Laminar Burning Velocity of Methane–Air Mixtures at Elevated

Article pubs.acs.org/EF

Laminar Burning Velocity of Methane−Air Mixtures at Elevated Temperatures Mohammad Akram,† Priyank Saxena,‡ and Sudarshan Kumar*,† †

Department of Aerospace Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India Solar Turbines Incorporated, San Diego, California 92101, United States

‡

ABSTRACT: The measured and computed laminar burning velocities of methane−air mixtures at higher mixture temperatures are reported in this paper. The experiments and computations were performed for a wide range of mixture temperatures and equivalence ratios. The unburned mixture temperature ranges from 370 to 650 K. Computational predictions of burning velocities were carried out with GRI-Mech 3.0, San Diego mechanism, and Konnov mechanism for methane−air mixtures. The measured burning velocities match very well with the numerical predictions for all mixture temperatures and existing experimental results for mixtures at ambient temperature. Another contribution of the present work is the variation of the measured power-law temperature exponent with mixture equivalence ratios. The maximum burning velocity (even at high mixture temperatures) and minimum temperature exponent magnitudes were observed to exist for slightly richer mixtures.

1. INTRODUCTION The characteristics of a combustion process are mainly governed by the laminar burning velocity of the fuel−air mixture, and it is defined as the velocity of a steady, onedimensional, laminar propagation of an adiabatic flame front into a premixed fuel−air mixture.1 The laminar burning velocity of the reactive mixture depends upon its equivalence ratio, initial pressure, and initial temperature of the fuel−air mixture. This has been correlated as2−9 ⎛ T ⎞α Su = Su,o⎜⎜ u ⎟⎟ ⎝ Tu,o ⎠

ratios is quite different for lean and rich mixtures. In many cases, the value for lean and very rich mixtures is substantially higher than the respective magnitude of the mixture burning velocity for stoichiometric mixtures. This behavior becomes worse at higher temperatures. Therefore, it is very important to investigate this issue and provide an accurate correlation, which would comply with the general observation of the temperature and mixture dependency of the burning velocity. It is also interesting to note that there is a large discrepancy in the data available for equivalence ratio dependency of the temperature exponent, as shown in Figure 1. Babkin and Kozachenkov12 found that the power exponent of the temperature effect α rapidly increases from stoichiometric to lean methane−air mixtures. However, their experiments were limited to lean mixtures only. Sharma et al.2 have given separate expressions for rich and lean mixtures, and their experiments were limited for a mixture equivalence ratio range of 0.8 ≤ Φ ≤ 1.2. They observed that a minimum value of the temperature exponent α exists for the stoichiometric mixture, which was later confirmed by Gu et al.,5 Liao et al.,6 and Hermanns et al.9 A slight decrease in α was observed by Iijima and Takeno3 for a range of 0.8 ≤ Φ ≤ 1.3. A slight decrease in α with a lean to rich mixture was observed by Bose et al.13 and Takizawa et al.7 In another study, Stone et al.4 have proposed a linear correlation, in which the temperature exponent α reduces linearly with the mixture equivalence ratio, as shown in Figure 1. The existence of the minimum value of α near the stoichiometric mixture ratio with a sharp decrease for leaner and very rich mixtures has been reported by Yan et al.,8 as shown in Figure 1. Considering the large variation of the temperature exponent in the reported literature and subsequent problems in using the temperature exponent for extrapolation of the laminar burning velocity of methane−air mixtures at a high temperature, it becomes important to readdress this issue

(1)

where α is termed as the temperature exponent and is a function of the pressure and mixture equivalence ratio and Su,o is the laminar burning velocity at ambient conditions. Various power-law correlations proposed in the literature for methane− air mixtures at higher mixture temperatures are summarized in Table 1. The range of mixture equivalence ratios, initial mixture temperature and pressure with magnitude, and existence of maximum burning velocity deduced from the correlations available in the literature for the methane−air mixtures are summarized in Table 2. Most of these correlations are given for a very short range of mixture temperatures and behave well in the given range of mixture temperatures. However, these correlations need to be extrapolated to obtain the burning velocities at high temperatures. Various combustion devices, such as gas turbine combustors and internal combustion engines, operate at temperatures way higher than the ambient temperature. Exhaust gas recirculation (EGR) and/or direct preheating of mixtures was observed to improve the combustion efficiency and, at the same time, to decrease the unwanted emission of pollutants. 10,11 If the available correlations for burning velocities at high temperatures are extrapolated, an inaccurate behavior can be observed.2−8 Although these correlations2−8 provide a closer value for stoichiometric fuel−air mixtures, the variation with equivalence © XXXX American Chemical Society

Received: March 14, 2013

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Table 1. Correlations Showing Simultaneous Mixture Equivalence Ratio, Temperature, and Pressure Dependency of the Laminar Burning Velocity of the Methane−Air Mixture researcher

burning velocity correlation

Sharma et al.2

1.68/ Φ

Su = C(Tu/Tu,o)

1.68 Φ

Su = C(Tu/Tu,o)

Φ ≤ 1.0

if

Φ ≥ 1.0

if

C = − 418 + 1287/Φ − 1196/Φ2 + 360/Φ3 − 15Φ log P Iijima and Takeno

3

Su = Su,o(Tu/Tu,o)β1[1 + β2 ln(Pu/Pu,o)] Su,o = 36.9 − 210(Φ − 1.12)2 − 335(Φ − 1.12)3

Stone et al.4

Su = Su,o(Tu/Tu,o)α (Pu/Pu,o)β Su,o = 37.6 + 15.1(Φ − 1) − 221(Φ − 1)2 − 458(Φ − 1)3 − 358(Φ − 1)4

α = 1.42 + 1.98(Φ − 1) β = − 0.314 + 0.608(Φ − 1) Liao et al.6

Su/Su,o = (Tu/Tu,o)α (Pu/Pu,o)β Su,o = −177.43Φ3 + 340.77Φ2 − 123.66Φ − 0.2297

α = 5.75Φ2 − 12.15Φ + 0.8 β = − 0.925Φ2 + 2Φ − 1.473 Takizawa et al.

7

Su = Su,o(Tu/Tu,o)α (Pu/Pu,o)β Su,o = 36.5 − 217(Φ − 1.07)2 − 180(Φ − 1.07)3 α = 1.88 − 0.095(Φ − 1)

β = − 0.36 + 0.13(Φ − 1)

Table 2. Range of Equivalence Ratios, Initial Temperature, and Pressure over Which Power-Law Correlations Are Provided for the Laminar Burning Velocity of the Stoichiometric Methane−Air Mixture with Maximum Burning Velocity and Temperature Exponent for the Stoichiometric Mixture researcher 2

Sharma et al. Iijima and Takeno3 Stone et al.4 Gu et al.5 Liao et al.6 Takizawa et al.7 Yan et al.8

Φ

Tu (K)

Pu (atm)

0.8−1.2 0.8−1.3 0.6−1.4 0.8−1.2 0.6−1.4 0.7−1.3 0.6−1.4

300−600 291−500 293−454 300−400 300−400 280−330 283−373

1−8 0.5−30 0.5−10.4 1−10 0.5−1.5 0.8−1.1 1.0

Su (Φmax) 34.1 36.9 37.6 36.0 39.1 36.5 38.0

(1.10) (1.12) (1.00) (1.00) (1.05) (1.07) (1.05)

Su,o (α) at Φ = 1.0 33.0 34.5 37.6 36.0 39.4 35.5 36.9

(1.68) (1.60) (1.42) (1.61) (1.58) (1.88) (1.72)

2. EXPERIMENTAL SECTION

through precise laminar burning velocity measurement at high mixture temperatures using an alternate method, such as preheated diverging channels.14−17 The burning velocity is measured with a preheated high aspect ratio mesoscale diverging channel as suggested in earlier work by the authors.14−17 The stabilized flames in such a channel were confirmed to be flat in both transverse and depth directions with near-adiabatic conditions.14−16 The burning velocity magnitudes obtained with this measurement were apparatus-independent.14 The proposed technique with a high aspect ratio preheated diverging channel has been adequately validated for the stoichiometric methane−air mixture,17 liquefied petroleum gas (LPG)−air mixtures,15 and pure and diluted propane−air mixtures16 by the authors. The study is extended to the prediction of the laminar burning velocity for methane−air mixtures at high temperatures for a range of equivalence ratios, Φ. Attention has been paid toward the mixture dependency of the temperature exponent and variation of the laminar burning velocity at higher mixture temperatures.

The experimental setup14−17 contains a diverging channel, an external heating device, and mass flow controllers connected to a computer via a command module and temperature measurement system, as shown in Figure 2. The quartz channel with 10° divergence and 25 × 2 mm inlet opening was used. A porous burner was used to preheat the mixture inside the channel. This external heating initiated the combustion and stabilizes the flame at high mixture temperatures. Methane gas of 99.99% purity was the fuel used in the present study. The methane−air mixture is supplied to the diverging channel, whereas the LPG−air mixture is supplied to the porous burner. Various electric mass flow controllers are connected with a command module to a dedicated computer to maintain the flow rates of the fuel and oxidizer. A 0.5 mm diameter K-type thermocouple was used to measure the inner wall temperature through a precisely controlled traverse. The maximum uncertainty in the temperature measurement is found to be less than ±5 K. The other details of the experimental setup can be found in refs 14−17. B

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⎛ A ⎞⎛ T ⎞ Su = Uinlet⎜ inlet ⎟⎜⎜ u ⎟⎟ ⎝ A f ⎠⎝ Tu,o ⎠

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The effect of the heat interaction between the stabilized flame and solid wall, including thermal feedback, boundary layer, and uncertainty in the temperature, was analyzed similar to earlier work by the authors.15,16 The total uncertainty was observed to be less than ±5%. The external heat supply is varied (800− 1100 W) to obtain a greater number of planar flames for a specific mixture and at different mixture temperatures.14 The repeatability of the laminar burning velocity for the same initial conditions for a set of 10 test runs conducted over a period of time is performed. The obtained laminar burning velocity is almost invariant for a large number of experiments, with a maximum deviation of less than 1.5% from the mean value. The premixed planar flames formed in the diverging channel are similar to steady one-dimensional adiabatic and freely propagating flames. Therefore, for comparison to experimental data, the computations for the burning velocity were performed for a freely propagating, steady, and adiabatic flame using PREMIX code.18 The essential transport and thermodynamic properties were obtained from Sandia National Laboratories.19,20 Multi-component mass and thermal diffusion were considered. The refinement of grid near the flame is achieved with an upwind difference scheme. The burning velocities computed were grid-independent for GRAD = 0.02 and CURV = 0.05. The reaction mechanisms for methane, such as GRIMech 3.0,21 San Diego mechanism,22 and Konnov mechanism 0.5, were used. The computational data of Konnov mechanism 0.5 is taken from ref 23.

Figure 1. Variation of the temperature exponent with the equivalence ratio for the methane−air mixture in existing literature.

3. BURNING VELOCITY CALCULATIONS AND COMPUTATIONS The wall/mixture temperatures were measured in advance for various inlet velocity conditions. The mixture temperatures were uniform in transverse direction because of the uniform velocity distribution in a high aspect ratio channel. The stationary planar flames appear for a range of mixture equivalence ratios and mixture temperatures. These planar flames were used to obtain the laminar burning velocities at those conditions. The stabilization position of these planar flames varies with both equivalence ratios and mixture temperatures. The location of the stabilized flame was determined through processing of direct photographic images of planar flames at various conditions. The laminar burning velocity is obtained using the relation14−17

4. RESULTS AND DISCUSSION The laminar burning velocities of methane−air mixtures have been measured for a wide range of mixture equivalence ratios and mixture temperatures. The range of mixture temperatures varies with the equivalence ratio of the mixture. The initial temperature and pressure of the unburned mixture were 300 K and 1.0 atm for all of the experiments. The burning velocity variation with the temperature ratio (Tu/Tu,o) for a particular mixture equivalence ratio is compared to the experimental and computational results available in the literature.21−23 A powerlaw correlation is fitted on the experimental data, which

Figure 2. Schematic diagram of the experimental setup.14−17 C

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same increment in the mixture temperature. The vertical error bars show uncertainty (< ±5%) in measured data. The burning velocity at 300 K and temperature exponent of the lean mixture (Φ = 0.8) is observed to be 26.4 cm/s and 1.806, respectively. Whereas for the mixture with Φ = 1.2, Su,o and α were 31.7 cm/ s and 1.65, respectively. The burning velocity for the lean mixture is in good agreement with the GRI-Mech 3.021 predictions. Slightly lower values were observed for the rich mixtures (Φ = 1.2) compared to numerical predictions.21 A similar comparison is performed for other equivalence ratios to obtain Su,o and α. 4.2. Temperature Exponent: Mixture Dependency. The variation of the temperature exponent α (obtained from power-law correlations; see eq 1) with the mixture equivalence ratio is shown in Figure 5. A significant influence of the

provides the power-law temperature exponent for that mixture. The procedure is repeated for other equivalence ratios. 4.1. Laminar Burning Velocity: Temperature Dependency. The measured laminar burning velocity of the stoichiometric methane−air mixture has been observed to increase with the initial mixture temperature, as shown in Figure 3. A power-law correlation is fitted on experimental data

Figure 3. Variation of the laminar burning velocity of the stoichiometric methane−air mixture at higher mixture temperatures.

and shown with a bold continuous line. The measured data match well, with both the values deduced from extrapolation of the existing correlations2−6 and computational predictions.21,24 A good agreement with other results available in the literature7−9,22,23 is also observed (not plotted for simplicity of the presentation). The burning velocity of the stoichiometric methane−air mixture at reference temperature (300 K) is 35.5 cm/s. The temperature exponent α for this mixture is 1.581. The vertical error bars show uncertainty in measured data. The temperature dependency obtained experimentally for a leaner mixture (Φ = 0.8) and a rich mixture (Φ = 1.2) is shown in Figure 4 in comparison to the computational predictions of GRI-Mech 3.0.21 These mixtures have a higher increment in burning velocity compared to the stoichiometric mixture for the

Figure 5. Variation of the temperature exponent with the equivalence ratio for methane−air mixtures.

equivalence ratio was observed on the temperature exponent of methane−air mixtures. The temperature exponent is minimum for slightly richer mixtures and rises off for both rich and lean mixtures. The present experimental measurements of the laminar burning velocity show that a minimum value of the temperature exponent α exists for Φ = 1.1. The variation of α with equivalence ratio Φ can be correlated as α = 1.782Φ3 − 1.595Φ2 − 2.575Φ + 3.934

(3)

The present temperature exponent α is in good agreement with the numerical computations,21,25 as shown in Figure 5. The qualitative agreement with some experimental data2,5,6,8,9,22 is also observed. To understand this peculiar variation of temperature exponent α with Φ, the normalized adiabatic flame temperature Tad,Tu/Tad,300 and mole fractions Xi were analyzed for two different mixture temperatures, 300 and 600 K, as shown in Figure 6. As the mixture temperature is increased, a higher concentration of CO is observed for near-stoichiometric and slightly richer mixtures. This can be attributed to increased dissociation26 of CO2 to CO because of comparatively higher adiabatic flame temperatures for the 0.85 < Φ < 1.15 range. This is true for other stable species also which dissociate at higher temperatures for 0.85 < Φ < 1.15. This results in a relatively smaller increase in the adiabatic flame temperature (see Tad,Tu/Tad,300 variation in Figure 6), and hence, the burning velocity of mixtures for the mixture equivalence range of 0.85 < Φ < 1.15 increases at a smaller rate. However, the absolute

Figure 4. Variation of the laminar burning velocity of lean and rich methane−air mixtures at high temperatures. D

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given in Table 3. The reaction H + O2 ⇔ OH + O is the main chain-branching reaction with high activation energy Ea,26,27 which results in the production of O and OH radicals, which further accelerates the combustion process. This reaction has negative temperature dependence b with high pre-exponential factor A. However, other dominant reactions 53 and 98 have positive b and comparatively small magnitudes of A and Ea. The variation of normalized sensitivity of the dominated reaction H + O2 ⇔ OH + O with the temperature appears to be significant. Figure 8 shows the variation of methane-

Figure 6. Variation of species mole fractions and normalized adiabatic flame temperature with the equivalence ratio at two different temperatures.

values of the adiabatic flame temperature and burning velocity remain highest for slightly richer mixtures, even for higher mixture temperatures of the fuel−air mixtures, as compared to lean and very rich mixtures. This confirms the existence of the minimum value of temperature exponent α for slightly richer mixtures. This behavior has been captured well as shown by the curve corresponding to the temperature ratio (Tad,Tu/Tad,300) in Figure 6. Detailed sensitivity analysis of chemical reactions was performed to understand the sensitivity of the laminar burning velocity on various dominant chemical reactions in the given mechanisms. This further helped our understanding on the mixture dependency of the temperature exponent. Methanenormalized sensitivity ((ai/Xmax k )(∂Xk/∂ai)) of most sensitive reactions is computed for the stoichiometric methane−air mixture (Tu = 300 K) at the flame location and shown in Figure 7. The reaction parameters of three dominant reactions are

Figure 8. Methane-normalized sensitivity of the main chain-branching reaction H + O2 ⇔ OH + O for various methane−air mixtures at two different mixture temperatures.

normalized sensitivity at the flame front for various equivalence ratios at two different mixture temperatures of 300 and 600 K. The contribution of this reaction is maximum for stoichiometric mixtures at ambient temperature of 300 K. The normalized sensitivity of this main chain-branching reaction increases with the temperature for near-limit mixtures, whereas it slightly decreases for stoichiometric mixtures. An increase in the normalized sensitivity of this dominant reaction leads to higher production rates of radicals (O and OH), which enhance the burning velocity. Therefore, the burning velocity for nearlimit mixtures increases at a comparatively faster rate than for near-stoichiometric mixtures. Because of this potential effect, the temperature exponent is minimum for a slightly rich mixture. The normalized sensitivity of the other two dominant reactions also shows a qualitatively similar behavior for nearlimit and -stoichiometric mixtures. 4.3. Laminar Burning Velocity: Mixture Dependency. Figure 9a shows the variation of laminar burning velocities at 300 K and 1.0 atm pressure (Su,o) obtained from the power-law correlations at different equivalence ratios. It can be noted that the laminar burning velocity is a strong function of the mixture equivalence ratio. The present results match well with the data obtained from recent experiments.5,7−9,28 The comparison of the present experimental results to the computational predictions with various mechanisms21−23 is shown in Figure

Figure 7. Methane-normalized sensitivity at the flame front for the stoichiometric methane−air mixture at ambient temperature and pressure conditions.

Table 3. Reaction Parameters of Three Dominant Reactions in GRI-Mech 3.021 reaction number

reaction

A

b

Ea

38 53 98

H + O2 ⇔ O + OH H + CH4 ⇔ CH3 + H2 OH + CH4 ⇔ CH3 + H2O

2.65 × 1016 6.60 × 108 1.00 × 108

−0.7 1.6 1.6

17041.0 10840.0 3120.0

E

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Figure 10. Comparison of the measured laminar burning velocity to computations at elevated temperatures.

5. CONCLUSION The mixture and temperature dependency of the laminar burning velocity of premixed methane−air mixtures at higher mixture temperatures is studied. The measured burning velocities have a good agreement with both experimental and computational data at ambient conditions. For slightly richer mixtures, the temperature exponent and an increase in adiabatic flame temperatures were observed to be minimum. This is due to the fact that the normalized methane sensitivity of dominant reactions increases with the temperature for near-limit mixtures and slightly decreases for stoichiometric mixtures. The linear variation of the temperature exponent with mixture equivalence ratios should be discouraged. The maximum burning velocity is observed for slightly richer methane−air mixtures, similar to the computed results and unlike available experimental results (which peaks for lean or very rich mixtures at high temperatures because of inaccurate magnitude and variation of the temperature exponent with equivalence ratios). The offstoichiometric peaking of the burning velocity is due to the combined effect of the adiabatic flame temperature and dissociation of products. The proposed correlations can be used to extract burning velocities for flammable methane−air mixtures at any intermediate and/or elevated mixture temperatures.

Figure 9. Comparison of the laminar burning velocity for the methane−air mixture measured at ambient pressure and temperature with (a) experiments and (b) computations.

9b. The burning velocity of the stoichiometric methane−air mixture was observed to be 35.6 cm/s. The peak burning velocity of 36.9 cm/s is observed for a slightly richer mixture (Φ = 1.1). The variation of the burning velocity with equivalence ratios (continuous bold line in Figure 9b) can be correlated as Su,o = −0.786Φ3 + 1.05Φ2 + 0.423Φ − 0.340

(m/s)

■

(4)

4.4. Laminar Burning Velocity at Elevated Temperatures. The burning velocity magnitude should peak for nearstoichiometric mixtures even at higher mixture temperatures. Although this fact is true for the numerical results,21−23 it is not true for the experimental results available in the literature.2−9 Using the present correlations, the variation of the burning velocity with equivalence ratios at high temperatures can be obtained. Figure 10 shows the comparison between the present correlation results and those obtained from various mechanisms21−23 at different mixture temperatures. A comparison to all three mechanisms21−23 is made at 500 K temperature only, to avoid ambiguity in the presentation. The present correlated results are in good agreement with the predicted results of laminar burning velocities of premixed methane−air mixtures, even at very high temperatures. The burning velocity of the methane−air mixtures is consistently maximum for slightly rich mixtures at a given mixture temperature.

AUTHOR INFORMATION

Corresponding Author

*Telephone: +91-22-2576-7124. Fax: +91-22-2572-2602. Email: [email protected]. Notes

The authors declare no competing financial interest.

■

F

NOMENCLATURE A = pre-exponential factor Ainlet = channel cross-section at the inlet (m2) Af = cross-section at the flame front (m2) b = temperature exponent in the Arrhenius equation Ea = activation energy of the reaction (J/mol) Su,o = burning velocity at Tu,o (m/s) Su = laminar burning velocity at Tu (m/s) Tad,Tu = adiabatic flame temperature at Tu (K) Tad,300 = adiabatic flame temperature at 300 K (K) Tu,o = reference mixture temperature (K) dx.doi.org/10.1021/ef4009218 | Energy Fuels XXXX, XXX, XXX−XXX

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Uinlet = velocity of the mixture at the channel inlet (m/s) X = mole fraction α = temperature exponent ai = reaction model parameter Φ = equivalence ratio

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REFERENCES

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