Mixture Fraction Variance Research Articles

Assessing LES models based on tabulated chemistry for the simulation of Diesel spray combustion

In the context of large-eddy simulation (LES) of Diesel engine combustion, two LES combustion models are proposed. Their ability to predict autoignition delays and heat release of an autoigniting liquid α-methylnaphthalene/n-decane jet injected into a constant-volume chamber under Diesel-like conditions is assessed. These models retain the tabulation of a complex chemistry scheme using autoigniting homogeneous reactors (HR) at constant pressure. This allows accounting for the chemical complexity of heavy hydrocarbon fuels over the wide range of conditions representative for Diesel engines, at comparatively low CPU time overhead. The tabulated homogeneous reactor (THR) approach assumes the local structure of the reaction zone to be that of an HR, while the approximated diffusion flame (ADF) approach is based on autoigniting strained diffusion flames. Two variants of each approach are considered, either neglecting sub-grid-scale mixture fraction variance (THR and ADF models), or accounting for it via a presumed β-PDF (THR-pdf and ADF–PCM models). LES results indicate that the ADF model assuming diffusion flame structures tends to predict faster propagation of the combustion toward less reactive mixture fractions then the THR model. Moreover, neglecting the mixture fraction fluctuations strongly overestimates initial experimental heat release rates after autoignition. Comparison between models shows that this assumption yields higher reaction rates and temperature levels close to the stoichiometric mixture fraction zones. Predictions in terms of autoignition are remarkably close with all models, and exhibit very few variations from one realization to the other. Variations in global heat release rate become more apparent for different realizations at later instants, in relation to the interaction of large flow scales with combustion.

Lagrangian modelling of turbulent spray combustion under liquid rocket engine conditions

In the field of liquid rocket propulsion, the use of computational design tools, such as computational fluid dynamics (CFD) solvers, may provide a great deal of help to proceed with the primary design choice. Considering the complexity of rocket engine geometries, as well as associated fluid flow conditions, the use of Reynolds-Averaged Navier–Stokes (RANS) numerical simulations remains very popular. Important modelling efforts are therefore still required to provide reliable computational models able to describe the complex interaction that takes place between turbulence and chemistry in such cryogenic high-speed flows. The present manuscript reports the results of some recent investigations conducted in this field. The modelling analysis relies on a Lagrangian framework, the salient features of which consist in approximating the Lagrangian path in a reduced composition space made up of the mixture fraction variable, i.e. a conserved scalar introduced to represent the variations of composition, and a progress variable, i.e. a reactive scalar to follow the departures from chemical equilibrium. The retained methodology allows to presume the joint probability density function of the two scalar fields without invoking the assumption of statistical independence between them. Equivalence ratio fluctuations induced by the vaporization of the liquid phase are considered as additional sources terms appearing in the transport equation of the mixture fraction variance. The transport of the corresponding mean scalar dissipation rate (SDR), which is a key quantity in the corresponding closure, is also affected by the vaporization processes. The proposed model has been implemented into the U-RANS CFD code N3S_Natur, while the liquid phase is described using a Lagrangian module. The capabilities of the computation model are evaluated through a detailed comparison with the experimental databases gathered on the ONERA Mascotte test bench. The corresponding test rig consists of a low-speed round jet of liquid oxygen surrounded by an atomizing high-speed co-flowing jet of gaseous-hydrogen. The obtained results confirm that (i) the additional fluctuations induced by the vaporization processes play an important role, (ii) the influence of transient droplet heating on turbulent combustion must be taken into account.

Manifold resolution study of the FGM method for an igniting diesel spray

Spray H (baseline n-heptane) cases of Engine Combustion Network (ECN) are investigated with the Flamelet Generated Manifold (FGM) method. In the FGM method, all thermo-chemical properties are stored as a function of controlling variables, here the mixture fraction and the progress variable. Two approaches are used to construct the FGM tables, igniting counterflow diffusion flamelets (ICDF) and homogeneous reactors (HR). To capture ignition delay times in a reliable way, a sensitivity study is performed to determine the optimal FGM table properties. It is observed that using quadratic discretization in progress variable space, i.e. more points in early stages of chemistry, is essential to predict accurate ignition timings. Once quadratic spacing is applied, the ignition delay time results show good correlation with those of experiments. This is observed with both ICDF- and HR-based FGM tables. The similarity between ignition delay results of two approaches indicates that the effect of mixing on chemistry is low and the diffusion process plays a minor role at elevated ambient conditions such as in conventional diesel engines. Finally, the effect of including the mixture fraction variance is analyzed and the impact is found mainly on the lift-off length. The ignition delay is hardly affected.

Large eddy simulation of dilute reacting sprays: Droplet evaporation and scalar mixing

Large eddy simulation (LES) of turbulent reacting sprays is performed to investigate the interactions of droplet evaporation and subfilter scalar mixing processes. A stochastic method is proposed to generate the subfilter fluctuations in gas-phase reactive scalars in the framework of a mixture-fraction-based combustion model. The subfilter fluctuations of the gas-phase temperature and composition, seen by droplets, are used to refine the estimates of the interphase heat/mass transfer rates. Gas-phase combustion is described by the flamelet progress variable approach. The effects of droplet evaporation on subfilter scalar mixing are considered by solving the transport equation for the subfilter mixture fraction variance. The mixture fraction that is valid instantaneously in both the gas and the liquid phases is adopted and its implication on the modeling of the evaporation source term in the subfilter variance equation is discussed. The modeling approach has been applied to the Sydney dilute reacting sprays. To account for uncertainty in the modeling of scalar dissipation rates in spray flames, a parametric study is performed for the constant in the scalar dissipation model for the subfilter variance equation. The effects of subfilter fluctuations on droplet evaporation are found to depend on the inflow condition of the pre-evaporated gas-phase mixture and the liquid injection rate in the present dilute reacting sprays.

Auto-ignition and combustion of diesel spray using unsteady laminar flamelet model

This work emphasises the modelling capabilities of the unsteady flamelet/reaction progress variable approach to implement diesel spray flames for capturing the auto-ignition and flame lift-off phenomena. The droplet size distribution based on the moment scheme characterises the poly-disperse spray model [1] employed in this work. The flamelet progress variable solutions embedded in a Reynolds-averaged Navier–Stokes (RANS) framework, together with the probability density function (PDF) approach, signify the turbulence–chemistry interaction. All thermochemical scalars are represented as a function of mean mixture fraction, mixture fraction variance, reaction progress variable and scalar dissipation rate. Mixture fraction is assumed to follow a beta-PDF distribution, because the reaction progress variable and scalar dissipation rate distributions are assumed to be a delta-PDF. In order to assess the capability of this developed model, the predicted results are compared with experimental data [2]. The developed model gives a reasonably good overall prediction performance in terms of auto-ignition, flame development and flame lift-off length. The flame temperature distributions are comparable with the formations of luminous flames. The predicted flame growth rate is consistent with the experimental results but there is a small over-prediction. Therefore, the present approach can accurately and efficiently capture the auto-ignition and flame lift-off phenomena of diesel spray flame.

Modelling effects of subgrid-scale mixture fraction variance in LES of a piloted diffusion flame

A posteriori analysis of the statistics of two large-eddy simulation (LES) solutions describing a piloted methane–air (Sandia D) flame is performed on a series of grids with progressively increased resolution reaching about 10.5 million cells. Chemical compositions, density and temperature fields are modelled with a steady flamelet approach and parametrised by the mixture fraction. The difference between the LES solutions arises from a different numerical treatment of the subgrid scale (SGS) mixture fraction variance – an important quantity of interest in non-premixed combustion modelling. In the first case (model I), the variance transport equation is solved directly, while in the second (model II), an equation for the square of the mixture fraction is solved, and the variance is computed from its definition. The comparison of the LES solutions is based on the convergence properties of their statistics with respect to the turbulence resolution length scale. The dependence of the LES statistics is analysed for velocity and the mixture fraction fields, and tested for convergence. For the most part, the statistics converge for the finest grids, but the variance of the mixture fraction shows some residual grid dependence in the high-gradient regions of the jet near field. The SGS variance given by model I exhibits realisability everywhere, whereas in regions of the flame model II is non-realisable, predicting negative variances. Furthermore, the LES statistics of model I exhibit superior convergence behaviour.

Transported probability density function modelling of the vapour phase of an n-heptane jet at diesel engine conditions

An n-heptane spray injected into a constant volume chamber at conditions representative of diesel engines is modelled with the probability density function (PDF) approach. The composition PDF transport is solved by a Lagrangian Monte Carlo method in conjunction with a standard Reynolds-averaged k−ϵ turbulence model to simulate transient fuel injection into a high temperature and high density ambient fluid in a constant volume chamber. Non-reacting cases are first considered with the focus on the ability of the method to predict the statistics of mixture fraction in the gas phase. The predictions are compared quantitatively against experimental measurements of mixture fraction and its variance obtained by Rayleigh scattering. The effects of mixing model and mixing constant (Cϕ) are examined. Good agreement for the mean mixture fraction is demonstrated. The mixture fraction variance is predicted well in the downstream region further than 20mm from the injector, given an appropriate choice of the mixing constant. In the region upstream of 20mm, the model variance is larger than the experimental variance, suggesting a problem with either the model or experiment. Cases are then simulated for chamber environments containing oxidiser. These cases feature transient ignition and combustion. A skeletal chemical mechanism is implemented with the PDF model and predictions of lift-off length and ignition delay are compared to experiment and to a set of results from a well-mixed model that ignores turbulence-chemistry interactions, as oxygen concentration in the chamber is varied. The results from the PDF model are noticeably different from the well-mixed model and quantitatively better in most cases.

Deterministic Multiple Mapping Conditioning (MMC) applied to a turbulent flame in Large Eddy Simulation (LES)

The scalar dissipation rate is a key quantity in turbulent combustion modelling, in particular for Conditional Moment Closure (CMC). In Large Eddy Simulation (LES), a subgrid-scale (SGS) mixing model must be provided to determine the SGS mixture fraction variance needed for the filtered scalar dissipation rate and the filtered density function. Multiple Mapping Conditioning (MMC) is selected as a SGS mixing model and the deterministic form is implemented for the first time in LES. The objective of the present study is to assess the capabilities of MMC to model the turbulent mixing field and the conditionally filtered scalar dissipation rate, N|η∼ needed in CMC.The MMC transport equation is implemented in a LES code coupled with CMC to simulate a lifted jet flame in a vitiated coflow. The MMC formulation and computational details are presented. MMC predictions are compared with LES for the turbulent mixing field using instantaneous and time averaged data, and experimental values are included whenever available.Reasonable agreement between MMC, LES and experimental data is found. Best fit is obtained close to the fuel exit and some discrepancies can be seen further downstream. The SGS variance is underpredicted for many parts of the jet. A thorough analysis is performed to assess the modelling and numerical assumptions. The two proposed sources of discrepancy are the linear model and neglect of a transverse component for convection in MMC. The MMC profiles of N|η∼ are significantly different from those of AMC and are sensitive to the SGS variance. Future work is suggested.

A mixing controlled direct chemistry (MCDC) model for diesel engine combustion modelling using large eddy simulation

A mixing controlled direct chemistry (MCDC) combustion model with sub-grid scale (SGS) mixing effects and chemical kinetics has been evaluated for Large Eddy Simulation (LES) of diesel engine combustion. The mixing effect is modelled by a mixing timescale based on mixture fraction variance and sub-grid scalar dissipation rate. The SGS scalar dissipation rate is modelled using a similarity term and a scaling factor from the analysis of Direct Numerical Simulation (DNS) data. The chemical reaction progress is estimated from a kinetic timescale based on local internal energy change rate and equilibrium state internal energy. An optical research engine operating at conventional operating conditions and Low Temperature Combustion (LTC) conditions was used for evaluation of the combustion model. From the simulation results, the effect of SGS scalar mixing is evaluated at different stages of combustion. In the context of LES, the new approach provides improved engine modelling results compared to the Direct Chemistry Solver (DCS) combustion model.

Large-eddy simulation of air entrainment during diesel spray combustion with multi-dimensional CFD

Large-Eddy Simulation (LES) was used to perform computations of air entrainment and mixing during diesel spray combustion. The results of this simulation were compared with those of Reynolds Averaged Navier Stokes (RANS) simulations and an experiment. The effect of LES on non-vaporizing and vaporizing sprays was evaluated. The validity of the grid size used for the LES analysis was confirmed by determining the subgrid-scale (SGS) filter threshold on the turbulent energy spectrum plot, which separates a resolved range from a modeled one. The results showed that more air was entrained into the jet with decreasing ambient gas temperatures. The mass of the evaporated fuel increased with increasing ambient gas temperatures, as did the mixture fraction variance, showing a greater spread in the profile at an ambient gas temperature of 920 K than at 820 K. Flame lift-off length sensitivity was analyzed based on the location of the flame temperature iso-line. The results showed that for the flame temperature iso-line of 2000oC, the computed lift-off length values in RANS matched the experimental values well, whereas in LES, the computed lift-off length was slightly underpredicted. The apparent heat release rate (AHRR) computed by the LES approach showed good agreement with the experiment, and it provided an accurate prediction of the ignition delay; however, the ignition delay computed by the RANS was underpredicted. Finally, the relationships between the entrained air quantity and mixture fraction distribution as well as soot formation in the jet were observed. As more air was entrained into the jet, the amount of air-fuel premixing that occurred prior to the initial combustion zone increased, upstream of the lift-off length, and therefore, the soot formation downstream of the flame decreased.

Turbulent mixing and fast chemical reaction in the confined jet flow at large Schmidt number

Turbulent mixing with fast chemical reaction was modeled in the confined jet flow at large Schmidt number (Sc∼1000). The Reynolds-Averaged-Navier–Stokes approach was employed to describe the turbulence–chemistry interaction. Numerical results were validated against data obtained by the two-color planar laser-induced fluorescence method. Based on these data the dissipation rates of the mixture fraction and the product reaction concentration were calculated. Their comparison showed essential differences both in dynamics and values. The influence of different-order finite-difference schemes for scalar gradient determination and of the noise-signal ratio on the dissipation rates was estimated. More accurate higher-order schemes caused both noised and corrected dissipation rates to increase. Eliminating the noise leveled essentially the order-effect of finite-difference schemes.The analysis of the mixing models was demonstrated that the mixing model with the constant mechanical-to-scalar time ratio R and the Multi-Time-Scale model overestimated the mixture fraction variance σf in comparison with experiment. To predict the dissipation in the jet flow at Sc∼1000 the low-Reynolds-number effects were considered: in the transport equation for σf the ratio R and the turbulent Schmidt number Scσ were the functions of turbulent Reynolds number. The accuracy of the used standard k–ε model was improved by coordinating the values of the model constants Сμ and Cε2 with the jet velocity decay and the expansion radius (Сμ=0.06 and Cε2=1.87).The examination of the known reaction rate models for the gas flow (Sc∼1) (the segregation intensity approach, the EDC-model or the PDF method) showed that the reaction rate was overestimated by these models in comparison with the one obtained from the measurements in the liquid flow. The proposed modification of the EDC-model took into account the specific micromixing in vortex structures of flow at Sc⪢1.

Modeling evaporation effects in conditional moment closure for spray autoignition

Simulations of an n-heptane spray autoigniting under conditions relevant to a diesel engine are performed using two-dimensional, first-order conditional moment closure (CMC) with full treatment of spray terms in the mixture fraction variance and CMC equations. The conditional evaporation term in the CMC equations is closed assuming interphase exchange to occur at the droplet saturation mixture fraction values only. Modeling of the unclosed terms in the mixture fraction variance equation is done accordingly. Comparison with experimental data for a range of ambient oxygen concentrations shows that the ignition delay is overpredicted. The trend of increasing ignition delay with decreasing oxygen concentration, however, is correctly captured. Good agreement is found between the computed and measured flame lift-off height for all conditions investigated. Analysis of source terms in the CMC temperature equation reveals that a convective–reactive balance sets in at the flame base, with spatial diffusion terms being important, but not as important as in lifted jet flames in cold air. Inclusion of droplet terms in the governing equations is found to affect the mixture fraction variance field in the region where evaporation is the strongest, and to slightly increase the ignition delay time due to the cooling associated with the evaporation. Both flame propagation and stabilization mechanisms, however, remain unaffected.

Laminar flamelet modeling of a turbulent CH 4/H 2/N 2 jet diffusion flame using artificial neural networks

The laminar flamelet concept is used in the prediction of mean reactive scalars in a non-premixed turbulent CH 4/H 2/N 2 flame. First, a databank for temperature and species concentrations is developed from the solutions of counter-flow diffusion flames. The effects of flow field on flamelets are considered by using mixture fraction and scalar dissipation rate. Turbulence–chemistry interactions are taken into account by integrating different quantities based on a presumed probability density function (PDF), to calculate the Favre-averaged values of scalars. Flamelet library is then generated. To interpolate in the generated library, one artificial neural network (ANN) is trained where the mean and variance of mixture fraction and the scalar dissipation rate are used as inputs, and species mean mass fractions and temperature are selected as outputs. The weights and biases of this ANN are implemented in a CFD flow solver code, to estimate mean values of the scalars. Results reveal that ANN yields good predictions and the computational time has decreased as compared to numerical integration for the estimation of mean thermo-chemical variables in the CFD code. Predicted thermo-chemical quantities are close to those from experimental measurements but some discrepancies exist, which are mainly due to the assumption of non-unity Lewis number in the calculations.

Assessment of a presumed joint pdf for the simulation of turbulence–radiation interaction in turbulent reactive flows

Turbulent reactive flows are an important problem in engineering, with a major impact on combustion efficiency, pollutant emissions and climate change. The numerical simulation of these flows is difficult, not only due to the need to address different physical phenomena, but also due to the interaction between them. The interaction between turbulence and radiation, due to the strong non-linearity between temperature and radiative emission, is the subject of the present work. To account for this interaction, the time-averaged form of the radiative transfer equation may be solved. The correlation between the absorption coefficient of the medium and the radiation intensity is often neglected in simulations, because the radiation intensity depends on the temperature and chemical composition along an optical path, and therefore it may be argued that it is relatively independent of local turbulent fluctuations. However, this approximation may introduce errors that are not negligible. A model has recently been proposed to determine that correlation, which relies on the assumption that the joint probability density function of mixture fraction and radiation intensity is a two-dimensional clipped Gaussian. This assumption is investigated here using experimental data for the mean and variance of mixture fraction for a turbulent free jet flame. It is shown that the presumed joint pdf accurately allows the evaluation of the mean radiation emission and absorption, but the prediction of the correlation between fluctuations of the absorption coefficient and fluctuations of the radiation intensity is not so good near the end of radial optical paths.

Application of flamelet model to large‐eddy simulation of turbulent reacting liquid flows

AbstractLarge‐eddy simulations using the flamelet models are applied to turbulent reacting liquid flows and validated by comparing with the experiments. The computations are performed for two reaction conditions, namely a rapid reaction and a moderately fast reaction in a grid‐generated turbulent flow. For the flamelet models, both the steady flamelet model and the unsteady Lagrangian flamelet model are tested. A second‐order, irreversible, and isothermal reaction is considered. The results show that the flamelet models inherently developed for turbulent combustion are applicable to turbulent reacting liquid flows, provided that the model coefficient in evaluating the subgrid scale variance of mixture fraction in the scale‐similarity model is set to be 5.0. The rapid reaction can be adequately predicted by both the steady and unsteady Lagrangian flamelet models, whereas the moderately fast reaction can be predicted only by the unsteady Lagrangian flamelet model which is capable to take slow chemical processes into account. © 2010 American Institute of Chemical Engineers AIChE J,, 2011

Combustion Simulation of a Diesel Engine in the pHCCI Mode with Split Injections by the Spatially Integrated CMC Model

Simulation is performed for a diesel engine in the partial homogeneous charge compression ignition (pHCCI) mode with split injections. The spatially integrated CMC model involves an additional heat loss term for the conditional enthalpy and the evaporation source terms for the mean mixture fraction variance. Two flame structures are defined to consider different evaporation and flame histories of the two split injection fuel groups. An independent transport equation is solved for each fuel vapor group with no mutual interaction between flame structures. The local mean mixture fraction and its variance determine the probability density functions (PDF) and the scalar dissipation rates (SDR). Calculated pressure traces show reasonable agreement with measurements for different loads and ratios between the two split injections. The overpredicted rate of pressure rise at ignition is attributed to simultaneous burning of all combustible premixture in the CMC model. The flammable limits are applied to consider extinction of lean mixture, wall film, or other possible factors for incomplete combustion of the pilot injection fuel, which burns completely after mixing with the second main injection fuel. Further research may be required for improved spray atomization and wall film models, which play a significant role in heat release and emissions of pHCCI engines.

Unsteady flamelet/progress variable approach for non-premixed turbulent lifted flames

The unsteady flamelet/progress variable approach has been developed for the prediction of a lifted flame to capture the extinction and re-ignition physics. In this work inclusion of the time variant behavior in the flamelet generation embedded in the large eddy simulation technique, allows better understanding of partially premixed flame dynamics. In the process sufficient simulations to generate unsteady laminar flamelets are performed, which are a function of time. These flamelets are used for the generation of the look-up table and the flamelet library is produced. This library is used for the calculation of temperature and other species in the computational domain as the solution progresses. The library constitutes filtered quantities of all the scalars as a function of mean mixture fraction, mixture fraction variance and mean progress variable. Mixture fraction and progress variable distributions are assumed to be β-PDF and δ-PDF respectively. The technique used here is known as the unsteady flamelet progress variable (UFPV) approach. One of the well known lifted flames is considered for the present modeling which shows flame lift-off. The results are compared with the experimental data for the mixture fraction and temperature. Lift off height is predicted from the numerical calculations and compared with the experimentally given value. Comparisons show a reasonably good agreement and the UFPV combustion model appears to be a promising technique for the prediction of lifted and partially premixed flames.

Hydrogen and Carbon Black Production from Thermal Decomposition of Sub-Quality Natural Gas

The objective of this paper is computational investigation of the hydrogen and carbon black production through thermal decomposition of waste gases containing CH4 and H2S, without requiring a H2S separation process. The chemical reaction model, which involves solid carbon, sulfur compounds and precursor species for the formation of carbon black, is based on an assumed Probability Density Function (PDF) parameterized by the mean and variance of mixture fraction and β-PDF shape. The effects of feedstock mass flow rate and reactor temperature on hydrogen, carbon black, S2, SO2, COS and CS2 formation are investigated. The results show that the major factor influencing CH4 and H2S conversions is reactor temperature. For temperatures higher than 1100° K, the reactor CH4 conversion reaches 100%, whilst H2S conversion increases in temperatures higher than 1300° K. The results reveal that at any temperature, H2S conversion is less than that of CH4. The results also show that in the production of carbon black from sub-quality natural gas, the formation of carbon monoxide, which is occurring in parallel, play a very significant role. For lower values of feedstock flow rate, CH4 mostly burns to CO and consequently, the production of carbon black is low. The results show that the yield of hydrogen increases with increasing feedstock mass flow rate until the yield reaches a maximum value, and then drops with further increase in the feedstock mass flow rate.

Implementation Issues of the Conditional Moment Closure Model in Large Eddy Simulations

Different ways of transferring information regarding the mixture fraction, its sub-grid scale variance and the scalar dissipation rate are examined in terms of a Large Eddy Simulation (LES)/Conditional Moment Closure (CMC) calculation. In such a simulation, information must be transferred from a fine LES grid to a usually coarser CMC grid. Different options of calculating conditional and unconditional quantities in the CMC resolution are assessed by filtering experimental mixture fraction and scalar dissipation rate data at various resolutions. It was found that when a presumed shape for the Filtered Density Function at the CMC resolution is used, special care must be given to the mixture fraction variance. It was also found that the Amplitude Mapping Closure model can be used for the conditional scalar dissipation rate. LES/CMC with detailed chemistry of a bluff-body stabilised burner was performed using two different ways of calculating the turbulent diffusivity. The structure of the flame is realistic, with little difference noticed when using the two diffusivities.

Applying an Extended Flamelet Model for a Multiple Injection Operating Strategy in a Common-Rail DI Diesel Engine

Subject of this work is the recently introduced extended Representative Interactive Flamelet (RIF) model for multiple injections. First, the two-dimensional laminar flamelet equations, which can describe the transfer of heat and mass between two-interacting mixture fields, are presented. This is followed by a description of the various mixture fraction and mixture fraction variance equations that are required for the RIF model extension accounting for multiple injection events. Finally, the modeling strategy for multiple injection events is described: Different phases of combustion and interaction between the mixture fields resulting from different injections are identified. Based on this, the extension of the RIF model to describe any number of injections is explained. Simulation results using the extended RIF model are compared against experimental data for a Common-Rail DI Diesel engine that was operated with three injection pulses. Simulated pressure curves, heat release rates, and pollutant emissions are found to be in good agreement with corresponding experimental data. For the pilot injection and the main or post injection, respectively, different ignition phenomena are pointed out and the influence of the scalar dissipation rate on these ignition phenomena is detailly investigated. 2009 SAE International.