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A numerical and experimental investigation of premixed methane-air flame transient response
A Numerical and Experimental Investigation of Premixed Methane-Air Flame Transient Response HABIB N. NAJM,* PHILLIP H. PAUL†, and ANDREW MCILROY Sandia National Laboratories, P.O. Box 969, MS 9051, Livermore, CA 94550
and OMAR M. KNIO
The Johns Hopkins University, Baltimore, MD 21218-2686 We report the results of a numerical and experimental investigation of the response of premixed methane-air flames to transient strain-rate disturbances induced by a two-dimensional counter-rotating vortex-pair. The numerical and experimental time histories of flow and flame evolution are matched over a 10 ms interaction time. Measurements and computations of CH and OH peak data evolution are reported and compared. Despite the matching of experimental operating conditions, the full resolution of flame length and time scales, and the use of a detailed C1C2 chemical mechanism and temperature-dependent transport properties, we find disagreements with experimental measurements of the transient response of both CH and OH. Besides quantitative disagreements in response time scales, the qualitative transient features of OH at rich conditions are not predicted in the computations. These disagreements suggest deficiencies in the chemical and/or transport models. On the other hand, evolution of computed and measured peak HCO mole fractions are in reasonable agreement, suggesting that certain components of flame chemistry may indeed be accurately predicted by the present model. We also report computed CH3O response, which exhibits a strong transient driven by changes to internal flame structure, namely temperature profile steepening, induced by the flow field. Steady state experimental PLIF CH3O data is reported and compared to numerical results, but experimental transient CH3O data is not available. In general, the present study highlights the importance of validation of chemical-transport models of flames in unsteady flow environments. © 2001 by The Combustion Institute
INTRODUCTION The formulation of accurate predictive models of combustion systems requires adequate understanding of turbulence-chemistry interactions at the small scales. One important element of this interaction is the transient response of flames to unsteady perturbations due to turbulent flow structures. The present work uses numerical and experimental studies of the interaction of premixed methane-air flames with two-dimensional counter-rotating vortex pairs to investigate transient flame response and examine comparisons between numerical and experimental results. There have been both experimental [1–7] and numerical [8 –16] studies of flame interaction with counter-rotating vortex pairs or torroidal vortex rings. Roberts et al. [1] and Mueller et al. [4, 6] studied the interaction of a propagating planar premixed flame front with a torroidal *Corresponding author. E-mail: [email protected]. † Present address: Eksigent Technologies LLC, Livermore, CA 94550. COMBUSTION AND FLAME 125:879 – 892 (2001) © 2001 by The Combustion Institute Published by Elsevier Science Inc.
vortex. A stationary planar premixed V-flame setup was used by Samaniego [2, 3], as well as Nguyen and Paul [5] and Paul and Najm [7], where a 2D counter-rotating vortex pair was generated and propagated into one leg of the V-flame. These studies examined the role of the vorticity field which contorts and strains the flame, and alters its internal structure. These structural changes were observed using Planar Laser-Induced Fluorescence (PLIF) imaging of OH, CH, HCO, CH2O, and other flame radicals. Early 2D numerical studies of vortex/vortex-pair interactions with premixed flames [8 –10] were generally concerned with singlestep kinetics, flow dynamics, and thermal effects, rather than internal flame chemical transients. Recent studies [12, 13] included C1 kinetics at stoichiometric conditions to investigate the effect of the vortical flow on internal flame structure. The inclusion of C1 kinetics allowed detailed analysis of the structure of premixed flames under unsteady strain-rate, and the transient process by which the flame approaches extinction. Vortex-pair interaction 0010-2180/01/$–see front matter PII S0010-2180(00)00245-5
880 with a non-premixed opposed-jet hydrogen-air flame was also studied by Katta et al. [15], and a parametric study of premixed flame interaction with a vortex-pair was conducted by Patnaik and Kailasanath [16]. The use of C1C2 mechanisms, which are necessary for accurate prediction of internal flame structure— especially at rich conditions, presents significant additional computational difficulties associated with stiffness and increased complexity due to the large number of species and reactions. These complications are a concern for both explicit and implicit numerical schemes, since the sizes of implicit-scheme matrices and convergence difficulties are accentuated by stiff C1C2 kinetics. Najm et al. [14] used a detailed C1C2 mechanism (GRImech1.2 [17]) to study flame response to unsteady strain-rate and curvature under stoichiometric and rich conditions. They found that the rich methaneair flame responds faster than the stoichiometric one. This was counter to earlier one-dimensional stagnation flame data [18], and was attributed to the role of H versus OH in the two flames. Knio & Najm [19] conducted a more recent flame-vortex-pair interaction study involving a parametric investigation of transient flame response for mixtures ranging from lean to rich, and with a wide range of flow time scales and levels of strain-rate, using GRImech1.2. The results confirmed the faster global response of the rich flame. In fact, the rate of decay of peak heat release rate was found to increase monotonically with equivalence ratio from ⌽ ⫽ 0.8 to 1.2. This rules out the robustness of the flame, in the sense of peak burning rate, as determining its response to strain-rate disturbances. On the other hand, it supports the hypothesis based on the relative roles of H and OH, as the dominance of H reactions increases monotonically with ⌽. These studies were limited to a short time span, and/or fast flow time scales, because of algorithmic limitations and associated computational costs. These limitations on operating conditions precluded direct time-evolution comparisons with available experimental results, which involved slower vortices and significantly longer interaction times. The present effort builds on recent numerical developments involving second-order accurate stiff operator-split time integration in multiple dimen-
H. N. NAJM sions [20, 21] to allow detailed resolved computations of 2D C1C2 flames at laboratory time scales; a hitherto impractical undertaking. This removes a barrier to quantitative comparisons with experiments in earlier work [14], and brings us a step closer to resolving key differences with experimental data. We also use a more detailed C1C2 mechanism described further below, with 40 species and 216 reactions, as compared to our earlier work [14, 19], which was based on GRImech1.2 [17], with 32 species and 177 reactions. We use a flow with vortex-strength similar to that in the experiment so that evolution of the flame topology in the two sets of data coincides over a time span of 10 ms. Similarly, we utilize the same numerical flame stoichiometry and dilution as in the experiment, as indicated later. The spatial extent of the numerical vortex-pair is about one-half that of the experimental vortex-pair. This was a necessity, given the fine spatial resolution requirements imposed by the flame structure, and associated computational costs required to integrate stiff detailed kinetics at each spatial location. Doubling the vortexpair size, while maintaining the resolution necessary to properly resolve the flame front, is not feasible given available computational resources. Moreover, the slightly increased numerical flame curvature associated with the smaller vortex-pair is not likely to play a significant role in the observed dynamics. The radius of curvature at the vortex-pair centerline is significantly larger than the flame thickness, so that the observed flame transients on the centerline are primarily driven by the strain-rate. We present superimposed transient time histories of computed and experimental flame radicals, and discuss comparisons between them. Despite the matching of operating conditions and the extent of detail in chemistry and transport, we find that the detailed transient flame time evolution in the computations is in fact significantly different from that in the experiment. This and other comparisons with the experimental data involving numerical and experimental transient OH, CH, and HCO results are presented and discussed. While disagreements are evident in the evolution of OH and CH, we do find reasonable agreement with the experimental results in the evolution of HCO. This suggests that at least some components of
TRANSIENT FLAME RESPONSE the flame chemistry are accurately predicted by the model. On the other hand, the disagreements in OH and CH suggest deficiencies in the chemical and/or transport models whose identification and elimination is work in progress. We also present experimental and numerical steady state CH3O profiles, investigate features of the computed transient accumulation of methoxy (CH3O) and other species on the reactants-side of the flame, and analyze the role of unsteady strain-rate in these internal flame dynamics. While no experimental data on the transient response of methoxy in this flame is available, it is hoped that these observations would motivate future measurements to examine their validity. MODEL FORMULATION AND NUMERICAL SCHEME The model formulation has been presented in detail elsewhere [20, 21]. The governing equations are developed in 2D using the low Mach number approximation [22]. The assumptions of zero bulk viscosity [23] and negligible body forces are used in the conservative continuity and momentum equations. In particular, we note that gravity is neglected in the model because it plays a negligible role in the present flow, as the Froude number (Fr ⫽ U/公gL) based on the maximum flow velocity and the vortex-pair centerto-center distance is larger than 10. We assume a detailed chemical reaction mechanism involving N species and a number of elementary reactions. The energy equation is developed allowing for temperature-dependent transport properties, and a constant stagnation pressure p o , that is, an open domain. We neglect Soret and Dufour effects [24] and radiant heat transfer, and assume a perfect gas mixture, with individual species molecular weights, specific heats, and enthalpies of formation, using Fickian binary mass diffusion. The N-th species, here N2, is assumed dominant such that the diffusion velocity of any other species i in the mixture is approximated by binary diffusion into N2 at the local temperature. For computational efficiency, mixture transport properties (, ) are set to those of N2 at the local temperature. Species conservation equations are used to integrate the mass fractions of N ⫺ 1 species,
881 while the mass fraction Y N is found from the N identity ⌺ i⫽1 Y i ⫽ 1. The production rate for each species is given by the sum of contributions of elementary reactions [24], with Arrhenius rates, including forward and backward rates, and third-body efficiencies [25]. We use a C1C2 chemical mechanism with 40 species and 216 reactions. It is based on a subset of the mechanism used in [26], which is in turn based on [27], and is available upon request. Additional detail about the mechanism is included in the Appendix. The governing equations are discretized using second-order central differences on a uniform mesh, with cell size ⌬x ⫽ 15.6 m. This resolution is necessary for adequate representation of internal flame structure. Najm et al. [14] list typical species profile thicknesses in an atmospheric methane-air flame. Generally speaking, minimum profile thicknesses are on the order of 100 m, hence the necessity of the fine spatial resolution used here. It is imperative that adequate resolution be maintained to accurately compute transport fluxes internal to the flame, especially when substantial effort is expended on computing the chemical source terms with detailed kinetics. The discrete equations are integrated using an operator-split stiff second-order predictor-corrector projection scheme. Construction of the stiff scheme is based on several refinements of the explicit construction originally introduced in [12]. A semi-implicit additive (non-split) stiff version is presented in [20]. The present work uses a stiff symmetrically-split [28] integration of the governing conservation equations. Diffusion and convection terms are integrated explicitly with multiple fractional steps, over half-time-step intervals, while the reaction terms are integrated implicitly over a full time-step interval. The explicit halfsteps are arranged symmetrically before and after the implicit step in each global step. Stiff integration of reaction terms is performed by using the ordinary differential equation integration package DVODE [29]. The formulation and convergence of the scheme are discussed in detail in [21]. EXPERIMENTAL SETUP AND DIAGNOSTICS The experiment has been described in detail in [5, 7]. A V-flame is stabilized on a wire in a
882 vertical channel, with premixed methane-air flowing up through flow straighteners upstream of the wire. Line-vortex pairs are ejected from an acoustically driven cavity on one side of the flow enclosure and allowed to impinge on one leg of the V-flame. PLIF imaging of CH, OH and HCO was performed by using a XeCl excimer-pumped dye laser and an intensified CCD array detector. For CH the laser was run on a BBQ dye and tuned to the Q1 (4.5) transition of the B-X (0,0) system near 389.5 nm, with non-resonant detection using 2 mm of Schott GG-420 and an F/1.2 camera lens. For OH the laser was run on a C153 dye, doubled in BBO and tuned to the Q1 (6.5) A-X (1,0) transition near 283 nm, with non-resonant detection using 2 mm of Schott WG305 and an F/4.5 UV camera lens. For HCO, the laser was run on a C500 dye, doubled in BBO and tuned to QR0 bandhead in the B-X (0,0,0) system near 254 nm, with non-resonant detection using 2 mm of Schott BG1, a 400 nm reflective shortpass and an F/2.2 transmissive UV lens system. The signal-to-noise ratio for the HCO data presented here is improved by about a factor of 2 to 3 from our earlier work [13] (50-frame averages were employed, as in [13]). This was achieved by improvements to the lens, detection filters, and excitation source employed. PLIF images of CH3O have also been successfully taken in the same burner, using the same laser/camera system but under steady conditions. The laser was operated as for pumping OH and tuned to excite overlapping transitions in the A-X 340 system near 292.8 nm with care taken to avoid excitation of adjacent OH and CH2O transitions. Non-resonant detection was performed using 2 mm of Schott WG320, a 400 nm reflective short-pass filter and an F/1.4 near-UV camera lens. As found with PLIF of HCO [13], CH3O PLIF signals are quite weak and frame averaging is required to achieve a useable image (nominally 50-frame averages are required for imaging in a premixed 36% N2diluted stoichiometric CH4-air flame). RESULTS In both the experiments and computations, two CH4-air reactants mixture conditions are inves-
H. N. NAJM tigated: one stoichiometric with 36% N2-dilution (over and above the air N2, thus with mole fractions of CH4:O2:N2:AR of 0.06:0.12:0.81: 0.01) and the other rich with 32% N2-dilution. This change in dilution between the two cases was necessary to maintain the same experimental V-flame angle in the stoichiometric and rich flames. Flow-Flame Evolution An open rectangular domain is considered, with dimensions 0.4 ⫻ 1.6 cm, and is overlaid by a 256 ⫻ 1024 uniform mesh. We apply symmetry boundary conditions in the horizontal x-direction, and outflow boundary conditions in the y-direction. The evolution of the flow over a 10 ms time span is illustrated in Fig. 1 for the stoichiometric flame. The evolution of the rich flame is similar. The vertical right edge of the domain is the centerline of the vortex pair under consideration, which is one member of a periodic row of vortex pairs along the x-direction. The initial condition is a superposition of the velocity (u,v) field induced by the periodic row of vortex pairs, and the temperature, density and mass fraction (T, ,Y i ) distributions corresponding to a horizontal premixed flame, with the initial structure in the y-direction from a 1D flame solution computed with Chemkin [25, 30]. The flame propagates downward by burning into the reactants, as shown in Fig. 1. Meanwhile, the vortex pair propagates upwards causing transient curvature and strain-rate disturbances to the flame. The flame region is delineated using CH mole fraction. The time scale of the vortex-pair interaction with the flame is matched with the available experiment. A typical experimental CH frame sequence, which exhibits comparable flame topology evolution with time as in Fig. 1, is reported in [5]. The time reference in the subsequent comparisons between experimental and numerical results is determined based on matching flame topology in the sequence of frames shown in the figure. This procedure involves first the identification of a time frame during the interaction where the experimental and numerical flame topologies/contortion are congruent. Thus, we find for ⌽ ⫽ 1.2, that the numerical flame topology at t num ⫽ 4 ms is identical to the
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Fig. 1. Evolution of CH mole fraction (shading) and vorticity (contours) for the stoichiometric flame.
experimental one at t exp ⫽ 6 ms. We then confirm that there is similar congruence in the two topologies at all times within the data time-span given that t num ⫽ t exp ⫺ 2 ms (at ⌽ ⫽ 1.0 a 3 ms time shift is used, based on a similar reasoning). By this we establish (1) a means of superposing experimental and numerical results on a single time axis in a consistent manner by applying this time shift, and (2) a degree of confidence in the similarity of the dynamics in both experimental and numerical flows where similar flame contortion is achieved in the same time intervals. Note that this procedure is necessary because of the difference in initial conditions between the numerical and experimental flows. The experimental vortex-pair is created in an acoustically forced chamber far away from the flame, while the numerical vortex-pair is created in space ahead of the flame (albeit at a given distance where the initial transient and its consequence on the flow are insignificant). Given this, the only feasible way to compare the flame transients in the two flows was using the above matching procedure. The peak vorticity is 9 ms⫺1 at t ⫽ 0, decaying to 2 ms⫺1 after 10 ms. The initial center-to-center distance ( ␦ cc ) of the vortex pair is 0.25 cm. The experimental vortex-pair center-to-center distance is about 0.4 cm, and the diameter of the flame bubble (e.g., 8 ms
frame in Fig. 1) is about 0.8 cm. Thus, the numerical flame bubble is about 1/2 that of the experimental one. As the numerical vortex-pair evolves, its vortex centers approach each other and its propagation speed increases. A similar speedup is observed in the experiment. Based on the numerical vortex-pair representative center-to-center distance ␦ cc ⬇ 0.2 cm, and selfinduced velocity V v ⬇ 50 cm/s, and the experimentally observed vortex-pair ␦ cc ⬇ 0.4 cm and V v ⬇ 100 cm/s (both in the rich flame), the convective time scales of the numerical and experimental vortex pairs are roughly the same, at t v ⬇ 3 ms. Hence the similarity in the topological development of the flame between the numerical and experimental results, and the expected consequent similarity in the rates of flame stretch (1/A) (dA/dt). By using time scales based on flame thermal thickness and burning speed, the two flames considered here (⌽ ⫽ 1.0 and 1.2) have time scales t f ⫽ 23.4 and 49.1 ms, respectively. On the other hand, as reported in [14] and further observed here, these propagation time scales are generally different from those exhibited by the response of the flame structure to the unsteady strain. Evidently, these propagation time scales are not adequate for characterizing transient flame response to flow disturbances. To begin with, the time scale of the transient response involves a
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Fig. 2. Evolution of the computed and experimental normalized peak CH and OH mole fractions on the rich flame centerline.
direct dependence on the strength of the vorticity field, and the ensuing unsteady strain-rate field. Moreover, as observed in [14, 19], it is evident that the rich flame, with longer propagation time scale, responds faster than the stoichiometric flame, which has the shorter propagation time scale. OH and CH Response The evolution of normalized peak rich flame quantities from the numerical and experimental results are shown on the same time axis in Fig. 2. As indicated earlier, the time references of the two data sets were matched based on observed flame topology in numerical and experimental frame sequences. The overall numerical flame response is seen to exhibit slow decay over a time interval of 6 to 7 ms. A roughly 50% drop in OH is evident. CH exhibits similarly slow decay, down to about 30% of its original level. The experimental flame on the other hand exhibits drastically different behavior. There is practically no drop in either OH or CH signals over the first 5 ms of flame evolution. This is then followed by simultaneous and opposite fast response of both signals. OH increases by a factor of 3.5 in 1 ms, and then decays over the remaining 4 ms. Meanwhile, CH signal drops quickly, reaching zero in 2 ms, and disappearing thereafter. Based on experimental signal-tonoise estimates, the CH signal zero corresponds
H. N. NAJM to a level below 1% of its initial undisturbed flame value. Given the similar flow and flame time scales in the numerical and experimental flows, these disagreements in qualitative response (of OH) and transient time scales (of both OH and CH) are remarkable. Note that the experimental signal-to-noise ratios, at peak signal, are nominally 10:1 for OH and 5:1 for CH on a per pixel/per image basis. The experimental data presented here has been averaged over 20 frames and over three pixels taken laterally to the cuts. This should provide a nominal seven- to eight-fold improvement in the signal-to-noise ratio (S/N) in the plotted data, resulting in an S/N larger than 50:1. The individual images were corrected with white and dark frames and for laser sheet variations. We estimate that these corrections reduce fixed pattern noise to order 2%. The primary systematic error remaining is due to residual temperature and quenching effects in the LIF signal. These are estimated to be less than 25%. Based on available quenching and spectroscopic data, the computed variation in temperature and composition provides that the OH signal would tend to decrease (by about 10%) under conditions where we observe an increase of over 3 fold. Consequently, we cannot justify the above observed burst in OH, or, by similar arguments, the disappearance of CH due to residual dependencies in the LIF signals (see also [5]). The evolution of the stoichiometric flame normalized peak quantities are shown in Fig. 3. In this case, the experimental and numerical flames exhibit qualitatively similar monotonically decaying behavior in both OH and CH, yet with significant quantitative disagreement. Let us first compare this data with that of the rich case in Fig. 2. There is significantly more decay of the numerical peak quantities in the weaker rich flame. The drop in peak CH mole fraction, which is about 10% in the stoichiometric flame, is close to 70% in the rich flame. On the other hand, the experimental CH data shows decay to zero in both cases, albeit with faster decay rate in the rich case as indicated in [14]. Moreover, the burst in OH observed at rich conditions is absent from the experimental stoichiometric data, with monotonic decay of OH observed down to 60% of the initial undisturbed flame value. Next, compare the experimental and nu-
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Fig. 3. Evolution of the computed and experimental normalized peak CH and OH mole fractions on the stoichiometric flame centerline.
merical stoichiometric flame results. As in the rich case, experimental signals of peak OH and CH exhibit faster time scales and higher degrees of change in amplitude than the corresponding numerical signals. These observations raise many questions regarding the ability of the present combination of chemical mechanism and transport model to adequately represent the dynamical features of transient flame response. At this time, an explanation for the burst in experimental OH at rich conditions is lacking. It is also not clear if the absence of this burst from the computational results is due to missing reaction pathways, inaccuracies in species transport properties [31], and/or reaction rate parameters. Note, however, that the accumulation of species during flame transients is not surprising since different reaction pathways have different characteristic time scales which generally depend on mixture stoichiometry [14]. Such transient accumulations are in fact observed in the computations, as further discussed below. Moreover, the significantly faster response of CH and OH in the experiment, versus the computed CH and OH, suggests that the present diffusion-reaction model does a poor job at the representation of the dynamical character of these species in this flame. Given that the time response of the governing equations is determined by the eigenvalues and associated eigenmodes of the system Jacobian, this sug-
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Fig. 4. Evolution of computed and experimental normalized peak HCO mole fraction, along with the computed normalized peak heat release rate w T , on the stoichiometric flame centerline.
gests that the eigenvalues/modes pertaining to these species are significantly in error. Determination of the actual causes of these disagreements requires detailed analysis of the eigenmodes of the coupled reaction ⫹ diffusion right-hand-sides of the governing equations, which is work in progress. Of course, if the reaction mechanism is deficient, in the sense that it is missing certain important reaction pathways that are not known at this point, then determining the eigenmodes governing the existing system response, and adjusting the rate constants of the corresponding reactions within their uncertainty bands, will not suffice to bring about the expected physical behaviour of the model. These missing pathways, if they indeed exist, would have to be identified and included in the mechanism in order to recover the correct transient flame response. HCO Response Figure 4 shows experimental normalized peak HCO measurements in the stoichiometric flame over a 4 ms time span, along with the corresponding numerical normalized peak HCO mole fraction and heat release rate. The HCO data has low signal to noise ratio, with 10% uncertainty. Still, it is interesting to note that the relative evolution of this signal does not deviate much from the numerical HCO. No
886 experimental HCO data is available later on in the cycle, which limits the scope of the comparison. Nevertheless, the agreement up to 6 ms is encouraging (even as the experimental CH deviates strongly downward) and suggests that the present mechanism may be reasonably capturing at least some components of transient flame structure. In earlier work [13, 32] we noted the fidelity with which peak numerical HCO mole fraction correlates with peak flame heat release rate of premixed methane-air flames. This observation is borne out in the present results as well. Computed peak HCO mole fraction provides a reasonably good representation of peak heat release rate in Fig. 4, with even better agreement evident at rich conditions. If we accept the correspondence between HCO and heat release rate, then the robustness of the experimental HCO signal at 6 ms in Fig. 4 suggests that the stoichiometric flame is in fact able to withstand the present rate of strain without extinction. This is despite the strong drop in CH signal evident in the figure. The drop in CH is of course indicative of significant disruption of flame chemistry in certain portions of the chemical mechanism. However, since the bulk of the carbon flux is through HCO and not through CH [13], these disruptions are not necessarily indicative of overall extinction of the flame. CH3O Response We also report on the response of the methoxy radical, CH3O, which exhibits transient accumulation during the flame-vortex-pair interaction. Methoxy is of interest because of its role in the low temperature chemistry on the reactants side of the flame. Modeling studies of its transient response provide a means of validating existing low-temperature chemistry models against experimental data in a transient flame environment. Moreover, its transient accumulation observed below is reminiscent of the experimentally observed burst in OH, and is therefore instructive as to the mechanism by which flow transients can lead to large transient accumulation in flame radicals—a potent example of ‘turbulence’-chemistry interaction. In the present mechanism, the methoxy rad-
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Fig. 5. Instantaneous computed CH3O mole fraction and CH4 consumption rate profiles along a normal cut at the rich flame centerline. Data is taken in a reference frame moving with the flame, with x-distance measured from the location of the fuel mass fraction contour corresponding to 10% of the reactants fuel mass fraction. Reactants are on the left, and products on the right. Solid lines are for [0 – 4] ms as indicated on the CH3O profiles, while the dashed line is at 8 ms. The CH4 consumption rate profiles are shown for the same time instances, exhibiting monotonic decay with time.
ical is produced primarily by the reaction CH3 ⫹ HO2 3 CH3O ⫹ OH, and consumed by CH3O(⫹M) 3 CH2O ⫹ H(⫹M). As such, it exists primarily in the fuel consumption layer and on the cold (reactants) side of the reaction zone. The mole fraction profile of methoxy in the undisturbed rich flame is shown in Fig. 5 (t ⫽ 0). We focus on the rich flame data because it exhibits more significant changes in time, though it is qualitatively similar to that in the stoichiometric flame. The t ⫽ 0 CH3O
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Fig. 6. Instantaneous tangential strain-rate profiles along a normal cut at the rich flame centerline. Data is taken in a reference frame moving with the flame as in Fig. 5. Solid lines are for [0 – 4] ms as indicated, while the dashed line is at 8 ms.
profile in Fig. 5 reveals two distinct peaks. The one nearer to the zero abscissa is within the fuel consumption zone, as may be seen in the plot of CH4 consumption rate profiles also shown in Fig. 5. Peak fuel consumption rate occurs at x ⫽ 0.014 and drops below 5% of peak at x ⫽ ⫺0.05. The outer peak at x ⫽ ⫺0.11 exists in a low temperature region (see Fig. 7). The methoxy profile in Fig. 5 shows different evolution of the two peaks. The high temperature peak decays in time, in accordance with decaying peak burning and heat release rates; while the low temperature peak exhibits a rising transient, increasing by a factor of 3 in the first 3 ms of the interaction, followed by a gradual decay, viz. the 8 ms profile. Strain-rate and temperature fields during this process, shown in Figs. 6 and 7, respectively, suggest the essential causes of this transient. The strain-rate, while decaying in space with increased distance from the vortex pair, rises globally in time in the flame reference frame, peaking at 3 to 4 ms, and then decays. Meanwhile, the temperature profile steepens due to the rising strain-rate, as shown in Fig. 7, leading to lower temperatures in the region with T ⬍ 1000 K. By t ⬃ 8 ms this steepening subsides and, despite the reduced burning rate, the temperature on the reactant side increases due to the inundation of the reaction zone with hot combustion products [12].
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Fig. 7. Instantaneous temperature profiles along a normal cut at the rich flame centerline. Data is taken in a reference frame moving with the flame as in Fig. 5. Solid lines are for [0 – 4] ms as indicated, while the dashed line is at 8 ms.
Despite the observed opposite trends in CH3O mole fraction in the two peaks in Fig. 5, we note that its dominant production and consumption channels both decay during the process, as shown in Fig. 8. On the other hand, the net production rate of methoxy clearly exhibits a fast rising transient in the low temperature region, as shown in Fig. 9, which leads to the observed transient accumulation in Fig. 5. In contrast, and consistent with the behavior of the high temperature peak in Fig. 5, both production and consumption rates in the high temper-
Fig. 8. Instantaneous profiles of the two dominant reaction rates involving CH3O along a normal cut at the rich flame centerline. Data is taken in a reference frame moving with the flame as in Fig. 5.
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Fig. 9. Instantaneous profiles of the net production rate of CH3O along a normal cut at the rich flame centerline. Data is taken in a reference frame moving with the flame as in Fig. 5. Solid lines are for [0 – 4] ms as indicated, while the dashed line is at 8 ms.
ature region in Fig. 9 decay in time. Analysis of the results indicates that the net increase in production rate of CH3O on the cold side of the flame is driven primarily by the local temperature drop in Fig. 7. Reaction 51 (CH2O ⫹ H(⫹M) ⫽ CH3O(⫹M)) has a high activation barrier in the reverse direction, such that a drop in temperature leads to a reduction in the reverse (consumption) rate. Despite opposing factors, namely the increasing mole fraction of CH3O and the reduction in the forward rate of Reaction 32 (CH3 ⫹ HO2 ⫽ CH3O ⫹ OH), a large net increase in the production rate of CH3O occurs, as seen in Fig. 9. Note that the balance of Reactions 51 and 32 (Fig. 8) in the high temperature region would have lead to a similar increase of CH3O production rate there, were it not for the decay of the reaction CH3OH ⫹ H ⫽ CH3O ⫹ H2, a production channel, because of reduced H. We have also observed this transient behavior of methoxy by using the GRImech1.2 [17] mechanism, and at other degrees of N2-dilution, as well as other flow time scales [19]. Generally, the extent of the rise in peak CH3O is higher with the less robust flames and with the faster flows. Moreover, the present results exhibit similar transient accumulation in two other species on the cold side of the flame, namely CH3O2 and C2H2OH, with similar—although
Fig. 10. Peak-normalized numerical (top) and experimental (bottom) profiles of CH3O, CH2O, HCO, and OH mole fractions for the stoichiometric 36% N2 diluted flame.
significantly milder— behavior in CH3CO. Formaldehyde, CH2O, also exhibits a transient increase in its production rate during the first 4 ms. On the other hand it experiences monotonic decay in mole fraction, which is in agreement with experimental measurements [7]. We do not have transient measurements of methoxy or the other species exhibiting the above transient accumulation to validate the above findings. However, PLIF data on methoxy in the steady V-flame is available; it is compared to the initial data from the computations in Fig. 10 where all profiles are normalized to a peak amplitude of unity. The relative spatial placement of the experimental PLIF profiles is as-
TRANSIENT FLAME RESPONSE measured, while their placement relative to the numerical profiles was based on matching the locations of peak CH2O profiles in the two sets of data. The two sets of results exhibit common features. The shapes and locations of the OH and HCO peaks are in good agreement. On the other hand, the numerical CH2O profile, while roughly of similar width as the experimental one at half-maximum, extends further towards the reactants than the experimental data suggests. Moreover, the experimental CH3O PLIF signal profile shows a single well-defined peak colocated with the reactant-side inflection point in the experimental CH2O profiles (see also [7]), in contrast with the numerical CH3O profiles which show a double-peaked structure. The single experimental CH3O peak is evidently co-located with the low-temperature numerical CH3O peak. PLIF signal is proportional to the mole fraction of the target species and to a complex function of temperature and composition of the collisional bath. For CH, OH, and HCO, which exist in a relatively limited range of conditions, transitions can be selected in the experiment to minimize these residual dependencies. CH3O, however, has four strong vibrational modes active under flame conditions [33], leading to a strong decrease in signal with temperature. Thus, it is possible that the absence of a double-peaked profile in the experimental data may be the result of the temperature dependence in the CH3O signal. To evaluate this hypothesis, we used the computed temperature and methoxy profiles to estimate the temperature attenuation of the methoxy PLIF signal at the location of the numerical high-temperature peak. The experimental methoxy signal cuts across the flame front were extracted from the CH3O PLIF images. Data from fifty frames were combined and the cuts averaged laterally over five pixels. Based on the observed signal-to-noise ratio and base-line in the processed CH3O data, we estimate that the absence of the high temperature peak in the PLIF profiles requires a signal reduction by a factor of 20 or more. On the other hand, the residual temperature dependence in the LIF signal is estimated to contribute a factor of 5 to 6 times signal reduction. This attenuation is not sufficient to explain the absence of the high temperature peak in the experimental data.
889
Fig. 11. Profiles of CH3O mole fraction for the stoichiometric 36%-N2-diluted case, with variations in the pre-exponential factors of reactions 32 and 51. Note that the case with high A 32 is referred to the right-hand-side vertical axis, while all other cases are referred to the left-hand-side vertical axis. The reference case corresponds to the reaction parameters in the existing mechanism. The ranges of variation of A 32 and A 51 are by factors of 10 and 2, respectively, around the reference case, based on the uncertainty bounds in existing pertinent data.
This suggests that the actual CH3O mole fraction at the high temperature peak may in fact be a factor of three or more times lower than the computed value. Let us examine next the effect of appropriate perturbations in the pre-exponential factors of reactions 51 and 32 ( A 51 and A 32 , see the full rate specification for each of these reactions in the Appendix) on the observed double-peaked profile structure of CH3O in the undisturbed stoichiometric flame. This is conducted to investigate whether variations in the parameters of these reactions could result in a single methoxy peak. Based on published rates, the uncertainty bounds of A 32 allow a factor of 10 range of variation on each side of the value cited in the Appendix [34], whereas the uncertainty bounds of A 51 correspond to a factor of 2 range [35]. Accordingly, we find that variation of A 51 from 2.7e11 to 10.8e11 leads to minor change in the CH3O structure, with little modification in the levels of both peaks, as shown in Fig. 11. This figure illustrates the dependence of the profile of methoxy mole fraction on the values of A 51 and A 32 , in the stoichiometric 36%-N2-diluted case, using 1D premixed flame computations with Chemkin [25, 30]. We have also varied the activation energy of Rn. 51 over a range of
890
H. N. NAJM much higher concentration of methoxy than the reference case, based on experimental signal-tonoise estimates. Thus, there is good evidence to suggest that the variation of A 32 above its reference value in the present mechanism may provide a more realistic model of methoxy chemistry in this flame. CONCLUSIONS
Fig. 12. Profiles of CH3O mole fraction versus temperature for the stoichiometric 36%-N2-diluted flame case, with variations in the pre-exponential factors of Reaction 32. Note that the case with high A 32 is referred to the righthand-side vertical axis, while other cases are referred to the left-hand-side vertical axis. The reference case corresponds to the reaction parameters in the existing mechanism. A 32 is varied by a factor of 10 above and below the reference case, based on the uncertainty bounds in existing data.
1223–3977 cal/mole (original value is 2600 cal/ mole), where the range endpoints were chosen to double and half the reaction rate at 1000 K. The resulting methoxy structure agrees roughly with the reference structure and the A 51 variations in Fig. 11. Note that Reaction 32 has zero activation energy. On the other hand, varying A 32 from 2e12 to 2e14 does lead to a significant change in the methoxy profiles. As shown in Fig. 11, the amplitude of the low-temperature peak is reduced significantly relative to the hightemperature peak when A 32 is set at the low limit of its range. Moreover, the high-temperature peak is shifted slightly towards higher temperature for low A 32 , as shown in Fig. 12. Nonetheless, the methoxy structure remains double peaked, with a stronger peak at high temperature, in this limit. Conversely, when A 32 is at its high limit, the low temperature peak becomes completely dominant, with the high temperature peak disappearing, its only trace being a shoulder and associated broadening of the profile at high temperature. Moreover, the level of computed CH3O mole fraction in the low temperature peak is higher by about a factor of 20 as compared to the reference case. Both these observations are significant, as the experimental observations not only show a single peak at low temperature, but also suggest a
We have presented time-matched numerical and experimental results describing the detailed interaction of a premixed methane-air flame with a counter-rotating vortex pair in 2D. We observe a transient rise in computed methoxy (CH3O) on the cold side of the flame during the interaction. We attribute this to changes in internal flame structure caused by the transient flow-induced strain-rate. In particular, the flow-induced steepening of the temperature profile lowers the temperature on the reactants side of the reaction zone, leading to reduced consumption of CH3O. Generally, we find the extent of the rise in peak CH3O to be higher in flames with lower burning rates and faster flow time scales, that is, lower Damko ¨hler numbers. Measurements of CH3O during the transient flame interaction with the vortex-pair are necessary to validate these observed transients. We discuss experimental measurements of CH3O in a steady V-flame, which outline potential challenges with PLIF of CH3O at high temperature due to signal attenuation. Relative locations and shapes of experimental and numerical CH3O, CH2O, HCO, and OH profiles in the undisturbed flame are presented and discussed. The absence of a high-temperature methoxy peak in the experiment cannot be attributed to signal attenuation of the existing high-temperature peak in the numerical results. Instead, the single low-temperature peak may be explained by a factor of 10 increase in the pre-exponential factor of Reaction 32 (CH3 ⫹ HO2 3 CH3O ⫹ OH), a variation that is within the expected uncertainty in this rate constant. We also report experimental measurements of peak HCO evolution that are in reasonable agreement with numerical results. The persistence of the experimental HCO signal during
TRANSIENT FLAME RESPONSE the interaction suggests continued burning despite the collapse of the CH signal. This agreement in HCO response suggests that the present reaction and transport models are adequate for the description of the dynamical response of some components of premixed methane-air flame chemistry, with the present operating conditions. On the other hand, we find significantly faster response of CH and OH in the experiment, versus the computed CH and OH, under both stoichiometric and rich conditions. We also observe qualitatively different response of OH at rich conditions, with an experimental OH burst that is absent from the numerical results. Moreover, although the experimental CH signal decays to zero at both stoichiometric and rich conditions, the degree of decay in the numerical peak CH mole fraction varies greatly with equivalence ratio. Evidently, the present diffusion-reaction model does a poor job at the representation of the dynamical character of OH and CH in this flame. Determination of the origin of these disagreements requires analysis of the coupled reaction-diffusion eigenmodes of the governing equations, which is work in progress. The qualitative disagreement in rich-flame OH response was observed earlier [14] by using GRImech1.2 [17] with ten-fold faster flow time scales, and is found here with flow time scales comparable to the experiment, using an alternate C1C2 chemical mechanism. These observations, and the above general disagreement in computed and measured flame time scales of OH and CH, indicate the extent to which validation of detailed unsteady flame models is lacking. This is true whether the cause of these disagreements is transport coefficients or the chemical mechanism. Clearly, validation under steady state conditions is insufficient. The dynamical response of the model requires experimental and computational studies that probe the transient structure of flames. Additional investigation of transient flame structure is necessary to provide clues as to the causes of these disagreements, and to examine the relative merits of alternative mechanisms or transport models.
891 This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division. Computations were performed at Sandia National Laboratories and at the National Center for Supercomputing Applications (NCSA). REFERENCES 1. 2.
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H. N. NAJM Najm, H. N., Wyckoff, P. S., and Knio, O. M., J. Comp. Phys. 143(2):381– 402 (1998). Knio, O. M., Najm, H. N., and Wyckoff, P. S., J. Comp. Phys. 154:428 – 467 (1999). Majda, A., and Sethian, J., Comb. Sci. Techn. 42:185– 205 (1985). Schlichting, H., Boundary-Layer Theory, McGraw–Hill, New York, 7th edition, (1979). Williams, F. A., Combustion Theory, Addison–Wesley, New York, 2nd edition, (1985). Kee, R. J., Rupley, F. M., and Miller, J. A., Sandia Report SAND89 – 8009B, Sandia National Labs., Livermore, CA, (1993). Prada, L., and Miller, J. A., Combust. Sci. Tech. 132:225–250 (1998). Miller, J. A., and Bowman, C. T., Prog. Energy Combust. Sci. 15:287–338 (1989). Strang, G., SIAM J. Numer. Anal. 5(3):506 –517 (1968). Brown, P. N., Byrne, G. D., and Hindmarsh, A. C., SIAM J. Sci. Stat. Comput. 10:1038 –1051 (1989).
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Kee, R. J., Grcar, J. F., Smooke, M. D., and Miller, J. A., Sandia Report SAND85– 8240, Sandia National Labs., Livermore, CA, (1993). 31. Paul, P., and Warnatz, J., Twenty-Seventh Symposium (International) on Combustion, The Combustion Institute, 1998, pp. 495–504. 32. Najm, H. N., Knio, O. M., Paul, P. H., and Wyckoff, P. S., Comb. Sci. Tech. 140(1– 6):369 – 403 (1998). 33. Garland, N. L., and Crosley, D. R., J. Phys. Chem. 92:5322–5326 (1988). 34. Baulch, D. L., Cobos, C. J., Cox, R. A., Esser, C., Frank, P., Just, Th., Kerr, J. A., Pilling, M. J., Troe, J., Walker, R. W., and Warnatz, J., J. Phys. Chem. Ref. Data 21:411– 429 (1992). 35. Baulch, D. L., Cobos, C. J., Cox, R. A., Frank, P., Hayman, G., Just, Th., Kerr, J. A., Murrels, T., Pilling, M. J., Troe, J., Walker, R. W., and Warnatz, J., J. Phys. Chem. Ref. Data 23:847–1033 (1994). Received 4 May 2000; revised 2 November 2000; accepted 7 November 2000
APPENDIX The chemical mechanism used in this work differs from that in [26] in that: 1. the parameters of the following reactions are altered as follows: Reaction H ⫹ O2 ⫹ M N HO2 ⫹ M H2O/10./ CO2/4.2/ H2/2.86/ CO/2.11/ OH ⫹ HO2 N H2O ⫹ O2 CH4 ⫹ H N CH3 ⫹ H2 CH3 ⫹ HO2 N CH3O ⫹ OH CH2O ⫹ H N HCO ⫹ H2 C2H5 ⫹ O2 N C2H4 ⫹ HO2 C2H3 ⫹ O2 N CH2O ⫹ HCO
A(mole-cm-sec-K) 0.361e18 N2/1.3/ 2.891e13 0.22e5 0.2e14 0.219e9 0.843e12 3.6e13
b
E(cal/mole)
⫺0.72
0.
0. 3. 0. 1.77 0. ⫺0.3
⫺496.75 8750. 0. 3000. 3875. 0.
where k ⫽ AT b exp(⫺E/RT)) is the forward rate for each reaction, and the line following the first reaction lists the 3rdbody efficiencies corresponding to the species indicated [25, 30]. 2. the species CH3OOH and its reactions are omitted, and 3. the following reactions are omitted: CH3O2 ⫹ CH3 N 2CH3O 2CH3O2 N CH3OH ⫹ CH2O ⫹ O2 C2H4 ⫹ CH3 N C2H3 ⫹ CH4 C2H5 ⫹ O N CH3 ⫹ CH2O C2H5 ⫹ O N C2H4 ⫹ OH C2H5 ⫹ HCO N C2H6 ⫹ CO C2H5 ⫹ CH3 N C2H4 ⫹ CH4 C2H3 ⫹ O2 N CH2HCO ⫹ O 2C2H3 N C2H4 ⫹ C2H2 CH3CO ⫹ H N CH2CO ⫹ H2 CH3CO ⫹ O N CH2CO ⫹ OH CH2CO ⫹ OH N CH3 ⫹ CO2
2CH3O2 N 2CH3O ⫹ O2 CH3 ⫹ HCO N CH4 ⫹ CO H ⫹ C2H5(⫹M) N C2H6(⫹M) C2H5 ⫹ O N CH3HCO ⫹ H C2H5 ⫹ OH N C2H4 ⫹ H2O C2H5 ⫹ CH2O N C2H6 ⫹ HCO 2C2H5 N C2H6 ⫹ C2H4 C2H3 ⫹ O2 N C2H2 ⫹ HO2 CH3CO ⫹ H N CH3 ⫹ HCO CH3CO ⫹ O N CH3 ⫹ CO2 CH3CO ⫹ OH N CH2CO ⫹ H2O
Moreover, we list below the rate specification [25, 30] for Rns. 51 and 32 pertaining to the CH3O discussion above. Reaction
A(mole-cm-sec-K)
(32) CH3 ⫹ HO2 N CH3O ⫹ OH 2.00e13 5.40e11 (51) CH2O ⫹ H(⫹M) N CH3O(⫹M) Low pressure limit: 0.154e31 ⫺0.48e1 0.556e4 TROE centering: 0.758 0.94e2 0.1555e4 0.42e4 H2O/8.58/ CO2/3./ H2/2./ CO/2./ N2/1.43/
b
E(cal/mole)
0. 0.5
0. 2600.
and OMAR M. KNIO
The Johns Hopkins University, Baltimore, MD 21218-2686 We report the results of a numerical and experimental investigation of the response of premixed methane-air flames to transient strain-rate disturbances induced by a two-dimensional counter-rotating vortex-pair. The numerical and experimental time histories of flow and flame evolution are matched over a 10 ms interaction time. Measurements and computations of CH and OH peak data evolution are reported and compared. Despite the matching of experimental operating conditions, the full resolution of flame length and time scales, and the use of a detailed C1C2 chemical mechanism and temperature-dependent transport properties, we find disagreements with experimental measurements of the transient response of both CH and OH. Besides quantitative disagreements in response time scales, the qualitative transient features of OH at rich conditions are not predicted in the computations. These disagreements suggest deficiencies in the chemical and/or transport models. On the other hand, evolution of computed and measured peak HCO mole fractions are in reasonable agreement, suggesting that certain components of flame chemistry may indeed be accurately predicted by the present model. We also report computed CH3O response, which exhibits a strong transient driven by changes to internal flame structure, namely temperature profile steepening, induced by the flow field. Steady state experimental PLIF CH3O data is reported and compared to numerical results, but experimental transient CH3O data is not available. In general, the present study highlights the importance of validation of chemical-transport models of flames in unsteady flow environments. © 2001 by The Combustion Institute
INTRODUCTION The formulation of accurate predictive models of combustion systems requires adequate understanding of turbulence-chemistry interactions at the small scales. One important element of this interaction is the transient response of flames to unsteady perturbations due to turbulent flow structures. The present work uses numerical and experimental studies of the interaction of premixed methane-air flames with two-dimensional counter-rotating vortex pairs to investigate transient flame response and examine comparisons between numerical and experimental results. There have been both experimental [1–7] and numerical [8 –16] studies of flame interaction with counter-rotating vortex pairs or torroidal vortex rings. Roberts et al. [1] and Mueller et al. [4, 6] studied the interaction of a propagating planar premixed flame front with a torroidal *Corresponding author. E-mail: [email protected]. † Present address: Eksigent Technologies LLC, Livermore, CA 94550. COMBUSTION AND FLAME 125:879 – 892 (2001) © 2001 by The Combustion Institute Published by Elsevier Science Inc.
vortex. A stationary planar premixed V-flame setup was used by Samaniego [2, 3], as well as Nguyen and Paul [5] and Paul and Najm [7], where a 2D counter-rotating vortex pair was generated and propagated into one leg of the V-flame. These studies examined the role of the vorticity field which contorts and strains the flame, and alters its internal structure. These structural changes were observed using Planar Laser-Induced Fluorescence (PLIF) imaging of OH, CH, HCO, CH2O, and other flame radicals. Early 2D numerical studies of vortex/vortex-pair interactions with premixed flames [8 –10] were generally concerned with singlestep kinetics, flow dynamics, and thermal effects, rather than internal flame chemical transients. Recent studies [12, 13] included C1 kinetics at stoichiometric conditions to investigate the effect of the vortical flow on internal flame structure. The inclusion of C1 kinetics allowed detailed analysis of the structure of premixed flames under unsteady strain-rate, and the transient process by which the flame approaches extinction. Vortex-pair interaction 0010-2180/01/$–see front matter PII S0010-2180(00)00245-5
880 with a non-premixed opposed-jet hydrogen-air flame was also studied by Katta et al. [15], and a parametric study of premixed flame interaction with a vortex-pair was conducted by Patnaik and Kailasanath [16]. The use of C1C2 mechanisms, which are necessary for accurate prediction of internal flame structure— especially at rich conditions, presents significant additional computational difficulties associated with stiffness and increased complexity due to the large number of species and reactions. These complications are a concern for both explicit and implicit numerical schemes, since the sizes of implicit-scheme matrices and convergence difficulties are accentuated by stiff C1C2 kinetics. Najm et al. [14] used a detailed C1C2 mechanism (GRImech1.2 [17]) to study flame response to unsteady strain-rate and curvature under stoichiometric and rich conditions. They found that the rich methaneair flame responds faster than the stoichiometric one. This was counter to earlier one-dimensional stagnation flame data [18], and was attributed to the role of H versus OH in the two flames. Knio & Najm [19] conducted a more recent flame-vortex-pair interaction study involving a parametric investigation of transient flame response for mixtures ranging from lean to rich, and with a wide range of flow time scales and levels of strain-rate, using GRImech1.2. The results confirmed the faster global response of the rich flame. In fact, the rate of decay of peak heat release rate was found to increase monotonically with equivalence ratio from ⌽ ⫽ 0.8 to 1.2. This rules out the robustness of the flame, in the sense of peak burning rate, as determining its response to strain-rate disturbances. On the other hand, it supports the hypothesis based on the relative roles of H and OH, as the dominance of H reactions increases monotonically with ⌽. These studies were limited to a short time span, and/or fast flow time scales, because of algorithmic limitations and associated computational costs. These limitations on operating conditions precluded direct time-evolution comparisons with available experimental results, which involved slower vortices and significantly longer interaction times. The present effort builds on recent numerical developments involving second-order accurate stiff operator-split time integration in multiple dimen-
H. N. NAJM sions [20, 21] to allow detailed resolved computations of 2D C1C2 flames at laboratory time scales; a hitherto impractical undertaking. This removes a barrier to quantitative comparisons with experiments in earlier work [14], and brings us a step closer to resolving key differences with experimental data. We also use a more detailed C1C2 mechanism described further below, with 40 species and 216 reactions, as compared to our earlier work [14, 19], which was based on GRImech1.2 [17], with 32 species and 177 reactions. We use a flow with vortex-strength similar to that in the experiment so that evolution of the flame topology in the two sets of data coincides over a time span of 10 ms. Similarly, we utilize the same numerical flame stoichiometry and dilution as in the experiment, as indicated later. The spatial extent of the numerical vortex-pair is about one-half that of the experimental vortex-pair. This was a necessity, given the fine spatial resolution requirements imposed by the flame structure, and associated computational costs required to integrate stiff detailed kinetics at each spatial location. Doubling the vortexpair size, while maintaining the resolution necessary to properly resolve the flame front, is not feasible given available computational resources. Moreover, the slightly increased numerical flame curvature associated with the smaller vortex-pair is not likely to play a significant role in the observed dynamics. The radius of curvature at the vortex-pair centerline is significantly larger than the flame thickness, so that the observed flame transients on the centerline are primarily driven by the strain-rate. We present superimposed transient time histories of computed and experimental flame radicals, and discuss comparisons between them. Despite the matching of operating conditions and the extent of detail in chemistry and transport, we find that the detailed transient flame time evolution in the computations is in fact significantly different from that in the experiment. This and other comparisons with the experimental data involving numerical and experimental transient OH, CH, and HCO results are presented and discussed. While disagreements are evident in the evolution of OH and CH, we do find reasonable agreement with the experimental results in the evolution of HCO. This suggests that at least some components of
TRANSIENT FLAME RESPONSE the flame chemistry are accurately predicted by the model. On the other hand, the disagreements in OH and CH suggest deficiencies in the chemical and/or transport models whose identification and elimination is work in progress. We also present experimental and numerical steady state CH3O profiles, investigate features of the computed transient accumulation of methoxy (CH3O) and other species on the reactants-side of the flame, and analyze the role of unsteady strain-rate in these internal flame dynamics. While no experimental data on the transient response of methoxy in this flame is available, it is hoped that these observations would motivate future measurements to examine their validity. MODEL FORMULATION AND NUMERICAL SCHEME The model formulation has been presented in detail elsewhere [20, 21]. The governing equations are developed in 2D using the low Mach number approximation [22]. The assumptions of zero bulk viscosity [23] and negligible body forces are used in the conservative continuity and momentum equations. In particular, we note that gravity is neglected in the model because it plays a negligible role in the present flow, as the Froude number (Fr ⫽ U/公gL) based on the maximum flow velocity and the vortex-pair centerto-center distance is larger than 10. We assume a detailed chemical reaction mechanism involving N species and a number of elementary reactions. The energy equation is developed allowing for temperature-dependent transport properties, and a constant stagnation pressure p o , that is, an open domain. We neglect Soret and Dufour effects [24] and radiant heat transfer, and assume a perfect gas mixture, with individual species molecular weights, specific heats, and enthalpies of formation, using Fickian binary mass diffusion. The N-th species, here N2, is assumed dominant such that the diffusion velocity of any other species i in the mixture is approximated by binary diffusion into N2 at the local temperature. For computational efficiency, mixture transport properties (, ) are set to those of N2 at the local temperature. Species conservation equations are used to integrate the mass fractions of N ⫺ 1 species,
881 while the mass fraction Y N is found from the N identity ⌺ i⫽1 Y i ⫽ 1. The production rate for each species is given by the sum of contributions of elementary reactions [24], with Arrhenius rates, including forward and backward rates, and third-body efficiencies [25]. We use a C1C2 chemical mechanism with 40 species and 216 reactions. It is based on a subset of the mechanism used in [26], which is in turn based on [27], and is available upon request. Additional detail about the mechanism is included in the Appendix. The governing equations are discretized using second-order central differences on a uniform mesh, with cell size ⌬x ⫽ 15.6 m. This resolution is necessary for adequate representation of internal flame structure. Najm et al. [14] list typical species profile thicknesses in an atmospheric methane-air flame. Generally speaking, minimum profile thicknesses are on the order of 100 m, hence the necessity of the fine spatial resolution used here. It is imperative that adequate resolution be maintained to accurately compute transport fluxes internal to the flame, especially when substantial effort is expended on computing the chemical source terms with detailed kinetics. The discrete equations are integrated using an operator-split stiff second-order predictor-corrector projection scheme. Construction of the stiff scheme is based on several refinements of the explicit construction originally introduced in [12]. A semi-implicit additive (non-split) stiff version is presented in [20]. The present work uses a stiff symmetrically-split [28] integration of the governing conservation equations. Diffusion and convection terms are integrated explicitly with multiple fractional steps, over half-time-step intervals, while the reaction terms are integrated implicitly over a full time-step interval. The explicit halfsteps are arranged symmetrically before and after the implicit step in each global step. Stiff integration of reaction terms is performed by using the ordinary differential equation integration package DVODE [29]. The formulation and convergence of the scheme are discussed in detail in [21]. EXPERIMENTAL SETUP AND DIAGNOSTICS The experiment has been described in detail in [5, 7]. A V-flame is stabilized on a wire in a
882 vertical channel, with premixed methane-air flowing up through flow straighteners upstream of the wire. Line-vortex pairs are ejected from an acoustically driven cavity on one side of the flow enclosure and allowed to impinge on one leg of the V-flame. PLIF imaging of CH, OH and HCO was performed by using a XeCl excimer-pumped dye laser and an intensified CCD array detector. For CH the laser was run on a BBQ dye and tuned to the Q1 (4.5) transition of the B-X (0,0) system near 389.5 nm, with non-resonant detection using 2 mm of Schott GG-420 and an F/1.2 camera lens. For OH the laser was run on a C153 dye, doubled in BBO and tuned to the Q1 (6.5) A-X (1,0) transition near 283 nm, with non-resonant detection using 2 mm of Schott WG305 and an F/4.5 UV camera lens. For HCO, the laser was run on a C500 dye, doubled in BBO and tuned to QR0 bandhead in the B-X (0,0,0) system near 254 nm, with non-resonant detection using 2 mm of Schott BG1, a 400 nm reflective shortpass and an F/2.2 transmissive UV lens system. The signal-to-noise ratio for the HCO data presented here is improved by about a factor of 2 to 3 from our earlier work [13] (50-frame averages were employed, as in [13]). This was achieved by improvements to the lens, detection filters, and excitation source employed. PLIF images of CH3O have also been successfully taken in the same burner, using the same laser/camera system but under steady conditions. The laser was operated as for pumping OH and tuned to excite overlapping transitions in the A-X 340 system near 292.8 nm with care taken to avoid excitation of adjacent OH and CH2O transitions. Non-resonant detection was performed using 2 mm of Schott WG320, a 400 nm reflective short-pass filter and an F/1.4 near-UV camera lens. As found with PLIF of HCO [13], CH3O PLIF signals are quite weak and frame averaging is required to achieve a useable image (nominally 50-frame averages are required for imaging in a premixed 36% N2diluted stoichiometric CH4-air flame). RESULTS In both the experiments and computations, two CH4-air reactants mixture conditions are inves-
H. N. NAJM tigated: one stoichiometric with 36% N2-dilution (over and above the air N2, thus with mole fractions of CH4:O2:N2:AR of 0.06:0.12:0.81: 0.01) and the other rich with 32% N2-dilution. This change in dilution between the two cases was necessary to maintain the same experimental V-flame angle in the stoichiometric and rich flames. Flow-Flame Evolution An open rectangular domain is considered, with dimensions 0.4 ⫻ 1.6 cm, and is overlaid by a 256 ⫻ 1024 uniform mesh. We apply symmetry boundary conditions in the horizontal x-direction, and outflow boundary conditions in the y-direction. The evolution of the flow over a 10 ms time span is illustrated in Fig. 1 for the stoichiometric flame. The evolution of the rich flame is similar. The vertical right edge of the domain is the centerline of the vortex pair under consideration, which is one member of a periodic row of vortex pairs along the x-direction. The initial condition is a superposition of the velocity (u,v) field induced by the periodic row of vortex pairs, and the temperature, density and mass fraction (T, ,Y i ) distributions corresponding to a horizontal premixed flame, with the initial structure in the y-direction from a 1D flame solution computed with Chemkin [25, 30]. The flame propagates downward by burning into the reactants, as shown in Fig. 1. Meanwhile, the vortex pair propagates upwards causing transient curvature and strain-rate disturbances to the flame. The flame region is delineated using CH mole fraction. The time scale of the vortex-pair interaction with the flame is matched with the available experiment. A typical experimental CH frame sequence, which exhibits comparable flame topology evolution with time as in Fig. 1, is reported in [5]. The time reference in the subsequent comparisons between experimental and numerical results is determined based on matching flame topology in the sequence of frames shown in the figure. This procedure involves first the identification of a time frame during the interaction where the experimental and numerical flame topologies/contortion are congruent. Thus, we find for ⌽ ⫽ 1.2, that the numerical flame topology at t num ⫽ 4 ms is identical to the
TRANSIENT FLAME RESPONSE
883
Fig. 1. Evolution of CH mole fraction (shading) and vorticity (contours) for the stoichiometric flame.
experimental one at t exp ⫽ 6 ms. We then confirm that there is similar congruence in the two topologies at all times within the data time-span given that t num ⫽ t exp ⫺ 2 ms (at ⌽ ⫽ 1.0 a 3 ms time shift is used, based on a similar reasoning). By this we establish (1) a means of superposing experimental and numerical results on a single time axis in a consistent manner by applying this time shift, and (2) a degree of confidence in the similarity of the dynamics in both experimental and numerical flows where similar flame contortion is achieved in the same time intervals. Note that this procedure is necessary because of the difference in initial conditions between the numerical and experimental flows. The experimental vortex-pair is created in an acoustically forced chamber far away from the flame, while the numerical vortex-pair is created in space ahead of the flame (albeit at a given distance where the initial transient and its consequence on the flow are insignificant). Given this, the only feasible way to compare the flame transients in the two flows was using the above matching procedure. The peak vorticity is 9 ms⫺1 at t ⫽ 0, decaying to 2 ms⫺1 after 10 ms. The initial center-to-center distance ( ␦ cc ) of the vortex pair is 0.25 cm. The experimental vortex-pair center-to-center distance is about 0.4 cm, and the diameter of the flame bubble (e.g., 8 ms
frame in Fig. 1) is about 0.8 cm. Thus, the numerical flame bubble is about 1/2 that of the experimental one. As the numerical vortex-pair evolves, its vortex centers approach each other and its propagation speed increases. A similar speedup is observed in the experiment. Based on the numerical vortex-pair representative center-to-center distance ␦ cc ⬇ 0.2 cm, and selfinduced velocity V v ⬇ 50 cm/s, and the experimentally observed vortex-pair ␦ cc ⬇ 0.4 cm and V v ⬇ 100 cm/s (both in the rich flame), the convective time scales of the numerical and experimental vortex pairs are roughly the same, at t v ⬇ 3 ms. Hence the similarity in the topological development of the flame between the numerical and experimental results, and the expected consequent similarity in the rates of flame stretch (1/A) (dA/dt). By using time scales based on flame thermal thickness and burning speed, the two flames considered here (⌽ ⫽ 1.0 and 1.2) have time scales t f ⫽ 23.4 and 49.1 ms, respectively. On the other hand, as reported in [14] and further observed here, these propagation time scales are generally different from those exhibited by the response of the flame structure to the unsteady strain. Evidently, these propagation time scales are not adequate for characterizing transient flame response to flow disturbances. To begin with, the time scale of the transient response involves a
884
Fig. 2. Evolution of the computed and experimental normalized peak CH and OH mole fractions on the rich flame centerline.
direct dependence on the strength of the vorticity field, and the ensuing unsteady strain-rate field. Moreover, as observed in [14, 19], it is evident that the rich flame, with longer propagation time scale, responds faster than the stoichiometric flame, which has the shorter propagation time scale. OH and CH Response The evolution of normalized peak rich flame quantities from the numerical and experimental results are shown on the same time axis in Fig. 2. As indicated earlier, the time references of the two data sets were matched based on observed flame topology in numerical and experimental frame sequences. The overall numerical flame response is seen to exhibit slow decay over a time interval of 6 to 7 ms. A roughly 50% drop in OH is evident. CH exhibits similarly slow decay, down to about 30% of its original level. The experimental flame on the other hand exhibits drastically different behavior. There is practically no drop in either OH or CH signals over the first 5 ms of flame evolution. This is then followed by simultaneous and opposite fast response of both signals. OH increases by a factor of 3.5 in 1 ms, and then decays over the remaining 4 ms. Meanwhile, CH signal drops quickly, reaching zero in 2 ms, and disappearing thereafter. Based on experimental signal-tonoise estimates, the CH signal zero corresponds
H. N. NAJM to a level below 1% of its initial undisturbed flame value. Given the similar flow and flame time scales in the numerical and experimental flows, these disagreements in qualitative response (of OH) and transient time scales (of both OH and CH) are remarkable. Note that the experimental signal-to-noise ratios, at peak signal, are nominally 10:1 for OH and 5:1 for CH on a per pixel/per image basis. The experimental data presented here has been averaged over 20 frames and over three pixels taken laterally to the cuts. This should provide a nominal seven- to eight-fold improvement in the signal-to-noise ratio (S/N) in the plotted data, resulting in an S/N larger than 50:1. The individual images were corrected with white and dark frames and for laser sheet variations. We estimate that these corrections reduce fixed pattern noise to order 2%. The primary systematic error remaining is due to residual temperature and quenching effects in the LIF signal. These are estimated to be less than 25%. Based on available quenching and spectroscopic data, the computed variation in temperature and composition provides that the OH signal would tend to decrease (by about 10%) under conditions where we observe an increase of over 3 fold. Consequently, we cannot justify the above observed burst in OH, or, by similar arguments, the disappearance of CH due to residual dependencies in the LIF signals (see also [5]). The evolution of the stoichiometric flame normalized peak quantities are shown in Fig. 3. In this case, the experimental and numerical flames exhibit qualitatively similar monotonically decaying behavior in both OH and CH, yet with significant quantitative disagreement. Let us first compare this data with that of the rich case in Fig. 2. There is significantly more decay of the numerical peak quantities in the weaker rich flame. The drop in peak CH mole fraction, which is about 10% in the stoichiometric flame, is close to 70% in the rich flame. On the other hand, the experimental CH data shows decay to zero in both cases, albeit with faster decay rate in the rich case as indicated in [14]. Moreover, the burst in OH observed at rich conditions is absent from the experimental stoichiometric data, with monotonic decay of OH observed down to 60% of the initial undisturbed flame value. Next, compare the experimental and nu-
TRANSIENT FLAME RESPONSE
Fig. 3. Evolution of the computed and experimental normalized peak CH and OH mole fractions on the stoichiometric flame centerline.
merical stoichiometric flame results. As in the rich case, experimental signals of peak OH and CH exhibit faster time scales and higher degrees of change in amplitude than the corresponding numerical signals. These observations raise many questions regarding the ability of the present combination of chemical mechanism and transport model to adequately represent the dynamical features of transient flame response. At this time, an explanation for the burst in experimental OH at rich conditions is lacking. It is also not clear if the absence of this burst from the computational results is due to missing reaction pathways, inaccuracies in species transport properties [31], and/or reaction rate parameters. Note, however, that the accumulation of species during flame transients is not surprising since different reaction pathways have different characteristic time scales which generally depend on mixture stoichiometry [14]. Such transient accumulations are in fact observed in the computations, as further discussed below. Moreover, the significantly faster response of CH and OH in the experiment, versus the computed CH and OH, suggests that the present diffusion-reaction model does a poor job at the representation of the dynamical character of these species in this flame. Given that the time response of the governing equations is determined by the eigenvalues and associated eigenmodes of the system Jacobian, this sug-
885
Fig. 4. Evolution of computed and experimental normalized peak HCO mole fraction, along with the computed normalized peak heat release rate w T , on the stoichiometric flame centerline.
gests that the eigenvalues/modes pertaining to these species are significantly in error. Determination of the actual causes of these disagreements requires detailed analysis of the eigenmodes of the coupled reaction ⫹ diffusion right-hand-sides of the governing equations, which is work in progress. Of course, if the reaction mechanism is deficient, in the sense that it is missing certain important reaction pathways that are not known at this point, then determining the eigenmodes governing the existing system response, and adjusting the rate constants of the corresponding reactions within their uncertainty bands, will not suffice to bring about the expected physical behaviour of the model. These missing pathways, if they indeed exist, would have to be identified and included in the mechanism in order to recover the correct transient flame response. HCO Response Figure 4 shows experimental normalized peak HCO measurements in the stoichiometric flame over a 4 ms time span, along with the corresponding numerical normalized peak HCO mole fraction and heat release rate. The HCO data has low signal to noise ratio, with 10% uncertainty. Still, it is interesting to note that the relative evolution of this signal does not deviate much from the numerical HCO. No
886 experimental HCO data is available later on in the cycle, which limits the scope of the comparison. Nevertheless, the agreement up to 6 ms is encouraging (even as the experimental CH deviates strongly downward) and suggests that the present mechanism may be reasonably capturing at least some components of transient flame structure. In earlier work [13, 32] we noted the fidelity with which peak numerical HCO mole fraction correlates with peak flame heat release rate of premixed methane-air flames. This observation is borne out in the present results as well. Computed peak HCO mole fraction provides a reasonably good representation of peak heat release rate in Fig. 4, with even better agreement evident at rich conditions. If we accept the correspondence between HCO and heat release rate, then the robustness of the experimental HCO signal at 6 ms in Fig. 4 suggests that the stoichiometric flame is in fact able to withstand the present rate of strain without extinction. This is despite the strong drop in CH signal evident in the figure. The drop in CH is of course indicative of significant disruption of flame chemistry in certain portions of the chemical mechanism. However, since the bulk of the carbon flux is through HCO and not through CH [13], these disruptions are not necessarily indicative of overall extinction of the flame. CH3O Response We also report on the response of the methoxy radical, CH3O, which exhibits transient accumulation during the flame-vortex-pair interaction. Methoxy is of interest because of its role in the low temperature chemistry on the reactants side of the flame. Modeling studies of its transient response provide a means of validating existing low-temperature chemistry models against experimental data in a transient flame environment. Moreover, its transient accumulation observed below is reminiscent of the experimentally observed burst in OH, and is therefore instructive as to the mechanism by which flow transients can lead to large transient accumulation in flame radicals—a potent example of ‘turbulence’-chemistry interaction. In the present mechanism, the methoxy rad-
H. N. NAJM
Fig. 5. Instantaneous computed CH3O mole fraction and CH4 consumption rate profiles along a normal cut at the rich flame centerline. Data is taken in a reference frame moving with the flame, with x-distance measured from the location of the fuel mass fraction contour corresponding to 10% of the reactants fuel mass fraction. Reactants are on the left, and products on the right. Solid lines are for [0 – 4] ms as indicated on the CH3O profiles, while the dashed line is at 8 ms. The CH4 consumption rate profiles are shown for the same time instances, exhibiting monotonic decay with time.
ical is produced primarily by the reaction CH3 ⫹ HO2 3 CH3O ⫹ OH, and consumed by CH3O(⫹M) 3 CH2O ⫹ H(⫹M). As such, it exists primarily in the fuel consumption layer and on the cold (reactants) side of the reaction zone. The mole fraction profile of methoxy in the undisturbed rich flame is shown in Fig. 5 (t ⫽ 0). We focus on the rich flame data because it exhibits more significant changes in time, though it is qualitatively similar to that in the stoichiometric flame. The t ⫽ 0 CH3O
TRANSIENT FLAME RESPONSE
Fig. 6. Instantaneous tangential strain-rate profiles along a normal cut at the rich flame centerline. Data is taken in a reference frame moving with the flame as in Fig. 5. Solid lines are for [0 – 4] ms as indicated, while the dashed line is at 8 ms.
profile in Fig. 5 reveals two distinct peaks. The one nearer to the zero abscissa is within the fuel consumption zone, as may be seen in the plot of CH4 consumption rate profiles also shown in Fig. 5. Peak fuel consumption rate occurs at x ⫽ 0.014 and drops below 5% of peak at x ⫽ ⫺0.05. The outer peak at x ⫽ ⫺0.11 exists in a low temperature region (see Fig. 7). The methoxy profile in Fig. 5 shows different evolution of the two peaks. The high temperature peak decays in time, in accordance with decaying peak burning and heat release rates; while the low temperature peak exhibits a rising transient, increasing by a factor of 3 in the first 3 ms of the interaction, followed by a gradual decay, viz. the 8 ms profile. Strain-rate and temperature fields during this process, shown in Figs. 6 and 7, respectively, suggest the essential causes of this transient. The strain-rate, while decaying in space with increased distance from the vortex pair, rises globally in time in the flame reference frame, peaking at 3 to 4 ms, and then decays. Meanwhile, the temperature profile steepens due to the rising strain-rate, as shown in Fig. 7, leading to lower temperatures in the region with T ⬍ 1000 K. By t ⬃ 8 ms this steepening subsides and, despite the reduced burning rate, the temperature on the reactant side increases due to the inundation of the reaction zone with hot combustion products [12].
887
Fig. 7. Instantaneous temperature profiles along a normal cut at the rich flame centerline. Data is taken in a reference frame moving with the flame as in Fig. 5. Solid lines are for [0 – 4] ms as indicated, while the dashed line is at 8 ms.
Despite the observed opposite trends in CH3O mole fraction in the two peaks in Fig. 5, we note that its dominant production and consumption channels both decay during the process, as shown in Fig. 8. On the other hand, the net production rate of methoxy clearly exhibits a fast rising transient in the low temperature region, as shown in Fig. 9, which leads to the observed transient accumulation in Fig. 5. In contrast, and consistent with the behavior of the high temperature peak in Fig. 5, both production and consumption rates in the high temper-
Fig. 8. Instantaneous profiles of the two dominant reaction rates involving CH3O along a normal cut at the rich flame centerline. Data is taken in a reference frame moving with the flame as in Fig. 5.
888
H. N. NAJM
Fig. 9. Instantaneous profiles of the net production rate of CH3O along a normal cut at the rich flame centerline. Data is taken in a reference frame moving with the flame as in Fig. 5. Solid lines are for [0 – 4] ms as indicated, while the dashed line is at 8 ms.
ature region in Fig. 9 decay in time. Analysis of the results indicates that the net increase in production rate of CH3O on the cold side of the flame is driven primarily by the local temperature drop in Fig. 7. Reaction 51 (CH2O ⫹ H(⫹M) ⫽ CH3O(⫹M)) has a high activation barrier in the reverse direction, such that a drop in temperature leads to a reduction in the reverse (consumption) rate. Despite opposing factors, namely the increasing mole fraction of CH3O and the reduction in the forward rate of Reaction 32 (CH3 ⫹ HO2 ⫽ CH3O ⫹ OH), a large net increase in the production rate of CH3O occurs, as seen in Fig. 9. Note that the balance of Reactions 51 and 32 (Fig. 8) in the high temperature region would have lead to a similar increase of CH3O production rate there, were it not for the decay of the reaction CH3OH ⫹ H ⫽ CH3O ⫹ H2, a production channel, because of reduced H. We have also observed this transient behavior of methoxy by using the GRImech1.2 [17] mechanism, and at other degrees of N2-dilution, as well as other flow time scales [19]. Generally, the extent of the rise in peak CH3O is higher with the less robust flames and with the faster flows. Moreover, the present results exhibit similar transient accumulation in two other species on the cold side of the flame, namely CH3O2 and C2H2OH, with similar—although
Fig. 10. Peak-normalized numerical (top) and experimental (bottom) profiles of CH3O, CH2O, HCO, and OH mole fractions for the stoichiometric 36% N2 diluted flame.
significantly milder— behavior in CH3CO. Formaldehyde, CH2O, also exhibits a transient increase in its production rate during the first 4 ms. On the other hand it experiences monotonic decay in mole fraction, which is in agreement with experimental measurements [7]. We do not have transient measurements of methoxy or the other species exhibiting the above transient accumulation to validate the above findings. However, PLIF data on methoxy in the steady V-flame is available; it is compared to the initial data from the computations in Fig. 10 where all profiles are normalized to a peak amplitude of unity. The relative spatial placement of the experimental PLIF profiles is as-
TRANSIENT FLAME RESPONSE measured, while their placement relative to the numerical profiles was based on matching the locations of peak CH2O profiles in the two sets of data. The two sets of results exhibit common features. The shapes and locations of the OH and HCO peaks are in good agreement. On the other hand, the numerical CH2O profile, while roughly of similar width as the experimental one at half-maximum, extends further towards the reactants than the experimental data suggests. Moreover, the experimental CH3O PLIF signal profile shows a single well-defined peak colocated with the reactant-side inflection point in the experimental CH2O profiles (see also [7]), in contrast with the numerical CH3O profiles which show a double-peaked structure. The single experimental CH3O peak is evidently co-located with the low-temperature numerical CH3O peak. PLIF signal is proportional to the mole fraction of the target species and to a complex function of temperature and composition of the collisional bath. For CH, OH, and HCO, which exist in a relatively limited range of conditions, transitions can be selected in the experiment to minimize these residual dependencies. CH3O, however, has four strong vibrational modes active under flame conditions [33], leading to a strong decrease in signal with temperature. Thus, it is possible that the absence of a double-peaked profile in the experimental data may be the result of the temperature dependence in the CH3O signal. To evaluate this hypothesis, we used the computed temperature and methoxy profiles to estimate the temperature attenuation of the methoxy PLIF signal at the location of the numerical high-temperature peak. The experimental methoxy signal cuts across the flame front were extracted from the CH3O PLIF images. Data from fifty frames were combined and the cuts averaged laterally over five pixels. Based on the observed signal-to-noise ratio and base-line in the processed CH3O data, we estimate that the absence of the high temperature peak in the PLIF profiles requires a signal reduction by a factor of 20 or more. On the other hand, the residual temperature dependence in the LIF signal is estimated to contribute a factor of 5 to 6 times signal reduction. This attenuation is not sufficient to explain the absence of the high temperature peak in the experimental data.
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Fig. 11. Profiles of CH3O mole fraction for the stoichiometric 36%-N2-diluted case, with variations in the pre-exponential factors of reactions 32 and 51. Note that the case with high A 32 is referred to the right-hand-side vertical axis, while all other cases are referred to the left-hand-side vertical axis. The reference case corresponds to the reaction parameters in the existing mechanism. The ranges of variation of A 32 and A 51 are by factors of 10 and 2, respectively, around the reference case, based on the uncertainty bounds in existing pertinent data.
This suggests that the actual CH3O mole fraction at the high temperature peak may in fact be a factor of three or more times lower than the computed value. Let us examine next the effect of appropriate perturbations in the pre-exponential factors of reactions 51 and 32 ( A 51 and A 32 , see the full rate specification for each of these reactions in the Appendix) on the observed double-peaked profile structure of CH3O in the undisturbed stoichiometric flame. This is conducted to investigate whether variations in the parameters of these reactions could result in a single methoxy peak. Based on published rates, the uncertainty bounds of A 32 allow a factor of 10 range of variation on each side of the value cited in the Appendix [34], whereas the uncertainty bounds of A 51 correspond to a factor of 2 range [35]. Accordingly, we find that variation of A 51 from 2.7e11 to 10.8e11 leads to minor change in the CH3O structure, with little modification in the levels of both peaks, as shown in Fig. 11. This figure illustrates the dependence of the profile of methoxy mole fraction on the values of A 51 and A 32 , in the stoichiometric 36%-N2-diluted case, using 1D premixed flame computations with Chemkin [25, 30]. We have also varied the activation energy of Rn. 51 over a range of
890
H. N. NAJM much higher concentration of methoxy than the reference case, based on experimental signal-tonoise estimates. Thus, there is good evidence to suggest that the variation of A 32 above its reference value in the present mechanism may provide a more realistic model of methoxy chemistry in this flame. CONCLUSIONS
Fig. 12. Profiles of CH3O mole fraction versus temperature for the stoichiometric 36%-N2-diluted flame case, with variations in the pre-exponential factors of Reaction 32. Note that the case with high A 32 is referred to the righthand-side vertical axis, while other cases are referred to the left-hand-side vertical axis. The reference case corresponds to the reaction parameters in the existing mechanism. A 32 is varied by a factor of 10 above and below the reference case, based on the uncertainty bounds in existing data.
1223–3977 cal/mole (original value is 2600 cal/ mole), where the range endpoints were chosen to double and half the reaction rate at 1000 K. The resulting methoxy structure agrees roughly with the reference structure and the A 51 variations in Fig. 11. Note that Reaction 32 has zero activation energy. On the other hand, varying A 32 from 2e12 to 2e14 does lead to a significant change in the methoxy profiles. As shown in Fig. 11, the amplitude of the low-temperature peak is reduced significantly relative to the hightemperature peak when A 32 is set at the low limit of its range. Moreover, the high-temperature peak is shifted slightly towards higher temperature for low A 32 , as shown in Fig. 12. Nonetheless, the methoxy structure remains double peaked, with a stronger peak at high temperature, in this limit. Conversely, when A 32 is at its high limit, the low temperature peak becomes completely dominant, with the high temperature peak disappearing, its only trace being a shoulder and associated broadening of the profile at high temperature. Moreover, the level of computed CH3O mole fraction in the low temperature peak is higher by about a factor of 20 as compared to the reference case. Both these observations are significant, as the experimental observations not only show a single peak at low temperature, but also suggest a
We have presented time-matched numerical and experimental results describing the detailed interaction of a premixed methane-air flame with a counter-rotating vortex pair in 2D. We observe a transient rise in computed methoxy (CH3O) on the cold side of the flame during the interaction. We attribute this to changes in internal flame structure caused by the transient flow-induced strain-rate. In particular, the flow-induced steepening of the temperature profile lowers the temperature on the reactants side of the reaction zone, leading to reduced consumption of CH3O. Generally, we find the extent of the rise in peak CH3O to be higher in flames with lower burning rates and faster flow time scales, that is, lower Damko ¨hler numbers. Measurements of CH3O during the transient flame interaction with the vortex-pair are necessary to validate these observed transients. We discuss experimental measurements of CH3O in a steady V-flame, which outline potential challenges with PLIF of CH3O at high temperature due to signal attenuation. Relative locations and shapes of experimental and numerical CH3O, CH2O, HCO, and OH profiles in the undisturbed flame are presented and discussed. The absence of a high-temperature methoxy peak in the experiment cannot be attributed to signal attenuation of the existing high-temperature peak in the numerical results. Instead, the single low-temperature peak may be explained by a factor of 10 increase in the pre-exponential factor of Reaction 32 (CH3 ⫹ HO2 3 CH3O ⫹ OH), a variation that is within the expected uncertainty in this rate constant. We also report experimental measurements of peak HCO evolution that are in reasonable agreement with numerical results. The persistence of the experimental HCO signal during
TRANSIENT FLAME RESPONSE the interaction suggests continued burning despite the collapse of the CH signal. This agreement in HCO response suggests that the present reaction and transport models are adequate for the description of the dynamical response of some components of premixed methane-air flame chemistry, with the present operating conditions. On the other hand, we find significantly faster response of CH and OH in the experiment, versus the computed CH and OH, under both stoichiometric and rich conditions. We also observe qualitatively different response of OH at rich conditions, with an experimental OH burst that is absent from the numerical results. Moreover, although the experimental CH signal decays to zero at both stoichiometric and rich conditions, the degree of decay in the numerical peak CH mole fraction varies greatly with equivalence ratio. Evidently, the present diffusion-reaction model does a poor job at the representation of the dynamical character of OH and CH in this flame. Determination of the origin of these disagreements requires analysis of the coupled reaction-diffusion eigenmodes of the governing equations, which is work in progress. The qualitative disagreement in rich-flame OH response was observed earlier [14] by using GRImech1.2 [17] with ten-fold faster flow time scales, and is found here with flow time scales comparable to the experiment, using an alternate C1C2 chemical mechanism. These observations, and the above general disagreement in computed and measured flame time scales of OH and CH, indicate the extent to which validation of detailed unsteady flame models is lacking. This is true whether the cause of these disagreements is transport coefficients or the chemical mechanism. Clearly, validation under steady state conditions is insufficient. The dynamical response of the model requires experimental and computational studies that probe the transient structure of flames. Additional investigation of transient flame structure is necessary to provide clues as to the causes of these disagreements, and to examine the relative merits of alternative mechanisms or transport models.
891 This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division. Computations were performed at Sandia National Laboratories and at the National Center for Supercomputing Applications (NCSA). REFERENCES 1. 2.
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APPENDIX The chemical mechanism used in this work differs from that in [26] in that: 1. the parameters of the following reactions are altered as follows: Reaction H ⫹ O2 ⫹ M N HO2 ⫹ M H2O/10./ CO2/4.2/ H2/2.86/ CO/2.11/ OH ⫹ HO2 N H2O ⫹ O2 CH4 ⫹ H N CH3 ⫹ H2 CH3 ⫹ HO2 N CH3O ⫹ OH CH2O ⫹ H N HCO ⫹ H2 C2H5 ⫹ O2 N C2H4 ⫹ HO2 C2H3 ⫹ O2 N CH2O ⫹ HCO
A(mole-cm-sec-K) 0.361e18 N2/1.3/ 2.891e13 0.22e5 0.2e14 0.219e9 0.843e12 3.6e13
b
E(cal/mole)
⫺0.72
0.
0. 3. 0. 1.77 0. ⫺0.3
⫺496.75 8750. 0. 3000. 3875. 0.
where k ⫽ AT b exp(⫺E/RT)) is the forward rate for each reaction, and the line following the first reaction lists the 3rdbody efficiencies corresponding to the species indicated [25, 30]. 2. the species CH3OOH and its reactions are omitted, and 3. the following reactions are omitted: CH3O2 ⫹ CH3 N 2CH3O 2CH3O2 N CH3OH ⫹ CH2O ⫹ O2 C2H4 ⫹ CH3 N C2H3 ⫹ CH4 C2H5 ⫹ O N CH3 ⫹ CH2O C2H5 ⫹ O N C2H4 ⫹ OH C2H5 ⫹ HCO N C2H6 ⫹ CO C2H5 ⫹ CH3 N C2H4 ⫹ CH4 C2H3 ⫹ O2 N CH2HCO ⫹ O 2C2H3 N C2H4 ⫹ C2H2 CH3CO ⫹ H N CH2CO ⫹ H2 CH3CO ⫹ O N CH2CO ⫹ OH CH2CO ⫹ OH N CH3 ⫹ CO2
2CH3O2 N 2CH3O ⫹ O2 CH3 ⫹ HCO N CH4 ⫹ CO H ⫹ C2H5(⫹M) N C2H6(⫹M) C2H5 ⫹ O N CH3HCO ⫹ H C2H5 ⫹ OH N C2H4 ⫹ H2O C2H5 ⫹ CH2O N C2H6 ⫹ HCO 2C2H5 N C2H6 ⫹ C2H4 C2H3 ⫹ O2 N C2H2 ⫹ HO2 CH3CO ⫹ H N CH3 ⫹ HCO CH3CO ⫹ O N CH3 ⫹ CO2 CH3CO ⫹ OH N CH2CO ⫹ H2O
Moreover, we list below the rate specification [25, 30] for Rns. 51 and 32 pertaining to the CH3O discussion above. Reaction
A(mole-cm-sec-K)
(32) CH3 ⫹ HO2 N CH3O ⫹ OH 2.00e13 5.40e11 (51) CH2O ⫹ H(⫹M) N CH3O(⫹M) Low pressure limit: 0.154e31 ⫺0.48e1 0.556e4 TROE centering: 0.758 0.94e2 0.1555e4 0.42e4 H2O/8.58/ CO2/3./ H2/2./ CO/2./ N2/1.43/
b
E(cal/mole)
0. 0.5
0. 2600.