homogeneous reaction and transport coupling during flame-wall interaction

Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 2693–2700

HETEROGENEOUS/HOMOGENEOUS REACTION AND TRANSPORT COUPLING DURING FLAME-WALL INTERACTION P. POPP and M. SMOOKE Yale University, Department of Mechanical Engineering M. BAUM NEC Europe Ltd.

The effect of surface chemistry and transport modeling on the head-on quenching process of laminar propane/air and methane/air flames is investigated numerically. The fully compressible, one-dimensional Navier–Stokes equations with detailed mechanisms for diffusion and chemical kinetics (gas-phase and surface) are solved using a sixth-order finite-difference scheme in space and a third-order Runge–Kutta scheme in time. Important applications are in the modeling of flame-wall interaction processes in piston engines, their related experimental measurements, and general surface chemistry modeling. The latter is due to the interaction being unsteady in contrast to typical boundary layer or stagnation point flow studies over reactive surfaces. Also the surface response takes place in the high coverage zone. It is found that in order to simulate quenching at higher wall temperatures accurately, the process of diffusion, adsorbtion, and surface recombination especially for the free radical H and OH have to be described. This results in an increasing wall heat flux with wall temperature in excellent agreement with existing experimental data. If the participation of the surface in the reaction channels of the near-wall gas-phase species is excluded (either because of the physical surface properties or because of the boundary treatment in the simulations), the quenching structure is completely changed with strongly exothermic radical recombination reactions dominating the interaction. The developed detailed surface mechanism contains 10 reactions, involving four surface species, and seven gas-phase species. It takes into account the breakdown of the Langmuir adsorption concept for high surface coverages and includes a precursor-state model for the adsorption of H2, H, and OH.

Introduction Whereas former engine codes did not use any specific corrections for flame-wall interaction, modern engine codes emphasize the importance of quenching models. Those are based on the concept of a quenching layer and assume that transport and surface effects are negligible. Recent research [1,2] indicates that (1) those assumptions might not be valid for high wall temperatures as encountered under operating conditions or even in insulated engines and (2) the experimental value of the wall heat flux during flame-wall interaction, which is the only parameter that is easily accessible and can be used to baseline numerical against experimental data, might depend on the surface material of the thin-film gauge used (which is, in general, platinum). To investigate this situation, we have studied, numerically the quenching situation as can be found in constantvolume combustion chambers [3–5] for an inert and a platinum surface over a range of wall temperatures between 300 and 600 K. A laminar flame approaches head-on the chamber wall and is quenched at atmospheric pressure. Special attention is given to the

homogeneous/heterogeneous reaction behavior and transport coupling at 600 K. We consider stoichiometric methane- and propane-air flames. Problem Setup Solution Method The complete set of Navier–Stokes equations is solved on a one-dimensional domain. The numerical scheme is sixth-order in space and third-order in time [1]. Chemistry is described by detailed reaction and diffusion mechanisms (TRANSPORT [6], CHEMKIN [7]). Cross-diffusional effects are taken into account [8]. Surface reaction data are calculated via SURFACE CHEMKIN [9]. For further details see Ref. 2. Gas-Phase Chemistry The gas-phase reaction scheme for the methaneflame calculations [10] consists of 52 elementary reactions and 17 species considering only the C1 path.

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TABLE 1 The detailed, kinetic surface-reaction mechanism. When rate coefficients are given, the rate expression is in Arrhenius form: k 4 A exp(1Ea/RT). Note that in the limit of high coverage, reactions 1, 3, and 6 are coverage independent. Reaction

A or c

Ea (kJ/mol)

Comment

Non dissociative radical adsorption 1.0 1.0 1.0

sticking coeff. sticking coeff. sticking coeff.

HO2 ` 2Pt(s) r OH(s) ` O(s) H2O2 ` 2Pt(s) r OH(s) ` OH(s)

Dissociative radical adsorption 1.0 1.0

sticking coeff. sticking coeff.

R6 R7

H2 ` 2Pt(s) r H(s) ` H(s) O2 ` 2Pt(s) r O(s) ` O(s)

Dissociative H2/O2 adsorption 0.023 0.046

sticking coeff. sticking coeff.

R8 R9 R10

H(s) ` O(s) s OH(s) ` Pt(s) H(s) ` OH(s) r H2O ` Pt(s) OH(s) ` OH(s) r H2O ` O(s)

R1 R2 R3

H ` Pt(s) s H(s) O ` Pt(s) s O(s) OH ` Pt(s) s OH(s)

R4 R5

Surface recombination reactions 1.0 E `21 1.0 E `21 1.0 E `21

The C2 path, i.e., the conversion of CH4 to higher hydrocarbons is neglected because recent research [1] demonstrated a negligible influence on flamequenching characteristics. The gas-phase reaction scheme for the propane-flame calculations [11] consists of 87 reactions and 31 species. Surface Chemistry Based on recent work [12–15], a detailed, kinetic surface-reaction mechanism (Langmuir–Hinshelwood type) for flame quenching on platinum surfaces has been developed (Table 1). It consists of 10 reactions involving four surface and seven gas-phase species. It considers nondissociative adsorption of H, O, and OH, dissociative adsorption of HO2 and H2O2, and dissociative adsorption of H2 and O2. It accounts for subsequent surface reactions between adsorbed species, and desorption of adsorbed products and intermediate species into the gas phase. The pre-exponential factors of the surface reactions are estimated by transition-state theory to be of the order of 1021. Activation energies are taken from Ref. 12. Reverse reactions are determined from thermochemistry [15]. Sticking coefficients are given for initially clean surfaces. The variation of all adsorption reactions with coverage but those involving H2, H, and OH is assumed to follow the Langmuir adsorption isotherm: RRads 4 [Xi]Um(Pt)fi(c) i

!

RT 2pWi

(1)

RRads is the adsorption rate of the ith gas-phase spei

11.5 17.4 48.2

rate coeff. rate coeff. rate coeff.

cies, [Xi] is its gas-phase concentration adjacent to the wall, Wi is its molecular weight, H(Pt) is the freesurface site fractions, and m is the order of the adsorption reaction (0 for the coverage-independent adsorption of H2, H, and OH, 1 for nondissociative adsorption, and 2 for dissociative adsorption). For small values of the sticking coefficient c, f(c) 4 c, and for high values, f(c) 4 c/(1 1 c/2) because the near-wall velocity distribution becomes non-Maxwellian [16]. The square root term in Eq. (1) denotes the collision frequency of the ith gas-phase species with the surface. Initial Conditions An undisturbed flame as calculated by PREMIX [17] is placed about five flame thicknesses away from the wall. For more details on the inert wall initial conditions, see Ref. 2. Initial conditions for the surface site fractions H(s), O(s), OH(s), and Pt(s) are determined by solving the full system of equations on a coarse grid without a flame. Initializing with other than the steady-state solution can lead to erroneous physical results, such as fuel depletion adjacent to the wall or large perturbations in the flow field adjacent to the wall due to extremely high Stefan velocities. Boundary Conditions The wall temperature boundary condition is TW 4 constant during one simulation in agreement with experimental evidence [5,18,19]. All other surface

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boundary conditions depend on the reactivity of the surface and the (numerical) treatment of the gasphase diffusion processes. Inert wall/no cross diffusion This boundary condition is the standard boundary condition in quenching simulations, whether in engine code or theoretical studies of this phenomena [3–5,20,21]. The corresponding velocity boundary condition is simply uW 4 0, and the species boundary condition is ]Yi/]x 4 0, i 4 1,2, . . . , Ng, where Ng is the total number of gas-phase species and Yi the mass fractions. This boundary condition is only valid for wall temperatures between 300 and 400 K [2]. Inert wall/cross diffusion Again uW 4 0; however, the driving force of species diffusion is no longer only the concentration gradient but also the temperature gradient that leads to the specification of species diffusion velocities. ¯) N Those are defined as Vi 4 1/(XiW gj?i WiDij ¹ Xj T 1 (Di ¹ T)/(qYiT), i 4 1, . . . , Ng. Xi are the gasphase mol fractions, W is the mean molecular weight, Dij is the ordinary multicomponent diffusion coefficient matrix, and DTi is the thermal diffusion coefficients. For a nonreacting wall, the diffusion velocity has to be zero normal to the surface; i.e.,

o

VWi 4 0

(2)

Reacting wall For heterogenous reactions, the gas-phase mass flux of each species to the surface is balanced by the creation or depletion rate s˙i of that species by surface reactions; i.e., qYi(Vi ` u) 4 s˙iWi, (i 4 1, . . ., Ng). This leads to an induced velocity, the so-called Stefan velocity, which occurs when there is a net mass flux between the gas and the surface: uW 4

1 q

Ng

o s˙iWi i 1

(3)

4

Once the Stefan velocity is known, the diffusion velocity can be readily evaluated: VWi 4

s˙jWi 1 uW qYi

(4)

Diagnostics Special attention is focused on the wall heat flux and the flame structure during quenching. The wall heat flux as measured by a thin-film gauge [22] for a reactive surface is given by qW 4 kW ]T/]x|W 1 g (N i41 s˙iWihi, with hi the specific enthalpy of the ith species. For an inert wall, this reduces to qW 4 kW 4 kW ]T/]x|W. Radiative heat transfer is neglected

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based on previous research [5,18,23]; qw is normalized using the laminar flame power to yield the nondimensional wall heat flux: U 4 qw /(q cp Sl DT), where q denotes the unburned gas density, cp its specific heat at constant pressure, Sl the laminar flame speed, and DT the temperature difference between the burned and the unburned gases. The maximum wall heat flux that occurs during flame-wall interaction will be denoted by UQ. The flame position is tracked as the location of the maximum heat release in the flame x(w˙max). The corresponding distance between the flame and the wall is normalized to yield a Peclet number: Pe 4 x(w˙max)/df. The laminar flame thickness is defined as df 4 (dT/dx|max)/DT as in Ref. 24. All times are normalized by the laminar flame time, which is given by tf 4 Sl/df. Thus, s 4 t/tf and sQ denotes the time when the maximum wall heat flux UQ is obtained and is referred to as the moment of quenching. Flame-Wall Interaction Gas-Phase Chemical Kinetic Results The influence of either an inert wall with crossdiffusion in the gas phase [Eq. (2)] or a reactive wall [Eq. (4)] on gas-phase chemistry in the near-wall region is demonstrated. Mass fraction and net heatrelease profiles per species at the moment of quenching are presented. The distance from the wall is nondimensionalized by the laminar flame thickness. The wall temperature is 600 K. For more information on the inert wall calculations as well as the low wall temperature domain, see Ref. 1. Figure 1 compares species profiles for both boundary conditions. For Peclet numbers larger than 1.0, the influence of the boundary condition on the species mass fractions is negligible as it is for their net heat-release rates (Fig. 3). However, there are large differences adjacent to the wall. The reactive surface results in (1) much larger mass fractions of fuel and oxygen (same spatial extension but higher peak values with differences in the peak value of methane of a factor of 2) but much lower radical wall concentrations (this is the opposite situation as can be found, for example, in boundary layer or stagnation point flow situations over reactive surfaces where the near-wall region is depleted of fuel but the radical concentrations are increased) and (2) higher near-wall concentrations of carbon monoxide but smaller concentrations of carbon dioxide and water. The behavior of the propane flame is the same as that of the methane flame in terms of the major product and radical profiles. However, the surface mechanism considered does not affect the intermediate hydrocarbons resulting in a peak of their mass fractions directly at the wall as well as a nearwall concentration that is of the same order as the

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Fig. 3. Species net heat-release rates for a CH4/air flame at the moment of quenching (comparison: inert–reactive wall).

Fig. 1. Species mass fractions for a CH4/air flame at the moment of quenching. Upper graph: inert wall [Eq. (2)]. Lower graph: reactive wall [Eq. (4)].

Fig. 2. Intermediate hydrocarbon mass fractions for a C3H8/air flame at the moment of quenching (reactive wall).

fuel (Fig. 2). Of particular importance is the large amount of acetylene, which is known as a major soot precursor. Large concentrations of intermediate hydrocarbons with peak values at the wall were also reported by Kiehne et al. [25]. Free radicals and most intermediates are trapped between the decaying induction zone of the flame and the wall because their concentration gradients during quenching are directed toward the wall. The only remaining reaction paths are low-activation energy recombination reactions or surface adsorption reactions. If the participation of the surface in the reaction channels of the gas-phase species is excluded (either because of surface properties or because of the boundary condition in the numerical simulations), reactions proceed through the highly exothermic recombination reactions. This results in large heat-release rates adjacent to the surface (Fig. 3) that are primarily due to the water formation via the radical recombination reaction H ` OH → H2O, the carbon dioxide formation via CO ` OH → CO2 ` H, and the recombination reaction of the methyl radical with the H radical to form methane. Those reactions are only possible because of the accumulation of especially the free and highly reactive radicals H and OH in this region. Other but less exothermic recombination reactions involve O, HO2, and H2O2. If the surface (at least a Pt surface) participates in the radical reaction channels, then radical adsorption reactions dominate radical recombination reactions, leading to a negligible near-wall concentration of free radicals and much smaller heat-release rates. This also explains why the reactive surface results in lower CO2 and higher CO concentrations adjacent to the wall. From Fig. 3 it becomes obvious that the boundary condition chosen not only influences the amount of heat released directly at the wall but also influences the shape, peaks, and distance from the wall of the heat-release

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creased only between 30 and 40% with respect to free flame values. Wall Heat Flux Variations

Fig. 4. Variation of the dimensional maximum wall heat flux with wall temperature for a stoichiometric methane/ air and propane/air flame.

Fig. 5. Variation of the dimensionless maximum wall heat flux with wall temperature for a stoichiometric methane/air flame.

profiles. The inert wall assumption results in profiles that are closer to the wall but with smaller peak values due to the more intense burning because of the high exothermic recombination reactions. Still, although the surface chemistry reduces significantly the near-wall heat-release rates (and a Pt surface yields certainly a maximum effect in comparison to other surface materials), a quenching layer does not exist under the conditions investigated in this study. This is of particular importance for the modeling in internal combustion engines where this concept, that is, the assumption of the existence of a thin layer adjacent to the wall where no major chemical reaction and heat release takes place, is commonly used. Our results reveal that in contrast to the low walltemperature region [1], such an assumption is never valid for higher wall temperatures. All heat-release rates peak within a distance close to the wall that is less than half a flame thickness. Peak values are de-

Figure 4 shows the variation of the dimensional maximum wall heat flux with wall temperature and its dependency on gas-phase modeling assumptions and surface conditions. The methane-flame simulations indicate the existence of two temperature domains: a low- (300–400 K) and a high-temperature domain (.400 K). In the low-temperature region, all numerical results overlap and are within the experimental uncertainty of the experiment (which used a Pt thin-film gauge [4]). This demonstrates that surface and cross-diffusional effects play only a minor role and thus, the species boundary condition can be modeled by a zero-concentration gradient condition. On the contrary, there is a large spread in the curves in the high wall-temperature region. The simulations neglecting cross-diffusion and surface chemistry predict the highest value of the peak wall heat flux and show the largest discrepancies with the experimental values. Accounting for cross-diffusional effects but keeping the inert wall condition reduces the wall heat flux over the whole high walltemperature domain but still yields values that are much outside the experimental uncertainty. The reduction in the maximum wall heat flux at the high end of the wall temperatures investigated (600 K) by taking cross-diffusion into account is 12%. The largest decrease in the numerical values is reached by considering surface chemistry. This contribution produces a larger decrease the higher the wall temperature, and this relationship results in an excellent agreement between the simulations and the experiment. The reduction in the maximum wall heat flux at 600 K is 18% in comparison to the calculations accounting for cross-diffusion, and 31% in comparison to the simulations without surface chemistry and cross-diffusion. The behavior of the propaneflame–wall interaction is, in principle, the same as for the methane flame with values for the maximum wall heat flux of the same order. However, the influence of surface chemistry is already felt earlier. This pattern is not surprising considering the fact that a propane flame ignites at much lower temperatures than a methane flame over a Pt surface. The evolution of the maximum nondimensional wall heat flux during the quenching of a methane flame is presented in Fig. 5. The wall heat flux for all modeling conditions increases rapidly up to a maximum value and decays slowly after quenching. Despite this similarity, there are some important differences. The neglect of cross-diffusional effects and surface reactions yields higher peak wall heat fluxes and heat losses through the wall. This effect is clearly visible before quenching occurs and even afterward. In addition, it leads to a faster burning during the

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interaction. Surface chemistry and cross-diffusion delay quenching. This effect was already observed in the heat-release profiles. UQ of the CH4 flame is almost constant (0.54) in the range of wall temperatures between 300 and 500 K and increases up to 0.60 at 600 K. UQ of the C3H8 flame is somewhat lower with a value around 0.52 in the low wall-temperature region, which decreases slightly to 0.49 at 600 K. Transport Effects Taking cross-diffusional effects (Soret and Dufour) as well as surface chemistry into account complicates strongly gas-phase modeling and the treatment of the wall boundary conditions. Especially with regard to engine codes, it is thus desirable to reduce the complexity of the physical problem to a level that is easier to handle. It turns out that the dominant effect is the Soret effect, even in the presence of a reactive wall. This effect accounts for a species flux that is inversely proportional to the molecular weight of the species and directly proportional to the temperature gradient in the flow field and is directed toward the hot gases. Because the maximum temperature gradient in the flow field is a factor of about 4 higher than in a free flame [2] during quenching, especially H radicals are removed from the near-wall region. This results in lower heatrelease rates of the exothermic radical recombination reactions adjacent to the wall even when surface chemistry is accounted for and, subsequently, in a lower wall heat flux. The Dufour effect is also important for lighter-weight species. In contrast to the Soret effect, it accounts for an energy flux that is due to concentration gradients. Because those concentration gradients are decreased, its influence is even smaller during quenching than it is for a freely propagating flame. The Stefan velocity was found to have very small values. Thus, in a next step, we imposed numerically a zero Stefan velocity (but kept the surface reactions), i.e., UW 4 0. This did neither affect the wall heat flux nor the flame structure during quenching. We conclude that the influence of the Stefan velocity on flame-wall interaction is negligible. Surface Chemistry Figure 6 illustrates the time-dependent surface response to the quenching of the methane flame at a wall temperature of 600 K as predicted by our surface mechanism Table 1. Prior to flame-wall interaction, the surface is dominated by adsorbed atomic oxygen [H(O) 4 0.99] and consists of only a few free surface sites [H(P) 4 1012]. The high oxygen coverage results from the very rapid O2 dissociation reaction. Due to its relatively low adsorption energy, the hydrogen coverage is very low [H(H) 4 10110].

So is the hydroxyl coverage [H(OH) 4 1014].1 Surface reactions proceed very slowly, and the stationary state is controlled by the diffusion of gas-phase species to the surface. The surface starts to feel the approaching flame at about sQ 1 0.2 via an increase in the H adsorption rates. H radicals diffuse farther in front of the flame due to their low weight. During the interaction, the hydroxyl and the atomic hydrogen coverage increase continuously and reach their maximum value shortly after sQ [H(OH) 4 1012, H(H) 4 1017]. The number of free surface sites decreases slightly up to the moment of quenching and increases continuously afterward. Oxygen coverage is seen to decrease throughout the interaction. During quenching, the interaction becomes controlled by radical adsorption kinetics. H radicals are quickly adsorbed on the surface and react readily with adsorbed oxygen atoms to form adsorbed hydroxyl radicals. The maximum of the O(s) consumption and the maximum of the OH(s) production both occur at sQ, whereas the maxima of the adsorption reactions occur shortly afterward. During the interaction, both water formation reactions compete effectively for OH(s) with the hydroxyl recombination reaction dominating at the moment of quenching. The maximum water formation occurs at sQ ` 0.2. At this time, the gas phase is almost completely depleted of radicals, and surface production rates are decaying. The surface thus delays the exothermic water formation via the radical recombination of H and OH to times larger than sQ. This indicates that a simplified global recombination step would probably overpredict the wall heat flux since such a model predicts the maximum in the water production at sQ and not afterward. If a Langmuir adsorption concept is assumed for all adsorption reactions, the surface mechanism is not capable any longer to remove sufficiently free radicals from the gas phase. This results in large radical recombination reactions (H, OH) adjacent to the wall and a wall heat flux, UQ, of 0.64 (instead of 0.60). The breakdown of this concept is not surprising since it is, strictly speaking, only valid in the low coverage domain. In the case of high surface coverage, adsorption reactions for hydrogen (as well as CO) on Pt surfaces are known to be coverage independent [12]. Their adsorption proceeds through a mobile precursor rather than an inmobile surface state. Due to the high mobility of H and OH, it 1The associative desorption of H and O was originally 2 2 included in the surface mechanism. Because it does not influence our obtained results but requires a much smaller time step in the calculations, they were omitted in Table 1. The same is true for H2O adsorption. CO adsorption was not considered since its rates are very small at 600 K and its further dissociation becomes only relevant for temperatures larger than 800 K.

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higher than in the free flame. This suggests that for the conditions under which the simulations were performed, their influence on the quenching process is negligible, but a possible influence at higher pressures can not be excluded. Third, considering only H adsorption reduces significantly the wall heat flux in comparison to the inert wall calculations but results in a higher value as well as in a phase error in comparison with the complete surface mechanism (Fig. 6). Conclusions

Fig. 6. Upper graph: surface coverage for the surface radical mechanism. Lower graph: surface reaction rates.

seems reasonable to assume that these radicals are adsorbed as well via a precursor state in which they can diffuse rapidly over large distances to find a free site. However, this is not true for O, HO2, and H2O2. Although the oxygen atom is quite mobile, it faces an increasing energy barrier for adsorption due to repulsive forces by already adsorbed O atoms. HO2 and H2O2 are not only much less mobile but they require as well the availability of two free neighboring adsorption sites, which is not likely for high surface coverages. Finally, we considered a reduction of the surface mechanism from Table 1: First, the hydrogen/oxygen adsorption reactions were neglected. This affected neither the wall heat flux nor gas-phase species distributions during the interaction but shifted the surface from high to low surface coverage [H(Pt) 4 0.51]. Second, additional neglect of the adsorption of HO2 and H2O2 did not further change the surface coverage and left as well the wall heat flux unaffected. However, their concentrations and net production rates adjacent to the wall become much

We presented the results of numerical simulations in combination with detailed reaction mechanisms for the head-on quenching of stoichometric methane- and propane-air flames at atmospheric pressure for 300 K , TW , 600 K with a focus on the high– wall-temperature domain. It is found that in this domain, transport and surface chemistry effects have a considerable influence on the near-wall flame structure and, in particular, decrease the peak wall heat fluxes. Hence, wall heat flux measurements using thin-film gauges have to be evaluated extremely carefully when the film material does not match the normal wall material, as is typically the case. Numerical simulations have to describe correctly the process of diffusion, adsorption, and surface recombination of especially the free radicals H and OH. Since the interaction takes place in the high–surfacecoverage region, the Langmuir adsorption concept breaks down. A precursor state model for at least H and OH has to be considered. The situation might be more complicated for higher hydrocarbons as indicated by the peaks of the intermediate hydrocarbons adjacent to the wall for the propane-flame wall ineraction. Acknowledgment Patrick Popp is grateful to the Commission of the European Communities (Science Foundation) who, by granting him an individual fellowship, made partly possible this work.

REFERENCES 1. Popp, P. and Baum, M., Combust. Flame, to appear, 1996. 2. Popp, P. and Baum, M., SAE F&L Meeting 1995; Toronto, 1995. 3. Connelly, L., Greif, R., Sawyer, R. F., and Lee, D., Fall Meeting, The Combustion Institute/Western States Section, Berkeley, CA, 1992, Vol. WSCI 92-109. 4. Connelly, L., Ogasawara, T., Lee, D., Greif, R., and Sawyer, R. F., Fall Meeting, The Combustion Institute/ Western States Section, Stanford, CA, 1993, Vol. WSCI 93-077.

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5. Ezekoye, O. A., Greif, R., and Lee, D., Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, p. 1465. 6. Kee, R. J., Warnatz, J., and Miller, J. A., Sandia National Laboratories (SAND83-8209), 1983. 7. Kee, R. J., Rupley, F. M., and Miller, J. A., Sandia National Laboratories (SAND89-8009B), 1989. 8. Popp, P., Hilka, M., Baum, M., and Poinsot, T., Using Direct Numerical Simulation to Study Turbulent Combustion, Centre de Recherche sur la Combustion Turbulente, 1995, pp. 67–95. 9. Kee, R. J., Rupley, F. M., and Coltrin, M., Surface chemkin 4.0: A fortran package for analyzing heterogeneous chemical kinetics at a solid-surface–gas-phase interface. Technical Report SAND90-8003C, UC-706, Sandia National Laboratories, August, 1994. 10. Warnatz, J., Ber. Bunsenges. Phys. Chem. 87:1008– 1022 (1983). 11. Peters, N. and Rogg, B., in Lecture Notes in Physics (S. Verlag, ed.), Springer-Verlag, Heidelberg, 1993. 12. Fridell, E., Rosen, A., and Kasemo, B., Langmuir 10:699–708 (1994). 13. Hellsing, B., Kasemo, B., and Zhdanov, V., J. Catalysis 132:210–228 (1991). 14. Ljungstrom, S., Kasemo, B., Rosen, A., Wahnstrom, T., and Fridell, E., Surf. Sci. 1(216):63–92 (1989). 15. Warnatz, J., Allendorf, M., Kee, R., and Coltrin, M., Combust. Flame 96 (1994).

16. Motz, H. and Wise, H., J. Chem. Phys. 32:1893–1894 (1960). 17. Kee, R. J., Grcar, J. F., Smooke, M., and Miller, J. A., PREMIX: A Fortran program for modeling steady laminar one-dimensional flames. Technical Report SAND85-8240, Sandia National Laboratories, 1985. 18. Huang, W. M., Vosen, S. R., and Greif, R., TwentyFirst Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, pp. 1853– 1860. 19. Yang, J. and Martin, J., SAE 900690:1551–1561 (1990). 20. Jennings, M., Int. Congress and Exposition, SAE Paper 920589, Detroit, 1992. 21. Jennings, M. J. and Morel, T., SAE (910459), 1990. 22. Lu, J. H., Ezekoye, O., Greif, R., and Sawyer, F., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 441–446. 23. Poinsot, T., Haworth, D., and Bruneaux, G., Combust. Flame 95(1/2):118–133 (1993). 24. Blint, R. J., Combust. Sci. Technol. 49:79–92 (1986). 25. Kiehne, T. M., Matthews, R. D., and Wilson, D. E., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, pp. 1583–1589.

COMMENTS Dr. R. Maly, Daimler-Benz AG, Germany. It appears to me that the modeling is systematically overpredicting the wall heat flux if compared to the experimental data for temperatures above 500 K, do you have an explanation for possible reasons? Author’s Reply. Please, note that (1) the numerical results are in general higher than the experimental results due to the absence of heat losses. (2) Since there are no experimental data for Tw . 523 K no conclusion can be drawn regarding the tendency of the experimental wall heat flux for higher wall temperatures. In addition, since the influence of surface chemistry was unknown to the experimentalist the experimental uncertainty at high Tw should be actually higher than the quoted 11%. ● Ofodike A. Ezekoye, University of Texas–Austin, USA. Our most recent computational work on flame quenching shows that in the low wall temperature range (Tw , 373 K, P 4 1 ATM) water film condensation has a notable effect (i.e., approximately 10%) on the magnitude of the wall heat flux. For complex chemistry simulations, I anticipate that the depletion of vapor H2O will also affect the overall quenching dynamics. Do you include water phase change in your present computations and what effect do

you think it would have on your predicted quenching results? Author’s Reply. Water phase changes were included in the complex chemistry calculations. ● C. Morley, Shell Research and Technology, UK. Your mechanism does not appear to include CH3O2 which could become an important radical at the low temperatures (,800 K) near the wall. The rate of radical removal in this region by radical-radical reactions could be affected by its inclusion. Author’s Reply. We looked at the effects of various radicals which become important at low temperatures. Those included not only CH3O2 but also HO2 or H2O2. Although their reaction rates are much larger adjacent to the wall during quenching than they are for a free flame, they are not the dominant radicals. For a more detailed discussion of how some species influence the quenching process one may wish to consult: P. Popp and M. Baum, “An Analysis of Heat Transfer, Reaction, and Pollutant Formation Mechanisms during Flame Wall Interaction,” Combust. Flame, 1996.