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air premixed flames at low pressure
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 6 3 1 7 e6 3 2 4
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Laminar burning velocities and flame stability analysis of hydrogen/air premixed flames at low pressure Jhon Pareja*, Hugo J. Burbano, Andre´s Amell, Julia´n Carvajal Science and Technology of Gases and Rational Use of Energy Group, Faculty of Engineering. University of Antioquia, Calle 67 N 53-108 Bloque 20-447 Medellı´n, Colombia
article info
abstract
Article history:
An experimental and numerical study on laminar burning velocities of hydrogen/air flames
Received 23 November 2010
was performed at low pressure, room temperature, and different equivalence ratios.
Received in revised form
Flames were generated using a small contoured slot-type nozzle burner (5 mm 13.8 mm).
8 February 2011
Measurements of laminar burning velocity were conducted using the angle method
Accepted 8 February 2011
combined with Schlieren photography. Numerical calculations were also conducted using
Available online 11 March 2011
existing detailed reaction mechanisms and transport properties. Additionally, an analysis of the intrinsic flame instabilities of hydrogen/air flames at low pressure was performed.
Keywords:
Results show that the behavior of the laminar burning velocity is not regular when
Low pressure
decreasing pressure and that it depends on the equivalence ratio range. The behavior of the
Hydrogen
laminar burning velocity with decreasing pressure can be reasonably predicted using
Laminar burning velocity
existing reaction mechanisms; however changes in the magnitude of the laminar burning
Flame instability
velocity are underestimated. Finally, it has been found experimentally and proved analytically that the intrinsic flame instabilities are reduced when decreasing the pressure at sub-atmospheric conditions. Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Hydrogen (H2) is viewed by many as the ultimate “endobjective” fuel in order to solve the problems about world high energy demands, a future shortage of conventional fuels, and environmental pollution [1]. The design of combustion devices fueled with hydrogen demands advanced knowledge of the combustion properties of hydrogen. One of the most important properties is the laminar burning velocity, SL, since it determines the structure and the stability of the flames. The laminar burning velocity of hydrogen has been extensively studied in the past mainly at atmospheric and high pressures [2e6] due to its importance in the development of high-power combustors. However, to the best of authors’ knowledge, the availability of works on SL of H2 at low pressures is still limited
[7e10]. Fig. 1 compiles some of the data on SL of H2 at atmospheric and low pressures found in those works. Fine [7] measured SL of H2/air mixtures using the burner method at pressures within the range 0.21e0.97 atm at different equivalence ratios. Aung et al. [8] reported experimental data on SL of H2/air flames at 0.35 and 0.5 atm at different equivalence ratios using the spherical bomb technique. Kwon and Faeth [9] performed measurements at 0.3 and 0.5 atm using the spherical bomb technique with H2/O2/Ar mixtures at two equivalence ratios (f ¼ 0.6 and f ¼ 4.5) and with a H2/O2/He mixture at f ¼ 0.6. Sun et al. [10] derived computationally SL of outwardly propagating spherical H2/air flames at 0.6 atm within the range 0.6 f 5.0. As can be seen in Fig. 1 there are limitations of experimental data on SL at many equivalence ratios, there is not good agreement between experimental and
* Corresponding author. Tel.: þ57 4 219 85 45; fax: þ57 4 211 90 28. E-mail address: [email protected] (J. Pareja). 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.02.042
Laminar burning ve elocity, SL (cm/s)
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presented in this paper in order to explain the appearance of flame instabilities at certain mixture and pressure conditions.
Fine [7] at 0.97atm
350
Fine [7] at 0.6atm
300
Aung et al. [8] at 0.5atm
Aung et al. [8] at 1atm
Kwo n and Faeth. [9] at 1atm
250
Kwo n and Faeth [9] at 0.5atm
2.
Experimental method
2.1.
Experimental setup
Sun et al. [10] at 1atm
200
Sun et al. [10] at 0.6 atm
150 100 50 0 0
1
2
3
4
5
6
Equivalence ratio φ Fig. 1 e Laminar burning velocities of H2/air flames at atmospheric and low pressures. Markers: experimental results [7e9]; lines: numerical results [10].
numerical data at the same pressure condition, and the tendency about the effect of pressure at sub-atmospheric conditions on SL of H2 calculated by Sun et al. [10] has not been confirmed experimentally. Information on SL of H2 at low pressure is particularly important in Latin- American countries since many cities, with considerable population and then high energy consumption, are located at high altitude about sea level (low pressure atmospheres). On the other hand, data on SL at different equivalence ratios is of practical importance since industrial combustors usually work with forced air at lean equivalent ratios in order to reduce thermal NOx emissions while domestic combustors generally work with induced air at rich equivalence ratios due to power requirement and costs issues. For these reasons, in the present study, laminar burning velocities of hydrogen/air flames were determined experimentally and numerically at low pressures and within a wide range of equivalence ratios (0.6 f 4.4). Experiments were conducted using the burner stabilized flame technique with instantaneous Schlieren photography, and values of SL were determined with the angle method. In this technique only average values of SL can be obtained since local burning velocities vary along the flame front due to effects of stretch, curvature at the flame tip, and heat losses near the burner walls; however, the experimental methodology by Pareja et al. [11] was implemented to reduce these effects. Unlike previous studies, where sub-atmospheric conditions were simulated in pressure chambers [7e9], experiments were conducted at real pressure conditions in two places located at altitudes of 500 m.a.s.l. (P ¼ 0.947 atm) and 2300 m.a.s.l. (P ¼ 0.767 atm). The use of the burner stabilized flame technique was convenient regarding transportation and price of the experimental setup, and simplicity to determine SL. Experimental data of SL were compared with numerical calculations using existing reaction mechanisms in order to evaluate their performance on reproducing present experimental data and the effect of low pressure on SL of H2. Additionally an analysis of the behavior of intrinsic flame instabilities (i.e., hydrodynamic instability and diffusive-thermal instability) at low pressure, using existing formulations, was performed and it is
Fig. 2 shows a schematic diagram of the experimental setup implemented in this study. Flames were generated using a small burner with a contoured slot-type nozzle (5 mm 13.8 mm) in order to keep laminar Reynolds numbers at every equivalence ratio studied as well as to reduce the effects of flame stretch and curvature in the direction of the burner axis. The design of the burner nozzle allowed obtaining nearly uniform exit velocity profiles, which gave defined triangular flames with fairly straight edges. Additionally, a cooling system was implemented in order to keep the mixtures at a constant temperature. For the Schlieren technique, a high-intensity discharge Xenon lamp was used as light source. This light was focused with a biconvex lens (diameter ¼ 50.8 mm, focus length ¼ 38.1 mm) and a pin hole with diameter of 1 mm in order to achieve high resolution images of the flames. Next, light rays were directed to the test zone through a plane-convex lens (diameter ¼ 50.8 mm, focus length ¼ 250 mm). After that, deflected and non-deflected rays were focused again with an identical plane-convex lens and deflected rays were blocked with an adjustable slit while nondeflected rays were captured with a monochromatic highresolution high-speed camera (Basler scA1400-30 gm, 1392x1040 pixels, 30 fps). In order to obtain high resolution images of such small flames, a Macro camera lens (Sigma, diameter ¼ 72 mm, focus length ¼ 150 mm, f/2.8) was employed. Images were transmitted to a computer through an Ethernet connection (1 Gbps) to monitor the flames in real time and to take the Schlieren photographs. High purity certified gases were used to generate the required mixtures at every equivalence ratio. Hydrogen and air flows were measured using variable area flowmeters specifically calibrated for each gas. Hydrogen and air were mixed before entering the burner and a mixture chamber inside the burner was used in order to guarantee a thorough mixing of the reactants. Errors in the final compositions of the mixtures were estimated lower than 2%.
2.2.
Determination of the laminar burning velocity
Laminar burning velocities were determined by the burner stabilized flame method with Schlieren photography. In this technique, the flame propagates toward the unburned mixture at an angle q as shown in Fig. 3. The velocity component of the unburned mixture which is normal to the flame front is identical to the laminar burning velocity, therefore SL is calculated as follows: SL ¼ UsinðqÞ
(1)
Where U is the average velocity of the unburned mixture at the burner exit. This method is usually called as the angle method. In this technique, local burning velocities vary along the flame front due to the effects of flame stretch and heat loss, and only average values can be obtained. Nevertheless,
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Fig. 2 e Schematic diagram of the experimental setup.
the methodology used by Pareja et al. [11] showed that the accuracy of the angle method can be enhanced with some improvements. That methodology includes: generating the flames with a contoured slot-type nozzle with the aim of obtaining a well defined triangular flame for determining q more accurately as well as obtaining a nearly uniform exit velocity profile; focusing the camera in the center of the length; and setting mean velocities at the nozzle exit about 2.5 and 4 times the expected laminar burning velocity in order to keep flame angles among 40 and 45 as well as to avoid flashback. The use of a slot-type nozzle enables to remove the effects of flame stretch and curvature in the direction of the burner axis and reduces curvature at the flame tip [11]. Recently Selle et al. [12] reported that the angle method is not adequate to determine SL of hydrogen flames since they found that the tip of the flames at f ¼ 0.6 and f ¼ 0.8 kept oscillating and they obtained flashback at f ¼ 0.8. However, those results were obtained by direct numerical simulations and such behaviors were not observed experimentally in any flame of the present study. The two parameters of equation (1) were determined as follows. The mean velocity at the exit of the burner nozzle was calculated from the nozzle area and the flows of hydrogen and air. The flame angle was measured from Schlieren photographs using a flame front detection program. A background image previously taken before experiments was subtracted from the flame image, and the contrast of the resulting image was increased to facilitate the flame front detection. Due to the high resolution achieved in the Schlieren images, the program detected the inner and outer edges of the flame front,
and thus the corresponding flame angles were calculated. However, differences between these two angles were found to be lower than 0.2% and therefore SL values reported in the present study correspond to the inner edge of the flame front.
2.3.
Experimental design and error
Experiments were performed at room temperature and two pressures of 0.947 atm and 0.767 atm. To reach those pressures the measurements were carried out in two Colombian towns, Santa Fe´ de Antioquia (500 m.a.s.l.) and Yarumal (2300 m.a.s.l.) and therefore pressure variations were negligible (2 mm Hg). Equivalence ratio was varied from lean conditions (f ¼ 0.6) to ultra-rich conditions (f ¼ 4.4). The mean velocity at the exit of the burner nozzle and the flame angle were defined as response variables. Room temperature affects the measurement of the hydrogen and air flows, however this effect is perfectly known for variable area flowmeters and its calibration curves were modified according to each temperature condition. For every equivalence ratio, 100 photographs were taken and processed in order to achieve reliable data of the flame angle. The errors of the measurement of SL at every condition studied were calculated as the error propagation of the measurement of the mean velocity at the exit of the burner nozzle and the measurement of the flame angle. The error of the measurement of U was calculated from the error of the measurement of the nozzle area and the H2 and air flows while the error of measuring the flame angle was calculated through statistical treatment of the 100 flame front photographs. Standard deviations of q were lower than 1 .
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Fig. 4 e Results of laminar burning velocities of H2/air flames at lean equivalence ratios and low pressure.
Fig. 3 e Burner stabilized flame technique (angle method).
3.
Numerical method
Numerical calculations of SL were conducted using the onedimensional premixed flame code PREMIX of the CHEMKINPRO package. For comparison, the present simulations considered the mechanisms proposed by Mueller et al. [13] and Li et al. [14]. For an accurate calculation of SL recommendations of Bongers and De Goey [15] were followed; transport properties were evaluated using the multicomponent diffusion model and thermal diffusion (Soret effect) was included in the calculations due to its importance on the hydrogen oxidation [16]. Additionally, it has been reported that the accuracy of the calculated SL is highly sensitive to the number of grid points used in the calculations; using a low number of points can lead to errors from 5 to 10% [17,18]. Therefore, according to Dlugogorski et al. [19], GRAD and CURV values were set lower than 0.01 to generate a grid of more than 1000 points, where SL values converged and the flame temperature approached the adiabatic flame temperature. It is important to mention that the mechanism of Li et al. [14] is an update based on the mechanism of Mueller et al. [13], it showed good agreement with previous experimental results of SL at high-pressure but it was not tested at low pressure in Ref. [14]
4.
pressures of 0.947 atm and 0.767 atm, along with results of the numerical calculations using the mechanisms of Mueller et al. [13] and Li et al. [14] at the same conditions as the experiments. As can be seen in Fig. 4, SL was unsuitable to be determine experimentally at f < 0.8 and f < 0.6, at P ¼ 0.947 atm and P ¼ 0.767 atm, respectively, due to the appearance of intrinsic flame instabilities at those conditions, which will be discuss in detail later. SL of H2/air flames increase with the decrease of pressure. The mechanisms of Mueller et al. [13] and Li et al. [14] predict that increase of SL, however, the results with the mechanism of Mueller et al. [13] are in better agreement with present experimental results while the mechanism of Li et al. [14] tends to underestimate them. It was found experimentally that the changes on the values of SL are higher than those predicted by the mechanisms. Additionally, at f < 1.1 SL is fairly equal at P ¼ 0.947 atm and P ¼ 0.767 atm, and both mechanisms fail to predict that behavior of SL. In the range of equivalence ratios of Fig. 5, SL decreases with the decrease of pressure. This tendency is also predicted by the numerical results using both reaction mechanisms
Results and discussion
4.1. Results of laminar burning velocities at low pressure Figs. 4e6 present the experimental results of the laminar burning velocities of H2/air flames for lean, rich, and ultra-rich equivalence ratios, respectively, at room temperature and
Fig. 5 e Results of laminar burning velocities of H2/air flames at rich equivalence ratios and low pressure.
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propagated uncertainty of the quantities measured to determine it at every equivalence ratio, and that since local burning velocities vary along the flame front due to the effects of flame stretch and heat loss, the angle method may deviate as much as 3.6% (around 11 cm/s) with respect to more accurate techniques [11] This may explained the variation of some experimental values of SL from the expected trend, particularly at ultra-rich conditions.
4.2.
Fig. 6 e Results of laminar burning velocities of H2/air flames at ultra-rich equivalence ratios and low pressure.
[13,14]. However, the mechanism of Mueller et al. [13] predicts better present experimental results at the highest values of SL than the mechanism of Li et al. [14], although both mechanisms fail to reproduce experimental values of SL within the range 2.1 < f < 2.4 Regarding Fig. 6, SL does not present a significant change with the decrease of pressure in this range of equivalence ratios. In this case, the numerical results using the mechanism of Li et al. [14] are in good agreement with present experimental results while the results using the mechanism of Mueller et al. [13] overestimate the experimental values of laminar burning velocity. For f > 4.4 and f > 4.0, at P ¼ 0.947 atm and P ¼ 0.767 atm, respectively, SL was unsuitable to determine experimentally because flame temperatures were very low, and therefore those flames were difficult to be detected using the Schlieren technique. Error of present data was estimated at every equivalence ratio studied as explained in Section 2.3. Error bars are plotted along with experimental data in Figs. 4e6. It was found that maximum error was around 2%, i.e. around 6 cm/s at the highest value of SL measured. However, it has to be kept in mind that this value represents the deviation of an average value of SL due to the
Sensitivity analysis
In order to understand the behavior of SL at sub-atmospheric pressure and at different mixture conditions, a sensitivity analysis of the laminar burning velocity of H2/air flames with respect to reaction rate coefficients was performed at three equivalence ratios (f ¼ 0.6, 1.6, 4.0) and the two pressures considered in this study. The mechanism of Mueller al. [13] was employed in this analysis and the results of normalized sensitivity coefficients of the most important reactions are summarized in Fig. 7. At f ¼ 0.6 results show that chain-propagating reaction R7, chain reaction R10, and chain-branching reactions R11 and R12 have important positive sensitivity coefficients while chainterminating reactions R2, R5, and R8 as well as chain-initiating reaction R6 have negative sensitivity coefficients where threeebody reaction R8 has the highest sensitivity. Reaction R8 competes with R7 and R12 for the consumption of H radical, and R5 competes with R10 for consumption of OH radical. Decreasing pressure, the sensitivity of R8 has a significant reduction while the sensitivity coefficients of the R7 and R12 decrease in smaller magnitudes, which may explain the increase of SL when decreasing the pressure at lean equivalence ratios. In comparison with lean conditions, at the equivalence ratios corresponding to the highest values of SL (f ¼ 1.6), the sensitivity of reactions R7, R10 and R11 decrease, while the sensitivity of reaction of R12 increases and the sensitivity of the threeebody reaction R8 becomes positive. On the other hand, negative sensitivity of threeebody reaction R3 becomes significant. When decreasing pressure the sensitivity coefficient of R12 diminishes while the coefficient of R6, its competitor reaction with respect to H radical consumption,
Fig. 7 e Normalized sensitivity coefficients for the mechanism of Mueller et al. [13] at different pressures and various equivalence ratios.
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remains almost constant, showing the important role of R6 in the reduction of SL at those equivalence ratios. Finally, at ultrarich equivalence ratios (f ¼ 4.4), positive sensitivity of reactions R7 and R12 increase while those of R10 and R11 decrease when comparing with lean and rich equivalence ratios. On the other hand, negative sensitivity of chain-initiating reactions R3 and R6 increase. However, when decreasing pressure the sensitivity coefficients of the most important reactions have similar reductions, which would explain the insensitivity of SL with pressure changes at ultra-rich conditions. As can be notice, the most important reactions that may be responsible of the behavior of SL of hydrogen at low pressures are reactions involving consumption/production of H radical.
4.3.
Intrinsic flame instabilities
Fig. 8 shows instantaneous Schlieren photographs of H2/air flames at different equivalence ratios, at room temperature and studied pressures. At P ¼ 0.947 atm, flames exhibited instabilities at f < 0.8 and flame tips occasionally split. However, with the decrease of pressure until P ¼ 0.767 atm, those instabilities disappeared, and smooth and stable flames were obtained at the same equivalence ratios. Deformations of the flame front mentioned before are due to intrinsic flame instabilities, namely, hydrodynamic instability, diffusivethermal instability, and buoyancy-driven instability [20]. The later is not significant in the present study since it is only present at very low burning velocities and equivalence ratios near flammability limits. Hydrodynamic instability is caused by the thermal expansion across the flame front; essentially this instability is always present and the flame is unstable to disturbances of all wavelengths. On the other hand, diffusivethermal instability is a direct consequence of the non-equidiffusive nature of the premixed gases, since there is no parity between the heat conduction from the flame to the unburned mixture and the reactants diffusion towards the flame. Diffusive-thermal instability is important for small-scale disturbances, and it restrains hydrodynamic instability or increases flame wrinkles depending on the Lewis number of
the mixture, Le, which is defined as the ratio of the heat diffusivity of the unburned mixture to the mass diffusivity of the limiting reactant into the abundant inert. When Le is larger than unity diffusive-thermal instability is expected to restrain hydrodynamic instability [21]. However this parameter is insensitive to pressure changes and it is not enough to explain the behavior of intrinsic flame instabilities at low pressure. In order to estimate the flame instability characteristics at low pressure, the growth rate of the flame front disturbances, s, was calculated using the formulation of Sivashinsky [21], later corrected by Yuan et al. [22] for the case of Le lower than unity. Then s was estimated as: s ¼ U0 SL k U1 ak2 4ad2T k4
(2)
Where U0 ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 þ 32 33 3 1þ3
U1 ¼
3ð1 3Þ2 3ln3ð2U0 þ 1 þ 3Þ 2ð1 3Þ½3 þ ð1 þ 3ÞU0
3ð1 U0 Þð3 þ U0 Þbð1 LeÞ 2ð1 3Þ½3 þ ð1 þ 3ÞU0
1=31 Z
0
lnð1 þ xÞ dx x
k is the wave number of the disturbance, 3 ¼ rb/ru the ratio of densities of the burned and unburned gases, a the thermal diffusivity, b the Zeldovich number, and dT the flame thickness. The first term of the right side of equation (2) represents the effect of hydrodynamic instability and it is positive at any wave number; the second term estimates the effect of diffusive-thermal effect (depending if U1 is positive or negative); and the third term includes the temperature relaxation by diffusion proposed by Yuan et al. [22]. Lewis numbers of the H2/air mixtures were determined using the relation proposed by Addabbo et al. [23]: Le ¼ 1 þ
ðLeE 1Þ þ ðLeD 1ÞA 1þA
Fig. 8 e Instantaneous Schlieren photographs of H2/air flames at different pressures and various equivalence ratios.
(3)
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2000 1800 1600 Growth rate σ (1/s) G
1400 1200 1000 P=0.947 atm P=0.767 atm
800 600 400 200 0 -200 0
Fig. 9 e Lewis number of H2/air as a function of equivalence ratio.
where, LeE and LeD correspond to the Lewis number of the reactant that is in excess or deficiency, respectively. A ¼ 1 þ b (F 1) is a measure of the mixture strength, where F ¼ 1/f at lean conditions and F ¼ f at rich conditions. The Zeldovich number was calculated as b ¼ EaðTb Tu Þ=R T2b , with R the universal gas constant, Tb the temperature of the burned gases, Tu the temperature of the unburned gases, and Ea the global activation energy. For off-stoichiometric conditions, Ea was determined with the methodology proposed by Egolfopolous and Law [17], where Ea ¼ 2R hdlnðf Þ=dð1=Tb ÞiP , with f the mass burning rate. For near-stoichiometric conditions, Ea was interpolated from the off-stoichiometric results, as recommended by Jomaas et al. [24]. The flame thickness was determined using the temperature profile of the final solution of the numerical calculation of SL, and through the following definition: dT ¼
ðTb Tu Þ ðdT=dxÞmax
(4)
Where (dT/dx)max is the maximum temperature gradient in the temperature profile [10,25]. The numerical results obtained with the mechanism of Mueller et al. [13] were used for this calculation.
Fig. 10 e Flame thickness of H2/air at low pressure as a function of equivalence ratio.
2000
4000
8000 10000 6000 Wave number k (1/m)
12000
14000
16000
Fig. 11 e Effects of pressure on the growth rate of flame front instabilities for a H2/air flame at f [ 0.6.
Figs. 9 and 10 show the results of the Lewis number of the mixture and the flame thickness at different equivalence ratios estimated by equations (3) and (4), respectively. Le of the mixtures at lean conditions (f < 0.9) are lower than unity, however flames did not exhibited intrinsic instabilities at f ¼ 0.8 for P ¼ 0.947 atm and 0.6 f 0.8 for P ¼ 0.767 atm. Fig. 11 shows the effects of low pressure on the growth rate of the flame front instabilities calculated by equation (2) at f ¼ 0.6. With the decrease of pressure the wave number region where flame front is unstable narrows to lower wave numbers and the maximum growth rate becomes smaller. This is because the thermal diffusivity is inversely proportional to pressure. The decrease of pressure increases thermal diffusivity and so flame thickness (Fig. 10), which results in a strong diffusivethermal effect and a weak hydrodynamic instability [25,26].
5.
Conclusions
Measurements of laminar burning velocities of H2/air flames at low pressure, room temperature, and different equivalence ratios were conducted using the angle method. Numerical calculations of SL were also performed using existing detailed reaction mechanisms and compared with experimental results. Additionally, the effect of low pressure on the intrinsic flame instabilities was analyzed. From the results, their analysis and discussion, the following conclusions can be stated: 1. The mechanism of Mueller et al. [13] predicted reasonably well the experimental results of the laminar burning velocities at lean and rich equivalence ratios; however it tended to overestimate experimental values of SL at ultrarich equivalence ratios. 2. The mechanism of Li et al. [14] underestimated the experimental values of SL at lean and rich equivalence ratios. However, at ultra-rich equivalence ratios, the experimental and the numerical results of SL are in good agreement using this mechanism. 3. The mechanisms of Mueller et al. [13] and Li et al. [14] predicted small changes in the magnitude of SL when
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decreasing pressure but the changes found experimentally were higher than those numerically predicted. 4. The behavior of the laminar burning velocity of H2/air flames at different equivalence ratios with the decrease of pressure is not regular. At lean equivalence ratios SL increases with the decrease of pressure; at rich equivalence ratios SL decreases with decreasing pressure; and at ultrarich equivalence ratios SL does not present significant variations when decreasing pressure. 5. Reactions of consumption/production of the H radical such as R6, R7, R8 and R12 have a significant role on the irregular behavior of SL at different equivalence ratios when decreasing pressure. 6. Intrinsic flame instabilities diminish with decreasing pressure allowing the measurement the laminar burning velocity at low equivalence ratios using burner-stabilized flames.
Acknowledgments Authors acknowledge the support of the Committee for Research Development e CODI and the Science and Technology of Gases and Rational Use of Energy Group, University of Antioquia, for funding the project MC-08-1-12. Authors thank to the Colombian Department of Science and Technology e COLCIENCIAS for the partial funding of Mr. Pareja and Mr. Burbano as “Jo´venes Investigadores e Innovadores2008” as well as to the directors of the campuses of University of Antioquia at Santa Fe de Antioquia and Yarumal for providing the facilities where present experiments were conducted. The authors also thank Professor Frederick Dryer at Princeton University for providing the reaction mechanism of Li et al. [14].
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[6] Dahoe AE. Laminar burning velocities of hydrogen-air mixtures from closed vessel gas explosions. J Loss Prev Process Ind 2005;18(3):152e66. [7] Fine B. Stability limits and burning velocities of laminar hydrogen-air flames at reduced pressure. NACA Technical Note 1956;3833. [8] Aung KT, Hassan MI, Faeth GM. Effects of pressure and nitrogen dilution on flame/stretch interactions of laminar premixed H2/O2/N2 flames. Combust Flame 1998;112(1e2): 1e15. [9] Kwon OC, Faeth GM. Flame/stretch interactions of premixed hydrogen-fueled flames: measurements and predictions. Combust Flame 2001;124(4):590e610. [10] Sun CJ, Sung CJ, He L, Law CK. Dynamics of weakly stretched flames: quantitative description and extraction of global flame parameters. Combust Flame 1999;118(1e2): 108e28. [11] Pareja J, Burbano HJ, Ogami Y. Measurements of the laminar burning velocity of hydrogeneair premixed flames. Int J Hydrogen Energy 2010;35(4):1812e8. [12] Selle L, Poinsot T, Ferret B. Experimental and numerical study of the accuracy of flame-speed measurements for methane/air combustion in a slot burner. Combust Flame 2011;158(1):146e54. [13] Mueller MA, Kim TJ, Yetter RA, Dryer FL. Flow reactor studies and kinetic modeling of the H2/O2 reaction. Int J Chem Kinet 1999;31:113e25. [14] Li J, Zhao Z, Kazakov, Chaos M, Dryer FL, Scire JJ. A Comprehensive kinetic mechanism for CO, CH2O, and CH3OH combustion. Int J Chem Kinet 2007;39(3):109e36. [15] Bongers H, De Goey LPH. The effect of simplified transport modeling on the burning velocity of laminar premixed flames. Combust Sci Tech 2003;175:1915e28. [16] Ferna´ndez-Galisteo D, Sa´nchez AL, Lin˜an A, Williams FA. One-step reduced kinetics for lean hydrogen-air deflagration. Combust Flame 2009;156(5):985e96. [17] Egolfopoulos FN, Law CK. Chain mechanisms in the overall reaction orders in laminar flame propagation. Combust Flame 1990;80(1):7e16. [18] Konnov AA, Riemeijer R, de Goey LPH. Adiabatic laminar burning velocities of CH4 þ H2 þ air flames at low pressures. Fuel 2010;89(7):1392e6. [19] Dlugogorski BZ, Hichens RK, Kennedy EM, Bozzelli JW. Propagation of laminar flames in wet premixed natural gasair mixtures. Trans IChemE 1998;76(B2):81e9. [20] Law CK. Combustion physics. 1st ed. Cambridge: Cambridge University Press; 2006. [21] Sivashinsky GI. Instabilities, pattern formation and turbulence in flames. Annu Rev Fluid Mech 1983;15:179e99. [22] Yuan J, Ju Y, Law CK. On flame-front instability at elevated pressures. Proc Combust Inst 2007;31(1):1267e74. [23] Addabbo R, Bechtold JK, Matalon M. Wrinkling of spherically expanding flames. Proc Combust Inst 2002;29(2):1527e35. [24] Jomaas G, Law CK, Bechtold JK. On transition to cellularity in expanding spherical flames. J Fluid Mech 2007;583:1e26. [25] Law CK, Kwon OC. Effects of hydrocarbon substitution on atmospheric hydrogeneair flame propagation. Int J Hydrogen Energy 2004;29(8):867e79. [26] Law CK, Jomaas G, Bechtold JK. Cellular instabilities of expanding hydrogen/propane spherical flames at elevated pressures: theory and experiment. Proc Combust Inst 2005;30 (1):159e67.
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Laminar burning velocities and flame stability analysis of hydrogen/air premixed flames at low pressure Jhon Pareja*, Hugo J. Burbano, Andre´s Amell, Julia´n Carvajal Science and Technology of Gases and Rational Use of Energy Group, Faculty of Engineering. University of Antioquia, Calle 67 N 53-108 Bloque 20-447 Medellı´n, Colombia
article info
abstract
Article history:
An experimental and numerical study on laminar burning velocities of hydrogen/air flames
Received 23 November 2010
was performed at low pressure, room temperature, and different equivalence ratios.
Received in revised form
Flames were generated using a small contoured slot-type nozzle burner (5 mm 13.8 mm).
8 February 2011
Measurements of laminar burning velocity were conducted using the angle method
Accepted 8 February 2011
combined with Schlieren photography. Numerical calculations were also conducted using
Available online 11 March 2011
existing detailed reaction mechanisms and transport properties. Additionally, an analysis of the intrinsic flame instabilities of hydrogen/air flames at low pressure was performed.
Keywords:
Results show that the behavior of the laminar burning velocity is not regular when
Low pressure
decreasing pressure and that it depends on the equivalence ratio range. The behavior of the
Hydrogen
laminar burning velocity with decreasing pressure can be reasonably predicted using
Laminar burning velocity
existing reaction mechanisms; however changes in the magnitude of the laminar burning
Flame instability
velocity are underestimated. Finally, it has been found experimentally and proved analytically that the intrinsic flame instabilities are reduced when decreasing the pressure at sub-atmospheric conditions. Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Hydrogen (H2) is viewed by many as the ultimate “endobjective” fuel in order to solve the problems about world high energy demands, a future shortage of conventional fuels, and environmental pollution [1]. The design of combustion devices fueled with hydrogen demands advanced knowledge of the combustion properties of hydrogen. One of the most important properties is the laminar burning velocity, SL, since it determines the structure and the stability of the flames. The laminar burning velocity of hydrogen has been extensively studied in the past mainly at atmospheric and high pressures [2e6] due to its importance in the development of high-power combustors. However, to the best of authors’ knowledge, the availability of works on SL of H2 at low pressures is still limited
[7e10]. Fig. 1 compiles some of the data on SL of H2 at atmospheric and low pressures found in those works. Fine [7] measured SL of H2/air mixtures using the burner method at pressures within the range 0.21e0.97 atm at different equivalence ratios. Aung et al. [8] reported experimental data on SL of H2/air flames at 0.35 and 0.5 atm at different equivalence ratios using the spherical bomb technique. Kwon and Faeth [9] performed measurements at 0.3 and 0.5 atm using the spherical bomb technique with H2/O2/Ar mixtures at two equivalence ratios (f ¼ 0.6 and f ¼ 4.5) and with a H2/O2/He mixture at f ¼ 0.6. Sun et al. [10] derived computationally SL of outwardly propagating spherical H2/air flames at 0.6 atm within the range 0.6 f 5.0. As can be seen in Fig. 1 there are limitations of experimental data on SL at many equivalence ratios, there is not good agreement between experimental and
* Corresponding author. Tel.: þ57 4 219 85 45; fax: þ57 4 211 90 28. E-mail address: [email protected] (J. Pareja). 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.02.042
Laminar burning ve elocity, SL (cm/s)
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400
presented in this paper in order to explain the appearance of flame instabilities at certain mixture and pressure conditions.
Fine [7] at 0.97atm
350
Fine [7] at 0.6atm
300
Aung et al. [8] at 0.5atm
Aung et al. [8] at 1atm
Kwo n and Faeth. [9] at 1atm
250
Kwo n and Faeth [9] at 0.5atm
2.
Experimental method
2.1.
Experimental setup
Sun et al. [10] at 1atm
200
Sun et al. [10] at 0.6 atm
150 100 50 0 0
1
2
3
4
5
6
Equivalence ratio φ Fig. 1 e Laminar burning velocities of H2/air flames at atmospheric and low pressures. Markers: experimental results [7e9]; lines: numerical results [10].
numerical data at the same pressure condition, and the tendency about the effect of pressure at sub-atmospheric conditions on SL of H2 calculated by Sun et al. [10] has not been confirmed experimentally. Information on SL of H2 at low pressure is particularly important in Latin- American countries since many cities, with considerable population and then high energy consumption, are located at high altitude about sea level (low pressure atmospheres). On the other hand, data on SL at different equivalence ratios is of practical importance since industrial combustors usually work with forced air at lean equivalent ratios in order to reduce thermal NOx emissions while domestic combustors generally work with induced air at rich equivalence ratios due to power requirement and costs issues. For these reasons, in the present study, laminar burning velocities of hydrogen/air flames were determined experimentally and numerically at low pressures and within a wide range of equivalence ratios (0.6 f 4.4). Experiments were conducted using the burner stabilized flame technique with instantaneous Schlieren photography, and values of SL were determined with the angle method. In this technique only average values of SL can be obtained since local burning velocities vary along the flame front due to effects of stretch, curvature at the flame tip, and heat losses near the burner walls; however, the experimental methodology by Pareja et al. [11] was implemented to reduce these effects. Unlike previous studies, where sub-atmospheric conditions were simulated in pressure chambers [7e9], experiments were conducted at real pressure conditions in two places located at altitudes of 500 m.a.s.l. (P ¼ 0.947 atm) and 2300 m.a.s.l. (P ¼ 0.767 atm). The use of the burner stabilized flame technique was convenient regarding transportation and price of the experimental setup, and simplicity to determine SL. Experimental data of SL were compared with numerical calculations using existing reaction mechanisms in order to evaluate their performance on reproducing present experimental data and the effect of low pressure on SL of H2. Additionally an analysis of the behavior of intrinsic flame instabilities (i.e., hydrodynamic instability and diffusive-thermal instability) at low pressure, using existing formulations, was performed and it is
Fig. 2 shows a schematic diagram of the experimental setup implemented in this study. Flames were generated using a small burner with a contoured slot-type nozzle (5 mm 13.8 mm) in order to keep laminar Reynolds numbers at every equivalence ratio studied as well as to reduce the effects of flame stretch and curvature in the direction of the burner axis. The design of the burner nozzle allowed obtaining nearly uniform exit velocity profiles, which gave defined triangular flames with fairly straight edges. Additionally, a cooling system was implemented in order to keep the mixtures at a constant temperature. For the Schlieren technique, a high-intensity discharge Xenon lamp was used as light source. This light was focused with a biconvex lens (diameter ¼ 50.8 mm, focus length ¼ 38.1 mm) and a pin hole with diameter of 1 mm in order to achieve high resolution images of the flames. Next, light rays were directed to the test zone through a plane-convex lens (diameter ¼ 50.8 mm, focus length ¼ 250 mm). After that, deflected and non-deflected rays were focused again with an identical plane-convex lens and deflected rays were blocked with an adjustable slit while nondeflected rays were captured with a monochromatic highresolution high-speed camera (Basler scA1400-30 gm, 1392x1040 pixels, 30 fps). In order to obtain high resolution images of such small flames, a Macro camera lens (Sigma, diameter ¼ 72 mm, focus length ¼ 150 mm, f/2.8) was employed. Images were transmitted to a computer through an Ethernet connection (1 Gbps) to monitor the flames in real time and to take the Schlieren photographs. High purity certified gases were used to generate the required mixtures at every equivalence ratio. Hydrogen and air flows were measured using variable area flowmeters specifically calibrated for each gas. Hydrogen and air were mixed before entering the burner and a mixture chamber inside the burner was used in order to guarantee a thorough mixing of the reactants. Errors in the final compositions of the mixtures were estimated lower than 2%.
2.2.
Determination of the laminar burning velocity
Laminar burning velocities were determined by the burner stabilized flame method with Schlieren photography. In this technique, the flame propagates toward the unburned mixture at an angle q as shown in Fig. 3. The velocity component of the unburned mixture which is normal to the flame front is identical to the laminar burning velocity, therefore SL is calculated as follows: SL ¼ UsinðqÞ
(1)
Where U is the average velocity of the unburned mixture at the burner exit. This method is usually called as the angle method. In this technique, local burning velocities vary along the flame front due to the effects of flame stretch and heat loss, and only average values can be obtained. Nevertheless,
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Fig. 2 e Schematic diagram of the experimental setup.
the methodology used by Pareja et al. [11] showed that the accuracy of the angle method can be enhanced with some improvements. That methodology includes: generating the flames with a contoured slot-type nozzle with the aim of obtaining a well defined triangular flame for determining q more accurately as well as obtaining a nearly uniform exit velocity profile; focusing the camera in the center of the length; and setting mean velocities at the nozzle exit about 2.5 and 4 times the expected laminar burning velocity in order to keep flame angles among 40 and 45 as well as to avoid flashback. The use of a slot-type nozzle enables to remove the effects of flame stretch and curvature in the direction of the burner axis and reduces curvature at the flame tip [11]. Recently Selle et al. [12] reported that the angle method is not adequate to determine SL of hydrogen flames since they found that the tip of the flames at f ¼ 0.6 and f ¼ 0.8 kept oscillating and they obtained flashback at f ¼ 0.8. However, those results were obtained by direct numerical simulations and such behaviors were not observed experimentally in any flame of the present study. The two parameters of equation (1) were determined as follows. The mean velocity at the exit of the burner nozzle was calculated from the nozzle area and the flows of hydrogen and air. The flame angle was measured from Schlieren photographs using a flame front detection program. A background image previously taken before experiments was subtracted from the flame image, and the contrast of the resulting image was increased to facilitate the flame front detection. Due to the high resolution achieved in the Schlieren images, the program detected the inner and outer edges of the flame front,
and thus the corresponding flame angles were calculated. However, differences between these two angles were found to be lower than 0.2% and therefore SL values reported in the present study correspond to the inner edge of the flame front.
2.3.
Experimental design and error
Experiments were performed at room temperature and two pressures of 0.947 atm and 0.767 atm. To reach those pressures the measurements were carried out in two Colombian towns, Santa Fe´ de Antioquia (500 m.a.s.l.) and Yarumal (2300 m.a.s.l.) and therefore pressure variations were negligible (2 mm Hg). Equivalence ratio was varied from lean conditions (f ¼ 0.6) to ultra-rich conditions (f ¼ 4.4). The mean velocity at the exit of the burner nozzle and the flame angle were defined as response variables. Room temperature affects the measurement of the hydrogen and air flows, however this effect is perfectly known for variable area flowmeters and its calibration curves were modified according to each temperature condition. For every equivalence ratio, 100 photographs were taken and processed in order to achieve reliable data of the flame angle. The errors of the measurement of SL at every condition studied were calculated as the error propagation of the measurement of the mean velocity at the exit of the burner nozzle and the measurement of the flame angle. The error of the measurement of U was calculated from the error of the measurement of the nozzle area and the H2 and air flows while the error of measuring the flame angle was calculated through statistical treatment of the 100 flame front photographs. Standard deviations of q were lower than 1 .
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Fig. 4 e Results of laminar burning velocities of H2/air flames at lean equivalence ratios and low pressure.
Fig. 3 e Burner stabilized flame technique (angle method).
3.
Numerical method
Numerical calculations of SL were conducted using the onedimensional premixed flame code PREMIX of the CHEMKINPRO package. For comparison, the present simulations considered the mechanisms proposed by Mueller et al. [13] and Li et al. [14]. For an accurate calculation of SL recommendations of Bongers and De Goey [15] were followed; transport properties were evaluated using the multicomponent diffusion model and thermal diffusion (Soret effect) was included in the calculations due to its importance on the hydrogen oxidation [16]. Additionally, it has been reported that the accuracy of the calculated SL is highly sensitive to the number of grid points used in the calculations; using a low number of points can lead to errors from 5 to 10% [17,18]. Therefore, according to Dlugogorski et al. [19], GRAD and CURV values were set lower than 0.01 to generate a grid of more than 1000 points, where SL values converged and the flame temperature approached the adiabatic flame temperature. It is important to mention that the mechanism of Li et al. [14] is an update based on the mechanism of Mueller et al. [13], it showed good agreement with previous experimental results of SL at high-pressure but it was not tested at low pressure in Ref. [14]
4.
pressures of 0.947 atm and 0.767 atm, along with results of the numerical calculations using the mechanisms of Mueller et al. [13] and Li et al. [14] at the same conditions as the experiments. As can be seen in Fig. 4, SL was unsuitable to be determine experimentally at f < 0.8 and f < 0.6, at P ¼ 0.947 atm and P ¼ 0.767 atm, respectively, due to the appearance of intrinsic flame instabilities at those conditions, which will be discuss in detail later. SL of H2/air flames increase with the decrease of pressure. The mechanisms of Mueller et al. [13] and Li et al. [14] predict that increase of SL, however, the results with the mechanism of Mueller et al. [13] are in better agreement with present experimental results while the mechanism of Li et al. [14] tends to underestimate them. It was found experimentally that the changes on the values of SL are higher than those predicted by the mechanisms. Additionally, at f < 1.1 SL is fairly equal at P ¼ 0.947 atm and P ¼ 0.767 atm, and both mechanisms fail to predict that behavior of SL. In the range of equivalence ratios of Fig. 5, SL decreases with the decrease of pressure. This tendency is also predicted by the numerical results using both reaction mechanisms
Results and discussion
4.1. Results of laminar burning velocities at low pressure Figs. 4e6 present the experimental results of the laminar burning velocities of H2/air flames for lean, rich, and ultra-rich equivalence ratios, respectively, at room temperature and
Fig. 5 e Results of laminar burning velocities of H2/air flames at rich equivalence ratios and low pressure.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 6 3 1 7 e6 3 2 4
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propagated uncertainty of the quantities measured to determine it at every equivalence ratio, and that since local burning velocities vary along the flame front due to the effects of flame stretch and heat loss, the angle method may deviate as much as 3.6% (around 11 cm/s) with respect to more accurate techniques [11] This may explained the variation of some experimental values of SL from the expected trend, particularly at ultra-rich conditions.
4.2.
Fig. 6 e Results of laminar burning velocities of H2/air flames at ultra-rich equivalence ratios and low pressure.
[13,14]. However, the mechanism of Mueller et al. [13] predicts better present experimental results at the highest values of SL than the mechanism of Li et al. [14], although both mechanisms fail to reproduce experimental values of SL within the range 2.1 < f < 2.4 Regarding Fig. 6, SL does not present a significant change with the decrease of pressure in this range of equivalence ratios. In this case, the numerical results using the mechanism of Li et al. [14] are in good agreement with present experimental results while the results using the mechanism of Mueller et al. [13] overestimate the experimental values of laminar burning velocity. For f > 4.4 and f > 4.0, at P ¼ 0.947 atm and P ¼ 0.767 atm, respectively, SL was unsuitable to determine experimentally because flame temperatures were very low, and therefore those flames were difficult to be detected using the Schlieren technique. Error of present data was estimated at every equivalence ratio studied as explained in Section 2.3. Error bars are plotted along with experimental data in Figs. 4e6. It was found that maximum error was around 2%, i.e. around 6 cm/s at the highest value of SL measured. However, it has to be kept in mind that this value represents the deviation of an average value of SL due to the
Sensitivity analysis
In order to understand the behavior of SL at sub-atmospheric pressure and at different mixture conditions, a sensitivity analysis of the laminar burning velocity of H2/air flames with respect to reaction rate coefficients was performed at three equivalence ratios (f ¼ 0.6, 1.6, 4.0) and the two pressures considered in this study. The mechanism of Mueller al. [13] was employed in this analysis and the results of normalized sensitivity coefficients of the most important reactions are summarized in Fig. 7. At f ¼ 0.6 results show that chain-propagating reaction R7, chain reaction R10, and chain-branching reactions R11 and R12 have important positive sensitivity coefficients while chainterminating reactions R2, R5, and R8 as well as chain-initiating reaction R6 have negative sensitivity coefficients where threeebody reaction R8 has the highest sensitivity. Reaction R8 competes with R7 and R12 for the consumption of H radical, and R5 competes with R10 for consumption of OH radical. Decreasing pressure, the sensitivity of R8 has a significant reduction while the sensitivity coefficients of the R7 and R12 decrease in smaller magnitudes, which may explain the increase of SL when decreasing the pressure at lean equivalence ratios. In comparison with lean conditions, at the equivalence ratios corresponding to the highest values of SL (f ¼ 1.6), the sensitivity of reactions R7, R10 and R11 decrease, while the sensitivity of reaction of R12 increases and the sensitivity of the threeebody reaction R8 becomes positive. On the other hand, negative sensitivity of threeebody reaction R3 becomes significant. When decreasing pressure the sensitivity coefficient of R12 diminishes while the coefficient of R6, its competitor reaction with respect to H radical consumption,
Fig. 7 e Normalized sensitivity coefficients for the mechanism of Mueller et al. [13] at different pressures and various equivalence ratios.
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remains almost constant, showing the important role of R6 in the reduction of SL at those equivalence ratios. Finally, at ultrarich equivalence ratios (f ¼ 4.4), positive sensitivity of reactions R7 and R12 increase while those of R10 and R11 decrease when comparing with lean and rich equivalence ratios. On the other hand, negative sensitivity of chain-initiating reactions R3 and R6 increase. However, when decreasing pressure the sensitivity coefficients of the most important reactions have similar reductions, which would explain the insensitivity of SL with pressure changes at ultra-rich conditions. As can be notice, the most important reactions that may be responsible of the behavior of SL of hydrogen at low pressures are reactions involving consumption/production of H radical.
4.3.
Intrinsic flame instabilities
Fig. 8 shows instantaneous Schlieren photographs of H2/air flames at different equivalence ratios, at room temperature and studied pressures. At P ¼ 0.947 atm, flames exhibited instabilities at f < 0.8 and flame tips occasionally split. However, with the decrease of pressure until P ¼ 0.767 atm, those instabilities disappeared, and smooth and stable flames were obtained at the same equivalence ratios. Deformations of the flame front mentioned before are due to intrinsic flame instabilities, namely, hydrodynamic instability, diffusivethermal instability, and buoyancy-driven instability [20]. The later is not significant in the present study since it is only present at very low burning velocities and equivalence ratios near flammability limits. Hydrodynamic instability is caused by the thermal expansion across the flame front; essentially this instability is always present and the flame is unstable to disturbances of all wavelengths. On the other hand, diffusivethermal instability is a direct consequence of the non-equidiffusive nature of the premixed gases, since there is no parity between the heat conduction from the flame to the unburned mixture and the reactants diffusion towards the flame. Diffusive-thermal instability is important for small-scale disturbances, and it restrains hydrodynamic instability or increases flame wrinkles depending on the Lewis number of
the mixture, Le, which is defined as the ratio of the heat diffusivity of the unburned mixture to the mass diffusivity of the limiting reactant into the abundant inert. When Le is larger than unity diffusive-thermal instability is expected to restrain hydrodynamic instability [21]. However this parameter is insensitive to pressure changes and it is not enough to explain the behavior of intrinsic flame instabilities at low pressure. In order to estimate the flame instability characteristics at low pressure, the growth rate of the flame front disturbances, s, was calculated using the formulation of Sivashinsky [21], later corrected by Yuan et al. [22] for the case of Le lower than unity. Then s was estimated as: s ¼ U0 SL k U1 ak2 4ad2T k4
(2)
Where U0 ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 þ 32 33 3 1þ3
U1 ¼
3ð1 3Þ2 3ln3ð2U0 þ 1 þ 3Þ 2ð1 3Þ½3 þ ð1 þ 3ÞU0
3ð1 U0 Þð3 þ U0 Þbð1 LeÞ 2ð1 3Þ½3 þ ð1 þ 3ÞU0
1=31 Z
0
lnð1 þ xÞ dx x
k is the wave number of the disturbance, 3 ¼ rb/ru the ratio of densities of the burned and unburned gases, a the thermal diffusivity, b the Zeldovich number, and dT the flame thickness. The first term of the right side of equation (2) represents the effect of hydrodynamic instability and it is positive at any wave number; the second term estimates the effect of diffusive-thermal effect (depending if U1 is positive or negative); and the third term includes the temperature relaxation by diffusion proposed by Yuan et al. [22]. Lewis numbers of the H2/air mixtures were determined using the relation proposed by Addabbo et al. [23]: Le ¼ 1 þ
ðLeE 1Þ þ ðLeD 1ÞA 1þA
Fig. 8 e Instantaneous Schlieren photographs of H2/air flames at different pressures and various equivalence ratios.
(3)
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2000 1800 1600 Growth rate σ (1/s) G
1400 1200 1000 P=0.947 atm P=0.767 atm
800 600 400 200 0 -200 0
Fig. 9 e Lewis number of H2/air as a function of equivalence ratio.
where, LeE and LeD correspond to the Lewis number of the reactant that is in excess or deficiency, respectively. A ¼ 1 þ b (F 1) is a measure of the mixture strength, where F ¼ 1/f at lean conditions and F ¼ f at rich conditions. The Zeldovich number was calculated as b ¼ EaðTb Tu Þ=R T2b , with R the universal gas constant, Tb the temperature of the burned gases, Tu the temperature of the unburned gases, and Ea the global activation energy. For off-stoichiometric conditions, Ea was determined with the methodology proposed by Egolfopolous and Law [17], where Ea ¼ 2R hdlnðf Þ=dð1=Tb ÞiP , with f the mass burning rate. For near-stoichiometric conditions, Ea was interpolated from the off-stoichiometric results, as recommended by Jomaas et al. [24]. The flame thickness was determined using the temperature profile of the final solution of the numerical calculation of SL, and through the following definition: dT ¼
ðTb Tu Þ ðdT=dxÞmax
(4)
Where (dT/dx)max is the maximum temperature gradient in the temperature profile [10,25]. The numerical results obtained with the mechanism of Mueller et al. [13] were used for this calculation.
Fig. 10 e Flame thickness of H2/air at low pressure as a function of equivalence ratio.
2000
4000
8000 10000 6000 Wave number k (1/m)
12000
14000
16000
Fig. 11 e Effects of pressure on the growth rate of flame front instabilities for a H2/air flame at f [ 0.6.
Figs. 9 and 10 show the results of the Lewis number of the mixture and the flame thickness at different equivalence ratios estimated by equations (3) and (4), respectively. Le of the mixtures at lean conditions (f < 0.9) are lower than unity, however flames did not exhibited intrinsic instabilities at f ¼ 0.8 for P ¼ 0.947 atm and 0.6 f 0.8 for P ¼ 0.767 atm. Fig. 11 shows the effects of low pressure on the growth rate of the flame front instabilities calculated by equation (2) at f ¼ 0.6. With the decrease of pressure the wave number region where flame front is unstable narrows to lower wave numbers and the maximum growth rate becomes smaller. This is because the thermal diffusivity is inversely proportional to pressure. The decrease of pressure increases thermal diffusivity and so flame thickness (Fig. 10), which results in a strong diffusivethermal effect and a weak hydrodynamic instability [25,26].
5.
Conclusions
Measurements of laminar burning velocities of H2/air flames at low pressure, room temperature, and different equivalence ratios were conducted using the angle method. Numerical calculations of SL were also performed using existing detailed reaction mechanisms and compared with experimental results. Additionally, the effect of low pressure on the intrinsic flame instabilities was analyzed. From the results, their analysis and discussion, the following conclusions can be stated: 1. The mechanism of Mueller et al. [13] predicted reasonably well the experimental results of the laminar burning velocities at lean and rich equivalence ratios; however it tended to overestimate experimental values of SL at ultrarich equivalence ratios. 2. The mechanism of Li et al. [14] underestimated the experimental values of SL at lean and rich equivalence ratios. However, at ultra-rich equivalence ratios, the experimental and the numerical results of SL are in good agreement using this mechanism. 3. The mechanisms of Mueller et al. [13] and Li et al. [14] predicted small changes in the magnitude of SL when
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 6 3 1 7 e6 3 2 4
decreasing pressure but the changes found experimentally were higher than those numerically predicted. 4. The behavior of the laminar burning velocity of H2/air flames at different equivalence ratios with the decrease of pressure is not regular. At lean equivalence ratios SL increases with the decrease of pressure; at rich equivalence ratios SL decreases with decreasing pressure; and at ultrarich equivalence ratios SL does not present significant variations when decreasing pressure. 5. Reactions of consumption/production of the H radical such as R6, R7, R8 and R12 have a significant role on the irregular behavior of SL at different equivalence ratios when decreasing pressure. 6. Intrinsic flame instabilities diminish with decreasing pressure allowing the measurement the laminar burning velocity at low equivalence ratios using burner-stabilized flames.
Acknowledgments Authors acknowledge the support of the Committee for Research Development e CODI and the Science and Technology of Gases and Rational Use of Energy Group, University of Antioquia, for funding the project MC-08-1-12. Authors thank to the Colombian Department of Science and Technology e COLCIENCIAS for the partial funding of Mr. Pareja and Mr. Burbano as “Jo´venes Investigadores e Innovadores2008” as well as to the directors of the campuses of University of Antioquia at Santa Fe de Antioquia and Yarumal for providing the facilities where present experiments were conducted. The authors also thank Professor Frederick Dryer at Princeton University for providing the reaction mechanism of Li et al. [14].
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