Lift-off and stabilization of n-heptane combustion in a diesel engine with a multiple-nozzle injection

Lift-off and stabilization of n-heptane combustion in a diesel engine with a multiple-nozzle injection

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Proceedings of the Combustion Institute 34 (2013) 3031–3038

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Lift-off and stabilization of n-heptane combustion in a diesel engine with a multiple-nozzle injection ¨ . Andersson b, X.-S. Bai a R. Solsjo¨ a,⇑, M. Jangi a, C. Chartier b, O a

b

Division of Fluid Mechanics, Lund University, S 221 00 Lund, Sweden Division of Combustion Engines, Lund University, S 221 00 Lund, Sweden Available online 19 July 2012

Abstract This paper presents a joint numerical and experimental investigation of flame lift-off and stabilization mechanisms in heavy-duty diesel engines. The injection strategy, employing different nozzle configurations, allows for quantification of the impact of varying inter-jet angle spacing in the presence of swirl. For this purpose, three different inter-jet angles are chosen in this study; 45°, 90° and 135°. Large-eddy simulations are performed utilizing a detailed chemical kinetic mechanism for n-heptane to resolve the turbulent fuel and air mixing and to capture the important species surrounding the ignition and flame-fronts to describe the flame stabilization process. Measurements are carried out for OH chemiluminescence to identify the flame lift-off position in an optical accessible engine. In general, the swirl flow in the ambient air shows a great impact on the lift-off, with a 15% difference in the lift-off lengths on the upwind and downwind side of the jet. The LES results show that important ignition reactions undergo in a broad region in front of the lift-off position. With decreasing inter-jet angle, it is shown that the impact of transportation of hot products from adjacent jets becomes more prominent. Hot reservoirs surrounding the lift-off length increase the local ambient temperature and augment the auto-ignition process by mixing of the cold injected fuel and hot air. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Jet–jet interaction; Flame stabilization mechanism; Auto-ignition; Flame propagation; Optical engine

1. Introduction In the past decade stringent emission legislations and concern about fuel economy have pushed forward the development of diesel engines. Simultaneous reduction of NOx and soot emissions requires both after-treatment and in-cylinder solutions, e.g. more flexible injection systems with high injection pressure and small nozzle orifice

⇑ Corresponding author. Fax: +46 462224717.

E-mail address: [email protected] (R. Solsjo¨).

diameters. This results in a high jet velocity, high intensity small-scale turbulence, fast primary breakup of the liquid fuel core and fast mixing of the fuel vapor with ambient air. Studies of the combustion characteristics and fluid dynamics in diesel combustion with modern injection systems have been the focus of recent research, e.g., activities within ECN, the Engine Combustion Network [1]. It is generally understood that NOx formation in diesel engines is more prominent at high temperatures due to the dominating Zel’dovich thermal-NO mechanism, whereas soot emission exhibits a non-monotonous dependence on temperature with a maximum at approximately

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.2012.06.111

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1800–2000 K, since soot formation is kinetically limited at lower temperatures and the rate of soot oxidation is higher than the rate of soot formation at higher temperatures [2]. In a quasi-steady jet, soot formation is influenced by the amount of air entrained into the jet [3]. The lift-off length is a dominant parameter in this process, as a significant part of the total air entrainment takes place between the nozzle orifice and the lift-off region. Under constant volume conditions, e.g. in the Sandia combustion vessel, systematic experimental studies of single fuel jets have been carried out under combusting and non-combusting conditions [4–7]. Based on such experiments, Pickett et al. [8] proposed an empirical expression for the lift-off length, H, H ¼ 7:04  108 T 3:74 q0:85 d 0:34 UZ 1 a a st ;

ð1Þ

where Ta and qa are the ambient temperature and density, d is the injector orifice diameter, U is the jet velocity (related to the injection pressure), and Zst is the stoichiometric mixture fraction. The lift-off process is closely related to the stabilization of diesel flames. For a lifted jet flame different lift-off/stabilization mechanisms have been identified as summarized in [9,10] and the references therein, e.g. premixed flame propagation at the flame base [11,12], local extinction due to high scalar dissipation rate [13], vortex/flame interaction [14,15], and auto-ignition due to entrainment of hot gas [8]. For an atmospheric jet at ambient condition, local extinction due to high scalar dissipation rate is responsible for the lift-off of an initially attached flame, whereas premixed flame propagations agree well with many experimental observations [9,10]. Under diesel engine conditions where the ambient temperature and pressure are much higher than at atmospheric conditions, auto-ignition of the charge may play a more important role in the lift-off process, as indicated in several experimental observations, e.g. the appearance of isolated ignition kernels upstream of the lift-off [16], shorter lift-off length for fuels with shorter ignition delays [8], and the close correlation between the timescale for jet mixing upstream of the lift-off with an Arrhenius type expression [8]. In a recent attempt to discriminate different mechanisms of flame lift-off and stabilization [16], experiments were carried out in the Sandia combustion vessel where laser-plasma ignition was placed at an upstream position to the natural position of the lifted flame. It was found that the flame moved slowly away from the laser-ignition site and eventually it was stabilized at its naturally stable lift-off position. This indicates that neither the premixed flame propagation nor the auto-ignition mechanisms may fully explain the flame stabilization in the lifted flame under diesel engine conditions. It was argued that the transient liftoff response to laser ignition is due to re-entrain-

ment of hot combustion products formed at the diffusion flame downstream of the flame base, which enhances the auto-ignition at the lift-off by raising the temperature locally. Such re-entrainment mechanism was examined in [17], which was shown to be more significant under high ambient temperature conditions owing to the high sensitivity of auto-ignition to temperature. The results obtained from studies of single fuel jets in large combustion vessels do not fully comply with the processes in a diesel engine. Trends towards increasing full load performance in combination with smaller nozzle holes mean that, to maintain reasonable injection durations in a diesel engine for a given fuel mass, the number of nozzle holes and the injection pressure must be increased. This leads to a reduction in the inter-jet spacing, resulting in a smaller air volume around each jet and thereby limiting the amount of air entrainment to the fuel stream. Several recent engine experiments have showed that, with multiple-nozzle injection systems, the lift-off length is considerably shorter than the prediction of Eq. (1) [18,19], and the correlation with ambient gas temperature is weaker [17]. Furthermore, the swirl motion in the cylinder can affect the temperature distribution of the mixtures surrounding the jet. The lift-off length on the downwind side of the jet has been found to be 7–15% shorter than on the upwind side of the jet [18,19]. This work reports on a joint numerical and experimental investigation of the effects of interjet spacing on flame lift-off and stabilization in the presence of swirl motion. Large eddy simulation (LES) is used to simulate the spray breakup, evaporation, mixing with the ambient gas, and the subsequent combustion process in a diesel engine modified for optical measurements [18]. The results are used to quantify the evolution of the flame propagation and the reaction zone structure. OH chemiluminescence imaging is performed to quantify the lift-off position. The mixtures upstream of the lift-off position are analyzed to understand the observed differences between the upwind and downwind sides of the lifted flame. 2. Experimental setup and engine operation conditions The experimental investigations were performed on a six cylinder Scania D12 truck sized engine, modified for optical access with Bowditch design [20]. The piston stroke and bore were 154 and 127 mm respectively, with a piston bowl diameter of 70 mm. A single cylinder was operating at 1200 rpm and 5 bar IMEP, with the remaining five cylinders running motored. The compression ratio was 15.1. An electrical heater and a two-stage screw-compressor conditioned the inlet air temperature and pressure. The engine was run at 20% of

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the possible full load with a common-rail injector of Cummins XPI type. n-heptane was used in this study since it has similar lift-off length trends and comparable cetane number to diesel fuel. It differs from diesel fuel in boiling point and molecular structure and is therefore known to be less sooty [21]. The intake gas was pure air and the overall equivalence ratio was about 0.33. The fuel injection pressure over each individual injector hole was 2500 bar, equivalent to a fueling rate of 52 mm3/stroke, and the fuel was injected at a 17° angle to the bowl, relative to the cylinder head plane. The intake air pressure and temperature were 1.49 bar and 373 K. To study the effect of inter-jet angle, two different injector nozzle configurations were employed. Both had four nozzle holes of 100 lm diameter. One had a symmetric hole configuration with inter-jet angles 90°, whereas the other had an asymmetric configuration, where the inter-jet angles varied from 45° to 135°. Combustion phasing (CA50, crank angle at which 50% heat was released) was kept at 10 crank angle degrees (CAD) after top dead center (TDC) for both configurations. The ambient density at TDC was maintained at 27.4 kg/m3 by adjusting the level of boost pressure. Fuel injection was initiated at 4.1 CAD before TDC and the injection durations were approximately 20 CAD, providing a long quasi-steady jet phase. Natural luminescence was captured with a Phantom V7.1 high-speed video (HSV) camera to visualize the flame lift-off and stabilization process. Lift-off length in the optical engine measurements is defined as the distance between the nozzle and first appearance of OH-chemiluminescence, following [3,17]. An interference filter centered at 310 nm together with a 105 mm UV-Nikkor lens with a Hamamatsu image intensifier were used to detect OH radicals. High-speed video images revealed that a quasi-steady lift-off was established at 2 CAD after TDC and all subsequent lift-off images were acquired at this timing. When the position of lift-off length was determined, the remaining lift-off length measurements were made using a Princeton ICCD camera equipped with similar interference filter as above. The OH-chemiluminescence images of the jet were divided into two parts along the propagating axis to separately evaluate the effect of swirl. The part facing the swirl flow is the upwind side and the opposite is the downwind side. This distinction is later important to interpret the lift-off process for the various jets. 3. Computational model To understand the effect of inter-jet angle on lift-off in the presence of complex flows, e.g. the spray jet flow and the swirling flow, it is necessary to capture the turbulent mixing between the ambi-

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ent gas and the fuel jet. LES is employed in this study owing to its capability in resolving the larger energy-containing flow structures, the dynamics of the flow, and reaction zone structures. The governing equations for the gas phase are made up of the spatially filtered continuity, momentum, enthalpy and species transport equations. The source terms in these equations are due to chemical reactions in the gas phase as well as the interaction with the liquid phase, e.g. through evaporation and drag force. The liquid phase is modeled using Lagrangian particle tracking approach. The subgrid scale terms in the gas phase governing equations are modeled using a one-equation model discussed in [22,23]. The spatially filtered source terms in the species transport equations and the energy equation are modeled using the time-scale model discussed in [24,25]. The central issue is the integration of the large chemical kinetic mechanism that is needed in simulation of the initial ignition process of the fuel jet. The computational cost is often prohibitively expensive. We employ a recently developed chemistry integration method, the socalled Chemistry Coordinate Mapping (CCM) approach [26,27]. The basic idea of the method is to map the thermochemistry identical cells in the physical space to a three dimensional phase space made up of temperature, mass fraction of H-atom, and scalar dissipation rate based on the H-atom. The mapping procedure in CCM may introduce errors that can be controlled by adjusting sample space resolution and using a low error tolerance. In the present simulation the resolution in the temperature, H-atom, and the scalar dissipation rate coordinate is respectively 1 K, 104, and 0.2. Details about the methods and error analysis are referred to [26,27]. An open source code, OpenFoam [28], is used in the present LES. The governing equations of the gas phase are discretized using a second order TVD finite volume scheme for compressible flows, and the time integration is performed using a second order implicit method. The choice of a second order finite volume scheme allows for consideration of complex grid around the sprays and for accommodation of cylinder and piston geometry. The engine’s in-cylinder domain is discretized with a multi-block grid system. A uniform Cartesian grid is used in the local domain around the fuel jet, up to 80 nozzle diameters radially from the location of injection. Outside this domain, a cylindrical grid is used to comply with the cylinder and the bowl geometry. Local refinement is performed for the Cartesian grid surrounding the injector covering 80D in the radial direction from the engine centerline and 15D in the axial direction, where D is the nozzle diameter (100 lm). The local refinement ensures a resolution of 150 lm, which is approximately on the order of the Taylor scale of the flow. For the cylindrical

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grid, stretching towards the injector region is employed with a smallest cell size of 150 lm. The computational grid for the engine consists of approximately 1,200,000 cells. Sensitivity tests show that this grid can adequately capture the basic features of the fuel jets. The walls are assumed to have constant temperature (piston, 570 K; liner, 430 K; cylinder head, 560 K) and as the intake manifold is not considered in the present study, the swirl motion is prescribed at bottom dead center (BDC) as solid-body rotational flow with a swirl number of 2. LES is carried out starting from BDC using a dynamic mesh motion algorithm described in [29] to accommodate the piston motion. The engine flow field at 5 CAD before TDC is stored and used as the initial field for the injection and combustion simulations. The fuel injection is modeled with 500,000 Lagrangian spray parcels for each nozzle jet and it is coupled to the gas phase via source terms. An initial droplet size distribution is assumed, with a droplet size interval ranging from 1– 25 lm, instead of modeling the primary breakup. Classical WAVE breakup theory is used to model further disintegration of droplets [30] and fuel evaporation is modeled following Crowe et al. [31]. In the LES the n-heptane mechanism of Rente et al. [32] is used. The mechanism involves 44 species and 174 reactions including soot precursors, PAH and NO formation. Apart from this, the mechanism includes reactions of very important low-temperature combustion species, e.g. C7H15 O2, as well as high-temperature species, e.g. OH. 4. Results and discussion Figure 1 shows the instantaneous temperature fields from LES at 2 CAD after TDC, in the bowl region for both the symmetric and asymmetric nozzle cases. To visualize all the four jets, we have projected the planes crossing the fuel jets to the same horizontal plane (the piston reciprocates in the vertical direction). The intake flow generated a clockwise swirling motion. In the symmetric nozzle setup (Fig. 1a), the four jets show similar behavior. On the upwind side the lift-off length is longer than the downwind side; the temperatures in the proximity of the lift-off positions of the four jets are similar. For the asymmetric nozzle setup (Fig. 1b) similar swirl effect can be identified. Furthermore, the middle jet, jet C, hereafter referred to as the confined jet, is clearly affected by the upwind jet B. The temperature on the upwind side of the lift-off position of jet C is higher than the corresponding one of jet A, owing to heat transfer from the downwind side of jet B. As such, the lift-off length of jet C is shorter than that of jet A. Owing to the complex three dimensional turbulent heat and mass transfer around the lift-off

Fig. 1. Instantaneous temperature fields at 2 CAD after TDC, in the bowl region in 2D planes crossing the jets for (a) the symmetric and (b) asymmetric nozzle cases. In the symmetric setup the upwind and downwind sides of the jets are shown as well as the swirl direction. In the asymmetric nozzle case the jets are labeled from A to D. Jet A: the free jet; jet C: the confined jet.

positions of the three neighboring jets (B, C, D) their lift-off lengths are fairly comparable. To improve the understanding of the lift-off process, we plot in Fig. 2 the instantaneous distributions of temperature and mass fractions of several key species from LES in a vertical crosssection of the engine, in the zoomed region around one of the four jets for the symmetric nozzle case at 2 CAD after TDC. All other jets in both the symmetric and asymmetric cases show similar distributions so that they are not displayed here for brevity. The instantaneous fields are superimposed to iso-contours of a threshold value for OH mass fraction of 105 and the unity equivalence ratio. The contour of stoichiometric equivalence ratio separates the jet flow into two zones; the fuel rich mixture in the inner part of the jet

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Fig. 2. Instantaneous temperature and key species in a vertical cross section for one of the jets in the symmetric nozzle case, at 2 CAD after TDC. Superimposed to the fields are two iso-contours of a threshold value for OH mass fraction of 105 (lines with squares), and unity equivalence ratio (solid lines).

and the fuel lean surrounding gas. OH radicals appear to be together with high temperatures around the stoichiometric mixture. In the fuel rich region where CO is abundant the oxygen concentration is low whereas in the oxygen rich region CO is absent. This indicates that, in the region downstream of the lift-off position, the reaction zone structure around the stoichiometric mixture is essentially of a typical mixing controlled diffusion flame. At the low right corner of the bowl, the high CO and oxygen concentration is a result of the 3D jet/swirl/wall interaction. At the lift-off position the reaction zone structure is not similar to a typical premixed flame as

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there is a clear evidence that chemical reactions are already ongoing in the stoichiometric and fuel rich mixtures in a broad region upstream of the lift-off position. In the inner part of the jet, a key low temperature reaction species, C7H15O2, is seen in the region enveloped by the iso-contours of OH mass fraction of 105 and the unity equivalence ratio. In this region temperature is low and the dominant reactions are those of the low temperature branch via C7H15O2. Downstream of this region, the temperature of the mixture is higher, likely owing to both heat release in the ignition reactions and heat transfer from the neighboring stoichiometric mixture where the temperature is high. As a result, the high temperature reaction branch dominates the ignition process in this region as evidenced by the high HO2 and low C7H15O2 mass fractions. At the downstream end of the C7H15O2 region CO is formed from the partial oxidation of the fuel, and at the downstream end of the HO2 region CO is highest. Further downstream no significant CO oxidation could occur owing to the depletion of oxygen in the inner part of the jet. To further analyze the species distribution around various jets at lift-off under the two nozzle configurations, Fig. 3 shows scatter plots in U–T space for HO2, C2H2, C7H15O2 and OH for the two nozzle cases. Consistent with the results shown in Fig. 2, C7H15O2 exists mainly at low temperatures, T = 500–1200 K and it is relatively less homogeneously spread for the jets in the asymmetric nozzle configuration. When inspecting carefully the species distributions around each jet (the figure is not shown here fore brevity), it is found that the presence of C7H15O2 is weak for the confined jet (jet C, Fig. 1b) in the asymmetric nozzle configuration, it can be comprehended that this is a result of the shorter lift-off length for the confined jet. As temperature increases to 800–2000 K, HO2 is found to scatter in both U and T, indicating an auto-ignition process. At even higher temperatures (T > 2000 K), HO2 falls into a narrow manifold corresponding to the diffusion flame downstream of the lift-off position discussed earlier. C2H2 may be considered as a soot precursor. As the temperature increases to above 1000 K C2H2 is seen to form, especially at large U. Since the lift-off length is shorter for the confined jet, the fuel and air mixing time is shorter than for the free jet (jet A, Fig. 1b) and symmetric case jets (Fig. 1a). Due to reduced oxygen content in the inner part of the jet, more C2H2 would be expected to form. This appears to be true when studying Fig. 3, as more C2H2 in the asymmetric case is present at U = 4–6 and T = 1500–2100 K, than in the symmetric case. Consistent with the 2D distribution shown in Fig. 2, Fig. 3 confirms that, for all jets and nozzle configurations, OH exists at high temperatures only. For various U the peak OH forms a mani-

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Fig. 3. Scatterplots of species HO2, C2H2, C7H15O2 and OH in the U–T plane for the asymmetric case and symmetric case, at 2 CAD after TDC.

fold in the U–T space that corresponds the diffusion flames discussed in Fig. 2. The fact that OH spreads over a wide temperature range, e.g. 1600–2800 K for U around unity, indicates that the mixtures in front of the lift-off position undergo auto-ignition. To examine the transient behavior of the liftoff process, (Fig. 4) shows the evolution of liftoff lengths on the downwind side for the three jets (jets A and C of the asymmetric case, and a jet of the symmetric case, cf. Fig. 1), based on the LES results. The lift-off position was calculated using the same threshold limit for OH as in Fig. 2. The onset of ignition occurs in all cases at approximately 1.8 CAD before TDC where the lift-off lengths are highest, indicating that ignition occurs at a downstream position of the jets. The confined jet (jet C) displays the overall shortest lift-off

length whereas the free jet (jet A) shows a relatively longer lift-off length. When the jets ignite, the lift-off length of the confined jet decreases to the quasi-steady position quicker than the other two jets. The lift-off length varies less than 5% for the confined jet from 0 CAD to 4 CAD after TDC; for the symmetric and free jets, the lift-off lengths vary less than 2% from 2 CAD to 4 CAD after TDC, indicating that the lifted flames are fairly stabilized. The same transient behavior has been observed in the present experiments. Analyzing further the lift-off lengths at 2 CAD after TDC, in Fig. 5, the upwind and downwind lift-off lengths for each individual jet from LES are presented together with the experimental results, and the theoretical lift-off length calculated according to Eq.(1). According to Eq.(1) the theoretical lift-off length with the overall

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Fig. 4. Evolution of lift-off length for the confined, free and symmetric jets, based on a threshold value for OH mass fraction of 105.

ambient temperature of 1020 K is approximately 18.5 mm, which is longer than the experimental result. This is likely owing to neglecting the effects of swirl flow and jet–jet interaction in Eq.(1).If the theoretical lift-off length were calculated according to a modified ambient temperature adjacent to the jets, e.g. with temperatures of 1500 K, 1200 K and 1150 K, respectively for the 45°, 90° and 135° jets, the lift-off lengths would become considerably shorter, Fig. 5. Based on the discussion so far, in the presence of swirl and jet–jet interaction, it is concluded that products of adjacent jets are convected in the swirling flow direction, creating hot gas regions surrounding the downstream jets. This increases the heat transfer to the low temperature fuel and

Fig. 5. Experimental and numerical lift-off lengths and the corresponding ones estimated from Eq. (1), at 2 CAD after TDC.

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air mixture, augmenting the onset of ignition of the fuel as it approaches the stabilized flame position of the downstream jets. It is interesting to note that the difference between the lift-off lengths on the upwind side and downwind side predicted in the LES is 12.5–18%, which agrees well with the experimental results reporting an average ratio of approximately 15% [18,19], almost irrespective of the inter-jet angle. Compared with the experiments, the present LES under-predicts the lift-off length. The difference between the LES data and the experimental data can be attributed to three sources of error; first, the ambient temperature in the numerical simulations is slightly higher than the reported one in the experiments. Second, the choice of chemical kinetic mechanism affects the results and, third, the droplet size interval was not tuned but rather chosen with respect to the mesh resolution to comply with the Lagrangian Particle Tracking model, which requires that the droplet size should be much smaller than the cell size. The first and third are model parameter issues. The present simulations were performed without tuning of the breakup parameters. The second source of error, the choice of kinetic mechanism, may have a great impact on the prediction of lift-off length and additional simulations with different reaction mechanisms need to be performed to clarify this issue. 5. Summary and conclusion OH chemiluminescence imaging and large eddy simulations are carried out to analyze the lift-off length and the flame stabilization mechanisms in a direct injection heavy-duty diesel engine. The numerical simulations employ a system of equations for gas combustion, spray evaporation and mixing, as well as a dynamic mesh motion. A detailed chemical kinetic mechanism is considered with 44 species and 174 reactions. Two different nozzle configurations are studied with 45°, 90° and 135° inter-jet angle at the same ambient conditions. It is found that the local ambient temperature adjacent to the lift-off position increases with decreasing inter-jet angle, indicating a profound effect from the transport of hot products from neighboring jets on the lift-off and flame stabilization. Both low and high temperature ignition reactions are found to be ongoing in the stoichiometric and rich mixtures upstream of the lift-off position, which together with the complex interaction between the ambient swirl flow and jet-jet interaction leads to a shorter liftoff length than the predictions from a theory developed from a single fuel jet. The present LES succeed in capturing the difference in the lift-off lengths on the upwind and downwind side of the jet, agreeing well with the experimental

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results. The present simulations with detailed chemistry provide insight into the soot and NO emissions process. Acknowledgements This work was supported by the Competence Center for Combustion Progress (KC-FP) at Lund University and Swedish National Research Council (VR). The simulations were performed using the computer facility HPC2N, a center for scientific and technical computing funded by the Swedish National Infrastructure for Computing (SNIC). References [1] ECN1 Workshop, available at http://www.sandia.gov/ecn/workshop/ECN1/baselinenheptane.pdf. [2] D.R. Tree, K.I. Svensson, Prog. Energy Combust. Sci. 33 (2007) 272–309. [3] L.M. Pickett, D.L. Siebers, Combust. Flame 138 (2004) 114–135. [4] D.L. Siebers, SAE 1999-01-0528, 1999. [5] D.L. Siebers, B. Higgins, SAE 2001-01-0530, 2001. [6] L.M. Pickett, J. Manin, C.L. Genzale, D.L. Siebers, M.P.B. Musculus, C.A. Idicheria, SAE 2011-010686, 2011. [7] S. Kook, L.M. Pickett, Proc. Combust. Inst. 33 (2011) 2911–2918. [8] L.M. Pickett, D.L. Siebers, C.A. Idicheria, SAE 2005-01-3843, 2005. [9] N. Peters, Turbulent Combustion, Cambridge University Press, 2000. [10] K.M. Lyons, Prog. Energy Combust. Sci. 33 (2007) 211–231. [11] K. Wohl, N.M Kapp, C. Gazely, in: Third Symposium on Combustion and Flame and Explosion Phenomena, 1949, pp. 3–21.

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