Auto- and Forced-Ignition Temperatures of Diffusion Flames Obtained

Dec 13, 2013 - Configuration of the Combustor System of. Katsuki and Hasegawa.11 To validate the modeling results, we simulate the diffusion flames of...
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Auto- and Forced-Ignition Temperatures of Diffusion Flames Obtained through the Steady RANS Modeling F. Wang, P. Li, Z. Mei, and J. Mi* State Key Laboratory of Turbulence and Complex Systems, Department of Energy & Resources Engineering, College of Engineering, Peking University, Beijing 100871, China ABSTRACT: The paper reports the autoignition and forced-ignition temperatures (AIT, FIT) of diffusion flames obtained through an iterative method using the steady RANS simulation. An eddy dissipation concept (EDC) model is used for all simulations with either a global or a detailed reaction mechanism. The present simulations are validated by the previous measurements of Katsuki and Hasegawa (Proc. Combust. Inst. 1998, 27, pp 3135−3146) and Fotache et al. (Combust. Flame 1997, 108, pp 442−470). It is revealed that FIT and particularly AIT can be properly predicted by the present method for various combustion configurations with different reactant conditions and operational parameters.

1. INTRODUCTION Ignition is a complex process with exothermic chemical reactions between fuel and oxidant, finally producing a continuous flame. This process can develop spontaneously or externally by a heat source, so that it is termed as “autoignition” or “forced-ignition”. The specific temperatures for the two ignition modes (denoted by AIT and FIT) are defined as the lowest temperatures of a flammable mixture at which ignition can lead to a self-sustaining combustion. These two temperatures are very important in technological applications to control flame stabilities.1−12 The FIT is a key issue for the spark-ignition engine and the aviation gas turbine.1,2 The AIT is crucial for homogeneous charge compression ignition (HCCI)3,4 engines, flameless oxidation (FLOX),5 moderate or intense low-oxygen dilution (MILD) combustion,6−10 and high-temperature air combustion (HiTAC).11,12 Thus far, AIT and FIT have been investigated in several typical combustors, for example, well-stirred reactor (WSR), 13−15 counter-flow, 16−21 coflow, 22,23 and crossflow.11,12 In the previous experiments,11−23 the autoignition and forced-ignition were induced by gradually increasing the reactant temperature, from which the AIT and FIT were determined. For the premixed combustion, Zabetakis 13 reviewed the flammability characteristics of the combustible gases and found that both temperatures grow as the carbon chain length of the hydrocarbon is increased. For the nonpremixed combustion or diffusion flame, Katsuki and Hasegawa11,12 experimentally examined the combustion stabilization of the cross-flow diffusion flame of a liquefied petroleum gas (LPG) jet perpendicularly issuing into the diluted oxidant stream. Both AIT and FIT were found to increase monotonously with decreasing the oxygen concentration in the oxidant stream. Law and his co-workers16−19 experimentally obtained the AIT of the counter-flow diffusion flames under different conditions (e.g., fuel type, strain rate, fuel dilution, and pressure). They found that, for a given system pressure, the AIT increases as the strain rate or the dilution of the fuel jet increases. Especially, at a constant strain rate, the AIT of the CH4/H2/air diffusion flame against the system pressure exhibits a Z-shaped three-limit behavior, which is © 2013 American Chemical Society

similar to the well-known homogeneous H2/air explosion limits. Despite the previous work noted above, there are few data of AIT and FIT available for practical combustors or furnaces. Considering the importance of the two temperatures in the control of flame stabilities, it should be significant to examine, experimentally or numerically, their dependence on varying operational conditions such as furnace configurations and reactant-injection parameters. Given that the experimental determination of AIT and FIT is highly laborious, it is more desirable to obtain them by numerical simulations. Indeed, there are several simulation methods currently available for predicting the time-dependent process of ignitions, that is, the unsteady Reynolds-averaged Navier−Stokes (RANS) modeling, large eddy simulation (LES), and direct numerical simulation (DNS). Unfortunately, however, both DNS and LES of the ignitions require too much computational time and are thus infeasible. In other words, only the unsteady RANS modeling is applicable for the simulations of the ignitions. Nevertheless, if AIT and FIT are considered only (instead of the ignition processes), their predictions can also be made through the steady RANS modeling using an iterative method (see Section 3.1 for more detail). In this context, the present study is designed to assess the use of the steady RANS modeling in predicting the AIT and FIT of diffusion flames. Calculations are carried out using eddy dissipation concept (EDC) model with global and/or detailed chemical mechanisms (GRI-Mech 3.0 for CH424 and San Diego mechanism25,26 for LPG). Validations of the present simulations are implemented by comparing the predictions with the previous measurements.11,18 Then, it is investigated whether FIT and AIT can be properly predicted by the iterative method described in section 3.1 for various combustion configurations and reactant conditions. Received: July 28, 2013 Revised: December 11, 2013 Published: December 13, 2013 666

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Figure 1. Furnace used in the experiments of Katsuki and Hasegawa,11 (a) boundary conditions and (b) grids of the computational domain.

2. MODEL DESCRIPTION 2.1. Configuration of the Combustor System of Katsuki and Hasegawa.11 To validate the modeling results, we simulate the diffusion flames of a fuel jet issuing perpendicularly into a preheated oxidant stream in the crossflow furnace system, the same as that of Katsuki and Hasegawa.11 Figure 1a shows some details of the combustor. The preheated oxidant flows upward from the bottom of the chamber, while the fuel jet issues horizontally from a burner located at a vertical wall, forming a cross-flow turbulent flow field inside the chamber. The inner diameter of the fuel nozzle is 0.8 mm, and the size of the rectangular combustion airports is 90 × 40 mm. From ref 11, the composition of the liquefied petroleum gas (LPG) as fuel is assumed as 97% C3H8 and 3% CO2 (by volume) at 50 °C. The thermal input is kept constant at 1.28 kW, thus the fuel-jet velocity is 26.3 m/s at the fuel nozzle exit with the corresponding Reynolds number kept at Re ≈ 4200. The oxidant consists of oxygen and nitrogen and the oxygen concentration (XO2) ranges from 0.5 to 21%. For each XO2, the oxidant temperature (Toxi) is varied to find the AIT and FIT, as discussed later. The effect of the oxidant velocity (Voxi) on the two temperatures is also checked. 2.2. Computational Approach. The commercial package FLUENT 6.327 is used to solve several transport equations (continuity, momentum conservation, turbulence kinetic energy and its dissipation rate, heat energy, and radiative intensity). Depending on which combustion model is used, additional transport equations (e.g., species mass fraction) are also solved. Realizable k-ε model with standard wall functions is used to model turbulence, which has been shown to provide accurate prediction of flow evolution and spreading of round jets.28 Considering the feature of flame thickening under HiTAC combustion conditions,11,12 the discrete ordinate (DO) radiation model29 with weighted sum of gray gas model (WSGGM) is used to model the radiation in this work. The DO model solves a radiative transfer equation for a number of discrete solid angles across the computational domain. For DO radiation model, theta division and phi divisions define the number of control angles used to discretize each octant of the angular space, and both parameters are set to 4.0. The WSGGM is a reasonable compromise between the oversimplified gray gas model and a complete model that takes into

account particular absorption bands. With the use of WSGGM model, all the species used for calculations are assumed to obey the ideal gas law. The spatial variation in the total emissivity is computed as a function of temperature (piecewise polynomial). The main challenge in modeling turbulent combustion is the handling of the mean reaction rate and the adequate representation of chemistry in the model. Under HiTAC or MILD conditions, the combustion should be considered as volumetric reactions.6,11 From this, the present study should use the volumetric reaction approaches, i.e., the eddy dissipation model (EDM) and the eddy dissipation concept (EDC) model.30 Since the EDM is valid only for chemical mechanisms with three or fewer reactions, we choose the EDC model, an extension of the EDM, which allows skeletal or detailed chemical kinetics to be included. In EDC model, the transport equations of species mass fraction are modeled as: ∂ (ρYi ) + ∇·(ρvYi ) = − ∇Ji + R i ∂t

(1)

where ρ is the mixture density, Yi is the local mass fraction of each species (i), v is the velocity vector, Ji is the diffusion flux of species (i), and Ri is the net rate of production of species by chemical reaction. The EDC model handles chemistry representation and turbulence−chemistry interaction and assumes that reactions occur in small turbulent structures, socalled the fine scales (ξ). The evolution of species concentrations is then computed by integrating the chemistry within those fine scales (ξ). Turbulence−chemistry interaction in the EDC model is handled using turbulent kinetic energy (k) and its dissipation rate (ε) to determine the fine scales (ξ), in which chemical reactions occur. The combustion is assumed to occur within the fine scales as a constant pressure reactor. The size of fine scales (ξ) is modeled as

⎛ vε ⎞ 2 ξ = Cξ⎜ 2 ⎟ ⎝k ⎠

(2)

where the constant Cξ = 2.138. Species are then assumed to react within the fine structures over a time scale (τ), which is expressed by: ⎛ v ⎞1/2 τ = Cτ ⎜ ⎟ ⎝ε⎠ 667

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Table 1. Global Combustion Mechanism Used for CH4 and C3H8 with Kinetic Data (Units in SI)a CH4 + 1.5O2 → CO + 2H 2O

5.012 × 1011

0

CO + 0.5O2 → CO2

2.239 × 1012

reaction orders [CH4]0.7[O2]0.8

0

1.7 × 108

[CO][O2]0.25[H2O]0.5

0

1.7 × 10

[CO2]

C3H8 + 3.5O2 → 3CO + 4H 2O

5.62 × 109

0

1.256 × 108

[C3H8]0.1[O2]1.65

CO + 0.5O2 → CO2

2.239 × 10

0

1.7 × 10

[CO][O2]0.25[H2O]0.5

0

1.7 × 108

CO2 → CO + 0.5O2 a

Ea (J/kgmol) 2 × 108

8

CO2 → CO + 0.5O2 three steps for C3H8

β

A

reactions three steps for CH4

5 × 10

12

5 × 108

β

8

8

[CO2] −1

Note: the reaction rate coefficient = AT exp(−Ea/RuT), where Ru is the universal gas constant (= 8315 J/kmol K ).

Figure 2. Comparison of mass fractions of CO2, O2, and H2O and the mean temperature along the z-direction at x = 105 mm and y = 0 mm for the cross-flow LPG diffusion flame of XO2 = 4%, Voxi = 1.16m/s, Toxi = 1200 °C, obtained from 400 000 and 1 000 000 cells.

simulations, the ISAT error tolerance of 0.001 is first used for the calculation stage. After the preliminary converged result is reached and the net energy balance is satisfactory, the ISAT error tolerance is then set to be 0.0001 for the final converged solution. The semi-implicit method for pressure-linked equations (SIMPLE) is utilized to solve pressure velocity coupling. The quadratic upwind interpolation for the convection kinetics (QUICK) scheme is employed for discretizing the equations in order to improve the accuracy of the calculations. Solution convergence is identified by two criteria. The first is to ensure that the residuals are less than 10−6 for temperature and radiation intensity and 10−5 for all other variables. The second is to ensure that the calculations are converged when both the variation in iteration process of the mean temperature 0 (i.e., the stable flame for the last case has been established, then end the searching process), as shown in Figure 4a,c. (b) If T > Ti (i.e., the temperature rise ΔTi = T − Ti > 0), the fuel jet is considered to be successfully ignited, and a stable flame has to be sustained for the case with Toxi = Ti; repeat (1) and (2) of the above procedure, by taking a lower value (Ti+1 = Ti − ΔT, e.g., ΔT = 50 °C for the present simulations) as Toxi for the next calculation, until Step (3) to obtain T = Ti+1 or ΔTi+1 = T − Ti+1 = 0, that is, extinction of the diffusion flame takes place for the last case, then end the searching process, as shown in Figure 4b,d. The obtained values of Tcfd = (1/2)(Ti+1 + Ti) are regarded as the predicted FIT (Figure 4a,b) or AIT (Figure 4c,d). Here, Ti+1 and Ti are values of Toxi for the last two cases used in the searching process. In other words, the stable diffusion flame can be maintained in one of the cases with Toxi = Ti+1 and Toxi = Ti, whereas the flame is extinguished in the other case. It should be pointed out that the true ignition temperature (Ttrue) is initially unknown but must logically lie between Ti+1 and Ti. Therefore, Ttrue can be approximated by Tcfd with the maximum error of δ = ± (1/2)ΔT, where ΔT (e.g., 50 °C for the present

3. HOW TO OBTAIN AIT AND FIT FOR DIFFUSION FLAME 3.1. Procedure of Obtaining AIT and FIT by the Steady Simulation. Experimental values of AIT and FIT are usually determined by gradually increasing Toxi. A similar method using the steady RANS modeling is developed here to find the two temperatures through an iterative procedure, as shown in Figures 4 and 5. The proposed procedure is somewhat similar to the searching steps used in the numerical studies.17−19,35 That is, for each given condition, several cases with different Toxi are calculated orderly by the steady RANS modeling to obtain AIT or FIT. On the basis of the converged solutions, it is easy to judge whether or not a successful forcedignition or autoignition has occurred, then the value of FIT or AIT can be determined. Such a searching process is summarized in the flowchart of Figure 5 and described below: (1) Using Ti as the initial value of Toxi for the beginning case of the searching process, switch off the CFD module of chemical reactions and calculate the nonreacting flow-field (so that the convergence of subsequent computations is achieved more quickly) (2) When the convergence of nonreacting flowfield has been achieved, (a) for FIT, activate the module of chemical reactions for subsequent iterations, and then set a “hot source” over the entire computational domain or a line ‘source’ at the fuel nozzle exit with a sufficiently high temperature (1600 °C), as the first iteration value of temperature for subsequent computations of reactive flow to forcibly start the chain branching reactions. Here, it should be stressed that the setting of a line “source” acts like adding a “external source of heat” into the converged nonreacting flow field. (b) For AIT, just activate the module of chemical reactions without setting any external source of heat, so that the converged nonreacting flow670

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Figure 5. Flowchart of the RANS modeling method to obtain AIT and FIT. Here, the variable of “n” in the flowchart is used to control the flow of the procedure, and the “i” is the attempt number for each ignition temperature searching.

for the counter-flow LPG diffusion flame with XO2 = 21%.

simulations) is the temperature step between every two attempts in the searching process to find the ignition temperatures. Obviously, one can obtain Ttrue ≈ Tcfd more accurately using a smaller ΔT in Step (3); ideally, Tcfd → Ttrue as ΔT → 0. 3.2. Simulation Examples of Obtaining AIT and FIT. Figure 6 illustrates how to obtain AIT and FIT for the LPG diffusion flames at XO2 = 21% (upper) and XO2 = 4% (lower). The oxidant injection velocity (Voxi) is kept at 1.16 m/s to maintain the similar flow pattern between fuel and oxidant for all the cases considered here. To find the two temperatures, calculations are conducted with Toxi ranging from −50 to 1400 °C using the detailed mechanism. For Toxi < 0 °C, no temperature rise exists or no flame can sustain even setting a heat source (high temperature) over the entire computational domain or at a line source near the fuel nozzle exit to forcibly ignite the LPG jet. When Toxi ≥ 0 °C, the temperatures rise exists in the chamber, which reflects the occurrence of stable flame, namely, a flame has been forcbily ignited. When Toxi ≥ 850 °C, a stable flame can be established even without setting any external heat source. That is, a flame is naturally or spontaneously ignited at Toxi ≥ 850 °C. Hence, the two temperatures FIT ≈ −25 °C and AIT ≈ 825 °C are obtained

Interestingly, for XO2 = 4%, stable diffusion flames can be established only when Toxi ≥ 950 °C, regardless of whether an external heat source is used or not. In other words, the two temperatures are identical for the LPG flame at XO2 = 4% (i.e., FIT = AIT ≈ 925 °C). Besides, the unsteady RANS modeling is also used to predict AIT and FIT. From the unsteady modeling, the timedependent process of ignition can be well-produced, with which it is easy to judge whether an ignition is successful. It is interesting to find that, even using unsteady modeling, the FIT and AIT are about −25 and 825 °C for the LPG cross-flow diffusion flame with XO2 = 21%, whereas the two temperatures are both approximated to be 925 °C for XO2 = 4%. That is, the predicted AIT and FIT from using the steady modeling are nearly identical to those from the unsteady modeling. This can be explained here. After a sufficient evolution time, the timemean solutions of the unsteady modeling should be close to those of the steady modeling (see Figure 3). In other words, the results from the two will lead to the same judgment of whether a successful ignition has occurred. Therefore, the 671

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Figure 6. Temperature contours of the counter-flow LPG jet flames at yz-plane with Toxi ranging from −50 to 1400 °C, Voxi = 1.16 m/s, for XO2 = 21% (upper) and XO2 = 4% (lower).

steady RANS modeling is appreciate and can be used to predict AIT and FIT. 3.3. Effects of External Heat Source on FIT. For the forced-ignition, the ignition probability is closely related to the properties of an external heat source (e.g., duration, energy, position, and even the geometric shape).37,38 In the present work, the action of introducing an external heat source is realized by setting a sufficiently high temperature (e.g., 1600 °C, this value is found not critical) at some certain region in the chamber. The effects of the position and size of the heat source are summarized below: (i). Heat Source Position. Here, three different positions of a heat source (spherical volume of 3 mm in diameter) are examined at A, B, and C (see Figure 7) in the furnace of Figure 1. As an example, for XO2 = 21%, the predicted FIT is highest (≈ 175 °C) when the heat source is located at A, whereas the lowest FIT (≈ −25 °C) is obtained with the heat source at C. The reason should be that the ignition probability is higher when the external heat source is near the fuel nozzle, as reported by Ahmed and Mastorakos.38 (ii). Heat Source Size. The effect of the heat source size is checked by setting a high temperature (1600 °C) over the entire computational domain or a sphere of diameter of 3 mm at B in Figure 7. Obviously, the probability at which the ignition is successful must be higher, or the predicted FIT must be lower, if using the former as a heat source because B only takes a small space in the entire domain. Indeed, our calculations

Figure 7. Velocity vectors of the nonreacting flow-field in the xz-plane for XO2 = 21%, Toxi = 35 °C, and Voxi = 1.16 m/s. On the plot, A, B, and C represent the three locations at (105, 0, 260), (105, 0, 15), and (150, 0, 15), at which an external spherical heat source of 3 mm in diameter is located.

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calculations by about 200 and 100 °C for the two cases. Those discrepancies should result partly from the difficulty in accurately capturing the maximal furnace temperatures and their locations during the experiments. To compare the predictions and the measurements in a more quantitative way, Figure 9 plots the temperature profiles along the z-direction at x = 95, 105, and 115 mm on the symmetry plane (y = 0) for the cases with XO2 = 21 and 4%, respectively. The profiles from using the global mechanism (GM) are also shown in Figure 9. Obviously, the use of GM predicts a higher peak temperature than using the detailed mechanism, consistent with the previous work.32,39 It is also shown that the calculations with the detailed mechanism agree better with the measurements than using the global one. That is, the steady RANS modeling with the San Diego mechanism is effective in simulating the thermal characteristics of the LPG jet diffusion flames. Hence, the use of the same model is appropriate to investigate the thermal features of the jet diffusion flames in the subsequent sections. 4.2. Validation of the Modeling Method for AIT and FIT. Following the procedure described in section 3.1, a number of the steady RANS calculations are implemented to obtain AIT and FIT of LPG diffusion flames occurring in the cross-flow furnace of Katsuki and Hasegawa,11 over a wide range of XO2 from 0.5 to 21% (by volume) and Voxi = 1.16 m/s. The GM and San Diego mechanism are both utilized. Figure 10 plots the predicted FIT and AIT and the measured counterparts11 as a function of XO2. From this figure, both the predicted and measured AIT and FIT are found to increase gradually as XO2 is decreased. Appearently, the predicted AIT using the detailed mechanism agree quite well with the measurements over the entire range of XO2, while the use of GM underestimates globally by about 200 °C. On the other hand, the predicted FIT is underestimated with either GM or the detailed mechanism, although the latter performs better. The better performances of the detailed mechanism can be explained as follows. Many immediate species or free radicals exist during combustion which are considered in the detailed mechanism but not in GM. Since some species may be produced and consumed slowly, the overall combustion reaction rate is then reduced. In other words, the GM’s three reactions occur more easily than do the 235 reactions in the detailed mechanism under the same given conditions. This indeed reflects in Figure 9, which shows that the use of GM results in higher temperatures than those obtained using the detailed mechanism. That is, the rate of heat loss of the reaction zone is relatively lower, and thus a higher temperature difference occurs between the reaction zone and its surroundings, when GM is used. In other words, a stable diffusion flame can maintain at a lower critical oxidant temperature, hence requiring a lower FIT or AIT, for the case using GM. Consequently, the use of the present method with GM underestimates the AIT and FIT. It is then suggested that an appropriate detailed mechanism should be employed when using the present method to quantitatively predict the AIT and FIT of diffusion flames.

obtain that FIT ≈ −25 °C for the former and FIT ≈ 25 °C for the other at XO2 = 21%. Accordingly, the choice of the external heat source is important when using the steady RANS modeling to predict FIT of diffusion flame. However, in the previous studies,11,18 no information about the external heat resource could be found. Therefore, the approach of setting a line of 1600 °C at the fuel nozzle exit as the external heat source is always utilized in the present work.

4. VALIDATIONS BY PREVIOUS MEASUREMENTS11 4.1. Validation of the Steady RANS Modeling. The steady RANS modeling is validated by calculating the counterflow LPG diffusion flames for XO2 = 21%, Voxi = 1.16 m/s, and Toxi = 35 °C (conventional air combustion) and for XO2 = 4%, Voxi = 1.16 m/s, and Toxi = 1200 °C (diluted combustion), which are identical to those used in the experiments of Katsuki and Hasegawa.11 Figure 8 compares the predicted (using the San Diego mechanism) and measured contours of the mean temperature for XO2 = 21 and 4%, respectively. Overall, the predictions of the two cases are roughly similar to the measurements, but with some inconsistencies. For instance, the peak temperatures are perhaps overestimated in the

Figure 8. Comparisons between the mean temperature contours predicted (left) and those measured (right). (a) XO2 = 21%, Voxi = 1.16 m/s, Toxi = 35 °C; (b) XO2 = 4%, Voxi = 1.16 m/s, Toxi = 1200 °C. The dashed-line box (left) corresponds to the solid-line box (right) for the measured region in ref 11

5. FURTHER APPLICATIONS OF THE PROPOSED METHOD The present modeling method is a searching procedure of obtaining AIT and FIT of diffusion flame and not related to any 673

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Figure 9. Predicted mean temperature profiles along the z-direction versus the measurements at x = 105 mm, y = 0 mm. (a) XO2 = 21%, Voxi = 1.16 m/s, Toxi = 35 °C and (b) XO2 = 4%, Voxi = 1.16 m/s, Toxi = 1200 °C.

Figure 10. AIT and FIT of the LPG flames predicted using the global mechanism and San Diego mechanism and those measured at Voxi = 1.16 m/s by Katsuki and Hasegawa.11

LPG) are used, respectively. The calculated ignition tempeatures against XO2 are shown in Figure 11. Figure 11 displays the predicted ignition temperatures against XO2. It is demonstrated that increasing Voxi shifts up the profiles of FIT and AIT wholly (Figure 11a). This can be interpreted as follows. The first is that increasing Voxi enhances the shear between the cross-flowing reactant jets, thus resulting in a higher strain rate. The higher strain rate then leads the combustion heat to be distributed over a larger volume and, consequently, reducing the global temperature of the reaction zone. In other words, an increase of Voxi can result in a higher rate of heat loss from the reaction zone to the surrounding,

use of the reactant feeding conditions, fuel types, and even furnace configurations. So it should be effective to obtain AITs and FITs of different diffusion flames, which is checked below by predicting the two temperatures under other conditions. 5.1. Predictions of AIT and FIT in the Cross-Flow Furnace of Katsuki and Hasegawa.11 With the present method, the ignition temperatures are calculated for the LPG diffusion flames at three different oxidant injection velocities, that is, Voxi = 0.1 m/s, 1.16 and 10 m/s, and for the CH4 diffusion flame at Voxi = 1.16 m/s in the furnace of Katsuki and Hasegawa.11 For all the calculations, the detailed mechanisms (i.e., GRI-Mech 3.0 for CH4 and San Diego mechanism for 674

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Figure 11. Predicted AIT and FIT of diffusion flames against XO2 in the cross-flow furnace of Katsuki and Hasegawa.11 (a) At three Voxi and (b) firing LPG and CH4.

Figure 12. AIT and FIT of the counter-flow diffusion flames versus CH4 concentration of the fuel mixture (CH4/N2) at the strain rate of (a) 150 and (b) 300 s−1. The inset in part (b) is a schematic of the counter-flow furnace arrangement.

which distabilizes the diffusion flame. The second reason might be that an increase of Voxi shortens the reactant residence time in the reactive region, which makes less heat released in the reaction zone, consistent with previous studies.17,18 Therefore, for higher Voxi, owing to the more heat loss and less heat released, a higher oxidant temperature is required to maintain the stable flame. Moreover, from Figure 11b, a similarity is observed between the AIT and FIT distributions of firing CH4 and LPG. It is also demonstrated that the predicted AIT and FIT for the CH4 diffusion flames are higher than those for LPG. This results likely from the fact that the activation energy of the CH4 oxidation is higher.

5.2. Predictions of AIT and FIT of the Counter-Flow Flame. To test the independence of the present method on the furnace configuration, we simulate the counter-flow combustion used in ref 16, whose system has two vertical tube burners separated by a distance of 20 mm with a heated oxidant (21% O2 + 79% N2 (vol)) stream downward against an upward flow of cold CH4/N2 mixture at 27 °C. A schematic of the counterflow arrangement is given as an inset of Figure 12b (see more details in ref 16). In the present calculations, the inlet oxidant velocity (v0) is set to be the same as that of the fuel mixture. According to ref 16, the flow strain rate (k) can be approximated with the maximum axial velocity gradient (i.e., k = −(∂vz/∂z)max), where vz is the axial velocity. 675

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experiments.11,18 In contrast, the predicted ignition temperatures are underestimated when using the global reactions. Hence, an appropriate detailed mechanism is required to predict the AIT and FIT of diffusion flame when using the present method. (4) The present method works well when predicting AIT and FIT of diffusion flame at various oxidant injection velocities and different fuels in the cross-flow furnace.11 It is also applicable in predicting the two temperatures at different furnace configurations. One would, therefore, anticipate that the present method should apply for diffusion flames under other practical conditions.

In the experiments of ref 16, the autoignition was induced by gradually increasing the oxidant temperature when keeping other conditions unchanged. Accordingly, the AIT was determined as the critical oxidant temperature, above which the ignition could take place spontaneously. Later, this experimental work was numerically investigated and extanded by Fotache et al.17,18 In those investigations, AIT was determined as the lower turning point temperature on the response S-curve. Those values of AIT and FIT for the counterflow flames can also be obtained conveniently using the present method. Following the procedure of Figures 4 and 5, a number of calculations of the counter-flow diffusion flames are carried out to obtain AIT and FIT at the two strain rates of k = 150 and 300 s−1, over wide ranges of Toxi and dilution of CH4 by N2. For those calculations, both GM (see Table 1) and GRIMech 3.0 for CH4 are used. Figure 12 compares the present predictions with the experimental data and the numerical results of Fotache et al.18 Apparently, for each strain rate, the present predicted AIT using GRI-Mech 3.0 and the previous numerical results of Fotache et al.18 both agree satisfactorily with the measurements. Consistent with the measurements, the dependence of the predicted AIT on the CH4 concentration follows: for low CH4 concentrations (approximately ≤30%), the AIT decreases sharply as the CH4 concentration increases, while, for the CH4 concentration >30%, the AIT is insensitive to the CH4 concentration. The present method can also predict FIT for the counter-flow diffusion flames. Obviously, the FIT decreases significantly with increasing the CH4 concentration. In addition, the curves of AIT and FIT merge to one at low CH4 concentrations (e.g., ∼ 10% for k = 150 s−1 and ∼12% for k = 300 s−1). As mentioned in section 4.2, the use of the reaction mechanism plays an important role in predicting AIT and FIT when using the present RANS modeling method. This is indeed confirmed in Figure 12. Obviously, the predicted AIT using GM can only qualitatively capture the ignition temperature dependence on the CH 4 concentration with an underestimation of about 75 °C. In contrast, the preditions using GRI-Mech 3.0 performs much better. Of note, the present modeling method was also preliminarily used in our previous work35 to predict the AIT and FIT of the coflow diffusion flames when firing CH4/H2, CH4, and C3H8. This demonstrates that, although the furnace configurations are varied, the two temperatures can still be predicted by RANS modeling through the procedure described in section 3.1. Accordingly, one would then expect that the iterative method, consisting of several steady RANS calculations, is appropriate and applicable for predicting AIT and FIT of the diffusion flame under other practical conditions.

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AUTHOR INFORMATION

Corresponding Author

*Email: [email protected]. Tel.: +86-10-62767074. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the support of the National Natural Science Foundation of China (no. 51276002) and Special Research Fund for the Doctoral Program of Higher Education of China (no. 20110001130014). They thank all the referees for their insightful comments and criticisms on the early version of the manuscript, the addressing of which has significantly strengthened the work.

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REFERENCES

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6. CONCLUSIONS The main conclusions drawn from this study are the following: (1) The present searching procedure, consisting of several steady RANS calculations that are iteratively converged, can be used to obtain the autoignition and forced-ignition temperatures (AIT, FIT) of diffusion flame. (2) The present modeling has been validated by the previous experiments11,18 through comparing the predicted and measured AIT and FIT of the cross-flow and counter-flow diffusion flames. (3) The reaction mechanisms play an important role in correctly predicting the AIT and FIT. The predictions of FIT and particularly AIT with the detailed mechanisms25,26 agree reasonably well with the 676

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Article

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