Laminar burning velocity of hydrogen–air premixed flames at elevated pressure

Laminar burning velocity of hydrogen–air premixed flames at elevated pressure

Experimental Thermal and Fluid Science 21 (2000) 58±63 Laminar burning velocity of hydrogen±air premixed ¯ames at elevat...

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Experimental Thermal and Fluid Science 21 (2000) 58±63

Laminar burning velocity of hydrogen±air premixed ¯ames at elevated pressure Xiao Qin, Hideaki Kobayashi *, Takashi Niioka Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan Received 20 June 1999; received in revised form 15 November 1999; accepted 1 December 1999

Abstract Experimental and numerical studies on the laminar burning velocity of hydrogen±air mixtures were performed. Measurements of laminar burning velocities were conducted using a new technique based on particle tracking velocimetry (PTV) and image processing for burner-stabilized ¯ames in a high-pressure chamber. Equivalence ratios of the mixtures were varied from 0.6 to 3.0 for the pressure range from 0.1 to 0.5 MPa. A numerical simulation was conducted considering detailed reaction mechanisms and transport properties. At high pressures, the experimental and numerical results agreed reasonably well with each other for mixtures of equivalence ratios of 1.0 and 2.0, while discrepancies were seen for the equivalence ratio 3.0. These discrepancies can be diminished e€ectively by modifying the rate-coecient expressions of recombination reactions. Ó 2000 Elsevier Science Inc. All rights reserved. Keywords: High-pressure combustion; Laminar burning velocity; PTV

1. Introduction Laminar burning velocities of premixed ¯ames at high pressures are of practical importance in the design and analysis of high-load combustors, such as internal combustion engines, rocket motors, power plant burners, etc. They are also essential characteristic parameters for evaluating theoretical models of ¯ame propagation and various combustion phenomena in an elevatedpressure environment. Of all fuels, hydrogen has a relatively simple reaction mechanism, although this mechanism includes the pressure-dependent reactions which are common to more complex hydrocarbon fuels. Therefore, the study of the reaction mechanism of hydrogen is of primary importance when investigating the e€ects of pressure on the reaction mechanism by comparing it with experimental data, e.g., the burning velocity. Although the burning velocities of hydrogen±air mixtures have been extensively studied at room temperature and atmospheric pressure in the past [1±8], there are relatively few experimental data available for elevated temperature and pressure environments be* Corresponding author. Tel.: +81-22-217-5272; fax: +81-22-2175323. E-mail address: [email protected] (H. Kobayashi).

cause of experimental diculties. Iijima and Takeno [1] and Shebeko et al. [2] have measured burning velocities of hydrogen±air mixtures using the spherical bomb technique, but their results disagreed with each other in terms of the variation of burning velocity at elevated pressures above 0.2 MPa. In the case of the spherical bomb method, ¯ame propagation is unsteady and combustion duration is very short. It is also dicult to determine whether the ¯ame-front remains smooth in the closed vessel at high pressures. Therefore, a method to measure the burning velocity with continuous observation for stationary ¯ames in a high-pressure environment is preferred. Recently, Kobayashi et al. [9] have measured the laminar burning velocity of methane±air premixed ¯ames stabilized with a nozzle burner in a high-pressure chamber using a new technique involving particle tracking velocimetry (PTV) and computer-aided image processing. Based on their experimental method, this paper presents measurements of the laminar burning velocities of hydrogen±air mixtures of various equivalence ratios at high pressures. Numerical simulations using detailed transport properties and chemical kinetic mechanisms are also presented. The experimental and numerical results are compared, and modi®cations of the rate-coecient expressions of recombination reactions are made to obtain a set of new parameters that can successfully reproduce the experimental results.

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2. Experimental apparatus and procedures Fig. 1 shows a schematic diagram of the experimental apparatus employed. The inner diameter and length of the high-pressure combustion chamber with an extension ridge are 150 and 1050 mm, respectively. Four quartz windows, 50 mm in diameter, are used for observing ¯ames and taking photographs. Compressed air from a tank is supplied continuously from the bottom of the chamber, and the pressure of the chamber is kept constant by adjusting the exhaust valve. During the experiment, the exhaust gases are continuously removed from the top of the chamber and fresh air is supplied from the bottom so that the temperature inside the chamber remains close to room temperature. A nozzle burner, 4 mm in diameter, was installed in the chamber and was water-cooled near the outlet of the burner. A double-pulsed Nd-YAG laser (Spectra-Physics, GCR250-10) was used for particle tracking velocimetry. The interval of the double pulses was controlled using a delay generator (Stanford Research Systems, Model DG535). The laser beam was transformed into a vertical sheet whose width was about 30 mm, and the thickness at the ¯ame was less than 0.3 mm using conical and cylindrical lenses. SiO2 particles with speci®c gravity and a mean diameter of 2.0 and 2.0 lm, respectively, were added to the mixtures as Mie scattering particles. As for Schlieren photography, a high voltage mercury lamp, as well as primary and secondary lenses, was installed along the direction normal to the laser sheet. Both particle images and Schlieren photographs were taken from the side opposite the mercury lamp using a highresolution CCD camera (Kodak, Megaplus Model 1.4). Numerical simulations of one-dimensional premixed ¯ames were carried out using the PREMIX code [10]. The thermochemical data and transport properties were


evaluated using the CHEMKIN II package [11]. For comparison, present calculations considered three detailed chemical reaction mechanisms, namely, those of Kee et al. [10], Yetter et al. [12], and Warnatz [13], respectively. In each of the three mechanisms, 9 species and 19 reversible reactions are involved. 3. Results and discussion The method to measure the laminar burning velocity using the PTV technique for burner-stabilized ¯ames has been described in detail elsewhere [9] and will only be reviewed brie¯y here. First, a binarized particle image is analyzed using a PIV analysis package, VISIFLOW (AEA Technology), and a map of instantaneous velocity vectors over the cross section of the ¯ame is generated. Then, from this map, the streamlines of particles are calculated by successive interpolation. Along each streamline, the point where the direction of a velocity vector changes abruptly is selected and is considered to be the front edge of the preheating zone. At this point, the gradient of the streamline upstream is calculated. In order to determine the gradient of ¯ame front, Schlieren images are analyzed and the ¯ame front is ®tted to a quadratic curve. At the intersection of the streamline and the ¯ame front, after calculating the angle, h1 , between the tangential line of the ¯ame front and the streamline, the local burning velocity, Sr , is obtained using the following equation Sr ˆ Ur sin h1 ;


where Ur is the magnitude of the local velocity vector at the front edge of the preheating zone mentioned above. Between the rip and center of the nozzle burner, there is a region where the local burning velocity is nearly

Fig. 1. Schematic diagram of the high-pressure combustion facility.


X. Qin et al. / Experimental Thermal and Fluid Science 21 (2000) 58±63

constant. The mean velocity in this region is considered to be the laminar burning velocity, SL [9]. Fig. 2 shows variations of the laminar burning velocity of hydrogen±air mixtures with equivalence ratios at room temperature and pressure along with data from the literature [1,3±8]. It can be seen that there are two groups of data, i.e., data obtained with a burner method [6±8], and those with a spherical bomb method [1,3±5]; the former is a little larger than the latter. The results of the present experiment are in good agreement with the former. Fig. 3 presents Schlieren photographs showing the e€ects of pressure and equivalence ratios on the shape of hydrogen±air premixed ¯ame. The ¯ame is very stable at 0.1 MPa for every condition in this experiment, but in the case of stoichiometric mixture, at 0.14 MPa, the ¯ame becomes unstable and the ¯ame tip occasionally splits. At 0.3 MPa, the ¯ame tip becomes very unstable and strongly splits, while the base of the ¯ame remains stable. With the increase in the equivalence ratio, the ¯ame becomes stable. In this experiment, the ¯ame could be considered as being stable till 0.24 MPa for / ˆ 2:0 and 0.40 MPa for / ˆ 3:0. At high pressures, the Reynolds number increases due to the decrease in kinematic viscosity. The Reynolds number for the ¯ow inside the burner tube (based on the inner diameter of the tube as the characteristic length) of all the present experimental conditions did not exceed the critical Reynolds number (about 2300 for circular tubes). Hence, it can be inferred that the corrugations of the ¯ame front are mainly due to the e€ects of hydrodynamic instability and to the di€usive-thermal e€ects of the ¯ame. The instability of premixed ¯ame depends on the Lewis numbers of fuel and oxidizer. Generally, the Lewis number of a mixture is determined by the de®cient reactant in the mixture and is insensitive to pressure changes. In the case of hydrogen±air mixtures, the Lewis number for oxygen is greater than unity for all equivalence ratios, whereas that for hydrogen increases with equivalence ratio from a value less than unity to a value

Fig. 2. Laminar burning velocities of hydrogen±air mixtures at atmospheric conditions as a function of equivalence ratios.

greater than unity. The fact that the ¯ame instability occurs even for the rich mixtures means that the e€ective Lewis number is close to the Lewis number of hydrogen. Therefore, it is presumed that the e€ective Lewis number of hydrogen±air mixtures changes from less than unity for fuel-lean mixtures to greater than unity for fuel-rich mixtures. For the mixtures of / ˆ 1:0, the e€ective Lewis number is less than unity, but at 0.1 MPa the di€usive-thermal e€ect stabilizes the ¯ame front. With the increase in pressure, the hydrodynamic instability of the ¯ame front becomes signi®cant because the di€usivethermal e€ects which restrain the hydrodynamic instability weaken. As the equivalence ratio is increased, the e€ective Lewis number also increases and the di€usivethermal e€ects gradually tend to restrain the hydrodynamic instability even at high pressure [14]. As a result, the stable range of the laminar ¯ame is extended to higher pressures especially for the mixtures of / ˆ 3:0, i.e., the ¯ame tip does not split until 0.8 MPa. In our experiments, the laminar burning velocities were measured by the PTV method only for the stable ¯ames in the pressure and equivalence ratio ranges mentioned above. The relationships between the laminar burning velocity and pressure are shown in Fig. 4. For / ˆ 1:0 (Fig. 4(a)), the laminar burning velocity changes little in the range of from 0.1 to 0.14 MPa. From Fig. 4(a), di€erent tendencies can be seen between the results of Iijima and Takeno [1] and Shebeko et al. [2]. For / ˆ 2:0 (Fig. 4(b)), the laminar burning velocity is almost constant from 0.1 to 0.24 MPa, but for / ˆ 3:0 (Fig. 4(c)), it increases a little at 0.12 MPa, and then decreases monotonously with the increase in pressure. Fig. 4 also shows the numerical results calculated using detailed chemical kinetic mechanisms of Kee et al. [10], Yetter et al. [12], and Warnatz [13], respectively. The results for di€erent mechanisms are in good agreement with the experimental results for stoichiometric hydrogen±air mixtures, but are di€erent from each other for larger equivalence ratios, especially at high pressures. The present experimental results agree well with Yetter's results for / ˆ 1:0, 2.0, although there are still a few discrepancies. For / ˆ 3:0, the data of measured SL are larger than all predictions and the gradient of decreasing SL for the experimental results is much steeper. These discrepancies indicate that the present mechanisms are less valid, especially for rich mixtures at high pressure. According to Warnatz [13], for the reaction mechanism of the hydrogen±oxygen system, the competition between the following two reactions strongly in¯uences the laminar burning velocities of hydrogen±air mixtures. H ‡ O2 ˆ OH ‡ O


H ‡ O2 ‡ M ˆ HO2 ‡ M


The chain-branching reaction (R1) is endothermic and strongly temperature-dependent, while the radicalterminating reaction (R2) is exothermic, weakly temperature-dependent, and strongly pressure-dependent. At low temperature and high pressure, reaction (R2)

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Fig. 3. Instantaneous Schlieren photographs showing e€ects of ambient pressure, P, and equivalence ratio, /, on hydrogen±air premixed ¯ames, where V is mean velocity at the burner outlet: (a) / ˆ 1:0; (b) / ˆ 2:0; (c) / ˆ 3:0.

competes with reaction (R1) for consumption of the H radical and produces an HO2 radical which has a relatively low reactivity. Sensitivity analysis shows that reaction (R1) and other chain-propagating reactions, such as OH ‡ H2 ˆ H2 O ‡ H and O ‡ H2 ˆ OH ‡ H, exhibit positive sensitivities, while reaction (R2) and other recombination reactions, such as H ‡ OH ‡ M ˆ H2 O ‡ M


exhibit negative sensitivities. At high pressure, the sensitivity of recombination reactions becomes signi®cant due to the increased concentrations of third bodies, particularly for reaction (R2). Therefore, modifying the rate-coecient expressions of these reactions may signi®cantly reduce the discrepancies between the experimental and numerical results of the laminar burning velocity.

Fig. 5 shows rate coecient data for reaction (R2) when the bath gas M is nitrogen [15], indicating that the data greatly vary. At 0.4 MPa, the adiabatic ¯ame temperatures for hydrogen±air mixtures of equivalence ratios 1.0 and 3.0 are 2420 and 1767 K, respectively, meaning a large di€erence of 653 K. As mentioned above, reaction (R2) dominates the ¯ame propagation phenomenon more signi®cantly at low temperatures. Here, we try to enhance this predominance further by decreasing the reaction rate coecient in the region over 2000 K and increasing it in the region below 2000 K. In order to achieve this, the following new approximation expressions were adopted  2:0  1018 T ÿ0:8 …T 6 850 K†; k2 ˆ 5:5  1030 T ÿ4:5 exp …ÿ26:0=RT † …T > 850 K†: …2†


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As for reaction (R3), i.e., H ‡ OH ‡ M ˆ H2 O ‡ M, the same procedure was used and the following new parameter for its rate-coecient expression was yielded k3 ˆ 4:5  1025 T 3:0 :


Substituting the above-mentioned rate coecients of reactions (R2) and (R3) into the mechanism of Yetter et al. [12], recalculations were performed. The results are also shown in Fig. 4 (curves of present work). It can be seen that for / ˆ 1:0, 2.0, the new numerical results agree better with the measurements than the original mechanism, and for / ˆ 3:0, the decreasing gradient becomes steeper. These improvements mean that the modi®ed rate-coecients of reactions (R2) and (R3) e€ectively in¯uence the laminar burning velocities in the low temperature regions.

4. Conclusions

Fig. 4. Relationships between laminar burning velocity and ambient pressure: (a) / ˆ 1:0; (b) / ˆ 2:0; (c) / ˆ 3:0.

Fig. 5. Rate-coecient data [15] for H ‡ O2 ‡ M ˆ HO2 ‡ M …M ˆ N2 †.

Laminar premixed ¯ames for hydrogen±air mixtures stabilized with a nozzle-type burner in a high-pressure combustion chamber were investigated both experimentally and computationally. Measurements of laminar burning velocities were conducted using a new technique based on particle tracking velocimetry and image processing. The computations took detailed reaction mechanisms and transport properties into consideration. The following results were obtained: 1. At high pressure, hydrogen±air premixed ¯ames exhibited strong ¯ame instability which results from the interactions between hydrodynamic instability and di€usive-thermal e€ects. 2. The experimental results of laminar burning velocities in the stable pressure regions are in good agreement with numerical results for stoichiometric mixtures, and are larger than numerical results for rich mixtures at high pressures. 3. Comparisons between the present measurements and calculations were made, and by modifying the ratecoecient expressions of recombination reactions, modi®ed rate-coecient parameters that can better reproduce the experimental results were obtained. Nomenclature k reaction rate coecient, cm6 /mol2 s P pressure, MPa R universal gas constant, J/mol K laminar burning velocity, m/s SL T temperature, K magnitude of local velocity vector at Ur the front edge of the preheating zone, m/s V velocity at the burner outlet, m/s / equivalence ratio of the mixture angle between the tangential line of h1 the ¯ame front and the stream line, °

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Acknowledgements The authors gratefully acknowledge the assistance of Mr. Susumu Hasegawa and Mr. Yasuhiro Ogami for performing experiments. This research was partially supported by Toyota Physical and Chemical Research Institute.

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