline profiles for 27 cm/s flame; points are measurements, solid lines results computed without thermal diffusion, dotted lines including thermal diffusion, dashed line is equilibrium temperature (see text).

opposite effect was observed [21] upon inclusion of thermal diffusion in the computation of the flame structure of a fuel-lean premixed hydrogen–air Bunsen flame. At this point, it is illustrative to compare the axial temperature profile with that expected at equilibrium. Whereas one would ordinarily characterize the mixture composition using the mixture fraction [22], the substantial differential diffusion in this system renders the definition of the mixture fraction problematical. Instead, we calculate the equilibrium temperature using the element composition from the computed species profiles. To do so, the temperature of the species composition at a given axial position is varied until the enthalpy of the mixture is the same as the room-temperature mixture of H2, N2, and O2 having the same element composition. Since the mole fractions of all the computed species are used, including the flame radicals, the temperature obtained includes any effects of ‘‘superequilibrium’’ radical concentrations; residual differences arise only from radiative losses and heat conduction. The equilibrium temperature calculated in this manner is also shown in Fig. 6, derived from the results without thermal diffusion. Whereas the peak equilibrium temperature is some 200 K higher than the detailed calculations, indicating significant heat transfer, the equilibrium temperature merges with the detailed curve downstream, where they remain within 10 K of each other until the end of the computational domain (z = 200 mm). Since no energy has been lost from the system, we argue that the radiative losses in this system are negligible (see below). The maximum equilibrium temperature is 1695 K, far below the 2023 K for the adiabatic stoichiometric temperature of the initial mixture burning in air. As suggested above, rapid radial diffusion substantially decreases the hydrogen mole fraction in the unre-

acted fuel; the equivalent H2/N2/air mixture having the same stoichiometric equilibrium temperature consists of slightly more than 31% H2. Similar results are obtained at 50 cm/s, shown in Fig. 7. Here, too, the major species are well predicted, with only the suggestion of higher measured oxygen mole fractions at larger axial positions, at the limits of the experimental uncertainty. The temperature profile excluding thermal diffusion describes the rising edge of the profile well, but the disparity downstream between the measured and computed temperatures is larger than at 27 cm/s, up to nearly 200 K by z = 100 mm. Although clearly measurable, the maximum relative discrepancy in temperature at 100 mm is only 20%. Also interesting are the much smaller differences in predictions arising from the two models. As in Fig. 6, the calculated equilibrium temperature merges with the computations downstream of the peak, also indicating negligible radiative losses. Computed results excluding radi-

Fig. 7. Axial centerline profiles for 50 cm/s flame, same use of symbols as in Fig. 6.

Fig. 8. Scaled axial centerline profiles (see text); points are measurements; solid lines computed results for 50 cm/s, dashed lines for 27 cm/s, and dotted lines for 18 cm/s.

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ation for this flame indeed show no contribution from radiative transfer to the temperature profile. Consequently, the difference between the computed temperature profiles and the equilibrium curves in Figs. 6 and 7 arises from heat conduction away from the centerline, since the local element composition would have a higher temperature under adiabatic conditions. The question arises as to the origin of the quantitative discrepancy in the temperature profiles. Since one expects the hydrogen–air flame to be dominated by transport effects, and given the discussion concerning the challenges in calculating transport coefficients (for example [23,24]), we examined the sensitivity of the computed solution to transport properties, as well as to chemical mechanism and flow velocities. We compared the solutions obtained by: increasing the diffusion coefficients for H2 and H by 50% with and without thermal transport, decreasing these coefficients by 25%, using another chemical mechanism (see above), varying the coflow by 20%, and reducing the fuel exit velocity by 10%. Only the changes associated with the incorporation of thermal diffusion altered the axial temperature profiles by more than 20 K, and these were to enhance the discrepancy with the measurements. The modest changes seen suggest more subtle differences in the conditions used are responsible for the disparity with the measurements. Although the inlet conditions have been chosen to match the boundary conditions of the computation, we anticipate that flow field variations between the experiment and the model can lead to the differences observed. We are currently investigating this possibility. Since these data are to our knowledge the first detailed study of laminar coflow diffusion flames in which the exit velocity of the fuel is varied, we pause briefly to consider the resultant changes in flame structure. For this purpose, it is illustrative to normalize the axial profiles by the average exit velocity, resulting in a residence time. The results are shown in Fig. 8, for temperature and mole fractions of H2O and O2. First, we note that the computed temperature and major species mole fractions (data without thermal diffusion), including those not shown, at the different velocities collapse to essentially a single curve. The largest differences are seen in the scaled temperature profiles, where the differences between the profiles are less than 30 K, with the exception of the 18 cm/s profile near the peak temperature, which is 100 K below the other data. In spite of complex differential transport coupled to chemical reaction, the development of the centerline profiles can still be characterized by the convective time scale. It is interesting to observe that the velocity scaling, used by Burke and Schumann to estimate [25] flame heights, scales the details of the axial profile as well. This similarity appears to obviate the necessity of computing the flame structure for


more than one velocity, at least regarding the centerline profiles. We also observe that the measured temperatures and major species collapse to one curve, within the experimental uncertainty; the scaling of the measured profiles is an important verification of the internal consistency of the results. That the scaling exercise is of limited value for the details of flame structure can be ascertained by comparing the radial temperature profiles at the same normalized axial distance. At z/v  33 ms, corresponding to z = 6.7 and 16.9 mm, for v = 18 and 50 cm/s, respectively, the radial temperature profile at 50 cm/s is 50% wider than that at 18 cm/s. 5. Conclusions We have discussed the experimental and computational results for major species and temperature in axisymmetric, laminar H2/N2/air diffusion flames. In the axial and radial cross sections examined, the peak mole fractions and temperatures are predicted quantitatively, and the axial species profiles are predicted to within the experimental uncertainty. The computed radial profiles tend to be broader than those measured, and the predicted axial temperatures downstream of the maximum are significantly higher than the measurements. The relative discrepancies observed are however never more than 25%. Variation of transport properties for H and H2, and of flow velocities yields modest changes in the base solution, suggesting other causes for the discrepancies seen. Acknowledgments We thank the EET program of the Dutch Ministry of Economic Affairs and the N.V. Nederlandse Gasunie for partial support of this work. One of the authors (M.S.) acknowledges support from the US Department of Energy Office of Basic Energy Science. References [1] M.D. Smooke, Y. Xu, R. Zurn, P. Lin, J. Frank, M.B. Long, Proc. Combust. Inst. 24 (1992) 813–821. [2] M.D. Smooke, P. Lin, J. Lam, M.B. Long, Proc. Combust. Inst. 23 (1990) 575–582. [3] M.D. Smooke, A. Ern, M.A. Tanoff, B.A. Valdati, R.K. Mohammed, D.F. Marran, M.B. Long, Proc. Combust. Inst. 26 (1996) 2161–2170. [4] S. Ishizuka, Proc. Combust. Inst. 19 (1982) 319–326. [5] D.P. Aeschliman, J.C. Cummings, R.A. Hill, J. Quant. Spectrosc. Radiat. Transfer 21 (1979) 293–307. [6] J.A. Shirley, Appl. Phys. B 51 (1990) 45–48. [7] R.D. Hancock, F.R. Schauer, R.P. Lucht, R.L. Farrow, Appl. Opt. 36 (1997) 3217–3226.


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[8] S. Fukutani, N. Kunioshi, H. Jinno, Proc. Combust. Inst. 23 (1990) 567–573. [9] R.D. Hancock, F.R. Schauer, R.P. Lucht, V.R. Katta, K.Y. Hsu, Proc. Combust. Inst. 26 (1996) 1087–1093. [10] T. Takagi, Z. Xu, M. Komiyama, Combust. Flame 106 (1996) 252–260. [11] J.A. Miller, R.J. Kee, J. Phys. Chem. 81 (1977) 2534–2542. [12] S. Itoh, M. Shinoda, K. Kitagawa, N. Arai, Y.-I. Lee, D. Zhao, H. Yamashita, Microchem. J. 70 (2001) 143–152. [13] T.S. Norton, K.C. Smyth, J.H. Miller, M.D. Smooke, Combust. Sci. Tech. 90 (1993) 1–34. [14] A.V. Mokhov, V.V. Toro, H.B. Levinsky, J. Appl. Phys. B (submitted). [15] A.V. Mokhov, H.B. Levinsky, C.E. van der Meij, Appl. Opt. 36 (1997) 3233–3243. [16] V. Giovangigli, N. Darabiha, in: C. Brauner, C. Schmidt-Laine (Eds.), Mathematical Modeling in Combustion and Related Topics, Martinus Nijhoff, Dordrecht, NATO Adv. Sci. Instr. Ser. E, vol. 140, 1987, p. 491.

[17] A. Ern, V. Giovangigli, Multicomponent Transport Algorithms Lecture Notes in Physics, vol. 24. Springer-Verlag, Heidelberg, 1994. [18] R.J. Hall, J. Quant. Spectrosc. Radiat. Transfer 49 (1993) 517. [19] R.J. Hall, J. Quant. Spectrosc. Radiat. Transfer 51 (1994) 635. [20] Bowman, C.T., Hanson, R.K., Davidson, D.F., Gardiner Jr., W.C., Lissianski, V., Smith, G.P., Golden, D.M., Frenklach, M., Wang, H., and Goldenberg, M., GRI-Mech version 2.11, 1995. Available from: . [21] A. Ern, V. Giovangigli, Combust. Theory Modelling 2 (1998) 349–372. [22] R.W. Bilger, in: P.A. Libby, F.A. Williams (Eds.), Turbulent Reacting Flows. Springer-Verlag, Berlin, Heidelberg, 1980, p. 65. [23] P. Paul, J. Warnatz, Proc. Combust. Inst. 27 (1998) 495–504. [24] P. Middha, B. Yang, H. Wang, Proc. Combust. Inst. 29 (2002) 1361–1369. [25] S.P. Burke, T.E.W. Schumann, Ind. Eng. Chem. 20 (1928) 998–1004.

Comment Derek Dunn-Rankin, University of California—Irvine, USA. Your results show spectacular agreement between the model without thermal diffusion and the experiment, where the model with thermal diffusion seems to do a bit more poorly. How does adding more physics reduce the agreement? Reply. The rather surprising result that the inclusion of a more realistic transport model in the calculations leads to poorer agreement between the computations and experiments needs further clarification. We first point out that the differences observed in the widths of

the radial profiles, at most slightly more than 1 mm, are outside the limits of the experimental reproducibility (a few tenths of a millimeter). Nevertheless, both models reproduce the experiments with remarkable accuracy. However, before reconsidering the transport properties of the hydrogen–air mixture in searching for the residual differences, we would like to mention another possible origin for the discrepancy: as mentioned in the paper, we cannot exclude subtle differences between the actual boundary conditions in the experiments and those used in the computations. We are considering performing experiments to explore this possibility.