Modeling the Transient Structure of Reacting Diesel Jets using Large Eddy Simulation

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1 Paper # 070IC-0085 Topic: Internal Combustion Engines and Gas Turbine Engines 8 th U. S. National Combustion Meeting Organized by the Western States Section of the Combustion Institute and hosted by the University of Utah May 19-22, 2013 Modeling the Transient Structure of Reacting Diesel Jets using Large Eddy Simulation Muhsin M Ameen 1* Vinicio Magi 1,2 John Abraham 1,3 1 School of Mechanical Engineering, Purdue University, West Lafayette, IN , USA 2 School of Engineering, University of Basilicata, Potenza, Italy 3 School of Mechanical Engineering, University of Adelaide, Adelaide, South Australia 5005, Australia Accurate modeling of the transient structure of reacting diesel jets is important as transient features like autoignition, flame propagation, and flame stabilization have been shown to correlate with combustion efficiency and pollutant formation. In this work, the large eddy simulation (LES) technique is used to computationally model a lifted jet flame at conditions representative of those encountered in diesel engines. An unsteady flamelet progress variable (UFPV) model is used for turbulence/chemistry interactions. The UFPV model has been proposed for predicting the averaged/filtered chemistry source terms when modeling turbulent non-premixed combustion. In the model, a look-up table of reaction source terms is generated as a function of mixture fraction Z, stoichiometric scalar dissipation rate χ st, and progress variable C st by solving the unsteady flamelet equations. In the present study, the progress variable is defined based on the sum of the major combustion products. A 37-species reduced chemical reaction mechanism for n-heptane is used to generate the UFPV libraries. The results show that ignition initiates at multiple points in the mixing layer around the jet, towards the edges of the jet, where the mixture fraction is rich, and the strain rates are within the ignition limits. These ignition kernels grow in time and merge to form a continuous flame front. Lift-off height is determined by the minimum axial distance from the orifice below which the local scalar dissipation rate does not favor ignition. The LES results are compared with Reynolds Averaged Navier-Stokes (RANS) simulation results from prior work. This comparison shows that though there are noticeable differences in the transient phenomena, lift-off heights predicted by both methods are within 25% and the predicted mechanism of lift-off is related to ignition in both cases. 1. Introduction Reducing emissions of particulate matter (PM) and nitrogen oxides (NO x ) from diesel engines is a continuing challenge that faces heavy-duty diesel engine manufacturers who, in turn, have invested significant resources to address it. Increasingly stringent regulations force engine designers to search for innovative ways to cut down emissions. Exhaust aftertreatment devices which remove the pollutants in the exhaust are effective and increasingly deployed by manufacturers. Nevertheless these devices add to the cost and size of the engine package and are, hence, not the preferred means of achieving emissions goals. Advanced combustion engines, such as homogeneous-charge compression-ignition (HCCI) engines, are promising but have not reached a * Corresponding author: mameen@purdue.edu

2 stage of development where they are practical. While progress is being made in the areas of exhaust aftertreatment and advanced combustion engines, it is imperative that any gains that can be achieved through improvements in conventional diesel engine combustion are exploited. Making improvements in conventional diesel engine combustion can be accelerated by improving the understanding of the in-cylinder fuel/air mixing and combustion processes. In recent years, it has been shown through experimental studies that flame lift-off in reacting diesel jets is related to soot concentration in the jets (Siebers and Higgins, 2001; Pickett and Siebers, 2004). The suggestion is that the higher the lift-off, the greater the mixing upstream of the lift-off height which results in lower soot formation downstream in the jet. If this is indeed the case, predicting lift-off in reacting diesel jets is important in the context of multidimensional modeling of the jets. Accurate modeling, however, requires an understanding of the physics of lift-off. This can be achieved through experimental and computational studies. It is important to point out that while the interest in flame lift-off in diesel engines is relatively more recent, it has been the subject of study in turbulent reacting jets for over 30 years (Pitts, 1989; Peters, 2000; Venugopal and Abraham, 2007b). There have been several efforts to computationally model lift-off in flames. Most of these studies employed the Reynolds Averaged Navier-Stokes (RANS) approach. Chomiak and Karlsson (1996) employed a partially stirred reactor (PaSR) model in combination with multi-step chemical kinetics in a RANS code to model lift-off height in diesel jets for varying conditions of injection pressure, orifice diameter, and ambient temperature and density. In the model, the computational cell is divided into reacting and non-reacting zones. The reacting zone is considered as the perfectly stirred reactor. It is coupled to the non-reacting zone through mass and energy transfer. Defining the volume fraction of these two regions in a given cell requires careful consideration. Time scales of turbulence and kinetics are employed in the model to estimate the volume fractions. It was shown that the computed results are in good agreement with the measurements of Winklhofer et al. (1992). Tao and Chomiak (2002) employed the PaSR model to numerically investigate flame lift-off in diesel sprays and reaction zone structure in the lift-off region. The computed lift-off heights were in reasonable agreement with the measurements of Siebers and Higgins (2001) when changes in chamber pressure and temperature were considered. Kärrholm et al. (2008) evaluated the PaSR model against the measurements of Siebers and Higgins (2001) and Siebers et al. (2002) under high EGR and varying ambient temperature conditions. Senecal et al. (2003) adopted an approach where each computational cell in a RANS simulation was considered as a perfectly stirred reactor (PSR). In other words, multistep kinetics were directly implemented in the RANS simulation. The numerical results were in good agreement with the measured results of Siebers and Higgins (2001) when an iso-line of 2200 K was employed to identify the lift-off height. Tap and Veynante (2005) employed a generalized flame surface density (GFSD) approach to model flame lift-off in diesel sprays. Their computed trends agreed well with the measured trends of Siebers and Higgins (2001) for varying orifice diameters and chamber densities. Errico et al. (2008) assessed two models of different complexity for lift-off predictions. One model was an extension of the eddy dissipation model (EDM) (Magnussen and Hjertager, 1976) in which the ignition delay is obtained from a tabulated database created by complex chemistry calculations and the other was the perfectly-stirred reactor (PSR) model which computes multistep chemical kinetics in each computational cell making use of an in-situ adaptive tabulation (ISAT) method (Pope, 1997) to reduce the computational time. Lift-off heights were compared with the results of Idicheria and Pickett (2006). The lift-off was identified by the 2200 K iso-line. It was shown that both models were able to predict the lift-off dependency on oxygen concentration and 2

3 mixture temperature. However, quantitative differences exist. With both models, the lift-off height was over-predicted. In the case of the EDM model, the differences were large and attributed to the inadequacies of the ignition model employed in the work. Venugopal and Abraham (2007a) modeled lift-off in diesel jets using diffusion flamelet extinction as the criterion for identifying lift-off. Two chemical kinetic mechanisms, a 37-species 56-step mechanism (Peters et al., 2002) and a 159-species 1540-step mechanism (Seiser et al., 2000) were employed to model kinetics. The computed results across the range of conditions considered were in agreement (in trends) with experimental results (Siebers and Higgins, 2001; Siebers et al., 2002). Also the measured extinction scalar dissipation rate correlated well with scalar dissipation rate at the measured lift-off height. Not surprisingly, the results were sensitive to the kinetic mechanism employed. Venugopal and Abraham (2007b) employed the representative interactive flamelet (RIF) approach of Pitsch et al. (1995), with multiple flamelets, to compute the lift-off height for varying conditions of injection pressure, ambient temperature and oxygen concentration. They showed that with multiple flamelets the lift-off height could be predicted. The approach is, however, computationally expensive since multiple flamelets have to be interactively solved. Bajaj et al. (2013) employed the unsteady flamelet progress variable (UFPV) model (Pierce and Moin, 2004; Ihme et al., 2005; Ihme and Pitsch, 2008; Ihme and See, 2010) to model ignition and flame lift-off in diesel jets. In this model, all thermochemical quantities are parameterized by mixture fraction, reaction progress parameter, and stoichiometric scalar dissipation rate by the solution of unsteady flamelet equations (Peters, 2000). A presumed PDF closure model was employed to evaluate Fávre-averaged thermochemical quantities. For this, a beta-distribution was used for the mixture fraction, and Dirac-delta function distributions for the reaction progress parameter and the stoichiometric scalar dissipation rate. These Fávre-averaged thermochemical quantities were tabulated in UFPV libraries and were used as the turbulent combustion model for the RANS simulations. Numerical simulations were conducted for a wide range of parameters including variations in chamber temperature, pressure, density, and oxygen fraction, and nozzle diameters. The computed ignition delay and flame lift-off heights agree within about 25% of the measured values (Pickett et al., 2005, This model also allows the use of detailed chemical kinetics through tabulation without considerably increasing the computational time. From this discussion, it can be concluded that if the only objective of the simulations is to predict ignition delay and model flame lift-off height, RANS models are adequate. The more important objective is, however, to also predict soot and NO x emissions accurately. The prediction of soot and NO x is likely to be dependent on the highly transient nature of the reacting turbulent jet. Furthermore, large scale turbulent structures and unsteady effects (e.g. extinction, re-ignition, flame weakening) are likely to influence mixing and subsequently soot and NO x formation. In fact, these structures have also been suggested to influence flame lift-off (Broadwell et al., 1984). The RANS models are unable to represent these effects. Large-eddy simulation (LES) is potentially a powerful tool to study the mechanism(s) of flame lift-off and the major factors affecting it because large-scale mixing and transient effects, which are believed to play an important role in flame dynamics near the lift-off height, are resolved in LES. The effect of unsteady flame dynamics and large structures on soot and NO formation can also be studied. In the present study, LES is carried out of a jet generated by injecting n-heptane vapor at 373 K into air at temperature of 1000 K and a pressure of 40 bar with a velocity of 150 m/s (corresponding to Re=250,000) through an orifice diameter of 200 µm. While the pressure, temperature, and orifice diameter and representative of diesel engine conditions, the injection velocity is about a factor of 4 smaller. It is selected to reduce the computational overhead. The 3

4 computational domain, and the subgrid models used to model the turbulence and turbulencechemistry interactions are discussed next. Results and discussion follow. The paper will end with summary and conclusions. 2. Computational Model The computations are performed in a three-dimensional domain which extended 150 diameters in the axial direction and 75 diameters in the radial direction. Figure 1 shows the computational domain and the boundary definitions. The computational grid consists of approximately 7.9 million grid points (350 x 150 x 150). The grid is stretched in both the axial and radial directions with the maximum resolution located along the jet centerline. The grid spacing in the axial direction varies from 0.25 jet diameters near the inlet boundary to 0.50 jet diameters near the outlet boundary, and the grid spacing in the radial direction varies from approximately 0.10 jet diameters at the jet axis to 1.70 jet diameters at the side boundaries. Except for the inlet boundary, all of the domain boundaries are implemented as subsonic non-reflecting outflow conditions. The implementation details of these boundary conditions were discussed in Abraham and Magi (1997) and Anders et al. (2007). Due to the presence of the higher velocity, temperature, and density gradients, the Artificial Diffusivity Scheme (ADS) sub-grid scale model introduced by Kawai and Lele (2010) was employed to obtain stable results. Figure 1. Computational domain and boundary conditions for LES. The UFPV model is used as the turbulence-chemistry interaction model. Note that this model has been employed by Bajaj et al. (2013) within the context of RANS simulations to model ignition and flame lift-off. n-heptane is employed as the surrogate fuel as in the work of Bajaj et al. (2013). A 37-species chemical reaction mechanism developed by Peters et al. (2002) is employed to generate the UFPV libraries. In this model, the reaction rates are tabulated as a function of 3 independent variables - mixture fraction Z, scalar dissipation rate χ st, and the progress variable C. For the tabulation, 51 points are used in the Z coordinate, 10 points in χ st coordinate and 21 points in the C coordinate. The accuracy of the resolution adopted has been assessed by refining the number 4

5 of points and repeating the computations. Additional details about the modeling approach can be found in Bajaj (2012) and Bajaj et al. (2013). 3. Results and Discussion The LES of the jet was carried out until 0.83 ms; the lift-off height reaches a steady value at approximately 0.65 ms. Figures 2 (a) - (f) show the transient evolution of the mixture fraction and temperature profiles in the central X-Y plane at several instants after start of injection (ASI). The left-hand side column shows the mixture fraction and the right-hand side column shows the temperature. The different stages of ignition, flame development and flame stabilization are evident in these figures. When the fuel is injected into the domain, it penetrates into the chamber while entraining the hot surrounding air. The mixing of the fuel and hot air is followed by the formation of product radicals and rise in temperature. It is found that the ignition delay is about 0.28 ms based on the criterion of when the temperature first reaches 1500 K. (a) (b) (c) 5

6 (d) (e) (f) Figure 2. Transient evolution of the mixture fraction (LHS) and temperature (RHS) profiles in the central X-Y plane at (a) 0.29 ms, (b) 0.33 ms, (c) 0.36 ms, (d) 0.42 ms, (e) 0.59 ms and (f) 0.83 ms ASI. Figure 2 (a) shows the mixture fraction and temperature profiles at a time of 0.29 ms. Ignition is noticeable at the leading edge of the jet. This ignition kernel grows with time as evident by comparing Fig. 2 (a) with Fig. 2 (b). Meanwhile additional ignition kernels are noticeable in the jet. These ignition kernels develop spatially in time, and then merge to form a continuous flame (see Fig. 2 (e)). Figure 2 (f) shows that the flame stabilizes at the lift-off location. The lift-off height for this case is seen to be at the approximate axial distance of x/d = 40, i.e. 8 mm. There is no noticeable propagation of the flame upstream and the stabilization occurs at approximately the distance where the farthest upstream ignition occurs. Figures 2 (c) to (e) also show the processes of local ignition and extinction at various locations upstream of the lift-off height. For example, it is seen that ignition occurs at an axial location of about 30D, upstream of the lift-off height, but the local strain rates which evolve in time extinguish these ignition kernels. This is discussed in more detail later in the section. Figure 3 shows the dynamics of the flame near the lift-off height. Figure 3 (a) shows the temperature contours and iso-lines of mixture fraction (Z=0.05 and Z=0.08), overlaid with the 6

7 velocity vectors, at a time of 0.65 ms. It is seen that the maximum temperatures are observed in regions where the mixture fraction lies between 0.05 and This is not surprising as the stoichiometric mixture fraction for n-heptane is There are regions of the jet where the mixture fraction lies in this range but high-temperature reactions do not occur because the strain rates are large. The flame stabilization location is seen to be strongly affected by the local flow field (Figs. 3 (b) to (e)). Another interesting aspect of the flame is the presence of a large vortex at the flame stabilization location, as seen in Fig. 3 (e). These vortices may play a role in stabilizing the flame, but this needs further investigation. (a) (b) (c) (d) 7

8 (e) Figure 3. Flame dynamics near the lift-off height (a) 0.65 ms, (b) 0.70 ms, (c) 0.75 ms, (d) 0.80 ms, (e) 0.83 ms ASI. The dimensions on the axes are in m. Orifice diameter is m. When discussing the results of Fig. 2, the occurrence of local extinction at locations upstream of the lift-off location was pointed out. Figure 4 shows the flooded temperature contours and the isocontour of scalar dissipation rate of value 500 s -1, i.e. close to the extinction scalar dissipation rate of n-heptane, in the central X-Y plane at different time instants between the formation and extinction of these ignition kernels. The ignition kernels are circled in the figure. At t=0.53 ms, ignition kernels appear at an axial location of about 7 mm. As seen in Figure 4 (a), the iso-contour of extinction scalar dissipation rate (χ e ) is located close to the ignition kernel. Also note that this kernel is very close to the edge of the potential core of this jet. With increasing time, the turbulent velocity field causes the χ e contour to start engulfing the ignition kernel as shown in Figs 4 (b) to (d). At a time of ms, the ignition kernel is seen to be completely extinguished. This discussion highlights that the processes near the lift-off height are highly unsteady. Furthermore, it shows that while flame stabilization is primarily controlled by the ignition scalar dissipation rate, extinction plays a role further upstream. In fact, the gradients in strain rates are relatively sharp near the lift-off height and the extinction and ignition scalar dissipation rates do not occur far apart. This may explain why liftoff heights computed on the basis of extinction scalar dissipation rates (Venugopal and Abraham, 2007a) also give reasonable agreement with measured values. 8

9 (a) (b) (c) Figure 4. Local extinction of ignition kernels at locations upstream of the lift off height (a) 0.53 ms, (b) ms, (c) 0.54 ms and (d) ms ASI. Figure 5 shows the transient development of the flame at a location downstream of the lift- off height. As in Fig. 3, the maximum temperature lies between the mixture fractions of 0.05 and At a time of 0.65 ms, the ignition kernels are still growing and not connected (see Fig. 5 (a)). As these kernels grow, they are stretched and advected by the local flow-field field as seen in Figs. 5(b) and (c). To show the growth and stretch of the kernels more clearly, one of the developing kernels is circled in Figs. 5 (a) to (c). At a time of 0.70 ms (Fig. 5 (b)), the kernel has convected downstream from its initial location at 0.65 ms. The shape of the kernel is highly stretched by the local flow-field. The high strain rates near the kernel also cause it to split into a large and a small kernel. These two kernels then grow in time and merge to form a single kernel at 0.75 ms (Fig. 5 (c)). A merged flame front is seen after time of 0.80 ms (Figs. 5 (d) and (e)). Notice that the minimum contour value is 1700 K. The development of the flame is seen to be highly unsteady. The flame thickness and the location of the maximum temperature vary strongly with time. The normal distance between the two mixture fraction contour values is indicative of the strain. Shorter distances correspond to greater strain. In general, no flames or (only) weak flames are observed when the distances are short, i.e. higher strain. In most cases, it appears as if ignition does not occur in these regions or the flame does not propagate into these regions. There are instances where an existing flame is weakened by increasing strain. These dynamics are also evident near the lift-off height (see Fig. 3). This shows that a lifted flame results from a complicated interplay of ignition, kernel growth, flame weakening and local extinction processes which determine the transient flame structure. (d) 9

10 (a) (b) (c) (d) 10

11 (e) Figure 5. Flame dynamics downstream of the lift-off height (a) 0.65 ms, (b) 0.70 ms, (c) 0.75 ms, (d) 0.80 ms, (e) 0.83 ms ASI. Figure 6 shows the vorticity (flooded contours) and temperature (line contours) distributions near the lift-off height. The vorticity is seen to have a patchy distribution, with very large values of vorticity interspersed between low values of vorticity. One noticeable aspect of Fig. 6 is that the liftoff height (X = 8mm) is characterized by the presence of large patches of high vorticity at nearby upstream locations. It can also be noted that the high temperature regions are all located at the edge of the jet, where the vorticity is relatively low (< 20,000 s -1 ). At the centre of the jet, the vortices are strong enough to prevent the formation or growth of ignition kernels. Of course, the fact that the mixture at the centre of the jet is rich can also be a reason for the absence of flames at the centre of the jet. Figure 6. Vorticity (flooded) and temperature (lines) distribution near the lift-off height at 0.83 ms ASI. 11

12 Figure 7 shows the evolution of the scalar dissipation (χ) contours with time near the lift-off height. Also shown are the iso-lines of temperature (1700 K, 1900 K, 2100 K and 2300 K). In the figure, white color indicates regions of low scalar dissipation rate (χ < 5 s -1 ). Similar to the distribution of the vorticity, χ is also seen to have a patchy distribution where regions of high χ are interspersed within regions of low χ. The high temperature regions are all seen to be located at regions where χ is low as is evident in Figs. 7 (a) to (e). To show the evolution of χ with time and its effect on the flame structure, one of the regions of low χ is circled in Figs. 7 (a) to (e). For convenience, this island of low χ is denoted as A in the following discussion. At a time of 0.65 ms (Fig. 7 (a)), the island A is located at a region of high temperature. In time, the island A grows in size and also gets advected away from its initial location (Figs. 7 (b) to (d)). Since, low values of χ favor the formation of ignition kernels, the iso-lines of temperature follow the motion of island A. (a) (b) (c) (d) 12

13 (e) Figure 7. Scalar dissipation rate and temperature evolution near the lift-off height (a) 0.65 ms, (b) 0.70 ms, (c) 0.75 ms, (d) 0.80 ms, (e) 0.83ms ASI. To compare the mechanism of flame development predicted by LES and RANS, a RANS simulation was performed for the same computational domain and boundary conditions. The same code and models employed by Bajaj et al. (2013) are employed for this simulation. Figure 8 shows the transient development of the flame predicted by RANS. The ignition delay predicted by RANS simulation is about 0.75 ms, as opposed to the value of 0.28 ms predicted by LES. One of the reasons for the difference in the predicted ignition delay is thought to be due to the differences in the definition of the scalar dissipation rate between the two methods. The RANS simulation also shows a single ignition kernel forming at the leading edge of the jet where the mixture is rich, as opposed to the formation of multiple ignition kernels in the case of the LES. An ignition front is then seen to propagate from the initial ignition location to the stoichiometric location. Then, a flame front propagates upstream until it stabilizes at the lift-off location. This is the same mechanism discussed by Bajaj et al. (2013), who also argued that the lift-off height is at the location where the local scalar dissipation rate is equal to the ignition scalar dissipation rate. The steady lift-off height predicted by RANS is found to be 10 mm, which is 25% higher than that predicted by LES. Although the mechanisms of flame development predicted by LES and RANS are different, the mechanism which leads to flame stabilization is related to ignition scalar dissipation rate in both cases. 13

14 Figure 8. Transient development of temperature contours for the vapor jet using RANS simulations. 4. Conclusions In the present study, LES of a lifted n-heptane turbulent reacting jet injected into a computational domain at high temperature and pressure conditions representative of those in diesel engines is performed. It is seen that ignition occurs at multiple locations along the edges of the jet. The ignition kernels grow in time and merge to form a continuous flame front. The lift-off height is determined by the minimum axial distance below which the local flow conditions do not favor the formation or growth of ignition kernels. The flame structure is seen to be highly unsteady, and affected strongly by the local flow-field. The unsteady flow-field leads to large variations in the 14

15 vorticity and scalar dissipation rate fields in the domain, which influence the processes of kernel growth, flame weakening and local extinction. The mechanism of ignition and flame development predicted by LES is seen to be different from that predicted by RANS. In RANS, ignition occurs at a location toward the leading edge of the jet and a flame propagates from the leading edge until it stabilizes at the lift-off height where the local scalar dissipation rate is equal to the ignition scalar dissipation rate. To the extent that the liftoff height is determined by the ignition scalar dissipation rate in both cases, there is agreement between RANS and LES. Acknowledgements The authors would like to thank the National Institute of Computational Sciences (NICS) and eresearch SA (ersa) for providing the computing resources for this work. Financial support for this work was provided by Caterpillar, Inc. References Abraham, J., and Magi, V., (1997). Comparisons of Transient Jets: RNG k-ε model Versus Standard k-ε Model, SAE Transactions 106(3): Anders, J. W., Magi, V., and Abraham, J., (2007). Large-eddy simulation in the near field of a transient multicomponent gas jet with density gradients, Computers and Fluids 36: Bajaj, C., (2012). Computational Investigations of Ignition and Flame Lift-Off in Diesel Jets, MSME Thesis, Purdue University, West Lafayette, IN. Bajaj. C., Ameen, M. M., and Abraham, J., (2013). Evaluation of an unsteady flamelet progress variable model for autoignition and flame lift-off in diesel jets, Combustion Science and Technology 185: Broadwell, J.E., Dahm, W.J.A., and Mungal, M.G., (1984). Blowout of Turbulent Diffusion Flames, Proceedings of the Combustion Institute 20: Chomiak, J., and Karlsson, A., (1996). Flame Lift-off in Diesel Sprays, 26 th Symposium (International) on Combustion Errico, G.D., Ettorre, D., and Lucchini, T. (2008) Simplified and detailed chemistry modeling of constantvolume diesel combustion experiments. SAE Paper Idicheria, C. and Pickett, L. (2006) Formaldehyde visualization near lift-off location in a diesel jet. SAE Paper Ihme, M., Cha, C. M., and Pitsch, H., (2005). Prediction of local extinction and re-ignition effects in nonpremixed turbulent combustion using a flamelet/progress variable approach, Proceedings of the Combustion Institite 30: Ihme, M., and Pitsch, H., (2008). Modeling of radiation and NO formation in turbulent non-premixed flames using a flamelet/progress variable formulation, Physics of Fluids 20:

16 Ihme, M., and See, Y.C., (2010). Prediction of Autoignition in a Lifted Methane/Air Flame Using an Unsteady Flamelet/Progress Variable Model, Combustion and Flame 157: Kärrholm, F.P., Tao, F., and Nordin, N., (2008). Three-Dimensional Simulation of Diesel Spray Ignition and Flame Lift-Off Using OpenFOAM and KIVA-3V CFD Codes, SAE Paper Kawai, S., and Lele, S. K., (2008). Localized artificial diffusivity scheme for discontinuity capturing on curvilinear meshes, Journal of Computational Physics 227: Magnussen, B.F. and Hjertager, B.J. (1976) On mathematical modeling of turbulent combustion. Proceedings of the Combustion Institute 16: Peters, N., (2000). Turbulent Combustion, Cambridge University Press, Cambridge, UK. Peters, N., Paczko, G., Seiser, R., and Seshadri, K. (2002) Temperature cross-over and non-thermal runaway at two-stage ignition of n-heptane. Combustion and Flame 128, Pickett, L.M., and Siebers, D. L., (2004). Soot in Diesel Fuel Jets: Effects of Ambient Temperature, Ambient Density and Injection Pressure, Combustion and Flame 138: Pickett, L.M., Siebers, D.L., and Idicheria, C.A., (2005). Relationship Between Ignition Processes and Flame lift-off Length in Diesel Fuel Jets, SAE Paper Pierce, C. D., and Moin, P., (2004). Progress-Variable Approach for Large-Eddy Simulation of Non-premixed Turbulent Combustion, Journal of Fluid Mechanics 504: Pitsch, H., Wan, Y.P., and Peters, N. (1995) Numerical investigation of soot formation and oxidation under diesel engine conditions. SAE Paper No Pitts, W.M., (1989). Assessment of Theories for the Behavior and Blowout of Lifted Turbulent Jet Diffusion Flames, Proceedings of the Combustion Institute 22: Pope, S. B. (1997) Computationally efficient implementation of combustion chemistry using in-situ adaptive tabulation. Combust. Theory Model., 1, Senecal, P.K., Pomraning, E., and Richards K. J., Briggs, T. E., Choi, C. Y., McDavid R. M., and Patterson, M. A., (2003). Multidimensional Modeling of Direct Injection Diesel Spray Liquid Length and Flame Lift-off Length Using CFD and Parallel Detailed Chemistry, SAE Paper Siebers, D.L., and Higgins, B. S., (2001). Flame Lift-Off on Direct Injection Diesel Sprays under Quiescent Conditions, SAE paper Siebers, D.L., Higgins, B.S., and Pickett, L.M., (2002). Flame Lift-off on Direct Injection Diesel Fuel Jets: Oxygen Concentration Effects, SAE paper Seiser, R., Pitsch, H., Seshadri, K., Pitz, W.J., and Curran, H.J. (2000) Extinction and autoignition of n- heptane in counterflow configuration. Proceedings of the Combustion Institute 28, Tao, F., and Chomiak, J., (2002). Numerical Investigation of Reaction Zones Structure and Flame Lift-Off of DI Diesel Sprays with Complex Chemistry, SAE Paper

17 Tap, F.A., and Veynante, D., (2005). Simulation of Flame Lift-Off on a Diesel Jet Using a Generalized Flame Surface Density Modeling Approach, Proceedings of Combustion Institute 30: Venugopal, R. and Abraham, J. (2007a) A numerical investigation of flame lift-off in diesel jets. Combustion Science and Technology 179: Venugopal, R. and Abraham, J. (2007b) A review of fundamental studies relevant to flame lift-off in diesel jets. SAE Paper No Winklhofer, E., Ahmadi-Befrui, B., Wiesler, B., and Cresnoverh, G., (1992). The Influence of Injection Rate Shaping on Diesel Fuel Sprays An Experimental Study, Proceedings Institute of Mechanical Engineers 206: