Experimental characteristics of turbulent premixed flame in a boosted Spark-Ignition engine

Experimental characteristics of turbulent premixed flame in a boosted Spark-Ignition engine

Available online at www.sciencedirect.com Proceedings of the Proceedings of the Combustion Institute 34 (2013) 2941–2949 Combustion Institute www.e...

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Proceedings of the Combustion Institute 34 (2013) 2941–2949

Combustion Institute www.elsevier.com/locate/proci

Experimental characteristics of turbulent premixed flame in a boosted Spark-Ignition engine C. Mounaı¨m-Rousselle ⇑, L. Landry, F. Halter, F. Foucher Laboratoire PRISME, Universite´ d’Orle´ans, Polytech Vinci – 45072 Orle´ans cedex, France Available online 12 October 2012

Abstract As combustion takes place in smaller combustion chambers at higher pressure, the development of boosted Spark-Ignition (SI) engines can induce non classical flame development. Moreover to limit abnormal combustion and thermal NOx production, a high dilution rate by exhaust gases is used. To improve the combustion processes occurring in SI engines and to validate new concepts, turbulent premixed combustion propagation is now estimated by using 3D CFD calculations, usually based on flamelet theory. However, this theory may be limited when the boosted engine is running in high diluted conditions. Therefore, in this paper, the flame characteristics of a stoichiometric iso-octane/air mixture were determined from in-cylinder measurements for a relatively high intake pressure and different dilution rates. By using an evaluation of both laminar and turbulent characteristics at real engine conditions, the trajectories of combustion processes occurring inside the cylinder were plotted in a Peters-Borghi diagram. Dilution induces a shift from the middle of the corrugated flamelet zone to the beginning of the thin reaction zones. Moreover, thanks to high speed PIV-flame tomography measurements, it was shown that dilution enhances flame-turbulence interactions and that the corrugation generated through dilution occurs at smaller scales than the integral length scales. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: SI engine; Dilution; Laminar burning velocity; Turbulent burning velocity

1. Introduction As underlined by Tan et al. [1], CFD modeling is increasingly used to investigate the phenomena occurring during combustion inside SI engines. This tool can help to design and build new engines to reduce fuel consumption, greenhouse gas CO2 emissions and pollutant emissions. A good overview of the different multi-zone models was given recently by Verhelst and Sheppard [2]. However,

⇑ Corresponding author. Fax: +33 238 71 83 73.

E-mail address: [email protected] (C. Mounaı¨m-Rousselle).

even if modeling has considerably improved, enabling, for example, the reproduction of cyclic combustion variability by an LES approach [3], the lack of dedicated studies to describe flame behavior is well known. A major way to provide high thermal efficiency by reducing pumping and friction losses [4–6] is the “downsizing” concept, i.e. reducing the engine size and increasing the intake pressure. In order to develop future Spark-Ignition engines in compliance with pollutant standards and fuel consumption objectives, the turbo-charged concept is widely applied. Increasing the intake pressure, however, can involve the knock phenomenon. To avoid this, one solution is to increase the

1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.09.008

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Exhaust Gas Recirculation (EGR) which decreases NOx emissions due to the dilution of the air–fuel mixture. It is evident that this kind of engine can induce changes in turbulent flow field, length scales, flame structures and therefore in flame behavior. Only a few studies in the literature have investigated real boosted SI engines conditions. The recent work [7], for example, performed numerical and experimental investigations to analyze and classify the flame structure in a turbo-charged direct injection gasoline engine. The objective of the present study is therefore to investigate experimentally the iso-octane/air flame propagation inside a boosted optical Spark-Ignition engine. A previous study [8] focused on the effect of the intake pressure on the in-cylinder turbulence level. It was observed that the turbulence level and length scales do not really change with the intake pressure as had also been previously found [9]. The parameter of interest in the present study is the dilution rate of the air–fuel mixture (i.e. EGR). It is well known that in SI engines, depending on the laminar and turbulent characteristics, combustion can take place in different regimes ranging from wrinkled or corrugated flamelet regimes to thin reaction zones regimes according to the Peters-Borghi diagram [7,10]. As most models are based on these regimes, it is pertinent to determine the combustion regime in the case of ‘downsized’ premixed combustion. As one of the most important parameters to characterize a premixed turbulent combustion is the turbulent combustion speed, simultaneous high speed laser sheet tomography and Particle Imaging Velocimetry were performed to estimate it as a function of the combustion development. 2. Experimental set-up The experiments were performed in a 0.5 l single cylinder engine. All the engine specifications are indicated in Table 1. Optical access was provided through a 50 mm diameter fused silicate window at the top of an elongated piston and through two lateral fused silicate windows. In this study, the engine was driven by an electric motor

and the engine speed fixed at 1200 rpm. This value can be representative of the average speed with boosting ‘downspeeding–downsizing’ future engines. Engine timings were provided by an optical encoder with 0.1 Crank-Angle Degree (CAD) resolution mounted on the end of the crankshaft. The intake port was connected to an air compressor and a regulator made it possible to maintain the mean intake pressure at 1.3 bars with an uncertainty lower than 5 mbar. All the intake gases were at 50 °C, due to the help of an electrical heating system. The Exhaust Gas system was a laboratory-simulated EGR system: different flows of C8H18, N2, CO2 and H2O were controlled in order to ensure a stoichiometric equivalence ratio. The EGR was simulated by 73.5% N2, 12.5% CO2 and 14.0% H2O by volume: this composition represents burned gases released by the complete combustion of a stoichiometric isooctane-air mixture. The air–fuel mixture was ignited with a standard spark plug with a fixed discharge duration of 1 ms. The spark timing was set to produce maximum indicated mean effective pressure without knock. Table 2 shows all the conditions as a function of the dilution rate. The indicated mean effective pressure range was from 9.00 to 13 bars. The dilution rate was limited to 30% in order to avoid misfires and partial burns. Indeed, for all cases, the coefficient of variation (COV) of the indicated mean effective pressure (IMEP) was less than 5%. To estimate the mass of burnt gases, the conventional apparent heat release was estimated from the pressure recorded via a Kistler 6043A60 (0–250 bars) pressure sensor and using a single-zone model with a perfect gas assumption with no heat transfer and constant properties and composition during the closed valve period. A classical two-zone model was used to determine the evolution of the fresh gases temperature in order to estimate the laminar combustion velocity with the Chemkin package [11]. Both zones were assumed to be homogeneous and the burnt gases in chemical equilibrium during the combustion and relaxation steps. For each zone (fresh gas and burnt gas zones), the differential energy and state equations were considered and linked using the volume conservation. Wall heat losses were considered for both zones and modeled using the Woschni model [12].

Table 1 Engine specifications. Item

Specifications

Type Bore Stroke Displacement volume Compression ratio Fuel Engine speed

4 valves 85 mm 88 mm 499 cm3 10.2 Isooctane (C8H18) 1200 rpm

Table 2 Operating conditions. ER (%)

Spark timing (°CA)

IME (bar)

10 15 20 25 30

28 34 44 68 60

13.00 12.60 11.70 10.70 9.00

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3. Optical measurement techniques The Particle Imaging Velocimetry set-up was composed of a double-pulsed high speed laser Nd:YLF Pegasus, which produced a beam at 527 nm, converted to a laser sheet by a combination of spherical and cylindrical lenses and a high speed CMOS camera (Photron Ultima APX). The laser sheet passes through the combustion chamber at the middle of the height and thickness was estimated to be 0.5 mm in the region imaged by the camera. The intake gases were seeded with silicon oil particles. The same apparatus was used for PIV and Mie scattering laser tomography. The frequency of the double-pulsed laser was fixed at 6.25 kHz, which induced a delay of 160 ls between the displacement of the two flames, set by using the software (Insight 3G from TSI) and a spatial resolution of the camera of 512  256 pixels2. The magnification ratio was then equal to 0.068 mm/pixel and, with an interrogation window of 32 pixels2 and the spatial resolution of the high frequency PIV equal to 2.17 mm. The delay between the two pulses was optimized to determine the fresh gases velocity along the flame front contour, and was set at 15 ls. This value was found as a compromise to keep the droplet inside the laser sheet according to the turbulence intensity and to get a relative good precision to measure only the large scale aerodynamic flow. The field of view is presented in Fig. 1, superimposed on a non-reactive mean flow fields determined at the TDC for a boosted pressure equal to 1.3 bar. It is limited but allowed to study the most part of the combustion area as the analysis was focused on the first 25% of the burned mass-fraction. Due to the size of the combustion chamber (88 mm bore and 12 mm height) and according to the mean flow field, the turbulent flame propagates in parallel to the piston, then the 3D effect can be just accorded to the turbulence. According

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to the magnification ratio and the delay between the two pulses and by considering the mean flow field velocity, the displacement of the particles inside de interrogation window was less than 1 pixel. This small value increases the measurement incertitude that can be considered equal to 0.1 m/s. In order to extract the local instantaneous flame front, background signals induced by reflexions and combustion emissions were also removed and a laser profile correction was used to remove inhomogeneity cause by laser sheet. Each adjusted image was then binarised with the Otsu thresholding method [13], in order to distinguish the unburnt and burnt zones. based on a very simple idea: find the threshold that minimizes the weighted within-class variance, to distinguish the unburnt and burnt zones. The extracted flame contour was then filtered with a 2 mm Chebychev low pass filter to remove all structures smaller than the integral scale. The integral length scale, determined with a low frequency and high resolution PIV [15], was found equal to 1.4 mm until the Top Dead Center (TDC). From the contours at t and t + Dt, the local displacement for all pixels along the contour was evaluated by considering a displacement normal to the flame front. This method was relevant: as the time is reduced between two pictures, the flame front shapes at t and t + Dt are related by a dilatation. Driscoll [14] reviewed three unambiguous and different definitions of the turbulent burning !

!

velocity, S T . Here S T is defined as a displacement speed, by determining the distance covered by the flame front for a certain period of time as !

!

!

!

!

!

S T : n ¼ ðU d  U gasz Þ: n , with U d the velocity of !

the flame front, U gas the velocity of the gas into which the flame front is propagating, and n the normal to the flame front, as schematized in Fig. 2. With simultaneous high speed Tomography-PIV systems, it is possible to estimate the local turbulent combustion velocity from the instantaneous fresh gas velocity, along the flame front contour by considering two tomography images with DTPIV (15 ls), time separation to avoid 3-D motion influence and the instantaneous flame front propagation speed by considering two tomography images separated by 1/laser frequency (160 ls), as shown in Fig. 3. As the flame fronts are slightly wrinkled and relatively homothetic, the main hypothesis is based on the !

!

low value of the angle between U d and n . Due to the complex cyclic variations involved inside the engine combustion chamber, especially at the highest dilution rate, the results presented here are the average of velocities along the contour !

Fig. 1. Field of view for PIV-Flame Tomography system.

!

!

!

!

!

and for 240 cycles ðS T : n ¼ U d : n  U gaz : n Þ, the upper bar denotes the average along the contour. An example of the local value of ST determined

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Fig. 4. Example of the evolution of the local and cumulative average value of ST along the contour. Case 10%EGR.

Fig. 2. Definition of the different velocities along flame front contour.

Fig. 5. Effect of the spatial filter of the contour on the average value of ST for all cases.

Fig. 3. Determination of Sd and Ugas at each point of the contour.

at each point along the contour is presented in Fig. 4 for the case of 10%EGR. As the number of points along the contour is sufficient, the average value along the contour is well converged, where the “cumulative” average value is plotted as function of the number of points. The main advantage of the high speed system is that it enables the evolution of the turbulent combustion speed to be determined as a function of the burnt mass fraction. Moreover, the effect of spatial filter on the contour was evaluated: in Fig. 5, the results obtained for the average turbulent flame velocities

are given for all cases and different filter values. It can be concluded than a variation of 33% of the filter around the integral scale value induces a variation less than 10% in average velocities values. A comparison with another methodology more global was also presented in [8]. Therefore as ST is equal to the difference between Sd and Ugas, if one considers an error of gas velocity measurement and flame contour displacement of both 10%, the turbulent flame speed velocity has an error of 20%. From these considerations, for the figures of ST values, the errors bars corresponding to 20% were added.

4. Results 4.1. Operating conditions Figure 6a shows the evolution of the mean incylinder pressure for all the operating conditions presented in Table 2. A non-firing cycle is

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Fig. 6. Evolution of the mean in-cylinder pressure and of the unburnt gas temperature for all conditions.

represented by the continuous grey line. The pressure evolutions of the five dilution levels presently investigated are plotted. For each of these curves, a continuous line has been added. It corresponds to the Crank-Angle-Degree (CAD) range during the flame propagation recorded in the observation area. The increase in the dilution rate involves a decrease in the maximum pressure peak with a strong modification of the spark timing, due to the decrease in the reactivity of the fresh gas enclosed inside the combustion chamber. 4.2. Classification of turbulent premixed flame propagation In this study, the turbulent premixed engine combustions are classified according to the Peters-Borghi diagram. Although the borders between the various identified combustion modes are permanently called in question, that gives a first outline of the probable behavior of the flame and its structure during the stroke as reminded Linse et al. recently [7]. As most of models are based on the flamelet regime assumption, the unusual conditions involved in downsizing engine can change the validity of the assumption. Even if the turbulent combustion diagram always generates intense debates, this first approach can be interesting. The turbulent intensity q’ and integral length scale

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were determined with PIV for non-reactant flows in Foucher et al. [15]. In this cited work, the PIV system was different: a CCD camera (2048  2048 pixels2) was used and observed a relatively small area, leading to a magnification of 12 microns per pixel. A 32  32 pixels2 interrogation spot and a 8 pixels maximal displacement were used in the processing. These experimental conditions allow a correct determination of the turbulent characteristics. The ‘real’ turbulence intensity, i.e. without the part of cyclic variations, was extracted from a PODbased procedure. The cutoff mode number was chosen from the compromise between the evolutions of integral length scales, turbulent intensity homogeneity and the kinetics energy spectra as function of the cut-off modes as fully described in [15]. The integral length scale was constant until the Top Dead Center (TDC) at the value of 1.4 mm and a slight evolution of the turbulent intensity (from 1.2 m/s at 40 CAD before TDC) until 1.3 m/s at TDC) was observed. After TDC no more evolution was obtained (until 10 CAD). Further details are given in [15,16]. The fresh gases flow through the intake valves and are directed towards the center of the combustion chamber, generating the two contra-rotative vortices with a vertical revolution axis. The compression and its associated tumble motion decrease the vortices intensity. Therefore the horizontal laser sheet, parallel to the piston surface, allows the correct visualization of the turbulent structures. Several studies [17–19] indicated that the laminar burning characteristics are affected by the thermodynamic conditions, i.e. initial unburnt gas pressure and temperature and the dilution rate, and that the chemistry and thermo-diffusion properties of hydrocarbons have a significant effect on the combustion process. In this study, the ‘real’ unburnt gas temperature and not the ‘cold’ gas temperature at the spark timing was used (determined from the 2-zone modeling) to determine the laminar burning velocity (Fig. 6b). It can be seen that the temperature rises from 670 K (at 15 CAD before TDC) up to 800 K (at 10 CAD after TDC) in the case of 25%EGR. Therefore, the value of the laminar burning velocity is significantly underestimated if the colder gas temperature at spark timing is used rather than the fresh gas temperature as function of CAD as stressed by Linse et al. [7]. Since the spark timing advance, the chamber temperature and the pressure are not kept constant for all the considered cases, the most appropriate parameter to plot the evolution of combustion parameters is not the CAD but the Burnt Mass Fraction (BMF), even if the temporal evolution of combustion is not well represented. The evolution of the BMF versus the CAD is shown for all conditions in Fig. 7, which indicates also how the dilution can affect the combustion phasing and duration. The stability of the highest diluted mixture

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Fig. 7. Evolution of burnt mass fraction versus crankangle degrees for all conditions.

(30%EGR) was highly deteriorated and after this value, it was not possible to stabilize the engine. Laminar burning velocities of the isooctane/air mixture were estimated, in the engine conditions, by using the PREMIX code (CHEMKIN package) and the Hasse et al. [20] reduced chemical kinetic mechanism (48 reactions and 29 species). The laminar burning velocity decreases as a function of the dilution rate and reaches a kind of plateau after 20%BMF (Fig. 8). The difference between the value at the spark timing and this value as a function of the burnt mass fraction can induce an error of up to 20% (in the case of 30% dilution) in the flame propagation velocity estimation. The highest dilution case (30% EGR) initially exhibits a strong increase due to a relative stagnation of BMF during the 25 first CAD. To classify the regime with the Peters-Borghi diagram, the laminar flame thickness, dl, was esti-

Fig. 8. Evolution of laminar burning velocity versus burnt mass fraction for all conditions.

mated by using the classical definition of dl = k/ cp/(quSl) with k the thermal conductivity, cp the fresh gas specific heat capacity and qu the unburnt density. Contrary to the laminar combustion velocity, the laminar thickness increases with an increase in dilution and decreases as the laminar burning velocity decreases. The impact on the flame structure due to the dilution rate is shown in Fig. 9, indicating the evolution of the flame structure: crosses indicate the conditions at the spark timing and diamonds indicate the conditions as a function of fresh gas consumption: the darker symbols correspond to the less diluted conditions. Since the turbulence level is maintained constant, the main effect is linked to laminar properties, i.e. flame speed and thickness. As in Dai et al. [21], the combustion process follows a right-down trajectory in the diagram. When dilution level is increased, a left-up shift from the corrugated flamelet zone to the thin reaction zones is observed. However, especially for a high EGR level, the shape of the flame structure plot presents a kind of turn, which was well predicted by Linse et al. from numerical work in similar conditions. This turn, clearly observable for the 30%EGR dilution case (and less for 25%EGR), corresponds to a combustion process occurring in the expansion stroke as can be seen in Fig. 6. In our case, however, first for the lower dilution rates, i.e. the highest loads, the combustion process takes place in the corrugated flamelet regime and as the dilution rate increases the flame thickness, combustion reaches the thin reaction zone regime. It could be expected that as the smallest eddies are able to penetrate into the preheated zone, there would be no dependence between the turbulent burning velocity and the turbulent intensity. To prove that, it is helpful to estimate the turbulent burning velocity as a function of the burnt mass fraction. 4.3. Evolution of turbulent burning velocity From the plot of the fresh gas velocity, averaged along the flame front contour, as a function of the BMF (Fig. 10), two main steps can be distinguished: during the first phase, the fresh gas velocity increases strongly until a BMF of less than 5% but after this step, the velocity remains constant in slightly diluted cases or decreases strongly in the case of highest dilution rate. For the case of 10%EGR, a fresh gas velocity of 2 m/s is reached: due to the macroscopic aerodynamic motions and to the expansion induces by the fresh/burnt gases density difference. When the dilution level is increased (15–25%EGR), fresh gas velocity exhibits quite similar evolutions during the combustion process with values between 0 and 1 m/s. The velocities of the highest dilution case are mostly negative indicating that the flame kernel fully undergoes the tumble motion. In these

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Fig. 9. Comparison of the combustion traces in Peters-Borghi diagram, 25%EGR, } 30%EGR.

Fig. 10. Evolution of local fresh gas velocity, averaged along the contour versus burnt mass fractions.

conditions, the flame is shifted and the burnt gases expansion becomes almost negligible compared to the in-cylinder motion. The value of the turbulent combustion velocities are classified according the dilution level, i.e. according the laminar combustion velocity value (Fig. 11). A strong decrease in the velocity is also observed after 5% of burnt mass fraction when the ignition energy does not affect the flame front development. Therefore, for 30% dilution, the

10%EGR,

15%EGR,

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20%EGR,

laminar flame speed will be low and propagation difficult. The ratio between turbulent combustion velocity and laminar combustion velocity, ST/SL, versus the burnt mass fraction is plotted in Fig. 12 for different dilution rates. Independently of the dilution level, ST/SL decreases linearly with the burnt mass fraction indicating a decrease of the global flame front corrugation. Except the highest dilution rate (30% EGR), for a fixed burnt mass fraction, the value of ST/SL increases with the dilution level. By referring to the Peters-Borghi diagram (Fig. 9), dilution induces a shift from the middle of the corrugated flamelet zone to the beginning of the thin reaction zones. Only the highest dilution rate is located in the thin reaction zone. Basing on Figs. 9 and 12, one can guess that, for a given turbulence level, dilution enhances flame-turbulence interactions through both a decrease of the burning speed and an increase of the flame thickness. The highest dilution level case should operate in the thin reaction zone. For this case, the laminar burning velocity is more than four times lower than the turbulence intensity (q0 ). The flame strongly undergoes the macroscopic aerodynamic motion and the turbulence. Peculiarly, ST/SL presents relative low values, consistent with a reduced flame front-turbulence interaction. One explanation could lie on the fact that the corresponding combustion process occurs mainly in the expan-

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8 30%EGR

Averaged turbulent flame velocity (m/s)

25%EGR 20%EGR 15%EGR 10%EGR

6

4

2

0 0

10

20

30

40

Burnt Mass Fraction (%) Fig. 11. Evolution of mean turbulent combustion velocity versus burnt mass fraction.

To assess the effect of dilution on the wrinkles, the mean curvature was estimated from the filtered contour (Fig. 13). After 15% of BMF, the mean curvature is near zero, with a slight shift on the negative side, which corresponds to a flame front shape, concave side through burnt gases as

Fig. 12. Evolution of the ratio ST/SL versus burnt mass fraction.

sion stroke when aerodynamic flow field and turbulent intensity are notably modified.

Fig. 13. Evolution of mean curvature versus burnt mass fraction.

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noted by Shepherd et al. [22]. But no real effect of the flame regime can be observed from this parameter. One must remember that flame fronts were filtered by using a low pass filter to remove all structures smaller than the integral scale. One can conjecture that the corrugation generated through dilution occurs at smaller scales than the integral length scales.

5. Conclusion The objective of this paper was to provide experimental turbulent burning velocity values determined in an optical SI engine at realistic conditions, i.e. boosted and diluted conditions by using simultaneous high frequency laser tomography imaging and particle image velocimetry. By using both laminar and turbulent information, the trajectories of combustion processes occurring inside the cylinder were plotted in a Peters-Borghi diagram to provide a first outline of the probable behavior of the flame and its structure during the stroke. The increase of the dilution rate (from 10% to 30%) induces a shift from the middle of the corrugated flamelet zone to the beginning of the thin reaction zones with the highest dilution rate case located in the thin reaction zone. The turbulent combustion velocity was first determined locally in SI engine by subtracting the fresh gas velocity just behind the flame front to the displacement speed of the flame front. ST/SL decreases linearly with the burnt mass fraction indicating a decrease of the global flame front corrugation but increases with the dilution level (except for the highest dilution rate). Moreover, we pointed out that dilution enhances flame-turbulence interactions through both a decrease of the burning speed and an increase of the flame thickness and the corrugation generated through dilution occurs at smaller scales than the integral length scales. The difference of behavior found for the highest dilution case needs to be verified by performing new experiments with higher resolution and 3 D considerations but also CFD modeling to confirm it.

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References [1] Z. Tan, R. Reitz, Combust. Flame 145 (2006) 1–15. [2] S. Verhelst, C.G.W. Sheppard, Energy Convers. Manage. 50 (2009) 1326–1335. [3] B. Enaux, V. Grant, O. Vermorel, et al., Proc. Combust. Inst. 33 (2011) 3115–3122. [4] P. Leduc, B. Dubar, A. Ranini, G. Monnier, Oil Gas Sci. Technol. 52 (1) (2003) 115–127. [5] L. Guzzella, U. Wenger, R. Martin, SAE Paper 2000-01-1019, 2000. [6] D. PetitJean, L. Bernardini, C. Middlemass, S.M. Shahed, SAE Paper 2004-01-0988, 2004. [7] D. Linse, C. Hasse, B. Durst, Combust. Theory Model. 13 (1) (2009) 167–188. [8] L. Landry, F. Halter, F. Foucher, E. Samson, C. Mounaı¨m-Rousselle, SAE Int. J. Fuels Lubr. 1 (1) (2009) 984–992. [9] H. Kobayashi, Exp. Therm. Fluid Sci. 26 (2002) 375–387. [10] N. Peters, Turbulent Combustion, Cambridge Univ. Press, Cambridge, UK, 2000. [11] R.J. Kee, F.M. Rupley, J.A. Miller, Report No. SAND87-8248, Sandia National Laboratories, 1988. [12] G. Woschni, SAE Paper 670931, 1967. [13] N. Otsu, IEEE Trans. Syst. Man Cybern. 9 (1) (1979) 62–66. [14] J.F. Driscoll, Prog. Energy Combust. Sci. 34 (1) (2008) 91–134. [15] Foucher, F., Landry, L., Halter, F., Mounaı¨mRousselle, C., Fourteenth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 2008. [16] L. Landry, Ph.D. dissertation, University of Orle´ans, France, 2007. [17] M. Metghalchi, J.C. Keck, Combust. Flame 48 (1982) 191–210. [18] D. Bradley, R.A. Hicks, M. Lawes, C.G.W. Sheppard, R. Wolley, Combust. Flame 115 (1998) 126– 144. [19] F. Halter, F. Foucher, L. Landry, C. Mounaı¨mRousselle, Combust. Sci. Technol. 181 (6) (2009) 813–827. [20] C. Hasse, M. Bollig, N. Peters, H.A. Dwyer, Combust. Flame 122 (2000) 117–129. [21] W. Dai, S.G. Russ, N. Trigui, K.V. Tallio, SAE paper 982611, 1998. [22] I.G. Shepherd, R.K. Cheng, Combust. Flame 127 (2001) 2066–2075.