measurement of laminar flame speed for high pressure and...

15th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 05-08 July, 2010

Measurement of laminar flame speed for high pressure and high temperature conditions: validation of the facility and development of new tool for post-

processing

Emilien Varea1, Alexis Vandel1, Vincent Modica1, Frédéric Corbin1, Gilles Godard1, Bruno Renou1

1: CORIA-UMR 6614, University and INSA of Rouen, 76801 Saint-Etienne du Rouvray cedex, France, [email protected]

Abstract The purpose of this work is to present a new procedure to extract the laminar burning speed in the case of spherically outwardly expanding flame. This methodology enables to determine directly the laminar burning velocity from the flame displacement speed and the fresh gas velocity near the preheat zone; it presents an alternative to the standard procedure that is commonly used in the literature and that is based on the flame front displacement and the ratio of unburned and burned gas densities. Two laser techniques, high speed laser tomography and particle image velocimetry (PIV), are used to visualize the temporal evolution of the flame front and the fresh gas velocity, respectively. The measurements of laminar flame speed are carried out in a high pressure (2 MPa) and high temperature (523 K) constant volume vessel over a wide range of equivalence ratios (0.6 – 1.3) for methane/air and isooctane/air mixtures. To validate the experimental facility and the post-processing of the flame images, the values of laminar burning velocities and Markstein lengths were calculated with both procedures and were compared with experimental and numerical results of the literature. List of symbols k flame stretch rate (s-1) T temperature (K) L laminar Markstein length (mm) un laminar burning velocity (cm.s-1) Lb burned gas Markstein length (mm) un° unstretched laminar burning velocity (cm.s-1) P pressure (MPa) ug fresh gas velocity (cm.s-1) r flame radius (cm) ρb density of burned gases s stretched flame speed (cm.s-1) ρu density of unburned gases s° unstretched flame speed (cm.s-1) Φ equivalence ratio 1. Introduction The laminar burning velocity plays an important role in studying the combustion process. It provides information for estimating the fuel burning rate in spark-ignition (SI) engine, the engine’s efficiency and exhaust emissions. The production of accurate measurements of laminar burning speed is also essential for validating chemical kinetic mechanisms for conventional and alternative fuels and for understanding the combustion process at high pressure and temperature. Laminar burning speed can be measured by several experimental approaches utilizing different flame configurations such as spherical expanding flames using closed vessels (Aung et al., 1995; Bradley et al., 1998; Burke et al., 2009; Chen et al., 2007; Gu et al., 2000; Halter et al., 2005; Hassan et al., 1998; Huang et al., 2006; Ilbas et al., 2006; Liao et al., 2004; Mandilas et al., 2007; Qin and Ju, 2005; Rozenchan et al., 2002; Stone et al., 1998; Tanoue et al., 2003; Taylor and Smith, 1995), counter-flow or stagnation flames (Dong et al., 2002; Egolfopoulos et al., 1989; Huang et al.,

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2004; Vagelopoulos and Egolfopoulos, 1998; Vagelopoulos et al., 1994), burner stabilized flat flames using heat flux method (Bosschaart and De Goey, 2003; Bosschaart and De Goey, 2004; Coppens and Konnov, 2008; Coppens et al., 2007; Hermanns et al., 2010; Van Maaren et al., 1994) and Bunsen flames (Kurata et al., 1994; Lewis and Von Elbe, 1987; Ogami and Kobayashi, 2006). Among these various techniques, the spherically outwardly expanding flame configuration is more similar to flame propagation in the spark-ignition engines and allows to reach thermodynamic conditions (elevated pressures and temperatures) closed to those encountered in internal combustion (IC) engines. These experimental conditions are very difficult to reach using steady-state methods (counter-flow, flat flame burner) which have operational ranges limited to a few atmospheres due to flame stability problems (Rozenchan et al., 2002). For these reasons, the first approach using closed vessel was chosen here. The objectives of this work are the following: - The validation of the experimental facility by measuring laminar burning velocities at elevated

pressure and temperature over a wide range of equivalence ratios for methane/air and isooctane/air mixtures.

- The development of new tool for post-processing in order to get simultaneously the flame displacement speed and the fresh gas velocity. Indeed, the laminar burning velocity can be determine from the displacement of flame speed and the ratio of unburned and burned gas densities (Bradley et al., 1996) or the burning velocity can also be determined as the difference between the flame speed and fresh gas velocity (Bradley et al., 1996; Lecordier, 1997).

In this study, experimental techniques used to measure velocities are the high speed laser tomography and the particle image velocimetry (PIV). 2. Experimental apparatus To measure laminar flame speed, experiments are conducted in a high pressure and high temperature constant volume vessel, equipped with different sensors and an optical system. Figure 1 shows the experimental setup. 2.1. High pressure and high temperature facility The maximum operating pressure of the experimental facility is 2 MPa and the maximum temperature is 523 K. The radius of the inner chamber is 85 mm and the inner volume of the stainless steel combustion chamber is 2.6 liters. Two types of fuels, gaseous or liquid, can be used in this experimental device. Fuels that are gaseous under ambient conditions are charged directly from bottles through mass controllers. Liquid fuels are first vaporized in a heated chamber, named in the figure 1 “Controlled Evaporator Mixer (CEM)” (Bronkhorst) and then charged through heated lines into the vessel. In order to obtain a homogeneous mixture, all gases are then premixed in a tank before injection into the combustion chamber and the equivalence ratio of the mixture is measured and regulated by coriolis or thermal mass flow controllers connected to a computer. An electrical heating system that is monitored by a proportional integral derivative (PID) controller regulates temperatures of the mixing tank and of the combustion chamber. Temperature is controlled inside the chamber by two thermocouples that ensure uniformity of the temperature field. The compressed mixture of fuel and air is supplied continuously from the bottom of the combustion chamber and the pressure level, which is checked in the vessel with a piezoelectric pressure sensor, is kept constant by adjusting the control valve. When the composition of the fuel mixture and thermodynamic conditions are achieved and unchanging, the combustion chamber is then closed by two stop valves. Finally, the mixture is one minute left at rest to avoid any perturbation during the flame propagation.

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The combustible mixture is spark-ignited at the center of this chamber by two stainless steel electrodes linked to a capacitive discharge ignition system using minimum spark energies to avoid ignition disturbances. The electrode diameter is 0.5 mm and the gap between electrodes is 1.5 mm. During the combustion process, the evolution of the chamber pressure is acquired by a dynamic pressure transducer. Once combustion is complete, the chamber is ventilated and purged with nitrogen to remove condensed water vapor. 2.2. Optical system The chamber is equipped with three transparent windows for optical diagnostics. Laminar burning velocities are measured by combination of two laser techniques: the laser tomography and the PIV. A double cavity Nd:YLF laser (Darwin Dual, Quantronix) delivering pulses of 6 mJ at 527 nm and at 5 kHz, is used for the lighting. The laser sheet is created by the association of one cylindrical lens of - 13 mm focal length and one spherical lens of 254 mm focal length. A high speed camera (Photron Fastcam SA1.1) records, at a frequency of 5 kHz, a 8 bit image couple of 1024 x 1024 pixels2. The camera, which is mounted with a Nikon lens of 105 mm focal length, has a field of view of 50 x 50 mm2 at a resolution of 0.049 mm/pixel. An interferential pass-band (527 ± 10 nm) is used to remove the flame chemiluminescence. 2.3. Experimental conditions For capturing tomography images, the chamber is seeded with silicone oil droplets which vaporize at an isotherm of about 580 K. This boiling point temperature is high enough that the seeding droplets will exist well into the preheat zone and can be used to capture the minimum velocity point upstream of the flame. The seeding particles do not survive in the post flame zone but this type of silicone fluid does not have any observable effect on the flame and in particular the effect of particle concentration on the measured flame speed is insignificant. In order to avoid the influence of the ignition energy (Bradley et al., 1996) and the chamber confinement effects, only spherical flame images, with radii larger than 6,5 mm and smaller than 19 mm, were used for the determination of flame speeds. Indeed, the value of 19 mm corresponds to a flame radius that is approximately 22 % of the radius of the inner chamber and from results of Burke et al. (Burke et al., 2009), the effect of confinement can be neglected for flame radii less than 30 % of the wall radius. Moreover within this region, the total chamber pressure can be considered as constant. In this study, laminar burning velocity measurements are performed for methane/air and isooctane/air mixtures for the following ranges of equivalence ratios Φ, pressure P and temperature T: 0.6 ≤ Φ ≤ 1.3, 0.1 ≤ P ≤ 2 MPa and 298 ≤ T ≤ 523 K. During the experiments, the following uncertainties are encountered on measuring the equivalence ratio of the mixture, the ambient temperature and the ambient pressure: 0.056 % < ∆Φ/Φ < 0.07 %, 0.6 % < ∆T/T < 6% and ∆P/P = 0.5%. For each experimental condition, experiments were performed thrice and the values presented in this work are the average of these three experiments. 3. Procedure to extract laminar burning speed and image processing In the case of spherically outwardly expanding flame, the propagation speed is defined as the temporal derivative of the flame radius evolution, r(t). During this temporal evolution, the flame front is affected by the stretch rate which influences the flame dynamic.

(1)

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Asymptotic developments have initially shown a non-linear relationship between flame stretch and propagation speed (Kelley and Law, 2009; Tahtouh et al., 2009b).

(2)

Where s° is the unstretched flame speed and Lb is the burned gas Markstein length. The flame stretch rate, k, is expressed, in the case of spherically expanding flame front, as follows:

(3) If we assume a ratio s/s° close to unity, the previous relationship between flame stretch and flame speed can be simplified:

(4) The unstretched flame speed, s°, is extrapolated as follows:

(5) The following sections present two methodologies enabling the determination of the laminar burning velocity: the standard procedure, which is developed in the first section, is commonly used by previous works (Aung et al., 1995; Bradley et al., 1998; Burke et al., 2009; Chen et al., 2007; Gu et al., 2000; Halter et al., 2005; Hassan et al., 1998; Huang et al., 2006; Ilbas et al., 2006; Liao et al., 2004; Mandilas et al., 2007; Qin and Ju, 2005; Rozenchan et al., 2002; Stone et al., 1998; Tanoue et al., 2003; Taylor and Smith, 1995) and is based on the flame front displacement and the ratio of unburned and burned gas densities. On the other hand, only very few studies (Balusamy et al., 2009; Bradley et al., 1996; Lecordier, 1997) try to deduce the laminar burning velocity from the difference between the flame speed and fresh gas velocity; this is the aim of this work that details, in the second section, a new tool for post-processing PIV images and directly calculating the burning velocity without using the properties of the fuel mixture. 3.1. Method 1: measurement of laminar burning velocity by laser tomography The laser tomography technique provides a visualization of the flame front propagation. The fresh gas mixture is seeded with silicon oil particles which evaporate at the entrance of the flame front (Tevaporation = 580 K). The flame surface is obtained by differentiation, on the flame images, of the dark and bright areas, representing burnt and unburnt states, respectively. To determine the flame speed, the contours of the different spherical laminar flame images captured at several stages of flame development are extracted with an edge detection algorithm, using thresholding procedures based on an adaptive binarization. The detected flame boundaries are smoothed to remove noise from the digitization steps and local flame radii are measured by using least square circle fit technique (Razet, 1997). For constant pressure flame propagation, the unstretched laminar burning velocity, un°, is then obtained from the unstretched flame speed, s°, extrapolated from equation (5) and the density ratio:

(6)

Where ρb is the density of adiabatically burned gases and ρu is the density of unburned gases. This expression involves several hypothesis: fresh and burned gases are considered as perfect gases and the combustion process is assumed to be isobaric. Thus, the density ratio depends on the ratio of the burned to unburned gas temperature and the burned gas temperature is determined for adiabatic conditions. Moreover, the expression (6) assumes zero flame thickness. In order to validate the processing, measured laminar flame speed are compared with previous works in the section 4 of the present study. 3.2. Method 2: measurement of laminar burning velocity by PIV

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The laminar burning velocity, un, can also be determined directly from the flame speed, s, and fresh gas velocity (at the entrance of the flame front), ug (Bradley et al., 1996):

(7) And also, the laminar burning velocity can be correlated to flame stretch rate, k, trough the linear relationship:

(8) Where L is the laminar Markstein length. Then from relation (8), the unstretched laminar burning velocity, un°, is extrapolated from the laminar burning velocity, un, at k = 0. This exact definition of the burning velocity requires the knowledge of the local fresh gas velocity which can be obtained by PIV. Based on this second definition which enables the measurement of the burning velocity without using the fuel properties, Balusamy et al. (Balusamy et al., 2009) has recently presented an experimental approach to determine the laminar burning velocities by using particle image velocimetry; in his study, the flame speed and the velocity of fresh gas were directly calculated from the PIV images. The determination of fresh gas velocity near the preheat zone of the flame front is solved by taking into account the local topology of the flame front. The PIV images are analyzed with an algorithm using adaptive interrogation window scheme. The aim of this present study is to adapt the PIV approach of Balusamy et al. (Balusamy et al., 2009) by proposing a new PIV algorithm which takes into consideration the overall topology of the flame front, because in the case of a laminar spherical expansion, the flame is homogeneous. The principle of the PIV procedure is described in the figure 2. This procedure is applied on flame front contours that were extracted from PIV images and smoothed with the detection algorithm that was described in the previous section. Then for a couple of PIV image, the interrogation algorithm adapts the shape of each interrogation window for suiting the entirety of the flame front contour. Thereby, this procedure involves only one overall interrogation area for each PIV frame. The length of interrogation window varies according to the extracted smoothed contour and its width can be adjusted from 1 to 10 pixels in order to have a good correlation between the two interrogation windows. As shown in the figure 2, the first stage of the image processing consists in finding the best correlation between the two interrogation areas by shifting by step of one pixel the second interrogation window alone in the direction normal to the flame front. Then, for a PIV image couple, the evolution of the intensity of the correlation peak versus the shift of the second interrogation area is plotted and presented in the figure 3. The intensity of the correlation peak increases up to an optimum displacement and then decreases. This optimum displacement, which is designated ∆r2

opti in the figure 2, corresponds to a maximum correlation and his value is used to calculate the velocity of fresh gas near the preheat zone. The relationship to determine the fresh gas velocity is defined as follows:

(9) Where r1 and r2 are respectively radii of a PIV image pair at time t and t + ∆t (∆t = 200 µs); ∆r2

opti is the optimum displacement of the second interrogation window and ∆r1 is the displacement of the first interrogation window. The second stage of post-processing consists in moving the first interrogation area in the direction normal to the flame front and then for each position (∆r1) of this window, the first step of the procedure is restarted and the relation (9) is used to calculate the fresh gas velocity. With this procedure, the velocity profile along normal to the flame front can be plotted. An example of instantaneous fresh gas velocity profile, which is calculated from real PIV images of methane/air mixture, is presented in the figure 4. As shown in this figure, the normal component of fresh gas velocity is the peak point of the velocity profile.

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Then, for each image pair, a value of the global velocity of fresh gas near the flame front is calculated and the laminar burning velocity is extracted using equation (7).

4. Results 4.1. Validation of the experimental facility and the laser tomography technique To validate the post-processing of tomography images, laminar burning velocity measurements of methane/air flames were carried out for various equivalence ratios at atmospheric pressure and room temperature. For each mixture, 50 images are taken covering the duration of flame propagation, free from ignition energy effects and pressure influences. The experimental results are deduced from equation (6) and the unstretched flame speed is calculated using linear and nonlinear formulations. Figure 5 shows the experimental values of laminar burning velocity with other recent data (Chen et al., 2007; Gu et al., 2000; Halter et al., 2005; Hassan et al., 1998; Huang et al., 2006; Liao et al., 2004; Qin and Ju, 2005; Rozenchan et al., 2002; Tahtouh et al., 2009a; Tanoue et al., 2003), which were acquired utilizing combustion vessel and were determined by linear extrapolation to zero strain rate, and numerical results using GRI-Mech 3.0 (Smith et al., 1999) and GRI-Mech 2.11 (Bowman et al., 1994). For an equivalence ratio range of 0.6 – 1.3, experimental data of the present work are in good agreement with those of other studies and specially with results of Tahtouh et al. (Tahtouh et al., 2009a). Concerning the numerical simulation, the influence of the equivalence ratio on the burning velocity is correctly described but at low equivalence ratios (0.7 ≤ Φ ≤ 1) some disparities, which are estimated in a range of 8 – 14 %, appear between our experimental data and numerical results calculated by GRI-Mech 3.0 and in particular by GRI-Mech 2.11. They might be due among other things to the optimization of mechanisms GRI-Mech 3.0 and GRI-Mech 2.11. The target values used in the optimization procedure were based on experimental data of Vagelopoulos et al. (Vagelopoulos and Egolfopoulos, 1998; Vagelopoulos et al., 1994), which were determined utilizing a stagnation flow configuration and without using the linear extrapolation to zero strain rate. Figure 6 compares values of laminar burning speed calculated by linear method to those determined by nonlinear method. In the case of lean and stoichiometric methane/air mixtures, both methodologies provide good results. The evolution of the burning velocity as function of the stretch rate is presented in figures 7 and 8 for two different equivalence ratios, respectively 0.7 and 1.3. However, according to the results of Tahtouh et al. (Tahtouh et al., 2009b) and Kelley et al. (Kelley and Law, 2009), the nonlinear method is more suitable for rich mixtures. In the present study, our data extracted by nonlinear formulation agrees with the conclusion of Tahtouh et al. (Tahtouh et al., 2009b). Thereby in figures 6 and 8, for equivalence ratios higher than 1, the linear approximation is no more valid and results in overestimation of the burning speed. Indeed, the assumption (s/s° = 1), which allows the formulation (4), is not reached and then the nonlinear extrapolation must be used. To test the combustion chamber under high pressure and high temperature, laminar burning velocity measurements of stoichiometric methane/air mixtures were performed at a pressure range of 0.1 – 2 MPa and at a temperature range of 298 – 523 K. Figure 9 shows the pressure effect on laminar burning velocity at 298 K and compares results of the present work to those of previous studies (Gu et al., 2000; Halter et al., 2005; Hassan et al., 1998; Ogami and Kobayashi, 2006; Rozenchan et al., 2002). The pressure range tested in most of these studies is included between 0.1 and 1 MPa (Gu et al., 2000; Halter et al., 2005; Hassan et al., 1998; Ogami and Kobayashi, 2006); only Rozenchan et al. (Rozenchan et al., 2002) have studied the

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influence of the pressure on laminar burning velocity up to 2 MPa. Increasing the pressure decreases the burning velocity. The pressure effect is the most important in the range of 0.1 – 0.5 MPa where the burning velocity decreases by 44 %. Then, for pressures higher than 0.5 MPa, the influence on burning velocity is weaker. For the following pressure ranges: 0.5 – 1, 1 – 1.5 and 1.5 – 2 MPa, the burning velocity decreases by 19 %, 15 % and 10 % respectively. From 0.1 to 1 MPa, the agreement is good, especially with data of Gu et al. (Gu et al., 2000). When the pressure increases from 1 MPa to 2 MPa, a decrease of the burning velocity is observed like in the numerical simulations (GRI-Mech 3.0 and 2.11) and in the experimental results of Rozenchan et al. (Rozenchan et al., 2002), but our values of laminar burning speed are respectively 14 % (at 1 MPa) and 25 % (at 2 MPa) higher than theirs. This divergence between numerical and experimental results under high pressure might be induced by the optimization process of both mechanisms GRI-Mech 3.0 and 2.11. In that case, the experimental targets used in the optimization procedure were defined from laminar flame speed measurements, which were carried out by Egolfopolous et al. (Egolfopoulos et al., 1989) for a pressure range limited to 0.1-3MPa and therefore they are not perfectly optimized for flame speed calculations under pressures higher than a few atmospheres. As observed in the figure 10, from 2 MPa the formation of a few cellular structures appears during the flame propagation. In the figure 11, the pressure dependence of the laminar burning velocity is plotted for different temperatures and as shown in the graph, the pressure effect is less important when the temperature increases. In the figure 12, the evolution of the normalized laminar burning velocity according to the pressure is presented for various temperatures and for example, from 0.1 MPa to 2 MPa, the burning velocity decreases by 66 % at 298 K and by 50 % at 523 K. The initial temperature effect on burning velocity is plotted in the figure 13. At constant pressure, increasing the temperature increases the burning velocity. Experimental measurements of Gu et al. (Gu et al., 2000), Stone et al. (Stone et al., 1998), Hermanns et al. (Hermanns et al., 2010), Hill et al. (Hill and Hung, 1988), Garforth et al. (Garforth and Rallis, 1978) and numerical data of Mishra (Mishra, 2003) are very close to our results. In the figure 14, the temperature dependence of the burning velocity is presented for different pressures and the evolution of the normalized laminar burning velocity according to the temperature is plotted in the figure 15. As presented in this graph, the influence of the temperature on the evolution of the burning velocity increases when the pressure increases; for example, from 298 K to 523 K, the burning velocity increases by 157 % at 0.1 MPa and by 274 % at 2 MPa. 4.2. Validation of the new procedure for the PIV images post-processing The new procedure for the PIV images post-processing, which is based on the difference between the flame speed and fresh gas velocity (cf. equation (7)), is compared to the standard procedure, which is based on the displacement of flame speed and the ratio of unburned and burned gas densities (cf. equation (6)). In the figure 16, the values of laminar burning velocities are calculated with both methodologies and the results are plotted as a function of flame stretch for a methane/air mixture (Φ = 1, P = 0.1 MPa, T = 298 K). As presented in this figure, both procedures give nearly the same laminar burning velocity when extrapolated to zero stretch rate: un° = 34 ± 0.5 cm.s-1. The gradients of the burning velocity curves in the figure 16 yield values of laminar Markstein lengths; two different gradients are observed: L = + 0.128 mm (with the standard procedure using equation (6)) and L = - 0.147 mm (with the new procedure using equation (7)). As presented in the table 1, the value of burned gas Markstein length Lb that is deduced from the relationship between flame speed and flame stretch (cf. equation (4)) agrees well with data of the

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literature, which have been calculated using the standard procedure. The values of Markstein lengths depend on the various definitions of burning speed, which involve different assumptions of calculation. Thereby, the expression (6) assumes zero flame thickness and is consequently erroneous. Contrary to this standard calculation, the new methodology has the advantage of a direct measurement of the Markstein length relative to the fresh gases and of the unstretched burning velocity without using the fuel properties. 4.3. Preliminary results for the isooctane/air mixtures Isooctane, which is liquid under ambient conditions, must be vaporized in a heated chamber before injection into the combustion vessel; to check the procedure of regulation and pre-vaporization, laminar burning velocity measurements of isooctane/air flames were performed for various equivalence ratios at 358 K and atmospheric pressure. During the experiments, the liquid fuel vaporization system showed no coking inside the vaporization chamber, no recondensation and no flow rate oscillation. In the figure 17, experimental values of burning speed were first calculated using equation (6); they are extracted with linear and nonlinear formulations and they are compared to data of Bradley et al. (Bradley et al., 1998) which have been calculated by linear expression. As observed in the figure 17, for data post-processed with linear methodology, a good agreement is found with results of Bradley et al. (Bradley et al., 1998). Both methodologies, linear and nonlinear, present similar results for an equivalence ratio range of 1.2 – 1.3 but burning speeds that are obtained with the linear methodology are higher for equivalence ratio lower than 1.2. Then in the figure 18, for an isooctane/air mixture (Φ = 1, P = 0.1 MPa, T = 373 K), the linearly extrapolated results are compared with values that are obtained by direct measurement of laminar burning velocity. As shown in this figure, if the burning velocity curves are extrapolated at zero stretch rate, the direct measurement of laminar burning velocities agrees well with the other method and both yield almost the same value of unstretched burning velocity: un° = 46 ± 1 cm.s-1. On the other hand, values of laminar Markstein lengths are different: L = + 0.193 mm (standard procedure) and L = - 0.049 mm (new procedure). Values of burned gas Markstein lengths are presented in the table 2. 5. Conclusion The experimental facility has been validated using measurements of laminar burning speed for spherically expanding flame of methane/air and isooctane/air mixtures, under high pressure (2 MPa) and high temperature (523 K) conditions. Two laser techniques, high speed tomography and PIV, have been applied and images of flame propagation have been processed with two approaches: the standard procedure which is based on the properties of fuel mixture and a new method which determines directly the burning velocity from the flame displacement speed and the fresh gas velocity near the preheated zone. Concerning the first approach of post-processing that extracts the laminar burning velocity from the flame speed and the ratio of unburned and burned gas densities, experimental results are in excellent agreement with data that are issued from literature. Two different formulations, one linear and one nonlinear, allowing to calculate the unstretched laminar burning velocity have been applied for different equivalence ratios at atmospheric pressure and ambient temperature. It has been observed that the use of the linear methodology overestimates burning velocities at equivalence ratios higher than 1 for methane/air mixtures and lower than 1.2 for isooctane/air mixtures and then the nonlinear methodology must be used. Then, the PIV images have been processed by the new algorithm and results of both approaches have been compared. Both methodologies give the same laminar burning velocity when extrapolated to zero stretch rate

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but they give rise to different values of Markstein length. Contrary to the standard procedure which involves several erroneous assumptions, the new methodology has the advantage of a direct measurement of the Markstein length relative to the fresh gases and the unstretched burning velocity without using the fuel properties. Acknowledgements: this research is sponsored by the European Regional Development Fund as part of the project INTERREG IV C5. Figures Fig. 1 Experimental setup

Static Pressure Transducer

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1st stage: For a PIV image couple, determination of the optimum displacement of the 2nd interrogation window in order to find the maximum correlation.

Fig. 2 Principle of image processing

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Fig. 3 Evolution of the intensity of the correlation peak as a function of the displacement between two interrogation windows.

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Fig. 7 Comparison of linear and nonlinear extrapolations of lean CH4/air experimental data (Φ = 0.7, P = 0.1 MPa, T = 298 K) Fig. 8 Comparison of linear and nonlinear extrapolations of rich CH4/air experimental data (Φ = 1.3, P = 0.1 MPa, T = 298 K) Fig. 9 Relationship between laminar burning velocity and pressure (CH4/air mixtures, Φ = 1, T = 298 K). Comparison with previous works and calculations with GRI-MECH 3.0 and GRI-MECH 2.11

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Fig. 10 Tomography images of laminar spherical flames of stoichiometric CH4/air mixtures for various pressures at T = 298 K

Fig. 11 Pressure dependence of the laminar burning velocity for different temperatures (CH4/air mixtures, Φ = 1)

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Vel

ocity

(cm

.s-1)

Pressure (MPa)

298 K323K373K423K473K523K

2

Fig. 12 Evolution of the normalized laminar burning velocity according to the pressure for different temperatures (CH4/air mixtures, Φ = 1) 0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 0,5 1 1,5

Nor

mal

ized

lam

inar

bur

ning

Vel

ocity

Pressure (MPa)

298 K323K373K423K473K523K

2

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Fig. 13 Relationship between laminar burning velocity and temperature (CH4/air mixtures, Φ = 1, P = 0.1 MPa). Comparison with previous works

30

40

50

60

70

80

90

273 323 373 423 473 523

Lam

inar

bur

ning

Vel

ocity

(cm

.s-1)

Temperature (K)

Present workStone et al.Hill et al.Garforth et al.Gu et al.Hermanns et al.Mishra et al.

1

1,5

2

2,5

3

3,5

4

273 323 373 423 473 523

Nor

mal

ized

lam

inar

bur

ning

Vel

ocity

Temperature (K)

0.1 MPa0.5 MPa1 MPa1.5 MPa2 MPa

Fig. 14 Temperature dependence of the laminar burning velocity for different pressures (CH4/air mixtures, Φ = 1)

0

10

20

30

40

50

60

70

80

90

273 323 373 423 473 523

Lam

inar

burn

ing

Velo

city

(cm

.s-1)

Temperature (K)

0.1 MPa0.5 MPa1 MPa1.5 MPa2 MPa

Fig. 15 Evolution of the normalized laminar burning velocity according to the temperature for different pressures (CH4/air mixtures, Φ = 1)

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0

40

80

120

160

200

240

0 50 100 150 200 250 300 350 400 450 500 550

Velo

city

(cm

.s-1)

k (s-1)

sUgUn (Eq. 6)Un (Eq. 7)

Fig. 16 Variation of flame speed, s, and fresh gas velocity, ug, as a function of flame stretch. Comparison of both procedures of calculation of burning velocity (CH4/air mixture, Φ = 1, P = 0.1 MPa, T = 298 K)


Fig. 17 Relationship between laminar burning velocity and equivalence ratio (Isooctane/air mixtures, P = 0.1 MPa, T = 358 K). Comparison of linear and nonlinear methodologies

0

5

10

15

20

25

30

35

40

45

50

0,8 0,85 0,9 0,95 1 1,05 1,1 1,15 1,2 1,25 1,3

Lam

inar

bur

ning

Vel

ocity

(cm

.s-1)

Equivalence ratio

Linear method (present work)

Nonlinear method (present work)

Bradley et al.

0

40

80

120

160

200

240

280

0 100 200 300 400 500 600 700 800

Velo

city

(cm

.s-1)

k (s-1)

sUgUn (Eq. 6)Un (Eq. 7)

Fig. 18 Variation of flame speed, s, and fresh gas velocity, ug, as a function of flame stretch. Comparison of both procedures of calculation of burning velocity (C8H18/air mixture, Φ = 1, P = 0.1 MPa, T = 373 K)

Table 1 Values of burned gas Markstein length Lb. Comparison with experimental data of previous works (CH4/air mixture, Φ = 1, P = 0.1 MPa)

References Lb (mm) standard procedure

Lb (mm) new procedure

This work 0.94 (at 300 K ) - 1.09 (Rozenchan et al., 2002) 1 (at 298 K ) (Gu et al., 2000) 0.9 (at 298 K ) (Bradley et al., 1996) 0.85 (at 298 K ) (Halter et al., 2009) 0.7 (at 298 K )

Table 2 Values of Lb. Comparison with experimental data of previous works (C8H18/air mixture, Φ = 1, P = 0.1 MPa)

References Lb (mm) standard procedure

Lb (mm) new procedure

This work 1.326 (at 373 K ) - 0.3365 This work 2.06 (at 358 K ) (Bradley et al., 1998) 1.477 (at 358 K )

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measurement of laminar flame speed for high pressure and...

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